www.seipub.org/des Development in Earth Science (DES) Volume 3, 2015 doi: 10.14355/des.2015.03.002
Modelling of Surface Air Temperature Element in Malaysia F. Yunus*1, N. K. Chang2, F. J. Fakaruddin3, M. K. Mat Adam4, J. Jaafar5, Z. Mahmud6 1‐4
Malaysian Meteorological Department, Jalan Sultan, Petaling Jaya, Selangor, Malaysia
5‐6
Universiti Teknologi MARA, Shah Alam, Selangor, Malaysia
fariza@met.gov.my; 2nursalleh@met.gov.my; 3fadila@met.gov.my; 4matkama@met.gov.my; 5jasmee@salam.uitm.edu.my; 6zamalia@tmsk.uitm.edu.my *1
Abstract In spatial interpolation approaches, attribute data assumes continuous over space and spatially dependence. The surface air temperature is a collection of data, which are observed at discrete locations. Normally, spatial interpolation analysis applies to produce a continuous surface of this discrete data. There are a number of spatial interpolation techniques available to create continuous distribution of surface air temperature. To generate map of surface air temperature, this study examined the interpolation technique of inverse distance weighting (IDW). In applying the IDW technique, two different types of main data were assessed, i.e. mean monthly temperature data of T and estimation error of T – T’, where T was observed mean monthly surface air temperature and T’ was estimated mean monthly mean surface air temperature from a multiple regression. The multiple regression model was developed based on eight independent variables of elevation, location of latitude and longitude, distances of a station to nearest coastline, four types of land use, which included water bodies, forest, agriculture and build up areas. Cross validation analysis was conducted to calculate five different measured of errors. Inverse distance weighting (IDW) spatial interpolation of T ‐ Tʹ main data was produced acceptable errors and reliable map for mean monthly mean surface air temperature element in Peninsular Malaysia. Keywords Temperature; Malaysia; Spatial Analysis; Interpolation Technique
Introduction Spatial interpolation technique plays a significant role in many environmental studies. The technique was used to generate continuous surface based on point data. There are a number of spatial interpolation technique established, such as inverse distance weighting (IDW), kriging, spline and trend surface regression (Myers, 1994). Although various types of kriging are among the best known spatial interpolation technique in earth science (Brown & Comrie, 2002; Myers, 1994), IDW is frequently used in spatially located of climate data (DeGaetano & Belcher, 2007; Dodson & Marks, 1997; Kurtzman & Kadmon, 1999; Price, McKenney, Nalder, Hutchinson, & Kesteven, 2002; K. Stahl, R.D. Moore, J.A. Floyer, M.G. Asplin, & I.G. McKendry, 2006a). Furthermore, previous studies (Jarvis & Stuart, 2001a; K. Stahl, R. D. Moore, J. A. Floyer, M. G. Asplin, & I. G. McKendry, 2006b; Valley, Drake, & Anderson, 2005; Yunus, 2005) have shown that the performance of kriging and IDW are almost the same. In relatively homogeneous flat surface, direct interpolation analysis of surface air temperature element produced acceptable errors (Serbin & Kucharik, 2009). However, in heterogeneous terrain surface, relationship of surface air temperature with elevation and others environmental elements preclude the direct interpolation of point‐based surface air temperature observation (Civerolo, Sistla, Rao, & Nowak, 2000; DeGaetano & Belcher, 2007; Dodson & Marks, 1997; Stahl et al., 2006a; Ustrnul & Czekierda, 2005). Elevation consistently influenced the distribution of surface air temperature element, where it has directed the spatial interpolation of surface air temperature in many studies (Johnsons, Daly, & Taylor, 2000; Kurtzman & Kadmon, 1999; Price et al., 2002). Other than main influence by elevation, location and distances to coastline and build up areas, are also significant variables in determining surface air temperature values (Jarvis & Stuart, 2001b). Stahl et al. (2006) were included meteorological stations location as independent variable in modeling surface air temperature over British Columbia, Canada. By considering elevation and urbanization, errors in interpolation of surface air temperature can be reduced up to 30% (Choi, 2003). Previous studies (Civerolo et al., 2000; Gallo, Owen, & Easterling, 1999; Shudo, Sugiyama, Yokoo, &
