1. Introduction

An air temperature control determines air temperature variation from one region to another region ^[1]. Elevation is a main control of air temperature in heterogeneous regions. Temperature lapse rate is an inverse correlation between air temperature values and elevation, where air temperature decreases when elevation is increased ^{[1, 2]}. In most of the previous studies, [3-7]^[3], the lapse rate values were approximated from data utilized in the studies. In Peninsular Malaysia for estimating mean air temperature, estimation by Yunus ^[8] considered only elevation as the independent variable. However in homogeneous terrain, such as climate region II of Peninsular Malaysia ^[9], the role of elevation is less significant in the variation of air temperature element ^[10]. Furthermore, it is possible to perform direct interpolation procedure for air temperature in areas with minor topographic variation ^[11].

Other air temperature controls are location, coastline and build up areas. These factors are significant environmental independent variables to estimate air temperature values ^[12]. Study by Choi ^[13] discovered that errors in interpolation of air temperature can be reduced up to 30% by considering urbanization. Previous studies ^{[14, 15, 16, 17]} suggested that there is a vital contribution of land use types in air temperature distribution. Main types of land use are agriculture, forest, build up, and water bodies ^{[14, 16, 18]}. The study conducted by Stahl ^[5] considered the location of meteorological stations as an independent variable in modeling air temperature over British Columbia, Canada. In general, important controls of air temperature are elevation, station’s location, coastline and land use types. However, there were limited studies that combined all the eight significant air temperature controls in estimation of air temperature element. Furthermore, the existing estimation by Yunus ^[8], for estimating mean air temperature in Peninsular Malaysia only considered elevation as an independent variable.

A multiple regression model is commonly developed to explain the effect of air temperature controls on the air temperature element ^{[5, 19, 20]}. To predict air temperature element, Stahl ^[5] and Brown & Comrie ^[22] employed station’s coordinate as independent variables in multiple regression. Jarvis & Stuart ^[19] developed a multiple regression model to examine the responses of elevation and land use over air temperature. Predictor of station’s locations and elevation were also selected to develop a multiple regression model in estimation of air temperature element ^[20]. The developed multiple regression model was integrated by an interpolation technique that interpolates the residual of T–T’, where T represents the observed air temperature and T’ is the estimation of air temperature from the multiple regression model ^{[19, 20]}.

Spatial interpolation technique plays a significant role in most environmental studies. The technique is used to produce a continuous surface from discrete data. There are some established techniques of spatial interpolation such as inverse distance weighting (IDW), kriging, spline, and trend surface regression ^[21]. Although kriging is the best known spatial interpolation technique in earth science ^{[21, 22]}, IDW is frequently used in spatially located climate data ^{[3, 4, 5, 20, 23]}. Furthermore, earlier studies have shown that the performance of kriging and IDW are roughly equal ^{[5, 8, 19, 24]}.

Currently, there are limited studies carried out in estimating air temperature at un-sampled sites in Malaysia. Yunus ^[8] proposed the IDW interpolation technique with constant temperature lapse rate as the appropriate technique in generating mean 10-day mean air temperature. However, the study only used data over a one year period and elevation was the only environmental factor considered in the study. Furthermore, the influence of elevation factor on air temperature variation becomes less significant in homogeneous terrain with minor topographic variation. Hence, the purpose of this study is to understand and evaluate all eight air temperature control of elevation, latitude, longitude, coastline and four types of land use, which can be used to estimate the air temperature over homogeneous terrain of climate region II in Peninsular Malaysia ^[9]. This process would also include the integration of multiple regression model and interpolation technique to generate continuous surface of air temperature.

2. Study Area and Data Source

The study area covers climate region II in the eastern part of Peninsular Malaysia. Generally climate in the peninsula is hot and humid, with relative humidity of between 70 and 90 percent. Annual air temperature is around 26.5°C ^[25]. This region experiences tropical climate. It has two annual monsoon seasons namely the southwest (May to September) and northeast (November to February). This area receives up to 2,500 mm of rain annually ^[25].

This study investigated the meteorological element of mean monthly mean air temperature. These monthly data are provided by the Malaysian Meteorological Department. The data were observed from 17 meteorological stations in the study area of climate region II. Figure 1 shows the distribution of 17 stations in the study area.

Monthly data of mean air temperature were acquired over a 10 year period of January 1999 to December 2008. All stations had sufficient data, where 16 stations or 94.1% of the total stations had at least 80% of completed data ^[26]. Additionally data of 90-meter Digital Elevation Model and year 2000 land use map were also used in this study. These data were also obtained from the Malaysian Meteorological Department.

