Estimating 1 km gridded daily air temperature using a spatially varying coefficient model with sign preservation

Abstract

Near-surface air temperature (Ta) is one of the key variables in a variety of studies such as hydrological modeling, assessment of heat waves, and energy modeling. Among existing methods, statistical algorithms are suitable for integrating auxiliary spatial data with station-based Ta data to produce gridded Ta over large areas. However, existing statistical algorithms (e.g., Geographically Weighted Regression (GWR)) cannot always correctly capture and preserve relationships between Ta and explanatory variables, which may increase uncertainties of relevant applications based on the estimated Ta with abnormal spatial patterns. This issue is mainly caused by the lack of enough observations due to the limited spatial coverage of weather stations, leading to abnormal relationships between Ta and explanatory variables. In order to address this issue, in this study, we introduced a new method named the Spatially Varying Coefficient Models with Sign Preservation (SVCM-SP) to estimate gridded Ta using gridded land surface temperature (LST) and elevation as explanatory variables with presetting positive and negative signs for coefficients, respectively. Using this method, first, we calculated the preset parameters of the bivariate spline surface. Second, we used the input data at weather stations and constrained least squares regression to obtain the coefficient surface for both the explanatory variables (i.e., elevation and LST) and the intercept. Third, we calculated the gridded Ta using the 1 km gridded LST and elevation data, and the estimated spatially varying coefficient surfaces. We evaluated the model performance for estimating 1 km gridded daily maximum and minimum Ta (i.e., Tmax and Tmin) data in mainland China from 2003 to 2016 using 10-fold cross-validation and compared its performance with the GWR model. The average root mean square error (RMSE) and mean absolute error (MAE) based on the SVCM-SP are 1.75 °C and 1.22 °C for Tmax, and 1.82 °C and 1.30 °C for Tmin, respectively. The SVCM-SP method showed better performance than the GWR in terms of accuracy, computing efficiency, and has more interpretable coefficients for explanatory variables to get more realistic spatial pattern of gridded Ta. More important, the sign preservation of the SVCM-SP method can mitigate the issue of abnormal relationships between Ta and explanatory variables in the traditional methods such as GWR, and therefore will contribute to future studies in developing better gridded air temperature or relevant data products.