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Oka, 1997; Taha, 1997) also found that there are significant effects of land use types in surface air temperature variations. The main types of land use are classified as agriculture, forest, build up and water (Civerolo et al., 2000; Othman Jaafar, Sharifah Mastura, & Alias Mohd Sood, 2009; Shudo et al., 1997). Multiple‐regression model is commonly used to explain the consequence of environmental factors, over surface air temperature element (Jarvis & Stuart, 2001a; Kurtzman & Kadmon, 1999; Stahl et al., 2006a). To predict surface air temperature element, Stahl et al. (2006) and Brown & Comrie (2002) used station’s coordinate as predictor variables in multiple‐regression model. Jarvis and Stuart (2001a) developed multiple regression model to analyze responses of elevation and land use on surface air temperature. In estimating surface air temperature element, locations of a station and elevation were also selected as predictors in the developed multiple regression model (Kurtzman and Kadmon 1999). However, there were limited studies that combined all significant environmental factors of elevation, locations and distances of station from the coastline and main types of land use, as predictors in multiple regression model to estimate surface air temperature element. The developed multiple regression model was then be integrated with interpolation technique by interpolating residual of T – T’, where T was observed surface air temperature and T’ was estimated surface air temperature from the developed multiple regression model (Jarvis & Stuart, 2001a; Kurtzman & Kadmon, 1999). Currently, there are limited studies carried out in estimating surface air temperature at un‐sample sites in Malaysia. The study by Yunus (2005) has proposed inverse distance weighting (IDW) interpolation technique, with constant temperature lapse rate as the appropriate model to generate map of mean 10‐day mean surface air temperature. However, the study only used data for one year period and elevation was the only environmental factor that considered in the study. Therefore, the purpose of this study is to understand and evaluate all eight environmental factors of elevation, location of latitude and longitude, and distances from the coastline and four main land use types of agriculture, forest, water bodies and build up areas, which can be used to estimate the surface air temperature. This process was also involved integration of multiple regression model and interpolation technique, to delineate the surface air temperature map. The output of this study obtained continuous data of surface air temperature element, which will be a vital input in any surface air temperature element related study. Study Area and Data Sources
FIG 1. DISTRIBUTION OF METEOROLOGICAL STATIONS IN THE STUDY AREA.
Area of study covered the whole Peninsular Malaysia. Peninsula’s climate is hot and humid with relative humidity of 70 to 90 percents. Annual surface air temperature as a whole is around 26.5oC (Lim & Azizan, 2004). The tropical climate is experiencing year‐round of rainy seasons with two annual monsoon seasons of southwest (May to September) and northeast (November to February). This area received up to 2,500mm of rain annually (Lim & Azizan, 2004). This study investigated meteorological element of mean monthly mean surface air temperature. These data were obtained from Malaysian Meteorological Department (MMD) and were observed at 62 meteorological stations in the study area of Peninsular Malaysia. Figure 1 shows the distribution of 62 stations in the study area.
