Error Analyses of the Sea Ice Draft Retrieval from Upward Looking Sonar

International Journal of Remote Sensing Applications Volume 4 Issue 4, December 2014 doi: 10.14355/ijrsa.2014.0404.01

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Error Analyses of the Sea Ice Draft Retrieval from Upward Looking Sonar Vera Djepa Department of Applied Mathematics and Thoretical Physics, University of Cambridge, UK vd256@cam.ac.uk Abstract Sea Ice Draft (SID) has been recorded in the last 40 years from Upload looking Sonar (ULS) on submarines, but not all data are error corrected. Error corrected SID with uncertainties is required for validation of climate models, satellite observations and for assessment of the seasonal and annual SID change due to climate impact.

The aim of this study is to analyse the uncertainties of the SID, derived from ULS and develop algorithms for error correction and validation of the retrieved SID from ULS. The uncertainties of the retrieved SID (from ULS on submarine) are analysed. Algorithms for error correction of SID with open water offset and beam width impact are developed and applied to correct SID, retrieved from ULS in the Beaufort Sea in 2007. A bias correction function of raw SID data is provided. The comparison of SID from ULS with collocated SID derived from Radar Altimeter (RA2/Envisat) demonstrated improved biases and correlation coefficient, which confirms the accuracy of the bias-corrected SID. Error corrected SID, derived from ULS, has been applied to validate an algorithm for SID retrieval from RA, using variable ice density. Algorithm for retrieval of sea ice density from the sea ice freeboard, derived from RA, is developed and results of retrieved sea ice density in Beaufort Sea are shown. The developed error correction algorithms of SID, retrieved from ULS, have global application for correction of SID, which are not yet error corrected. Error corrected SID and the derived sea ice densities are essential climate variables (ECV) important for improved climate forecast and validation of satellite observations. European Space Agency (ESA), National Snow and Ice Data centre (NSIDC), climate change and numerical prediction programs will benefit the results of this paper.

Keywords Remote Sensing; Sea Ice Draft; Upward Looking Sonar; Error; Uncertainties Analyses; Statistic; Validation

Introduction Arctic sea ice plays an important role in regulating global weather by maintaining the energy balance between Arctic and mid-latitudes. Satellite, airborne, buoy and Upward Looking sonar (ULS) (moored or on Submarine) data have been used to estimate the sea ice

thickness (SIT) changes due to climate impact [Rothrock et al, 2008, Laxon et al, 2003]. Sea Ice Draft from ULS (SID(ULS)) have been used for mapping ice bottom topography, or investigation the SID decline, but still not all SID(ULS) data are processed and error corrected [Wadhams et al, 2011]. There are a number of environmental, random and systematic factors, contributing to the accuracy of the sea ice draft, derived from ULS on submarine, where the open water and the impact of beam width are the most important errors [Rothrock et al, 2007]. Error corrections have been applied for SID, derived from ULS observations at NSIDC [Rothrock et al, 2007], but the SID derived from ULS on UK submarine (‘Tireless’ cruise) in March 2007 have not been corrected [Wadhams et al, 2011]. Methodology and algorithms have been developed in this study for error correction of SID, derived from ULS on submarine. The retrieved SID from ULS, operating on UK submarine in Beaufort Sea has been error corrected in the following Sections and the correction function has been provided.

The error corrected SID, derived from ULS is important not only for investigation of SID decline in the Arctic but also for validation of SID, derived from Radar Altimeter (RA) (on board ERS 1, 2 , Envisat CryoSat-2 and future Sentinel missions). Error corrected SID, derived from ULS in Beaufort Sea, has been used in this study for validation of collocated SID, derived from RA2/Envisat, applying an algorithm of variable ice density.

Sea ice density (ρi), snow depth (hs) and density (ρs) are input variables in the equations for hydrostatic equilibrium, used to calculate SIT and SID from the sea ice freeboard [Kwok, 2010]. Sea ice density has also important role in energy balance and ice atmosphere interactions, which makes ρi Essential climate Variable (ECV). The wide range of sea ice density and its dependence on freeboard, ice type and snow properties have been reported by various authors [Kovacs,1996, Alexandrov, 2010], but still it is not

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available ρi product, derived from the freeboard, and retrieved from satellite altimetry. A sea ice density has been derived in the following sections from SID, retrieved from RA and validated with collocated error corrected SID, from ULS.

is about 1m. The impact of beam width and open water offset on SID retrieved from ULS on the submarine will be estimated in the next sub sections.

