SR11

Observation of the System Earth from Space The magnetic and gravity field of the Earth are important sources for dynamic processes on its surface and the interior. The investigation of these fundamental physical forces by satellite technologies have received wide international attention in the past years. Research satellites like CHAMP (German/US) and GRACE (US/German) as well as the planned GOCE Mission (ESA’s first Core Earth Explorer mission) allow measurements of the gravitational and magnetic field of hitherto unreached accuracy. Combined with terrestrial observations and computer models these data will help to develop a more detailed understanding of how the Earth's interior system works.

In Germany a significant part of the data evaluation and interpretation is carried out under the umbrella of the R&D-Programme GEOTECHNOLOGIEN. Eight collaborative research projects are recently funded by the Federal Ministry for Education and Research (BMBF). They are carried out in close co-operation between various national and international partners from academia and industry and focus on a better understanding of the spatial and temporal variations in the magnetic and gravity field of the earth and their impact on the dynamic processes taking place in the Earth´s interior and the global climate. The projects are integrative to the recent activities of the Priority Programme »Mass Transport and Mass Distribution in the Earth System«, funded by the German Research Council (DFG).

The abstract volume contains the presentations given on a science meeting held in Munich, Germany, in November 2007. The presentations reflect the multidisciplinary approach of the programme and offer a comprehensive insight into the wide range of research opportunities and applications.

Science Report

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GEOTECHNOLOGIEN

11:33 Uhr

Observation of the System Earth from Space

01.11.2007

GEOTECHNOLOGIEN Science Report

Observation of the System Earth from Space Status Seminar 22-23 November 2007 Bavarian Academy of Sciences and Humanities, Munich

Programme & Abstracts

The GEOTECHNOLOGIEN programme is funded by the Federal Ministry for Education and Research (BMBF) and the German Research Foundation (DFG)

ISSN: 1619-7399

No. 11

Umschlag_SR11.qxd

No. 11

GEOTECHNOLOGIEN Science Report

Observation of the System Earth from Space Status Seminar 22–23 November 2007 Bavarian Academy of Sciences and Humanities, Munich

Programme & Abstracts Number 1

No. 11

Impressum

Schriftleitung Dr. Ludwig Stroink © Koordinierungsbüro GEOTECHNOLOGIEN, Potsdam 2007 ISSN 1619-7399 The Editors and the Publisher can not be held responsible for the opinions expressed and the statements made in the articles published, such responsibility resting with the author.

Die Deutsche Bibliothek – CIP Einheitsaufnahme GEOTECHNOLOGIEN; Observation of the System Earth from Space, Status Seminar 22–23 November 2007, Bavarian Academy of Sciences and Humanities, Munich, Programme & Abstracts – Potsdam: Koordinierungsbüro GEOTECHNOLOGIEN, 2007 (GEOTECHNOLOGIEN Science Report No. 11) ISSN 1619-7399 Bezug / Distribution Koordinierungsbüro GEOTECHNOLOGIEN Heinrich-Mann-Allee 18/19 14473 Potsdam, Germany Fon +49 (0)331-620 14 800 Fax +49 (0)331-620 14 801 www.geotechnologien.de geotech@gfz-potsdam.de Bildnachweis Titel / Copyright Cover Picture: ESA

Table of Contents Scientific Programme Status Seminar »Observation of the System Earth from Space«. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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More accurate and faster available CHAMP and GRACE gravity fields for the user community Status of CHAMP and GRACE release 04 gravity field products Flechtner F., Schmidt R., Meyer U., Dahle C., Neumayer K.-H. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

5

ISDC Metadata Management Mende V., Ritschel B., Palm H., Gericke L., Freiberg S.

.......................................

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Optimized Algorithms and Methods for Improved CHAMP and GRACE Gravity Fields Neumayer K.-H., Flechtner F., König R., Michalak G., Snopek K., Köhler W. . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 ISDC Services: Data Management, Catalog Interoperability and International Cooperation Ritschel B., Mende V., Palm H., Kopischke R., Bruhns C., Gericke L., Freiberg S. . . . . . . . . . . . . . . . . . . . . . . . . . 18

Near-real-time provision and usage of global atmospheric data from CHAMP and GRACE (NRT-TO) Near-real time satellite orbit determination for GPS radio occultation Michalak G., Wickert J., König R., Rothacher M. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 Assimilation of CHAMP and GRACE-A Radio Occultation Data in the GME Global Atmospheric Model of the German Weather Service Pingel D., Rhodin A., Wergen W., Tomassini M., Gorbunov M., Wickert J.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 Global atmospheric data from CHAMP and GRACE in near-real time Wickert J., Beyerle G., Falck C., Flechtner F., Galas R., Grunwaldt L., Healy S. B., Heise S., Köhler W., König R., Massmann F. H., Michalak G., Offiler D., Pingel D., Poli P., Ozawa E., Rothacher M., Schmidt T., Tapley B., Wergen W.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

Sea Level Variations – prospects from the past to the present (SEAVAR) Precise orbits of altimetry satellites and analysis of GPS data at tide gauges for sea level research Rudenko S., Schöne T., Gendt G., Zhang F., Thaller D. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

SEAVAR - Reconstruction of Sea Level anomalies Sadowsky N., Schöne T., Esselborn S. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 Inverse modelling of the North Atlantic Ocean from ocean observations and tide gauge data Sidorenko D., Danilov S., Schröter J., Wenzel M., Ivchenko V., Reinhard H., Richter F., Wang Q.

. . . . . . . . . . . . . . . . 50

Combined assimilation of GEOSAT and TOPEX/poseidon data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

Wenzel M. and Schröter J.

Integration of space geodetic techniques as the basis for a global geodetic-geophysical oberserving system (GGOS-D) Consistent VLBI, GPS and SLR Time Series of Station Positions and Troposphere Parameters Böckmann S., Artz T., König R., Müller H., Nothnagel A., Panafidina N., Steigenberger P., Thaller D., Tesmer V.

. . . . . . . . 60

Contribution of Altimetry Time Series for a Global Geodetic Observing System Bosch W. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 Combination of Ground Observations and LEO Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67

König D., König R., Panafidina N.

GGOS-D Reference Frame Computations Krügel M., Angermann D., Drewes H., Gerstl M., Meisel B., Tesmer V., Thaller D.

. . . . . . . . . . . . . . . . . . . . . . . . 70

Integration of Space Geodetic Techniques as the Basis for a Global Geodetic-Geophysical Observing System (GGOS-D): An Overview Rothacher M., Drewes H., Nothnagel A., Richter B. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75 Time Series From Inter-technique Combinations Thaller D., Krügel M., Meisel B., Panafidina N., Steigenberger P. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80

GOCE - Gravitationsfeldanalyse Deutschland II - GOCE – GRAND II Terrestrial Data Sets for the Validation of GOCE Products . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85

Denker H., Voigt C., Müller J., Ihde J., Lux N., Wilmes H.

Status and Goals of the GOCE Mission and the GOCE-GRAND II Project Rummel R., Gruber T. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93

GOCE data processing: the numerical challenge of data gaps Siemes C., Schuh W.-D., Cai J., Sneeuw N., Baur O. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99 GOCE Validation Over Land and Ocean Stammer D., Gruber T., Ilk K., Köhl A., Romanova V., Rummel R.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106

Gravity Field Analysis: Global Combination and Regional Refinement Approaches Stubenvoll R., Eicker A., Abrikosov O., Löcher A., Förste C., Mayer-Gürr T., Ilk K.-H., Kusche J. . . . . . . . . . . . . . . . . . 112

Improved GRACE level-1 and level-2 products and their validation by ocean bottom pressure Development of a patch-filtering method for a more accurate determination of ocean bottom pressure anomalies derived from GRACE solutions Böning C., Macrander A., Schröter J., Timmermann R. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118 Periodic and transient short-term mass variations in numerical simulations of atmosphere-ocean dynamics Dobslaw H. and Thomas M. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122 Regional GRACE gravity determination using L1B data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127

Eicker A., Mayer-Gürr T., Ilk K.H. .

Results from increase of the temporal resolution of the AOD1B products Flechtner F. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131 GRACE gravity field models using alternative L1B data (WP120) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134

Frommknecht B., Meyer U., Schmidt R., Flechtner F.

GRACE validation using in-situ Ocean Bottom Pressure data Macrander A., Böning C., Boebel O., Schröter J. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138 Global gravity fields from simulated L1-products (WP330) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143

Meyer U., Frommknecht B., Schmidt R., Flechtner F.

Improvement of the CHAMP magnetic field data set for generating high-resolution magnetic field models and global magnetisation maps (MAGFIELDS) Lithospheric component of GRIMM – the GFZ Reference Internal Magnetic Model Lesur V., Wardinski I., Rother M., Quesnel Y., Mandea M. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149

World Digital Magnetic Anomaly Map. GAMMA – the GFZ contribution Mandea M., Lesur V., Rother M., Quesnel Y., Hamoudi M., Thébault E. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154 Data Compression for Global Field Modeling Minchev B., Holschneider M., Mandea M., Chambodut A., Panet I. and Schoell E.

. . . . . . . . . . . . . . . . . . . . . . . . 159

Time-variable gravity and surface mass processes: validation, processing and first application of new satellite gravity data (TIVAGAM) Estimation of global terrestrial water storage change using the WaterGAP Global Hydrological Model (WGHM) Fiedler K., Döll P., Hunger M. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163 Multiscale Filter Methods Applied to GRACE and Hydrological Data Freeden W., Nutz H., Wolf K. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167 Comparison of crustal deformations from a global GPS reprocessing and from GRACE surface mass variation products: progress and challenges Horwath M., Rülke A., Fritsche M., Dietrich R., Schmidt R., Döll P. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172 Periodic Components of Water Storage Changes from GRACE and Global Hydrology Models Petrovic S., Schmidt R., Wünsch J., Barthelmes F., Hengst R., Kusche J. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177 Calibration techniques for a global hydrological model and their interface to GRACE data analysis Werth S., Günter A., Merz B., Schmidt R., Petrovic S. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183

Authors’ Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 188 GEOTECHNOLOGIEN Science Reports – Already published/Editions. . . . . . . . . . . . . . . . 191

Scientific Programme Status Seminar »Observation of the System Earth from Space« 22–23 November 2007 Thursday, 22 November 2007 8.30 – 9.00

Registration and Poster Mounting

9.00 – 9.15

Welcome

9.15 – 10.15 9.15 – 9.25 9.25 – 10.15 10.15 – 11.00 10.15 – 10:25 10.25 – 11.00 11.00 – 11.45

Talks More accurate and faster available CHAMP and GRACE gravity fields for the user community Introduction by the project-coordinator Presentation of the R&D – results Near-real-time provision and usage of global atmospheric data from CHAMP and GRACE (NRT-TO) Introduction by the project-coordinator Presentation of the R&D – results

11.00 – 11.10 11.10 – 11.45

Sea Level Variations – prospects from the past to the present (SEAVAR) Introduction by the project-coordinator Presentation of the R&D - results

11.45 – 13.00

Lunch Break

13.00 – 14.15 13.00 – 13.10 13.10 – 14.15

Integration of space geodetic techniques as the basis for a global geodetic-geophysical oberserving system (GGOS-D) Introduction by the project-coordinator Presentation of the R&D – results

14.15 – 15.30 14.15 – 14.25 14.25 – 15:30

GOCE - Gravitationsfeldanalyse Deutschland II - GOCE – GRAND II Introduction by the project-coordinator Presentation of the R&D - results

15.30 – 16.30

Coffee Break and Poster Session

16.30 –

approx. 19.00

Discussion Round table discussion – Interactions within and between the joint projects – Potential applications and market opportunities – Perspectives for cooperation for other GEOTECHNOLOGIEN topics Dinner

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Friday, 23 November 2007:

8.30 – 10.15 8.30 – 08.40 8.40 – 10.15 10.15 – 11.00

Talks Improved GRACE level-1 and level-2 products and their validation by ocean bottom pressure Introduction by the project-coordinator Presentation of the R&D – results

10.15 – 10.25 10.25 – 11.00

Improvement of the CHAMP magnetic field data set for generating high-resolution magnetic field models and global magnetisation maps (MAGFIELDS) Introduction by the project-coordinator Presentation of the R&D – results

11.00 – 11.30

Coffee Break

11.30 – 12.45

11.30 – 11.40 11.40 – 12.45

Time-variable gravity and surface mass processes: validation, processing and first application of new satellite gravity data (TIVAGAM) Introduction by the project-coordinator Presentation of the R&D – results

12.45 – 14.00

Lunch Break

14.00 – 14.30

Final discussion

14.30

End

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Status of CHAMP and GRACE release 04 gravity field products Flechtner F., Schmidt R., Meyer U., Dahle C., Neumayer K.-H. GFZ Potsdam, Department 1 »Geodesy and Remote Sensing«

Introduction The project »More Accurate and Faster Available CHAMP and GRACE Gravity Fields for the User Community« consists of two main work packages.

WP200 optimizes the algorithms and procedures used to derive CHAMP and GRACE gravity field solutions with the GFZ EPOS (Earth Parameter and Orbit System) software package. This includes work on parallelization and high performance computing (e.g. modularization for distributed memory architecture, migration to Linux cluster) which accelerated the processing time necessary especially in the case of reprocessing of long time series, implementation of new observation models (e.g.

GPS ambiguity fixing and phase wind up or use of measured non-gravitational accelerations as observations instead of fixed disturbing forces (planned for 3rd funding year) or improved background models (e.g. from projects »Improved GRACE Level-1 and Level-2 products« (atmosphere and ocean de-aliasing) or »TIVAGAM« (hydrological short-term mass variations, implementation also planned for 3rd funding year)). Further details can be found in the extended abstract by Neumayer et al. (»Optimized algorithms and methods for improved CHAMP and GRACE gravity fields«).

As a consequence of this optimized EPOS load module, the base CHAMP and GRACE processing (WP100) has been improved step by step resulting in a new long-term GRACE time series of higher quality gravity field products for the user community and other projects within the GEOTECHNOLOGIEN pro-

gram. Additionally, ancillary products such as the atmosphere and ocean de-aliasing product, the SLR predictions or Rapid Science Orbits for the analysis of radio occultation data have been and will be generated with higher rate and/or higher quality. All data are provided in a user-friendly way via an optimized web portal of the ISDC (Integrated System and Data Center, http://isdc.gfz-potsdam.de). Details are described in the extended abstract by Ritschel et al. (»ISDC Services – Data Management, Catalog Interoperability and International Cooperation«).

The EIGEN-GRACE05S/GFZ-RL04 time series The recently homogeneously reprocessed fourth release of time series of monthly GRACE satellite-only gravity models is called EIGEN-GRACE05S respectively GFZ-RL04. It currently consists of 56 monthly solutions between August 2002 and July 2007 covering 5 years. Only four months are missing due to unavailable accelerometer or K-band data (June 2003 and January 2004, respectively) or less-quality Level-1B instrument data which complicate data pre-processing and precise gravity field determination (September and December 2002). The latter two are expected to be available soon. The series will be continued for future months as the mission L1B data comes in.

EIGEN-GRACE05S is based on the following improvements: – Updated background models for the static gravity field (EIGEN-GL04C up to degree and

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–

–

– – –

–

order 150) and for the de-aliasing of shortterm non-tidal atmospheric and oceanic mass variations (AOD1B RL04 developed within the project »Improved GRACE Level-1 and Level-2 products«), Inclusion of secular rates for C21 and S21 (besides C20, C30 and C40 of release 03) and change of the reference epoch to 01.

January 2000 (IERS Conventions 2003), Substitution of the inaccurate K2 FES2004 ocean tide by the FES2002 values (Lyard et al., 2006) and inclusion of the non-linear M4 tide in FES2004, Extension of relativity by Lense-Thirring and de Sitter effects (IERS Conventions 2003), Switch to IERS 2003 nutation and precession model, Integration in the Conventional Inertial System (CIS) instead in the True of Date System (TDS), and Azimuth-elevation dependent phase centre corrections for GRACE-A and GRACE-B GPSSST observations (provided by JPL).

The processing strategy, e.g. the two-step method (Reigber et al., 2005), using GFZprocessed GPS constellations and the processing of daily instrument data batches, the orbit parameterization, in particular for accelerometer and K-band data, and the calculation of partial derivatives up to degree and order 150 (solution space truncated to degree and order 120)

remained the same as in the precursor release 03. Further details can be found in the GFZ Processing Standard Document for Level-2 Product Release 04 (Flechtner, 2007).

The quality of the EIGEN-GRACE05S gravity field solutions could be definitely improved w.r.t. its precursor models. This becomes clear when looking e.g. at the calibrated (Figure 1, left) and accumulated (Figure 1, right) error degree variances in terms of geoid height of the EIGEN-GRACE05S mean field, which could be further reduced compared to previous GRACE-only mean field models. For the static field the cm-geoid is now available at a halfwavelength of about 226 km and the mmgeoid at a half-wavelength of about 388 km, respectively. It should be noted that the given values can only interpreted in terms of a mean error of the geoid per spherical harmonic degree or accumulated over the spatial wavelengths over the whole sphere as the degree variances describe the average signal power per spherical harmonic degree or spatial wavelength. In this way, in the spatial distribution of the errors (not shown) larger, but also smaller values can occur. Secondly, it is clear that the given accuracy is only representative for the solved gravity parameters. Any contributions from shorter wavelengths are missing of course, which it has to be considered e.g. in comparisons with in-situ gravity data.

Figure 1: Error degree variances (left) and accumulated errors (right) in terms of geoid heights for EIGEN-GRACE01S (RL00) up to EIGEN-GRACE05S (RL04)

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For the monthly models the average errordegree variances have been reduced from a factor of 17.5 above the GRACE baseline to a factor of 15 above the GRACE baseline, which still gives room for further improvements.

The improvements of the EIGEN-GRACE05S models become also clearly visible in the spatial domain, where the spurious meridional striping features are further reduced, being of further benefit for the exploitation and application of the GRACE-based gravity and surface mass data in e.g. hydrology, glaciology and oceanography.

For example, the analysis of EIGEN-GRACE05S models, applying a novel approximate decorrelation method (Kusche, 2007) for the reduction of correlated GRACE, clearly shows the distinct changes in the gravity field in the Sumatra-Andaman region due to coseismic and postseismic deformation caused by the disastrous earthquake on December 26, 2004 (see Fig. 2). The GFZ-RL04 GRACE results agree well with gravity signals derived from external GRACE-only models (e.g. CSR-RL04

models, not shown), but also with results from independent viscoelastic-gravitational dislocation models (which incorporate GPS deformation and seismological data). Another example are ice mass change and glacial-isostatic adjustment (GIA) in Antarctica derived from EIGEN-GRACE05S which fits quite well with predictions of glacier melting at the tip of the Antarctic Peninsula and in the Amundsen Sea Sector, and of GIA over the Ronne Ice Shelf.

In this context another major advantage of the EIGEN-GRACE05S series w.r.t its precursor EIGEN-GRACE04S is that this gravity field time series can again be directly used to determine mass distribution trends on continental areas instead of re-adding the GAB-product needed for the EIGEN-GRACE04S series (see GRACE Technical Note 04 for details). This is due to the fact that the ocean model used for the correction of non-tidal short-term mass variations (OMCT) is parameterized for AOD1B release 04 in a way that the ocean mass is conserved (Flechtner, 2007) avoiding artificial trend signals in the previous EIGENGRACE04S/GFZ-RL03 release.

Figure 2: Gravity change due to coseismic deformation from the Sumatran-Andaman earthquake (Dec 26, 2004, Mw = 9.3) derived the difference of averages of monthly GRACE-only models of the EIGEN-GRACE05S series before and after the event (left). Expected coseismic signal from the geophysical model in Han et al. 2006 (right)

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Besides the monthly time series, additionally, based on more than 2 years of instrument data, a GRACE satellite-only mean field has been derived which has been combined with GRACE and Lageos normal equation systems of GRGS (Groupe de Recherches de Geodesie Spatiale, Toulouse) and improved terrestrial gravity information (new GFZ MSSH model, edited NIMA gravity anomalies). This model called EIGEN-GL04C is complete to degree and order 360 and was chosen for the official Jason data reprocessing. It can be downloaded, as well as the Lageos/GRACE-combined satelliteonly field EIGEN-GL04S1 at http://www.gfzpotsdam.de/pb1/op/grace/results.

The EIGEN-CHAMP05S time series The reprocessing of CHAMP data using the GRACE RL04 standards is currently ongoing.

To be consistent with GRACE the new monthly CHAMP time series is called EIGENCHAMP05S respectively CHAMP-RL04. All preliminary tests show a decrease of the GPS code and phase residuals and further improved CHAMP gravity fields. As for CHAMP release 03, it is planned to apply moving averages over 3 months to compare the low degree and order Stokes coefficients with GRACE monthly solutions. It is expected that the already high correlations for most of the coefficients will increase further (but moderately). Another important study will be to use CHAMP data, especially with data from 2007, when the CHAMP orbit altitude decreased to about 350 km, for the generation of a combined satellite-only CHAMP/GRACE/LAGEOS mean gravity model to see whether CHAMP could help to improve to stabilize the very long-wavelength gravity parameters.

References: Flechtner, F. (2007). AOD1B Product Description Document V3.1, online available at http://isdc.gfz-potsdam.de/grace.

Flechtner, F. (2007). GFZ Processing Standard Document for Level-2 Product Release

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04, online available at http://isdc.gfz-potsdam.de/grace.

Han, S.-C., Shum, C. K., Bevis, M., Ji, C., and Kuo, C.-Y., (2006). Crustal Dilatation Observed

by GRACE After the 2004 Sumatra-Andaman Earthquake. Science, Science, doi:10.1126/science.1128661 Lyard, F., Lefevre, F., Letellier, T., and Francis, O., 2006. Modelling the global ocean tides: modern insights from FES2004. Ocean Dynamics, 56: 394, doi:10.1007/s10236-006-0086-x.

Kusche, J., 2007. Approximate decorrelation and non-isotropic smoothing of time-variable GRACE-type gravity field models. Journal of Geodesy, doi:10.1007/s00190-007-0143-3.

Reigber, C., Schmidt, R., Flechtner, F., KÜnig, R., Meyer, U., Neumayer, K. H., Schwintzer, P., and Zhu, S. Y., 2005. An Earth gravity field model complete to degree and order 150 from GRACE: EIGEN-GRACE02S. Journal of Geodynamics, 39: 1–10.

ISDC Metadata Management Mende V., Ritschel B., Palm H., Gericke L., Freiberg S. GeoForschungsZentrum Potsdam, Data Centre, 14473 Potsdam, Germany, Email: vmende@gfz-potsdam.de, rit@gfz-potsdam.de, palm@gfz-potsdam.de, lg@gfz-potsdam.de, sebast@gfz-potsdam.de

The Information System and Data Center (ISDC) is managing more than 10TB of geoscience data and information. By now, these data are coming from 11 missions1 with nearly 300 product types, approximately 16 Mio products and more than 1500 users. One main part of the »WP173: Metadata, Information and Product Retrieval« consists of the metadata management for the retrieval of product independent information and data. This paper is giving a short overview about the developed and used metadata concept.

A product type of a geoscience mission or project consists of a set of products (data file(s) + metadata). This relation is shown exemplarily in figure 1 in respect to orbit products of the new satellite mission TerraSAR-X. In order to describe and manage the data products we are using an evolution of the

NASA’s Directory Interchange Format (DIF) standard (version 9.x). The Global Change Master Directory (GCMD) defines metadata as: »Descriptive information that characterizes a set of quantitative and/or qualitative measurements and distinguishes that set from other similar measurement sets.« (L. Olsen) For the management of product types this format is excellent. The ISDC DIF conform base schema of the parent DIF XML documents is stipulated in the »base-dif.xsd« file. The ISDC XML schema has been defined on the basis of the GCMD XML schema definition: http://gcmd.nasa.gov/Aboutus/xml/dif/dif_v9.7.

1.xsd. In order to describe single products, it was necessary to extend the DIF standard and to modify the GCMD XML schema. Even the structure of the ISDC DIF XML schema is different from the GCMD schema, the ISDC parent DIF XML documents are valid in relation to the

Figure 1: ISDC Relations

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GCMD schema. Additionally, the ISDC is using a parent – child DIF combinationt. The metadata of product types are described in associated parent DIF XML files according to the basedif.xsd schema. The parent DIF XML files are validated and stored in an Oracle XML database. The product (data file) specific metadata are documented in child DIF XML files. Each product type has its own schema for the child DIF XML files. So, child DIF documents are used in order to describe the data file specific properties. The complex XML type <Data_Parameters> in the child DIF XML document provides the specific extension of the parent DIF XML structures. This includes specific metadata of

the product, like data filename, data file size, revision, satellite ID and others. In order to realize this data model, we are using the redefine XML technique for the definition of complex XML types for the <Data_Parameters>. By redefining the ISDC »base-dif.xsd« schema all child DIF XML documents are derived. Using the GCMD XML schema, this approach would not be possible because of the definition of XML reference structures.

The extended metadata of the child DIF XML documents are stored in product type related tables in a relational DB. The connection between the child DIF XML files and the parent

Figure 2: Schema, DIF XML and Storage

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DIF XML document is given by the equality of parts of the <Entry_ID> element in both, the product type and the related product metadata documents. Additionally the content of the <Parent_DIF> element in the child DIF XML document refers to the appropriate parent DIF document. The relation between the schemata, the XML metadata files and the storage structures is shown in figure 2.

Using the parent DIF XML structures it is possible to realize a thematic search concerning the content of the different product type documents as well as to provide interoperability to other catalogue systems. Now It is possible to transform the XML DIF files into ISO 19115 standard documents in order to use OGC compliant Web Services like the »deegree CWS 2.0«. Furthermore an efficient harmonisation with other catalogue systems can be realized by international standards. The structure of XML easily allows extending the DIF standard in future. Using the parent-child DIF concept, only a small amount of mandatory metadata must be put both in the parent and child DIF XML documents.

1

ISO19115/ISO19119 Application Profile for CSW 2.0.; OpenGIS Consortium, Wayland, Massachusetts [4] Burgess, Ph., Palm, H., Ritschel, B., Bruhns, Ch., Freiberg, S., Gericke, L., Kase, St., Kopischke, R., Loos, St., Lowisch, St., Implementing modern data dissemination concepts in the ISDC Portal, »Status Seminar ›Erkundung des Systems Erde aus dem Weltraum‹« (Bonn 2006).

[5] Deegree Project: http://www.deegree.org [6] Global Change Master Directory: http://gcmd.nasa.gov/ [7] XML & XSLT: www.w3.org/TR/xslt, http://selfhtml.org/

CHAMP; GRACE, TerraSAR-X, GASP, GNSS, GGP, GPSPDR and others

References [1] Braune, S., Czegka, W., Klump, J., Palm, H., Ritschel, B., Lochter, F. A. (2003): Anwendungen ISO-19115-konformer Metadaten in in Katalogsystemen aus dem Bereich umweltund geowissenschaftlicher Geofachdaten. – Zeitschrift für Geologische Wissenschaften, 31,1, 37–44 [2] Ritschel,B., Bruhns, C:, Kopischke R., Mende V., Palm H., Freiberg S., Gericke L.: The ISDC concept for long-term sustainability of geoscience data and information, PV 2007 Conference, Symposiums-Proceeding, (Oberpfaffenhofen 2007) [3] Voges, U., Senkler, K. (2005): OpenGIS® Catalogue Services Specification 2.0 –

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Optimized Algorithms and Methods for Improved CHAMP and GRACE Gravity Fields Neumayer K.-H., Flechtner F., König R., Michalak G., Snopek K., Köhler W. GeoForschungsZentrum Potsdam, Dept. 1 »Geodesy and remote sensing«

In the work package »WP200/ Optimization of Algorithms and Procedures« of the project »More Accurate and Faster Available CHAMP and GRACE Gravity Fields for the User Community« some open ends had to be tied up in the so-called TOTSOL part of the software that covers modification and inversion of normal equations. It concerns the part of the adjustment problems that are strictly linear in the parameters. Furthermore, some improvements concerning the integrator had to be implemented, and a speedup of the ambiguity fixing part has been achieved.

We start with a sketch of the overall structure of the software. The core package – named EPOS-OC – is a (growing) bundle of (at the moment eight) fortran90 main programs that use one and the same subroutine library. The father of all of those programs is the eposoc executable, an universal tool for the adjustment of satellite orbits and their parameters, station coordinates, atmospheric parameters, quantities that describe reference systems and, above all, the recovery of the Earth gravity field from satellite observations of various data types. At the moment, even applications to the lunar gravity field are under investigation. Originally separate is the so-called TOTSOL package designed to manipulate normal equations that have traditionally been considered to be »too large« for EPOS-OC proper. With the evolution of the project, however, and with the transition to exclusively dynamical data structures and common subroutine libraries, the boundary between EPOS-OC and TOTSOL becomes more and more indistinct.

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Let us first have a look at observation equations and normal equations in the TOTSOL part of the overall software. There are two main data structures in the context of normal equation processing and their re-parameterization: First, there is the normal equation itself. The state vector has a dimension ndim, the number of observations that constitute the normal equation are nobs, and the number of reduced parameters is nred.

Finding the solution of a normal equation amounts to obtaining the minimal value of the quadratic polynom z → zTCz – 2dTz + q where C = (cij) is the normal equation matrix, d = (d1 … dndim)T is the right hand side vector, and q is the value of the quadratic target function if the vector y = (y1 … yndim)T of solve-for parameters is set to its starting value y0. With z we abbreviate the difference y – y0.

How the storing in a direct-access file is done traditionally in the TOTSOL package has been illustrated in Fig. 1.

Secondly, there is the so-called mapping of normal equation. y – y0 = M · (x – x0) + m i.e. the above-mentioned vector z = y – y0 has to be replaced by some expression linear in a different set of parameters

Figure 1: The essential part of an EPOS-OC/TOTSOL normal equation that is stored in a binary direct-access file. The number of records equals the dimension of the normal equation plus one for the target function. The individual records contain one row of the normal equation matrix, headed by the corresponding right hand side and terminated by a dummy entry

x = (x1, x2, â&#x20AC;Ś). M is a matrix whose row number coincides with the dimension of y and whose column number coincides with the dimension of x. The vector m on the right hand side of the last equation has the same dimension as y. Just as in the case of the normal equation, the essential data are stored in a binary direct-access file; for the details see Fig. 2.

Mapping occurs in two contexts, namely reparametrization and back-substitution of reduced variables. That the re-construction of the reduced parameter and error propagation is achieved by linear mapping in the latter case is clear.

An example for re-parametrization, consider Stokes coefficient time series of a gravity

field, like moving-average time series of 3 months length with one month stepping size in the case of CHAMP, or monthly gravity fields in the case of GRACE. If we now, right from the beginning on, assume the Stokes coefficient of a given degree and order to be represented by a trigonometric polynom with annual and semi-annual frequency, then the vector u would consist of the polynom coefficients, and the matrix M contains dedicated sine and cosine terms with periods of a year and six months.

The whole computation/manipulation of TOTSOL format normal equations that has already existed in the form of shell scripts and encapsulated F95 programs, has been re-cast into a

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Figure 2: Binary body file of a normal equation map. The storing is achieved in a direct access file with records that contain ndim + 2 real numbers each

Figure 3: Internal data structure for a normal equation, as defined in the module modul_neq. The items C_matrix, d_rhs and q_ltpl are system matrix, right hand side and target functional of the normal equation, x0_vector(ndim) contains the initial values of the parameters and sigels(ndim) is an array of parameter names, providing something like a non-ordinal index for the vector of parameters

F90 library and the parameter substitution features have been added. The modular and object-oriented features of the f90/f95 programming language have been exploited as far as possible.

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EPOS-OC already possesses corresponding interfaces for reading and writing TOTSOL normal equations in binary as well as in ASCII format. Traditionally, the normal equations are manipulated on the unix/linux command shell level, appearing here as data

files. The whole concept has now been recast in such a manner that no longer f90 programs and encapsulating shell scripts operate on files, but that f90 subroutines manipulate corresponding data structures.

Both data structures (i.e. objects) and their manipulation (i.e. the methods) have been bundled up in two f90 modules, namely modul_neq and modul_totsol. They are incorporated into appropriate f90 programs via an USE directive.

As an example for the transition from file to structure, see the appearance of the normal equation in Fig. 3. A similar data structure has been adopted for the parameter map.

This approach makes development work inherently easy, as the programmer uses the high-level commands like reduce_core_neq, solve_neq etc. without having to refer to details. Furthermore, the method is backward-compatible, as there exist the subrou-

tines like read_neq, write_neq etc. that allow to establish a convenient interface to the traditional way of shell commands operating on files.

It is clear that inside the EPOS-OC & TOTSOL parameter adjustment and normal equation package, the position of a parameter in the parameter vector is uniquely determined by its index. The matter becomes tricky if normal equation intelligence is handed to (interfaced with) the outside world, as assigning indices to the elements of a given set of parameters is somewhat arbitrary. For the external world, parameters are better identified by unique names, and the concept of an indexed vector of parameter values has to be replace with a so-called hash, or, in the language of perl or awk, an associative array: Instead of indexing j â&#x2020;&#x2019; zj j = 1, 2, 3, â&#x20AC;Ś ndim we have a sequence of pairings

Figure 4: 3D difference between the extrapolation-method integrator ODEX and the traditional Adams-Cowell multistep integrator, for a GPS satellite over one day. Note that the difference is in micrometres, and therefore negligible

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name_string → z(name_string) where name_string runs through a set of (not necessarily ordered) parameter names. The concept of parameter vector substitution, matrix multiplication, parameter reduction etc. had to be modified in order to satisfy this more flexible concept not only outside, but also inside a f90 program. Fundamental matrix and vector operations had to be re-formulated in a manner that the sequence in which the name_string items appear in a given parameter set does no longer play a role.

The integrator of EPOS-OC is a predictor-corrector Adams-Cowell multistep algorithm of fixed order seven. The order can be chosen by the user now and, as a side effect, admits to estimate the global integration accuracy.

Not only the order of original integrator, but also the integration method itself has been made an item to be changed if desired. For

low orbiting Earth satellites with on-board measured surface accelerations, the multistep approach with a stepping size governed by the accelerometer data spacing is the method of choice. For the GPS satellites, however, we have no abrupt steps in the system dynamics, and all force models are infinitely many times differentiable. This is the ideal situation for extrapolation methods that are distinguished by a very small number of very large integration steps – e.g. 10–12 for one day for GPS satellites, see Fig. 5 – thus realizing dramatic savings for the integration time without perceptible loss of accuracy, see Fig. 4.

Using measured surface accelerations, just as they are, on the right hand side of the satellite orbit differential equation prohibits the choice of time-saving extrapolation methods for integration. The reason is the lacking smoothness of the system dynamics. However, this obstacle can be circumvented if the on-board accelerometer data are considered

Figure 5: Integration by extrapolation, demonstrated with a GPS satellite (PRN8) over 24 hours. Note the very few integration steps. The trajectory in between is obtained by high-order Hermite interpolation, which is only possible because of the smooth system dynamics. The method is not suited for measured on-board accelerations that are not genuine observations

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to be genuine observations to which the parameters of a model for the sum of air drag, solar radiation pressure and Earth albedo have to be fitted.

The implementation of this approach allows also deal with a situation where measured accelerations in all three dimensions, due to the defect of a measurement channel, cannot be provided. This is the situation e.g. for CHAMP where the radial channel is inherently flawed. Furthermore, irregular and large acceleration data gaps are no longer a problem.

Ambiguity fixing has been used for the GPS/ground station processing chains on a regular basis for the past two years. As this feature was implemented by shell scripts and commands external to the core EPOS-OC processing package it is clear that this part of the processing shows a large potential for time saving. This has been achieved by calling the ambiguity fixing part from within EPOS-OC, like subroutines of the original program package. Thus the processing time could be cut in half.

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ISDC Services: Data Management, Catalog Interoperability and International Cooperation Ritschel B., Mende V., Palm H., Kopischke R., Bruhns C., Gericke L., Freiberg S. GeoForschungsZentrum Potsdam, Data Centre, 14473 Potsdam, Germany, E-Mail: rit@gfz-potsdam.de, vmende@gfz-potsdam.de, palm@gfz-potsdam.de, roko@gfz-potsdam.de, cbruhns@gfz-potsdam.de, lg@gfz-potsdam.de, sebast@gfz-potsdam.de

The new GFZ Information System and Data Center (ISDC) portal is integrating important data management services for satellite missions like CHAMP, GRACE and TerraSAR-X as well as for geodetic projects like Global Geodetic Project (GGP) and GPS data reprocessing (GPS-PDR) [1], [2], [3], [4]. According to the work package (WP) 170 of the German Geotechnologien program ÂťObservation of System Earth from SpaceÂŤ, main components of the ISDC portal system, like portal framework and content management (WP 171), user management (WP 172) and product

Figure 1: ISDC portal GUI

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management, monitoring and statistic (WP 174) are developed and in operation. The enhancement of the ISDC product philosophy (WP 173) using parent and child DIF XML documents [5], [6] for the documentation of product type and product (data file) specific metadata is in progress.

The entrance to the main functions and features of the new ISDC portal (http://isdc.gfzpotsdam.de) realized by a three-tier graphical user interface (GUI) is shown in figure 1. The portal frame work is realized by the open

Figure 2: ISDC user development

Figure 3: ISDC user â&#x20AC;&#x201C; country statistics

source software Postnuke. In addition to the portal frame and standard components, like user registration, content management and a user forum, most of the components are developed by the ISDC team.

At present the ISDC is managing almost 290 different product types covering different geoscience domains like geodesy, geophysics as well as atmosphere and ionosphere physics.

More than one third of these product types are accessible by public users and user groups.

The other product types are used for operational, restricted and internal use only. More than 10 terra byte and 16 millions data prod-

ucts are long-term stored at the ISDC product archive and online accessible via the ISDC online product archive. Since the start of the new ISDC portal in March 2006, the number of international users and user groups has been increasing exponentially. Whereas figure 2 is representing the increase of registered users and user groups within the last seven years, figure 3 gives an overview about the actual and international use of the ISDC data, headed by users from China, United States, India and Japan.

The ISDC is providing solutions for almost all parts of a science data lifecycle management.

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Figure 4: Extended ISDC product philosophy

Figure 5: Mapping of standards

Due to a standardized ISDC product philosophy, the management of almost 300 different product types has been possible. As mentioned in the introduction already, all product types are described by standardized parent DIF (NASA’s Directory Interchange Format) metadata documents (figure 4). This means, all product type dependent information, like entry id (unique identifier), entry title, parameters (science keywords), topic category, data center, summary, personnel, instrument, quality as well as the temporal and spatial coverage of the whole data set are recorded in parent DIF files. In order to deal with single prod-

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ucts (data files) of a specific product type, a further development of the DIF standards was necessary. In comparison to the old ISDC metadata standards, the product dependent metadata of all new ISDC product types are stored in separate child DIF metadata documents. Detailed information about the new ISDC product philosophy based on XML structures are available in the »ISDC Metadata Management« article [1]. The input of data intto the ISDC as well as the output of data is realized by ISDC data pumps, which are not only responsible for the transfer of data but also for the filling of the ISDC product catalog

Figure 6: Connecting different worlds

(figure 4). In order to guaranty the sustainability of data in the GFZ ISDC, there are not only appropriate archive structures and techniques necessary but also scheduled science driven data review processes, which are not realized by now. These review processes are part of the data lifecycle management, and assure the keeping of the operational status and the enhancement of data interoperability over a long-term period.

In order to improve the integration and the interoperability of the ISDC catalog, which is consisting of product type and product related data, the usage of standardized Service Oriented Architecture (SOA) driven concepts is necessary. The decision to use XML as representation language for the documentation of ISDC product type and product dependent metadata, provides the opportunity to transform metadata documents via XSLT processes (figure 5). Appropriate XSLT documents are containing the mapping specifications for the transformation process of documents from one metadata standard to another one. As shown in figure 5, the ISDC is using the Open Geospatial Committee (OGC) ISO 19115 metadata standard [7] in order to become interoperable. In addition to the metadata

transformation process, SOA compliant catalog software is necessary in order to provide a standardized Catalog Web Service (CSW) interface. The ISDC is using the open source software ÂťdegreeÂŤ (http://www.deegree.org) [8], [9], which is providing an OGC compliant CSW 2.0 catalog service. Complementary to this OGC ISO catalog web service, it is planned to network main parts of the ISDC catalog via techniques, based on the Protocol for Metadata Harvesting (PMH) developed by the Open Archives Initiative (OAI).

Most of the ISDC connection to the Internet is based on committee driven standards and techniques. As illustrated in figure 6, additionally, there are a lot of community driven activities and developments, which are composing the interactive Web 2.0. Recently the ISDC team is studying such Web 2.0 techniques, like tagging and social navigation for the usage at the ISDC, and appropriate user interfaces are in development already. Now and in future it is necessary to validate Web 2.0 techniques for the capability within the ISDC in order to improve the general and specific knowledge about the ISDC products on one hand and to enhance the distribution of products on the other hand.

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Due to the capabilities of the ISDC system as well as the active work of the ISDC team within important international organizations, like the Committee on Data for Science and Technology (DATA), the Electronic Geophysical Year (eGY) and the Working Group on Information Systems and Services (WGISS), the GFZ ISDC not only has become a part of the NASA’s International Directory Network (IDN) and GEO’s Global Observing System of Systems (GEOSS) but also an accepted partner within the Earth and Space Science Informatics (ESSI) community related to European and American Geophysical Unions (EGU, AGU).

References Deegree Project: http://www.deegree.org Global Change Master Directory: http://gcmd.nasa.gov/ XML & XSLT: www.w3.org/TR/xslt, http://selfhtml.org/ [1] Reigber Ch., Schwintzer P., Lühr H., Massmann F.-H., Galas R., Ritschel B.: CHAMP Mission Science Data System Operation and Generation of Scientific Products, GEOTECHNOLOGIEN Science Report, Observation of System Earth from Space, Status Seminar, Bavarian State Mapping Agency (BLVA), Munich, 12–13 June 2003, 129–131 [2] Flechtner F., Ackermann Ch., Meixner H., Meyer U., Neumayer K.-H., Ritschel B., Schmidt, A., Schmidt R., Zhu S., Reigber Ch.: Development of the GRACE Science Data System, GEOTECHNOLOGIEN Science Report, Observation of System Earth from Space, Status Seminar, Bavarian State Mapping Agency (BLVA), Munich, 12–13 June 2003, 48–50 [3] Ritschel B., Behrends K., Braune St., Freiberg S., Kopischke R., Palm H., Schmidt A.: CHAMP/GRACE-Information System and Data Center (ISDC) – The User Interfaces for Scientific Products of the CHAMP and GRACE Mission, GEOTECHNOLOGIEN Science Report, Observation of System Earth from Space,Sta-

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tus Seminar, Bavarian State Mapping Agency (BLVA), Munich, 12–13 June 2003, 132–133 [4] Ritschel, B., Bruhns, Ch., Burgess, Ph., Freiberg, S., Gericke, L., Kase, St., Kopischke, R., Loos, St., Lowisch, St., Palm, H.: The integration of CHAMP and GRACE products as well as associated scientific services in the new ISDC portal, GEOTECHNOLOGIEN Science Report, Observation of System Earth from Space, Status Seminar, Oberpfaffenhofen 2006 [5] V.Mende, B. Ritschel, H. Palm, L. Gericke, S. Freiberg.: ISDC Metadata Management, GEOTECHNOLOGIEN Science Report, Observation of System Earth from Space, Status Seminar, München 2007 [6] Ritschel,B., Bruhns, C:, Kopischke R., Mende V., Palm H., Freiberg S., Gericke L. The ISDC concept for long-term sustainability of geoscience data and information, PV 2007 Conference, Symposiums-Proceeding, Oberpfaffenhofen 2007 [7] Braune, S., Czegka, W., Klump, J., Palm, H., Ritschel, B., Lochter, F. A. (2003): Anwendungen ISO-19115-konformer Metadaten in in Katalogsystemen aus dem Bereich umweltund geowissenschaftlicher Geofachdaten. – Zeitschrift für Geologische Wissenschaften, 31,1, 37–44 [8] Voges, U., Senkler, K. (2005): OpenGIS® Catalogue Services Specification 2.0 – ISO19115/ISO19119 Application Profile for CSW 2.0.; OpenGIS Consortium, Wayland, Massachusetts [9] Burgess, Ph., Palm, H., Ritschel, B., Bruhns, Ch., Freiberg, S., Gericke, L., Kase, St., Kopischke, R., Loos, St., Lowisch, St.: Implementing modern data dissemination concepts in the ISDC Portal, GEOTECHNOLOGIEN Science Report, Observation of System Earth from Space, Status Seminar, Oberpfaffenhofen 2006

Near-real time satellite orbit determination for GPS radio occultation Michalak G., Wickert J., König R., Rothacher M. GeoForschungsZentrum Potsdam, Contact: michalak@gfz-potsdam.de

1. Introduction One of the CHAMP and GRACE mission objectives is to perform radio occultation measurements of GPS signals propagating through Earth’s atmosphere. From these measurements it is possible to derive vertical profiles of bending angles, temperature and humidity of the atmosphere on a global scale which can be used by numerical weather prediction systems. To fulfil this mission objective, precise orbits and clock offsets both for occulting GPS satellites and the Low Earth Orbiters (LEOs) are required. For efficient occultation data assimilation, the weather prediction systems require a 3 h time line. For this purpose a Near-Real Time (NRT) orbit processing system was developed to generate precise GPS, CHAMP, GRACE-A and TerraSAR-X orbits with a mean latency of 15–30 minutes, which is a crucial precondition to reduce the delay for the provision of atmospheric data below 2 hours.

2. NRT orbit processing system The Near-Real Time LEO orbit processing system is based on the so called two step approach in which the LEO orbits are estimated using fixed GPS orbits and clocks. For this reason the system consists of two independent subsystems. One is designed to generate NRT GPS orbits and clocks; the second one generates LEO NRT orbits. The estimation of the GPS orbits and clocks is performed by using data of 30–60 stations of a globally distributed GPS ground network. Since the processing of the GPS ground data is the most time consuming part, for the NRT application this processing was split into a long and a short arc.

So the long 24 h (or 12 h) GPS arcs (see details below) are generated on an hourly basis and parallel to this the short 3 h arcs extending the long arcs are generated every 15 minutes. The generation of the short arcs is fast and gives access to GPS orbits and clocks with low latencies of ~ 5 minutes after downloading the data. Subsequent 14 h LEO NRT arcs are based on the combination of the most recently generated long+short GPS arcs. The LEO NRT processing starts as soon as new GPS satellite-tosatellite (SST) dump data become available (so called dump-related processing). Typical delay in access to SST dump data is in the range of 5–10 minutes. The NRT system is currently activated for CHAMP (since August 2006), GRACE-A (since February 2007) and for the recently launched TerraSAR-X satellite (since August 2007).

To assure high reliability and to test possible accuracies and latencies, the NRT orbit processing system was split into three separate chains which generate LEO orbits based on different sets of GPS orbits. The description of the chains (CHAIN 1, CHAIN 2 and CHAIN 3) is given below, accuracies and latencies for all LEOs and chains are summarized in Table 1.

2.1. CHAIN 1: GPS-based Processing In this chain, called »GPS-based«, the 14 h LEO orbits are based on the combination of 24 h + 3 h GPS orbits and clocks, estimated with 5 minutes spacing. The 3 h arcs are predictions originating from the long 24 h arcs, but the 5 minutes clocks are estimated. The latency of the 3h GPS orbits is currently ~ 20 minutes, where ~15 min is the waiting and data downloading time, the remaining 5 min-

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Table 1: Summary of the accuracies and latencies of the 14h NRT LEO orbits for various NRT processing chains.

For calculation of the position and velocity overlap values, the last two hours of the LEO arcs are used.

Latency is defined as the difference between the orbit generation time and the epoch of the last available SST observation used in the processing.