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Monthly data of mean surface air temperature was acquired for 10 years period of January 1999 to December 2008. All stations had sufficient data, where 59 stations or 95.2% of the total stations had at least 80% of completed data (Malmgren & Winter, 1999). The 90‐meter Digital Elevation Model (DEM) and year 2000 land use map also were used in this study. These data were also obtained from MMD. Methodology In this study, eight independent variables (Civerolo et al., 2000; DeGaetano & Belcher, 2007; Dodson & Marks, 1997; Shudo et al., 1997; Stahl et al., 2006a; Ustrnul & Czekierda, 2005) were evaluated in developing regression models for mean monthly mean surface air temperature element. These independent variables were station’s location of latitude and longitude, station’s elevation and nearest distances of a station to the coastline and four main types of land use, which were water bodies, forest, agriculture and build up area (Shudo et al., 1997). Data of independent variables for latitude, longitude and elevation, for each station was obtained together with surface air temperature element data from MMD. However, data for other five independent variables had to determine from point’s data of a station, line data of the coastal area and polygon data of land use. Application in Geographical Information System (GIS) of ArcGIS 9.3 to measure the nearest distance was carried out to estimate all these distances. Data at 62 stations with all the eight independent variables then were used to generate multiple regression model for mean monthly mean surface air temperature element. In creating the multiple regression model, hierarchical regression approached was adopted since this method is the most flexible method among regression analysis techniques (Hair, Black, Babin, & Anderson, 2010; Ho, 2006). Statistical software used in this analysis was SPSS version 16.0. All five regression assumptions of linearity, homoscedasticity, independence term of error, normality of error distributions and multicollinearity (Hair et al., 2010; Ho, 2006), were compiled in the development of the multiple regression model. This study adopted residual method of T – T’ (Jarvis & Stuart, 2001a; Kurtzman & Kadmon, 1999), by executing the developed multiple regression model. By using estimating values of T’, new data field of T–T’ was generated for mean monthly data. This study employed interpolation technique of inverse distance weighting (IDW), since this technique is most frequently used in interpolating surface air temperature element data and among the accurate interpolation method (DeGaetano & Belcher, 2007; Dodson & Marks, 1997; Kurtzman & Kadmon, 1999; Price et al., 2002; Stahl et al., 2006a). In this IDW technique, number of station selected was eight and number of power was two (Dodson & Marks, 1997; Kurtzman & Kadmon, 1999). The developed multiple regression model was integrated with IDW technique by interpolating of T – T’ data. As a comparison, direct IDW interpolation of mean monthly data of T was also performed (Serbin & Kucharik, 2009). In this analysis, 70% of both types of data in each month were involved in the spatial interpolation analysis. To apply this analysis, ArcGIS 9.3 software was used. This analysis was repeated for all 120 months for both types of main data. In each case for both types of data, cross validation analysis was carried out by using the rest of 30% of the data. The five errors values were calculated in this analysis. These errors included mean absolute error (MAE), root mean square error (RMSE), systematic root mean square error (RMSEs), unsystematic root mean square error (RMSEu) and index of agreement value, d (Willmott, 1981; Willmott et al., 1985). These five error values were calculated in general of the whole study area and all seasons (Yunus, 2005), each season (DeGaetano & Belcher, 2007; Jarvis & Stuart, 2001a; Serbin & Kucharik, 2009) and each climate region (Fariza Yunus, Aziz Shafie, Jasmee Jaafar, & Zamalia Mahmud, 2011; Rusticucci & Kousky, 2002; Ustrnul & Czekierda, 2005), to assess the performance of both analyses. Maps of mean monthly mean surface air temperature was also compared and evaluated. IDW interpolation of T main data was directly producing the map of mean monthly surface air temperature. Meanwhile, to generate map of T – T’ main data, surface of T – T’ data was added to surface of T’, where the T’ surface was produced by using the developed multiple regression model, DEM and raster data of nearest distances to the coastline and the four types of land use. Performance of the generated model was compared with the previous model, which was developed by Yunus (2005). Based on cross validation analysis, generated maps of mean monthly mean surface air temperature and