Figure 1. Distributions of meteorological stations in the study area

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3. Methodology

In this study, eight independent variables ^{[3, 4, 5, 6, 14, 16]} were evaluated in developing the regression model for the mean monthly mean air temperature element. These independent variables included station’s location of latitude and longitude, station’s elevation, the nearest distances of station to coastline and the nearest distances of station to each of the four main types of land use, which were water bodies, forest, agriculture and build up area ^[16]. Independence variables of latitude, longitude and elevation; for each station were obtained together with air temperature element data from MMD. However, the other five independent variables have to be determined from the point’s data of station, line data of coastal area and polygon data of land use. Application in Geographical Information System (GIS) of ArcGIS 9.3 to measure the nearest distances was carried out to estimate all these distances.

Data at 17 stations with all eight independent variables then were used to generate a multiple regression model for mean monthly mean air temperature element. In creating this multiple regression model, the hierarchical regression approach was adopted since this method is the most flexible method among regression analysis techniques ^[27], ^[28]. The 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 ^{[27, 28]} has to be complied in developing this multiple regression model.

In this study, the residual method of T – T’ ^{[19, 20]} is applied to develop the multiple regression model. By using estimated values of T’, new data fields of T – T’ were generated for mean monthly data. This study utilized the Inverse Distance Weighting (IDW) interpolation technique since it is most frequently used in interpolating air temperature element data and is amongst the most accurate interpolation method ^{[3, 4, 5, 20, 23]}. In this IDW technique, the number of station selected was eight and number of power was two ^{[4, 20]}. 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. In this analysis 70% of both types of data in every month were involved in this spatial interpolation analysis. To apply this analysis, the ArcGIS 9.3 software was used. This analysis was repeated for all 120 months for both types of main data.

Table 1. Results of Hierachical Multiple Regression for Mean Monthly Mean Air Temperature

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In every case for both types of data, cross validation analysis was carried out by using the rest of 30% of the data, where five errors values of mean absolute error (MAE), root mean square error (RMSE), systematic root mean square error (RMSEs), unsystematic root mean square error (RMSEu) and d values ^{[29, 30]} were calculated. Maps of mean monthly mean air temperature were also compared and evaluated. IDW interpolation of T main data was directly used to produce the map of mean monthly air temperature, whereas to generate the map of T – T’ main data, T – T’ data was added to the surface of T’, where this T’ was produced by using the developed multiple regression model, DEM and raster data of nearest distances to coastline and the four types of land use.

Performance of the developed estimation was also compared with the previous estimation developed by Yunus ^[8]. Based on cross validation analysis, generated map of mean monthly mean air temperature and comparison with the previous estimation ^[8], the appropriate estimation was recommended to predict mean monthly mean air temperature.

4. Results and Discussion

Distances of each station to the nearest coastal area and distances of each station to each type of land use were estimated. Complete information for each station included all the eight independent variables, together with data of mean monthly mean air temperature were used in developing multiple regression models. In the development of multiple regression model which employed hierarchical multiple regression method, all the five assumptions were complied.

Table 1 illustrates the parameters used in the multiple regression model developed to predict the mean monthly mean air temperature element using the hierarchical multiple regression approach. Results in Table 1 shows that among the eight environmental factors, five variables were significant in developing the multiple regression model of mean monthly mean air temperature. Coefficient of determination, r² of this model is relatively low with value of 0.14. This low value of r² is due to modeling air temperature over homogeneous areas in which the role of environmental factors are reduced ^[11]. The r² of 0.14 means that by adding five independent variables, 14% of variability in mean monthly mean air temperature can be explained. Referring to Table 1, a complete multiple regression model for mean monthly mean air temperature is as follows:

(1)

Estimated values of T’ for mean monthly mean air temperature data were calculated by using the developed multiple regression model. New data fields of T - T’ were also developed by utilizing calculated values of T’ and observed data for mean monthly mean air temperature of T. Complete data of T and T - T’ were utilized in further analysis using the IDW spatial interpolation technique.