SLR RMS (cm)

3-D Position Overlap (cm)

3-D Velocity Overlap (cm)

Latency (min)

CHAMP Period 2006/08/17 – 2007/10/08 CHAIN 1 (GPS-based)

6.7

11.2

0.12

31

CHAIN 2 (IGU-based)

9.7

20.0

0.21

14

CHAIN 3 (IGU-fixed-30s)

5.0

6.8

0.07

30

GRACE-A Period 2006/08/22 – 2007/10/08 CHAIN 1 (GPS-based)

8.2

11.0

0.12

31

CHAIN 2 (IGU-based)

11.5

21.0

0.23

14

6.4

7.0

0.06

30

CHAIN 3 (IGU-fixed-30s)

TerraSAR-X Period 2007/08/27 – 2007/10/08 CHAIN 1 (GPS-based)

–

–

–

–

CHAIN 2 (IGU-based)

7.8

18.9

0.19

90

CHAIN 3 (IGU-fixed-30s)

3.7

5.9

0.06

90

utes is the data processing proper. Currently the 3-D accuracy of the short 3 h GPS arcs, when compared to the estimated part of the Ultra Rapid Orbits (IGU) of the International GNSS Service is 11 cm; the radial accuracy is much better and amounts to 5.7 cm. The LEO orbits are generated with a mean latency of ~ 30 min and an accuracy of ~ 4–8 cm validated by independent Satellite Laser Ranging (SLR) measurements. This chain is not active for the TerraSAR-X satellite.

2.2. CHAIN 2: IGU-based Processing In this chain, designated as »IGU-based«, the 14 h LEO orbits are based on purely predicted IGU orbits and clocks. Because there is no ground GPS data processing involved, the LEO orbits are generated with a mean latency of ~14 min, but a rather low accuracy of ~7–11 cm (SLR). This low accuracy is mainly caused by the predicted IGU clocks used as fixed in the LEO processing. This chain is very robust

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because it depends solely on the availability of the IGU orbits and the SST dump data.

2.3. CHAIN 3: IGU-fixed-30s Processing This chain, designated as »IGU-fixed-30s«, generates LEO orbits based on fixed predicted IGU orbits, but 30 s clocks estimated from ground data. Since estimation of the dense 30 s clocks is time consuming, the length of the hourly generated long GPS arc was reduced from 24 h to 12 h, the short arc remains of 3 h length.

This chain is a kind of mixture of the two above chains, generates LEO orbits with an acceptable mean latency of ~30 min but with the highest accuracy of 3.7 cm–6 cm. For TerraSAR-X the latency (90 min) is dictated mainly by the dump data delay (see Table 1) but will be improved in the nearest future.

Summary Within the »Geotechnologien NRT-RO« project, GFZ Potsdam has developed a new NRT orbit processing system for GPS and LEO orbits to support NRT radio occultations. The system generates NRT LEO orbits of lower accuracy (~ 20 cm for position, ~ 0.20 mm/s for velocity) with a latency of ~14 min when using predicted IGU orbits, and also more precise LEO orbits (6–7 cm for position, 0.06 mm/s for velocity) with a latency of ~30 min when using IGU predicted orbits and estimated 30 s clocks.

In all processing chains the orbit latency assures generation of occultation products with average delay well below 3 h required for Numerical Weather Prediction systems. The new NRT processing system is designed for easy extension to other LEOs delivering NRT data, what was demonstrated by inclusion of the TerraSAR-X data already three months after the launch of the satellite on Jun, 15, 2007. The variety of the approaches to the NRT orbits (three independent chains for each of the LEOs) assures high reliability of the system. The system is fully operational and automatic, requires however constant human activities to account for new unexpected situations hindering automatisation. The system therefore is permanently developed into a knowledge based system.

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Assimilation of CHAMP and GRACE-A Radio Occultation Data in the GME Global Atmospheric Model of the German Weather Service Pingel D. (1), Rhodin A. (1), Wergen W. (1), Tomassini M. (1), Gorbunov M. (2), Wickert J. (3) (1) Deutscher Wetterdienst, Offenbach, Germany (2) Obukhov Institute for Atmospheric Physics, Moscow, Russia (3) GeoForschungsZentrum Potsdam, Potsdam, Germany

Data assimilation Prior to a numerical weather forecast run, the state of the meteorological model has to be updated using observational information. This operation is called the assimilation step in the process of weather forecasting. Common observational data sources include in-situ data such as radiosondes, SYNOP-measurements, data from aircrafts and buoys. In the meantime, satellite remote-sensing measurements play a major role in weather prediction. Most remotesensing observations are radiances, quantifying the radiances of a given wavelength at nadir.

Radio occultation data, however, are a relatively new source of observational information.

Quantities that describe an occultation process, like bending angles of the individual rays or the refractivity field, depend directly on the temperature and the humidity along the ray’s path.

Therefore, radio occultations can be assimilated in order to include additional information on temperature and humidity into the model. They have been proven to be a valuable source of information in atmospheric research and weather prediction [1, 2].

The information of radio occultations about the earth’s atmosphere is complementary to radiance observations in several senses: Whereas temperature and humidity retrievals derived from radiances have a relatively low vertical resolution, the radio occultation obser-

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vations are sensitive to vertical structures on a much smaller scale. Unlike radio occultation, radiance measuremments generally fail in cloudy areas [3]. Another beneficial property is the lack of fundamental biases, which is an advantage when taking into account the elaborate procedure of radiometer calibration.

When comparing radio occultation data with radiosonde observations, which are of primary importance in both data assimilation and verification, the temperature information content is similar in the profiles of both observational sources. However, the spatial distribution, which is crucial for the optimal assimilation of this information, is quite different: Whereas the radio soundings are concentrated in the northern hemisphere in the USA, Europe and China, the radio occultations are spread far more evenly. Fig. 1 shows the locations of radio sounding within 12 hours, together with the radio occultation locations of four of the six FORMOSAT-3/COSMIC (Taiwan’s Formosa Satellite Mission no. 3/Constellation Observing System for Meteorology, Ionosphere & Climate) satellites in the same time window. Considering these four low orbiting satellites (LEO), the number of radio occultations and radiosondes is comparable and about 700 per 12 h.

At the German weather service, the assimilation of radio occultation data will be per-

Figure 1: Location of radiosonde observations (light grey) and radio occultations measuremment of four of the six FORMOSAT-3/COSMIC satellites (dark grey) 0â&#x20AC;&#x201C;12 AM, 20070510

formed by the three-dimensional variational (3D-Var) assimilation method. It has proceeded to the last experimental steps and is planned to replace the current operational assimlation system, based on the method of optimum interpolation (OI), within the next 6 months. Currently, the performance of the 3D-Var in assimilation of conventional (in-situ) data is at least as good as the OI (in terms of forecast impact).

The assimilation of satellite data (both radiances and radio occultations) is in process at the present time.

The assimilation of observational data is done in a statistically optimal way, taking into account the observations, the preceeding forecast and error characteristics of both model and observations. Therefore, a thorough specification of observational and forecast errors is of high relevance in data assimilation. Within the asssimilation process, a cost function containing penalty terms for deviances of the analysis state both from the background and the observations is minimized as a function of the analysis. For the 3D-Var, this numerical minimisation is performed in observation

space. This has two advantages in comparison with a minimisation in model space: First, it reduces the size of the numerical problem, as the number of model grid points generally outnumbers the number of observations. The second advantage is related to the necessity to apply a function to the model data, in order to obtain first guess values in the observation space. This transition from model to observation space allows to consider observations which depend on the model background data in a highly nonlinear way, such as satellite radiances and radio occultations. Therefore, the prognostic variables of the atmospheric model such as temperature and humidity fields are to be related to the radio occultation data. Basically, phase delay, bending angles or refractivity fields can play the role of the observations to be assimilated. At the DWD, bending angles have been chosen as observations, as they allow for a reliable specification of significant background and observational errors.

Hence a forward operator is to be implemented to map the model background at the location of the observation to the corresponding first guess bending angle.

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Activities of the DWD in the NRT-RO project The first objective of the DWD participation in the Near Real Time-Radio Occultation (NRTRO) research project is to find a reasonable setup for the forward observation operator that is suitable for data assimilation under the specific terms of operational application. In addition to the bending angles themselvs, the optimal observation errors have to be specified. This assimilation setup is then to be put to the test in assimilation experiments. The impact of the radio occultation observations on the weather forecast quality is then to be assessed. Accompanying these experiments, a long-term monitoring of the radio occultation observations is arranged. To this end, the statistical parameters of the differences of observations and background values (O-B) are determined on a monthly basis.

Evaluation of bending angle forward operators The evaluation of a possible forecast operator setup is a prerequisite for both the accomplishment of the monitoring as well as for the assimilation experiments of radio occultation observations. Two intrinsically different models have been considered to serve as forward operators: A three-dimensional ray tracing model and a one-dimensional model.

The ray-tracing model is supposed to be the best fit to the physical reality, as it takes into account the horizontal gradients of the temperature and humidity atmospheric fields as well as the drift of the rayâ&#x20AC;&#x2122;s tangental points in the course of an occultation [4]. A certain disadvantage of the ray-tracing operator is the high demand of computing ressources (time and memory).

The one-dimensional forward operator is based on the assumption of spherically symmetric atmospheric fields. It applies an inverse Abel transform to the refractivity profile that is derived from the temperature and humidity profile at a single point, the occultation point.

The reduction of the horizontally extended

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occultation event to a single point ignores the fact of the tangential point drift. Furthermore, the choice of this occultation point introduces a certain indefiniteness to the forward model.

To model the drift of the tangential points at least to some extent, three modifications of the one-dimensional forward operator have been implemented for test purposes, each of them considering a differently determined occultation point: The first modification performs the inverse Abel transform at the occultation point as given in the corresponding observation data set of bending angles. For the second modification, the occultation point is determined as the mean of the individual rayâ&#x20AC;&#x2122;s tangential points in the lowest 20 km of the occultation profile (an approach applied also in the ROPIC study). The third modification applies the inverse Abel transform to each ray of the occultation profile separately. This aproach is expected to model the tangential point drift best compaired to the two preceeding modifications.

The data set to test the performance of the different forward operators is a CHAMP phase delay data set (phase delays by the GFZ, baseline data set for the ROPIC study). It is processed to yield bending angles with the method of canonical transform (CT2, by M. Gorbunov) at the DWD [5]. It contains bending angles and observation error estimates from the two months January and June 2005. The monitoring is performed, using the DWD global meteorological model GME [6] tree-hourly forcast fields as model background. The statistical properties of the innovations, i.e. of the differences of observation and first guess, are then taken into account to evaluate the different forward operators.

A decrease of the standard deviation can be observed from the one-dimensional forward operator compared to the ray-tracing operator (Fig. 2). When comparing the different onedimensional operators, the modification applying the inverse Abel transform to each individual ray performed best, whereas the forward operator that accepts the occultation

Figure 2: Ratio of the O-B standard deviation of the three modifications of the inverseAbel-transform bending angle forward operator to the respective value of the threedimensional ray-tracing operator

point as given in the bending angle data set performed poorest. However, above ca. 8 km the standard deviations for the partly optimized one-dimensional forward operators differ only by less than 3% from the ray-tracing results. Below this height, the ray tracing forward operator is significantly better. This is due to the fact that at this height the bending angle signal contains predominantly humidity information (especially in the tropics).

Water vapour is, contrary to temperature, a quantity that fluctuates significatly on a horizontal scale comparable with the extent of the occultation. These fluctuations are considered for by the ray-tracing operator, but not by the one-dimensional forward operator. However, for data asssimilation, the lowest part of the occultation profil is generally of low statistical weight due to high observation error of the radio occultation observations in the lower troposphere. This result is in agreement with results of other studies [7, 8]. It suggests the

usage of a appropriately optimized onedimensional bending angle forward operator for the operational assimilation of RO observations. The approach of combining the onedimensional operator with the ray-tracing operator to a hybrid model, which was proposed in the beginning of the project, seems not to be necessary. For the following monitoring and assimilation experiments, optimized one-dimensional forward operators are applied rather than the ray-tracing operator.

Monitoring The bending angle observations are compared with the corresponding background equivalents, derived from the forecast fields of the GME by application of one of the modifications of the one-dimensional inverse Abel transform forward operators. Near real time bending angle data sets of CHAMP and GRACE-A by the GFZ, COSMIC by COSMIC/UCAR (University Corporation for

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Figure 3: Estimated bending angle observation error (functional approach)

Figure 4: Estimated bending angle background error (GME, one-dimensional bending angle forward operator)

Atmospheric Research) and METOP-A/GRAS by EUMETSAT (European Organisation for the Exploitation of Meteorological Satellites) are considered. The statistical properties of the corresponding differences, the innovations, are taken into account to assess the consistency of model and observational bending angle values and corresponding error estimates. As the CHAMP and GRACE-A near real time data as well as the data from the METOP-GRAS instrument not yet include estimates for the obser-

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vational error, a simple, partially linear functional dependence of the observation error on the impact height is assumed [9]. Fig. 3 to 7 show zonally averaged means of statistical parameters of the O-B innovations of the combined CHAMP and GRACE-A near real time bending angle data set of July 2007. In general, the CHAMP and GRACE-A observed bending angles agree with the corresponding background equivalents reasonably well and within the assumptions made for the back-

Figure 5: Quadratic sum of estimated observation and background bending angle error.

The sum is generally an estimate for the O-B standard deviation.

The background error is the dominating contribution

Figure 6: Actual standard deviation of O-B statistics

ground and observation error in the assimilation system. The estimated observational errors (Fig. 3) are considerably smaller than the model background errors (Fig. 4), especially in the upper troposphere of the extra tropics.

This is probably due to an overestimation of the background error in these regions and implies a relatively high statistical weight of the radio occultation observations in the assimilation process. The quadratic sum of the observation error and background error estimate (Fig. 5) is an estimate for the expected

standard deviation of the O-B statistics. Fig. 6 displays the actual O-B standard deviation of the observation data set. The ratio of the actual standard deviation with respect to the estimated error (Fig. 7) is less than one for most areas and height levels, indicating a better agreement of observations and background values than estimated from the error specification of the assimilation system. In some regions, e.g. the upper tropical troposphere, the relatively high value of the O-B standard deviation might be explained by the occur-

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Figure 7: Ratio of actual standard deviation of the innovation (Fig. 6) and the estimated error (Fig. 5)

Figure 8: Bias of the innovation statistics

rence of gravity waves. The bias of the innovations is reasonably small, but shows a remarkable vertically oscillating pattern in the upper troposphere and stratosphere in the tropics and mid-latitudes (Fig. 8).

Assimilation experiments A first assimilation experiment with radio occultation observations has been performed.

In order to estimate the maximal impact of the radio occultation data, and therefore to apply

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the necessary optimization to the assimilation system more easily, the near real time data of FORMOSAT-3/COSMIC has been chosen as source of data. As the radio occultation data originates from six satellites with receivers for both rising and setting occultations, the FORMOSAT-3/COSMIC data largly outnumbers the amount of occultation data collected by a single LEO like CHAMP. However, as soon as the most necessary adjustments of the assimilation system will have been done, a further assimi-

Figure 9: Impact of radio occultation data on forecast quality: Assimilation of radio occultation data results in an increase of the anomaly correlation coefficient (ANOC), which indicates a significant improvement of the forecast scores (see text for details)

lation experiment is planned to be run with near real time bending angles from the CHAMP and GRACE-A satellites.

The assimilation experiment is carried out for the time of May 2007 with assimilation intervalls of three hours. In the experiment, radio occultation bending angles are assimilated together with conventional in-situdata. In the corresponding control experiment, conventional data is the only observational source. Subsequent forecast runs are performed to assess the impact on the forecast results.

The forecast quality can be quantified by the anomaly correlation coefficient (ANOC) of an atmospheric field. It measures the correlation of deviances of forecasts with those of coinciding analysis with respect to the model climatology.

The larger the value of the ANOC is, the closer is the forecast to the analysed value. A value of 0.6 is agreed to be the lower limit for forcasts with significant synoptic information.

Figure 9 shows the anomaly correlation coefficient for the control experiment, the experiment additionally including radio occultation observation, and an experiment that assimilates conventional observations and AMSU-A data, for 18 forecasts on the southern hemisphere. The ANOC is calculated for the geopotential field at 500 hPa, which is a reliable indicator for the over-all quality of a numerical weather forecast.

In terms of the anomaly correlations of the 500 hPa geopotential, the assimilation of radio occultation results in a significant increase of the ANOC in the southern hemisphere. A similar result holds for the temperature field. It is remarkable that the improvement of the forecast scores due to radio occultation is already half of the improvement to be expected when assimilating AMSU-A radiance observations in addition to conventional data. In the northern hemisphere, still a slight degradation of the ANOC is visible for geopotential and temperature, the reason for this feature is still to be identified.

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The verification of the assimilated temperature and humidity against corresponding measurements of radio soundings and aircraft data shows a significant reduction of the standard deviation for the experiment with assimilation of radio occultation observations.

Conclusions and Outlook The performance of three different modifications of a one-dimensional and a three-dimensional ray-tracing bending angle forward operator is evaluated for use in a three-dimensional variational data assimilation system. The raytracing operator takes horizontal gradients and the ray’s tangential point drift into account. The modifications of the one-dimensional operator apply the inverse Abel transform, assuming spherically symmetric atmospheric fields, and reflect the tangential point drift each to a different degree. Considering the standard deviation of the differences of first guess to observed occultation data above the impact height of 8 km, the four forward operators differ by less than 2%. Therefore, a choice of a properly optimized, numerically less expansive one-dimensional forward operator for the use in an operational data assimilation system seems legitimate.

Monitoring of near real time radio occultation bending angle data sets from CHAMP, GRACEA, and FORMOSAT-3/COSMIC has been carried out for the time of several month. The standard deviation of the observations-first guess differences are well within the error bound estimation of the assimilation system.

An experiment assimilating bending angle observations shows a significant improvement of the forcast quality in the southern hemisphere and proved radio occultation data to be a valuable source of meteorological information.

Acknowledgements We thank the GeoForschungsZentrum Potsdam for reliably providing CHAMP and GRACE-A data sets of radio occultation data, both offline and near real time processed. We thank the FORMOSAT-3/COSMIC project for provision of radio occultation data. We thank

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Michael Gorbunov for making the CT2 processing method and both bending angle forward operators available to us. The German Ministry for Education and Research supported the research project NRT-RO related to the near real time provision and usage of radio occultation data within the GEOTECHNOLOGIEN research program.

References [1] J. Wickert, G. Michalak, T. Schmidt, G. Beyerle, C.Z. Cheng, S. B. Healy, S. Heise, C. Y. Huang, N. Jakowski, W. Köhler, C. Mayer, D. Offilier, E. Ozawa, A.G. Pavelyev, M. Rothacher, B. Tapley, C. Viehweg: GPS radio occultation: Results from CHAMP, GRACE and FORMOSAT-3/COSMIC, submitted for publication [2] S. B. Healy, J. Wickert, G. Michalak, T. Schmidt, G. Beyerle: Combined forecast impact of GRACE-A and CHAMP GPS radio occultation bending angle profiles, Atmos. Sci. Let., 8, 43–50, 2007.

[3] A. P. McNally: A note on the occurence of cloud in meteorologically sensitive areas and the implications for advanced infrared sounders, Q.J. R. Meteorol. Soc., 128, 2551–2556, 2002.

[4] M. E. Gorbunov, L. Kornblueh: Principles of variational assimilation of GNSS radio occultation data, Report 350, Max-Planck-Institut für Meteorologie, Bundesstrasse 55, D-20146 Hamburg, 2003.

[5] M. E. Gorbunov, Operational processing of CHAMP data: Mathematical methods, data filtering and quality control, and software implementations, Report, German Weather Service, 2004.

[6] D. Majewski, D. Liermann, P. Prohl, B. Ritter, T. Hanisch, G. Paul, W. Wergen: The operational global icosahedral-hexagonal gridpoint model GME: Description and highresolution tests, Mon. Wea. Rev., 130, 319–338, 2002.

[7] S. Healy, J. R. Eyre, M. Hamrud, J.-N. Thépaut: Assimilating GPS radio occultation measurements with two-dimensional bending angle observation operators, Q.J.R. Meteorol. Soc., 133, pp. 1213–1227, 2007.

[8] P. Poli and J. Joiner: Effects of horizontal gradients on GPS radio occultation observation operators. II: A Fast Atmospheric Refractivity Gradient Operator (FARGO), Q.J.R. Meteorol. Soc., 130, 2807–2825, 2006.

[9] S. B. Healy, J.-N. Thépaut: Assimilation experiments with CHAMP GPS radio occultation measurements, Q.J.R. Meteorol. Soc., 132, 605–623, 2006.

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Global atmospheric data from CHAMP and GRACE in near-real time Wickert J. (1), Beyerle G. (1), Falck C. (1), Flechtner F. (1), Galas R. (1), Grunwaldt L. (1), Healy S. B. (2), Heise S. (1), Kรถhler W. (1), Kรถnig R. (1), Massmann F. H. (1), Michalak G. (1), Offiler D. (3), Pingel D. (4), Poli P. (5), Ozawa E. (6), Rothacher M. (1), Schmidt T. (1), Tapley B. (7), Wergen W. (4) (1) GeoForschungsZentrum Potsdam (GFZ), Germany, Contact: jens.wickert@gfz-potsdam.de (2) European Centre for Medium-range Weather Forecasts (ECMWF), Reading, UK (3) Met Office, UK (4) Deutscher Wetterdienst (DWD) (5) Meteo-France (6) Japan Meteorological Agency (JMA) (7) University of Texas, U.S.

Abstract The German geoscience satellite CHAMP (CHAllenging Minisatellite Payload) almost continuously provides global atmospheric measurements since early 2001. It currently generates a unique long-term set of GPS radio occultation (RO) data. Around 315,000 occultation measurements were performed as of mid September 2007. Currently the mission is expected to last at least until end 2008. Data and analysis results are provided to the international scientific community and stimulated several activities to improve GPS RO data analysis and the application in atmospheric research and for global weather forecasts. The data are currently in use by more than 40 research groups worldwide.

Occultation data from the U.S.-German GRACE mission (Gravity Recovery and Climate Experiment) are operationally available since May 22, 2006. A near-real time data provision from CHAMP and GRACE is demonstrated by GFZ within a GEOTECHNOLOGIEN research project. A major goal of this project, the provision of RO data with average delay between measurement aboard the satellites and provision of corresponding analysis results below 2 hours is operationally reached since spring 2007.

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1. Introduction The application of the GPS Radio Occultation (GPS RO) technique aboard Low Earth Orbiting (LEO) satellites allows for the derivation of vertical profiles of atmospheric parameters on a global scale. Main characteristics of GPS RO measurements are: all-weather, calibration

Figure 1: Title page of the Near-Real Time Radio Occultation (NRT-RO) research project proposal (in German)

Figure 2: Number of globally distributed vertical profiles of atmospheric profiles per day from the CHAMP mission as of day of the year 260 in 2007

Figure 3: Number of globally distributed vertical profiles of atmospheric profiles per day from the GRACE-A satellite as of day of the year 273 in 2007

free, high accuracy and high vertical resolution. A detailed introduction to GPS RO is given, e.g., by Kursinski et al. (1997). Currently GPS RO is continuously applied aboard the German CHAMP and the U.S./German GRACE satellites (Wickert et al., 2005), the 6 satellites of the FORMOSAT-3/COSMIC mission (launched April 14, 2006; see, e.g. Rocken et al., 2000) and aboard Metop (Loiselet et al., 2000; Launch Oct. 18, 2006; operational provision not yet activated). The NRT activities are funded within the research project »Near-Real Time – Radio Occultation« (NRT-RO) of the GEOTECHNOLOGIEN programme of the Ger-

man Ministry for Education and Research). In focus here are CHAMP and GRACE. 2. Status of champ and grace radio occultations CHAMP reached its 7th anniversary in orbit on July 15, 2007. As of mid September, 2007 around 315,000 globally distributed vertical atmospheric profiles are provided (Fig. 2). The measurements from CHAMP form the first long-term RO data set, which very probably can be extended until 2009.

GRACE (e.g., Tapley et al., 2004) had 5th anniversary in orbit on March 17, 2007. As of

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mid September 2007 more than 60,000 vertical profiles are available from GRACE-A (Fig. 3).

3. Near-real time occultation infrastructure and data analysis at GFZ GFZ Potsdam operates an operational infrastructure for the processing of GPS RO data (overview see Fig. 4). The GPS data (navigation and occultation) from CHAMP and GRACE are transferred to the ground via receiving antennas at Neustrelitz, Germany and Ny-Ă&#x2026;lesund, Spitsbergen. Together with GPS data from the operational global GPS ground network (jointly operated by GFZ and JPL) these data form the main input for the automated processing systems to derive precise satellite orbit and atmospheric data (for

more details, see, e.g. Wickert et al., 2007 and Michalak et al., 2007).

Generated data products are: atmospheric excess phase data and vertical profiles of bending angles, refractivity, temperature and water vapor (Wickert et al., 2007). In near real-time are provided: atmospheric excess phase data for each occultation and vertical profiles of bending angle, refractivity and dry temperature. In parallel to the standard data processing a near-real time provision of atmospheric data is demonstrated. The NRT data are provided continuously with average delay between measurement aboard the satellites and provision of corresponding analysis results at GFZ of less than 2 hours (Fig. 4).

Figure 4: GPS radio occultation infrastructure at GFZ (Overview)

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Figure 5: GFZ provides near-real time occultation data (bending angle and refractivity profiles in BUFR) from CHAMP and GRACE-A. The figure shows the time delay between CHAMP (above) and GRACE-A (middle) occultation measurements aboard the satellites and availability of corresponding analysis results at NRT ftp-server at GFZ. Red triangles indicate the daily mean of the time delay between measurement and availability of bending angle and refractivity profiles for all occultation events. The significant reduction of the time delay in end of February (CHAMP) and June (GRACE-A) is due to the activation of an improved NRT processing mode. Data are provided since February 2007 in BUFR format and are currently distributed also via the Global Telecommunication System (GTS)

4. Monitoring and assimilation of CHAMP and GRACE data to global weather models The NRT processing is an essential key in ensuring that the GPS radio occultation data collected by CHAMP and GRACE are fully exploited and benefit the numerical weather prediction. Various weather forecast centers monitor and assimilate GPS Radio occultation data from COSMIC, CHAMP and GRACE since Sept. 2006. These centers are ECMWF, MetOffice, Japan Meteorological Agency, Meteo-France, National Center for Environmental Prediction (NCEP, U.S), and Deutscher Wetterdienst. Results of a recent impact study with GPS RO data were published by Healy et al. (2007).

5. Gps radio occultation with TerraSAR-X The German TerraSAR-X satellite (Fig. 5) was launched on June 15, 2007 with a Dnepr-1 from Aerodrome Baikonur. The main science

instrument aboard is a new generation X-band radar (9,65 GHz) for Earth observation with up to 1â&#x20AC;&#x201C;2 m resolution (spotlight mode). GFZ (together with University Texas) is operating an IGOR GPS receiver. Operational activation of occultation is planned for late autumn 2007.

The multi mission reception of data from CHAMP, GRACE-A and TerraSAR-X at the receiving station Ny Alesund was successfully demonstrated by GFZ. Three test campaigns took place in July, August and September 2007 using the second GFZ antenna for either redundant or parallel satellite reception.

6. Summary and outlook The operational ground infrastructure of GFZ allows for an near-real time provision of GPS RO analysis results with maximum delay of 2 hours. The data are assimilated to various numerical weather prediction centers, providing them with valuable information to better estimate the state of the atmosphere.

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Figure 6: TerraSAR-X in orbit (Artist’s view)

Acknowledgements We thank the CHAMP, GRACE and TerraSARX teams for their great work to guarantee the availability of GPS occultation data. The near-real time activities at GFZ and DWD are supported by the German Ministry for Education and Research within the GEOTECHNOLOGIEN programme (Research project NRT-RO). This project is also significantly aided by ECMWF, MetOffice, Meteo-France and Japan Meteorological Agency. We are grateful for this support.

References Healy, S.B., J. Wickert, G. Michalak, T. Schmidt, and G. Beyerle, Combined forecast impact of GRACE-A and CHAMP GPS radio occultation bending angle profiles, Atmospheric science letters, 8: 43–50, DOI: 10.1002/asl.149,, 2007.

Kursinski et al., Observing Earth’s atmosphere with radio occultation measurements using the Global Positioning System. J. Geophys.

Res. 102, 23429–23465, 1997.

Loiselet, M., N. Stricker, Y. Menard, and J. Luntama, GRAS MetOps GPS based atmospheric sounder, ESA Bulletin, May, 102, 38–44, 2000.

Michalak, G., Wickert, J., R. König, and M. Rothacher, Precise satellite orbit determination for GPS radio occultation in near-real time (NRT), EGU General Assembly, EGU2007-A08740, Vienna, Austria, 2007.

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Rocken, C., Y.-H. Kuo, W. Schreiner, D. Hunt, S. Sokolovskiy, and C. McCormick, COSMIC system description, Terrestrial, Atmospheric and Oceanic Sciences, 11, 21–52, 2000.

Tapley B, Bettadpur S, Watkins M, Reigber C., The gravity recovery and climate experiment: Mission, overiew and early results. Geophys.

Res. Lett., 31: L09607, DOI: 10.1029/2004GL019920, 2004.

Wickert, J., G. Beyerle, R. König, S. Heise, L. Grunwaldt, G. Michalak, Ch. Reigber, T. Schmidt, GPS radio occultation with CHAMP and GRACE: A first look at a new and promising satellite configuration for global atmospheric sounding, Annales Geophysicae, Vol. 23, 653–658, 2005.

Wickert, J., G. Michalak, T. Schmidt, G. Beyerle, C.Z. Cheng, S.B. Healy, S. Heise, C.Y. Huang, N. Jakowski, W. Köhler, C. Mayer, D. Offiler, E. Ozawa, A.G. Pavelyev, M. Rothacher, B. Tapley, and C. Viehweg, GPS radio occultation: Results from CHAMP, GRACE and FORMOSAT-3/COSMIC, in print, TAO, 2007.

Precise orbits of altimetry satellites and analysis of GPS data at tide gauges for sea level research Rudenko S., Schöne T., Gendt G., Zhang F., Thaller D. GeoForschungsZentrum Potsdam (GFZ), Telegrafenberg, 14473 Potsdam, Germany, E-mail: rudenko@gfz-potsdam.de

Sea level change being a result of the climate change on the Earth in the form of global warming is a phenomenon influencing the current and future mankind generations. Tide gauge measurements and satellite altimetry measurements are the primary tools to determine sea level variations The mean rate of sea level change obtained from tide gauges in 1955–2005 is +1.8 ± 0.3 mm/year, while altimeter measurements from TOPEX/Poseidon and Jason-1 give the mean rise of +3.1 ± 0.4 mm/year since 1993 (Nerem et al., 2006). Recent studies show acceleration of sea level rise in the recent decade.

Radar altimetry provides a unique tool to measure the sea level globally at various time scales. Precise orbits of altimetry satellites are a prerequisite for the analysis of altimetry measurements. To achieve consistency over longer time periods, the unification of orbit quality is very important. The progress reached in the recent years in orbit modeling and Earth’s gravity field determination due to CHAMP and GRACE missions made it possible to extend the existing time series of sea level measurements back to the GEOSAT period (1985–1989), allowing to analyze now global sea level change for over two decades.

New precise orbits of altimetry satellites GEOSAT (March 1985–December 1989), ERS1 (August 1991–June 1996), TOPEX/Poseidon (September 1992–October 2005) and ERS-2 (May 1995–February 2006) have been recently derived using EPOS-OC software in the same (ITRF2000) (Boucher et al., 2004) reference frame for all satellites using common,

most precise models and standards available.

The orbits cover the major time span of each satellite mission. The orbits are called GFZ EIGEN-GRACE04S (REL01) ones after the geopotential model used (Reigber et al., 2005). The new orbits show improved quality, as compared to earlier GFZ (Rudenko et al., 2006b) and external orbits. The improvement is due to the use of the recent EIGEN-GRACE04S geopotential, FES2004 ocean tide and other models, as well as to the improved, denser, satellite dependent parameterization.

Orbits of altimetry satellites were derived using different types of observations. GEOSAT orbit is derived using Doppler and single crossover (SXO) data. ERS-1 and ERS-2 orbits are based on the use of Satellite Laser Ranging (SLR) and SXO data. TOPEX/Poseidon orbit is computed using SLR and Doppler Orbitography Integrated by Satellite (DORIS) observations.

Progress reached in GEOSAT orbit quality, as compared to (Rudenko et al., 2006a), is due to the use of SXO and Doppler data from 25 Magnavox-1502 stations, additionally to Doppler data from 24 TRANET-II stations used before, as well as due to denser parameterization. Thus, adding of SXO data reduced RMS crossover differences from 11.4 to 11.0 cm.

Denser parameterization reduced RMS crossover differences from 11.0 to 9.5 cm, and adding Doppler data from Magnavox-1502 stations reduced them from 9.5 to 9.0 cm.

The quality of the new GFZ orbits has been compared with the quality of some external orbits available. These are GEOSAT orbit

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Figures 1, 2: RMS crossover differences for GEOSAT and ERS-1 orbits

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Figures 3, 4: RMS crossover differences for TOPEX/Poseidon and ERS-2 orbits

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Figure 5: The original GEOSAT orbit shows volatile mean crossover differences leading to seasonal artificial variations

Figure 6: Relative global mean sea level derived with old and new orbit parameters

derived at the National Aeronautics and Space Administration (NASA) using JGM-3 geopotential model (Fig. 1), ERS-1 and ERS-2 orbits computed at the Department of Earth Observation and Space Systems of the Faculty of AeroSpace Engineering (DEOS) at the Delft Technical University using DGM-E04 and EIGEN-GRACE01S geopotential models, ERS orbits computed at the Centre for Space Research (CSR) at the University of Texas at Austin using TEG-3P geopotential model (Figs. 2, 4), and TOPEX/ Poseidon orbits derived at Centre National dâ&#x20AC;&#x2122;Etudes Spatiales (CNES) and NASA using JGM-3 geopotential models (Fig. 3).

Use of optimal, denser parameterization for empirical accelerations and especially for

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atmospheric drag coefficient allowed us to get rid of most outliers in RMS crossover differences. Some remaining outliers for ERS-1 (Fig. 2) are due to the degraded quality of SXO data at the beginning of ERS-1 mission and gaps in SLR data, not allowing us to apply denser parameterization.

With the continuous and uniform processing of GEOSAT, ERS-1, ERS-2 and TOPEX/Poseidon orbits a new mean sea surface height model is being computed. Sea level anomaly maps for TOPEX/Poseidon are also derived on a new level of consistency and will be derived for all other missions.

Analysis of tide gauge measurements requires a well defined reference frame. Such reference

Figure 7: Network of GPS stations processed at GFZ Potsdam for TIGA and SEAL projects

frame can be realized through precise positions of GPS stations located near tide gauges.

The number of such GPS stations increased from 1 in 1994 till about 180 in 2007. The Tide Gauge Benchmark Monitoring (TIGA) Pilot Project was approved by the International GPS Service (IGS) in 2001 with the purpose to provide time series of coordinates for analyzing vertical motions of tide gauges and tide gauge benchmarks (Schoene, 2006). The required accuracies are about 510 mm for positions and <1 mm/year for vertical motion.

Several TIGA Analysis Centres around the world contribute to these activities, one of them is at GFZ Potsdam. A time series of GPS station positions was derived at GFZ Potsdam in 20022006 (Zhang et al., 2007) using EPOSPotsdam software. The global network of GPS stations includes about 370 stations (Fig.7).

The EPOS-Potsdam software has been recently improved. The main improvements include use of absolute phase centre variations, implementation of IERS Conventions 2003 (McCarthy et al., 2003), development of a new ambiguity fixing scheme allowing to fix 95% versus 80% of ambiguities, use of ITRF2005 reference frame (Altamimi et al., 2007) as an a priori reference frame, FES2004 ocean tide loading model, a new geopotential model (EIGEN-

GL04C, up to n = m = 12) and other improvements. Additionally, a new data processing strategy for huge GNSS networks (Ge at al., 2006) was implemented in the software allowing to process GPS data from a few hundred stations in one network solution. Moreover, more data from TIGA stations became available in the recent years. All this requires and makes possible reprocessing of TIGA GPS data for the period 1994â&#x20AC;&#x201C;2007. Preparation for the reprocessing is in progress.

A strategy for data reprocessing has been developed. The processing will be performed mainly in the same way, as by GFZ IGS Analysis Center with the following important exception. The global network of GPS stations will be split into two clusters. The first cluster includes IGS stations, data of which were already cleaned for the period from 1994 till 2006 during the previous processing in 2002â&#x20AC;&#x201C;2006. The second cluster includes TIGA stations (analyzed, additional and missing), and IGS stations for TIGA, as well as about 30 stations from the cluster 1 for combining the solutions of the two clusters. To save the computer time, cleaned GPS data of the cluster 1 will be used to compute satellite orbits, clocks and Earth rotation parameters being an input for cluster 2 processing. Data cleaning of the

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cleaned stations of the cluster 2 will be performed from the residual analysis, the rest stations from the very beginning. Positions of stations of both clusters in the SINEX format will be a result of reprocessing. Some results of GPS data processing will be presented.

Acknowledgements This research is supported by German Ministry of Education and Research (BMBF) within the GEOTECHNOLOGIEN geoscientific R&D programme (SEAVAR Project).

References Altamimi, Z., Collilieux, X., Legrand, J., Garayt, B., and Boucher, C. (2007) ITRF2005: A new release of the International Terrestrial Reference Frame based on time series of station positions and Earth Orientation Parameters, J. Geophys. Res., 112, B09401, doi: 10.1029/2007JB004949.

Boucher, C., Altamimi, Z., Sillard, P., and Feissel-Vernier, M. (2004) The ITRF2000, IERS Technical Note, No.31.

Ge, M., Gendt, G., Dick, G., Zhang, F.P., and Rothacher, M. (2006) A new data processing strategy for huge GNSS networks, Journal of Geodesy, 80: 199–203.

McCarthy, D. D., and Petit, G. (Eds.) IERS Conventions (2003), IERS Technical Note, No.32.

Nerem, R.S., Leuliette, E., and Cazenave, A. (2006) Present-day sea-level change: A review.

Comptes Rendus Geosciences 338: 1077–1083.

Reigber, Ch., Schmidt, R., Flechtner, F., König, R., Meyer, U., Neumayer, K.-H., Schwintzer, P., Zhu, S.Y (2005) An Earth gravity field model complete to degree and order 150 from GRACE: EIGEN-GRACE02S, Journal of Geodynamics, 39, 1, 1–10.

Rudenko, S., Schoene, T. (2006a) Orbit determination for GEOSAT, ERS-1, ERS-2 and TOPEX/Poseidon, GEOTECHNOLOGIEN Status-

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Seminar »Observation of System Earth from Space«, September 18–19, 2006, Bonn, Germany, Programme and Abstracts.

Rudenko, S., Schoene, T., Raimondo, J.-C. (2006b) Precise orbits of altimetry satellites ERS-1, ERS-2 and TOPEX/Poseidon, Proceedings of the Symposium on 15 Years of Progress in Radar Altimetry, 13–18 March 2006, Venice, Italy (ESA SP-614, July 2006).

Schoene, T. (2006) The IGS Tide Gauge Benchmark Monitoring Project, Proceedings of the Symposium on 15 Years of Progress in Radar Altimetry, 13–18 March 2006, Venice, Italy (ESA SP-614, July 2006).

Zhang, F.-P., Gendt, G., Ge, M. (2007) GPS Data Processing at GFZ for Monitoring the Vertical Motion of Global Tide Gauge Benchmarks, Technical report for projects TIGA and SEAL. GeoForschungsZentrum Potsdam, Scientific Technical Report STR07/02, 28 pages.

SEAVAR – Reconstruction of Sea Level anomalies Sadowsky N., Schöne T., Esselborn S. GeoForschungsInstitut Potsdam (GFZ), Telegrafenberg, D-14473 Potsdam, Germany, E-Mail: nana@gfz-potsdam.de

Given the environmental risks of sea level rise, there is considerable interest in estimating future – regional and global – sea level anomalies (SLAs) as well as in reconstructing consistent time series for the 20th century. Project SEAVAR aims to achieve this by combining satellite altimetry data – with its global coverage – with the longer time series available from tide gauge measurements. Since tide gauge measurements are strongly affected by land movement, the emphasis of this project is to better separate land movement signals from sea level change in the tide gauge data by means of GPS vertical corrections.

Correcting spurious trends from GPS timeseries On closer inspection, the quality of the GPS time series varies strongly – some of the time series have gaps ranging from a few days to several years; others show sudden jumps.

These flaws mirror the unavoidable difficulties of extracting multi-year consistent time series from a living and moving source. It is important to correct these flaws to separate actual land movement processes from systematic errors.

In the example shown in (Fig. 1) – the CGPS station ALBH at Albert Head on Vancouver Island, the time series clearly shows a jump caused by the antenna change performed in

Figure 1

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Figure 2

Figure 3

mid-2003. Leaving this event unaccounted for results in a vast overestimation of the negative linear trend by more than 400%.

The correction (Fig. 2) shows that, at Albert Head, we are actually facing a rising sea level, when the uncorrected spurious trend would have suggested that the increase in RSL were caused by subsidence. Given that most of the time series are affected by such systematic errors, it is crucial that all stations

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should be corrected individually to avoid severe misinterpretations.

Reconstruction algorithm For the reconstruction of SLAs, we are using a gap-filling algorithm (MSSA) developed by Ghil and Kondrashov (2006). In contrast to the more commonly used Optimal Interpolation scheme (OI), MSSA (Multichannel Singular Spectrum analysis) uses temporal as well as spatial correlations for extracting EOFs. The

EOFs are computed from a combined covariance matrix, where the GPS-corrected tide gauge time series have been added to the TOPEX altimetry data set as an additional spatiotemporal channel. The gaps in the respective timeseries are filled iteratively by using the estimated values from the first EOF, then updating the covariance matrix and EOFs, before repeating the process with the next EOF. The example in (Fig. 3) shows two time series from the Galveston I and II tide gauges. The two adjacent gauges measure the same events, but of course differ in their individual measurements. Three gaps have been added artificially. The reconstruction shown here uses only the first EOF, calculated from the combined covariance matrix. The comparison with the original data shows that MSSA performs very well in reconstructing the nonlinear trend.

A comparison with the traditional OI algorithm will be shown in the presentation.

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As explained in Sidorenko et al. [2006] the success of IFEOM heavily relies on using information on deep pressure gradient from the full prognostic model run on the same numerical grid. It removes the inconsistency between the density field and bottom topography, similarly to the effect of including the prognostic phase in Ezer et al. [1995] and Schiller [1995]. Thus deep pressure gradient of the inverse model solution is constrained to that of the prognostic model run with J5.

Finally, to improve model performance in the equatorial belt, adding momentum advection as part of the solution and constraining this term by (J6) was found necessary. Terms J1–J6 are quadratic penalty functions. For example, J 1 = … + ( T j – T d – j ) 2 W T d – j + … with j numbering the nodes where data are known and WTd – j being weights selected appropriately. For more details see Sidorenko et al. [2006].

Prognostic model The prognostic finite-element ocean circulation model is derived from early efforts described in Nechaev et al. [2003]; Danilov et al. [2004], [2005]. It has been set for the North Atlantic on a triangular grid with the basic resolution of one degree covering the domain from 28º S to 80º N. The grid is regular everywhere except for coastlines where smaller triangles are used. In vertical, it consists of 20 unevenly spaced levels. The model is forced by relaxation to monthly surface temperature and salinity of the WOA01 [Conkright et al. 2002] and by the monthly mean wind stress computed from the NCAR/NCEP reanalysis [Kalnay et al. 1996] as a mean over years 1990–1999. Sponge layers with strong relaxation to WOA01 climatology are used in zones adjacent to the southern and northern boundaries of the model in the prognostic run. The prognostic model is spun up for 4 years. Its mean deep pressure gradients below 2000 m and momentum advection in equatorial belt of ±5 degrees averaged over last year are used for the inverse model.

Inverse model The North Atlantic grid employed here is the same as used in the prognostic run. The area where the Lozier et al. [1995] data are present is limited to latitudes between 0 and 70º N. The missing hydrographic data in the far northern and southern parts of the grid is replaced with the Gouretsky et al. [2004] climatology. These parts are included to minimize the influence of open boundaries but do not enter the assimilation.

The presence of the equatorial belt introduces a major difficulty for the inverse model and requires a careful selection of weights and auxiliary constraints. The reason is the quasistationary character of IFEOM, and its neglect for the momentum advection. The latter is appropriate at the resolution used everywhere except for the western part of the equatorial belt. To overcome this difficulty the missing momentum advection is treated as an additional control field on the rhs of the momentum equation which is penalized to the mean momentum advection term of the prognostic run in some vicinity of the equator (term J6).

The meridional overturning streamfunction turns to be very sensitive to minor inconsistencies of the inverse solution close to the equator (it easily breaks into northern and southern cells when an appropriate care is not taken) and thus serves as an indicator of the quality of the inverse solution.

Solutions for each pentad were sought for using mean NCEP reanalysis wind averaged for the corresponding period of time. There are nine pentads in the data set by Lozier et al.

[1995] starting from 1950–1954. It was found that before 1960 they appear too patchy, a consequence of poor sampling. For the analysis below we use seven pentads starting from 1960–1964 for the NAO study and the full set (nine pentads) for the comparison with the tide gauges.

Correlation with NAO Instead of exploring changes between separate pentads we study the correlation of the

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modes of variability with the NAO index (obtained from http://www.cru.uea.ac.uk/ cru/data/nao.htm). As the fields used for the analysis we select the transport and overturning streamfunctions. The NAO index has been averaged over the winter months of corresponding periods of pentads lagged (negatively) with respect to the beginning of the pentad by 0 to 7 years. We tested that full pentadal averaging of the NAO index did not change the correlation significantly. The strongest correlation (0.96) takes place between the principal component of the second mode, which explains 26% of variability and the NAO index lagged for 1 year. High correlation (0.79) is also observed between the first mode of transport variability (39% of the explained variance) and the NAO index lagged for 3 years. The first two modes of transport variability are shown in Fig. 2. and the correlation map is presented in Fig. 1 (right).

Qualitatively the pattern of the first mode resembles those presented by Bellucci and Richards [2006] yet it has a larger amplitude, its cyclonic cells are of very small amplitude compared to that of the anticyclonic cell and the anticyclonic cell does not penetrate into the subpolar gyre as one would have expected following the idea of intergyre gyre by Marshall and Goodman [2001]. This difference to the known modeling results lies entirely in the data.

To prove this we computed the main variability mode of the steric height estimated for every pentad with respect to the depth of 2000 m. It shows a very similar pattern of variability as that of the transport streamfunction and its principal component lags the NAO index by three years (NAO leads) too. Similarly, it shows mostly the anticyclonic anomaly the amplitude of which exceeds that of the cyclonic parts. Since our solutions reflect only that part of the variability which is contained in the pentadal climatology, they snow a similar variability pattern as the steric height (wind variability leads to a much smaller response in the transport streamfunction as explained below).

The second mode of transport variability shows a tripolar structure similar to that observed in the study by Eden and Jung [2001]. It has anomalies in subpolar and subtropical gyres and corresponds to the direct (one year lag) response to the NAO index. The higher modes of variability do not show a clear correlation with the NAO index and thus are not discussed here.

