Introducing Variations of Predictors as Optional Predictors Offers the Potential to Improve the Downscaling Performance of Geographically Weighted Regression Model

Abstract

Are the variations of the fine predictors at the spatial scale of the target variable to be downscaled helpful for spatial downscaling? However, few studies have explored this topic. In this study, one of the most frequently downscaled satellite products (Tropical Rainfall Measuring Mission (TRMM) precipitation) and one of the most commonly employed downscaled models (geographically weighted regression (GWR)) were chosen as the target variable to be downscaled and the downscaling model, respectively. Three widely adopted auxiliary variables were selected as basic predictors. Variations of the three 1-km basic predictors at the 25-km (a TRMM cell) spatial scale (hereafter termed variation predictors (VP)) were captured by the employment of the “standard deviation” operators. A procedure was designed to determine the monthly optimal trend component model, and area-to-point kriging (ATPK) was applied to retrieve residual components. The monthly TRMM precipitation in the main body of the north-south transitional zone of China (MBNSTZC) from January 2010 to December 2019 (120 months in total) was spatially downscaled. When VP was introduced into the predictor family, performance improvements were observed for more than two-thirds of 120 months, and the average relative improvements in the coefficient of determination $^{}$ ( $\text{R}^{2}$ ), root-mean-square error (RMSE), mean absolute error (MAE), and information entropy (IE) were 9.01%, 9.37%, 10.56%, and 28.21%, respectively. Our study suggests that: i) VP incorporation, which can improve downscaling performance to some extent, is important for GWR downscaling modeling; ii) Residual correction is unnecessary, especially for GWRs with VP incorporation; iii) GWRs with VP incorporation can not only downscale target variable but also have a certain interpolation ability.

Keywords

• Variation predictor
• spatial downscaling
• disaggregation
• unmixing
• scaling
• geographically weighted regression (GWR)