###### Abstract
Therefore, in order to improve the availability of satellite precipitation data, it is essential to downscale datasets and merge them with the rain gauge observations to further improve the accuracy of the precipitation dataset [42; 43; 44; 45]. Usually, spatial downscaling mainly relies on constructing the regression relationship between the target variable and the control variable/influencing variable under the coarse-scale condition. Then, on this basis, the control variable/influence variable under the fine-scale condition is used to predict the target variable under the fine-scale condition [46]. For instance, the relationship between the vegetation index and the surface radiation temperature was used to achieve the spatial downscaling of the surface temperature [47]. Similarly, a regression model was proposed to improve the resolution of soil moisture data from 40 to 1 km. This method was based on the response relationship between surface temperature, vegetation index and soil moisture [48]. The spatial downscaling of satellite precipitation data is mainly achieved by establishing the regression relationship between precipitation and land vegetation cover, temperature, terrain, geographic location, and altitude through different methods [49]. Considering the response relationship between satellite precipitation data and the normalized difference vegetation index (NDVI), a downscaling regression model was introduced to downscale TRMM precipitation data to a 1 km resolution [50]. Based on the regression relationship between the monthly scale precipitation dataset, digital elevation model (DEM) and NDVI in the tropical mountainous areas of Ecuador, the resolution of satellite precipitation data not only realizes the transformation from 0.25\({}^{\circ}\) to 1 km on the spatial scale, but also downscales the temporal resolution from monthly to weekly [51]. The artificial neural network model was employed to correlate satellite precipitation datasets with elevation information and NDVI correlations to accomplish the downscaling of satellite data [52]. The non-stationary relationship between vegetation index, terrain factor, surface temperature and precipitation was applied to the Cubist spatial mining algorithm to obtain annual-scale precipitation downscaling data for the Qinghai-Tibet Plateau [53]. A machine learning-based random forest spatial algorithm is proposed for precipitation downscaling that establishes a non-linear relationship between fine-resolution precipitation and coarse/fine-resolution covariates to better describe the observed precipitation structure and distribution [54]. Among the above-mentioned precipitation downscaling methods, downscaling methods for building regression models of precipitation and other auxiliary factors (NDVI, DEM, latitude and longitude, surface temperature, slope, etc.) are widely employed. Based on the non-linear relationship between the annual mean NDVI and annual precipitation, a new downscaling exponential regression model was established for downscaling annual precipitation from TRMM data [31]. Scholars substituted the non-linear relationship between precipitation and multiple surface features into a multiple linear regression model with a calibration procedure in northern China to downscale TRMM data to a 1 km resolution [55]. The above downscaling regression models apply global regression techniques and it is assumed that the functional relationship between precipitation and other auxiliary variables is consistent. However, according to [PERSON]'s first law, the relationship between precipitation and other auxiliary variables is unstable and determined by the scale of the data [56; 57; 58]. Therefore, the application of global regression techniques to construct functions between precipitation and other auxiliary variables ignores crucial local relationships and has considerable limitations.