The anomaly in the meridional overturning streamfunction shows a wide positive cell instead of a dipolar structure seen in other studies. The MOC variability pattern found in Eden and Willebrand [2001] using canonical correlation analysis shows a dipolar structure

Figure 2: The first mode (39% of the explained variance) of variability in the barotropic transport streamfunction (left) and the second mode (26% of the explained variance, right)

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with the minimum in the north and maximum in the south which change the sign if three year lagged NAO index is used. The pattern characterizing the inverse solutions is very different from that. This is unsurprising, because the five year averaging mixes different patterns of the response. The first mode pattern of inverse solutions shows only very small correlation with the short lag NAO index. The lower correlation and different lag (as compared to the vertically integrated transport anomalies) can be attributed to different ways the wind and temperature/salinity anomalies influence the vertically integrated transport and MOC. Indeed, direct wind influence corresponds to zero lag. Its indirect influence

together with the influence of surface buoyancy forcing is imprinted in temperature and salinity anomalies.

Correcting for model dynamic topography The variability of transport streamfunctions and not the dynamic topography was analyzed above because the satreamfunction field is free of an arbitrary shift from one realization to another. The shift comes from the fact that the model circulation is driven by the spatial gradient of the dynamic topography and the presence of an arbitrary constant in it does not affect the model circulation. In order to correct for the interpentadal shifts we resort to using the tide gauge data. Of the

Figure 3: Correlation/regression between the tide gauge data and the inverse model solutions at the data locations (left) and the trend in the dynamic topography as computed from the inverse solutions. The squares mark the positions of tide gauges. The trend corresponds to the main mode of variability in model dynamic topography

Figure 4: Variability of the tide gauge data (thin line) and the model dynamic topography (thick line) shown at three single locations

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Figure 5: The anomaly of steric height (ASH, thick line) and anomaly of satellite altimetry (ASA, thin line) averaged over the Northern Atlantic. a â&#x20AC;&#x201C; full anomalies; b â&#x20AC;&#x201C; the seasonal cycle of the ASH and ASA; the averaging time is between 1999 and 2005 and between 1993 and 2005 for the ASH and ASA, respectively; c â&#x20AC;&#x201C; The anomalies after removing the seasonal cycle. The thickest curve shows ASH for the experiment with the half of the data excluded. The ASA curve is shifted down by the difference between the mean over last six years and the total mean. Both the seasonal cycle and trend in ASA and ASH agree reasonably well

entire database 36 tide gauge positions located in the North Atlantic are chosen to correct for model outputs of dynamic topography against the same reference level. This data have been averaged over the corresponding periods of pentads and the inverse solutions are corrected so that the pentadal mean of inverse solutions computed at the tide gauge locations matches those.

Further studies of model dynamic topography show that the inverse fields highly correlate with the tide gauge data while the regression shows a noticeable spread for some locations.

This is an expected result since the model variability is affected by the spatial smoothing applied to the pentadal hydrography. As the opposite, the tide gauge data reflect only the local variability. The correlation/regression coefficients between the inverse solutions and data are shown in Fig. 3 (left). The pattern of the first mode of the inverse field variability (60% of the explained variance) resembles the trend shown in Fig. 3 (right). It shows a strong raise (0.04 cm/pentade) in the Gulf Stream region and a more moderate depression of the subpolar gyre (0.015 cm/pentade).

The variability of the tide gauge data and the model dynamic topography is compared in Fig. 4 for three locations. It shows that the correspondence persists for the whole period of analysis.

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Summary We study the sea surface in the North Atlantic Ocean using a combination of pentadal hydrology with the available tide gauge data for the area of the North Atlantic to asses the variability there on interpantadal time scale.

The importance of tide gauge data is that they allow correcting for otherwise unknown shifts in mean dynamic topography between separate pentads.

The first mode of variability seen in the barotropic streamfunction shows largely an anticyclonic anomaly which follows the path of the Gulf Stream and its extension, while cyclonic anomalies are marginally expressed.

The second mode reflects the tripole structure what is consistent with previous work. Both modes are highly correlated with the NAO index (the three year lag correlation is observed for the first mode, while the direct response can be associated with the second mode of variability).

Adding tide gauge information allows for correcting the stationary model solutions. Good correlation between the inverse solutions and the data from tide gauges is observed.

Pure diagnostic studies carried by us as well also show high correspondence between the tide gauge/altimetric data and in situ measurements as exemplified in Fig. 5 showing the result of analysis performed for the North

Atlantic and based on Argo float data. The model used here is a step forward and allows one to compute dynamic topography free from any assumptions on reference pressure and respects the laws of ocean dynamics.

References 1. Bellucci, A., and K. J. Richards, Effects of NAO variability on the North Atlantic Ocean circulation, Geophysical research letters., 33(L02612), doi: 10.1029/2005GL024890, 2006.

2. Conkright, M., et al., World Ocean Database 2001. Vol. 1: Introduction. NOAA Atlas NESDID 42, 159 pp., U.S.Gov. Printing office, Washington, D.C., 2002.

3. Danilov, S., G. Kivman, and J. Schröter, A finite-element ocean model: principles and evaluation, Ocean Modelling, 6, 125–150, 2004.

4. Danilov, S., G. Kivman, and J. Schröter, Evaluation of an eddypermitting finite-element ocean model in the North Atlantic, Ocean Modelling, 10, 35–49, 2005.

5. Eden, C., and T. Jung, North Atlantic Interdecadal Variability: Oceanic Response to the North Atlantic Oscillation (1865–1997), Science, 14, 676–691, 2001.

6. Eden, C., and J.Willebrand, Mechanism of interannual to decadal variability of the North Atlantic circulation, Journal of Climate, 14(10), 2266–2280, 2001.

9. Kalnay, E., et al., The NCEP/NCAR 40-Year Reanalysis Project, Bull. Amer. Meteor. Soc., 77(3), 437–471, 1996.

10. Lozier, M. S., W. B. Owens, and R. G. Curry, The climatology of the North Atlantic, Prog. In Oceanogr., 36, 1–44, 1995.

11. Marshall, J., and H. J. J. Goodman, A study of the interaction of the North Atlantic Oscillation with ocean circulation, Journal of Climate, 14(7), 1399–1421, 2001.

12. Nechaev, D., J. Schröter, and M. Yaremchuk, A diagnostic stabilized finite-element ocean circulation model, Ocean Modelling, 5, 37–63, 2003.

13. Schiller, A., The mean circulation of the Atlantic Ocean north of 30 S determined with the adjoint method applied to an ocean general circulation model, J. Mar. Res., 53, 453–497, 1995.

14. Sidorenko, D., The North Atlantic circulation derived from inverse models, 111 pp., Bremen University, 2004.

15. Sidorenko, D., S. Danilov, G. Kivman, and J. Schröter, On the use of a deep pressure gradient constraint for estimating the steady state ocean circulation from hydrographic data, Geophysical research letters., (L02610), doi: 10.1029/2005GL024716, 2006.

7. Ezer, T., G. L. Mellor, and R. Greatbatch, On the interpentadal variability of the North Atlantic Ocean: Model simulated changes in transport, meridional heat flux and coastal sea level between 1955–1959 and 1970–1974., J. Geophys Res., 100, 10,559–10,566, 1995.

8. Gouretski, V. V., and K. P. Koltermann, WOCE Global Hydrographic Climatology, 52 pp., Bundesamt für Seeschifffart und Hydrographie, Hamburg und Rostock, Germany, 2004.

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Combined assimilation of GEOSAT and TOPEX/poseidon data Wenzel M. and Schröter J. Alfred Wegener Institute for Polar and Marine Research, Bussestrasse 24, 27570 Bremerhaven, Germany

1. Introduction The global sea level is exceedingly reacting on variations of the climate. A warming of the world ocean or the melting of large continental icesheets for example would lead to a sea level rise that would affect directly a large part of mankind. These effects are reasonable well understood on the global scale but they are still uncertain on regional or even local scale.

For the period of the TOPEX/Poseidon altimetric measurements Wenzel and Schröter (2006, 2007) showed that the sea level trends vary substantially in space and time and that they are closely associated to heat and salt anomalies in the ocean. By assimilating the TOPEX/Poseidon measurements into a global ocean circulation model they were able to separate the individual parts contributing to the sea level change (steric effects, oceanic fresh water budget). But longer time-series of the global distribution of sea level variability are needed to confirm these results because the climate-induced decadal and secular sea level changes may be concealed by seasonal, annual and interannual variations, which may act as noise masking long-term trends. One step in this direction is to utilize data from the GEOSAT altimetric mission (1987–1989) in combination with the TOPEX/Poseidon data (1993–2000). Both datasets will be assimilated into the global ocean circulation model. By doing this the data gap between GEOSAT and TOPEX/Poseidon can be filled in a dynamically consistent manner.

2. Model and data For our purpose we use the Hamburg Large Scale Geostrophic model (LSG, Maier-Reimer

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and Mikolajewicz 1991). In conjunction with its adjoint this model has been used successfully for ocean state estimation (e.g. Wenzel and Schröter 2006, 2007). It has 2 × 2 degree horizontal resolution, 23 vertical layers (varying from 20 m thickness for the top layer to 750 m for the deepest ones) and the implicit formulation in time allows for a time step of ten days. The utilized global OGCM has a free surface, i.e. it conserves mass rather than volume, and it has the steric effects (thermal expansion, haline contraction) included. This offers the possibility to combine altimeric measurements with hydrographic data in a dynamically consistent manner. The datasets used in the assimilation experiment are: – monthly sea surface temperatures (SST) for the period 1993–2000 (Reynolds et al. 2002) – gridded fields of ten day averages of sea surface height anomalies (SSHA) as measured by the TOPEX/Poseidon altimetric mission for the period 1993–2000, provided by Geoforschungszentrum Potsdam (GfZ; S. Esselborn, pers. communication). These anomalies are combined with the SHOM98.2 mean sea surface height (MSSH; available online at the time of writing at: http://www.cls.fr/html/oceano/projets/mss/ cls_shom_en.html) referenced to the EIGENGRACE01S geoid (available online at the time of writing at: http://www.gfz-potsdam.de/grace/results/grav/g001_eigengrace01s.html) to give absolute dynamic height values.

– preliminary re-processed gridded fields of ten day averages of sea surface height anomalies (SSHA) as measured by the GEO-

Figure 1: Global mean sea level anomaly (GMSLA) for experiment GETO20 (thick line) as function of time. For comparison the measurements from TOPEX/Poseidon (dotted line) and GEOSAT (dashed) are included. The GEOSAT data are adjusted to the corresponding model mean because of the missing absolute reference.

Additionally the data from Church and White (2006) reconstructed from tide gauge measurements are shown (thin line) with their error bars (grey shading)

SAT altimetric mission for the period 1987– 1989, provided by Geoforschungszentrum Potsdam (GfZ; T. Schöne, pers. communication). These anomalies are referenced to their own temporal mean.

– temporal mean transports of mass, freshwater and heat as obtained by different authors and as they are summarized e.g. by Bryden and Imawaki (2001) and by Wijffels (2001).

Transport constraints are not applied for the Antarctic Circumpolar Current (ACC).

– the climatological mean temperatures and salinities from the WOCE Global Hydrological Climatology (WGHC; Gouretski and Koltermann 2004) in combination with the mean annual cycle from the most recent World Ocean Atlas (WOA01; Conkright et al.

2002). These data are supplied to the assimilation procedure with small weights thus serving only as background information.

– the mean annual cycle of temperatures, salinities and horizontal velocities on two sections in the Weddell Sea area and on four sections in the Ross Sea. These data are taken from high resolution model experiments of the Weddell Sea (Schodlok et al.

2002) and the Ross Sea (Assmann and Timmermann 2005) whose water mass characteristics and circulation are in good agreement with local observations.

3. Results Figure 1 shows the modeled global mean sea level anomaly (GMSLA) after assimilation in comparison to the above mentioned datasets.

While the model (experiment: GETO20) reproduces the GMSLA derived from the TOPEX/Poseidon measurements quite well this is not the case for GEOSAT. Even the trend for the period 1987–1989 is not reproduced. The model prefers a positive trend while the data show a negative one. That the modeled positive trend is more realistic to some extend, one can conclude from the GMSLA reconstructed

by Church and White (2006) from tide gauge records, that shows a positive trend throughout the period 1986–2000. Even the spatial structure of the GEOSAT anomalies are not well reproduced by the assimilation procedure while for TOPEX/Poseidon measurements there

Figure 2: Spatial correlation between the sea level anomalies from the altimetric measurements and the model results without assimilation (dashed lines) and for experiment GETO20

Figure 3: Root mean square error (RMS) between the sea level anomalies from the altimetric measurements and the model results without assimilation (dashed lines) and for experiment GETO20

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is good success as can be seen from Fig. 2 and 3. The reason for this behaviour is not well understood yet.

Furthermore, Fig. 1 shows the disadvantage of not having an absolute reference for the GEOSAT data. From hydrographic data alone the assimilation has no reason for producing a sea level rise as large as given e.g. by Church and White (2006). This can be improved when the information about the evolution of the GMSL is applied accordingly as can be seen from Fig. 4 (experiment: GETO45). In this experiment the Church and White (2006) data are supplied additionally as background information. From this we conclude that an absolute reference is needed for the GEOSAT data before reliable statements are possible for the past 20 years. For future work we will utilize time dependent global sea level reconstructions instead that will be made available

Figure 4: same as Figure 1 but for experiment GETO45

Figure 5: Global mean sea level anomaly (GMSLA) from experiment GETO45 (thick line) broken down to the halosteric (dotted), thermosteric (dashed) and eustatic (dash- dotted) contribution

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Figure 6: Global ocean heat content anomaly from GETO45 for the total water column (thick line) as well as for the depth ranges [0–700 m] (dash-dotted), [700–2750 m] (dotted) and [2750 m-bottom] (dashed).

For comparison the heat content anomalies of the upper 700m from Levitus et al (2005) are included (staircase with dots)

by GFZ Potsdam. The necessity of this additional information can also be gathered from Fig. 5. In this figure the modeled GMSLA is decomposed into the parts that arise from steric effects (thermal expansion, haline contraction) and from the ocean fresh water budget (eustatic contribution). The latter contributes about twice as much (2.52 mm/year) to the total sea level rise (3.71 mm/year) as the thermosteric part (1.13 mm/year), while the halosteric contribution is neglegible on global scale (0.06 mm/year) but should not be neglegted on regional or even local scale (see e.g. Wenzel and Schröter 2006, 2007). The hydrographic data can sufficiently constrain the thermosteric contribution only. Further inspection of this preliminary result shows that the thermosteric contribution to sea level rise mainly stems from the upper 700 m of the water column (Fig. 6). For this depth range we find a global ocean warming, increasing heat content that fits well to the estimates taken from Levitus et al (2005). The contributions from the lower depth ranges (700–2750 m and 2750 m-bottom) are neglegible and they even partially compensate each other.

References Assmann K. M. and Timmermann R. (2005) Variability of dense water formation in the Ross Sea, Ocean Dynamics, 55(2), 68–87, doi: 10.1007/s10236-004-0106-7

Bryden H. L. and Shiro Imawaki (2001) Ocean Heat Transport, in: Ocean Circulation and Climate, Siedler G., J. Church and J. Gould, Ed., Academic Press, International Geophysics Series Vol 77, pp. 455–474 Church, J. A., and N. J. White (2006), A 20th century acceleration in global sea-level rise, Geophys. Res. Lett., 33, L01602, doi: 10.1029/2005GL024826 Conkright M. E. et al.: World Ocean Atlas 2001 (2002) Objective Analysis, Data Statistics and Figures, CD-ROM Documentation, National Oceanographic Data Center, Silver Springs, MD, 17 pp.

wijk, The Netherlands, ISBN 92-9092-925-1, ISSN 1609-042X, CD-ROM Wenzel, M. and Schröter, J. (2007). The global ocean mass budget in 1993–2003 estimated from sea level change, Journal of physical oceanography, 37(2), 203–213., doi: 10.1175/JPO3007.1 Wijffels S. E. (2001) Ocean Transport of Fresh Water, in: Ocean Circulation and Climate, Siedler G., J. Church and J. Gould, Ed., Academic Press, International Geophysics Series Vol. 77, pp. 475–488

Gouretski V. V. and Koltermann K. P. (2004) WOCE Global Hydrographic Climatology, A Technical Report, Berichte des Bundesamtes für Seeschifffahrt und Hydrographie, No. 35, 50 pp. + 2 CD-ROM Maier-Reimer E. and Mikolajewicz U. (1991) The Hamburg Large Scale Geostrophic Ocean General Circulation Model (Cycle 1), Technical Report, 2, Deutsches Klimarechenzentrum, Hamburg Levitus, S., J. Antonov, and T. Boyer (2005), Warming of the world ocean, 1955–2003, Geophys. Res. Lett., 32, L02604, doi: 10.1029/2004GL021592 Reynolds R. W. et al. (2002): An improved in situ and satellite SST analysis for climate, Journal of Climate, 15, 1609–1625 Schodlok M. P. et al. (2002) On the transport, variability, and origin of dense water masses crossing the South Scotia Ridge, Deep Sea Research II, 49, 4807–4825 Wenzel, M. and Schröter, J. (2006) Understanding measured sea level rise by data assimilation, in: »Proceedings of the Symposium on 15 Year of Progress in Radar Altimitry«, SP-614, ESA Publication Division, Noord-

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Consistent VLBI, GPS and SLR Time Series of Station Positions and Troposphere Parameters Böckmann S. (1), Artz T. (1), König R. (2), Müller H. (3), Nothnagel A. (1), Panafidina N. (2), Steigenberger P. (2, 4), Thaller D. (2), Tesmer V. (3) (1) Institut für Geodäsie und Geoinformation Universität Bonn, IGG (2) GeoForschungsZentrum Potsdam, GFZ (3) Deutsches Geodätisches Forschungsinstitut, DGFI (4) Institut für Astronomische und Physikalische Geodäsie, Technische Universität München

1. Introduction A critical issue when comparing and especially combining parameters of different spacegeodetic techniques are systematic differences between the a priori models and the parameterisation of different software packages, as this can lead to a misinterpretation of the combined results. Within the Geotechnologien project »GGOS-D«, a detailed adaption of different software packages has been performed and GPS, SLR and VLBI data have been reprocessed consistently for the complete time span. As a result, consistent time series of station positions from the GPS, SLR and VLBI data as well as time series of troposphere parameters from GPS and VLBI have been calculated. Co-location stations of at least two techniques have been used to compare the different time series in order to detect systematic or episodic signals.

2. Data processing The GPS processing was carried out with the Bernese GPS Software 5.0 (Dach et al. 2007) at GeoForschungsZentrum Potsdam (GFZ), using data from 1994 to 2007. The VLBI sessions between 1984 and 2007 were analysed independently with two different VLBI analysis software packages: At the Deutsches Geodätisches Forschunginstitut (DGFI), München, the OCCAM v6.0 software package (Titov et al. 2004) was used, the Calc/Solve software (Petrov 2002) at the Institut für Geodäsie und Geoinformation (IGG), Universität Bonn. Simi-

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lar to the VLBI analysis, two different SLR software packages EPOS and DOGS were used at GFZ and DGFI to process the SLR observations between 1984 and 2007.

Identical models for solid earth tides, pole tide, ocean loading, nutation and subdaily EOP variations, as well as the same a priori Earth orientation parameters, tropospheric a priori zenith delays and mapping functions have been used in all analysis software packages.

Furthermore, the parameterisation of all common parameters is identical. The GPS and VLBI station positions have been estimated as daily and session-wise solutions, while the SLR station positions have been calculated weekly. In order to define the datum in the GPS and VLBI analysis, no-net-rotation (NNR) and no-nettranslation (NNT) conditions with respect to IGS05 (for GPS, geocenter estimated) and ITRF2005 (for VLBI) were applied. SLR station positions have been computed by applying NNR conditions with respect to ITRF2005.

The tropospheric path delay ΔL is represented as a function of elevation angle ε and azimuth α of the vector between the ground station and the observed GPS satellite or quasar. The azimuth-independent part of the neutral atmosphere around a station is described as a sum of a zenith hydrostatic delay (ZHD) Lh and a zenith wet delay (ZWD) Lw (Eq. 1). For an observation with elevation angle ε both zenith delays are mapped using the Vienna Mapping Functions (VMF1, Boehm et al. 2006). The

azimuth dependency of the tropospheric delay of the observation is considered with coefficients for gradients in north-south (Gn) and east-west direction (Ge), mapped with the gradient mapping function mg(ε) to the elevation of the observation. ΔL(α, ε) = ΔLhhmh(ε) + ΔLwmw(ε) + mg(ε) × [Gn cos (α) + Ge sin (α)]

(1)

While for each GPS and VLBI station, the ZHD is corrected a priori (with interpolated ECMWF grid data), the ZWD is estimated in the leastsquares adjustment. However, the estimated part cannot be completely interpreted as the real wet delay since it is also affected by the miscorrected part of the ZHD. For the gradient mapping function the simple equation by MacMillan (1995) with the wet mapping function has been used (Eq. 2) mg(ε) = mw · cot (ε)

(2)

The troposphere zenith delay parameters are estimated as piece-wise linear functions for each station with a temporal resolution of one hour for VLBI and of only two hours for GPS, as the number of parameters in the GPS processing is much higher. The GPS-derived gradients are estimated for each site once per day as linear function. In the VLBI solutions the

gradients are estimated as linear function for each 24 h-session. A priori values for the gradients are zero.

In contrast to GPS, the VLBI-derived troposphere zenith delay parameters and gradients could not be estimated completely free, due to the poor observing geometry of some VLBI sessions, especially the older ones: the rate of the troposphere zenith delay parameters had to be constrained to zero with a standard deviation of 1cm/hour while the troposphere gradients were constrained to zero with standard deviations of 2.5 mm and 5 mm/day.

To be able to better compare the VLBI- and the GPS-derived troposphere parameters, both were always referred to intervals of full UTC hours, which is not typical for the VLBIonly solutions. The GPS troposphere parameters have been estimated from weekly solutions providing continuous results over a one week period, the VLBI-derived parameters do not provide such continuity, as there are only about 3–4 sessions per week with changing observing networks.

3. Comparison of station position and troposphere parameter time series 3.1. Station position time series Figure 1 shows the temporal evolution of the GPS and VLBI height component of station

Figure 1: GPS and VLBI time series of Tsukuba height component (daily estimates, smoothed with a 70 days median filter computed each 7 days)

Figure 2: GPS and SLR time series of Monument Peak east component (GPS daily estimates, SLR weekly, both smoothed with a 70 days median filter computed every seven days)

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Tsukuba in Japan (with offset and a trend removed from each time series). The GPS and VLBI results follow a very similar pattern with annual variations which may be linked to periodic ground water extraction (Munekane et al.

2004). Figure 2 illustrates the east component of the SLR-GPS co-location station Monument Peak. Although these two examples show a good agreement between series of different techniques, this is not the case for all stations.

3.2. Troposphere parameter time series The comparisons of the estimated zenith wet path delays from GPS and VLBI show a very

good agreement with correlations larger than 0.9.

The GPS and VLBI time series of the ZWD estimates as well as their differences for Hartebeesthoek are displayed in Figure 3.

The differences show an offset of 5 mm with a standard deviation of 1 mm and a weighted RMS of 8 mm after removing the offset. In addition, a seasonal pattern is visible in the differences. In summertime, when the water content of the atmosphere as well as the variability is larger, the ZWD differences show a larger scatter (see Steigenberger et al. 2007).

a)

b) Figure 3: (a) Time series of zenith wet delays for GPS and VLBI, (b) differences of the series (VLBI minus GPS)

Figure 4: Time series of GPS and VLBI north gradients of Ny-Alesund (smoothed with 35 day median filter)

Figure 5: Time series of GPS and VLBI north gradients of Westford (smoothed with 35 day median filter)

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Beside the zenith wet delays, the tropospheric horizontal gradients from GPS and VLBI can also be compared. Figures 4 and 5 illustrate the temporal variations of the north gradient from both techniques for Ny-Ålesund and Westford. While the gradients agree very well for Ny-Ålesund, the time series for Westford have a similar episodic behavior, but are offset by about 0.2 mm.

The reason for this offset might be the constraints on the a priori values (see Sec. 3) for the gradients determined by VLBI as also discussed in (Steigenberger et al. 2007). Another possibility might be due to correlations of the tropospheric horizontal gradients with the horizontal components of the station coordinates (MacMillian 1995, Krügel 2007).

Steigenberger P, Tesmer V, Krügel M, Thaller D, Schmid R, Vey S, Rothacher M (2007) Comparisons of homogeneously reprocessed GPS and VLBI long time series of troposphere zenith delays and gradients. J Geod (2007) 81: 503–514, doi: 10.1007/s00190-006-0124-y Titov O, Tesmer V, Boehm J (2004) Occam v6.0 software for VLBI data analysis. In: Vandenberg NR, Baver KD (eds) International VLBI Service for Geodesy and Astrometry 2004 General Meeting Proceedings.

NASA/CP-2004-212255, NASA, Greenbelt, pp. 267–271

References Boehm J, Werl B, Schuh H (2006) Troposphere mapping functions for GPS and very long baseline interferometry from European centre for medium-range weather forecasts operational analysis data. J Geophys Res 111(B2): B02406.

DOI: 10.1029/2005JB003629 Dach R, Hugentobler, U, Fridez P and Meindl M (eds.) (2007) Bernese GPS Software Version 5.0 Astronomical Institute, University of Bern Munekane H, M Tobita, K Takashima (2004) Groundwater-induced vertical movements observed in Tsukuba, Japan; Geophysical Research Letters, Vol. 31, L12608, doi: 10.1029/2004GL020158 Krügel M, Thaller D, Tesmer V, Schmid R, Rothacher M, Angermann D (2007) Tropospheric parameters: Combination studies based on homogeneous input data. J Geod (2007) 81: 515–527, doi 10.1007/s00190-006-0128-8 MacMillan D (1995) Atmospheric gradients from very long baseline interferometry observations. Geophys Res Lett 22(9):1041–1044 Petrov L (2002) Mark IV VLBI analysis software Calc/Solve. Web document: http://gemini.gsfc.nasa.gov/solve

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Contribution of Altimetry Time Series for a Global Geodetic Observing System Bosch W. DGFI München, E-mail: bosch@dgfi.badw.de

Importance of altimetry Satellite altimetry has demonstrated its high value in Earth system science. It provides precise maps of the mean sea level. Time series of nearly 15 years enable reliable estimates of low frequency and large scale climatic signals (sea level rise). Tides in open ocean, seasonal, as well as intra-seasonal variations have been quantified with high precision. Synergies between missions with different space-time sampling have the additional capability to resolve mesoscale variability (eddies). Finally, high resolution data from a few geodetic phases enable invaluable improvements of bathymetry and gravity anomalies. All this underlines that altimetry has to be an essential component of the Global Geodetic Observing System.

The GGOS-D project focuses on an utmost rigorous integration of all relevant observation techniques. While the combination of techniques for precise point positioning (GNSS, SLR, VLBI) is already exercised in the context of the ITRF solutions, the integration of satellite altimetry has not been considered so far. The question is therefore: how to combine the altimetry observations with other space geodetic techniques? What are the specific contributions of satellite altimetry and where are intersections with the parameter space of other space techniques?

Contribution of Satellite Altimetry Obviously, satellite altimetry cannot contribute to point positioning. However, as the mean sea level is nearly coinciding with an equipotential surface of the Earth gravity field, the

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measurement of sea surface heights allows to derive precise information on the marine gravity field. The algorithms to obtain gravity anomalies from satellite altimeter data are well established and high resolution data (with grid spacing of up to 2′ × 2′) from Sandwell & Smith or Anderson & Knudsen are available since long time. The high resolution gravity field determination is however not a primary goal of the GGOS-D project. GGOS-D focuses on the consistent combination of all geodetic space techniques and considers temporal variations in particular for the low degree harmonic coefficients of the Earth gravity field.

Consistency and Standards Consistency requires to verify if the processing of altimeter data is performed with the standards that were agreed on in the context of the GGOS-D project. In most cases standards can be easily applied (e.g. the use of a specific reference ellipsoid or a common ocean tide model). However, there are also inconsistencies which are difficult to avoid. The treatment of permanent tides is realized differently in point positioning and satellite altimetry. While altimetry does not correct for the permanent deformation of the solid Earth (which corresponds to a »zero-tide system« and is in agreement with the IAG resolution of 1983) the point positioning techniques apply such corrections and provide coordinates for an »unobservable« tide-free system.

Impact of ocean water mass redistribution Temporal variations of the low degree harmonics of the Earth gravity field can be

derived from water mass redistribution. Satellite altimetry observes the geometric variations of the mean sea level composed by two effects, water mass redistribution and volume change. In order to identify changes in the water mass the steric effect, e.g. the expansion/contraction of water due to changes in salinity and temperature are to be estimated and subtracted from the observed sea level anomalies. For these computations following approach was applied: 1. Sea level anomalies (the deviation of the instantaneous sea level from a mean sea level) were performed for every 10-day cycles of TOPEX, the most stable altimeter mission with an observation period of 10 years. The significant seasonal variations of the sea level anomalies is well known from previous investigations.

2. Steric anomalies, e.g. the water level deviation from a standard ocean due to density variations in the upper layer were first taken from the OMCT model. The available model run lacks however on a significant change of the driving forces in the year 2000.

Therefore new computations were based on monthly dynamic heights derived by Ishii for the period 1950â&#x20AC;&#x201C;2005 through

integration of objectively analysed Temperature/Salinity profiles down to 700 m depth (see Figure 1). These steric anomaly time series was interpolated to the 10 day cycles of TOPEX. 3. Mass anomalies have been estimated by subtracting the steric anomalies from the sea level anomalies. These mass anomalies were finally transformed to surface mass loads which were developed to a series of spherical harmonics coefficients describing up to degree and order two the effect of water mass redistribution on the Earth gravity field (see Figure 2) The time series are to be compared with results achieved by data from gravity field missions, by satellite laser ranging to the LAGEOS satellites, by solutions of low Earth orbiting (LEO) satellites or the C04 time series of the International Earth Rotation Service (IERS). However, the comparison must consider that the ocean mass redistribution is not the only source for the variations of the harmonic coefficients. There are comparable density variations in other components of the Earth system, e.g. in the atmosphere, in the cryosphere or the continental hydrology.

Figure 1: Steric anomalies for December 2005, an example of the data provided

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Figure 2: Time series of selected harmonic coefficients (scaled by the radius of the Earth R), derived from ocean water mass anomalies for the period 1993â&#x20AC;&#x201C;2005. Left: all degree one coefficients (C10, C11, S11) related to variations in the centre-of-origin. Right: some of the degree two coefficients, related to the variations in flattening (C20 on top) and to the orientation of the rotation axis (C21, S21). All coefficients show more or less clear the expected seasonal variations.

The outstanding variation of S11 (the y-shift of the centre-of-origin) is related to the strong December 1997El-Nino event

A reprocessing of the altimeter time series will include the mass variations in other system components. The altimeter time series can also be extended by using the additional observation of the Jason-1 altimeter mission.

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Combination of Ground Observations and LEO Data König D., König R., Panafidina N. GeoForschungsZentrum Potsdam, Telegrafenberg, 14473 Potsdam

Introduction The idea of the Integrated approach is to determine the orbits of GPS satellites and Low Earth Orbiters (LEOs) as well as Earth system parameters in a common orbit determination and parameter estimation process (see Zhu et al., 2004). Thus all available space geodetic observations are combined on the observation level considering all correlations. Thereby the high-orbiting GPS satellites provide stability to the whole configuration whereas the LEOs scan the Earth’s gravity field very densely with a high temporal resolution. Furthermore, the feasibility of simultaneously estimating the Earth’s geometry – represented by a ground stations polyhedron – and the Earth’s center of gravity is investigated.

There are already proofs of the integrated method delivering more accurate results than a corresponding two-step procedure where the orbit determination for the GPS satellites and for the LEOs is done in two subsequent steps. The time span investigated has been extended to almost the full year 2004, as well the constellation of satellites involved has been enlarged step by step leading to a configuration of GPS ground stations, GPS satellites, and the LEOs CHAMP, GRACE-A, GRACE-B. Constellations Processed In this context, the constellation of the orbit determination and parameter estimation processes is mainly characterised by the observational data used, the satellites involved, and the constraints imposed on certain estimated parameters.

The data used comprise GPS/ground measurements (from the IGS and GFZ GPS networks), GPS/SST measurements (from the on board Precise Orbit Determination receivers), Satellite Laser Ranging normal points (SLR, from the ILRS network), K-band range-rate measurements (from the GRACE-A/-B intersatellite link), measured accelerations (from the LEO on board accelerometers), and measured attitude (from the LEO on board star sensors).

The constellations assembled and processed all include the ground station network. Concerning the satellites the constellations so far included a GPS/CHAMP configuration (in integrated mode), a GPS/CHAMP configuration (in two-step mode), a GPS/GRACE configuration (in integrated mode with and without K-Band), a GPS/CHAMP/GRACE configuration (in integrated mode with and without K-Band).

The processing is nominally subdivided into periods of 24 h length (processing periods). In case of K-band data gaps the processing periods can be less than 24 h.

The parameters estimated comprise the positions of the ground stations, the harmonic coefficients of the Earth’s gravity field up to degree and order two, the residuals of the observations, and auxiliary parameters for adjusting the force model acting on the satellites and those for correcting the observations.

Outside the proper orbit determination and parameter estimation process for each processing period a 7-parameter Helmert transformation has been carried out between the estimated and the a priori station positions

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yielding a 3D translation, a global scale, and three rotation angles.

In order to keep the solution near to the a priori values that are assumed to be good there are imposed constraints on the ground stations’ positions and on the harmonic coefficients in form of pseudo-observations with a priori sigmas of equivalently 10 cm on the Earth’s surface.

Improvements by the Integrated Method Comparing a GPS/CHAMP configuration in a two-step mode and in an integrated mode reveals better results for the integrated mode. This is clearly indicated by a smaller RMS of the GPS/SST phase residuals that decreases from 0.95 cm to 0.51 cm as well as by a reduced bias (from –3.7 cm to 2.6 cm) and a reduced standard deviation (from 6.2 cm to 1.0 cm) of the z-translation of Helmert transformations.

Between a GPS/CHAMP and a GPS/GRACE configuration, both in integrated mode, the GPS/GRACE case leads in general to reduced scatter in the time series as the twin GRACE satellites – even without using K-band data – act as »two times CHAMP« with double the amount of GPS/SST data.

Going from a GPS/GRACE configuration to GPS/CHAMP/GRACE, both using K-Band data,

Figure 2: C20 time series for different integrated configurations, and for the SLR-only GFZ Lageos solution

several improvements appear. As shown by Fig. 1 the standard deviation in the z-translation of Helmert transformations decreases significantly from 6.81 cm to 0.74 cm. Also the standard deviation of the scale of Helmert transformations is lessened from 1.44 ppb to 1.01 ppb. Concerning the C10 harmonic coefficient (i.e. the z-component of the geocenter) the standard deviation is reduced from 7.45 cm to 1.46 cm, see Fig. 1. The rather strange shift in C20 between the GPS/GRACE configuration and the SLR-only GFZ Lageos solution (see König et al., 2006, and König et al., 2007) is reduced, as can be seen in the middle time series shown in Fig. 2. Moreover, comparing a GPS/CHAMP/GRACE configuration with and without K-band the offset in C20 is further reduced from about –4.841650E-04 to –4.841655E-04, as shown in the lower graph of Fig. 2.

Level of Accuracy Reached Recently, tests have been made changing the original scheme of weighting GPS ground and SST data. For the weighting scheme yielding best results the level of accuracy is presented in the following.

Figure 1: Z-translation of Helmert transformations (»Geometric Z«) and C10 harmonic coefficient (»Dynamic Z«) for a GPS/GRACE and a GPS/GRACE/CHAMP configuration

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A suitable measure for assessing the accuracy of satellite orbits is the RMS of residuals of laser observations that have been used with a very low weight. Also the RMS of GPS phase residuals indicates the internal accura-

cy of the determined orbit configuration. The global RMS of laser residuals ranges for the LEOs between 3.5 cm and 4.1 cm, and for the GPS satellites PRN 5 and PRN 6 it is 7.7 cm and 8.0 cm, respectively. The global RMS of GPS phase residuals for ground stations comes out at 0.56 cm, and for the LEOs at around 0.4 cm.

The accuracy of the estimated geometric frame can be characterised by the standard deviations of the time series of its translational components, of its scale, and of its rotation angles. The standard deviations of the translational x- and y-component are 1.24 cm and 1.46 cm, respectively, whereas the time series of the z-translation is rather stable with a standard deviation of 0.74 cm. The scale is rather stable, too, at a standard deviation of 1.01 ppb. The time series of the rotational angles turn out to be 0.68 cm, 0.71 cm, and 0.16 cm for the rotations about the x-, y-, and z-axis, respectively. Thus, the orientation of the estimated geometric frame is very stable, especially around the z-axis.

The dynamic frame is represented by the dynamic origin, the so-called geocenter, and the dynamic scale. The dynamic scale is given by the C00 harmonic coefficient, whereas the dynamic origin is given in x-, y-, and z-direction through the C11 , S11 , C10 harmonic coefficients, respectively. The time series of C00 does not yet show reasonable behaviour probably due to very high correlation with radial accelerometer biases. Nevertheless, it acts as an indicator of outliers, and it can be fixed by subsequent calculations on normal equation basis. The geocenter turns out to be rather stable with standard deviations of about 1 cm in all three components. First tests indicate that imposing global constraints on the ground stations positions in form of no-net translation, no-net rotation, and no-net scale conditions delivers geocenter time series showing a certain structure that is probably suited for geophysical interpretation.

Conclusions and Future Activities As shown there are significant improvements detectable by changing an orbit determination and parameter estimation process from a twostep mode to an integrated mode. Even within the integrated method it helps significantly to enlarge the number of LEOs incorporated.

These results are clearly confirmed by reduced standard deviations in the geometric and dynamic z-components. Concerning the C20 harmonic coefficient there is a shift introduced with respect to the GFZ Lageos solution that is obviously a K-band effect. In this case as well it is very helpful to incorporate another LEO in form of CHAMP reducing this shift.

In order to impose not more constraint on the parameter adjustment as necessary it seems to be worthwile to replace the constraints currently applied individually to a broad set of parameters by global constraints that exactly remove the datum defect. Thus, unnecessary constraint would be avoided that might distort the estimated parameters.

Literature König, R., Reigber, C., Zhu, S. (2005) Dynamic model orbits and Earth system parameters from combined GPS and LEO data. Advances in Space Research 36, doi: 10.1016/j/asr/2005.03.064, pp. 431–437.

König, R., Müller, H. (2006) Station Coordinates, Earth Rotation Parameters, and Low Degree Harmonics from SLR within GGOSD-D. Proceedings 15th International Laser Ranging Workshop, 15–20 October 2006, Canberra, Australia.

König, R., König, D., Neumayer K.H. (2007) Station Coordinates and Low Degree Harmonics with Daily Resolution from GPS/CHAMP Integrated and with Weekly Resolution from LAGEOS. Proceedings IAG Symposium Geod.

Ref. Frames 2006.

Zhu, S., Reigber, C., König, R. (2004) Integrated Adjustment of CHAMP, GRACE and GPS Data. Journal of Geodesy, Vol. 78, No. 1–2, pp. 103–108.

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GGOS-D Reference Frame Computations Krügel M. (1), Angermann D. (1), Drewes H. (1), Gerstl M. (1), Meisel B. (1), Tesmer V. (1), Thaller D. (2) (1) Deutsches Geodätisches Forschungsinstitut (DGFI), Alfons-Goppel-Straße 11, 80539 München (2) GeoForschungsZentrum Potsdam (GFZ), Telegrafenberg A17, 14473 Potsdam

1. Introduction Reference frames of high accuracy are the basis for the analysis and interpretation of geodetic parameters and their temporal behavior. Modern reference frames are generated by combining the data of the space geodetic techniques VLBI, SLR and GPS. The consistency in time of the analysis strategies for each data series but also between the techniques is essential to obtain a reference frame of highest accuracy. The International Terrestrial Refer-

ence Frame (ITRF2005) is not based on such homogeneous data sets. Thus, the computation of a reference frame within the GGOS-D project is fundamental for the analysis of the results. The adaptation of the software packages is an extensive part of this project. Examples are given in Nothnagel et al. (2007).

2. Global terrestrial reference frame (TRF) The computation strategy for the terrestrial reference frame is displayed in Fig. 1. In a first

Figure 1: Scheme of the terrestrial reference frame computation

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part of the processing daily or weekly normal equations are combined to a multi-year solution separately for each technique. The most important task in this step is the adequate modelling of the temporal behavior of the station coordinates (Meisel et al., 2007).

In the second part the technique normal equations are combined to a terrestrial reference frame. Here, the selection of terrestrial difference vectors (local ties) in view of accuracy and consistency of the combined solution is the most complex problem, which has to be solved. A detailed description of the strategy is given in Angermann et al. (2007). a) Modelling of station positions An important part in the computation of a terrestrial reference frame is to identify and consider discontinuities in the station coordinate behaviour. We started with a discontinuity table provided by each technique, the same as was done in the ITRF2005 computation at DGFI (ITRF2005D, see Meisel et al., 2007). In the ITRF2005 computations a large number of discontinuities had to be introduced, which were apparent in the station position time

series but could not be correlated with an instrumental or geophysical cause. This is especially the case for GPS, where 221 discontinuities are applied for 332 stations in the ITRF2005D solution. With the consistent data sets of GGOS-D this could be reduced to 124 discontinuities in 240 stations.

A further important task is to introduce discontinuities in a similar way for different techniques, especially stations with earthquakes such as Arequipa or Fairbanks. The problem is, that not only the jump caused by the event but also the post-seismic nonlinear movement of the station has to be modelled. Especially Fairbanks is critical to VLBI, as it was one of the stations used the most and thus important for UT1 determination.

ITRF2005 was computed using the traditional parameterization of station positions at a reference epoch and constant velocities. It is clear that the station positions show variations that cannot be accounted for by a linear model. So the question arises, how we can extend the existing model. One possibility is to estimate sine/cosine functions with a period of one year in addition to the linear velocities. To investi-

Figure 2: Mean annual signals of the two GPS stations Brasilia (left) and Ankara (right)

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gate this we compute a mean annual signal of the GPS time series for each station.

The results show for most stations a small signal (few millimetres amplitude) in the north and east component that has the shape of a sine/cosine function. The variation in the height component is somehow larger (few millimetres up to 1â&#x20AC;&#x201C;2 centimeters). The majority of stations show a characteristic seasonal signal that is somehow asymetric (see example Brasilia in Fig. 2). But there are also stations that show either two maxima/minima in one year or a flat curve for half of the year and a maxima in the other half (see station Ankara in Fig. 2). b) Selection of terrestrial difference vectors for the combination of the different space techniques For the combination of the station networks of different space geodetic techniques, terrestial difference vectors between the reference points of the different instruments at co-location sites are necessary. As for some of the colocations the difference vectors do not fit well to the estimates of the space geodetic solutions, a selection of difference vectors is essential to obtain a TRF of high accuracy. Fig. 3 shows the discrepancies for some of the GPSVLBI co-locations. Additionally, the corresponding discrepancies derived from the ITRF2005 computations at DGFI are displayed.

Especially for the co-locations at the southern hemisphere the discrepancies are smaller than in the ITRF2005D, except for station Hobart

(HOB2). For some of the co-locations in Europe the discrepancies become a bit larger, compared to ITRF2005D. The reason for the differences are changes in the modelling of the space geodetic techniques. The most important ones are the switch from relative to absolute phase center corrections for GPS antennae (Steigenberger et al., 2007) and the change of the pole tide model in the VLBI data (BĂśckmann et al., 2007). Both lead to changes in station coordinates of up to 1 cm.

To select useful terrestrial difference vectors two criteria are defined, which have to be fulfilled by the set of difference vectors: 1) the consistency of the combined solution must be maximal and 2) the deformation of the network due to the combination should be minimal.

To investigate the consistency, the station networks of the techniques are combined but not the EOP. The mean difference between the pole coordinates is an expression of the consistency and must be minimized. The deformation can be quantified by the mean residuals resulting from a similarity transformation between the combined and the one technique only solutions.

To identify the best set of co-location sites, different solutions are computed, varying the colocations and the assumed accuracy of the introduced difference vectors. Five sets of difference vectors are selected, which fit the estimates of the space geodetic techniques within 8, 10, 12, 14 and 18 mm, respectively. The a priori formal errors of the vectors is varied

Figure 3: Differences [mm] between terrestrial difference vectors and the coordinate differences derived from GPS and VLBI solutions at co-location sites. Green: GGOS-D data. Grey: ITRF2005D. The sites are named by the 4-character ID of the GPS station. Stations of the southern hemisphere are marked by an orange background

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Figure 4: Mean pole coordinate differences and mean residuals of station coordinates resulting from the similarity transformation between the combined and the VLBI-only solution for different solution types

Figure 5: Time series of x-pole coordinates wrt. IERS C04 derived from GPS (red) and VLBI (blue) for the years 2002 to 2005. The station networks of both techniques are combined

from 0.1 to 2 mm. Fig. 4 shows the results of this analysis. The solution obtained introducing a set of difference vectors, that fit to the space techniques within 12 mm with an accuracy of 2 mm gives a small pole difference and the smallest deformation of the station network.

Thus, this solution type is used for the computation of the reference frame.

The GPS and VLBI time series of the x-pole derived from this solution are displayed in Fig. 5. They show an excellent agreement.

3. Celestial reference frame (CRF) The common computation of the terrestrial and the celestial reference frame in one adjustment guarantees consistency between

the two frames as well as the corresponding Earth rotation parameters. As only the VLBI technique provides an access to the CRF, a common adjustent of both frames was performed using VLBI data. A minimum datum was applied to the station coordinates (no-netrotation and no-net-translation condition) as well as to the quasar coordinates (no-net-rotation-condition) to obtain undeformed reference frames.

Such a solution reveals correlations between coordinates of single stations and sources, which are due to an insufficient redundancy in the observation geometry (mainly for stations or sources in the south). Most of such stations did not observe in sufficiently varying net-

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works, weak sources often were only observed by one or two baselines. A combination of the VLBI station network with other space geodetic techniques, especially GPS, will stabilize the weakly determined VLBI stations and thus the southern radio sources. Even more stability can be achieved, if the troposphere parameters of GPS and VLBI are also combined (Krügel et al., 2007).

References Angermann D., H. Drewes, M. Gerstl, M. Krügel, B. Meisel. DGFI combination methodology for ITRF2005 computation. submitted to proceedings of IAG workshop Geodetic Reference Frames, 2007.

Böckmann S., T. Artz, A. Nothnagel, V. Tesmer.

Comparison and combination of consistent VLBI solutions. Proc. of the 18th European VLBI for Geodesy and Astrometry (EVGA) Working Meeting, 12–13 April 2007 in Vienna, 2007.

Krügel M., D. Thaller, V. Tesmer, M. Rothacher, D. Angermann, R. Schmid. Tropospheric parameters: combination studies based on homogeneous VLBI and GPS data. Journal of Geodesy, Vol. 81, No. 6–8, pp 515–527.

Meisel B., D. Angermann, M. Krügel. Influence of time variable effects in station positions on the terrestrial reference frame. submitted to proceedings of IAG workshop Geodetic Reference Frames, 2007.

Nothnagel A., T. Artz, S. Böckmann, P. Steigenberger, D. Thaller, V. Tesmer, R. König, H. Müller. Consistent VLBI, GPS and SLR Time Series of Station Positions and Troposphere Parameters. Extendet Abstract for the 2nd Statusseminar »Erfassung des Systems Erde aus dem Weltraum II«, this issue.

Steigenberger P., M. Rothacher, R. Schmid, A. Rülke, M. Fritsche, R. Dietrich, V. Tesmer.

Effects of different antenna phase center models on GPS-derived reference frames. submitted to proceedings of IAG workshop Geodetic Reference Frames, 2007.