Considering above factors, the aim of this study is to analyse the uncertainties of the retrieved SID from ULS, to develop algorithms for error correction of the derived SID from ULS on Submarine and demonstrate SID applications for validation of SID derived from RA and retrieval of sea ice density. The paper is organised as follows: i) the SID (ULS) retrieval technique, error correction algorithms and correction function for SID(ULS), derived in the Beaufort Sea are summarised in Section 1; ii) Retrieval of SID from RA, algorithm for variable ice density and SID applications are given in Section 2. The results are summarised in conclusion.

The main sources of biases, impacting the SID, which is retrieved from ULS on a submarine, are open water correction and footprint error. Mean total bias of 29 cm and standard deviation of about 25 cm, accounting for the footprint error of ULS (with 2o beam width) and open water correction is reported for SID, which is retrieved from ULS and is available in NSIDC [Rothrock, et al, 2007]. This estimate is valid for SID, retrieved from US submarines if open water correction has been applied. If the SID, which is retrieved from ULS, is not corrected with the open water offset, negative draft can be observed due to wrongly identified open water in presence of thin ice. The open water correction bias (Wc) can be derived from the statistic of negative drafts (δmean <0m, δmin<0m, where δmean, δmin are the mean and minimum values of the negative drafts recorded in each 50km region). In presence of negative draft, the Wc is equal to the mean negative ice draft in corresponding region (if the impact of thin ice is not corrected). No open water correction is applied if the mean and minimum SID in any (50 km) region are positive.

Retrieval of SID from ULS The sea ice draft (d) measured by sonar transducer mounted on the submarine is calculated from the difference between the depth of the transducer (DT) below the sea surface and the sonar measured range to the ice bottom by: d = DT – r , (1). where DT = D - H, where H is the vertical distance from the pressure sensor to the sonar transducer (H=15.7m for US submarines [Rothrock et al, 2007] and D is the keel depth (Figure 1), determined by a sensor that measures the pressure. The range r is a distance to the ice, measured by r=2tc, where 2t is the return signal as a function of time (t ) and c is the mean sound speed in the water column. The system precision for measured draft, when the submarine is stationary under smooth ice, is +6 cm [Rothrock et al, 2007] and the spatial resolution ice

K

β

α E

d

r

DT

O

D

H a)

FIGURE 1. RELATION OF THE SUBMARINE, ULS AND ICE DRAFT.

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The mean draft in each 50 km region (dwc), corrected with open water offset (Wc), is calculated by subtracting the open-water correction from the mean draft (dm) in the corresponding region. Because Wc is negative, the open water offset appears as a positive bias: dwc = dm - Wci (2) One can see that wrongly identified open water due to presence of thin ice, or change of the speed and depth of the submarine could lead to negative bias in the retrieved SID and has to be corrected.

Apart from the open water bias the error due to beam width impact is essential and has to be considered in the retrieved SID.

B

γ

Open Water Correction of SID Derived from ULS

Beam Width Impact on Retrieved SID Because the sonar beam is not narrow, the sonar observes an area of the under-ice surface called the “footprint” (Figure 1). A finite footprint diameter causes the first return (FR) to be biased toward deeper draft (dFR) compared to the mean draft within the footprint (f) (dmf) or the draft exactly in the centre of the footprint. The footprint error (εb) can be measured

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as a difference between the deepest draft (dFR) and the mean draft (dmf) within the footprint and depends on footprint width. εb=dFR – dmf (3) The footprint bias varies with the nominal footprint diameter or width (Wf), which in turn is proportional to the beam width (γ) and to the transducer depth. The deeper the submarine, the broader the footprint is (Wf) and the larger the bias is. The footprint width on the sea level is: Wf =2DTtg(γ/2) (4) where γ is the beam width and DT is the transducer depth. For beam width 2o (NSIDC ULS), Wf = 0.035DT [Rothrock et al, 2007]. For the ULS on UK submarine with 3o beam width, Wf = 0.052DT. Vinje et al. (1998) used high resolution two-dimensional maps of ice draft measured in situ in the Greenland and Barents Seas to estimate the footprint error (εb) defined as the difference between the deepest draft (d) within the footprint and the draft (dmf) exactly in the centre of the footprint. By forming averages over various footprint sizes, Vinje et al. (1998) derived relationship between the footprint error and the footprint (Wf): εb= a + bWf ,