Table 2 contains the general results of cross validation analysis using the IDW spatial interpolation technique for both types of data. In Table 2, results of cross validation analysis shows that interpolation of T – T’ main data had better performance compared to direct interpolation of T main data, with lower error values and a higher d value of 0.91. The RMSE value for T – T’ main data was smaller with smaller RMSEs and RMSEu value approaching the RMSE value. These results indicate that the model of T – T’ main data is a ‘good’ model ^[29] since both the MAE and RMSE values were small, with RMSEs near to zero and RMSEu is close to the RMSE value which showed that most of the RMSE values were from unsystematic errors. Furthermore, the coefficient of determination, r², of the interpolated T – T’ data was 0.67 which is higher compared to the r2 for the direct interpolation of T.

Table 2. Results of Cross Validation Analysis

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Figure 2 and Figure 3 show sample maps of mean monthly mean air temperature in May 2000 generated from both analyses.

As in Figure 2, the map generated by interpolating T – T’ data produced more reliable estimated values of mean monthly mean air temperature compared to the map generated by direct interpolation of T main data (Figure 3). The map created by interpolating T-T’ was producing a smooth visualization and nicely presented topographical patterns of Peninsular Malaysia.

The performance of the model developed in this study was compared with the previous estimation by Yunus ^[8]. It was found that interpolation of T – T’ main data is a better model with lower error values as compared to the previous model with errors of 1.06°C, 1.29°C, 1.14°C and 0.56°C, for MAE, RMSE, RMSEu and RMSEs respectively, and d value of 0.9. The model developed in this study produced lower errors with significant reductions of 58% for MAE, 56% for RMSE and 80% for RMSEs and showed an increase of 1.1% for d value. Meanwhile the RMSEu showed a slight decrease of about 7%, indicating that the developed model is a better model since most of the RMSE error was related to the unsystematic error of RMSEu, as compared to the previous model, where most of the RMSE was related to the systematic component.

Figure 2. Sample of Generated Map for Interpolation Analysis of T-T’ Main Data

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Figure 3. Sample of Generated Map for Interpolation Analysis of T Main Data

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The performance of the model developed in this study was compared with the previous estimation by Yunus ^[8]. It was found that interpolation of T – T’ main data is a better model with lower error values as compared to the previous model with errors of 1.06°C, 1.29°C, 1.14°C and 0.56°C, for MAE, RMSE, RMSEu and RMSEs respectively, and d value of 0.9. The model developed in this study produced lower errors with significant reductions of 58% for MAE, 56% for RMSE and 80% for RMSEs and showed an increase of 1.1% for d value. Meanwhile the RMSEu showed a slight decrease of about 7%, indicating that the developed model is a better model since most of the RMSE error was related to the unsystematic error of RMSEu, as compared to the previous model, where most of the RMSE was related to the systematic component.

In this study, direct interpolation of T was found to have lower errors compared with the previous estimation by Yunus ^[8], with error reduction of 44%, 56% and 70% for MAE, RMSE and RMSEs. RMSEu value for direct interpolation of T produced a slightly higher error of 3% compared to the previous model. This result shows direct interpolation of T data is a better model because the majority of RMSE error was related to unsystematic error of RMSEu. In descending order, performances of these three models are: interpolation of T – T’ data, direct interpolation of T and previous estimation by Yunus ^[8].

5. Conclusion

Air temperature controls of elevation, latitude and nearest distances to three main types of land use which are water bodies, forest and build up are significantly vital in estimating mean monthly mean air temperature over homogeneous terrain 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 a ‘good’ model to estimate mean monthly mean air temperature. This model produced acceptable error values ^[11] of 0.45°C, 0.58°C, 0.23°C, 0.52°C for MAE, RMSE, RMSEs and RMSEu, respectively, with high d value of 0.91. Although the generated multiple regression model had low r2 of 0.14, the role of the five independent environmental factors are obviously significant with reduction of errors between 7% and 80% compared with direct interpolation. Furthermore, map generated from interpolation of T – T’ main data estimated reliable values of mean monthly mean air temperature values with smooth s that followed topographic pattern of Peninsular Malaysia. The model developed in this study is also a better estimation with lower error values, compared to the previous estimation developed by Yunus ^[8] which considered only elevation as an independent variable. This study discovers that in estimating air temperature element in homogeneous areas, all air temperature controls have to be evaluated. By considering only elevation as a predictor, the final value of air temperature is not an appropriate estimation. Furthermore, the direct interpolation of T performed better with lower errors compared to the estimation using only the elevation predictor. This study revealed that there are significant contribution of five independent variables of latitude, elevation and the three nearest distances of station to water bodies, forest and build up areas, in the estimation of air temperature element over homogeneous terrain areas of Peninsular Malaysia.

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