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Tesmer, V., H. Kutterer, H. Drewes: Simultaneous estimation of a TRF, the EOP and a CRF. In: Vandenberg, N., K. Baver (Eds.): IVS 2004 General Meeting Proceedings. NASA/CP-2004212255, 311–314, 2004

Integration of Space Geodetic Techniques as the Basis for a Global Geodetic-Geophysical Observing System (GGOS-D): An Overview Rothacher M. (1), Drewes H. (2), Nothnagel A. (3), Richter B. (4) (1) GeoForschungsZentrum Potsdam, Potsdam (2) Deutsches Geodätisches Forschungsinstitut, München (3) Institut für Geodäsie und Geoinformation der Rheinischen Friedrich-Wilhelms-Universität Bonn, Bonn (4) Bundesamt für Kartographie und Geodäsie, Frankfurt/Main

1. Introduction In view of the alarming global change in the Earth system and the multitude of natural hazards with huge effects on humans and economy it is of greatest importance to develop a better understanding of the processes that describe and excite these continuous as well as abrupt changes. To achieve this, the structure of all elements of the Earth system (primarily the geosphere, the oceans, the hydrosphere and the atmosphere) have to be measured and monitored exactly, and the interactions between them have to be modeled correctly, i.e. a comprehensive global Earth observing system has to be built up.

The expected outcome of such a system are consistent geodetic-geophysical time series that refer to a highly accurate reference frame that is stable over decades. Based on the knowledge of the past (resulting from having high-precision long-term series available), conclusions may be drawn for the future development of the Earth system. On the international level, the Global Geodetic Observing System (GGOS), now a full component of the International Association of Geodesy (IAG), is the geodetic contribution to a comprehensive global observing system as it is presently setup by the Group on Earth Observation (GEO) in the form of the Global Earth Observing System of Systems (GEOSS).

On the national level, the project GGOS-D can be considered an important German con-

tribution to GGOS (and to GEOSS in the broader sense).

The integration and combination of the various space geodetic techniques is one of the major goals and challenges of GGOS and of the project GGOS-D. This integration is important not only for the realization of a highly accurate and long-term stable reference frame as the basis of all Earth observation, but also for the generation of homogeneous, highquality time series of geodetic/geophysical parameters describing the processes in the Earth system.

Because of the very close cooperation between the partner institutions, that are working together within the GGOS-D project, we have the chance to go far beyond the level of consistency and homogeneity that can be reached at present on an international level.

The major improvements of GGOS-D compared to the international status of today are: – Implementation of common standards for modelling and parameterization in all software packages involved.

– Extension of the parameter space to link for the first time geometry, Earth rotation, sea surface heights and gravity field from SLR, VLBI, GPS, altimetry and Low Earth Orbiters (LEOs). Additional parameters (not yet considered in solutions of the official services) are quasar coordinates, nutation offsets

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and rates, tropospheric zenith path delays and gradients and low-degree coefficients of the Earth gravity field.

– Higher resolution in time, as, besides weekly, also daily solutions are generated and Earth rotation parameter (ERPs) with sub-daily time resolution.

– Usage of the SINEX (Solution INdependent EXchange) format for the exchange of all time series of parameters and solutions.

– The definition of a meta data standard for the SINEX format to allow the exchange of meta data.

The experiences of the GGOS-D project will help considerably to establish new guidelines for GGOS also on the international level.

The time series of global solutions produced based on these improvements are the basis for the generation of a very precise and stable reference frame and long-term, consistent and homogeneous time series of geodetic/geophysical quantities that can be used to monitor, model and, finally, predict the processes in the Earth system.

2. Common Standards and Parameterization The consistency among the various solutions from the different techniques used within the GGOS-D project is of crucial importance.

Because the solutions are not only compared but rigorously combined, the definition of common standards and a unique representation and parameterization of the relevant quantities is absolutely necessary to be able to interpret the combined solutions. As seven different software packages are used to generate the solutions of the different techniques contributing to GGOS-D, all these packages had to be modified to follow the same common standards. A first set of standards was implemented during the first phase of the project (Steigenberger et al. 2006). These standards were then reviewed based on the experience gathered with the initial set and a second, more demanding and complete set was agreed upon by the partners and subsequently implemented into the seven different soft-

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ware packages used within this project. The most important standards are listed in Table 1.

Not just the standards for the modelling of geodetic and geophysical effects had to be homogenized but also the parameterization of the solutions. The following was achieved: – Site coordinates: a common, very detailed list of site coordinate discontinuities for all techniques was composed. These discontinuities are mainly due to equipment changes at the stations and earthquakes.

– Earth rotation parameters (polar motion and UT1): common parameterization as piecewise linear, continuous functions and with a time resolution as high as 1 hour.

– Nutation offsets and rates were set up for VLBI and GPS. – Quasar coordinates estimated by VLBI were included into the SINEX files.

– Low-degree harmonics of the gravity field up to degree/order 2 were setup for the SLR and integrated GPS/Low Earth Orbiter solutions to allow for the connection of gravity field, geometry and Earth rotation.

– Troposphere zenith delays and gradients: a common parameterization as piece-wise linear, continuous functions was realized with exactly the same binning starting at the full hours.

The implementation of all these features and options was quite a challenge and took a considerable amount of time of the project. But this effort had to be made, as it is crucial for all the combination efforts and results.

3. Generation of Fully Reprocessed Time Series (SINEX Files) Based on these parameterizations and the common standards mentioned above (second realization), the data of the various space geodetic techniques involved in this project have been completely reprocessed once again. Table 2 gives an overview of the present status of the reprocessing effort.

From Table 1 we see that most of the time series have been completed applying the sec-

Table 1: Common standards for the 2nd iteration of GGOS-D. Changes with respect to the first iteration are given in bold

Station coordinates/Sea surface heights Solid Earth tides Permanent tide Ocean Tides Pole tides

IERS Conventions 2003 Not considered for coordinates FES2004, Letellier (2004) Linear trend for mean pole offsets: IERS Conventions 2003 FES2004 including the CoMcorrection for the motion of the Earth due to the ocean tides1 Not applied

Ocean Loading Atmospheric Loading

Earth Orientation Parameters Daily values of the C04 05 series2 (x-pole, y-pole, UT1) linear interpolation between daily values of x-pole and y-pole 1) reduction of UT1 to UT1R 2) linear interpolation between daily values of UT1R 3) conversion of UT1R to UT1 IERS2003 IAU2000A (without free core nutation), Mathews et al.

(2002)

A priori information Interpolation polar motion Interpolation UT1 Subdaily ERP Model Nutation

Lower harmonics of the Earthâ&#x20AC;&#x2122;s gravity field EIGEN-GL04S13 including temporal variations of C20, C30, C40

A priori model

Troposphere modeling radio techniques Hydrostatic delay Mapping function for hydr. delay Wet delay Gradients

Computed from 6-hourly ECMWF grids4 Hydrostatic VMF1 (Boehm et al., 2006) No a priori model, wet delay estimated (see Table 1) Zero a priori values

Troposphere modeling SLR Troposphere model

Mendes and Pavlis (2004) Technique-specific effects GPS

Phase center model Radome calibrations Antenna height Hor. antenna offsets 2nd and 3rd order iono. corr.

igs05 1421.atx5, Schmid et al. (2007) igs05 1421.atx igs.snx6 + IGSMAIL/IGSSTATION7 Applied Applied according to Fritsche et al. (2005) Technique-specific effects SLR

CoM corrections (reflector offsets) ILRS conform8 Range bias For selected stations, ILRS conform Arc length 7 days Technique-specific effects VLBI Thermal deformations

Gravitational sag 1 2 3 4 5 6 7 8

Applied, IVS conform (Nothnagel et al., 1995; Skurikhina, 2001), mean value of the temperature recordings during the VLBI sessions used as station-specific reference temperature Not applied

http://www.oso.chalmers.se/~loading/ http://hpiers.obspm.fr/iers/eop/eopc04_05/eopc04.62-now http://www.gfz-potsdam.de/pb1/op/grace/results/ http://mars.hg.tuwien.ac.at/~ecmwf1/GRID/ ftp://igscb.jpl.nasa.gov/igscb/station/general/ ftp://igscb.jpl.nasa.gov/igscb/station/general/ http://igscb.jpl.nasa.gov/mail/mailindex.html http://ilrs.gsfc.nasa.gov/satellite_missions/center_of_mass/index.html

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Table 2: Generation of consistent time series (SINEX-Files)

Technique

Work package

Institution

Software

Period

SLR SLR

WP3200 WP3200

DGFI GFZ

DOGS EPOS

11/1992–05/2007 10/1992–01/2007

VLBI VLBI

WP3300 WP3300

DGFI GIUB/BKG

OCCAM CALC/SOLVE

01/1984–12/2006 01/1984–12/2005

GPS GPS

WP3400 WP3400

GFZ GFZ

EPOS Bernese V5.0

Several months 01/1994–03/2007

LEOs

WP3500

GFZ

EPOS

01/2004–12/2004

Altimetry

WP3600

DGFI

DGFI-Software

01/1993–12/2005

ond iteration of the standards and parameterization. The second GPS solution (EPOS) is not yet finished, because of the huge effort it requires. We expect it to be fully available in the first quarter of 2008. To the extent possible, the SLR time series will be prolonged further into the past (i.e. back to 1984) and the LEO integrated solutions will be extended to cover at least a few years.

Special solutions were also produced for VLBI and GPS with a 1-hour (instead of a 1-day) resolution for the Earth rotation parameters.

These are very interesting solutions to study the subdaily variations of Earth rotation, mainly caused by the ocean tides and, to a smaller part, by the atmosphere.

4. Comparison and Combination Studies Many interesting comparisons and combination studies were already performed with the first version of SINEX files from the individual techniques. But with the second version available, not only the consistency was once more improved but also the number of common parameter types was significantly extended (adding troposphere zenith delays and gradients to both VLBI solutions, quasar coordinates, and low-degree harmonics coefficients).

The following list contains some of the studies performed so far (as examples for the wide variety of studies possible with the data material now available): – Comparisons of station coordinate time series between GPS, VLBI and SLR: Many

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–

–

–

–

interesting differences were found between the techniques, but also fascinating signals common to all techniques.

Detailed comparison studies of the time series of troposphere zenith delays and gradients from VLBI and GPS: These studies showed once again the importance of having more than one technique available to assess the quality and possible systematic biases in the solutions. Antenna changes or changes in the elevation cut-off angle for the processing may cause considerable biases in the troposphere parameter series and have to be carefully identified and corrected.

Combination of time series from VLBI and GPS including the tropospheric zenith delays and gradients as common parameters: These combination tests gave interesting insights into how to combine the troposphere parameters (»local troposphere ties«), if the instruments are located at different altitudes and how systematic effects from GPS antenna phase center pattern show up in the troposphere zenith delays. It became also clear that »troposphere ties« can be used to validate, to a certain extent, the quality of the terrestrial geometrical local ties.

Comparsions of subdaily Earth rotation parameters from VLBI and GPS and the estimation of ocean tidal terms from the long homogeneous time series. Also the combination of subdaily ERPs has been done.

Initial solutions for a global combined reference frame realizations have been genera-

ted. They already indicate a considerable improvement compared to the last international realization ITRF2005. The strategy of how to apply local tie information has to be further refined, as it is crucial for the accuracy and consistency between the individual technique frames.

– Based on the solutions including low-degree spherical harmonics, the relationships and correlations between parameter types have been studied (degree-1 terms of the gravity field and geocenter coordinates, degree-2 terms and Earth rotation, GM and scale).

More details on the results achieved within the GGOS-D project are given in specific papers contained in this volume.

5. Next Steps Whereas the main focus of the first two years was on the generation of the consistent and homogeneous time series and on the implementation of the necessary software options and algorithms, the last year will be used to: – Finalize the consistent realization of a terrestrial and celestial referenced frame (TRF and CRF) based on the GGOS-D time series as a high-quality product for the international community.

– Interpretation of the various time series computed by using the high-precision reference frames mentioned in the previous item and the comparison with global geophysical fluid information and external results.

– Assess the benefit from a combination of the three pillars of geodesy: the geometry, the Earth rotation and the gravity field (lowdegree coefficients).

6. Conclusions and Outlook Compared to the international efforts to develop consistent and rigorously combined products for the Global Geodetic Observing System (GGOS), the GGOS-D project has already made enormous progress. Not only the implementation of common standards and parameterizations, but also the variety of parameters included into the combination work has reached a status far beyond that of the international IAG Services and the many analysis centers (ACs). Whereas »only« seven software packages had to be adapted within the GGOS-D project, around 30 packages will have to be considered on the international level, a huge effort of coordination still to be achieved. The GGOS-D project, which we may consider to be a very small copy of the international services (IGS, IVS, ILRS, IDS, IERS), is an extremely valuable project for the international community to see the benefits of a rigorous combination of the space geodetic techniques on the one hand and the problems, hurdles and intricatenesses to be overcome on the other hand. GGOS-D may be considered a major step forward toward the realization of a consistent, highly accurate set of time series for all major geodetic-geophysical parameters and, thus, a crucial contribution to GGOS. Especially, it is to be expected that the consistency of the GGOS-D solutions will allow for a realization of the terrestrial and celestial reference frames with an accuracy and consistency well beyond that of the present realizations (i.e., the ITRF2005 and the ICRF). The reference frames, however, are the critical basis for all other geodetic-geophysical results and their interpretation and, thus, for the understanding of the processes in the Earth system.

The project is proceeding according to the time schedule. Many new interesting insights may be expected for the final year of the project, where the focus can be put much more on the interpretation of the outcome.

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Time Series From Inter-technique Combinations Thaller D. (1), Krügel M. (2), Meisel B. (2), Panafidina N. (1), Steigenberger P. (1, now 3) (1) GeoForschungsZentrum Potsdam (GFZ) (2) Deutsches Geodätisches Forschungsinstitut (DGFI), München (3) Institut für Astronomische und Physikalische Geodäsie (IAPG), TU München

1) Strategy for Combination In order to combine normal equation systems, common parameters have to be identified first.

Once the parameters are found, a strategy how they can be combined has to be developed. In principle, the methods used for the combination can be subdivided into two groups: – The parameters are identical. Therefore, they can directly be stacked.

– The corresponding parameters are not identical but their relationship is known, so that a condition forcing the difference between the related parameters to a known value can be applied.

Concerning the parameters considered within the project GGOS-D, the first method mentioned above is applied to the Earth orientation parameters (EOP), the horizontal troposphere gradients and the gravity field coefficients. In the contrary, the station coordinates derived from different space-geodetic techniques normally do not refer to the same reference point, so that additional information has to be used if the individual contributions should be combined. A similar situation exists for the troposphere zenith delays (ZD),

although only the height difference is of interest for combining the ZD. Undoubtedly, the so-called local ties play a key role within the inter-technique combination as they do not only connect the station coordinates but they have a significant influence on the other parameters as well. The method of identifying good local ties for a multi-year combined TRF solution is described in Krügel et al.

(2007). But when generating time series of parameters based on daily or weekly solutions, the selection of good local ties is not of minor importance than for the multi-year solution.

In the following we will concentrate on the combination of GPS and VLBI as the singletechnique SLR solution still has to be investigated in more details. Altogether 1377 daily combined solutions were generated for the time span 1994 until 2006, i.e. the VLBI sessions have been combined with that daily GPS normal equation that covers the major part of the session. The datum definition was done by applying no-net-rotation and no-net-translation conditions based on a sub-set of GPS core sites, and appending the VLBI network by the geometrical local ties. The number of available

Figure 1: Number of official GPS-VLBI local tie values available for each daily combined solution

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Figure 2: Reference epochs of the EOP for the VLBI sessions (i.e., the mean epoch of the session)

local ties differs from day to day (see Fig. 1): The daily combined solutions rely on one to 15 local ties, with 5.75 local ties as a mean value, and for the major part of the daily solutions three to eight local ties are available. It is clear that appending the VLBI network to the GPS network by only one or two local ties does not give enough datum information to the VLBI part of the combined solution as VLBI has three translational and three rotational degrees of freedom. Therefore, either additional parameters have to be combined (e.g. the pole coordinates) or those parameters relying solely on the VLBI contribution must not be interpreted.

Another topic that has to be considered in advance of including the VLBI sessions into an inter-technique combination is the reference epoch for the EOP. As EOP are epoch-specific parameters, they must refer to the same epoch if they are to be stacked. This requirement causes no problem for GPS and SLR because the observations are continuously available and the intervals for the 24-hour resolution can easily be set from midnight to midnight. In the contrary, as VLBI observations are not continuously available and the 24-hour sessions are not scheduled from midnight to midnight, the reference epochs for the EOP do not coincide with those from GPS and SLR. Figure 2 gives an overview of the reference epochs for all VLBI sessions used within GGOS-D. Thus, the EOP contributed by VLBI has to be transformed to epochs common with GPS and SLR, although this procedure weakens the VLBI contribution, of course.

In the following, the focus will be on the EOP. The TRF-related issues are treated in KrĂźgel et al.

(2007), and the combination of the troposphere parameters is only in a test phase up to now.

2) Time Series of Earth Orientation Parameters Three types of solutions were studied: singletechnique solutions, a combined solution of GPS and VLBI where only the station coordinates were combined, and a solution where station coordinates and polar motion have been combined. The intention of this threestep procedure is to evaluate whether the solution gains stability due to the combination of each parameter type. For an external comparison, the IERS-C04 series will be used. a) Polar Motion The weighted RMS (WRMS) of the differences w.r.t. IERS-C04 after removing a bias and a linear trend are listed in Table 1 for several solution types. In view of validating whether the time series benefit from a combination, the comparisons for the single-technique solutions are listed as well. It can be seen from these comparisons, that the GPS and VLBI solutions as well as their combination agree with the IERS-C04 series at the same level of about 90 to 110 Âľas. The residuals of the combined pole coordinates w.r.t. the IERS-C04 series are shown in Fig. 3.

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Figure 3: Comparison of the combined pole coordinates with the IERS-C04 series (grey). The black line represents the weighted mean values every week sampled over +/– 35 days

b) Universal Time The parameter UT1-UTC can be determined solely by VLBI. If daily combined solutions are considered, the estimates of UT1-UTC strongly depend on the number of local ties applied.

Therefore, multi-year instead of daily solutions will be considered in the following. Comparing the three solution types with the IERS-C04 series, the WRMS of the residuals are 5.5 µs, 5.8 µs and 6.4 µs for the VLBI-only solution, the solution with combined TRF and the solution with combined TRF and polar motion, respectively. Thus, it seems that the contribution of a stable reference frame and polar motion by combining VLBI with GPS cannot deliver more stability to the UT1-UTC time series, although it must be kept in mind, that taking the IERS-C04 series as a reference has

some deficiencies as well. However, an external validation with geophysical data (AAM, OAM) still has to be done. c) Nutation Similar to UT1-UTC, the two nutation angles can be determined only by VLBI in an absolute sense, whereas the satellite-techniques GPS and SLR can contribute solely the time-derivative, i.e., the nutation rates. Therefore, we first look at the time series derived from VLBI-only multi-year solutions for the time span 1984 to 2006. Three different types of solutions were computed: For the first solution, the temporal resolution of the nutation angles was not changed, i.e., one set of nutation angles has been estimated for each session. The resulting time series is shown in Fig. 5. For the second

Table 1: WRMS of the residual pole coordinates from a comparison of different multi-year solutions with the IERS-C04 series. A bias and a linear trend have been removed

µas] WRMS x-pole [µ

µas] WRMS x-pole [µ

VLBI-only

109.0

100.7

GPS-only

99.5

99.5

SLR-only

207.9

214.1

TRF combined, VLBI pole

117.7

106.4

TRF combined, GPS pole

95.9

94.0

Combined pole

93.4

91.9

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and third solution, the session-specific parameters have been transformed into a piecewise linear polygon with an interval length of 14 days (not shown) and 28 days (see Fig. 5).

As the major difference between the estimated nutation angles and the a priori model IAU2000 is the so-called free core nutation (FCN) with a period of about 432 days, the representation with such long intervals is justified in order to reduce the scatter in the time series, as it is visible from Fig. 5. It can be seen

from this figure as well, that the amplitude of the FCN is not constant. Therefore, a sinus fit with sliding time windows has been performed for estimating the time-dependent amplitude of the FCN. The time windows are separated by seven days, each with a length of 865 days. As it is known from theory that the FCN is a retrograde signal, the sinus fit was done for both nutation angles together, so that the phase shift of 90째 is automatically guaranteed. The estimated amplitudes are

Figure 4: Comparing the UT1-UTC estimates of the multi-year solution of GPS and VLBI with combined station coordinates and polar motion with the IERS-C04 series

Figure 5: Nutation in obliquity and longitude estimated from VLBI-only multi-year solutions with two different temporal resolutions. The estimates are corrections to the IAU2000 model

Figure 6: Amplitude of the FCN estimated by a two-dimensional sinus fit to the multi-year VLBI-only solutions using sliding time windows

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shown in Fig. 6 for all three types of solutions.

Except of the fact that the 14-day polygon is very weak during the first years, the two polygon time series deliver results for the amplitude with less scatter than the solution with a session-wise parameterization. The estimated amplitudes of the FCN are around 0.12 mas, except of the time span 1997 until 2002. During these years, the amplitude rapidly decreased and increased again, with zero value around the middle of 1999. This result agrees well with earlier analysis, e.g. by Herring et al. (2002) who states that there is an indication that the amplitude of the FCN is increasing again after 2000.

The solutions with combined station coordinates or combined coordinates and polar motion deliver time series for the nutation angles that are similar to that of a VLBI-only solution, therefore, the results are not shown here. The inclusion of the GPS-derived nutation rates into the time series has not yet been performed.

References Krügel M., Angermann D., Drewes H., Gerstl M., Meisel B., Tesmer V., Thaller D. (2007): Combined GGOS-D Reference Frame Computations. Extended Abstracts for the 2nd Statusseminar »Erfassung des Systems Erde aus dem Weltraum II«, this issue.

Herring T.A., Mathews P.M., Buffett B.A. (2002): Modeling of nutation-precession: Very long baseline interferometry results. Journal of Geophysical Reseach, Vol. 107(B4), doi: 10.1029/2001JB000165.

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Terrestrial Data Sets for the Validation of GOCE Products Denker H. (1), Voigt C. (1), Müller J. (1), Ihde J. (2), Lux N. (2), Wilmes H. (2) (1) Institut für Erdmessung, Leibniz Universität Hannover, Schneiderberg 50, D-30167 Hannover, Germany; E-mail: denker@ife.uni-hannover.de; Fax: ++49 511 762-4006 (2) Bundesamt für Kartographie und Geodäsie, Richard-Strauss-Allee 11, D-60598 Frankfurt am Main, Germany; E-mail johannes.ihde@bkg.bund.de; Fax: ++49 69 6333-235

1. Abstract and Introduction The gravity mission GOCE aims at providing the global geoid and gravity anomalies with an accuracy of about 0.01 m and 1 mgal (1 mgal = 10–5 ms–2) respectively, both at a spatial resolution of 100 km (ESA, 1999). For this purpose, a three-axis gravity gradiometer and high-low satellite-to-satellite-tracking from GPS satellites are combined to derive the gravity field information. In this respect, many error sources affect the final GOCE products, and thus the calibration (procedure to achieve »correct« observations) and validation (procedure to assess the quality of end products) are essential tools for reaching the mission goals (Bouman and Koop, 2003). Calibration and validation (cal/val) includes on-ground and inorbit techniques with internal and external (independent) data.

Within the GOCE-GRAND II project, internal and external cal/val procedures are investigated. Internal cal/val studies include the use of cross-overs for accuracy and integrity monitoring (WP310; e.g, Jarecki and Müller, 2007) as well as the utilization of the integrals of motion (WP340, Löcher and Ilk, 2007). External cal/val procedures are developed using terrestrial gravity field data (WP220, WP320) and ocean data (WP330).

Further investigations involve upward continued regional gravity field data for the external calibration and validation of the GOCE gravity gradient observations (WP310; e.g., Wolf, 2007).

In this contribution, the emphasis is put on the development of accurate terrestrial gravity field data sets for the external validation of the GOCE products, which is one of the main issues within WP220 of the GOCE-GRAND II project. Gravity, GPS and levelling, astrogeodetic deflections of the vertical, and quasigeoid models are utilized as external terrestrial data sets. At last, the filtering of the terrestrial data is addressed, aiming at the removal of short wavelength gravity field signals outside the measurement bandwidth of GOCE. 2. Gravity Data High quality and high resolution regional gravity data sets are important independent data sources for the validation of the GOCE products. Furthermore, the combination of the terrestrial data with the GOCE global gravity field models will allow the determination of the complete gravity field spectrum (all wavelengths) with high accuracy (about 0.01 m for geoid and 1 mgal for gravity). In this connection, a thorough check of the existing gravity data sources with respect to systematic errors (e.g., errors due the used gravity reference stations, network structure or gravimeter calibrations) and random errors is mandatory.

Within WP220 of the GOCE-GRAND II project, Germany is used as a test area for validation and combination experiments. About 250,000 gravity observations with a spacing of 2 to 5 km are available for Germany at the Bundesamt für Kartographie und Geo-

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Figure 1: Terrestrial gravity data (thin dots) and GPS and levelling control points (thick dots) for Germany

däsie (BKG), Frankfurt am Main, and the Institut für Erdmessung (IfE), Leibniz Universität Hannover (see Fig. 1). In Germany, an absolute gravity network (DSGN94) exists, which includes 30 station groups observed with FG-5 absolute gravity meters. This network was densified with relative gravimeters by the state survey agencies, yielding the first order network DHSN96 with stations about 30 km apart. Then the 2nd and 3rd order relative networks of the federal states were adjusted to the DHSN96 network. In addition to the gravity stations down to the 3rd order networks of the federal states, a significant number of other, partly older, gravity values exist, for which in many cases clear information about the gravity and position reference systems is missing.

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In order to check the quality of the terrestrial gravity data base for Germany, spot-checks at 100 evenly distributed stations are performed

by BKG with an A-10 absolute gravity meter.

The selected stations are about 60–80 km apart and cover entire Germany. All stations belong to the DHSN96 1st order gravity network and are mostly field stations. Hence, an absolute gravity meter of type A-10 had to be employed, as it is the only instrument which can work under field conditions (the more accurate FG-5 instruments work only under laboratory conditions). The A-10 accuracy is specified by the manufacturer as 10 µGal for an observation time of about one hour.

In order to check the accuracy of the A-10 instrument, comparisons are done with FG-5

Figure 2: Gravity control points in Germany observed with absolute gravity meter A-10 (triangles) and astrogeodetic profiles (thick lines)

results at the reference station in Bad Homburg before and after each particular field campaign. Up to now, more than 20 comparisons exist, confirming the accuracy specification of the manufacturer. Regarding the gravity control sites, 90 stations have been completed. On each site, two instrument set-ups in opposite directions are used. The differences between both set-ups show a mean value of 6 µGal (1 µGal = 10–8 ms–2) and a standard deviation of 7.5 µGal. Furthermore, the entire observation procedure was examined and optimized with respect to the number of measured drops and sets as well as a proper wind shielding and power supply.

Supplementary to the A-10 observations, the vertical gravity gradients are measured using a Scintrex CG-5 relative gravity meter and a specially constructed tripod. The gradients are needed in order to reduce the observed absolute gravity values (sensor height about 0.7 m) to the corresponding bench marks. The necessary height transfer from the absolute sites to the DHSN96 bench marks is done by spirit levelling.

All absolute gravity control points observed with the A-10 instrument are depicted in Fig. 2. The differences between the A-10 and DHSN96 gravity values show a mean of 6 µGal

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and a standard deviation of 8 µGal (Fig. 3).

Only in the southern part of Germany, south of about 48° latitude, slightly larger and systematic differences of about 20–40 µGal are found, with the A10 values being lower than the DHSN96 values. This subject is under further investigation at the moment. Futhermore, the A-10 results are also compared with gravity values from sources not originating from the state survey agencies, e.g., the socalled »Deutsches Schwerearchiv«.

A corresponding gravity data base was set up for entire Europe within the framework of the

»European Gravity and Geoid Project (EGGP)«, a project within commission 2 of the International Association of Geodesy (IAG) (for details see Denker et al., 2007). The present data base that was used for the computation of the gravimetric quasigeoid model EGG07 consists of 5,354,653 gravity observations from 709 sources. In addition, 195,840 gravity values from the Arctic Gravity Project (ArcGP; Forsberg and Kenyon, 2004) as well as 951,251 altimetric anomalies from the KMS2002 data set (Andersen et al., 2005) were utilized. The entire data set is very valuable with regard to the validation of the GOCE products, because

Figure 3: Differences of the A10 and DHSN96 gravity values

Figure 4: Comparison of the north-south astrogeodetic profile with GPS/levelling as well as the quasigeoid models GCG05 and EGG07 (both based on gravity and other data)Figure 4: Comparison of the north-south astrogeodetic profile with GPS/levelling as well as the quasigeoid models GCG05 and EGG07 (both based on gravity and other data)

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Figure 5: 5′ × 5′ mean gravity anomalies for Europe (left) and corresponding anomalies after Gaussian filtering with a radius of 50 km (right)

it covers large parts of Europe with high quality gravity data (see Fig. 5).

3. GPS and Levelling Data A data set with approximately 900 GPS and levelling control points (with a spacing of 25 to 30 km) was collected by BKG (see Fig. 1).

The GPS coordinates are based on the readjusted SAPOS reference station coordinates, which were introduced at the beginning of 2004. However, the federal states of Germany used individual procedures to implement the new SAPOS reference frame, ranging from reobservation and re-adjustment to different transformation procedures, which may introduce some inhomogeneities in the GPS coordinates. The gravity field related heights are normal heights referring to the official DHHN92 system. Hence, quasigeoid heights can be computed directly. For further details cf. Liebsch et al. (2006).

The GPS and levelling data are essential in two respects. Firstly, they are important for the direct validation of GOCE and other global gravity field models, and secondly they can be used for the cross-validation of astrogeodetic and gravimetric geoid and quasigeoid models. Moreover, the GPS and levelling data can also be combined with the afore-mentioned data sets.

4. Gravimetric Quasigeoid Models High resolution geoid and quasigeoid models are commonly computed using corresponding terrestrial gravity data (with a spacing of a few km), a global geopotential model and a detailed digital terrain model (with block sizes down to 30 m). A typical example is the latest European quasigeoid model EGG07. The evaluation of this model by GPS and levelling data indicates an accuracy potential in the order of 0.03–0.05 m at continental scales and 0.01–0.02 m over shorter distances up to a few 100 km, provided that high quality and resolution input data are available. This is a very significant improvement compared to the last published (quasi)geoid model EGG97, the key elements being improved terrestrial and satellite gravity field data from the CHAMP and GRACE missions (Denker et al., 2007).

Furthermore, GPS and levelling data can also be included as input data in the geoid and quasigeoid modelling. This was done in Germany, where the GPS and levelling data described in the previous section, was used for the computation of the model GCG05 (Liebsch et al., 2006). This model was developed as a joint effort of BKG and IfE. Two different methods were applied, and the final result was simply obtained by averaging of the two individ-

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ual solutions due to insignificant differences. In Germany, the GCG05 model now serves as a standard for the conversion between GPS ellipsoidal heights and normal heights. The evaluation of the model with independent GPS and levelling points suggests an accuracy of about 1 to 2 cm (Liebsch et al., 2006).

As high resolution geoid and quasigeoid models are relying on a global geopotential model (so far based on CHAMP and GRACE), comparisons with GPS and levelling data can also be regarded as a validation tool for the corresponding global models. Moreover, as for the gravity data, direct comparisons with the GOCE products are possible.

5. Astrogeodetic Deflections of the Vertical In recent years, a digital transportable zenith camera system (TZK2-D) was developed at IfE, allowing an economic and precise determination of the direction of the plumb line. Then, in combination with ellipsoidal coordinates observed by a GPS receiver, the deflections of the vertical can be derived with an accuracy of approximately 0.1« (cf. Hirt and Flury, 2007).

With regard to the validation of the GOCE products, the astrogeodetic observations can be considered as another completely independent data set, which also allows a cross-validation with GPS and levelling data as well as gravimetric geoid and quasigeoid models.

Within the framework of the GOCE-GRAND II project (WP220), the IfE zenith camera system, one of two systems existing in Europe, was employed for the determination of vertical deflections along a north-south and an eastwest profile in Germany (see Fig. 2). Both profiles have a spacing of about 2.5 to 5 km between adjacent stations, where the station separation is reduced in areas with rapid gravity field changes. The north-south profile has a length of 540 km and consists of 137 stations, extending from the Harz Mountains in the north to the Bavarian Alps in the south.

The east-west profile has a length of 518 km and 133 stations, extending from Lusatia in

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the east to the Münsterland region in the west. In the east-west profile, a few stations are not yet completed. In order to allow a cross-validation with the available GPS and levelling data, each of the two profiles traverses through approximately 20 nearby GPS and levelling control points. Due to the high degree of automation, up to 12 vertical deflection stations could be observed in a single night. On 23 stations, dual observations were carried out; the mean difference was less than 0.03« and the standard deviation was about 0.1« (cf.

Voigt et al., 2007).

The method of astronomic levelling was used to compute quasigeoid height differences. In this context, the normal correction was computed and a digital terrain model was utilized for the interpolation of the deflections of the vertical. The accuracy estimate for the quasigeoid height difference over the entire profile length is 0.022 m, implying random noise with a magnitude of 0.1« for the vertical deflection data. The results of the comparison of the north-south astrogeodetic quasigeoid profile with GPS/levelling data and the gravimetric quasigeoid models GCG05 (Liebsch et al., 2005) and EGG07 (Denker et al., 2007) are shown in Fig. 4. Regarding the differences between the astrogeodetic profile and GPS/ levelling, two station groups can be distinguished, namely points no. 1–4 and 5–20.

When looking only at the Bavarian GPS/levelling stations (no. 5–20), a small long wavelength difference exists, while the differences in the northern section (no. 1–4) appear to be quite random. Between the northern and the Bavarian section, a jump of almost 0.06 m shows up, which is exactly at the border between the two federal states Thuringia and Bavaria. For clarification, the vertical deflection stations were densified in this traverse section, but this did not lead to a significant change of the results. Preliminary investigations seem to indicate that the problem may be partly related to the GPS/levelling control points (see previous section). However, on the other hand, the pure gravimetric quasigeoid EGG07 seems to follow quite nicely the GPS/levelling control

points; only at station no. 4 a larger difference exists, and in addition a long wavelength difference signal is present, as could be expected. Furthermore, the GCG05 models follows closely the GPS and levelling control points, which is expected because the latter control points are used as input data for GCG05. Further investigations are necessary to straighten out the inconsistencies between the different data sets.

6. Data Filtering Regarding the validation of the GOCE gravity field models by the above mentioned high resolution terrestrial data sets, it is advantageous to filter out from the terrestrial data all highfrequency signals, which are outside the measurement bandwidth of GOCE. For this purpose, standard filter techniques and the spectral combination approach can be used, and additional information from ultra-high degree geopotential models (e.g., EGM200x) and terrestrial gravity and terrain data can be utilized.

As a typical example, Fig. 5 shows the unfiltered gravity anomalies for Europe as well as a corresponding low-pass filtered data set, derived by applying a Gaussian filter with a radius of 50 km. Other gravity field parameters can be filtered correspondingly.

within the federal states of Germany, but also the levelling may contribute to this. With regard to the renewal of the German 1st order levelling network until 2011 and the parallel GNSS campaign 2008, considerable improvements are expected.

References Andersen, O.B., P. Knudsen, R. Trimmer (2005). Improved high resolution altimetric gravity field mapping (KMS2002 Global Marine Gravity Field). IAG Symposia 128, 326–331, Springer Verlag.

Bouman, J., R. Koop (2003). Geodetic methods for calibration of GRACE and GOCE. Space Science Reviews 108, 293–303.

Denker, H., J.-P. Barriot, R. Barzaghi, D. Fairhead, R. Forsberg, J. Ihde, A. Kenyeres, U. Marti, M. Sarrailh, I.N. Tziavos (2007). The development of the European gravimetric geoid model EGG07. IUGG General Assembly, Perugia, Italy, July 2–13, 2007, IAG Symposia, Springer Verlag, submitted for publication.

ESA (1999). Gravity field and steady-state ocean circulation mission. Reports for Mission Selection, The Four Candidate Earth Explorer Core Missions, ESA SP-1233(1).

7. Conclusions Within the framework of WP220 of the GOCEGRAND II project, valuable regional terrestrial gravity field information was collected, including gravity, GPS/levelling, astrogeodetic and quasigeoid data. Spot-checks with the A-10 absolute gravimeter have proved a high quality of the existing terrestrial gravity data base for Germany (about 250,000 points); the detected gravity differences are insignificant regarding geoid and quasigeoid computations with an envisaged accuracy level of about 0.01 m.

Hirt, C., J. Flury (2007). Astronomical-topographic levelling using high-precision astrogeodetic vertical deflections and digital terrain model data. Journal of Geodesy, Online First, doi: 10.1007/s00190-007-0173-x.

The existing GPS/levelling quasigeoid heights are not at the 1 cm accuracy level. Reasons for this are the inhomogeneities of the threedimensional coordinates, especially the ellipsoidal heights, resulting from different measurement epochs and processing schemes

Jarecki, F., J. Müller (2007). GOCE gradiometer validation in satellite track cross-overs. Proceed. 1st Internat. Symp. of the Internat. Gravity Field Service, »Gravity Field of the Earth«, Harita Dergisi, Special Issue 18, 223–228, Ankara, Turkey.

Forsberg, R., S. Kenyon (2004). Gravity and geoid in the Arctic Region – The northern GOCE polar gap filled. Proceed. 2nd Internat.

GOCE Workshop, Esrin, March 8–10, 2004, CD-ROM Proceed.

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Liebsch G., U. Schirmer, J. Ihde, H. Denker, J. Müller (2006). Quasigeoidbestimmung für Deutschland. DVW-Schriftenreihe, No. 49, 127–146.

Löcher, A., K.-H. Ilk (2007). A validation procedure for satellite orbits and force function models based on a new balance equation approach. Internat. Assoc. of Geodesy Symp., Vol. 130, 280–287, Springer Verlag.

Voigt, C., H. Denker, C. Hirt (2007). Regional astrogeodetic validation of GPS/levelling data and quasigeoid models. IUGG General Assembly, Perugia, Italy, July 2–13, 2007, IAG Symposia, Springer Verlag, submitted for publication.

Wolf, K.I. (2007). Kombination globaler Potentialmodelle mit terrestrischen Schweredaten für die Berechnung der zweiten Ableitungen des Gravitationspotentials in Satellitenbahnhöhe (Diss.). Wiss. Arb. Fachr. Geodäsie u.

Geoinformatik der Leibniz Universität Hannover, ISSN 0174-1454, Nr. 264.

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Status and Goals of the GOCE Mission and the GOCE-GRAND II Project Rummel R., Gruber T. Institut für Astronomische und Physikalische Geodäsie, Technische Universität München

Abstract & Introduction GOCE is the first core mission selected for the ESA Earth science satellite programme »Living Planet«. The objective of this programme is to provide data from space necessary for an improved understanding of the interactions of atmosphere, oceans, ice and solid Earth.

GOCE will be launched in spring 2008. It aims at the determination of the stationary part of the Earth’s gravity field and geoid with maximum spatial resolution and accuracy (1–2 cm geoid height accuracy with spatial resolution of approximately 100 km). The mission is complementary to GRACE, which is primarily designed to measure the temporal variations of gravity and geoid.

The first phase of the GOCE-GRAND project (2002–2004) was dedicated to the development of a gravity analysis system for GOCE data. It included kinematic orbit computation, the determination of the long wavelength gravity field from these orbits and from common mode accelerometry based on the so-called energy conservation method, several gradiometric gravity analysis methods and development of algorithms for data reduction (temporal effects) and for external calibration and internal validation. GOCE-GRAND II is refining and extending the developed algorithms aiming at the adaptation of these algorithms to the final characteristics of the sensor system as it will be brought into orbit. This implies that all design changes are taken into account, that realistic stochastic models are developed for all sensor components and that the analysis algorithms are capable to cope with a large number of measurements and unknown parameters. In addition GOCE-GRAND II will address questions

concerning the combined GRACE/GOCE data analysis and validation of the GOCE results by means of methods such as GPS-levelling and ocean dynamic topography. In short, GOCE GRAND II yields an important segment of GOCE gravity field analysis, of GOCE data combination and of in-depth and independent validation of GOCE gravity products.

GOCE Mission To reach the science goals, precondition is that GOCE can determine gravity and geoid with a precision of 10–6 · g (corresponding to 1 mgal) and 1–2 cm, respectively, both with a spatial resolution of better than 100 km half wavelength and that these results are achieved free of long wavelength systematic errors. The mission performance depends on the gravity sensor system on-board GOCE. Core instrument is a three axis gravity gradiometer. It consists of three pairs of orthogonally mounted 3-axis accelerometers. The gradiometer baseline of each axis is about 50 cm. The accelerometer precision is 10–12 m/s2 per square-root of Hz along two axes and a third axis with less sensitivity. From the measured gravitational acceleration differences the three main diagonal terms of the gravitational tensor can be determined with high precision. The extremely high gradiometric performance of the instrument is confined to the so-called measurement bandwidth (MBW). In addition, the gradiometer yields the angular acceleration about the outof-plane axis of the gradiometer. It is required for angular control and for the removal of the angular effects from the gradiometer data.

The gradiometric angular rates (in the MBW) in combination with the angular rates as

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derived from the star sensor readings are used for angular control of the spacecraft. The satellite has to be guided well controlled and smoothly around the Earth in one full revolution per orbit revolution. Angular control is attained via magnetic torquers, which leaves part of each orbit revolution uncontrolled. In order to prevent non-gravitational forces acting on the spacecraft to »sneak« into the measured differential accelerations as secondary effect, the satellite is kept »drag-free« in along-track direction by means of a pair of ion thrusters. The necessary control signal is derived from the available »common-mode« accelerations (= mean accelerations) along the three orthogonal axes of the accelerometer pairs of the gradiometer. The gradiometric and angular contribution to the common mode acceleration, which is a result of the imperfect symmetry of the gradiometer relative to the spacecraft centre of mass, has to be modelled.

The second gravity sensor device is a newly developed European GPS receiver. From its measurements the orbit trajectory is computed to within a few centimetres, either purely geometrically, a so-called kinematic orbit, or by the method of reduced dynamic orbit determination. As the spacecraft is kept in an almost drag-free mode (at least in along-track direction

within an extended measurement bandwidth) the orbit motion is purely gravitational. It complements the gradiometric gravity field determination by covering the long wavelength part.

The orbit altitude is extremely low, only about 250 km. This is essential for a high gravitational sensitivity. No scientific satellite has been flown at such low altitude. Its altitude has to be maintained through orbit manoeuvres, which are carried out at regular intervals.

Again, this very low altitude results in high demands concerning drag-free and attitude control. Finally, any time varying gravity signal of the spacecraft itself must be excluded. This results in very high requirements on metrical stiffness and thermal control.

In summary, GOCE is a technologically very complex and innovative mission. The gravitational field sensor system consists of a gravitational gradiometer and GPS receiver as core instruments. Orientation in inertial space is derived from star sensors. Common mode and differential mode accelerations from the gradiometer and orbit positions from GPS are used together with ion thrusters for drag-free control and with magneto-torquers for angular control. The system elements are summarized in the following table.

Sensor

Measurements

3-axis gravity gradiometer

Gravity gradients Γxx, Γyy, Γzz in instrument system and in MBW (measurement bandwidth) Angular accelerations (high accurate around y-axis, less accurate around x, z axes) Common mode accelerations

Star sensors

High rate and high precision inertial orientation

GPS receiver

Orbit trajectory with cm-precision

Drag control with 2 ion thrusters

Common mode accelerations from gradiometer and GPS orbit

Angular control with magnetic torquer

Based on angular rates from star sensors and gradiometer

Orbit altitude maintenance

Based on GPS orbit

Internal calibration (and quadratic factors removal) of gradiometer

With cold gas thrusters (random pulses)

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GOCE-GRAND II Project Overview GOCE GRAND-II aims at (1) an accurate high resolution gravity modelling from a combined analysis of gravity gradiometry measurements and high-low GOCE to GPS tracking taking into account the actual GOCE sensor configuration, orbit characteristics and mission profile, (2) a combination of GOCE with on the one hand CHAMP and GRACE data and on the other hand regional terrestrial data with the objective to attain best possible global and regionally refined gravity and geoid products and (3) a comprehensive external calibration, quality assessment and validation based on independent data.

This is to be achieved before the background of the novelty of the sensor system and spacecraft characteristics as well as the expected high quality of the GOCE gravity and geoid products. The project leads to fully operational processing modules that will be applied to actual GOCE mission data. GOCE GRAND II will be based on the algorithms and findings of GOCE GRAND I.

The project is organized along three main blocks in accordance with the three basic objectives given above. Each block consists of several work packages (compare with the figure below showing the work packages and the partners involved). There is a logical flow of results from block one to block two to block three. Combined gravity modelling requires an exchange of data and know-how with the GRACE project. In turn GRACE and CHAMP will benefit from validation experiments carried out in GOCE GRAND II. In more details the three major blocks address the following research topics: Block 1: GOCE Gravity Field Processing The major challenges of GOCE gravity analysis are as follows: â&#x20AC;&#x201C; Adequate exploitation of the high resolution gravity sensor system requires a very large and complex system of equations to be solved. â&#x20AC;&#x201C; The gravity gradiometer on-board of GOCE has a limited measurement bandwidth.

Thus, at long wavelengths the gravity gradiometer data has to be complemented by high-low GPS to GOCE tracking. This, in turn requires very precise orbit determination,

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high quality gravity reconstruction from these orbits and an optimal mechanism of data combination of satellite-to-satellite tracking with gradiometry.

– The GOCE sensor system had to be modified. The originally planned FEEP’s had to be replaced by angular control by magneto-torquing. This has severe implications on the measurement model, on the gravity field recovery procedure and on the stochastic model of the gradiometer components.

– It is expected that global gravity representation e.g. in terms of a spherical harmonic series does not fully exploit the information content in certain regions with high gravity variations. Regional adaptive methods will lead to local focussing in these areas.

– GOCE will have a sun-synchronous orbit. As a result the polar caps with an opening circle of 6.5° will not be covered with data.

Adequate analysis strategies and complementary polar gravity data are needed to cope with this problem.

The resulting work packages of the GOCEGRAND II project (as shown in the figure above) are studies in a close cooperation by the project partners IAPG (Technical University Munich), ITG (University Bonn) and GIS (University Stuttgart).

Block 2: Combined Gravity Modelling The GOCE and GRACE global gravity field models and terrestrial data sets complement each other in various ways. GOCE models will contribute to the highly accurate medium and short wavelength gravity field components up to degree and order 200 in terms of spherical harmonics, while GRACE is able to provide the long wavelength part and the temporal variations of Earth’s potential. Global and regional terrestrial data sets add shorter wavelength field structures (above degree and order 200).

Hence, global and local combination solutions of GOCE, GRACE and terrestrial data have the potential to provide the complete geoid spectrum covering all wavelengths with a total accuracy of about 1 cm. Within GOCE-GRAND II global as well as a local combinations are

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investigated by the project partners GFZ, BKG and IFE (University Hannover).

For global solutions, several terrestrial and altimetric data sets are collected and unified in one homogenous data base. These data will be combined on the basis of rigorous normal equations, with all available GOCE and GRACE data, in particular GOCE-SGG data, using the classical direct combination method, and block diagonal techniques for the short wavelength part. The resulting high resolution gravity field model, complete up to degree and order 360, will be the basis for local refinements.

Within a regional validation and combination experiment in Germany, terrestrial gravity and terrain data, GPS/levelling data and deflections of the vertical are employed. Before combination, the terrestrial gravity data are validated by spot-checks with absolute gravity data at selected points. In addition, a transportable zenith camera is used for the observation of deflections of the vertical along two profiles, one North-South and one East-West with a length of several hundred kilometres each. This allows a cross validation of GPS/levelling and astronomic results. The validated terrestrial data sets then are combined with GOCE geopotential models using various modelling techniques.