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comparison with the previous model (Yunus, 2005), appropriate model was selected to model mean monthly mean surface air temperature element in Peninsular Malaysia. Results and Discussion Nearest distances of a station to the coastline and, to every land use type were estimated. Complete information for each station included all eight independent variables, together with data of mean monthly mean surface air temperature were used in developing multiple regression models. In the development of multiple‐regression model, which employing hierarchical multiple regression method, all the five assumptions were complied. Table 1 is the developed multiple‐regression model for mean monthly mean surface air temperature by using hierarchical multiple‐regression approached. TABLE 1 RESULT OF HIERARCHICAL MULTIPLE REGRESSION FOR MEAN MONTHLY MEAN SURFACE AIR TEMPERATURE r2 0.757 Significant independent variables (alpha = 0.005) Constant 57.188 Latitude ‐0.003 Longitude ‐0.291 Elevation ‐0.007 Coastline 0.037 Water Bodies 0.021 Forest 0.024 Build Up Area ‐0.021 Agriculture 0.118
Results in Table 1 show that all eight independent variables of latitude, longitude, elevation and five nearest distances from station to coastline, water bodies, forest, build up area and agriculture, were significant in developing multiple regression model of mean monthly mean surface air temperature. Coefficient of determination of this model is relatively high with value of 0.76, where 76% of variability in mean monthly mean surface air temperature can be explained by the eight independent variables. Refer to Table 1, a complete model for mean monthly mean surface air temperature, T’ is as follows: T’ = 57.188 – 0.003 Latitude – 0.291 Longitude – 0.007 Elevation + 0.037 Coastline + 0.021 Water Bodies – 0.024 Forest – 0.021 Built Up + 0.118 Agriculture (1) Estimated value of T’ for each mean monthly mean surface air temperature data were calculated by using the developed multiple regression model. New data field of T‐T’ was also developed by utilizing the calculated values of T’ and observed data of T for mean monthly mean surface air temperature. Complete data of T and T ‐ T’ were utilized, in further analysis of IDW spatial interpolation technique. Table 2 is general results of the whole study area and all seasons, for cross validation analysis of IDW spatial interpolation analyses for both types of data. TABLE 2 GENERAL RESULTS OF CROSS VALIDATION ANALYSIS No. of station Season Main Data r2 Type of error MAE RMSE RMSEs RMSEu d value
All (62 stations) All (four seasons) T‐T’ 0.837
T 0.024
0.581 0.718 0.227 0.682 0.956
1.014 1.924 1.605 1.044 0.349
In Table 2, general result of cross validation analysis shows interpolation of T–T’ main data was obviously better compared to direct interpolation of T main data, with lower error values and higher d value of 0.96. Values of MAE, RMSE and RMSEs for T – T’ main data were relatively small, with RMSEu approached to RMSE. These results indicate the model of T – T’ main data is an appropriate model (Willmott, 1981), because MAE and RMSE values
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were small, with RMSEs near to zero and RMSEu was about RMSE. The developed model of T – T’ illustrates, most of the RMSE values came from unsystematic errors. Furthermore, coefficient of determination, r2 of 0.84 for observed and estimated values for interpolations of T – T’ main data was extremely higher as compared to T main data. Direct interpolation of T main data produced extremely low r2 value of 0.02. Therefore, this direct interpolation technique is not suitable to estimate mean monthly mean surface air temperature in Peninsular Malaysia. Table 3 is cross validation analysis results of mean monthly mean surface air temperature element for every season of northeast monsoon (NE), spring transition (SP), southwest monsoon (SW) and autumn transition (AU). TABLE 3 CROSS VALIDATION ANALYSIS RESULT FOR EACH SEASON No. of station
All (62 stations)
Season
NE
SP
Main Data
T‐T’
T
T‐T’
MAE
0.60
1.14
0.58
SW T
T‐T’
AU T
T‐T’
T
Type of error 0.90
0.56
0.97
0.63
0.95
RMSE
0.73
2.15
0.72
1.76
0.69
1.82
0.77
1.81
RMSEs
0.25
1.86
0.26
1.41
0.23
1.52
0.11
1.69
RMSEu
0.69
1.04
0.67
1.06
0.66
0.99
0.76
0.67
d value
0.96
0.29
0.96
0.32
0.95
0.3
0.96
0.24
Table 3 shows in all four seasons, main data of T – T’ consistently produced lower error values and higher d values as compared to analysis used T as main data. Performances of the residual method of T – T’ were almost the same in all four seasons. Analysis used T – T’ as main data performed better in every season compared to analysis used T as main data. The model was an appropriate model (Willmott, 1981) in all four seasons. Table 4 is the result of cross validation analysis of mean monthly mean surface air temperature element in each climate region (Fariza Yunus et al., 2011) for the both types of data. TABLE 4 CROSS VALIDATION ANALYSIS RESULT FOR EACH CLIMATE REGION Seasons