TABLE 1. BEAM WIDTH ERROR (M) AS A FUNCTION OF ICE TYPE AND TRANSDUCER DEPTH DT

DT75 (m) DT100 (m) DT130 (m) DT (m) DmT (m) 75 100 130 190 123.7 Fw 0.08 0.07 0.38 0.48 0.60 0.84 0.58 Mw 0.18 0.05 0.39 0.47 0.55 0.72 0.53 Ms 0.04 0.04 0.21 0.27 0.34 0.48 0.32 dm na na 0.33 0.37 0.5 0.69 0.48 0.10 0.11 0.14 0.19 σ na na Wf na na 3.9 5.2 6.76 9.88 a

b

In rough ice (when α>0) the observed draft is higher than the real draft because the ‘first return’ (FR) arriving at the point O does not come from the point directly above O but from the greatest detectable draft in the footprint, Wf. For smooth ice, the FR target must be at the zenith above the ULS and the resulting SID is unbiased. In rough ice the FR target may not be at the zenith, which will introduce a positive bias into the retrieved ice drafts. The ‘lowest return’ LR is the smallest detectable draft in the real footprint, and in rough ice, the LR may not be at the zenith also and the difference between the FR and LR defines ice roughness (Figure 1). Knowledge of transducer depth along the track is required for estimation of beam width bias. If the transducer depth is not known along the submarine track, the beam width error can be calculated for more likely transducer depth.

The total error, due to open water offset Wc and beam width impact is calculated along the submarine track by: ε= Wc+ εb (6)

(5)

where the coefficients (a, b) depend also on ice type, roughness and slope and are given in Table 1 for FYI (First year winter ice (Fw)) and MYI (Multi- Year summer (Ms) and Multi- Year winter (Mw). The beam width errors, calculated by Equation 5, (for beam width 3o (ULS of UK cruise), different transducer depths (75m, 100m, 130m, 190m) and ice type) are provided in Table 1 and Figure 2. Considering Table 1, the retrieved draft could be positively biased in the range from 39.5cm to 55.2cm for transducer depth in the range between 75 and 130m and multi-year winter ice. The ice slope impact within the footprint is not considered in Table 1. The footprint, mean biases for FYI and MYI and different transducer depth with corresponding standard deviations are also listed in Table 1. The mean bias for 3o beam width for all ice types and seasons is estimated to be 0.48m with mean standard deviation 0.15m.

Ice

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Std (m) 0.2 0.14 0.11 0.15 -

FIGURE 2. IMPACT OF TRANSDUCER DEPTH AND ICE TYPE ON FOOTPRINT ERROR BIAS OF THE SID DERIVED FROM ULS.

The mean corrected sea ice draft (dmc) within the length (50km) is calculated by: dc = dm- ε

(7)

where dm is the mean raw draft within the region of 50km. The method for bias correction of ULS on submarine is similar to that, applied for ULS data correction from NSIDC. The error analyses show that open water and footprint biases are the most important biases, which have to be corrected along the submarine track, using the algorithms described in this section. The results of open water offset, total 147

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biases and corrected SID derived from ULS, are presented in the next sections.

Bias Correction of SID, Derived from ULS on UK Submarine in Beaufort Sea in 2007.

The sea ice draft, measured during the “Tireless” cruise in March 2007, in the Arctic, is obtained from an along-track single-beam ULS, Admiralty Type 780 echo sounder, with 3° beam width [Wadhams et al, 2011]. The mean raw and corrected ice draft in 50km spatial resolution with corresponding statistic (variance, standard deviation, confidence interval, minimum and maximum), open water offset and total correction functions have been calculated. The εb is calculated along the submarine track by Equation (5) and ε is calculated by Equation (6), considering the footprint for 3o beam width and DT=75 m. The algorithm allows to select the ice type and coefficients (a, b) from Table 1. The location of the regions with 50km resolution is shown on Figure 3/a. The raw and corrected sea ice draft, derived in March 2007 from ULS on submarine in the Beaufort Sea, are compared in Figure 3/b and the total bias correction and open water offset for all ULS available regions with 50km spatial resolution are shown in Figure 3/c.

The raw draft is usually higher than the corrected draft because the ULS records the first return, which is from the highest SID within the footprint. The mean values of the SID from ULS, before, dm, and after correction, dc, and the bias (dm-dc) are listed in Table 2.