Block 3: Calibration and Validation A first quality assessment of GOCE gradiometer measurements can be performed at satellite level by comparing the observed gravity gradients with reference gradients. These reference values are computed from existing geopotential models and from terrestrial gravity data by upward continuation or obtained from satellite measurements itself. For the latter purpose, a near real-time validation by cross-over (XO) analysis is investigated and applied operationally. In addition, regional gravity data are upward continued to gradients at GOCE altitude, serving as reference gradients for the calibration and validation of the GOCE data. In this context, also the functional model for the external calibration is

investigated, and appropriate statistical quality parameters are defined to assess the calibration results. The validation on gradient level is performed by IFE (University of Hannover).

The gravity models are validated by means of independent gravity field information, i.e. information not already included in the GOCE gravity field determination. Thus, validation means independent assessment or control of GOCE gravity field models. Such independent information is: – terrestrial point or mean gravity anomalies (based on gravity measurements and levelling), – ocean point, profile or mean gravity anomalies (based on ship gravimetry or satellite altimetry), – geoid height differences (derived from GPS and levelling), – sea surface topography (from ocean modelling or ocean levelling), – assimilation of GOCE fields in ocean circulation models for estimation of ocean circulation and transports.

– satellite orbits, – gravity models (from previous missions such as GRACE, CHAMP and others).

A fundamental difficulty of any validation experiment is that GOCE is expected to provide the best possible gravity field model ever.

In other words, the GOCE gravity field model is expected to be the best global gravity information in the spherical harmonic »band« up to its maximum degree. At most, the independent validation data sets can be expected to be of comparable (or better) quality regionally and/or in certain spectral windows.

Employing for validation regional data sets with point or mean values leads to the problem of how to compare their quality with that of a set of spherical harmonics, representing global but band limited information. As a result within GOCE-GRAND II methods are investigated and developed to validate the global GOCE gravity field models with independent information as listed above taking into account the problem of comparability of the band-limited spherical harmonic series with these »test« data sets. This work is per-

formed by the project partners IAPG (Technical University Munich, IFM (University Hamburg) and ITG (University Bonn).

Summary and Conclusions During the first two year of the GOCEGRAND II project significant progress has been made in all three of the above areas. In order to test the implemented algorithms for gravity field determination a realistic simulated data set is used. For the combination and validation activities an observation campaign mostly has been executed, which provides a significant amount of new test data. Also several validation methods on gradient and on gravity field level (including oceanographic methods) have been implemented and successfully applied.

Further Information and Related Theses Further information on the GOCE mission and its applications can be found on the Webpages of the German GOCE Project Office and ESA (see: www.goce-projektbuero.de and www.esa.int/esaLP/LPgoce.html ).

As a result from the GOCE-GRAND project a series of PhD theses has been published or are close to finalization. The following list provides an overview of finalized and planned dissertations related to the GOCE GRAND project: – Boxhammer Ch./ITG Universität Bonn: Effiziente numerische Verfahren zur sphärischen harmonischen Analyse von Satellitendaten (16.6.2006).

– Wolf, K.I./IFE Universität Hannover: Kombination globaler Potentialmodelle mit terrestrischen Schweredaten für die Berechnung der zweiten Ableitungen des Gravitationspotentials in Satellitenbahnhöhe (13.2.2007).

– Baur O./GIS Universität Stuttgart: Die Invariantendarstellung in der Satellitengradiometrie (20.3.2007).

– Alkhatib, H./ITG Universität Bonn: On Monte Carlo methods with applications to the current satellite gravity missions (1.6.2007).

– Kargoll, B./ITG Universität Bonn: On the Theory and Application of Model Misspecification Tests in Geodesy (20.6.2007).

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– Siemes Ch./ITG Universität Bonn: Digital Filtering Algorithms – Tools for Decorrelation within Large Least Squares Problems in the Context of Satellite Gravity Gradiometry (in preparation 2007).

– Wermuth M./IAPG TU München: Gravity field analysis from satellite missions (in preparation 2007).

– Eicker A./ITG Universität Bonn: Regionale/ globale Schwerefeldbestimmung mit ortslokalisierenden Basisfunktionen aus SST- und SGG-Daten (in preparation 2007).

– Löcher A./ITG Universität Bonn: Die Verwendung von Bewegungsintegralen zur Schwerefeldbestimmung und zur Evaluierung von Schwerefeldmodellen (in preparation 2007).

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GOCE data processing: the numerical challenge of data gaps Siemes C. (1), Schuh W.-D. (1), Cai J. (2), Sneeuw N. (2), Baur O. (2) (1) Bonn University (2) Stuttgart University

1. Introduction The sensors onboard the GOCE satellite will collect hundreds of millions observations during the 12 month mission period. The observations are used to determine the Earthâ&#x20AC;&#x2122;s gravity field, which will be described by tenth of thousands of parameters. Therefore, in the case of the GOCE mission the sheer number of observations and parameters makes the processing of the data a challenge for scientists and software engineers. In order to overcome the computational efforts supercomputers are used and parallel computing techniques come into play.

The satellite gravity gradiometer (SGG) is the core sensor onboard GOCE. It is extremely sensitive to high frequencies. What makes the processing the SGG observations so difficult, is the fact that the SGG observations are highly correlated. For this reason tailored algorithm were derived for the processing of the SGG observations. For example digital filters are used to decorrelate the SGG observations. However, in the presence of data gaps, the application of the algorithms is delicate. The need arises to extend the algorithms to be able to safely handle data gaps. These data gaps can be roughly divided into short and long data gaps, which require different treatment.

One special kind of data gap is the polar cap. It is not a data gap in a strict sense. Due to the sun-synchronous orbit of the satellite, the data does not cover the polar regions. There exist numerous ways to approach this problem. The most straight forward way would be to incor-

porate additional measurements over the polar regions. Another way is to introduce prior knowledge about the gravity field, which is known as regularization. Finally, one can chose a different set of base functions, known as Slepians, which are not defined over certain regions.

2. Gravity field recovery from GOCE data The gravity field recovery is performed by a least-square adjustment of the observations.

Herein, the observation vector l is expressed by the product of the design matrix A with the parameter vector x. The design matrix contains the base functions while the parameter vector consists of the gravity field parameters.

Because of measurement errors, the resulting system of observation equations is inconsistent. Therefore, the residual vector v is introduced to compensate these errors.

l + v = Ax The base functions are typically spherical harmonics. Thus, the gravity field parameters are typically the spherical harmonic coefficients.

As the observations can be considered as a stationary time series along the satellites orbit, digital filters can be used to decorrelate the observations. Such a decorrelation corresponds to a multiplication of the observation equations by a lower triangular Toeplitz matrix F, which we call filter matrix.

Fl + Fv = FAx Each line of the filter matrix F can be interpreted as a moving-average filter. The least-

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squares estimates of the parameters are then obtained by minimizing the residual sum of squares.

v TF TFv â&#x2020;&#x2019; min .

The covariance matrix C of the observations is connected to the filter by the following formula.

C â&#x20AC;&#x201C;1 = F TF 3. Data gaps The filtering of the observation equations can be considered as an approach to take the high correlations of the SGG observations into account. For the filtering it is assumed that the observation time series is uninterrupted, which is violated if the observation time series contains data gaps. In this case we need to extend the processing strategy in order to be able to process observations time series.

Data gaps can be roughly divided into long and short data gaps, which require a different treatment. Before a long data gap, the decorrelating filter is stopped and restarted after the gap. This way any correlations between the observations before and after the gap are neglected. For short data gaps, fill-in values are computed such that the filter can run over the gap. After the filtering the fill-in values are removed. This way the correlations between the observations before and after the gap are taken into account.

4. Filter warm-up and long data gaps The filter warm-up is an effect which arises at the beginning of the filtering, i.e. at the beginning of the observation time series and after each long data gap. The filtered observations during in the warm-up of the filter should not be used within the least-squares adjustment.

This way, one can lose many observations due to the filter warm-up. Therefore, a procedure to avoid the filter warm-up has been developed, which is presented in the following. In order to analyse the problem we look at filter matrix F. Each row of the filter matrix is in principle a moving-average filter. Because the filters are stable, the coefficients of the moving-average filters converge to zero the farther they are away from the main diagonal. Therefore, in addition to its lower triangular Toeplitz structure the filter matrix can be approximated be a banded matrix. In the upper triangle of the band the moving-average filters are truncated. The more filter coefficients are truncated, the greater is the change in the filter characteristics. This change of the filter characteristics affects only the first filtered observations after the filter start and is the reason for the filter warm-up.

Figure 2: The filter matrix is a lower triangular Toeplitz matrix. In addition it can be approximated by a banded matrix. Each row of the filter matrix is a moving-average filter. In the upper triangle of the band, these filters are truncated, which causes the filter warm-up

Figure 1: The processing strategy for long and short data gaps is different. Long data gaps require a restart of the filter after the gaps. Short data gaps require the computation of fill-in values for the data gaps, which are removed after the filtering

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Figure 3: The first part of the filter matrix is replaced in order to avoid the filter warm-up. The computation of the short filters is subject to the Levinson-Durbin algorithm

The solution of this problem is to replace the truncated filters by shorter ones which fit in the row and approximate the filter characteristics as good as possible.

This approximation has to be performed with respect to the decorrelating capabilities of the filter. Thus, the autocovariance function of the original filter has to be approximated by the shorter moving-average filters. The wellknown Levinson-Durbin algorithm is tailored for the computation of the shorter filters.

Within the algorithm moving-average filters from order zero to a desired order are recursively computed. Thus, in each step of the recursion, the algorithm provides one row of the filter matrix.

In order to analyse the performance of this new method the following test has been performed. A correlated time series has been filtered as a reference. In the middle of the time series the same filter has been started one time by the conventional method and one time by the new method.

The filter characteristics of the filter which has been used for the analysis of the performance of the new method for the warm-up are given in figure 5. It shows the power spectral density of the filter which is the Fourier transform of the autocovariance function. Thus, it describes the decorrelating capabilities of the filter.

The impact on the filtered residuals is depicted in figure 6. The filtered residuals of the conventional method are clearly not decorrelated during the warm-up after the filter start.

In contrast, the filtered residuals of the new method are very well decorrelated.

Figure 4: Setup for the comparison of the conventional filter start which causes a warm-up and the new method for the filter start

Figure 5: The power spectral density of the filter which has been used for the analysis of the performance of the new method for the filter warm-up

Figure 6: Impact of the new method for the filter warmup on the filtered residual time series. The conventional filter produces an overshoot at the beginning of the filtering. This phenomenon is called the filter warm-up. During the filter warm-up, the filtered residuals apparently do not correspond to a white noise time series. The new method for the start of the filtering prevents the filter warm-up

The effect of the warm-up can also be analysed by the investigation of the covariance matrix C, which is computed by the filter matrix. Because we assume that the observations are stationary, the covariance matrix of the observations has a Toeplitz structure. Figure 7 shows two covariance matrices. One is computed by the filter matrix of the conventional filter start and the other is computed by the filter matrix of the new method. Apparently the covariance

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matrix of the conventional filter start deviates from the desired Toeplitz structure for the covariances of the first observations.

This is the effect of the filter warm-up on the covariance matrix. The covariance matrix of the new method is still not a Toeplitz matrix, but it comes much closer to the desired Toeplitz structure. In fact, the covariances sufficiently reflect the accuracy of the observations.

5. Fill-in values and short data gaps Short data gaps do not require a restart of the filter. Instead, fill-in values for the observations are computed for the short data gaps such that the filter can run over the gaps without doing damage to the filtered residuals. For the computation of the fill-in values one has to be aware of that the observations not only contain a deterministic part, but also a stochastic part, i.e. the gravity field information and the measurement errors. The deterministic part of the observations is represented by the adjusted observations

l˜ = Ax˜ ,

The deterministic part of the fill-in values can be computed by prior knowledge about the parameters of or by interpolation techniques.

More difficult is the computation of the deterministic part of the fill- in values. It has to accommodate both the residuals before and after the short data gaps and the filter characteristics. This can be achieved by minimizing

v TF TFv → min , whereas the filter matrix F is fixed and the missing residuals are treated as parameters.

The missing residuals can be isolated by splitting the product Fv into two parts.

Fv = F1v1 + F2v2 Herein, v1 contains the residuals which are not missing while v2 contains the missing residuals. The matrices F1 and F2 contain the corresponding columns of matrix F. Then, the function which we want to minimize is expressed in terms of the vectors v1 and v2.

v TF TFv = (F1v1 + F2v2)T (F1v1 + F2v2) = v 1TF 1TF1v1 + 2v 1TF 1TF2v2 + v 2TF 2TF2v2

wherein x˜ denotes the least-squares solution for the parameters x. The stochastic part is represented by the residuals

The minimum is obtained by setting the gradient to zero

v = l˜ – l .

2F 2TF1v1 + 2F 2TF2v2 = 0

Figure 7: Impact of the new method for the filter warm-up on the covariance matrix of the observations. The left panel shows the conventional covariance matrix of the observations derived from the filter. Clearly, during the warm-up of the filter, the covariance matrix deviates from the desired Toeplitz structure. The right panel shows covariance matrix of the observations derived from the filter for the case, that the new method for the warm-up is applied. Though this matrix does not posses a Toeplitz structure, it still comes very close to it. The unit of the elements of the covariance matrices is Eötvös [E 2 = 10–9 m/s2]

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Figure 8: Impact of the fill-in values on the residual time series. The left panel shows the correlated residual time series.

The data gap is highlighted by a grey background. The reference time series has no data gaps. The fill-in values tend to be much smoother than the reference time series. The right panel shows the effect of the fill-in values on the filtered residual time series, which should be uncorrelated. Apparently, filling in zeros for the stochastic part leads to an unsatisfactory result. Filling in the fill-in values results in a time series, which resembles the filtered reference time series very fast

and solving the equation for v2, which yields

v2 = –(F 2TF2)–1 F 2TF1v1.

This corresponds to a least-squares adjustment. The number of parameters can be very great in the case of many small data gaps. In order to overcome this problem, the normal equations are directly computed and stored in a sparse storage scheme. The storage scheme which best suits the problem is the shell-oriented storage scheme. In this storage scheme the elements of each column are stored contiguously in a vector, beginning at the first non-zero element and ending at the diagonal element of each column. This storage scheme allows for the in-place computation of the least-square solution via the Cholesky decomposition, forward and backward substitution.

6. Polar Gaps From the mathematical point of view, global gravity field modelling is typically based on spherical harmonic expansion of the potential function. Legendre functions, and thus surface spherical harmonics, are defined globally and satisfy the orthogonality relations on the sphere. However, GOCE satellite ground tracks leave out a double polar cap with a radius of more than six degrees, cf. figure 9.

Figure 9: GOCE mission configuration. The shaded area indicates the spherical belt of data coverage

The misfit between data measurements and the geopotential modelling is conventionally treated by augmenting data in the polar regions (spatial stabilization), or tailored regularization in the spectral domain using a priori information in terms of spherical harmonic coefficients.

For solving the polar gap problem we apply the α-Weighted BLE (Best Linear Estimation), a uniform Tykhonov-Phillips regularization (Cai, et al. 2004) subject to –1 T –1 xˆ = (AT ∑–1 l A + αR) A ∑ l l

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complemented by the Mean Square Error matrix MSE{xˆ } := E{(xˆ – x) (xˆ – x)T} = D{xˆ } + ββ T with the bias vector β = E{xˆ } – x.

R is the regularization matrix, which is typically symmetric and positive definite. In this context, the optimal determination of the regularization parameter is of prior importance. It balances the variance D{xˆ } and the squared bias ββ T, cf. figure 10. Cai, et al. (2004) and Cai (2004) developed a method to compute the optimal regularization parameter (or weight factor) α by A-optimal design according to

Figure 11: Slepian functions (m = 0, L = 50). The first four functions (index 1–4) are mainly concentrated in the polar caps C. From the seventh Slepian function on (index 7–51), the signal content in the polar caps is negligible

αˆ = arg {tr MSE{xˆ } = min} .

In terms of spatial stabilization, the external observations which will have to be supplied in order to overcome the polar gaps may be provided in two ways: (1) terrestrial or airborne gravity data and (2) data from other satellite missions with a higher inclination, such as GRACE. The combination of GOCE observables and external data, together with regularization is given by –1 T –1 xˆ = (A1T Σ–1 l1 A1 + A2 Σ l2 A2 + αR) × T –1 T –1 × (A1 Σ l1 l1 + A2 Σ l2 l2) ,

where subscript 1 represents GOCE observables l1 and subscript 2 represents the external observations l2 with the assumption that both kind of observations are not correlated with each other. The regularization matrix R

Figure 10: The relationship between the variance, the squared bias and the weight factor α. The variance term decreases as α increases while the squared bias increases with α

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may be chosen to the Gramian matrix, Kaula matrix or a priori information in the loworder domain.

Alternatively, we investigate the Slepian approach (Slepian 1978) to the GOCE mission configuration (Baur and Sneeuw 2007). The philosophy of the method is not to adapt the observation scenario to the modelling but, instead to adapt the parameterization of the geopotential to the observations. This results in band-limited base functions that are optimally concentrated on the spherical belt of data coverage. As shown in Simons et al.

(2006), Slepian functions are uniquely defined in case of an axisymmetric polar gap as outlined in figure 9. Figure 11 displays the spatial concentration of Slepian functions.

7. Conclusions Data gaps in the observation time series can be treated by different strategies. For long data gaps a special procedure to start the filtering is very useful to avoid a loss of data due to filtering. Short data gaps can be filled with fill-in values, if these are computed with respect to both the deterministic and stochastic part of the observations. The main difference between the two strategies is, that for long data gaps correlations are neglected while for short data gaps correlations are taken into account. Both method perform very

well in the case of highly correlated observations such as the SGG observations of GOCE. To solve the polar gap problem in terms of gravitational field recovery we incorporate three strategies: (1) augmenting data in the polar regions, (2) introducing a priori information in the low-order domain in combination with A-optimal regularization; and (3) the Slepian approach, characterized by a set of base functions that are defined within the area of GOCE data coverage. Numerical tests show the applicability of the Slepian approach with regard to solvability and stability in the case of polar data gaps.

Schuh, W.-D. (1996) Tailored numerical solution strategies for the global determination of the earth’s gravity field. Number 81 of the notes of the Graz University. Graz University.

Simons, F. J. (2006) Spherical Slepian functions and the polar gap in geodesy. Geoph. J. Int., 166(3): 1039–1061, doi: 10.1111/j.1365-246X.2006.03065.x.

Slepian D (1978) Prolate spheroidal wave functions, Fourier analysis and uncertainty. V. The discrete case. Bell. Syst. Tech. J. 57(5): 1371–1430.

References Baur O, Sneeuw N (2007) Slepian approach revisited: New studies to overcome the polar gap. ESA SP-627, Proceedings 3rd GOCE User Workshop, Frascati, Italy.

Cai J (2004) Statistical inference of the eigenspace components of a symmetric random deformation tensor. Dissertation, Deutsche Geodätische Kommission (DGK) Reihe C, Heft Nr. 577, 138 Seiten, München.

Cai J, Grafarend E und Schaffrin B (2004) The A-optimal regularization parameter in uniform Tykhonov-Phillips regularization – α-weighted BLE. IAG Symposia 127 »V Hotine-Marussi Symposium on Mathematical Geodesy«, Matera, Italy, 17–21 June 2002, edited by F. Sanso, Springer, 309–324.

Farhang-Boroujeny, B. (1998) Adaptive Filters – Theory and Applications. John Wiley and Sons, Chichester.

Frederik JS, Dahlen FA, Wieczorek MA (2006) Spatiospectral localization on a sphere. SIAM Review 48(3): 504–536, doi: 10.1137/S0036144504445765.

Klees, R., Ditmar P. and P. Broersen (2003) How to handle colored noise in large least-squares problems. Journal of geodesy, 76: 629–640.

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GOCE Validation Over Land and Ocean Stammer D., Gruber T., Ilk K., Köhl A., Romanova V., Rummel R. Institut für Meereskunde (IfM), Universität Hamburg, Bundesstraße 53, 20146 Hamburg, stammer@ifm.uni-hamburg.de

1. Introduction The objective of the GOCE (Gravity Field and Steady-State Ocean Circulation Explorer) mission is the determination of the Earth’s gravitational field with high spatial resolution and accuracy (1–2 cm geoid at 100 km resolution).

The key observables are gravitational gradients, i.e., the second derivatives of the gravitational potential. With theses measurements, the diagonal components of the gravitational tensor shall be determined with an accuracy of

about 10 mE/Hz1/2 in a frequency range from 5 to 100 mHz. An intrinsic challenge of the project is to test the quality of the resulting gravity field and part of this GOCE GRAND II project is to test the consistency with the new observations against independent information.

To test the high quality of the GOCE results, various validation procedures are being applied over oceans, e.g. using altimetric and in situ observations and ocean models. Exam-

Figure 1: Difference of the mean dynamic topography as estimated from the 1º state estimation to the estimate based on altimeter data and the EGM96 (left) and GRACE (middle) geoid. The difference between the result from a forward simulation and the GRACE product is shown on the right. The contour increment is 5 cm

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ples and the status quo for all these validation procedures are presented in this talk and are being explained in more detail below. Among those, GOCE gravity models are planned to be validated by means of independent information, i.e. information not already included in the GOCE gravity field determination. Such independent information may include: â&#x20AC;&#x201C; satellite altimetry and dynamic topography (from ocean modelling or ocean levelling), â&#x20AC;&#x201C; satellite orbits, â&#x20AC;&#x201C; gravity models (from previous missions such as GRACE, CHAMP and others).

An important element of a validation campaign needs to be a test of the new geoid field against information available from ocean observations and ocean dynamics, embedded in ocean circulation models, which is being pursued in package 330. The results shall be evaluated again by data sets not included in the solution, like bottom pressure, tide gauge timeseries or other oceanographic measurements.

2. GOCE Validation via Ocean State Estimation Ocean circulation estimates, combined with altimetric observations, provide important independent means to test existing geoid fields and their error estimates against ocean observations: Ocean models provide estimates of the dynamic topography which is part of the total sea surface height (SSH) as it is measured by altimetry. The inclusion of an ocean modeling component into the validation of the GOCE gravity field provides therefore independent insight into the quality of gravity field products, including the geoid field and the geoid error covariance matrix. Within the ocean state estimation framework, the MIT/ECCO ocean circulation model is combined with most of the available ocean data sources. A time varying circulation is estimated that is consistent with the dynamics and the data. The resulting dynamic topography is thereby expected to be closer to the observations, which are obtained as the difference of SSH and geoid, than a pure

Figure 2: Amplitude (in Pa; left) and phase (day of max. value; right) of annual cycle in ocean bottom pressure from GRACE monthly products and hydrodynamic models (OMCT/ ECCO). Note the varying reference periods

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simulation (Wunsch and Stammer, 2003). Fig. 1 shows the reduction of the difference between the modeled dynamic sea surface height and the TOPEX-geoid estimate, using the EGM96 model (left) and after replacing the EGM96 geoid with a more modern geoid based on GRACE measurements (middle panel). Details are provided by Stammer et al. (2006). Consistently larger residuals exist for the model-based estimate from an unconstrained model, i.e., based on a pure forward simulation (right panel).

use GRACE Level-2 data to calculate the mean seasonal cycle of ocean bottom pressure from 5 years of GRACE gravimetric data. Differences to two general ocean circulation models are shown in fig. 2 and are discussed: (1) the Ocean Model for Circulation and Tides (OMCT), which is also used in the dealiasing process to produce GRACE Level-2 data, and (2) results from the Estimation of the Circulation and Climate of the Ocean (ECCO) project.

In summary, findings are: – The filter reduces essentially leakage of land signals compared to a pure spectral filter and at the same time retains a significant part of the ocean signal along the coast lines; – The two hydrodynamic models exhibit comparable (semi)annual variability of ocean bottom pressure while discrepancy to GRACE (GSM+GAD) is comparably large; – (Semi)annual variability is subject to large variability on interannual to decadal time scales.

3. Preparation of GRACE Monthly Solutions Gravity fields as derived from the GRACE satellite mission require smoothing to reduce the effects of errors present in short wavelength components. For the ocean special care is needed since here the signals are generally smaller than on the continent. In addition, the highest variability is found near the coast and is thus subject to leakage of external land signals due to the representation of the GRACE fields as a (finite) set of spherical harmonic coefficients, and the filtering process. Here we present a simple sequence of filters designed to both minimize the leakage of land signals into the ocean and maximize the spatial resolution. The sequence of filters consists of the Svenson and Wahr [2006] decorrelation filter, a spectral filter, a land-sea mask and a spatial Gaussian filter. Using this filter technique, we

4. EOF Analysis The quality assessment of the existing GECCO ocean estimate (German part of the Estimating the Circulation and Climate of the Ocean) based on available ocean data is a prerequisite before using it for the validation of the GRACE gravitational field. The time series of the bottom pressure (BP) anomalies from the ocean synthesis, BP sensors, and GRACE are analyzed and compared to each other for different time periods. Their corre-

Figure 3a: Global first EOF of GRACE bottom pressure anomalies (the land is masked). The explained variance is 33%. The scale is –5 : 5 and the interval is 1

Figure 3b: Global first EOF of GECCO bottom pressure anomalies. The explained variance is 34%. The scale is –5 : 5 and the interval is 1

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Figure 4a: Bottom pressure time series at station at Bouvet Island in the Indian Ocean. Upper panel: BP measurements – black, GECCO – red; time period 1992–1996; correl = 0.76; Lower: GRACE – black, ECCO- red; time period 2003–2004, correl = 0.60

Figure 4b: Bottom pressure at the station CK2 in the South Atlantic: Upper panel; BP measurements – black, GECCO –red; time period 1992–1994: correl = 0.72. Lower panel: GRACE – black, ECCO – red, time period 2003–2004, correl = 0.54

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Figure 5: Comparison of bottom pressure time series in the subtropical Atlantic at station MOVE1: GECCO – black, OMCT – red, MOVE1 (51.3W,15.3N) – green. Correlation: OMCT and MOVE: -0.01 GECCO and MOVE: 0.31 for the year 2001

lations at locations, where the observations are available (mostly in the Southern, Indian Ocean and central Atlantic), are calculated.

The spatial RMS and the correlation patterns of the global BP anomalies are calculated for results from the GECCO ocean estimate, the GRACE product, and also the OMCT model, which was used for dealiasing short term BP fluctuations in the GRACE product. The EOFs of GRACE BP calculated over the tropical Atlantic Ocean, show coincidence with the GECCO seasonal signal of the mass change due to the corrected Amazona’s river run-off and freshwater fluxes (fig 3a,b). These results were compared to the independent long term observations of the river discharge.

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5. GOCE Validation via Bottom Pressure Measurements The GRACE geoid model provides only monthly gravity maps, which are affected by aliasing of the short term variability into 30 days average. Detecting short term variability in the BP may be possible only by assimilating the available oceanographic data. We study the short variability of BP through comparison with in situ data.

Most of the moorings are located in the Southern Ocean and Indian Ocean focusing on the transport at Drake Passage and on determining the ACC. They were carried out at the Proudman Oceanographic Laboratory, the University of Kiel (MOVE – Meridional Overturning Variability Experiment) and the Oregon State University. The time series of the bottom pressure anomalies from the model (GECCO) are compared with the measured anomalies.

The OMCT model data are also compared to GECCO and the independent data.

The correlation coefficients of the measured data and the model results range from 0.32 for the tropical Atlantic to 0.72 for the Southern Ocean (fig. 4a, b). The coherence spectra show high coherence at a period of around 12 days for all observed time series (not shown). The correlation of GRACE and GECCO BP show lowering of the correlation of around 20% for the GRACE period. Fig. 5 represents the daily time series of the MOVE, OMCT and GECCO bottom pressure. The use of gravity field products as part of the data constraints used in the state estimation provides additionally also an assessment of the impact of a more accurate gravity field on the ocean circulation.

7. Conclusions Validation plays an important role for GOCE to overcome instrumental and measurement errors and to achieve the anticipated high accuracy. In this context, we addressed various internal and external validation procedures.

These procedures have been prepared and will be further developed for successful GOCE validation and a reliable quality assessment.

1. The model shows skill in estimating the high frequencies in the bottom pressure fields (the correlation with the independent data is up to 0.72). The correlation with the GRACE BP monthly fields for 2003–2004 is slightly lower – up to 20%.

2. The estimated freshwater flux input over region of Amazon river mouth from the assimilation are close to the seasonal cycle of the Amazon’s river discharge.

3. The seasonal cycle of GRACE fields is important to be included as a constrain in the assimilation to produce better state estimate.

and GOCE Gravitationsfeldanalyse Deutschland II (GOCE-GRAND II) granted by the German Federal Ministry of Education and Research (BMBF).

References Cretaux J.F., Soudarin L., Davidson F., Gennero M.C., Berge-Nguyen M. and Cazenave A., Seasonal and interannual geocenter motion from SLR and DORIS measurements: Comparison with surface loading data, J. Geophys. Res., 107,B12, 2374, DOI: 10.1029/2002JB001820, 2002 Stammer, D., A. Köhl and C. Wunsch (2006): Tests of geoid height skill through estimates of the ocean circulation. Submitted for publication.

Swenson,S., and J. Wahr (2006), Post-Processing removal of correlated errors in GRACE data, Geophys. Res. Lett., 33, L08402, doi: 10.1029/2005GL025285.

Wahr, J., M. Molenaar, and F. Bryan (1998), Time variability of the Earth’s gravity field: Hydrological and oceanic effects and their possible detection using GRACE, J. Geophys. Res., 103(B12), 30,205?30,230.

Wunsch and D. Stammer (2003): Global ocean data assimilation and geoid measurements, in G. Beutler, R. Rummel, M.R. Drinkwater, and R. von Steiger, Earth Gravity Field from Space – from Sensors to Earth Sciences, Space Sciences Series of ISSI, Vol. 18, Kluwer Academic Publishers, Dordrecht, Netherlands, 460 pp., and Space Science Reviews, 108, 147–162.

Acknowledgements The OMCT model results were provided by Maik Thomas from the GeoForschungsZentrum Potsdam (GFZ). This work is a contribution to the DFG priority program SPP1257 granted by the German Science Foundation,

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Gravity Field Analysis: Global Combination and Regional Refinement Approaches Stubenvoll R. (1), Eicker A. (2), Abrikosov O. (1), LĂścher A. (2), FĂśrste C. (1), Mayer-GĂźrr T. (2), Ilk K.-H. (2), Kusche J. (1) (1) GeoForschungsZentrum Potsdam (2) Institute for Geodesy and Geoinformation, University of Bonn

Introduction As a result of the dedicated space-borne gravity field missions CHAMP in orbit since 2000 and especially GRACE, in orbit since 2002, a breakthrough in accuracy and resolution of gravity field models has been achieved. Subsequent solutions by using the observations collected over a period of time of, e.g., one month, enables the derivation of time dependencies of the gravity field parameters. The third satellite in the sequence of dedicated gravity satellite missions will be GOCE (Gravity field and steady-state Ocean Circulation Explorer), launched in a couple of months. The high resolution spectral part of the gravity field will be derived with unprecedented accuracy by a gravity gradiometer consisting of six three-axis accelerometers to measure in-orbit gravity gradients in three spatial directions. For a gravity field model which satisfies the various different demands, this satellite-borne gravity field information has to be combined with additional terrestrial, airborne gravity field information and altimetric measurements, as well as with indirectly derived gravity field information such as the effects of topographic-isostatic masses.

Therefore, the combination of these various gravity field information is an important and extremely non-trivial problem if biased combination results have to be avoided.

Because of the inhomogeneous gravity field of the Earth the signal content varies in the space domain. This fact has to be considered properly in the modeling of the gravity field. The global gravity field features should be param-

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eterized by series in terms of spherical harmonics up to a reasonable degree and the regional gravity field structures should be represented by space localizing base functions, e.g., by spherical spline functions, spherical wavelets or any other set of base functions with local support. Various gravity field recovery examples approve the usefulness of this focus-in procedure. This technique can be used also to derive indirectly gravity field models represented by spherical harmonics. Several regional solutions with global coverage can be merged by means of numerical quadrature methods to obtain a global solution, in principle, up to an arbitrary degree, only limited by the signal content of the gravity observations.

The regionally adapted strategy can be applied already at the gravity field recovery level. This approach provides better results than calculating a spherical harmonic solution by recovering the potential coefficients directly.

The combination and focusing problems are treated in two work packages within GOCEGRAND II: WP140 solves the combination and focusing problematic at the gravity field recovery level within the unitized Gravity Recovery Object-Oriented Programming System (GROOPS) which is in development at the Institute for Geodesy and Geoinformation, University of Bonn. WP210 solves this problem at the normal equation level. In order to compute a new standard, high-quality global Earth gravity field model, normal equations derived from GOCE SGG data will be combined with GRACE, terrestrial and altimetric normal equations.

WP210: High Quality Combination Solutions The main goal of WP210 is the computation of a high-resolution gravity field model up to degree of at least 360 in terms of spherical harmonics, with global coverage and outstanding quality. Therefore all available GOCE and GRACE satellite data describing the Earth potential (GPS high-low SST for GRACE and GOCE, KBR low-low SST for GRACE, gradiometry for GOCE) will be used by GFZ Potsdam.

The combination of these data implies: – de-correlation of GOCE-SGG measurements with non-recursive filter techniques based on a deconvolution of the covariance function of the gradiometer noise; – dealiasing and reduction of annual and highfrequency mass variations in the GOCEmeasurements using appropriate models for atmosphere and oceans and GRACE derived time series for the effects of hydrology (since the current models seem to be rather uncertain (Petrovic et al. 2004)); – setting up normal equations up to degree and order 250.

The software for these tasks has been developed and was tested. Figure 1a and 1b show a solution with simulated AR2 GOCE-data and simulated surface data for the polar gaps. The solution is based on normal equations up to degree and order n, m = 210 for SGG, and

n, m = 150 for GOCE SST. In figure 1a the geoid erros w.r.t. EGM96 are shown in the space domain, while 1b shows the spectrum of these errors. Note that it is not possible to attain the GOCE mission objectives (1–2 cm accumulated geoid error at degree 200) because only two months of data were used for this simulation.

The final high-resolution combination model will result after combination of GOCE with GRACE and surface data sets. GRACE data are necessary for the very long wavelength part of the Earth’s gravity field (which is only poorly observed by GOCE), while the surface data yield information for the wavelengths beyond degree and order 250. For this, several independent terrestrial and altimetric data sources had been gathered, properly unified (to avoid geodetic datum problems), and homogenized in a preprocessing step (applying the necessary correction terms) as described in Förste et al. 2007b.

Of special importance are the data sets of the polar regions, because they close the GOCE polar gap. After the critical evaluation and selection of the terrestrial data sets, their unification leads to one data set with global coverage.

In the final combination step, the GOCE, GRACE and surface normal equations will be combined in a special band-limited combination method in order to preserve the high accuracy from the satellite data in the lower

Figure 1: Simulation study with AR2 data. a) Geoid errors w.r.t. to EGM96 in space domain (left); b) Spectrum of the geoid errors w.r.t. EGM96 (right)

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frequency band of the geopotential and to form a smooth transition to the high-frequency information coming from the surface data (Förste et al. 2005). This procedure is well tested by GFZ in its ongoing calculations of gravity field models, e.g. EIGEN-GL04C being the latest (Förste et al. 2007a and 2007b).

In order to be able to set up complete normal equations for the surface data, the existing software package ADP was optimized considerably which lead to a drastical reduction of computation time (see table 1 for details). Furthermore, the software optimization opened up the opportunity to set up complete normal equations up to degree and order n, m = 359.

This means, that it is no longer necessary to make use of the block-diagonal technique for the highest frequencies (beyond n, m = 250), but that the complete solution will be calculated using complete normal equations. The advantages of this are immense: – The measurements receive an individual weighting based on their accuracy; – Measurements of different data types can be combined; i.e. altimetry over the oceans contributes directly to the highest frequencies. It is not necessary to transform the altimetric geoid undulations to gravity anomalies.

– Problems in the »transition zone« between the complete and block diagonal normal equations will be eliminated (Förste et al. 2007a).

Summarizing it can be stated that the WP210 is in so far finished that only the real

GOCE measurements are missing in order to calculate an earth gravity field model of highest quality.

WP140: Regional Gravity Field Refinement Regional gravity field recovery at the example of GOCE At the Institute for Geodesy and Geoinformation in Bonn there has been developed a unitized Gravity Recovery Object-Oriented Programming System (GROOPS) which is tailored to the in-situ observables of the new generation of gravity satellite missions such as CHAMP, GRACE and GOCE. The programming system consists of various modules allowing to flexibly combine different types of observations (precise satellite orbits, satellite-to-satellite tracking, gradiometry, altimetry, airborne and terrestrial data) with different types of gravity field representations (global modelling by spherical harmonics and regional parameterization by space localizing basis functions).

Furthermore GROOPS enables the integrated calculation of static and temporal gravity field models. Most of the components of GROOPS are on a rather advanced development level, already being in operation for the real-data analysis of CHAMP and GRACE. The recovery procedure as realized in GROOPS consists of various steps which can be applied independently as well: – Global gravity field recovery based on a spherical harmonic expansion up to a

Table 1: Comparison of computation times of old and new ADP-software versions; normal equations were set up for 3800 observations on a sun work station using 6 processors. Note that the time for writing the output files is not included

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moderate degree to provide a basis for further refinements, – Temporal gravity field models as part of the global solution with moderate upper series degree, – Regional refinements of the gravity field by spherical splines as space localizing base functions, adapted to the specific gravity field features, if possible covering the globe, – Determination of a global gravity field model by merging the regional refinement solutions and deriving potential coefficients by a numerical quadrature technique.

It should be pointed out that a combination of data sets of different origin is simply possible, in principle, at every step of the multistep procedure.

Simulation scenarios have proofed the general functionality of the regional refinement strategy and have provided very promising results, see for example Eicker et al. 2005a. The simulation example was based on a realistic consistent data set of one month of simulated GRACE and GOCE observations based on the EGM96. From this simulated data set a global gravity field solution based on the GRACE low-low satellite-to-satellite observations up to a spherical harmonic degree of n = 150 was derived. The regional refinements to this global spherical harmonic solution were then calculated as residual gravity field for individual patches, using a parameterization by splines as space localizing base functions with a resolution corresponding to a spherical harmonic expansion of degree 300. Based on these individual regional refinement patches a spherical harmonic expansion can subsequently be calculated using the Gauss-Legendre-Quadrature, for further information refer to Eicker et al.

2005b. Since the method principally works very well already, recent research has been dedicated to improving the accuracy of the solution and to extracting additional information out of the provided observations. In this context especially the use of an adapted regional regularization procedure (as described in the next section) has to be pointed out. Further investigations have been performed

regarding the optimal distribution of the space localizing basis functions on the surface of the sphere and concerning the optimal choice of the shape of the basis functions.

Regionally adapted regularization Due to the ill-posedness of the downward continuation process the solution has to be regularized. Here the Tikhonov regularization has been applied and the regularization parameter has been determined by means of variance component estimation as proposed

by Koch and Kusche (2001).

The process of variance component estimation delivers the optimal regularization parameter under consideration of the given signal to noise ratio. In case of a regional gravity field determination this results in one regularization parameter optimally tailored to the respective region. This is an improvement in comparison to a global gravity field parameterization which allows only one regularization factor for the complete Earth resulting in an overall mean damping of the gravity field features.

But even within smaller geographical areas the gravity field features may vary significantly.

Therefore it seems reasonable to further adapt the regularization procedure. The proposed approach takes not only one regularization matrix with one associated regularization parameter per region into account but allows several matrices with respective parameters: N=

1 T 1 1 A PA + 2 R1 + … + 2 R n . σ e2 σ x1 σ xn

For each regional regularization group i the regularization matrix Ri is a diagonal matrix that contains a one for each regional spline parameter located inside this particular region and a zero for parameters belonging to basis functions outside the regularization group.  1 for R ( j, j ) =  0 for

j inside i j outside i

The original identity matrix as applied in the Tikhonov regularization process has thus been divided into single diagonal matrices according

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Figure 2: Differences to pseudo truth: One uniform regularization (left, RMS: 9.24 cm) versus two adapted regularization parameters for land and ocean areas (right, RMS: 8.08 cm)

to the membership of the respective unknown parameters to the different regularization groups.

tugal, IAG International Symposium, International Association of Geodesy Symposia, Vol. 129, pp. 66–71, Springer

R1 + … + Rn = I The possibility of adapting the regularization procedure in this particular way is a unique feature of a field parameterization by space localizing basis functions, as each unknown parameter is related to a particular geographical location. This is an inevitable premise when the elements of the regularization matrix are supposed to be assigned to a certain region.

The improvement achieved by the adapted regularization procedure is illustrated by Fig. 2.

The left hand side displays the differences of the simulation example, compared to the pseudo truth, when applying only one uniform regularization parameter, the right hand side shows the improvement induced by the introduction of a second regularization area.

References Eicker A., T. Mayer-Gürr, K. H. Ilk (2005a): Global Gravity Field Solutions Based on a Simulation Scenario of GRACE SST Data and Regional Refinements by GOCE SGG Observations, in C. Jekeli, et al. (eds.): Gravity, Geoid and Space Missions, GGSM2004, Porto, Por-

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Eicker A., T. Mayer-Gürr, K. H. Ilk (2005b): An integrated global/regional gravity field determination approach based on GOCE observations, in: J. Flury, R. Rummel, C. Reigber, G. Boedecker, M. Rothacher und U. Schreiber (eds.), Observation of the Earth System from Space, pp. 225–237, Springer.

Förste C., Flechtner F., Schmidt R., Meyer U., Stubenvoll R., Barthelmes F., Rothacher M., Biancale R., Bruinsma S., Lemoine J.-M. (2005): A new high resolution global gravity field model from the combination of GRACE satellite mission and altimetry/gravimetry surface gravity data. Geophysical Research Abstracts, Vol. 7, 04561, 2005 Förste C., Flechtner F., Schmidt R., König R., Meyer Ul., Stubenvoll R., Rothacher M., Barthelmes F., Neumayer H., Biancale R., Bruinsma S., Lemoine J.-M., Loyer S. (2007a): Global Mean Gravity Field Models from Combination of Satellite Mission and Altimetry/ Gravimetry Surface Data. Proceedings »The 3rd International GOCE User Workshop«, ESA-ESRIN, Frascati, Italy, 6–8 November 2006, ESA SP627, January 2007, pp. 163–167

Förste C., Schmidt R., Stubenvoll R., Flechtner F., Meyer Ul., König R., Neumayer H., Biancale R., Lemoine J.-M., Bruinsma S., Loyer S., Barthelmes F., Esselborn S. (2007b): The GFZ/GRGS Satellite and Combined Gravity Field Models EIGENGL04S1 and EIGEN-GL04C. Journal of Geodesy.

DOI:10.1007/s00190–007–183–8, in press.

Koch K.R. and Kusche, J. (2001): Regularization of geopotential determination from satellite data by variance components. Journal of Geodesy 76 (5):259–268.

Petrovic S., Reigber Ch., Schmidt R., Flechtner F., Wünsch J., Güntner A. (2004): Comparing temporal gravity variations derived from GRACE satellite observations and existing physical models. Geophysical Research Abstracts, Volume 6, 2004, EGU04-A-06903.

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Development of a patch-filtering method for a more accurate determination of ocean bottom pressure anomalies derived from GRACE solutions Böning C., Macrander A., Schröter J., Timmermann R. Alfred Wegener Institute for Polar and Marine Research, E-Mail: carmen.boening@awi.de

Validation of satellite measurements with ground truth data invariably raises the question of comparability due to differences between the typical horizontal scales. This is particularly true for the validation of satellitederived GRACE gravity anomalies by using in situ measurements of ocean bottom pressure which are pointwise by nature. Further complications arise from the lower accuracy of and noise in satellite measurements. Applying a Gaussian filter to the ocean bottom pressure (OBP) anomalies derived from GRACE gravity retrievals over the ocean is a well-established method but suffers from spurious signals arising from land leakage effects and the symmetry of the Gauss function. This calls for a refinement of the filtering method.

An analysis of simulated OBP anomalies derived from the Finite Element Sea Ice Ocean Model (FESOM) indicates that on a monthly time scale OBP anomalies are coherent over a large area of complex geometry. While simulated timeseries of OBP monthly anomalies from 1958 to 2005 were available, we only used data for the period 2002–2005 to be consistent with the start of the GRACE mission. To eliminate the seasonal cycle (which yields the dominant signal but on a much larger, hemispheric scale), a five months high-pass filter has been applied. From the resulting dataset, we determined areas of high coherency by calculating the cross-correlation between the timeseries at the bottom pressure recorder (BPR) positions and timeseries at all points of

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the model domain within a 20° radius. The pattern of high coherency (»coherence patch«) is then defined as the area with correlations larger than 0.7 (Fig. 1).

We found that OBP anomalies with a period of less than five months are spatially coherent over a large area which is strongly related to the bottom topography. Fig. 1 for example shows regions of high correlation around two BPR positions in the AWI ACC array with a patch radius of approximately 750 km. OBP measurements at these positions are representative for the area defined by the coherence patch.

We use these coherence patches to filter the GRACE data by weighting the data for each position inside the coherence patch with the pre-computed correlation coefficient. The result is a timeseries that is comparable to the point measurement of the OBP recorder.

To enhance the contribution from positions with a high correlation coefficient, squared correlation coefficients are used as weighting factors.

Applying this to different GRACE GFZ releases leads to an improved correlation with in situ OBP timeseries. We used the data contained in the global in situ OBP database which has been compiled by Andreas Macrander (see also WP410/420/440) for an evaluation of OBP anomalies derived from GRACE GFZ RL04 using spherical harmonics of degree and order 2–50 and filtered with a usual Gaussian filter with a 750 km radius on the one hand (Fig. 2)

Figure 1: Two examples for areas of high coherency of OBP anomalies obtained from model simulations

Figure 2: Correlation between Gauss filtered OBP anomalies derived from GRACE and in situ OBP anomalies

and weighted with the correlation coefficients of the patch method on the other hand (Fig. 3). Using the new filtering method yields an improved correlation between GRACE and in situ data.

Especially at the northwestern coast of North America (BPR in the NOAA DART tsunami warning system) and in the Atlantic (AWI ACC and Framstrait PIES deployments, IFM MOVE BPR Array) the agreement between GRACE

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and in situ measurements is improved. The quality of the improvements can be clearly seen by comparing the patch-filtered time series of OBP anomalies derived from GRACE and the ocean model FESOM to the Gauss-filtered time series with reference to the in situ observations. One example are the OBP anomalies in the AWI ACC Array (Fig. 4/5).

The OBP anomalies derived from the GRACE solution filtered with the 750 km Gauss filter

fail to reproduce the characteristic minima and maxima of the in situ time series in many cases. Data filtered with the patch method feature a much better agreement: Most of the significant peaks are captured rather well, and the amplitude is close to that of the observations. Filtering the simulated OBP timeseries with the same coherence patches also leads to a good agreement with the observations. The model reproduces the observed seasonal cycle

Figure 3: Correlation between patch filtered OBP anomalies derived from GRACE and in situ OBP anomalies

Figure 4: OBP anomalies from ACC PIES (black solid), GRACE filtered with a 750 km Gauss filter (black dash-dotted), FESOM

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Figure 5: OBP anomalies from ACC PIES (black solid), GRACE filtered with the patch filter (black dash-dotted), FESOM filtered with the patch filter

of OBP in phase and magnitude. The agreement is particularly good for the southern position. At the PIES which is located on the northern slope of the Atlantic-Indian Ridge in the region of influence of the Agulhas Current, deviation increases due to eddies not captured by the model at 1.5째 resolution. A refinement of the grid in the South Atlantic which is intended for the near future will help to resolve this problem.

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Periodic and transient short-term mass variations in numerical simulations of atmosphere-ocean dynamics Dobslaw H. (1, 2) and Thomas M. (2) (1) Dresden University of Technology, Institute for Planetary Geodesy, 01062 Dresden.