All (four seasons)
No. of stations
CR I
CR II
Main Data
T‐T’
T
T‐T’
MAE
0.555
0.759
0.651
RMSE
0.692
1.246
0.765
CR III T
T‐T’
T
0.615
0.560
2.048
0.733
0.719
3.493
Type of error
RMSEs
0.233
1.034
0.460
0.441
0.240
3.060
RMSEu
0.652
0.643
0.611
0.586
0.678
1.684
d value
0.928
0.477
0.820
0.813
0.983
0.213
From Table 4, results of interpolation analysis used main data as T – T’ in climate region I (CR I) and climate region III (CR III), continued to perform better than main data of T. Furthermore, the model was an appropriate model in both climate regions. On the other hand, in climate region II (CR II) performance of T main data was slightly better as compared to T – T’ main data. To detect any significant difference in the four error variables between both analyses, Mann Whitney U test was conducted since errors variables in both analyses not normally distributed and their variance were not homogenous (Hair et al., 2010). Results of this test proved that there were no significant differences of the four error values in both analyses, where show performances of both analyses were the same in climate region II. All stations in climate region II located at flat areas, of between 0 to 300m from mean sea level (MSL) (Malaysian Meteorological Service (MMS), 1993), and direct interpolation work well for stations located in flat areas (Serbin & Kucharik, 2009). Therefore, performances of both analyses were equal in climate region II. Figure 2 shows sample maps of mean monthly mean surface air temperature in July 2005, generated from both analyses of T‐T’ and T main data, respectively. As in figure 2, map generated by interpolating of T‐T’ main data, produced more reliable estimated values of mean monthly surface air temperature values with smoothed and nicely presented topography pattern of Peninsular Malaysia. Compared to map generated by direct interpolation of T main data.
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Performance of the model developed in this study was compared with the previous model by Yunus (2005). Results show interpolation of T‐T’ main data is a better model, with lower error values, compared to the previous model.
FIG 2. SAMPLE OF GENERATED MAPS FOR BOTH INTERPOLATION ANALYSES: MAP OF T‐T’ MAIN DATA ON THE TOP AND MAP OF T MAIN DATA ON THE BOTTOM.
The previous model had errors of 1.06℃, 1.29℃, 1.14℃ and 0.56℃, for MAE, RMSE, RMSEu and RMSEs, respectively, and d value of 0.9. The model developed in this study produced lower errors, with reductions of 45% for MAE, 44% for RMSE and 80% for RMSEs, and shows increase of 7% for d value. Meanwhile, RMSEu increased about 20%, and this shows, the developed model is a better model since most of RMSE error related to unsystematic error of RMSEu, as compared to the previous model, most of RMSE related to systematic component. Conclusions Environmental variables of elevation, latitude, longitude, nearest distance to the coastal area and nearest distances to four main types of land use which are agriculture, water bodies, forest and built‐up, are significant in estimating mean monthly mean surface air temperature in Peninsular Malaysia. Cross validation analysis shows, integration model of the developed multiple regression interpolation and IDW interpolation technique, in interpolation of T – T’ main data, is an appropriate model to estimate mean monthly mean surface air temperature. This model produced acceptable error values (Serbin & Kucharik, 2009) of 0.58℃, 0.72℃, 0.23℃, 0.68℃ for MAE, RMSE, RMSEs and RMSEu, respectively, with high d value of 0.96. This model also consistently produced low error values in all four seasons, as well in every three climate regions. Furthermore, map generated from interpolation of T – T’ main data estimated reliable values of mean monthly mean surface air temperature values with smooth surfaces that followed topographic pattern of Peninsular Malaysia. As compared to the previous model, developed by Yunus (2005), which considered only elevation as independent variable, the model developed in this study is an improved model with lower error values. This study shows the seven added independent variables of latitude, longitude and five nearest distances of a station to the coastline and four main types of land use of agriculture, water bodies, forest and build up areas are significant, in estimating mean monthly surface air temperature element in Peninsular Malaysia. REFERENCES [1]
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