Use of not corrected sea ice draft will overestimate SID in the Beaufort Sea with 23cm. The estimated bias and standard deviation (std) between the raw and corrected SID (ULS) on UK submarine is similar to that reported in [Rothrock et al, 2007] for SID, available in NSIDC. TABLE 2. MEAN

(dm) AND CORRECTED (dc) SID, RETRIEVED FROM ULS ON

UK SUBMARINE IN BEAUFORT SEA, 03/2007

(m)

dm 3.548

dc 3.317

Bias 0.231

std 0.118

The collocated open water offset and the total correction averaged in 50 km and centred at the SID, retrieved from RA2, are shown on Figure 3/d and the locations are given in Table 3.

TABLE 3. LOCATION OF COLLOCATED SECTIONS OF ULS AND RA2 AVERAGED AREA

La Lo

80.61 -4.04

81.06 -4.02

81.51 -4.05

81.96 -4.07

75.40 -144.6

75.10 -144.51

The corrected SID, which have been derived from ULS, confirm that the open water and footprint errors have significant impact on accuracy of retrieved SID and have to be corrected. Bias corrected SID (with location given in Table 3), have been validated with collocated SID from RA2 (Envisat).

Applications of SID, Derived from ULS

a)

b)

c)

d)

FIGURE 3. A) LOCATION OF SID(ULS), 03/2007, BEAUFORT SEA; B) RAW AND CORRECTED (RED) SID FROM ULS, 03/2007; C) CORRECTION FUNCTIONS (WC AND ε); D) ε AND WC WITH 50KM RESOLUTION COLLOCATED WITH SID FROM RA.

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Collocated SID from moored ULS and ULS on Submarine in Beaufort Sea with SID from RA2 (Envisat) from the data base (Round Robin Data Package (RRDP)), developed as part of the European Space Agency (ESA) Climate Change Initiative (CCI) sea ice Essential Climate Variable (ECV) project [SICCI, 2013] have been used for SID validation and retrieval of sea ice density. The data base used for this study includes collocated snow depth and density from WC with the same spatial resolution, time and location as RA2 data and SID from ULS on submarine averaged over 50 km along track, collocated with the mean freeboard, derived from RA and RA2, averaged within an area of 100 km radius centered at each transect center. The sea ice freeboard is derived from ERS-1/2 RA and Envisat/ RA-2 as a difference of the measured ice floe elevation and the local sea level, applying necessary corrections and is averaged over one month

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[SICCI, 2013].

Validation of the Bias Correction Algorithm for SID from ULS The impact of bias correction on retrieved SID from ULS has been examined by comparison of collocated SID (retrieved from ULS before and after bias correction) with SID, which have been derived from RA. On Figure 4/a are shown collocated SID, derived from ULS in Beaufort Sea (BS) before and after bias correction and SID, retrieved from Envisat/RA2. The SID has been retrieved from the freeboard, derived from RA2, applying the equation for hydrostatic equilibrium: dra=hi-hfi = (hsρs +hfiρi)/( ρw − ρi),

(8)

where hi is the SIT and hfi is the retrieved freeboard from RA. Collocated snow depth (hs) and density (ρs) are taken from WC as a function of latitude, longitude and month of the year in the Arctic [Warren and Rigor, 1999]. The algorithm (A1) used to calculate hi from the freeboard derived from ERS1/2 and Envisat with ice density (ρi=900kg/m3) and water density (ρw=1030kg/m3) inserted in Equation 8 is applied to derive dra, collocated with SID(ULS).

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The mean and correlation coefficients for collocated SID (RA) and SID (ULS) with 50km spatial resolution (before (dm) and after bias correction (dc)) are listed in Table 5. The mean absolute difference (abs (dms – dra)= 0.1) of the raw SID derived from ULS and SID retrieved from RA2 (dra) is reduced from 10cm to less than 1mm after applying the algorithm for error correction and the correlation coefficient is increased, which confirms the improved accuracy of the retrieved sea ice draft from ULS after error corrections (Table 4, Figure 4).