(2) GeoForschungsZentrum Potsdam, Section 1.5 Earth System Modeling, 14473 Potsdam, E-Mail: dobslaw@gfz-potsdam.de, mthomas@gfz-potsdam.de

Abstract Atmospheric surface pressure data from the European Centre for Medium-Range Weather Forecasts (ECMWF) analyses and forecasts are combined in order to provide a precise description of the short-term variability in the atmosphere with 3 h temporal resolution. Together with numerical simulations performed with the Ocean Model for Circulation and Tides (OMCT), high-resolution atmosphere-ocean mass anomalies including atmospheric tides and their corresponding oceanic response are obtained.

While the semidiurnal pressure tide S2(p) is well resolved in 3 hourly sampled data only, transient short-term dynamics in both atmosphere and ocean are found to be sufficiently described by 6 hourly data with respect to the precision requirements of current geodetic applications.

Introduction The dynamics of the atmosphere are highly variable on short time-scales from hours to days.

Beside transient variations connected with synoptic changes of the weather conditions, longterm observations of atmospheric pressure variations contain also distinct harmonic signals with diurnal and semidiurnal periods (Chapman and Lindzen, 1970). These so-called atmospheric tides S1(p) and S2(p) are predominantly related to variations of solar insulation causing sunlight absorption of water vapor and ozone heating.

Since mass variations in the atmosphere and the corresponding oceanic response cause

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significant deformations of the Earthâ&#x20AC;&#x2122;s crust and changes in the gravity field, they are relevant for most geodetic observation techniques. Therefore, the representation of subdaily periodic and transient mass variations in numerical simulations of atmosphere-ocean dynamics will be re-assessed in this paper. It will be especially focused on short-term variability in order to indicate the temporal resolution required for a proper reduction of these sub-daily atmospheric and oceanic effects from observations.

ECMWF data Atmospheric dynamics are realistically described by modern numerical weather prediction models, as, e.g., operated by the European Centre for Medium-Range Weather Forecasts (ECMWF). Based on in-situ and remote sensing observations, atmospheric conditions are analyzed every 6 h, followed by subsequent forecast runs with up to 3 h temporal resolution.

Since the sampling interval of 6 h corresponds exactly to the Nyquist-frequency of the semidiurnal tide, S2(p) aliases into a standing wave in the analyses. Instead, it can be fully recovered by means of 3 hourly short-term forecasts.

Since the reliability of the tides represented in these forecasts has been verified (Dobslaw and Thomas, 2005), analyses and forecasts can be combined according to C 3 = F3 +

( A0 + A6 ) â&#x2C6;&#x2019; ( F0 + F6 ) 2

Figure 1: Estimates of mean diurnal (a) and semidiurnal (b) periodic mass variations in the atmosphere [hPa] obtained from 3 hourly combinations of ECMWF analyses and forecasts. Iso-lines indicate Greenwich phase lags in [°] of the tidal wave

Figure 2: Diurnal (a) and semidiurnal (b) global sea level variations [cm] obtained from OMCT simulations forced by 3 hourly transient combinations of ECMWF analyses and forecasts. Iso-lines indicate Greenwich phase lags in [°] of the tidal wave

in order to both retain the high accuracy of the analyses and the temporal resolution of the forecasts (Dobslaw and Thomas, 2005).

Here, A0 denotes an arbitrary analysis, A6 the subsequent analysis 6 h later and F0, F6 denote the corresponding forecast fields from the latest available forecast run. The intermediate combination field, C3, is therefore deduced from 3 hourly forecasts adjusted to the surrounding analyses. The combined 3 hourly data set consisting of the original analyses and the intermittent combinations will be labeled as ECMWF combinations throughout the remainder of this paper.

For the period 2002 to 2005, mean oscillation patterns of the diurnal as well as the semidiurnal atmospheric pressure tide are derived from 3 hourly combinations (Fig. 1). As compared to analyses and forecasts given in Dobslaw and Thomas (2005), the S1(p) oscillation

system derived from the combinations corresponds to the results based on analysis data only, while the S2(p) pattern agrees with the forecast results, avoiding the erroneous aliasing into a standing wave. Therefore, 3 hourly combinations will be used to further investigate the required temporal resolution for geodetic applications.

OMCT ocean model The oceanic response to atmospheric dynamics is obtained from simulations with the Ocean Model for Circulation and Tides (OMCT; Thomas 2002), which has been developed from the Hamburg Ocean Primitive Equation model (HOPE; Drijfhout et al., 1996). The model has a time-step of 30 minutes, a horizontal resolution of 1.875° in latitude and longitude and 13 layers in the vertical. OMCT has been applied to analyse the impact of ocean circulation and tides on the Earth’s rotation and the gravity field

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(Thomas et al., 2001, WĂźnsch et al., 2001) and is currently in use to de-alias short-term ocean mass anomalies within the GRACE gravity field processing (Flechtner, 2005).

After 265 years simulated with cyclic boundary conditions to obtain a quasi steady-state circulation, OMCT has been forced by 6 hourly wind stresses, atmospheric surface pressure, 2m-temperatures and freshwater fluxes from the latest ECMWF re-analysis ERA-40 covering the period 1958 to 2001. Subsequently, OMCT has been forced by 3 hourly ECMWF combinations for the period 2002 â&#x20AC;&#x201C; 2005 in order to study short-term ocean mass variations. Sea level anomalies from that simulation have been stored every 3 h concurrent with the atmospheric forcing fields. In accordance with the atmospheric data, the S1(p) oscillation patterns deduced from ocean simulations forced with analyses and combinations almost exactly agree, while amplitudes and, thus, energy of S2(p) are significantly enhanced when the combination of analyses and forecasts are applied to force the ocean model.

Required temporal resolution The 3 hourly atmosphere-ocean data from ECMWF and OMCT are used to estimate potential errors introduced by a reduced sampling rate of 6 or even 12 h of transient atmosphere and ocean dynamics. Rms values of differences between 3 hourly data and linear interpolations of 6 (12) hourly sampled data are interpreted as the additional information contained in the denser time-series. In a second step, time-invariant models of atmospheric tides (see Fig. 1 and 2) are removed in order to discriminate between periodic and non-periodic short-term mass variations in atmosphere and ocean.

Focusing on atmospheric mass variations (Fig. 3), 6 hourly data contain significant additional information compared to 12 hourly sampled data. Differences of up to 2.5 hPa (roughly corresponding to 2.5 cm of water thickness) are evident in middle latitudes over the oceans and signals of up to 1 hPa are reached in various continental regions. While the variability over the continents is signifi-

Figure 3: Additional information on atmospheric mass variability [hPa] contained in 6 hourly ECMWF combination data compared to 12 hourly data before (a) and after (c) the reduction of a time-invariant model of the diurnal atmospheric tide, as well as additional information on atmospheric mass variability [hPa] contained in 3 hourly ECMWF combination data compared to 6 hourly data before (b) and after (d) the reduction of a time-invariant model of the semidiurnal atmospheric tide

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Figure 4: Additional information on sea level variability [cm] contained in 6 hourly OMCT data forced by ECMWF combination compared to 12 hourly data before (a) and after (c) the reduction of a time-invariant model of the diurnal ocean tide, as well as additional information on sea level variability [cm] contained in 3 hourly OMCT data forced by ECMWF combination data compared to 6 hourly data before (b) and after (d) the reduction of a time-invariant model of the semidiurnal ocean tide

cantly reduced by a time-invariant model of the diurnal tide, the atmospheric signals over the oceans remain nearly unaffected. Shortterm mass anomalies are primarily connected to transient phenomena in these areas, i.e., to meso-scale variability and atmospheric fronts.

The additional information gained by increasing the temporal resolution from 6 to 3 h resolved data is significantly smaller compared to the step from 12 to 6 h, reaching only up to 1.5 hPa in the tropics. Moreover, most of these signals are related to the semidiurnal tide, which can be removed by applying a corresponding time-invariant model. Remaining signals are almost entirely concentrated over the oceans in middle latitudes, but hardly exceed 1 hPa. Analogous estimates have been also obtained for ocean mass anomalies (Fig. 4). Largest deviations between 6 and 12 h temporal resolution are found in coastal regions with regional signals of up to 2 cm sea surface height variability. Larger discrepancies appear

in very limited places only, as, e.g., near Bering strait or on the Patagonian shelf. Differences are reduced by almost one third in several regions by removing a model of the atmospheric induced diurnal ocean tide S1(p), but significant variability remains which can only be considered for geodetic applications using 6 hourly resolved fields of the transient ocean dynamics. In turn, differences between 3 and 6 h reach up to 6 cm, but more than two thirds of the signal can be removed using a time-invariant model of the semidiurnal ocean tide S2(p), leaving signals of up to 1 cm unconsidered.

Summary and conclusions 3 hourly resolved ECMWF combinations can be created in order to combine the advantages of both analyses and forecasts while retaining the high accuracy of the analyses and the higher temporal resolution of the forecasts. 3 hourly temporal resolution is especially required to analyse the semidiurnal atmospheric tide which otherwise aliases into a standing wave when data with 6 hourly spacing are used. In order to

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properly describe transient mass variations in atmosphere and ocean, a 6 h temporal resolution is sufficient for most geodetic applications.

3 h resolution provides only limited additional information of up to 1 hPa in mid-latitude regions of the atmosphere and approximately 1.5 cm sea level variability in selected coastal regions, which is beyond the present accuracy threshold of most currently applied geodetic applications.

Acknowledgments We thank Deutscher Wetterdienst, Offenbach, Germany, and European Centre for MediumRange Weather Forecasts, Reading, U.K., for providing data from ECMWF’s operational forecast model. This work was supported by the German Ministry of Education and Research (BMBF) and the Deutsche Forschungsgemeinschaft within the GEOTECHNOLOGIEN research program under grant 03F0423D. References Chapman, S., Lindzen, R. S. (1970), Atmospheric Tides, 200 pp., Springer, New York.

Dobslaw, H., Thomas, M. (2005), Atmospheric induced oceanic tides from ECMWF forecasts, Geophys. Res. Lett., 32, L10615.

Drijfhout, S., Heinze, C., Latif, M., MaierReimer, E. (1996), Mean circulation and internal variability in an ocean primitive equation model, J. Phys. Oceanogr., 26, 559–580.

Flechtner, F. (2005), AOD product description document, GRACE 327–750, rev. 2.1, 40 pp., GeoForschungsZentrum Potsdam.

Thomas, M. (2002), Ocean induced variations of Earth’s rotation – Results from a simultaneous model of global circulation and tides, Ph.D. diss., 129 pp., Univ. of Hamburg.

Thomas, M., Sündermann, J., Maier-Reimer, E. (2001), Consideration of ocean tides in an OGCM and impacts on subseasonal to decadal polar motion, Geophys. Res. Lett., 28(12), 2457–2460.

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Wünsch, J., Thomas, M., Gruber, Th. (2001), Simulation of oceanic bottom pressure for gravity space missions, Geophys. J. Int., 147, 428–434.

Regional GRACE gravity determination using L1B data Eicker A., Mayer-Guerr T., Ilk K.-H. Institute of Geodesy and Geoinformation, University of Bonn, Nussallee 17, D-53115 Bonn, Germany E-Mail: annette@geod.uni-bonn.de

Introduction In the approach presented here in a first step a global gravity field represented by a spherical harmonic expansion up to a moderate degree has to be derived. It is then refined by regionally adapted high resolution refinements being parameterized by splines as space localizing base functions. This procedure provides several advantages. The regional approach allows to exploit the individual signal content in the observations and a tailored regularization for regions with different gravity field characteristics. The advantage compared to a uniform global regularization is that the regularization factor is selected for each region individually such that there is no overall filtering of the observations which would lead to a mean dampening of the global gravity field features.

Even within a recovery region different regularization areas with individual regularization parameters can be assigned to take care of the varying signal content. This way it is possible to extract more information out of the given data than would be possible with a global gravity field determination. Areas with a smooth gravity field signal for example can be regularized stronger without dampening the signal, and in areas with strong high frequency signal no unneccessary dampening has to be performed.

Furthermore, besides a high resolution static gravity field, GRACE enables the recovery of temporal gravity variations as well. These temporal variations are often regional phenomena, thus a regional representation seams reasonable.

Regional gravity field recovery The functional model applied to the regional analysis of the original GRACE data is described in Mayer-Gürr 2006. The parameterization of the potential is performed in terms of spherical harmonics for the global solution, in case of a regional gravity field recovery the potential has to be parameterized by space localizing base functions. It can be modeled as a sum of base functions as follows I

V ( rP ) = ∑ ai φ ( rP , rQi ) , i =1

with the field parameters ai arranged in a column matrix and the base functions R  Φ ( rP , rQi ) = ∑ kn  E   r  n=0 N

n +1

Pn ( rP , rQi )

The coefficients kn are the degree variances of the gravity field spectrum to be determined, M

2 2 kn = ∑ ( Δc nm + Δsnm ) m=0

RE is the mean equator radius of the Earth, r the distance of a field point from the geo-centre and Pn (rP, rQi) are the Legendre’s polynomials depending on the spherical distance between a field point P and the nodal points Qi of the set of base functions. With this definition the base functions can be interpreted as isotropic and homogeneous harmonic spline functions (Freeden et al. 1998). The nodal points are generated on a grid by a uniform subdivision of an icosahedron of twenty equalarea spherical triangles. In this way the global pattern of spline nodal points Qi shows approximately uniform nodal point distribution.

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Regionally adapted regularization Due to the ill-posedness of the downward continuation process the solution has to be regularized. Here the Tikhonov regularization has been applied and the regularization parameter has been determined by means of variance component estimation as proposed by Koch and Kusche 2002. The process of variance component estimation delivers the optimal regularization parameter under consideration of the given signal to noise ratio. In case of a regional gravity field determination this results in one regularization parameter optimally tailored to the respective region. This is an improvement in comparison to a global gravity field parameterization which allows only one regularization factor for the complete Earth resulting in an overall mean damping of the gravity field features. But even within smaller geographical areas the gravity field features may vary significantly. Therefore it seems reasonable to further adapt the regularization procedure. The proposed approach takes not only one regularization matrix with one associated regularization parameter per region into account but allows several matrices with respective parameters: N=

1

σ

2 e

AT PA +

1

σ

2 x1

R1 + … +

1

σ 2xn

Rn .

For each regional regularization group i the regularization matrix Ri is a diagonal matrix that contains a one for each regional spline parameter located inside this particular region and a zero for parameters belonging to basis functions outside the regularization group.  1 for R ( j, j ) =  0 for

j inside i j outside i

The original identity matrix as applied in the Tikhonov regularization process has thus been divided into single diagonal matrices according to the membership of the respective unknown parameters to the different regularization groups.

feature of a field parameterization by space localizing basis functions, as each unknown parameter is related to a particular geographical. This is an inevitable premise when the elements of the regularization matrix are supposed to be assigned to a certain region.

As mentioned above the regional solutions are calculated as refinements to a global gravity field. This global reference field is commonly represented by spherical harmonics and the regional solution, represented by space localizing splines, models the residual gravity field.

Presented in this paper are two different calculations. In the first one the EGM96 was chosen as global reference field and regional refinements have been calculated from one month of GRACE data. The calculation of monthly solutions has the advantage that a solution determined from more data (and thus assumably higher accuracy) can serve as comparison and accuracy measures can be obtained. For this one-month solution the resolution as defined by the grid of spline nodal points corresponds to a spherical harmonic degree of Nmax = 140 which results in approximately 153km nodal point distance. The spline kernel was expanded up to this maximum degree as well. In the second calculation the global gravity field ITG-Grace02s (MayerGürr 2006) served as reference field and a high resolution regional refinement was determined from 4.5 years of GRACE data. Its resolution can be compared to a maximum spherical harmonic degree of Nmax = 170, the spline point distance averages about 126 km.

In the same calculation step a lower resolution time variable regional gravity field was calculated from the same data set. Therefore a second set of spline kernels was introduced, the shape of the kernel and the grid pattern corresponding to Nmax = 170. To represent the time variabilities the spline coefficients ai were assumed to be time variable and a trend and a yearly period was estimated.

R1 + … + Rn = I The possibility of adapting the regularization procedure in this particular way is a unique

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Monthly solution Fig. 1 shows the differences between the regional solution calculated from one month

Figure 1: Differences of monthly solution compared to the ITG-Grace02s, Nmax = 140: One uniform regularization (left, RMS: 16.51 cm) versus two adapted regularization parameters for land and ocean areas (right, RMS: 12.86 cm)

Figure 2: Temporal gravity field variations: Yearly period in the Mekong delta (left) and the effect of the SummatraAndaman Earthquake (right)

of data for the area of the Andes compared to the ITG-Grace02s. The global gravity field ITGGrace02s was calculated from 3 years of GRACE data, therefore it is expected to be of superior accuracy and is used as reference solution. On the left hand side one uniform regularization parameter was determined for the region and in on the right hand side the regularization procedure was adapted by calculating two different parameters, one for the ocean area and one for the continental areas.

The introduction of the additional regularization area improves the RMS significantly from 16.51 cm to 12.86 cm.

For several applications a global gravity field model represented by spherical harmonics without losing the details of a regional zoomin proofs to be useful. When regional refinements cover the complete surface of the Earth, the spherical harmonic coefficients can be calulated in a stable computation step, in

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principle up to an arbitrarily high degree, by means of quadrature methods. In our approach we make use of the GaussLegendre-Quadrature. More details concerning the combination of regional gravity field solutions can be found in Eicker et al.(2006).

References Eicker A, Mayer-Guerr T, Ilk KH (2006), An Integrated Global/Regional Gravity Field Determination Approach based on GOCE Observations. Observation of the Earth System from Space, Springer, Berlinâ&#x20AC;&#x201C;Heidelberg.

Timevariable gravity field As described above in one simultaneous recovery step the high resolution stationary gravity field was estimated together with a lower resolution timevariable gravity field from 4,5 years of GRACE data. The calculations were performed for the Mekong delta area. The left hand side of Fig.2 shows the yearly amplitude of the gravity field signal in this area. The right hand side of Fig.2 illustrates the gravitational effect of the Summatra Andaman Earthquake in December 2004. Displayed are the differences between a gravity field calculated from 2 years of data before the Earthquake and a gravity field originating from data of 2 years after the incident. The differences in the gravity signal due to mass displacements in the area of the Earthquake become obvious.

Freeden W, Gervens T, Schreiner M (1998), Constructive Approximation on the Sphere.

Oxford University Press, Oxford.

Conclusions The regional recovery approach presents very promising results, in the case of a static high resolution gravity field as well as for the task of calculating gravitational time variablilities. In this case the individual adaption of the regularization process has to be pointed out as it allows a tailored filtering according to the regional gravity field features and therefore improves the regional refinements significantly. If neccessary a global spherical harmonic solution can be derived as well, in this context the combination of regional solutions to a global gravity field solution seems to be a reasonable alternative to deriving a global gravity field solution directly. It was shown that timevariablities can be detected by regional recovery methods as well. As especially many of the temporal variations take place on a regional scale, a regional modelling of those phenomena seems particularly reasonable.

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Koch K.R. and Kusche J (2001). Regularization of geopotential determination from satellite data by variance components. Journal of Geodesy 76 (5):259â&#x20AC;&#x201C;268.

Mayer-Guerr T, (2006), Gravitationsfeldbestimmung aus der Analyse kurzer Bahnboegen am Beispiel der Satellitenmissionen CHAMP und GRACE, Dissertation University of Bonn, http://hss.ulb.uni-bonn.de/diss\_online/landw\_fak/2006/mayer-guerr\_torsten

Results from increase of the temporal resolution of the AOD1B products Flechtner F. GFZ Potsdam, Department 1 »Geodesy and Remote Sensing«

Introduction Short-term tidal and non-tidal mass variations on sub-daily to annual time scales caused by mass redistributions in the Earth’s subsystems, i.e. the atmosphere, the oceans, the hydrosphere or the cryosphere are aliased into the mean GRACE gravity field solutions if not corrected properly. To eliminate short-period nontidal atmospheric and oceanic mass anomalies from monthly mean GRACE gravity estimates the AOD1B (Atmosphere and Ocean De-aliasing Level-1B) RL04 (release 4) product was developed within the project »Improved GRACE Level-1 and Level-2 products and their validation by Ocean Bottom Pressure« which is based on 6-hourly ECMWF (European Center for Medium-range Weather Forecasts) Integrated Forecast System meteorological data and output from the baroclinic ocean model OMCT (Ocean Model for Circulation and Tides, Thomas et al., 2001). AOD1B RL04 products are provided as 6-hourly spherical harmonic gravity time series up to degree and order 100 and are related to a bi-yearly 2001 + 2002 mean field. These products are also used within the latest GRACE Science Data System RL04 gravity field reprocessing. Further details can be found in Flechtner, 2007.

Within GFZ GRACE Precise Orbit Determination, which is usually performed with 5s integration step size, the 6-hourly AOD1B products are treated as follows: First, the atmospheric tide, which is included in the ECMWF pressure data and thus in the atmospheric part of the AOD1B, is removed after reading of the coefficients using the model of Biancale and Bode (2006) to avoid double-bookkeeping

with the atmospheric tide correction (again using the Biancale and Bode model) applied every integration step size during POD. Secondly, these 6-hourly »atmospheric-tide free« AOD1B spherical harmonics are then linearly interpolated to the 5s integration time steps to be used in POD as disturbing force besides other sources such as static gravity field, atmospheric tides, Earth and ocean tides, accelerometer measured non-gravitational forces etc.

The OMCT component of the atmosphere and ocean combined AOD1B product has been generated with a surface pressure forcing where the S2-tide (the dominant component of the atmospheric tides) has been reduced using a strategy suggested by Ponte and Ray (2002). This avoids double-bookkeeping with the atmospheric part of the ocean tide model S2 constituent during POD. An interesting question, which has been investigated within this project, is, if there could be any benefit if the AOD1B 6-hourly temporal resolution could be further increased.

ECMWF 6-hourly analysis versus 3-hourly forecast data Besides the operational (with only 2–3 days delay) 6-hourly analysis data used to generate the AOD1B products, ECMWF also provides daily updated 10-days forecast data. Here, the first three days have a 3-hourly resolution; the rest is provided on a 6-hourly time scale. Generally, the differences between the two data sets at 6-hourly (0, 6, 12 and 18 hours) time steps are very small (less than 0.2 mm in terms

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of geoid heights) but the differences at intermediate time steps (3, 9, 15 and 21 hours) based on linear interpolation and direct observation show a clear S2 tide signal with an amplitude of about 1.5 mm in terms of geoid heights which cannot be tracked by the 6-hourly sam-

pling of the analysis data. But, as stated above, this signal is corrected for during POD using the Biancale and Bode atmospheric tide model. Nevertheless, any real 3-hourly data could show some advantages w.r.t. a pure model correction.

Table 1: GPS phase, GPS code and K-band range-rate residuals for August 1, 2003 using different combinations of AOD1B products and atmospheric tide corrections

Figure 1: Simulation study result showing the current GRACE error level, the pre-launch GRACE baseline accuracy and the error when neglecting an atmospheric S2 tide correction, both with and without adjustment of accelerometer (ACC) and K-band range-rate (KRR) parameters (in [mm] geoid height)

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Gravity field determination using 6-hourly and 3-hourly AOD1B products In the next step alternative 3-hourly RL04 AOD1B products for August 2003 and February 2004 have been calculated which are based, both in the atmospheric and in the oceanic contribution, on forecast data and then precise orbits and gravity fields were derived which differ only by the applied dealiasing product (standard 6-hourly or alternative 3-hourly temporal resolution).

The result is that no difference can be seen in the resulting K-band and GPS observation residuals, in the comparisons with external gravity functionals (e.g. NIMA gravity anomalies or CLS01-ECCO derived oceanic geoid) or in the resulting GRACE geoids even if no atmospheric tide model is used to compensate for the interpolation error. Also, the AOD1B caused accelerations are below 2 · 10–9 m/s2 and the resulting orbit differences are below an mm in all three directions. As an example the following table shows the GPS phase, GPS code and K-band range-rate residuals for August 1, 2003 for all 4 combinations (6hourly/3-hourly time resolution and with/without S2 atmospheric tide correction).

This surprising result is confirmed by a simulation study which is performed in parallel within this project (see Meyer and Frommknecht »GRACE simulation study«). Figure 1 shows the GRACE baseline accuracy as simulated before launch and the present GRACE error level introduced to the simulations, which is about a factor of 15 higher. Between these two curves the error when neglecting the S2 atmospheric tide (without and with (as applied in the regular GRACE processing) adjusting for accelerometer and K-band parameters) is shown. Both curves are well below the current GRACE error level and thus, if no other improvements towards the GRACE baseline will be implemented, »GRACE is not able to see these small signals«.

the applied Bode and Biancale atmospheric tide model corrects the S2-type signal in the interpolated 6-hourly AOD1B products sufficiently. This is due to the fact that this model is based on 6-hourly and 3-hourly ECMWF surface pressure data, Additionally, at the present level of accuracy, GRACE does also not »see« the influence of the atmospheric tide, e.g. this disturbing force could even be neglected!

References Biancale R and Bode A (2006) Mean annual and seasonal atmospheric tide models based on 3-hourly and 6-hourly ECMWF surface pressure data, Scientific Technical Report STR06/01, GeoForschungsZentrum Potsdam, Potsdam Flechtner F (2007) AOD1B product description document, Version 3.1, GRACE Project Document JPL 327-750, http://isdc.gfzpotsdam.de/grace, Last accessed October 10, 2007 Thomas M, Sündermann J, Maier-Reimer E. (2001) Consideration of ocean tides in an OGCM and impacts on subseasonal to decadal polar motion excitation. Geophys Res Let, 12, 2457 Ponte R and Ray R (2002) Atmospheric pressure corrections in geodesy and oceanography: A strategy for handling air tides. Geophys Res Let, 29(6)

To conclude, a higher temporal resolution of the AOD1B product is not necessary because

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GRACE gravity field models using alternative L1B data (WP120) Frommknecht B. (1), Meyer U. (2), Schmidt R. (2), Flechtner F. (2) (1) Technische Universität München, Institut für Astronomische und Physikalische Geodäsie (2) GeoForschungsZentrum, Department 1: Geodesy and Remote Sensing

Introduction The current performance of the gravity field models derived from GRACE data is unprecedented, but does still not reach the predicted baseline. Among others, a sub-optimal signal processing of the sensor data could be the reason for the degraded performance.

In this study the processing of the raw instrument data – so called L1a data – to the data level that is used for the gravity field model determination – so called L1b data – is investigated. The sensors, that are mainly relevant for the gravity field model determination, are the GPS receiver, the Kband measurement system, the accelerome-

ter and the star sensor. Our analysis focuses on the latter three. First results are available for the processing of the K-band data, concerning the star sensor data and the accelerometer data, we will give an outlook on future work.

K-band data processing Figure 1 shows an overview of the applied processing steps. We focus on the application of the low-pass filter.

During this processing step a low-pass filter is applied to the principal measurement of the Kband system, the inter-satellite biased range, to reduce its bandwidth from 10 Hz to 0.2 Hz.

Figure 1: Overview of the processing steps applied to the L1a K-band data

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In addition, the inter-satellite range rate and range acceleration are derived by application of the first respectively second order derivative of this filter. The official data processing conducted by the Jet Propulsion Laboratory (JPL) in Pasadena foresees the use of a CRN-class digital filter that evolves from a repeated self convolution of a rectangle in the spectral domain, the convoluted rectangle filter. The filter we propose is designed using the window method. The chosen window function is

the Kaiser window, therefore the filter is designated as Kaiser filter. Figure 2 shows a comparison of both filters in terms of the absolute filter error magnitude.

The absolute filter error magnitude is derived by multiplication of the filter error with the signal that is to be filtered. The error of the convoluted rectangle filter is below the instrument error specification except for frequencies close to the cut-off frequency of the filter and

Figure 2: Comparison of the convoluted rectangle filter and the Kaiser filter

Figure 3: Root PSD of the L1b range rate

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around the frequency of 1–2 × 10–4 Hz. The Kaiser filter error is significantly smaller, but at the cost of an increased filter length of 140.7 seconds compared to the filter length of the convoluted rectangle filter of 70.7 seconds. An increased filter length leads to increased data loss in case of gaps.

Gravity field model determination results The two different K-band datasets were evaluated at GFZ. They were complemented with standard JPL-processed accelerometer, star camera and GPS observations and in a preprocessing step two combined observation files were created. During the split-up of the data into daily arcs a major difference to the JPLdata became apparent. While the standard Kband data contains about 70 gaps due to phase breaks per month, the alternative data contains more than 600 gaps. The reason lies in the fact that for both alternative data sets no gaps were closed by interpolation. After each gap, the derived range bias takes on a different value than before the gap. Therefore new K-band instrument parameters have to be estimated. Moreover four days of alternative data had only very little or no observations at all.

Another aspect to consider is the selection of the cut-off frequency of the low-pass filter.

Figure 3 shows the root PSD of the range rate, which is the observable that is mainly used for the gravity field model determination. We notice that starting at about 2–3 × 10–2 Hz, a signal-to-noise ratio of one is reached. At higher frequencies, noise dominates the measurement. In addition there are spikes visible at 4 × 10–2 Hz and 8 × 10–2 Hz. We suggest therefore to reduce the measurement bandwidth, at least for the determination of monthly gravity fields. The advantage of the reduced bandwidth would be a smoothing of the measurement.

Then daily orbits were computed for the two GRACE satellites using the alternative observations files. The RMS residuals from the orbital fit of the range rate observations of the first data set dropped slightly from 0.32 my/s to 0.29 my/s compared to standard JPL data. This is probably due to the increased number of K-band instrument parameters. In case of the data with the reduced bandwidth the RMS dropped signifi-

The data set we used for the generation of the alternative L1b data comprises one month of data from August 2003. The properties of the two different K-band data sets we provided to GFZ are summarized in table 1.

Table 1: Properties of the delivered K-band data sets

Data set number

Filter type

Filter cut-off frequency

1

Kaiser (140.7 seconds)

0.1 Hz

2

Kaiser (300.7 seconds)

0.02 Hz

Table 2: Comparison of the gravity field models derived from different data sets

CLS-ECCO wrms in [m]

Data set

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NIMA96 wrms in [mGa]

10°

5°

3°

10°

5°

3°

JPL

0.117

0.147

0.283

0.314

1.558

4.580

1

0.117

0.149

0.289

0.314

1.607

4.675

2

0.117

0.149

0.289

0.314

1.609

4.672

cantly to 0.24 my/s since the observations are smoother than the standard ones.

From the GPS- and K-band range rate residuals daily normal equations for gravity field coefficients were computed. The days missing in the alternative data sets were filled with normal equations from the standard processing to cover a comparable time span. The normal equations were accumulated and a monthly gravity field model was estimated for each data set. To evaluate the gravity field models, they were compared to altimeter data as well as an ocean circulation model. The global fit of these comparisons is nearly identical for both alternative data sets, see table 2. The difference to the gravity field model derived from the JPL data seems not to be significant.

The comparison of alternative models with the model derived from the JPL data at geoid level reveals stripes that probably resemble the satellite ground tracks. Further investigation is needed before a final conclusion regarding the quality of the alternative data sets can be drawn.

Conclusions Both alternative data sets provide almost identical results, therefore it seems that the reduction of the data bandwidth has not effect, at least for monthly derived gravity field models.

The difference to the model derived from the JPL data seems not to be significant, meaning that the alternative data is comparable to the JPL data in terms of data quality. The data quality improvement through the application of the Kaiser filter seems not to be exploitable for this data set.

Outlook Star sensor data: On each satellite, there are two star sensor camera heads delivering the orientation of the satellite. During the standard processing, the data from both heads is combined to derive the orientation of the satellite. The accelerometer measurements also provide information about the orientation of the satellite in terms of the angular acceleration. In general the data quality of the star sensor is better at low frequencies, while that of the accelerometer is better at high frequencies. A prototype for the combination of both data has been developed, but further research is necessary before it is operational. Another aspect to be considered are Sun or Moon intrusions that deteriorate the data quality of the affected sensor head. It would be useful to include an appropriate weighting algorithm to the data processing.

Accelerometer data: At high frequencies the accelerometer data is affected by the so-called peaks and twangs.

The elimination of these effects by modeling them can improve the accelerometer data quality. The effect on the derived gravity field models is to be investigated.

However, we think it is sensible to extend the data set at least to two or more months of data to investigate the effect of the alternative processing methods on gravity field models derived from data sets spanning more than one month.

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GRACE validation using in-situ Ocean Bottom Pressure data Macrander A., Böning C., Boebel O., Schröter J. Alfred-Wegener Institut für Polar- und Meeresforschung, Bremerhaven, Germany, E-Mail: Andreas.Macrander@awi.de, Fax: +49 471 4831 1797)

Abstract In order to validate oceanic mass transport variability from GRACE satellite gravity measurements, the GRACE data is compared with in-situ measurements of ocean bottom pressure (OBP) provided by Pressure Sensors/ Inverted Echo Sounders (PIES) located at the sea floor. An OBP database has been established at AWI containing in-situ time series from the Southern Ocean, tropical Atlantic, Arctic Ocean and Pacific Ocean.

The comparison with GRACE reveals good agreement at many locations, particularly in high latitude regions, where high oceanic variability and denser satellite coverage improves the signal-to-noise ratio. In contrast, correlation in tropical regions is still lower. Recent GRACE RL04 products and GAC/GAD de-aliasing models provided by GFZ and CSR show improvements in both signal amplitude and correlation at the majority of locations.

1. Introduction The GRACE satellite mission provides monthly estimates of the gravity field of the Earth. Differences between the monthly solutions are induced by mass redistribution across the Earth. On the continents, the hydrological cycle generates the largest signals, which are readily observed by GRACE. Over the oceans, however, gravity field changes are about an order of magnitude smaller, close to the accuracy limits of the present GRACE solutions. Nevertheless, GRACE measurements may prove as an important tool to obtain integral estimates of water mass redistribution, sea level changes and geostrophic current variabili-

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ty. In order to validate and improve the gravity field products, GRACE solutions must be compared against ocean models and in-situ observations of Ocean Bottom Pressure (OBP).

A dedicated array of OBP sensors, optimized for GRACE in-situ comparisons, was deployed

by AWI in the Southern Ocean. The array’s concept, technology and available time-series are discussed here. Data from this array, as well as time series from other OBP sensors deployed by cooperating institutions at different locations in all oceans are included in an OBP database that has been established at AWI. OBP time-series from different regions are compared with all available GRACE solutions provided by CSR, GFZ, GRGS, ITG and JPL. The improvements made by recent GRACE releases are evaluated.

2. Ocean Bottom Pressure recorder – Technology and Work at Sea (WP 410) Ocean Bottom Pressure data is an integral measure of the overlying oceanic and atmospheric mass at any given location. It can be measured by Bottom Pressure Recorders (BPR) or Pressure sensor equipped Inverted Echo Sounders (PIES) deployed at the sea floor.

To facilitate a head-start of the data analysis within the project’s time frame, PopUp buoys were developed with the PIES. On 24 Apr 2007, the first PopUp surfaced, that retrieved 6 months of recent PIES time series. Extensive sea-trials near Helgoland carried out in Feb and Aug 2007 proved the reliability of the autonomous underwater release mechanism, and the data transmission under all current and weather conditions.

Figure 1: PIES array in the ACC region. Large symbols show past, present and future PIES deployments by AWI, respectively. Small crosses denote proposed additional PIES positions (see Garzoli, 2007). TOPEX/Poseidon – Jason altimetry groundtracks shown as curved lines. Bathymetry: ETOPO 5

In the framework of this project, an array of 9 PIES has been deployed in the Antarctic Circumpolar Current (ACC) by R/V Polarstern from 2002 to 2006 (Fig. 1). The region was chosen due to its high, mostly barotropic, OBP variability, which provides a high signal-tonoise ratio for GRACE validation. A better quality GRACE data set can be expected there as the region is far away from any continents where the hydrological cycle may mask the oceanic signal, and due to the denser satellite coverage at high latitudes, The 2-dimensional layout was optimized by a spatial coherence analysis. This study revealed a 2000 x 2000 km area of coherent OBP variability in the Atlantic sector of the Southern Ocean, both in the GRACE data (Fig. 2) as well as in the numerical FESOM model (see WP 450, Böning et al., this volume). This situation is apt for comparisons between in-situ point

measurements and large-scale smoothed GRACE data. All moorings are located at TOPEX/Poseidon and Jason satellite crossover points to allow for additional PIES/satellite altimetry comparisons.

At present, time series of two PIES deployed from 2002–2005 are available; results of the GRACE / in-situ validation are discussed below.

Time series from the 2-D array are expected for 2008, when several PIES will be exchanged

by R/V Polarstern and G.O.Sars. Relocated funding by BMBF allows to extend the ACC array farther to the south (Fig. 1), and to deploy several new PIES/PopUp systems. These PopUps will provide regular updates of the time series independent of infrequent research vessel cruises, while the PIES remain on the sea floor until 2011/2012 to obtain uninterrupted multiyear OBP time series over the entire GRACE mission period.

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Table 1: OBP data contained in database as of 12 Oct 2007. For locations, see global maps in WP 450 (Böning et al., this volume)

Region

Project

Institute, PI

Framstrait 79° N

ASOF-N/Damocles

AWI, A. Beszczynska-Möller

ACC 45–50° S

GRACE

AWI, O. Boebel

Tropical Atlantic 16° N

MOVE/GRACE

IFM-GEOMAR, J. Karstensen

Kerguelen

IFREMER, P. LeGrand

Southern Ocean, Drake Passage

GLOUP, POL-ACCLAIM

POL, C. Hughes

Pacific (also Atl. & Indian Oceans)

NOAA-DART, NDBC

NOAA, C. Meinig

3. OBP Database – Data Processing and Evaluation (WP 420) To assess the performance of GRACE to measure oceanic mass transport changes, a global validation against in-situ OBP time series from all different parts of the world oceans is essential.

In 2006/7, all available data have been included in an OBP database maintained at AWI (Table 1).

At present, the database contains time series from 85 mostly year-long deployments at 38 different locations. Quality controlled data that take account for measurement errors and sensor drifts are available for GRACE validation upon request. The database shall be extended further to include more time series from other projects and regions.

4. Validation of Gravity Fields against OBP – in-situ Time Series (WP 440) The comparison of the most recent GRACE GFZ RL03 GSM+GAD monthly solutions with in-situ OBP data reveals moderate to good agreement both in amplitude and phase at most locations, with correlation levels reaching 0.7 to 0.9 in many places (see also WP 450, Böning et al., this volume). In particular, at high-latitude sites, where monthly oceanic RMS variability exceeds 0.05 dbar, GRACE captures real oceanic mass changes.

As a typical example, Fig. 2 shows good agreement between in-situ and satellite observations in Framstrait at 79° N 03° E.

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The correlation between in-situ data and GRACE is 0.55 for GFZ RL03 GSM + GAC. Due to improved data processing and reduction of short-term noise, RL04 GSM + GAC raises the correlation to r = 0.70. Even better performs the ocean-optimized RL04 GSM + GAD solution (r = 0.76). Here, the land mask in the GAD model might have reduced possible leakage from the nearby Greenland ice shield. It is also evident, that the GAC/GAD ocean/atmosphere de-aliasing model alone does not reproduce the observed OBP variability (Fig. 2); the actual GRACE gravity observations (GSM geoid) are essential to obtain realistic estimates of the oceanic mass transport variability. In the Southern Ocean, similarly high correlations were found in the ACC array (Fig. 1 and Böning et al., 2007) and the Kerguelen region (Rietbroek et al., 2007).

In the tropics, OBP variability is much smaller (O(0.01 dbar)). Here, GRACE gravity estimates display unrealistically high variability. This agrees with earlier findings of Kanzow et al.

(2005). However, noise levels and unrealistic annual cycles are reduced and correlations are improved by the most recent GRACE solutions (not shown).

For the global validation, all in-situ OBP time series were compared with all available GRACE products provided by CSR, GFZ, JPL, ITG and GRGS. On a global scale, the average correlation with in-situ OBP observations is significantly im-

Figure 2: OBP anomalies from three subsequent PIES deployments in Framstrait (AWI, data: A. Beszczynska-Möller).

Comparison with GRACE solutions from GFZ (upper panel) and CSR, GRGS, ITG and JPL (lower panel). All GRACE data calculated using degree/order 2–50, 750 km Gauss filter smoothing

proved by the recent RL04 GSM + GAD products. This holds both for GFZ and CSR products, although the overall performance of GFZ appears to be slightly better at most places.

The overall performance of the JPL and ITG solutions is in a similar range. The GRACE solution provided by GRGS, however, performs best at most sites (Fig. 2) and also in global average. This might be attributed to the different data processing and 10day time axis with running monthly means applied by GRGS. In each correlation analysis, there are some ground-truth sites with low or even negative correlation. Some of these lie in regions where GRACE is apparently unable to capture the real oceanic variability (e.g. tropical Atlantic, Kanzow et al., 2005). For the other sites, further evaluation is necessary to identify potential OBP sensor errors, de-aliasing model errors or GRACE deficiencies.

Possible deviations due to the different spatial scales of in-situ point measurements and the large-scale smoothed GRACE data need to be determined by the analysis of spatial correlation patterns in GRACE and numerical

ocean model (FESOM, WP 450, Böning et al., this volume).

Conclusions At the majority of ground-truth sites, good agreement between in-situ OBP time series and GRACE gravity field solutions is found, in particular at high latitudes. The most recent GRACE product releases reveal significant improvements, although regions exist where GRACE amplitudes are still unrealistically high.

The OBP database shall be extended to cover also large areas that are only sparsely covered by the present dataset. Multi-year OBP time series that span the entire GRACE mission period prove extremely valuable to validate the space-born gravity measurements and identify regions where GRACE needs to be further improved to obtain reliable satellite-based oceanic mass transport estimates.

References Garzoli, S. (2007) SAMOC Executive Summary.

A monitoring system for heat and mass transports in the South Atlantic as a component of

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the Meridional Overturning Circulation. http://www.aoml.noaa.gov/phod/SAMOC/SA MOC%20Executive_Summary_MAy24.pdf Kanzow, T., F. Flechtner, A. Chave, R. Schmidt, P. Schwintzer, and U. Send (2005), Seasonal variation of ocean bottom pressure derived from Gravity Recovery and Climate Experiment (GRACE): Local validation and global patterns, J. Geophys. Res., 110, C09001, doi: 10.1029/2004JC002772.

Rietbroek R., P. LeGrand, B. Wouters, J.-M. Lemoine, G. Ramillien, C. W. Hughes (2006), Comparison of in situ bottom pressure data with GRACE gravimetry in the Crozet-Kerguelen region, Geophys. Res. Lett., 33, L21601, doi: 10.1029/2006GL027452.

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Global gravity fields from simulated L1-products (WP330) Meyer U. (1), Frommknecht B. (2), Schmidt R. (1), Flechtner F. (1) (1) GeoForschungsZentrum, Department 1: Geodesy and Remote Sensing (2) Technische Universit채t M체nchen, Institut f체r Astronomische und Physikalische Geod채sie

Introduction The GRACE mission is in orbit for more than five years now providing gravity data of unprecedented accuracy. However, the projected pre-launch baseline accuracy of GRACEbased gravity fields has still not been reached.

The purpose of this workpackage is to reconstruct and verify the projected baseline accuracy (which was derived from some simplified analytical approach) based on the dynamic approach using the software and processing strategy applied at GFZ Potsdam for the current GRACE gravity field estimation.

In order to separate the different effects from observation noise, model errors and orbit and instrument parameterization, a closed loop simulation, investigating several principle cases, is performed. In a 1st test series we perform a gravity recovery on the basis of error free observation data in combination with only gravity model errors to get some insight into data combination strategies and study the influences from data gaps and a truncation of the static background model (omission error).

In a 2nd test series, using error-free observation data again and only introducing gravity model errors, we study the impact from the orbit and instrument parameterization, in particular to get an insight into correlations between instrument and gravity field parameters. In the 3rd test series we leave the closed loop scenario and look at some of the suspected background model errors for time-variable gravity field, i.e. errors in the ocean tide models, atmospheric tide model and the so-called atmosphereocean de-aliasing (AOD) models. Finally obser-

vation noise is introduced and some of the experiments repeated in a 4th test series.

In this presentation current results will be shown. In the sequel we use degree variances of the differences of the recovered and the input gravity field as a measure for the error of the recovered model and compare to the projected baseline accuracy.

Closed Loop Simulation We simulate noise free K-band, GPS, star camera and accelerometer observations from GRACE orbits that were integrated using realworld GRACE orbital elements for August 1st, 2003. Accelerometer measurements are derived from the output of non-gravitational force models (drag, solar flux and Earth albedo) along the orbit. For the attitude data the nominal orientation angles along the orbit are used. High-low GPS observations between the GPS sender and the GRACE receivers are simulated using the real-world GPS sender constellation for August 2003.

All data are transformed into the official GRACE Level 1B (L1B) data format to be used

by TU Munich in WP130, where colored noise as defined in (Thomas, 1999) is added for use in the 4th test series. Only the high-low GPS observations, i.e. code and phase measurements of the onboard BlackJack receivers, are contaminated by white noise where we apply a value of 35 cm for code measurements of the ionosphere-free L3 combination and a value of 0.85 cm for phase measurements.

These values are taken from results of the

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Figure 1: Gravity field recovery from error-free observations

orbital fits of our real-world GRACE data processing and may in this way not only represent the accuracy of the receiver measurements but also include other effects (model errors, orbit parameterization, etc.).

For the 1st test series we perform gravity recovery using error-free observations in the presence of only gravity model errors. Here we apply the differences between the two static GRACE-based combination gravity field models EIGEN-CG03C (GFZ) and GGM02C (CSR). The level of the differences is moderate (cf. Fig. 1). In order to accelerate the processing time we limit the maximum degree and order to 70. It can be seen that when using the GPS and the K-band range rate (KRR) observations, the gravity field is well recovered, at least two orders of magnitude better than the claimed baseline accuracy (cf. Fig.1). Even the GPS-only case out performs the baseline up to degree 65.

When K-band range (KRA) observations are included, the recovery is significantly degraded. This may be a hint to numerical effects when evaluating the inter-satellite distance at the Âľm-level using absolute

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satellite positions at nearly 7000km from the origin of the coordinate system at the center of the Earth.

As an extension of this test series we investigate the impact from data gaps and a truncation of the solution space. For the investigation of the latter we increase the expansion of the true gravity field to degree and order 150, which is at the expected sensitivity of the GRACE K-band data. Analyzing a nominal month of data (with a dense ground track coverage, i.e. without repeat orbit patterns) the field up to degree and order 150 is well recovered, cf. Fig. 2. Introducing a data gap of 10% (i.e. 3days), as often experienced in real data analysis, causes no significant degradation of the solution. If, on the other hand, the gravity field is solved only up to degree and order 120 a significant degradation of the solution can be observed: the truncation of the solution space leads to an omission error higher than the baseline accuracy. However, in the presence of observation errors this effect is less dramatic as the observation errors â&#x20AC;&#x201C; in particular from the accelerometers â&#x20AC;&#x201C; dominate the accuracy of the solutions.

Since the computational effort for gravity field estimation is high, all further tests are restricted to simulation and gravity recovery up to degree 70.

Impact of orbit and instrument parameterization In order to compensate systematic errors of the instruments (e.g. biases and scale factors of the accelerometers, clock errors of the

Figure 2: Influence of data coverage and omission error

Figure 3: Influence of instrument parameters

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onboard GPS receivers, low-frequency errors in the K-band measurements introduced by the ultra-stable oscillators (USOs) of the Microwave ranging system) corresponding parameters are estimated in the orbit and gravity recovery process. In the standard processing daily biases and scale factors are estimated for the accelerometers. K-band observations are parameterized by range, range-rate and range-acceleration biases every 90 minutes as well as once per revolution oscillations. Receiver clocks are estimated every 30 seconds. To study potential correlations with gravity parameters in the 2nd test series, a number of runs with noise free observations and different sets of instrument parameters are performed (see Fig. 3). It can be seen that for none of the selected instrument parameterizations a significant degradation of the gravity field solution is obtained. However, it is worth noting that a high correlation between accelerometer and K-band parameters is visible. This fits well to the observation that a dense parameterization of the K-band may be replaced by a dense parameterization of the accelerometer and vice versa.

