## 3 Results
### Geographically Weighted Regression  
The groundwater depth exhibits low-value aggregation characteristics in forest land, whereas the eastern cultivated and bare land areas exhibit high-value aggregation characteristics. Based on this, a geographically weighted regression analysis of the three land types and groundwater depth was performed, and NDVI, NRI, and NDDI were used to represent forest land, cultivated land, and bare land, respectively. NDVI, as a spectral band index, mainly reflects the characteristics of vegetation cover on the surface. For mountain forest land with high coverage, it is feasible to use NDVI as the index of the forest land. For the cultivated land in the study area, repeated tests on NRI, RVI (Ratio Vegetation Index), SAVI (Soil-Adjusted Vegetation Index), and GNDVI (Green Normalized Difference Vegetation Index) and other band indexes that can reflect the growth of crops could be implemented. NRI is the band that reflects the index of the nitrogen element of the crop. NRI can be used as the band index to reflect the cultivated land due to nitrogen fertilizer application. The central part of the study area is bare land and there are significantly large areas of desertification. NDDI effectively refers to the central bare land. The results of the geographically weighted regression model of cultivated land in the four years of 2005, 2009, 2013, and 2017 are shown in both Figure 10 and Table 4, which shows the standardized residuals of the geographically weighted regression model of cultivated land and NRI. Patches with absolute residuals greater than 2.5 have a poor fitting effect. The closer the absolute value comes to 0, the better the fitting effect of the geographically weighted regression model. According to the graph and table analysis, the result of the geographic weighted regression of cultivated land is an improvement when compared to other methods. In four years, the coefficient R is greater than 0.8 and the R\({}^{2}\) is greater than 0.75, which shows that the geographically weighted regression model has a strong correlation with the fitting of cultivated land NRI and groundwater depth. To further analyze the response mechanism, the standardized residual error is lower in the cultivated land in the middle of the study area, adjacent to the forest land in the west and the bare land in the middle and east, and the fitting effect of geographically weighted regression is also better than the other methods. The cultivated land in the southern and northeast corners of the study area is close to the boundary of the study area, resulting in the deviation of the fitting effect. The independent variables of geographically weighted regression of cultivated land in four years are between \(-4\) and \(10\). The fitting coefficient of cultivated land and groundwater depth is mainly negative in the central and western parts of the study area. The higher the NRI, the smaller the groundwater depth. The cultivated land in the area is close to the river and the woodland in the western mountain area. The developed root system of the woodland allows for water conservation. The NRI coefficient of the cultivated land is mainly positive in the northeast of the study area. Although the cultivated land in this area is also close to the Xilamulun River, the large area of cultivated land requires more water, and the wasteland on the west side will also divert groundwater runoff. The water conservation function is not high enough to maintain a better groundwater environment in the case an increase in the range of water demand. Figure 11 and Table 5 show the geographically weighted regression results of NDVI of forest land and groundwater depth. During 2005, 2009, 2013, and 2017, the NDVI of the forest land and the groundwater depth R\({}^{2}\) were all above 0.6, and the adjusted R\({}^{2}\) was above 0.5. NDVI and the groundwater depth have a strong correlation.