TABLE 4. MEAN AND CORRELATION COEFFICIENTS OF THE RETRIEVED FROM ULS AND ERROR CORRECTED SID (ULS).

mean Mean(m) Correlation

dm 2.4437 0.9

dra 2.343 1

dc 2.335 0.927

One can see that the total mean of the raw draft is overestimated compared with the mean SID derived from RA2 and the corrected one. The residuals between corrected SID and that derived from radar altimeter have decreased after applying error correction algorithm. Error corrected SID(ULS) have been used to retrieve ρi from the freeboard derived from RA. Retrieval of Sea Ice Density from SID Sea Ice density is important ECV. It varies in wide range [Kovacs, 1996, Alexandrov et al, 2010, Ackley, et al, 1976]. Constant ice densities have been inserted in the equation for hydrostatic equilibrium (Equation 8) to retrieve SID from the freeboard, derived from RA, leading to different SID with unknown accuracy. Sea ice density dependence on sea ice freeboard has been confirmed with field observations [Ackley, 1976], laboratory study [Kovacs, 1996] and sensitivity analyses [Djepa, 2014]. Djepa, (2014) developed and validated an algorithm to retrieve variable sea ice density considering the impact of ice type, snow density and depth. The algorithm has been validated with surface observations [Ackley et al, 1976], laboratory study [Kovacs, 1996], sensitivity analyses and collocated ULS and satellite observations. The variable sea ice density (ρi) is retrieved from the freeboard, derived from RA2, using the algorithm developed by [Djepa, 2014] :

a)

b)

c)

FIGURE 4. COLLOCATED SID FROM ULS AND RA: A) BEFORE AND AFTER ERROR CORRECTION; B) SID(ULS) VERSUS SID FROM RA2 BEFORE ERROR CORRECTION; C) AFTER ERROR CORRECTION

ρi = -c hfie + d

(9)

where hfie = hfi + (hsρ s/ρimean) c=214, d=948,

for 0.18m <hfie <0.37m,

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freeboard derived from RA2/Envisat is given in Table 7. The mean ρi corresponds to presence of MYI, which is confirmed with the mean draft (2.4m), corresponding also to MYI .

ρiMYmean= 882kg/m3 , over MYI c=36.54, d=903.7, for hfie >0.37m, ρiMYmean= 882kg/m3 , over MYI c=95.05, d=930.4, for hfe<0.18m,

TABLE 6. STATISTIC OF THE ρI (KG/M3) RETRIEVED FROM RA2

ρiFYmean= 910kg/m3 , over FYI The SID (dra(FD2)) retrieved from the freeboard, derived from RA2 (by Equation 8), inserting variable ice density (Equation 9) is validated with error corrected collocated SID, derived from ULS in Beaufort Sea and the statistic is given in Table 5.

TABLE 5. DRAFT STATISTIC OF BIAS CORRECTED SID (ULS), COLLOCATED WITH SID (RA2) IN BEAUFORT SEA, 03/2007.

Variable (m) Mean Std Bias RMSE

dc(ULS) 2.365 0.582 0 na

dra(FD2) 2.351 0.562 -0.014 0.102

min 0.893

max 902.5

mean 895.8

Median 893.8

mode 893

std 3.709

The ice density is calculated as a function of ice type and ice freeboard. The effective freeboard (the ice scattering surface) is determined from the snow depth and density. Equation 10 allows sea ice density retrieval from the freeboard, measured by RA on board ERS1, 2, Envisat, CryoSat-2 and future Sentinel ESA missions, providing long time series of sea ice densities distribution in the Arctic.

Conclusions

One can see that the bias (B=(dra(RA2)-dc(ULS)) and RMSE are minimum when variable ice density (Equation 9) is inserted in Equation 8.

FIGURE 5. SEA ICE DENSITY CALCULATED FROM THE FREEBOARD DERIVED FROM RADAR ALTIMETER ON BOARD ENVISAT

Equation 9 allows retrieving a new product, ρi, from the freeboard, derived from RA. The sea ice density calculated from the sea ice freeboard, retrieved from RA2/Envisat is shown on Figure 5. The following relationship of sea ice density and the freeboard, retrieved from RA2 / Envisat has been derived:

Error corrected SID, derived from different ULS on submarine with corresponding uncertainty analyses are required for validation of SID, derived from satellite altimetry, and for climate assessment.

Algorithms for correction of SID (retrieved from ULS on a submarine) with open water offset and beam width error, have been developed and applied to correct SID, which has been retrieved from ULS in the Beaufort Sea in 2007. A bias correction function of raw SID, retrieved from ULS on Submarine is provided and is compared with biases of the derived SID from NSIDC. The obtained biases and standard deviation are in the same range as reported ones for SID, derived from ULS on US submarines. The comparison of dc from ULS in Beaufort Sea with SID derived from RA2 (on board Envisat) demonstrated decreased biases between the sea ice draft derived from ULS and satellite radar altimetry, which confirms the improved accuracy of the bias corrected SID derived from ULS. The algorithms, developed for SID error correction, have global application for SID correction (derived from ULS on submarine cruises), providing long term corrected SID in the Arctic.