Figure 4: Influence of model errors

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Impact from background model errors for the time-variable gravity field To determine the residual time-variable gravity field of the Earth using GRACE data, known time variable gravity signals originating e.g. from atmospheric and oceanic tides as well as short time mass variations in the atmosphere and oceans have to be corrected for during the orbit recovery by means of analytic and data-driven models. Any error in these background models will affect the estimation of the gravity field. Currently, deficiencies in ocean and atmospheric tide models as well as the short-term mass de-aliasing models are suspected to contribute to the correlated errors of GRACE-only gravity models showing up as characteristic striping features in global maps of GRACE-derived gravity functionals. In the 3rd test series we considered the following cases: â&#x20AC;&#x201C; Omission of the atmospheric S2 tide signal â&#x20AC;&#x201C; Omission of the atmospheric and oceanic short-term mass variations â&#x20AC;&#x201C; Errors in the amplitudes of ocean tide constituents

As can be seen from Fig. 4 the omission of the S2 atmospheric tide signal causes a much smaller degradation of the solution than the omission of atmospheric-oceanic short-term mass signals. However, the S2 atmospheric tide signal nevertheless has to be included in the background modeling as the deviations are clearly above the GRACE baseline. For the ocean tides an error of about 10% in the amplitudes of the tidal constituents of the FES2004 model also causes a significant degradation of the solution, illustrating the critical impact of model errors in this forcing term.

Impact from noisy observations By means of this 4th series we investigate the contributions from noisy observations. In order to isolate the individual contributions we perform the gravity recovery including only one noise data sets at a time. An exception to this rule is the exploitation of the noisy KRR data which has to be evaluated together with noisy GPS data. As can be seen, accelerometer noise is the dominant error source. This is due to the fact that the accelerometer data, in the current

status of the software, is not treated in the classical sense, but is used as true observation for the non-conservative accelerations in the orbital equation of motion. Hence, the numerical integration typically applied in the dynamic orbit recovery introduces the colored noise from the accelerometer signals into the orbital motion. As it was shown in previous studies this effect is reduced by introducing accelerometer biases (which have to be estimated anyway) but also K-band instrument parameters, reducing the degradation of the solution (cf.

Fig. 5). Since the level of the deviations is still above the GRACE baseline the results could indicate that the selected accelerometer and Kband parameterization is not optimal and needs to be refined. On the other hand iteration could improve the situation.

For the other data sets the impact from colored noise seems to be negligible, i.e. the potential impact is well compensated by the estimated instrumental parameters and the deviations of the obtained solutions are below the GRACE baseline accuracy.

Figure 5: Influence of observation noise

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Conclusions and Outlook Current investigations show that deficiencies in background models for the time-variable gravity field (e.g. ocean tides, atmospheric and oceanic short-term mass variations) may well explain deviations of the quality of the current GRACE-only gravity models. With respect to the impact of instrumental noise the solutions are mostly affected by the colored noise in accelerometer data and a proper parameterization of the accelerometer instrument has to be applied. Since the results indicate that there are no prominent correlations with the gravity field parameters, a denser parameterization may be helpful. Future work will give a special attention to this and will include a combination of all error sources studied so far to allow for a more comprehensive verification of the GRACE baseline accuracy.

Literature Kim, J. (2000): Simulation Study of a Low-Low Satellite-to-Satellite Tracking Mission, Dissertation at the University of Texas at Austin Thomas, J.B. (1999): An Analysis of Gravityfield Estimation Based on Intersatellite Dual-1Way Biased Ranging, JPL Publication 98â&#x20AC;&#x201C;15

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Lithospheric component of GRIMM â&#x20AC;&#x201C; the GFZ Reference Internal Magnetic Model Lesur V., Wardinski I., Rother M., Quesnel Y., Mandea M. GeoForschungsZentrum Potsdam, Telegrafenberg, 14473 Potsdam

Abstract Mapping the lithospheric field over the Earth for wavelengths ranging from 2500 km down to 200 km is only possible from satellite data.

Several models have been proposed over the last few years that cover this full wavelength range, but they appear to be contaminated by noise. We present here the lithospheric component of the GRIMM model. This model was built from a carefully selected data set and by using new techniques of representation. The lithospheric field covers spherical harmonic degrees 16 to 60, and is shown to be reliable up to degree 45 by comparison with the other magnetic field models. Progresses in modeling the external fields of the Earth are necessary in order to resolve properly shorter wavelengths.

Introduction Airborne magnetic survey is a common way of mapping the lithospheric magnetic field for mineral exploration or for studying regional crustal structures. However, because of the involved costs and other technical difficulties, these surveys are of limited extent and the information for wavelength larger 200 km are seldom reliable. As a result, to map the lithospheric magnetic field for wavelengths longer than 200 km, satellite data are needed. At the other end of the spectrum, anomalies with wavelength longer than 2500 km are unknown because the strength of the core field is then much larger than the crustal field amplitude and the contribution from these fields cannot be separated from magnetic data alone. Several models of the lithospheric field and its magnetization were produced from early satellite missions as MAGSAT

(1979â&#x20AC;&#x201C;1980), but significant progress have been made in the recent years with the launch of the German CHAMP satellite.

The main difficulty in dealing with magnetic data arises from the contribution of the magnetic fields generated in the magnetosphere, ionosphere and by Field Aligned Currents (FAC). Of particular concern is the part generated in the ionosphere that is seen as an internal source by satellites. To circumvent these problems one approach is to process (sometimes referred to as filtering) the survey data and to remove, as far as possible, these undesirable contributions. This is the approach used for the MF series of lithospheric magnetic field models. The first of these successful models was the MF1, released in 2002 (Maus et al., 2002). It goes up to Spherical Harmonic (SH) degree 80, and is based on CHAMP scalar magnetic data. The MF2 came one year later and included vector satellite data. It was followed by the version 3 and 4, but none of these models have an acceptable behavior everywhere at the Earthâ&#x20AC;&#x2122;s surface. The MF4x model (Lesur and Maus, 2006), was built from exactly the same data set as the MF4, but the system of representation uses localized functions which allow a varying resolution of the model depending on locations. This new way of regularizing the model lead to a model with an acceptable behavior at ground level. The MF4x model goes up to SH degree 60 at high latitudes and degree 90 at mid and low latitudes. In 2006, the last of the MF series models was released, the version 5 (Maus et al., 2007), providing a SH representation of the lithospheric field up to a maximum degree 100. The data used are scalar and vector

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CHAMP measurements from August 2003 to August 2006. The model has an acceptable behavior at the ground level and was used as the background field for the World Digital Magnetic Anomaly Map (Korhonen et al., 2007). Although the MF5 model is visually striking, we show that this model is contaminated by noise of the order of 20 to 40 nT that consists in East-West oscillations. A lithospheric field model can also be obtained using a comprehensive approach. It consists in modeling as accurately as possible all the main sources of the magnetic field. Even though this approach has been very efficient in providing accurate models of the core magnetic field, it has been less successful regarding the lithospheric field. However, by comparison between models, it is clear that this approach leads to robust estimation of the lithospheric field. We present here the lithospheric component of the GRIMM magnetic field model (Lesur et al., 2007) and compare this model with the xCHAOS model (Olsen and Mandea, 2007) and the MF5 model (Maus et al., 2007).

In the next section we present the data selection technique used in order to minimize the noise due to the magnetic fields generated by external sources. The third section is dedicated to the presentation of the obtained lithospheric field. We conclude in the last section.

Data selection As we are not able to accurately model the rapidly time varying magnetic fields generated

in the ionosphere and magnetosphere, a necessary first step for modeling the lithospheric field is a data selection process. This selection process tends to minimize, in a given data set, contributions of un-modeled sources. Dst as well as Kp indices are traditionally used in the data selection process, where one selects magnetic survey data only during local night time, and when the corresponding Dst and Kp indices are small. Certainly, in the present era, there are many more, readily available, geomagnetic and solar wind activity indicators. A review of how these can be used is given in Thomson and Lesur (2007). The above indicated criteria have proved to be appropriate for models of the core field however, for models of the lithospheric field these are not sufficient.

We therefore apply here two further technique: 1. at high latitudes, satellite data are selected at all local times; 2. at mid and low latitudes, the vector magnetic component along the dipole axis is rejected.

Selecting the data at all local times at high latitudes significantly improves the separation between ionospheric fields and the lithospheric field simply because the lithosphere rotates with the Earth in the Solar Magnetic system of coordinates whereas the ionospheric field is nearly static (i.e. it does not present significant time periodicities over several days). At mid and low latitudes the vec-

Figure 1: Left panel: Power spectrum of three lithospheric magnetic models GRIMM, xCHAOS and MF5. Right panel: Coherency for the same three models

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Figure 2: Upper panel: Lithospheric component of the GRIMM model plotted at Earthâ&#x20AC;&#x2122;s reference radius and truncated to spherical harmonic degree 45. Lower panel: Difference with MF5 model truncated to the same maximum degree

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tor magnetic component aligned with the dipole axis clearly has the highest level of noise. By rejecting data in this direction, it is still possible to determine in a unique way the field generated in the lithosphere (Lesur et al., 2007), and the dataset presents a much lower level of noise. This selection technique, however, does not resolve all problems because sectorial Gauss coefficients at high spherical harmonic degrees are controlled by the vector magnetic component in the East direction. These sectorial coefficients remain the most noisy coefficients in all lithospheric magnetic field models.

Lithospheric field model Figure 1 presents the power spectrum (i.e. energy as a function of the spherical harmonic degree) and the degree correlation of the GRIMM model, the xCHAOS model and the MF5 lithospheric model for degrees 16 to 60, all computed at the Earth’s reference radius (6371.2 km). Both GRIMM and xCHAOS models are focused on the core field.

We observe nonetheless that they present similar spectra and high correlation up to SH degree 45. This is an improvement compared to the correlation between CHAOS (Olsen et al., 2006) and the BGS/G/L/0706 model (Thomson and Lesur, 2007) and it clearly shows that not only the MF5 lacks power but also presents spurious features at these low degrees. When the differences between xCHAOS and GRIMM are mapped, they do not exceed 20 nT and stay below 10 nT at mid and low latitudes. Therefore, we are confident that the lithospheric field model of GRIMM for spherical harmonic degree from 16 to 45 is robust. The model is mapped in Figure 2. This figure also presents the differences between GRIMM model and the MF5 models. These differences are relatively large (up to 40 nT) and have the characteristic shape of spurious anomalies generated by along track filtering. This step in the MF5 process is probably not directly related to the lack of power in the MF5 model, but is due to some other part of its data processing (Thebault et al., 2007).

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Conclusion We briefly presented and discussed the lithospheric component of the GRIMM model. The resolution may not be as high as the MF5, but the noise level is low enough making further interpretation work possible. The model proves to be reliable at least up to spherical harmonic degree 45. Above this limit the level of noise in the model is uncertain. Further improvements in lithospheric magnetic models are expected if the recent progresses in understanding the external fields behavior are integrated in the modeling process.

Acknowledgments We would like to acknowledge CHAMP mission operated and supported by GeoForschungsZentrum Potsdam, and to thanks the institutes and observatories providing data and indicies. This work was done with the financial support of GEOTECHNOLOGIEN project 03F0442A. References Korhonen, J., Fairhead, J., Hamoudi, M., Hemant, K., Lesur, V., Mandea, M., Maus, S., Purucker, M., Ravat, D., Sazonova, T., and Thebault, E. (2007). Magnetic anomaly map of the world. Commission for Geological Map of the World. 1st Edition.

Lesur, V. and Maus, S. (2006). A global lithospheric field model with reduced noise level in the polar regions. Geophysical Research letters, 33(L13304). doi: 10.1029/2006GL025826.

Lesur, V., Wardinski, I., Rother, M., and Mandea, M. (2007). GRIMM – the GFZ reference internal magnetic model based on vector satellite and observatory data. Geophys. J. Int. Under minor-revisions.

Maus, S., Lühr, H., Rother, M., Hemant, K., Balasis, G., Ritter, P., and Stolle, C. (2007).

Fifth-generation lithospheric magnetic field model from CHAMP satellite measurements.

Geochem. Geophys. Geosyst., 8(Q05013). doi: 10.1029/2006GC001521.

Maus, S., Rother, M., Holme, R., Lühr, H., Olsen, N., and Haak, V. (2002). First scalar magnetic anomaly map from CHAMP satellite data indicates weak lithospheric field. Geophys. Res. Lett., 29(14). doi: 10.1029/2001GL013685.

Olsen, N., Lühr, H., Sabaka, T., Mandea, M., Rother, M., Tøffner-Clausen, L., and Choi, S. (2006). Chaos – a model of the earth’s magnetic field derived from CHAMP, Oersted, and SAC-C magnetic satellite data. Geophys. J. Int., pages 1– 200.

Olsen, N. and Mandea, M. (2007). Rapid changing flows in the earth’s core. in preparation.

Thebault, E., Lesur, V., and Hamoudi, M. (2007). The shortcomings of the along-track satellite filtering in geomagnetism. Geophys. J. Int. Submitted.

Thomson, A. and Lesur, V. (2007). An improved geomagnetic data selection algorithm for global geomagnetic field modelling.

Geophys. J. Int., 169: 951–963. doi: 10.1111/j.1365-246X.2007.03354.x.

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World Digital Magnetic Anomaly Map. GAMMA – the GFZ contribution Mandea M. (1), Lesur V. (1), Rother M. (1), Quesnel Y. (1), Hamoudi M. (2), Thébault E. (3) (1) GeoForschungsZentrum Potsdam (2) Université des Sciences et de la Technologie H. Boumediène Algiers (3) Institut de Physique du Globe de Paris

Abstract Combing the magnetic surveys data from disparate platforms (marine, ground, aeromagnetic and satellite) has aimed to realise the World Digital Magnetic Anomaly Map (WDMAM), 1st edition. Existing regional grids and, when available, individual surveys, have been merged to give a more uniform spatial variation of the magnetic anomalies. The effects of merging the grids have been examined by plotting profiles and difference maps of the overlapping regions. A global map, one of the candidate map to WDMAM was proposed by the GFZ team. Forthcoming availability of new datasets, as well as improvements in the modeling techniques, will help to produce increasingly reliable maps.

1. Introduction Magnetic surveys have played a key role in unraveling the structure and dynamics of the Earth’s surface. Various important geologic problems have been difficult to solve when using information from the existing separate magnetic grids. A consistent World Digital Magnetic Anomaly Map (WDMAM) can help to evaluate different hypotheses of geologic origin of such regions. In addition, numerous scientific problems can be addressed by analysing magnetic anomaly data for understanding the variable structure, temperature, and rheology of the lithosphere. Moreover, a good knowledge of the lithosphere magnetic field can bring insights in a better separation of the internal contributions, indeed between

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the field originating in the core and that of the lithosphere.

Towards this end, efforts have been made to compile a world magnetic anomaly map by combining ground-based, airborne and marine magnetic data, under the auspices of a working group of International Association of Geomagnetism and Aeronomy (IAGA).

Note that these efforts have been ongoing over some three decades, as since 1977 IAGA has invited its member organizations to provide magnetic anomaly maps and data for a world scale compilation. In 2006, using the available ground, near-Earth and satellite magnetic data, five candidate models were produced by teams at the Geological Survey of Finland (GTK), GeoForschungsZentrum (GAMMA), GSFC-NASA, NOAA and University of Leeds1.

The WDMAM committee has worked to produce a compiled magnetic anomaly map consisting of all possible wavelengths that would be useful for geological and tectonic mapping of the Earth’s crust. We summarise here the GFZ contribution to the WDMAM project (Hamoudi et al., 2007), and also outline and illustrate some of the difficulties one has to face for obtaining a self-consistent global map. Indeed, merging aeromagnetic data of different quality, which were reduced using different procedures and core field models, causes significant differences and leveling errors between separately collected and processed adjacent magnetic surveys. We end by showing the final WDMAM map.

2. Data sets and preliminary processing 2.1. Ground and aeromagnetic datasets The distribution of available magnetic datasets is shown in Figure 1. These datasets consist in more than 50 years of aero-magnetic surveys, research vessel magnetometers crossing the seas, observations from satellites, supplemented by anomaly values obtained from oceanic crustal ages. The coverage is uneven between the continental and ocean areas, as well as between Northern and Southern hemispheres.

As magnetic compilations are available in various formats and projections, before applying any filtering or merging procedures, all grids were transformed from their local reference system to a common representation on the global reference ellipsoid, WGS84. Marine data were reprocessed to produce grids at mean sea level, when possible.

The continental-scale aeromagnetic compilations were produced after stitching together different regional anomaly grids. These regional surveys were flown at various epochs and hence use various core field models to reduce the observed data. The patch-worked grids are prone to errors and mismatch in anomaly shapes and presumed strengths are clearly noticeable across overlapping regions, introducing fictitious anomalies. The lack of

absolute reference makes it difficult to recover this long wavelength information. Despite their decimation on a regular grid, the final resolution may not be uniform and only a spectral analysis such as wavelet techniques could help locating precisely the regions of varying resolution. Furthermore, the core field models used to reduce these regional surveys are mostly unknown as each individual compilation panel was usually reduced using a local polynomial. This lack of information prevents us from further correcting the grids for a more homogeneous core field model. According to the WDMAM recommendations, the grids are resampled to 0.05 degree (~3 minute or 10 km wavelength at the equator).

The detailed anomaly features are compared over overlapping regions between two adjacent grids. The example shown in Figure 2 concerns with the European and Eurasian grids. The European grid shows anomalies that are smoother than the neighboring grid. Two reasons may be invoked. Firstly, the European grid is upward continued to 3 km altitude while the Eurasian grid is produced by combining many disparate aeromagnetic surveys of smaller dimension without upward continuing the final grid. Secondly, a spectral analysis carried out on the European grid showed sudden power decay for wavelengths lower

Figure 1: Data distribution: from aeromagnetic and marine surveys (light grey), satellite observations (dark grey) and oceanic crustal ages (white)

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Figure 2: The juxtaposition of the European and Eurasian grids; the black curve indicates large differences between the two grids

than 30 km and it seems that European grid was filtered in order to produce a homogenous resolution map. The anomaly features across the boundary of European and Eurasian grids show partial disagreement of anomalies.

Comparing the strength of total field anomaly over some profiles crossing the boundaries between the two grids indicates discrepancies up to some 200 nT, as in the marked area (Figure 2). Such differences are also observed between some other grid boundaries (not shown here). To find the sources causing differences in the shape, size and strength of anomalies between various grids, as demonstrated for European and Eurasian grids, a detailed procedure was followed on to process the individual grids.

Two different techniques were envisaged for filtering and smoothing the final grid. A first option consists in filtering the grid using Fourier transforms. This procedure is relatively fast but the main drawback is that it is a nonpotential method, and the coefficients could not be used for predicting the three components of the magnetic field. Another method is based on the spherical harmonics analysis.

The grid is interpolated on the Gauss-Legendre knots and the parameters up to spherical harmonic degree 500 are obtained by leastsquares (maximum resolution of 80km). Above degree 500, the coefficients are difficult to obtain as the signal/noise ratio is very low. This is also due to data gaps and heterogeneous resolution at the global scale.

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2.2. Satellites datasets In many regions, lithospheric magnetic anomalies have a large spatial extent and are strong enough to be mapped by low-orbiting satellites. Choosing a global magnetic lithospheric field model is not a trivial task and a systematic quality analysis is required. Several models, based on different datasets, have been recently produced, and they follow basically two different philosophies.

The comprehensive approach (CM4), proposed

by Sabaka et al. (2004), uses POGO, Magsat, Ă&#x2DC;rsted, CHAMP and SAC-C data to derive a comprehensive model. The model accounts for magnetic sources from the core to the magnetosphere and their temporal variations.

However, lithospheric field representation is hampered by the consideration of noisy dayside data and is not calculated beyond degree 65, giving a 600 km maximum resolution at the mean Earthâ&#x20AC;&#x2122;s radius.

In contrast to the comprehensive approach, the second one strictly focuses on the lithospheric field representation. Prior to the modeling, selection and processing are performed to clean the data from non lithospheric sources. This subjective approach requires many independent corrections. Maus et al.

(2006) used CHAMP data to produce MF5 model, which extends up to degree 100 (400 km resolution). Also the WDMAM committee recommended to use the MF5 for the substitution of large wavelengths, which is a good compromise between resolution at the

Figure 3: Magnetic Anomaly Map of the World (Mercator projection).

The anomaly field is shown at an altitude of 5 km above the WGS84 elipsoid

ground and smoothness of the lithospheric field at 5 km altitude.

3. Final map and conclusions A world magnetic anomaly map is derived by combining ground-based, airborne and marine magnetic data with the satellitederived magnetic anomaly map that consists of all resolvable wavelengths (Figure 3). A prior thorough analysis of the grids is inevitable to detect outliers, incorrect coordinate systems or shifts in the data in order to merge them properly.

Careful examination of the data suggest that near-surface compilations contain long wavelengths (> 400 km) that differ significantly, both in strength and shape, with the adjoining compilation or global lithospheric field models. The difference maps indicate that discrepancies are of the order of the strength of long wavelength anomalies of the merging grids. In contrast, the wavelengths smaller than 400 km are naturally attenuated in the present satellite data. The satellite model is therefore used only to replace incorrect long wavelengths in the near-surface compilations (MF5 model).

The WDMAM project will also benefit from improved global magnetic field models. Analyzing the compatibility of ground survey and

satellite data will be helpful in order to correct data and fill in the spectral gap. This could be done using regional modeling to jointly invert aeromagnetic and satellite data.

The forthcoming Swarm mission, selected by the European Space Agency, will provide new highly accurate satellite measurements at low altitudes, and we expect a great improvement in the representation of the intermediate wavelength lithospheric field. In summary, with the method proposed here, it will be possible to regularly update the WDMAM without excessive effort, in order to continuously improve the representation of the world magnetic anomalies.

Acknowledgments We would like to acknowledge all geological surveys and group members who provided aeromagnetic and marine magnetic anomaly data for World Digital Magnetic Anomaly project. The CHAMP mission is operated and supported by GeoForschungsZentrum Potsdam, the German Aerospace Center (DLR) and the German Federal Ministry of Education and Research (BMBF). This work has got financial support in the frame of GEOTECHNOLOGIEN project 03F0442A. 1

http://projects.gtk.fi/WDMAM/project/

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References Hamoudi, M., E. Thébault, V. Lesur and M. Mandea, GeoForschungs Zentrum Anomaly Magnetic Map (GAMMA): A candidate model for the World Digital Magnetic Anomaly Map, Geochem. Geophys. Geosyst., 8, Q06023, doi: 10.1029/2007GC001638, 2007.

Korhonen, J.V., J.D. Fairhead, M. Hamoudi, K. Hemant, V. Lesur and M. Mandea, S. Maus, M. Purucker, D. Ravat, T. Sazonova, E. Thébault, Magnetic Anomaly Map of the World (and associated DVD), Scale: 1: 50,000,000, 1st edition, Commission for the Geological Map of the World, Paris, France, 2007.

Maus, S., H. Lühr, M. Rother, K. Hemant, G. Balasis, P. Ritter and C. Stolle, Fifth generation lithospheric magnetic field model from CHAMP satellite measurements, Geochem.

Geophys. Geosyst., doi: 10.1029/2006GC001521, 2007.

Sabaka, T. J., N. Olsen, and M. Purucker, Extending comprehensive models of the Earth’s magnetic field with ørsted and CHAMP data, Geophys. J. Int., 159(2), 521–547, 2004.

See also: http://www.gfz-potsdam.de/pb2/pb23/index_e.html

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Data Compression for Global Field Modeling Minchev B. (1), Holschneider M. (1), Mandea M. (2), Chambodut A. (3), Panet I. (4) and Schoell E. (5) (1) Institute for Applied Mathematics, University of Potsdam, Germany.

(2) GeoForschungsZentrum Potsdam, Germany.

(3) Ecole et Observatoire des Sciences de la Terre de Strasbourg, France.

(4) Space Geodesy Research Division, Geographical Survey Institute, Japan.

(5) Institute of Theoretical Physics, Berlin University of Technology, Germany.

1. Introduction The launch of the Danish satellite Ørsted in February 1999 has initiated a new era for geopotential field research, known as International decade of geopotential fields.. Ørsted satellite was followed by other gravity and/or magnetic missions, as CHAMP, SAC-C and GRACE, launched in July 2000, November 2000 and March 2002, respectively. These satellites have provided a large amount of gravity and/or magnetic data. Evidently, the total number of data used in producing a gravity or magnetic model is reduced with respect of the large number of raw data. To overcome this drawback, it appears necessary to use data compression techniques, which allow dealing with the huge amounts of data.

In this context, we use local multipole approximations of the basis functions at satellite altitude. The idea is to take advantage of the rather smooth behaviour of the internal field at the satellite altitude and to replace the full data by a collection of local moments (see Minchev et al., 2007). In the inverse problem, the expansion of the related potential fields in spherical harmonics or wavelets are replaced by a power series of local multipolar expansion, around a defined point inside a unity-volume of the discretized space. In this way, a piecewise decomposition of potential fields at satellite altitude is obtained. The coefficients of each local expansion are then used in global field modelling.

The considered data compression technique makes it possible: (i) to reduce the amount of data for computational and memory reasons; (ii) to get precomputed datasets; (iii) to make available standardised data for databases. All these improvements are obtained without losing the quality of the final obtained model.

2. Development into Local Multipolar Expansions We consider the following kind of linear model, where an arbitrary function, s(x) is expanded into a family of basic functions gn, with coefficients γn, n = 0, …, N – 1, N −1

s ( x ) = ∑ γ n gn ( x ) . n=0

(1)

In practice gn are typically spherical harmonics or wavelets. We suppose that the measurements fk, k = 0, …, K – 1, at the observational points xk, are the »true« values of the measured physical quantity contaminated which some Gaussian noise ek, with covariance matrix Σ = (Σk, k´). If is a quadratic form representing some a priori information about the model, a function s(x) satisfying the following minimisation problem Γ(s, s) ⇒ min , for Σ (s(xk) – fk)T Σ–1 k, k´ s(xk´) – fk´) = 1, can be computed as the solution of the following normal equation (F · Σ –1F + λΓ ) γ = F · Σ –1f ,

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where F = (gn(xk)) is the system matrix of the basic functions at the measurement points and λ is a Lagrange multiplier.

Let us also denote by Dj the maximal number of data points inside the prism Qj Dj = #{k : xk k Qj},

We suppose that each function gn can be expanded, around a given point at satellite altitude, as a linear combination of simpler functions hl, l = 0, …, L – 1, where L 9 K. One can think of a local expansion into spherical harmonics, i.e. a linear combination of unity-volumenic polynomials up to a certain degree, restricted to some suitable unityvolumes. We then can write all basic functions gn using a local coefficient matrix C, with entries Cl, n, namely: L −1

gn @ ∑ C l, n hl . l =0

If the difference between the left and the right-hand side of the above approximation is a fraction of the measurement noise, a model based on the functions on the righthand side cannot be distinguished from a model based on the functions on the lefthand side. The system matrix F may then be factorised as:

F ( HC, where H is the system matrix of the local functions hl, Hk, l = hl (xk). Based on this factorisation, the normal equations can be rewritten as

Γ ) γ˜ = C · Σ˜ –1f˜ (C · Σ˜ –1C + λΓ where Σ˜ –1 = H · Σ –1H and f˜ = Σ˜ H · Σ –1f = H –1f.

2.1. Operation count What do we gain by using the above factorisation? To answer this question, let us first suppose that all local functions are restrictions to some spherical prisms Qj, j = 0, …, J – 1 of spherical harmonics of low degree and let Qj(n) denotes the support of Hn. The maximal number of hn that share the same support, we denote by E Ej = #{n : support hn = Qj} ,

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E = max {Ej} .

D = max {Dj} . j

The following relations are obviously satisfied D ≤ K ≤ DJ,

and

E ≤ L ≤ EJ.

Note that, since a matrix multiplication of an A × B matrix with a B × C matrix takes O(ABC) operations, for a general matrix Σ, the total operation count may actually increase, if we compute the normal equations by using the above proposed factorisation. However, if the errors are not correlated between the different Qi (or only between neighbouring Qj), we may gain in computation time. In this case, the direct computation of the normal equation requires opcount1 = KN(N + 1)/2 operations. On the other hand, we can take advantage from the special block diagonal structure of the matrix H and first compute the matrix X = H · Σ –1H, followed by the computation of the matrix C · H · Σ –1HC = C · XC. This process takes at most opcount2 ≤ DJL(L + 1)/2 + JL2N + JLN(N + 1)/2 .

Clearly, opcount2 is dominated by the largest of its first and last terms. We can conclude that, in order to achieve computational savings, the choice of the parameters L and J should be done such that R 9 K, where: R = JL, is the total number of local coefficients used in the approximation, or in other words the rows number in C. Since neither L nor J depends on K, the last requirement can be fulfilled by simply increasing the number of measurements used in the model.

2.2. Data storage Additionally to the computational speed-up, achieved by using local multipolar approximations of the basic functions, the proposed approach leads to memory savings. This is due

to the fact that instead of solving the original inverse problem, we solve the approximated one, which for R 9 K, has much smaller dimensionality. In practice, this allows to either increase the number of observations used in the model, or to increase the number of the basic functions. We also note that since the entries of the matrix C depend only on the number of the local functions used in the approximation and the total number of the basic functions, for a space discretisation which uses a measurement independent definition of the centre of mass, the matrix C can be precomputed once and for all. This fact can lead to additional computational savings, when the size of the unity-volumes used in the space discretisation is small and the number of data inside each unity-volume is large.

gravity and magnetic potential fields. As basic functions, we use spherical harmonics and their approximations by local harmonic polynomials up to degree 2(L = 9). The space discretisation is based on generation of six subdivisions of the icosahedron, with 20 480 total numbers of facets at the Earthâ&#x20AC;&#x2122;s surface. Tables 1 and 2 summarise some of the main compression parameters obtained for the gravity and the magnetic datasets, respectively, for degree 30 and 60 spherical harmonics models.

For booth examples the obtained residuals are at the noise levels. The spatial distribution of the residuals is related to the distribution of the data around the centres of masse inside the prisms that may lead to a bad approximation of the spherical harmonics of high degrees (above 30) for data points far from the centres.

3. Applications in Geopotential Field Modeling We tested the considered local multipolar expansion approach for modelling the Earthâ&#x20AC;&#x2122;s

Table 1: Local approximations applied in gravity modelling tests.

A subdivision of space with one layer with total of 20 480 prisms, all of which are filled, is used

Expansion order Number of reduced data/prism Average number of original data/prism Total number of reduced data Total number of original data Size reduction of the normal eq.

Nb of reduced data/SH coefficient (deg. 30) Nb of reduced data/SH coefficient (deg. 60)

0

2

1 23 20 480 481 356 96% 21 6

9 23 184 320 481 356 62% 193 50

Table 2: Local approximations applied in magnetic modelling tests. A subdivision of space with one layer with total of 20480 prisms, all of which 7652 filled, is used

Expansion order Number of reduced data/prism Average number of original data/prism Total number of reduced data Total number of original data Size reduction of the normal eq.

Nb of reduced data/SH coefficient (deg. 30) Nb of reduced data/SH coefficient (deg. 60)

0

1

1 9 7652 70 511 89% 8 2

8 9 22 956 70 511 68% 24 6

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4. Conclusions The use of local harmonic polynomial approximation to the basic functions in potential field modelling, provides some clear advantages over the traditional approach, based on evaluation of the basic function themselves. The approach allows to reduce the size of the inverse problem, which we have to solve. In addition, the computation of the coefficient matrix C can be performed before the actual solution of the minimisation problem. Thus, we can reduce the total number of operations in the case, when the solution of the inverse problem, for different components of the potential field, is needed.

Acknowledgments This work was supported within the framework of the project BMBF/DFG ÂŤGEOTECHNOLOGIENÂŤ.

References Epton, M. and Dembart, B.(1995), Multipole translation theory for the three-dimensional Laplace and Helmholtz equations, SIAM J. Sci. Comput., 16, 4, 865897.

Holschneider, M., Chambodut, A. and Mandea M. (2003), From global to regional analysis of the magnetic field on the sphere using wavelet frames, Phys. Earth Planet. Inter., 135, 107124.

Minchev, B., Chambodut, A., Holschneider, M., Panet, I., Scholl, E., Mandea M., (2007), Local multi-polar expansions in potential field modelling, submitted at Geophys. J. Int.

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Estimation of global terrestrial water storage change using the WaterGAP Global Hydrological Model (WGHM) Fiedler K., Döll P., Hunger M. Department of Physical Geography, University of Frankfurt am Main, P.O. Box 11 19 32, 60054 Frankfurt am Main, Germany (fiedler@em.uni-frankfurt.de)

Introduction Terrestrial water storage plays an essential role within the global hydrological cycle. It is of particular importance for the existence of many ecosystems and for the satisfaction of human water demands. Observation based information about the spatial distribution and temporal variations of water storage on a global scale is limited. However, it is crucial e.g. for the assessment of water resources worldwide. A varying volume of water stored on or beneath the earth’s surface implicates mass transport and mass redistribution, thus causing temporal variations of the earth’s gravity field. Since the GRACE satellite mission provides gravity field solutions with unprecedented accuracy, an increase in our understanding of macro-scale hydrological processes is expected from the application of this additional information from space. The integral GRACE gravity signal is separated into its individual components which can each be attributed to different phenomena related to mass redistributions on or beneath the earth’s surface. In order to evaluate the hydrological signal obtained from pre-processed GRACE data, the state-of-the-art WaterGAP Global Hydrological Model (WGHM) (Döll et al., 2003) is improved and applied to calculate terrestrial water storage change at daily and monthly time scales worldwide. WGHM calculates terrestrial water storage as the sum of snow, soil moisture, canopy storage, groundwater and surface water including lakes, wetlands and rivers.

In this contribution we 1) investigate the model sensitivity to different climate data used for model forcing, 2) present recent and projected model improvements and 3) show results of comparison between model output and GRACE data for selected basins.

1. Model sensitivity to climate input Precipitation is considered to be one of the main driving forces for the continental hydrological cycle. Global hydrological models are therefore highly sensitive to the applied precipitation input data. To estimate the uncertainty of computed water storage change due to the uncertainty of precipitation input, WGHM is driven by different climate data sets.

Two monthly precipitation data sets based on gridded station observations are applied: 1) the CRU (Climate Research Unit) TS 2.1 data set, available until 2002, and 2) the GPCC (Global Precipitation Climatology Centre) Full Data Product Version 3, available up to almost real-time. Both data sets are not corrected for measurement errors. Therefore, a general algorithm to account for precipitation undercatch is introduced, which, for the period of 1961–1990, lead to an increased mean annual precipitation of 11.6% on average over the global land surface areas. Daily precipitation was modeled internally by distributing the monthly precipitation sum equally over the number of rain days per month.

In order to improve results at the sub-monthly scale, a third daily global precipitation data set has been developed taking into account

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Figure 1: Latitudinal profile of seasonal water storage change [mm] calculated with WGHM based on four different precipitation input data sets (mean over 1992 â&#x20AC;&#x201C; 2002), other climate input was left unchanged

gridded observation based precipitation (GPCC) as well as data from an operational weather forecast system (ECMWF). Daily precipitation values are obtained by scaling daily values from ECMWF to match the monthly GPCC precipitation totals.

As can be seen in Figure 1, different precipitation data sets as model input lead to significant differences of calculated seasonal water storage change. The latitudinal profile reveals the main differences to be most evident in the northern hemisphere. Precipitation correction generally increases the storage change amplitude in northern regions where snow makes up an important component of total water storage. Solid precipitation generally requires a higher correction factor than precipitation that falls as rain.

The higher sub-monthly precipitation variability, taking daily precipitation from ECMWF into account, increases water storage change dynamics at daily time steps (not shown).

Therefore, daily water storage changes calculated with WGHM might contribute to improved GRACE de-aliasing. Furthermore, the influence of different radiation and temperature data from CRU and ECMWF on water

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storage change as modeled with WGHM was evaluated. Unlike precipitation, other climate variables like temperature or radiation only marginally influence the seasonal water storage change dynamics. Precipitation can therefore be identified as the climate variable to which the model is most sensitive.

2. Recent model improvements 2.1. Calibration against discharge measurements WaterGAP was developed to assess water resources and water use in river basins worldwide under the conditions of global change. The model is tuned against river discharge observations to adjust the simulated long-term average discharge at the outflow point of a (sub-)basin to the observed long-term average discharge and thus to obtain rather realistic water flows in the basins. The most recent model version WaterGAP 2.1f differs from the former versions by, among other changes, an increased number of now 1,235 river discharge observation stations that are used to tune the model which lead to an improved spatial representation of total runoff (Hunger and DĂśll, submitted). How-

ever, the calibration strategy followed here does not necessarily improve the representation of water storages within the hydrological model since river discharge is only one part of total water storage. Therefore, a multi-objective calibration approach is currently developed at GFZ Dept. 5.4 to calibrate the model not only against discharge observations but also against basinaverage storage variations derived from GRACE. For further details, we refer to the report of the

TIVAGAM team members of GFZ Dept. 5.4 by Werth et al. (2007).

2.2. Improved representation of lateral water transport By now, reservoirs are treated like natural lakes in WGHM. However, it is well known that reservoir operations significantly alter the terrestrial water cycle. Reservoir storage volumes as well as river discharge of downstream areas

Figure 2: Monthly water storage change in mm w.eq. derived from GRACE and WGHM (with and without precipitation correction) for the Amazon (top) and the Danube (bottom) river basin (a Gaussian-type spatial filter with an averaging radius of 500 km was applied)

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are strongly influenced by reservoir management schemes depending on the intended purpose of the reservoir, e.g. irrigation, water supply, flood control or hydroelectricity. Therefore, in order to better represent anthropogenic impacts, it is planned to integrate a reservoir operation scheme into the global hydrological model using available global data such as reservoir storage capacity, intended purpose and water demand in the lower reaches. We expect that not only the modeled river discharge but also the total water storage and its seasonal change will be strongly influenced within basins that are dominated by large reservoirs in their river network.

3. Comparison between WGHM and GRACE Finally, continental water storage change as computed with WGHM is compared with GRACE results for two large river basins.

Figure 2 shows a comparison between monthly water mass variations derived from GRACE and calculated with WGHM for the Amazon and the Danube. Especially in the Amazon basin, the seasonal amplitude of water storage change is underestimated by the hydrological model. However, in the Danube river basin, the amplitude is slightly increased by the application of precipitation correction. Additionally, a phase shift of one to two months between WGHM and GRACE can be identified in both diagrams which could be due, among other reasons, to the assumption of a constant river flow velocity of 1 m/s within WGHM. In order to further investigate the reasons for the above mentioned differences between the global hydrological model and GRACE, the multi-objective calibration approach (Werth et al., 2007) is expected to reveal additional information about sensitive parameters and model uncertainty. It shows that the GRACE satellite mission represents a unique source of information as there are no other observations of total, terrestrial water storage changes at the global scale. The application of GRACE data can therefore be considered as an impor-

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tant contribution to our understanding of macro-scale hydrological processes.

References Döll, P., Kaspar, F., and Lehner, B.: A global hydrological model for deriving water availability indicators: model tuning and validation, J. Hydrol., 270, 105–134, 2003.

Hunger, M., and Döll, P.: Value of discharge information for global-scale hydrological modelling, submitted to Hydrology and Earth System Sciences, 2007 Werth, S., Güntner, A., Merz, B., Schmidt, R., Petrovic, S.: Calibration techniques for a global hydrological model and their interface to GRACE data analysis, Proceedings of »2. Statusseminar Geotechnologien«, Munich, Germany, 2007.

Multiscale Filter Methods Applied to GRACE and Hydrological Data Freeden W., Nutz H., Wolf K. TU Kaiserslautern, Geomathematics Group, P.O. Box 3049, 67653 Kaiserslautern, Germany

Abstract A multiscale analysis (also called multiresolution) of temporal and spatial variations of the Earth’s gravitational potential based on tensor product wavelets is presented. The time-space multiscale filtering is realized by combining Legendre wavelets for the time domain and spherical wavelets for the space domain. In consequence, a multiresolution analysis for both, temporal and spatial resolution, is formulated within a unified concept. The method is numerically realized by using GRACE and hydrological data (WGHM, H96 and LaD).

approach are kernel functions based on spherical harmonics which filter out certain degrees of the spherical harmonic expansions. In order to extend the (spherical) wavelet analysis to the case of time series of spherical harmonic coefficients or water columns as given in case of GRACE (Gravity Recovery and Climate Experiment) data or hydrological data (WaterGap Hydrology Model, H96, Land Dynamics Model) we apply the classical method of tensor product wavelets and establish pure and hybrid parts which measure both temporal and spatial changes in the signal.

1. Introduction The spherical multiresolution method is a filter method which allows to model spatial variations of Earth’s gravitational potential and has been developed by the Geomathematics Group, TU Kaiserslautern. The multiscale technique avoids smearing the detail information around the entire globe because the region around the investigated point influences the calculations. This is achieved by describing the signal at each point on the sphere as an adequate band of frequencies which changes continuously (space evolution of the frequencies).

The spherical wavelets under use in our

2. Theory of Time-Space Multiresolution Analysis The basic idea of the time-space multiresolution is to split the signal F which is assumed to be of finite energy (i.e. an element of the space L2([–1, 1] × Ω), Ω being the unit sphere and [–1, 1] the normalized time interval) into a smoothed part and several details. We compute the smoothed part by convolving the signal with the so-called scaling function ΦJ0 of a lowest scale J0 and the details by convolving the signal with the (pure and hybrid) wavelets Ψji, j = J0,… J; i = 1, 2, 3 of several scales from the lowest scale J0 up to the highest scale J.

Figure 1: Time-Space Multiresolution

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Symbols of the Cup-Wavelet for scales 3, 4 and 5

Kernels of the Cup-Wavelet for scales 3, 4 and 5

Figure 2: Cu(bic) P(olyomial) Wavelet

Thus, the scaling function can be interpreted as a low pass filter and the wavelets serve as band pass filters of spherical harmonic coefficients where the bandwidth depends on the scale.

The higher the scale the finer are the spatial and temporal details which are filtered out (zooming-in property). The lower scales represent the coarse parts of the signal whereas the higher scales represent the smaller structures.

According to the theory of tensor product wavelets we have to introduce pure and hybrid parts which measure both temporal and spatial changes in the data. A schematic representation of the resulting time-space multiresolution method is given in Figure 1.

From mathematical point of view the scale dependent scaling functions are kernel functions, ΦJ : [–1, 1] × [–1, 1] × Ω × Ω → IR, of the form ∞

∞

Φ j ( s, t; ξ, η ) = ∑ n ′ = 0 ∑ n = 0 ( Φ j )∧ ( n ′; n ) 2n +1 ∑ k = 1 Pn∗′ ( s ) Pn∗′ ( t ) Yn , k ( ξ ) Yn , k ( η ),

s, t k [–1, 1], ξ, η k Ω, where {Yn, k}n = 0, 1, …; k = –n, …, m is an orthonormal set of spherical harmonics, {P* n′}n′ = 0, 1, … are orthonormal Legendre Polynomials and (Φj) ∧ (n′, n) is the symbol of the scaling function. The symbol has to fulfill several conditions in order to assure the multiresolution, but for sake of brevity we will not go into the details and just refer to the literature listed at the end of this paper. According to the theory of tensor

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wavelet analysis the symbol of the scaling function is the product of the symbols of the temporal scaling function ∞

Φtj ( s , t ) = ∑ n ′ = 1( Φtj )∧ ( n ′ ) Pn∗′ ( s ) Pn∗′ ( t ) and the spatial scaling function Φ sj ( ξ , η ) 2n +1

∞

= ∑ n = 0 ( Φ sj )∧ ( n ) ∑ k = 1 Yn , k ( ξ ) Yn , k ( η ) that is (Φj) ∧ (n′, n) = (Φjt ) ∧ (n′) (Φsj ) ∧ (n). In analogy to the scaling function the corresponding temporal and spatial wavelets are given by ∞ Ψ tj ( s , t ) = ∑ n ′ = 1( Ψ tj )∧ ( n ′ ) Pn∗′ ( s ) Pn∗′ ( t ) and ∞

2n +1

Ψ sj ( ξ , η ) = ∑ n = 0 ( Ψ sj )∧ ( n ) ∑ k = 1 Yn , k ( ξ ) Yn , k ( η ).

The symbols of the temporal and spatial scaling function and wavelets, respectively, fulfill refinement equations, that is ( Ψ tj )∧ ( n ′ ) = ( Φtj + 1)∧ ( n ′ ) − ( Φtj )∧ ( n ′ ) , ( Ψ sj )∧ ( n ) = ( Φ sj + 1)∧ ( n ) − ( Φ sj )∧ ( n ) .

Since both refinement equations have to be fulfilled simultaneously we are led to pure and hybrid parts. The first and second hybrid parts are computed combing the symbol of the temporal scaling function with the symbol of the spatial wavelet and vice versa, that is we convolve the signal with the kernel functions

( Ψ1j ) ( s, t; ξ, η ) =∑

∞ n′ = 0

∑

∞ ( Φtj )∧ n=0

( n ′ ) ( Ψ sj )∧ ( n )

2 n+1

× ∑ k =1 Pn∗′ ( s ) Pn∗′ ( t ) Yn, k ( ξ ) Yn, k ( η ) , ( Ψ 2j ) ( s, t; ξ, η ) ∞

∞

= ∑ n ′ = 0 ∑ n = 0 ( Ψ tj )∧ ( n ′ ) ( Φ sj )∧ ( n ) 2n +1

× ∑ k = 1 Pn∗′ ( s ) Pn∗′ ( t ) Yn, k ( ξ ) Yn, k ( η ) whereas in case of the pure part we convolve the signal with the kernel function ( Ψ 3j ) ( s, t; ξ , η ) ∞

∞

= ∑ n ′ = 0 ∑ n = 0 ( Ψ tj )∧ ( n ′ ) ( Ψ sj )∧ ( n ) 2n +1

× ∑ k = 1 Pn∗′ ( s ) Pn∗′ ( t ) Yn, k ( ξ ) Yn, k ( η ) .

The weighting of the spherical harmonic coefficients for the calculation of the smoothed part and the details is determined by the symbols of the scaling functions and wavelets, respectively. The cubic polynomial wavelet which has been used for the computations is shown in Figure 2. Detailed information about the time- space multiresolution can be found in the literature given in the list of references.

3. Numerical Results for GRACE and Hydrological Data In this section we present some results based on Earth’s gravitational data sets from the satellite mission GRACE and from WGHM. We base our calculations on time series of 47 data sets from February 2003 till December 2006.

In order to show the changes in the spatial and temporal dimension, respectively, we use the pure detailed parts of the multiresolution analysis. For the visualization of the spatial changes we plot the maximum of the absolute values over the whole time interval, whereas in case of the temporal variations we fix the position and present the time dependent courses.

The plots shown in Figure 3 demonstrate the regions where the greatest variations in the potential are, as for example in the Amazonas basin in South America. With increasing scale we can recognize the better space localization but at scale 4 and 5 the satellite tracks appear.

In case of the time dependent courses (see Figure 4) we show three different cities located in both Southern and Northern hemisphere. Kaiserslautern is located within a

Figure 3: Maximum of the absolute values of the pure detailed part calculated with CuP-wavelet in time and space based on GRACE data

Figure 4: Time dependent courses of the pure detailed part calculated with CuP-wavelet in time and space based on GRACE data

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Figure 5: Maximum of the absolute values of the pure detailed part calculated with CuP-wavelet in time and space based on WGHM data

Figure 6: Time dependent courses of the pure detailed part calculated with CuP-wavelet in time and space based on WGHM data

Figure 7: Local correlation of the pure detailed parts calculated with CuP-wavelet at scale 4 in time and space for different hydrological models

region with moderate seasonal variations in the water balance, whereas the other two cities show the time dependent courses in well-known regions of great changes.