(10)

The bias corrected SID, have been used for validation of SID retrieval from the freeboard, which was derived from RA2/Envisat. Comparison of SID, derived from RA2, using variable ice density, with collocated error corrected SID from ULS demonstrated minimum bias and RMSE.

where p1 = -5.3364*105, p2 = 5.6431*105, p3 = -2.3308*105, p4 = 46833, p5 = -4587.3 with norm of residuals 0.067.

The statistic of the retrieved ice density from the

Low resolution sea ice density product is retrieved from the freeboard, derived from RA. The retrieved variable ice density is essential climate variable

ρi=p1hfi5+p2hfi4+p3hfi3+p4hfi2+p5hfi+1072.1

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required for improved energy balance and model forecast.

Considering the importance of SIT and SID for climate, NWP models and sea ice balance in the Arctic, the above results will benefit current and future ESA and NASA programs, climate change and numerical prediction programs, providing more accurate SID from ULS on Submarine for validation of climate models and SID, which is derived from satellite altimetry. The provided algorithm for sea ice density retrieval from the freeboard derived from RA on board ERS1, 2, Envisat, CryoSat-2 and future Sentinel missions is essential contribution to climate research and satellite remote sensing of the north latitudes.

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Djepa V. ‘’Sensitivity Analyses of Sea Ice Thickness Retrieval from Radar Altimeter.‘’ Journal of Surveying and Mapping Engineering (JSME), v. 2, iss. 2, (2014) Kovacs A.. ‘’Sea Ice. Part II. Estimating the full scale tensile, flexural and compressive strength of first year ice.‘’ (1996), CRREL Rept.

Kwok R. ‘’Satellite remote sensing of sea ice thickness and kinematics a review.’’ J. Glaciology. ( 2010).

Laxon, S. et al. ‘’CryoSat-2 estimates of Arctic sea ice thickness and volume. ‘’ Geophysical Research Letters, 40, (2013): 1–6.

Laxon, S., N. Peacock, and D. Smith.’’ High inter-annual variability of sea-ice thickness in the Arctic region’’.

ACKNOWLEDGEMENT

Nature, 425 (2003): 947–950.

The work is supported from the Newton Trust, Cambridge University, UK and ESA SICCI project.

Thanks ESA/SICCI project partners for funding and providing collocated satellite and submarine data.

Rothrock, D., and M. Wensnahan. ’’The accuracy of sea-ice

REFERENCES

Rothrock, D., D. B. Percival, and M. Wensnahan. ‘’The

Ackley, S. F., W. D. Hibler, F. Kugzruk, A. Kovacs, and W. F. Weeks. ‘’Thickness and roughness variations of Arctic multiyear sea ice.’’ CRREL Rep. (1976): 76-18, 24 pp., U.S. Army Cold Regions Res. and Eng. Lab., Hanover, N.H. Alexandrov V., S. Sandven, J. Wahlin, and O. M. Johannessen. ‘’The relation between sea ice thickness and freeboard in the arctic.’’ The Cryosphere Discussion. 4 (2010): 373-380.

Theoretical

Basis

Document.

SICCI-ATBD

(http://icdc.zmaw.de/fileadmin/user_upload/ESA_SeaIce-ECV/SICCI_ATBDv1_D2.6_Issue1.1.pdf) (2013) v104-13.

Atmospheric

and

Oceanic

Technology,

(2007),

24(11:1936-49. decline in arctic sea-ice thickness: Separating the spatial,

Acad. Publish. Co., Ltd.

Algorithm

drafts measured from U.S. Navy submarines.’’ Journal of

annual, and interannual variability in a quarter century of submarine data.’’ J. Geophysical. Research, (2008), 113, C05003, doi:10.1029/2007JC004252.

Vinje, T., N. Nordlund, and A. Kvambekk, 1998: Monitoring ice thickness in Fram Strait. J. Geophys. Res., 103, 10 437– 10 450, (1998).

Wadhams P., N. Hughes and J. Rodrigues. ‘’Arctic sea ice thickness characteristics in winter 2004 and 2007 from submarine sonar transects.’’ J. Geophysical Res.,(2011), 116, C00E02 Warren S. and I. Rigor. ‘’Snow depth on Arctic sea ice.’’ J. Climate, 12, (1999).

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