As expected the results in case of WGHM data are quite similar to those achieved for GRACE data (see Figure 5 and Figure 6).

4. Correlation Coefficients and Signal Variances After having performed a multiresolution of both GRACE data and hydrological data we are in the position to compute the scale

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depending local and global correlation coefficients as shown in Figure 7 and Table 1.

The correlation coefficients are good up to a certain scale which raises the question of how to extract a hydrological model from GRACE data using the multiresolution analysis. As has been explained in Section 3 the multiresolution analysis provides a ›reconstruction‹ FJ of the signal F which tends to the original signal when the scale tends to infinity, i.e. FJ = ΦJ · F and limJ → ∞ FJ = F. In order to estimate how much of the signal has already been reconstructed we calculate the signal variances which measure the percentage of the reconstruction on the

Table 1: Global correlation coefficients calculated using the pure detailed parts on the continents

original signal. Both the correlation coefficients and the average signal power measured using signal variances help to give an answer to the abovementioned question.

5. Outlook Local calculations for regions of great accuracy of the hydrological models as for example the Mississippi delta will be performed in order to approve the technique. The results we achieved using the CuP-Wavelet are quite promising and we will start further calculations using other types of wavelets as, for example, Abel-Poisson and Gauß-Weierstraß. The aim is to be able to state an ‘ideal’ reconstruction of the signal in view of extraction of the hydrological model from the GRACE data.

mathematik, 36, 2007, submitted to Studia Geophysica et Geodaetica.

W. Freeden. Multiscale Modelling of Spaceborn Geodata. Teubner, Stuttgart, Leipzig, 1999.

A.K. Louis, P. Maaß, and A. Rieder. Wavelets: Theorie und Anwendungen. Teubner, Stuttgart, 1998.

Acknowledgements The scientific works are supported by the BMBF-project TIVAGAM. The Geomathematics Group TU Kaiserslautern thanks our project partners from GeoForschungsZentrum-Potsdam (Department 1.3) for providing the used data sets for all computations within this paper.

List of References M.J. Fengler, W. Freeden, A. Kohlhaas, V. Michel and T. Peters. Wavelet Modelling of Regional and Temporal Variations of the Earth Gravitational Potential. Journal of Geodesy, 81: 5–15, 2007.

H. Nutz, K. Wolf. Time-Space Multiscale Analysis by Use of Tensor Product Wavelets and its Application to Hydrology and GRACE Data, Schriften zur Funktionalanalysis and Geo-

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Comparison of crustal deformations from a global GPS reprocessing and from GRACE surface mass variation products: progress and challenges Horwath M. (1), Rülke A. (1), Fritsche M. (1), Dietrich R. (1), Schmidt R. (2) and Döll P. (3) (1) Technische Universität Dresden, Institut für Planetare Geodäsie, Dresden (2) GeoForschungsZentrum Potsdam, Department 1 Geodesy and Remote Sensing, Potsdam (3) Johann Wolfgang Goethe-Universität Frankfurt, Institut für Physische Geographie, Frankfurt/Main, E-mail: horwath@ipg.geo.tu-dresden.de

1. Introduction Geophysical mass variations not only affect the gravity field but also deform the solid earth. In particular, load variations such as related to the global hydrological cycle induce an elastic deformation which is commonly described by the load Love number formalism. GPS observations of crustal deformations are valuable for a cross-comparison with GRACE mass variation datasets. This comparison may validate either dataset and, finally, contribute to the improvement of mass transport estimates.

Here we present results from our ongoing work following this strategy.

2. Provision of homogeneous GPS coordinate time series in a consistent reference frame GPS observations of globally distributed ground stations are suitable to derive parameter estimates either as quantities for the realization of a terrestrial reference system (e.g. station coordinates) or as quantities directly related to geophysical phenomena (e.g. tropospheric refraction, Earth orientation).

In any case, a meaningful geophysical interpretation of these estimated quantities requires both homogeneously processed observations and a stable realization of the terrestrial reference system. In a joint effort TU Dresden and TU Munich/GFZ Potsdam

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reprocessed a global GPS network of more than 200 stations.

The homogeneity of processing results guarantees that parameter time series are not affected by changes of applied a priori observation models or modifications of the processing strategies. First results on the impact of refined a priori observation models concerning troposphere and ionosphere are illustrated in Vey et al. [2006] and Fritsche et al. [2005], respectively. Furthermore, Steigenberger et al.

[2006] gives an impression on the benefit of completely reprocessed GPS observation compared to products available from the International GNSS Service.

A rigorous combination of daily normal equations from 1994 to 2005 was performed in order to determine a global GPS-only reference frame, namely PDR05/Potsdam-DresdenReprocessing Reference Frame [Rülke et al., 2007]. By solving for station coordinates and velocities, satellite positions and surface load coefficients in a consistent way the implemented realization strategy follows the center of mass approach in consideration of loadinduced deformation of the Earth’s crust due to redistributed surface masses [Blewitt, 2003].

Finally, daily station coordinate solutions are compared to that reference by a 7-parameter

Figure 1: Changes in C_20 obtained from the GPS reprocessing and from GRACE (GFZ Release 04 with background fields re-added)

similarity transformation. The related site-specific coordinate residuals are then considered as coordinate time series.

3. GPS versus GRACE low degree load variations Global low degree surface mass variations terms can be directly compared between the GPS solution and the GRACE solutions. Figure 1 shows such a comparison for the zonal degree-2 terms. Good qualitative agreement is visible. Other low-degree terms solved within the GPS analysis show less agreement with GRACE and appear to solve rather as nuisance parameters in the GPS analysis.

4. GPS versus geophysical reduction models Station-wise GPS deformation time series were compared to deformation time series computed from the GRACE geophysical reduction models. Figures 2a and 2b show examplary results for vertical deformations at a number of stations. Here, the geophysical models include the GFZ Release 04 atmospheric and oceanic dealiasing models and, in addition, a daily version of the WGHM hydrology model which was used for GRACE dealiasing experiments within the TIVAGAM project.

In Europe and in other GPS station clusters the models capture a significant part of the defor-

mations observed by GPS. In other regions, too, the models explain part of the GPS variations, but larger differences remain. In general, the discrepancies between GPS and models contain both uncorrelated GPS noise and some longer-term (e.g. seasonal) signal.

5. Considerations on long-term trends Long-term trends in mass variations and, respectively, in vertical deformations need special attention since they may reflect either long-term load changes or signals other than contemporary load changes, in particular glacial isostatic adjustment (GIA) processes. As a result of a closer analysis of the long-term vertical deformations in the GPS data they can be mostly explained by GIA effects or known local effects. As an example Figure 3 shows a comparison of vertical rates in North America and Fennoscandia with the GIA model ICE-4G [Peltier, 1998].

6. GPS versus GRACE monthly models From the GRACE monthly solutions and their background models, the induced total crustal surface load variations were computed. To avoid large effects of GRACE errors in the high spherical harmonic degrees, GRACE data had to be smoothed (e.g. by a 500 km half-width gaussian filter). In order to avoid damping of geophysical signals by this smoothing, hydrological signals modelled by

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Figure 2: a: Daily vertical deformations in the year 2003 from GPS and from GRACE dealiasing models. The station locations applying for all subfigures are indicated between subfigures b and c. Units are mm everywhere. b: Differences between the two time series shown in a. c: monthly vertical deformations from GPS and from GRACE (monthly solutions + background fields). d: Differences between the two time series shown in c

the WGHM hydrological model were reduced prior to smoothing and then re-added. The GPS time series were averaged to monthly means. Contributions from degree-1-deformations were reduced from the time series since they are not contained in the GRACEderived deformations.

Figures 2c and 2d show exemplary stationwise comparisons between GRACE-derived and GPS-derived deformations. There is a general agreement, except for the shown Antarctic station Casey. The remaining GPS-GRACE discrepancies seem regionally correlated. In

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some cases (e.g. for Brasilia) the relatively lower amplitude of the GRACE-derived seasonal variations may be due to damping by the gaussian filtering.

Figure 4 (circles) shows the standard deviations of the GPS-GRACE discrepancies for all included positions. The background colours show a propagation of GRACE calibrated errors to the considered vertical crustal deformations. (An additional correction due to the empirically detected effect of error correlations is applied after Horwath and Dietrich [2006]).

Figure 3: Comparison of vertical crustal deformation rates from the GPS reprocessing (circles) with predictions from the ICE-4G model of glacial isostatic adjustment [Peltier, 1998] (background image with contour lines) in North America (left) and Fennoskandia (right)

Figure 4: Circles show colour-coded standard deviations of GPS-GRACE discrepancies (as shown in Figure 2d for selected sites). The background grayshading (showing less than 1 mm everywhere) shows the expected contribution from GRACE errors to this standard deviation

Clearly, the GPS-GRACE discrepancies are far larger than the expected GRACE errors. This is particularly striking at ocean island stations. Closer analyses indicate that residual errors in the GPS coordinate solutions are the dominating cause of these discrepancies.

A large part of the discrepancies is a largescale annual signal. In the horizontal components, GPS-GRACE discrepancies are even more severe.

Nevertheless, the comparison between GPS and GRACE-derived deformations shows differences

e.g. with respect to different GRACE solution releases. The progress of Release 04 compared to Release 03 can be shown despite the partly systematic errors in the GPS solutions.

7. Discussion and outlook The analyses show that the task we are facing is rather a comparison between GPS and GRACE than a validation of GRACE by GPS. Understanding and, finally, resolving the GPSGRACE discrepancies is part of the challenges envisaged by the IAG Global Geodetic Observing System.

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In the meantime, analyses of regional parts of the GPS network and of their relative deformations may circumvent some of the largescale systematics of the GPS solution. Indeed, regional analyses for Europe show good agreement between GPS and GRACE even for the horizontal components. It is expected that such regional analyses offer an improved ability for actual GRACE validation, e.g., for demonstrating the progress between successive GRACE monthly solution releases. Thus, apart from its value in a broader geodetic context, the project will continue to serve the joint TIVAGAM project by evaluating uncertainties of the various mass variation products involved.

References Blewitt, G.: Self-consistency in reference frames, geocenter definition, and surface loading of the solid Earth. J. Geophys. Res. 108(B2), doi: 10.1029/2002JB002082, 2003.

Döll, P., F. Kaspar and B. Lehner: A global hydrological model for deriving water availability indicators: model tuning and validation.

J. Hydrology, 270: 105–134 2003.

Fritsche, M., R. Dietrich, C. Knöfel, A. Rülke, S. Vey, M. Rothacher, P. Steigenberger: Impact of higher-order ionospheric terms on GPS estimates. Geophys. Res. Lett. 32. L23311, doi: 10.1029/ 2005GL024342, 2005.

Horwath, M., R. Dietrich: Errors of regional mass variations inferred from GRACE monthly solutions. Geophys. Res. Lett., 33, L07502, doi: 10.1029/2005GL025550, 2006.

Peltier, W. R. Postglacial variations in the level of the sea: Implications for climate dynamics and olid-earth geophysics. Reviews of Geophysics, 36(4): 603–689, 1998.

Rülke, A and Dietrich, R and Fritsche, M and Rothacher, M and Steigenberger, P. Realization of the Terrestrial Reference System by a reprocessed global GPS network. J. Geophys.

Res., submitted, 2007

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Steigenberger, P., M. Rothacher, R. Dietrich, M. Fritsche, A. Rülke, S. Vey: Reprocessing of a global GPS network. J. Geophys. Res., 111, B05402, doi: 10.1029/2005JB003747, 2006.

Vey, S., R. Dietrich, M. Fritsche, A. Rülke, M. Rothacher, P. Steigenberger Influence of mapping function parameters on global GPS network analyses: Comparisons between NMF and IMF. Geophys. Res. Lett. 33, L01814, doi: 10.1029/2005GL024361. 2006.

Periodic Components of Water Storage Changes from GRACE and Global Hydrology Models Petrovic S., Schmidt R., WĂźnsch J., Barthelmes F., Hengst R., Kusche J. GeoForschungZentrum Potsdam, Department 1 Geodesy and Remote Sensing, Telegrafenberg, 14473 Potsdam, Germany, E-Mail: sp@gfz-potsdam.de

1. Introduction The Gravity Recovery and Climate Experiment (GRACE) satellite mission has widely demonstrated its sensitivity to ongoing mass redistributions within the various subsystems of the Earth, opening a new era for process modeling in the fields of hydrology, oceanography, glaciology, geophysics and others. At a special focus are currently mass redistributions due to the continental water cycle derived from gravity changes traceable in time series of monthly GRACE-based gravity field models. Such variations dominate the observable gravity variability and shall be used for the validation and calibration of state-of-the-art hydrology models.

In order to exploit such GRACE-based estimates of surface mass variations for this purpose (as well as for any other application of GRACE-based surface mass data) three fundamental questions need to be resolved: 1) The reduction of spurious gravity signals in the GRACE models caused by various kinds of temporal-spatial aliasing. 2) The signal-signal separation, i.e. the separation of individual mass terms originating from different phenomena (e.g. hydrology, deglaciation, post glacial rebound, etc.) out of the integral satellite gravity signals. 3) The development of the methodology how to use the GRACE-based surface mass estimates (i.e. preprocessed data in the sense that the issues 1) and 2) are considered effectively) for the process modeling.

In this contribution we present results of our research related to topics 1) and 2) in view of the generation of GRACE-based surface mass

variations for the calibration of the WaterGAP Hydrology Model (WGHM, DË&#x2020;sll et al. 2003) by the TIVAGAM team members at GFZ section 5.4. To this end we determine for the first time the actual spectrum of the dominating hydrologically induced gravity changes found in the GRACE data in combination with an accuracy assessment of these terms. As a result, a) we get insight into the morphology of these variations in general and b) this allows for the creation of GRACE data series that contain only these dominating but significant portions of the GRACEbased surface mass anomalies to be used for the actual hydrology model calibration. As it will be shown, such GRACE data series benefit from a clear signal-noise separation which also accounts for a signal-signal separation as the included periodic components are verified by comparison with corresponding spectra derived from independent hydrology models.

2. Approach As a preprocessing step to resolve the spectra of the spatial variability in gravity induced by the hydrological mass redistributions we apply the statistical method of Empirical Orthogonal Functions (EOF, also known as Principal Component Analysis (PCA), e.g. Wilks 1998) to monthly time series of spatial grids of surface mass anomalies derived from GRACE gravity models of the current GFZ-RL04 series and from four independent hydrology models. We use global grids, i.e. data points located over land as well as data points located inside 18 major river basins (see Fig. 1).

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Figure 1: Location and distribution of 18 drainage basins investigated in this study

To account for the spurious gravity signals of the GRACE models prior to the EOF analysis we apply Gaussian averaging for a filter radius of 500 km for both the GRACE-based data as well as for the hydrology model output data to preserve consistency. As the result of the EOF decomposition we obtain the so-called eigenvectors and principal components, which in our case describe the spatial respectively the temporal variability patterns of the input data and give insight into the morphology of the traced changes in surface mass anomalies. For illustration Fig. 2 shows as a typical example the first three modes of the EOF decomposition of surface mass variations in the Amazon basin obtained from 45 monthly maps from GRACE and WGHM in the period 02/2003â&#x20AC;&#x201C; 12/2006. The graphs in the top row display the principal components for each mode, which represent the temporal variability of the associated spatial variability (eigenvectors), which are shown for GRACE in the middle row of Fig. 2 and for WGHM in the bottom row of Fig. 2, respectively. It can be seen that the derived spatial and temporal patterns, which result from independent EOF analyses of each data set, agree quite well.

To underline this agreement Fig. 2 also displays the correlation coefficients derived separately for principal components and eigenvectors per mode, which highlight that the two independent data sets describe a common physical quantity indeed. For a more stringent inter-

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pretation of the correlations one should consider correlation coefficients for the synthezised case (i.e. the product of eigenvector times principal component per mode, for explanation see caption of Fig. 2).

For the determination of the characteristic spectra of the surface mass variations we perform a spectral analysis of the principal components, i.e. we investigate the temporal variability patterns for distinct periodicities. However, instead of a classical Fourier analysis, we apply here a novel frequency analysis method that allows for the determination of periodic terms with arbitrary frequency (Mautz and Petrovic 2005). The major advantage is that we are able to derive a few distinct periodicities which are actually contained in the input data. This is in contrast to the conventional Fourier approach where the spectral content is forced to fit to some basic frequency and its overtones. Since this basic frequency is in general not known in advance and the data may contain frequencies which are not overtones of it, the resulting Fourier spectrum may not well represent the actual periodic content of the data, causing a limited or sometimes even implausible physical interpretation. This is clearly overcome by the frequency analysis proposed here.

In order to allow for a separation of the significant periodic terms found in the GRACE data we perform an accuracy assessment of the derived spectra. This is achieved by means

Figure 2: Eigenvectors and principal components for the first three modes for the Amazon basin from GRACE and WGHM data. The eigenvectors from WGHM and GRACE were normalized (and scaled by a factor of 1000) making the scale of these plots (middle and bottom row) dimensionless and the scale on the y-axis of the plots of the principal components (top row) can be regarded as surface mass in terms of the height of an equivalent mass of water in mm.

The actual value of the surface mass anomaly at some location of the grid can be inferred by multiplying the spatial and temporal variability data per mode and then summing up over all or a subset of modes

of a Monte-Carlo method using state-of-theart calibrated error estimates of the GRACEonly gravity models. In brief, we create a time series of GRACE-based surface mass anomalies including the strongest periodic terms found by the frequency analysis to obtain a filtered or synthetic time series of surface mass variations containing a set of well-defined but also physically plausible variations. To this data series we add 200 realizations of correlated errors of the GRACE-only gravity field models, rigorously propagated into errors of surface mass anomalies, and perform the combined EOF and frequency analysis on each noisy data set. From the empirical distribution of the obtained spectra we derive standard deviations of the spectral parameters (i.e. periods, phases and amplitudes) and can check the significance of each periodic term. Since we do not know which periodic terms are significant

when we construct the initial filtered series from the GRACE data, the whole procedure has to be repeated several times taking into account more or fewer periodic terms (but the same noise data) in order to avoid an over- or under-noising until the results confirm the assumption on the significant periods.

3. Results Our analysis for global continental grids as well as for the selected catchment basins (cf.

Fig. 1) reveals that the spectra of hydrologically induced gravity changes are indeed dominated by a limited set of periodic terms. As obvious from Fig. 2 the strongest component is due to annual variations representing 60 to more than 90% of the total observed variability. This holds for the global case as well as on the level of catchment areas as is e.g. illustrated by the results for the Amazon basin dis-

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played in Tab. 1. Note that 1) the derived annual periods clearly deviate from a conventional value of the annual period and 2) several annual periods are found. This is related to the fact that the hydrologically induced variations are variable in space and time and in general cannot be described by some single variability pattern associated to some constant period. In this way, this result demonstrates the advantage of our frequency method.

In addition to annual terms, significant long periodic variations with a period of about 2–3 years can be detected in many cases. For example for the Amazon Tab. 1 reveals a significant 2.6- to 2.8-yearly signal. Although, a stringent recovery of the actual parameters of such variations may be still limited due to the rather short period of about 4 years covered by the GRACE data, these terms seem to represent plausible mass redistribution signals as consistent values can be derived from the corresponding 4 years and from long-term data series (12 years) from the independent hydrological models. Moreover, first comparisons to the spectra derived from also independent climatological indices, e.g. the Southern Oscillation Index, reveal similar long-periodic variations and seem to indicate a link to mass redistributions induced by large scale mechanisms like the El Nino Southern Oscillation (ENSO).

With respect to semiannual variations our analysis shows that such terms only play a minor role (in terms of the contribution to the total signal amplitude) and only occur in a few

basins in the world (e.g. in the Ganges, the Congo, the Lena and Ob).

In view of an actual model calibration the study shows that for the derived signal phases a systematic advance of the change of surface mass anomalies from hydrology models with respect to GRACE-based mass redistributions can be observed. For the WGHM these offsets lie in the range of 1 to 6 weeks and may in general point to systematic deficiencies in the modeling of water runoff and water retention in WGHM and the other hydrological models.

Finally, in order to perform the quantitative model calibration we reconstruct filtered GRACE-data series – in the same way as it was done for the Monte-Carlo method – considering only the significant terms found by the accuracy assessment. Since the model calibration is to be performed effectively on the level of drainage basins we provide corresponding spatial grids or basin averages, respectively.

As an example for the spatial case we show in Fig. 3 (a) the filtered surface mass anomaly signal for the Amazon basin for the month of February 2005. This map is based on the periodic terms No. 1–4 from Tab. 1. Figure 3 (b) displays the residual signal of the map in Fig. 3(a) subtracted from the total GRACE-based signal of the original input data at that epoch.

As can be seen from the percentages in Tab. 1 the anomalies in Fig. 3 (a) represent about 92% of the total signal, while the residual signal in Fig. 3 (b) represent only about 8% the variability. Although it is clear, that both maps

Table 1: Results of frequency analysis of the principal components for the Amazon basin from GRACE and WGHM input data, respectively. n is a numbering of the periodic terms found. m denotes the mode number of the principal component. T denotes the period in [days], is the phase in [days] (relative to Jan 1st, 2005). A denotes the amplitude.

The unit of the amplitude is relative in the sense that the absolute signal is not given by the principal component alone but has to be multiplied by its eigenvector (see caption of Fig. 2). The column [%] gives the fraction of signal power explained by the individual component relative to the total power of the original input signal

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still contain GRACE data errors, the spatial distribution in particular of the residual signal, which is dominated by North-South oriented striping features very comparable to the correlated GRACE gravity model error, indicates a

clear signal-noise separation obtained by the applied approach.

To further illustrate the effectiveness of the method, we consider the results for the periodic signal for the Mississippi basin reconstructed from GRACE data. In this basin the

Figure 3: (a) Synthesis of GRACE-based surface mass anomalies in the Amazon derived from the first four harmonic terms from Tab. 1 at epoch 15-Feb-2005. (b) Residual of total surface mass anomaly map minus the map shown in (a).

Units: cm water column

Figure 4: Time series of basin averages for the Mississippi basin from Gaussian averages (filter radius 500 km) of surface mass anomalies in cm water column. Plots (a) and (b) show the original and reconstructed data series for GRACE (a) and WGHM (b). The reconstructed signal is derived from two periodic components (one annual and one 2.5-yearly term) in both cases. Plot (c) displays the reconstructed periodic signals from (a) and (b) after a scaling of the amplitude of the WGHM-based curve. Plot (d) depicts the same as plot (c), however, the WGHM curve has been additionally shifted to match the filtered GRACE signal curve

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reconstruction of grids representing surface mass changes in the space domain for all considered epochs (like in Fig. 3 (a) for the Amazon) based on two dominating periodic components (one annual and one 2.5-yearly term) explains only 53% of the original input signal.

In order to answer the question whether this still can be regarded as a meaningful signalnoise separation we compute basin average data series as latitude-dependent weighted arithmetic means from all grid points inside the basin both from the original input (GRACE monthly solutions subjected to Gaussian averaging) and from the periodic signal reconstructed by our method. For these basin averages the reconstructed signal explains about 87% of the input as it is visible in Fig. 4 (a).

This means that the residual variations, in contrast to the reconstructed signal, reveal typical features of the noise and they are attenuated considerably in the process of averaging of the original data.

Fig. 4 (a) and Fig. 4 (b) display the original and the reconstructed data series for GRACE and WGHM with obviously stronger amplitudes for GRACE. However, as it can be seen from Fig. 4 (c) – after a scaling of the amplitude of the periodic signal curve from WGHM – the GRACE and WGHM signal curves match remarkably well and also highlight the typical signal advance for the hydrology model. Correcting the WGHM signal curve additionally for this phase offset, as shown in Fig. 4 (d), an almost perfect match of the two signals can be obtained. This result demonstrates the capability of our approach to provide input for the calibration of hydrology models with respect to dominating periodic terms, even in case of basins where such variations are less prominent.

4. Conclusions and Outlook We have developed a method to estimate the characteristic spectra of hydrologically induced gravity variations observed by GRACE which allows for the reconstruction of the dominating periodic signal components to be used for hydrology model calibration. Due to a clearly improved signal-noise separation in the GRACE-based surface mass anomaly data it is

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expected to improve global hydrology models with respect to the amplitude and the phase of these dominating periodic components of water storage changes. As the method is not restricted to hydro-climatologically induced gravity variations it is expected to contribute to the calibration and validation of other geophysical process models as well. These should include secular phenomena as the method will give access to accurate estimates of trends as the derived periodic components may be more reliable than from classical Fourier techniques.

More details and references can be found in: Petrovic, S., Schmidt, R., Wünsch, J., Barthelmes, F., Güntner, A., Rothacher, M. (2007), Towards a characterization of temporal gravity field variations in GRACE observations and global hydrology models, Proceedings of the 1st International Symposium of the International Gravity Field Service »Gravity Field of the Earth«, Istanbul, General Command of Mapping, Journal of Mapping (ISSN 1300-5790), Special Issue: 18, pp. 199–204.

Schmidt, R., Petrovic, S., Güntner, A., Barthelmes, F., Wünsch, J., Kusche, J. (2007), Periodic components of water storage chagnes from GRACE and global hydrology models, submitted to Journal of Geophysical Reaseach – Solid Earth.

Calibration techniques for a global hydrological model and their interface to GRACE data analysis Werth S., GĂźnter A., Merz B., Schmidt R., Petrovic S. GeoForschungsZentrum Potsdam, Section 5.4 Engineering Hydrology, Telegrafenberg, 14473 Potsdam, Germany, E-Mail: swerth@gfz-potsdam.de

Introduction The satellite gravity mission GRACE (Gravity Recovery And Climate Experiment) is valuable to study ongoing mass redistributions on and near to the Earthâ&#x20AC;&#x2122;s surface, caused from geophysical and climatologically-driven processes. Due to the current processing strategies of the GRACE data centres, GRACE derived mass variations are mainly dominated by mass transfers within the continental water cycle. Therefore, they are invaluable as a novel input for the calibration of large scale hydrology models like the WaterGAP Global Hydrology (WGHM). WGHM simulates the continental water cycle and its most important components (soil, snow, groundwater and surface water), hitherto with significant differences to GRACE measurements, especially for the seasonal amplitude. Towards the calibration of WGHM three fundamental work steps have to be resolved: 1) Derivation of GRACE-based surface mass variations that are reduced for signals of other than hydrological phenomena and for contributions of spurious gravity signals by various kinds of temporal-spatial aliasing. 2) Calculation of filtered time series of area-averaged water mass variations for river basins reducing satellite errors and leakage effects from surrounding areas. 3) Development of a multiobjective model calibration routine to use both, basin-average water storage variations from GRACE and observed river discharge data for the calibration of WGHM. In this contribution we mainly present results of our research related to topic 2). In addition, for topic 3) the general outline of the calibration

approach is given and its present status in terms of implementation of the software in the modelling framework and test runs are presented.

Details with respect to topic 1) are given in the report of the TIVAGAM team members of GFZ Department 1 by Petrovic et. al. 2007. Using a spectral analysis on top of a Principal Component Analysis for data from GRACE and hydrological models including WGHM, characteristic hydrological spectra of the surface mass variations were identified. Including an accuracy assessment of the derived spectra by means of a Monte-Carlo method, a methodology was developed that allows for creating GRACE time data series that contain only the dominating but significant hydrological components of the GRACE-based surface mass anomalies and that invoke a clear signal-tonoise separation. Such time series will then be of direct use for calibration of WGHM as explained below.

Filtered time series for river basins GRACE gravity fields are widely used to derive time series of regionally averaged total mass variations, i.e. for river basins. However, because of errors in higher resolution of GRACE data, application of filter techniques are indispensable. As filters smooth the original data to lower spatial resolution, the user has to balance between remaining errors and spatial resolution when selecting an appropriate filter method. Until now, a lot of filter types have been developed, differing in constraints on the signal-noise properties of the

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GRACE and the to-be detected processes. To this end six of the currently reported external methods to derive regionally averaged water mass variations from GRACE data were evaluated. These comprise isotropic and anisotropic filters, respectively de-correlation methods (see Tab. 1 for a method overview). Questions mainly addressed by the evaluation in this study are: a) Which filter is optimal for which scale, location or basin shape? and b) Which filter tends to be optimal for which local signal properties and, hence, for which sources of mass variations?

To evaluate several filter techniques measured (filtered GRACE GFZ-RL04 data) and simulated (filtered WGHM data) time series are compared.

Therefore a criterion of correspondence, the Nash-Suttcliffe Coefficient (NSC), is applied. This criterion is additionally weighted by a normalized signal damping factor, which leads to wNSC. Values for wNSC were computed for different filter methods and intensities for the 22 worldwide largest river basins and are presented here for the Amazon River basin in Fig. 1.

The filter parameter of GF, OF and SF are very sensitive to wNSC values of the Amazon. Since the Amazon basin is located close to ocean to

the east and the west (inhering different signal properties) and at the equator to the north (with shifted seasonality of water storage), basin averages for the Amazon are quite sensitive to leaking signals for high filter intensities.

By contrast, the anisotropic MF filter type is comparatively insensitive in terms of wNSC values to correlation lengths greater than 300 km and standard deviations greater than 50mm.

This confirms that an exponential signal model is a good approximation to estimate the leakage error and does not strongly depend on the exact estimation of its parameter values. CEF is less effective in equatorial regions; hence, its decorrelation does not improve the correspondence between filtered GRACE and hydrological model time series for the Amazon. DDK gives a wNSC value very close to the optima of the other filter methods.

The best results for each filter type and corresponding wNSC values for the Amazon basin are shown in Tab. 1 and identify OF and SF as the best methods. Among other features, basin shape and signal characteristics mostly determine which filter type might be optimal in a specific basin. As shown in Fig. 2 for Amazon, Ganges and Nile, results widely vary

Table 1: Filter types (column one) used for evaluation analyses are Gaussian (GF), Basin Optimized (OF), Signal Optimized (MF), SNR optimized (SF), decorrelation method CEF, decorrelation method DDK. GF is an isotropic, all others are non-isotropic methods. CEF demands additional application of one of the first four techniques. Corresponding references and parameter are given in colums two, three and four. Optimal parameter and wNSC values are noted for the Amazon basin (colums five and six)

Table 2: Optimal filter types for different river basins derived from correspondence between time series of basin averaged total water mass variation for GRACE data against WGHM simulations

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between different regions. Furthermore, basin specific optimal filter types are confirmed through the alternative global hydrological models GLDAS and LaD, which provide very similar results to that of WGHM. Multi-objective calibration routine for WGHM In its original version, the model is calibrated against observed river runoff at 1235 discharge stations world wide. The station-based

calibration of WGHM results in locally fitted discharge data, but model accuracy might decrease with distance from the calibration stations and within storage compartments that contribute to river discharge such as groundwater, soil moisture or snow. Furthermore, previous studies of measured (by GRACE) and simulated (by WGHM) seasonal variability of total water storage in large river basins partially show significant differences, especially for the seasonal amplitude.

Figure 1: Weighted NSC of several filter types for the Amazon River basin. Blue: GF, red: OF, purple: MF, green: SF, thin graphs: decorrelation method CEF, black dashed constant value: decorrelation method DDK

Figure 2: GRACE derived (blue) and original WGHM simulation (green) of monthly total water mass variation.

Simulation results from a single-objective and single-parameter calibration (red) show significant amplitude improvement, corresponding GRACE time series for the Amazon basin and slight improvement for the Lena river basin

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Figure 3: Multi-objective validation against river discharge and storage change of 2000 model simulations for different parameter sets is given by black dots. The green dots show objective values of the original WGHM simulation. While both objectives are improved for the Lena basin after a single-objective and singel-parameter calibration (red dots), discharge simulation is degraded for the Amazon basin

A first calibration test against GRACE data is done within a single-objective framework and for the most sensitive parameter. As shown in Fig. 2, a single-objective calibration improves the seasonal amplitude compared to GRACE data for river basins as Amazon and Lena.

Nevertheless, amplitude corrections might either not be satisfying (i.e. Lena) or the improved simulations of continental water storage after calibration cause at the same time a decline in the performance of simulated river discharge (Amazon in Fig. 3).

Hence, these results confirm the necessity of a multi-objective and multi-parameter calibration approach, from which more realistic and further improved simulations are expected.

Multi-objective denotes the evaluation of model parameters through their simulation performance against more than one model output objective. This approach enables a combination of the present station-based accuracy of the model in terms of river discharge and the integrative nature of the GRACE data with global coverage. Therefore, the source code of WGHM was extended with multi-objective calibration algorithms. The Dynamically Dimension Search (DDS) calibration method was extended for multi-objective

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problems and implemented into WGHM parameterization. A second method, the full multi-objective Non-dominated Sorting Genetic Algorithm II (NSGA-II) was also installed.

Within the multi-objective WGHM calibration studies, basin-average water storage variations from GRACE that have been pre-processed in different ways will be used. For example, different filter types will be taken into account.

Similarly, reduced time series after extracting the significant signal components from the full GRACE signal provided from GFZ Dpt. 1 (see topic 1 above) will be used as GRACE input for first calibration runs. The concept and the interfaces between GRACE data analyzes and WGHM calibration for this work are shown in Fig. 4. The first results of the multi-objective calibration of WGHM against GRACE data are expected to highlight significant improvements for simulations of total water storage changes as well as river discharge.

Conclusion and Outlook Recent results for the major work steps towards the calibration of WGHM with GRACE derived water mass variations were outlined. Pre-studies on GRACE data as well as filter analyses and model studies were com-

Figure 4: Concept and interfaces between hydrological model calibratlion and GRACE data analyzes

pleted. Furthermore, the implementation of calibration algorithms into the global hydrological model was concluded. In our forthcoming work, a variety of multi-objective calibration runs of WGHM with different input data will be executed. In this way, limitations of the current state of the global hydrological model will be identified, and improved model version can be set up. This will finally fully expose the innovative contribution of the GRACE satellite mission to the field of hydrological modelling.

Further literature Petrovic, S., R. Schmidt, J. Wünsch, F. Barthelmes, R. Hengst, J. Kusche (2007). Periodic Components of Water Storage Changes from GRACE and Global Hydrology Models, Proceeding of »2. Statusseminar Geotechnologien«, Munich, Germany, 2007 (this volume).

Werth. S., A. Güntner, R. Schmidt, J. Kusche (2007). Evaluations of GRACE filter tools from a hydrological perspective, in preparation.

Petrovic, S., Schmidt, R., Wünsch, J., Barthelmes, F., Güntner, A., Rothacher, M. (2007), Towards a characterization of temporal gravity field variations in GRACE observations and global hydrology models, Proceedings of the 1st International Symposium of the International Gravity Field Service »Gravity Field of the Earth«, Istanbul, General Command of Mapping, Journal of Mapping (ISSN 1300-5790), Special Issue: 18, pp. 199–204.

Schmidt, R., Petrovic, S., Güntner, A., Barthelmes, F., Wünsch, J., Kusche, J. (2007), Periodic components of water storage changes from GRACE and global hydrology models, submitted to Journal of Geophysical Research – Solid Earth.

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Author’s Index

A Abrikosov O. . . . . . . . . . . . . . . . . . 112 Angermann D. . . . . . . . . . . . . . . . . . 70 Artz T. . . . . . . . . . . . . . . . . . . . . . . . 60 B Barthelmes F. . . . . . . . . . . . . . . . . . 177 Baur O. . . . . . . . . . . . . . . . . . . . . . . 99 Beyerle G. . . . . . . . . . . . . . . . . . . . . 36 Böckmann S. . . . . . . . . . . . . . . . . . . 60 Boebel O.. . . . . . . . . . . . . . . . . . . . 138 Böning C. . . . . . . . . . . . . . . . 118, 138 Bosch W. . . . . . . . . . . . . . . . . . . . . . 64 Bruhns C.. . . . . . . . . . . . . . . . . . . . . 18 C Cai J. . . . . . . . . . . . . . . . . . . . . . . . . 99 Chambodut A.. . . . . . . . . . . . . . . . 159 D Dahle C. . . . . . . . . . . . . . . . . . . . . . . 5 Danilov S. . . . . . . . . . . . . . . . . . . . . 50 Denker H. . . . . . . . . . . . . . . . . . . . . 85 Dietrich R. . . . . . . . . . . . . . . . . . . . 172 Dobslaw H. . . . . . . . . . . . . . . . . . . 122 Döll P. . . . . . . . . . . . . . . . . . . 163, 172 Drewes H. . . . . . . . . . . . . . . . . . 70, 75 E Eicker A. . . . . . . . . . . . . . . . . 112, 127 Esselborn S. . . . . . . . . . . . . . . . . . . . 47 F Falck C. . . . . . . . . . . . . . . . . . . . . . . 36 Fiedler K. . . . . . . . . . . . . . . . . . . . . 163 Flechtner F. . . 5, 12, 36, 131, 134, 143

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Förste C. . . . . . . . . . . . . . . . . . . . . 112 Freeden W. . . . . . . . . . . . . . . . . . . 167 Freiberg S. . . . . . . . . . . . . . . . . . . 9, 18 Fritsche M.. . . . . . . . . . . . . . . . . . . 172 Frommknecht B. . . . . . . . . . . 134, 143 G Galas R. . . . . . . . . . . . . . . . . . . . . . . 36 Gendt G. . . . . . . . . . . . . . . . . . . . . . 41 Gericke L. . . . . . . . . . . . . . . . . . . 9, 18 Gerstl M. . . . . . . . . . . . . . . . . . . . . . 70 Gorbunov M. . . . . . . . . . . . . . . . . . . 26 Gruber T. . . . . . . . . . . . . . . . . . 93, 106 Grunwaldt L. . . . . . . . . . . . . . . . . . . 36 Günter A. . . . . . . . . . . . . . . . . . . . 183 H Hamoudi M. . . . . . . . . . . . . . . . . . 154 Healy S.B. . . . . . . . . . . . . . . . . . . . . 36 Heise S. . . . . . . . . . . . . . . . . . . . . . . 36 Hengst R.. . . . . . . . . . . . . . . . . . . . 177 Holschneider M.. . . . . . . . . . . . . . . 159 Horwath M. . . . . . . . . . . . . . . . . . . 172 Hunger M. . . . . . . . . . . . . . . . . . . . 163 I Ihde J. . . . . . . . . . . . . . . . . . . . . . . . 85 Ilk K. . . . . . . . . . . . . . . . . . . . . . . . 106 Ilk K.-H. . . . . . . . . . . . . . . . . . 112, 127 Ivchenko V. . . . . . . . . . . . . . . . . . . . 50 K Köhl A. . . . . . . . . . . . . . . . . . . . . . 106 Köhler W. . . . . . . . . . . . . . . . . . 12, 36 König D. . . . . . . . . . . . . . . . . . . . . . 67 König R. . . . . . . . . . 12, 23, 36, 60, 67

Kopischke R. . . . . . . . . . . . . . . . . . . 18 Krügel M. . . . . . . . . . . . . . . . . . 70, 80 Kusche J. . . . . . . . . . . . . . . . . 112, 177 L Lesur V. . . . . . . . . . . . . . . . . . 149, 154 Löcher A. . . . . . . . . . . . . . . . . . . . . 112 Lux N. . . . . . . . . . . . . . . . . . . . . . . . 85 M Macrander A.. . . . . . . . . . . . . 118, 138 Mandea M. . . . . . . . . . . 149, 154, 159 Massmann F.H. . . . . . . . . . . . . . . . . 36 Mayer-Guerr T.. . . . . . . . . . . . . . . . 127 Mayer-Gürr T.. . . . . . . . . . . . . . . . . 112 Meisel B. . . . . . . . . . . . . . . . . . . 70, 80 Mende V. . . . . . . . . . . . . . . . . . . . 9, 18 Merz B. . . . . . . . . . . . . . . . . . . . . . 183 Meyer U. . . . . . . . . . . . . . . 5, 134, 143 Michalak G. . . . . . . . . . . . . . 12, 23, 36 Minchev B.. . . . . . . . . . . . . . . . . . . 159 Müller H. . . . . . . . . . . . . . . . . . . . . . 60 Müller J.. . . . . . . . . . . . . . . . . . . . . . 85 N Neumayer K.-H. . . . . . . . . . . . . . . 5, 12 Nothnagel A. . . . . . . . . . . . . . . . 60, 75 Nutz H. . . . . . . . . . . . . . . . . . . . . . 167 O Offiler D. . . . . . . . . . . . . . . . . . . . . . 36 Ozawa E. . . . . . . . . . . . . . . . . . . . . . 36 P Palm H. . . . . . . . . . . . . . . . . . . . . 9, 18 Panafidina N. . . . . . . . . . . . . 60, 67, 80

Panet I. . . . . . . . . . . . . . . . . . . . . . 159 Petrovic S. . . . . . . . . . . . . . . . 177, 183 Pingel D. . . . . . . . . . . . . . . . . . . 26, 36 Poli P. . . . . . . . . . . . . . . . . . . . . . . . . 36 Q Quesnel Y. . . . . . . . . . . . . . . . 149, 154 R Reinhard H. . . . . . . . . . . . . . . . . . . . 50 Rhodin A. . . . . . . . . . . . . . . . . . . . . 26 Richter B. . . . . . . . . . . . . . . . . . . . . . 75 Richter F. . . . . . . . . . . . . . . . . . . . . . 50 Ritschel B. . . . . . . . . . . . . . . . . . . 9, 18 Romanova V. . . . . . . . . . . . . . . . . . 106 Rothacher M.. . . . . . . . . . . . 23, 36, 75 Rother M. . . . . . . . . . . . . . . . 149, 154 Rudenko S. . . . . . . . . . . . . . . . . . . . 41 Rülke A.. . . . . . . . . . . . . . . . . . . . . 172 Rummel R. . . . . . . . . . . . . . . . . 93, 106 S Sadowsky N. . . . . . . . . . . . . . . . . . . 47 Schmidt R.. 5, 134, 143, 172, 177, 183 Schmidt T. . . . . . . . . . . . . . . . . . . . . 36 Schoell E. . . . . . . . . . . . . . . . . . . . . 159 Schöne T. . . . . . . . . . . . . . . . . . . 41, 47 Schröter J. . . . . . . . . . 50, 56, 118, 138 Schuh W.-D. . . . . . . . . . . . . . . . . . . 99 Sidorenko D. . . . . . . . . . . . . . . . . . . 50 Siemes C.. . . . . . . . . . . . . . . . . . . . . 99 Sneeuw N. . . . . . . . . . . . . . . . . . . . . 99 Snopek K. . . . . . . . . . . . . . . . . . . . . 12 Stammer D. . . . . . . . . . . . . . . . . . . 106 Steigenberger P . . . . . . . . . . . . . . . . 80 Steigenberger P. . . . . . . . . . . . . . . . . 60

189

Stubenvoll R. . . . . . . . . . . . . . . . . . 112 T Tapley B. . . . . . . . . . . . . . . . . . . . . . 36 Tesmer V. . . . . . . . . . . . . . . . . . . 60, 70 Thaller D.. . . . . . . . . . . . 41, 60, 70, 80 ThĂŠbault E. . . . . . . . . . . . . . . . . . . 154 Thomas M. . . . . . . . . . . . . . . . . . . 122 Timmermann R. . . . . . . . . . . . . . . . 118 Tomassini M. . . . . . . . . . . . . . . . . . . 26 V Voigt C. . . . . . . . . . . . . . . . . . . . . . . 85 W Wang Q. . . . . . . . . . . . . . . . . . . . . . 50 Wardinski I. . . . . . . . . . . . . . . . . . . 149 Wenzel M. . . . . . . . . . . . . . . . . . 50, 56 Wergen W. . . . . . . . . . . . . . . . . 26, 36 Werth S. . . . . . . . . . . . . . . . . . . . . 183 Wickert J. . . . . . . . . . . . . . . 23, 26, 36 Wilmes H. . . . . . . . . . . . . . . . . . . . . 85 Wolf K. . . . . . . . . . . . . . . . . . . . . . 167 WĂźnsch J. . . . . . . . . . . . . . . . . . . . 177 Z Zhang F. . . . . . . . . . . . . . . . . . . . . . . 41

190

GEOTECHNOLOGIEN Science Reports – Already published/Editions

No. 1 Gas Hydrates in the Geosystem – Status Seminar, GEOMAR Research Centre Kiel, 6–7 May 2002, Programme & Abstracts, 151 pages.

No. 2

No. 3

No. 4

Information Systems in Earth Management – Kick-Off-Meeting, University of Hannover, 19 February 2003, Projects, 65 pages.

Observation of the System Earth from Space – Status Seminar, BLVA Munich, 12–13 June 2003, Programme & Abstracts, 199 pages.

Information Systems in Earth Management – Status Seminar, RWTH Aachen University, 23–24 March 2004, Programme & Abstracts, 100 pages.

No. 5

Continental Margins – Earth’s Focal Points of Usage and Hazard Potential – Status Seminar, GeoForschungsZentrum (GFZ) Potsdam, 9–10 June 2005, Programme & Abstracts, 112 pages.

No. 6

Investigation, Utilization and Protection of the Underground – CO2-Storage in Geological Formations, Technologies for an Underground Survey Areas – Kick-Off-Meeting, Bundesanstalt für Geowissenschaften und Rohstoffe (BGR) Hannover, 22–23 September 2005, Programme & Abstracts, 144 pages.

No. 7

Gas Hydrates in the Geosystem – The German National Research Programme on Gas Hydrates, Results from the First Funding Period (2001–2004), 219 pages.

No. 8

Information Systems in Earth Management – From Science to Application, Results from the First Funding Period (2002–2005), 103 pages.

No. 9

1. French-German Symposium on Geological Storage of CO2, Juni 21./22.

2007, GeoForschungsZentrum Potsdam, Abstracts, 202 pages.

No. 10 Early Warning Systems in Earth Management – Kick-Off-Meeting, Technical University Karlsruhe, 10 October 2007, Programme & Abstracts, 136 pages.

191

Notes

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Observation of the System Earth from Space The magnetic and gravity field of the Earth are important sources for dynamic processes on its surface and the interior. The investigation of these fundamental physical forces by satellite technologies have received wide international attention in the past years. Research satellites like CHAMP (German/US) and GRACE (US/German) as well as the planned GOCE Mission (ESA’s first Core Earth Explorer mission) allow measurements of the gravitational and magnetic field of hitherto unreached accuracy. Combined with terrestrial observations and computer models these data will help to develop a more detailed understanding of how the Earth's interior system works.

In Germany a significant part of the data evaluation and interpretation is carried out under the umbrella of the R&D-Programme GEOTECHNOLOGIEN. Eight collaborative research projects are recently funded by the Federal Ministry for Education and Research (BMBF). They are carried out in close co-operation between various national and international partners from academia and industry and focus on a better understanding of the spatial and temporal variations in the magnetic and gravity field of the earth and their impact on the dynamic processes taking place in the Earth´s interior and the global climate. The projects are integrative to the recent activities of the Priority Programme »Mass Transport and Mass Distribution in the Earth System«, funded by the German Research Council (DFG).

The abstract volume contains the presentations given on a science meeting held in Munich, Germany, in November 2007. The presentations reflect the multidisciplinary approach of the programme and offer a comprehensive insight into the wide range of research opportunities and applications.

Science Report

Seite 1

GEOTECHNOLOGIEN

11:33 Uhr

Observation of the System Earth from Space

01.11.2007

GEOTECHNOLOGIEN Science Report

Observation of the System Earth from Space Status Seminar 22-23 November 2007 Bavarian Academy of Sciences and Humanities, Munich

Programme & Abstracts

The GEOTECHNOLOGIEN programme is funded by the Federal Ministry for Education and Research (BMBF) and the German Research Foundation (DFG)

ISSN: 1619-7399

No. 11

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No. 11