# Downscaling of Remote Sensing Soil Moisture Products That Integrate Microwave and Optical Data
## 3 Results and Discussion  
### Feature Selection and Feature Importance Assessment  
This study used machine learning methods to explore the effect of combining optical and microwave remote sensing data for soil moisture downscaling. In terms of feature selection, the physical mechanisms that affect soil moisture changes and variables with a high correlation with soil moisture were considered. By evaluating the R between NDVI, LST, topography, backscatter coefficient, and soil moisture, the feature with a strong correlation with SMAP_10 km was selected, and the acceptable threshold of the absolute value of the R was set to 0.2. The correlation analysis of model data (Figure 3) shows that LST, NDVI, and VV/VH have a high correlation with soil moisture and are suitable feature vectors. Although SLOPE has a weak correlation with soil moisture, it also was used as a machine learning feature to distinguish different surface conditions [35].  
After analysis, ALB, LAI, LST, NDVI, SLOPE, VV, and VH were used as the input features for modeling in the Shandian River, and LAI, NDVI, SLOPE, VV, and VH were used as input features in Wudaoliang. The corresponding downscaling models were trained using their respective input features.  
To enhance the reliability of the downscaling model, we compared the MSE and R\({}^{2}\) values of the RF and XGB models during training, selecting the model with the higher performance as the downscaling model, as presented in Table 3.  
When RF trains the downscaling model, it calculates the average value of the impurities that can be reduced by each feature in each decision tree to obtain the importance of each feature. By comparing the fitting results of different algorithms, the contribution rate of each feature shown by the optimal RF algorithm is shown in Figure 4.  
Through a feature importance assessment, it was determined that the factor with the greatest impact on soil moisture was the backscatter coefficient, followed by LST and NDVI. However, the importance of factors affecting soil moisture varies under different surface types [5,36]. In river basins with complex surface types, surface temperature is the most important variable reflecting the spatiotemporal changes in soil moisture. Vegetation conditions also have a significant impact on soil moisture monitoring. In plateau areas with high altitudes, topography is a very important factor.  
Figure 3: Heat map of R values between model data used for downscaling. **(a)** The Shandian River; **(b)** Wudaoliang. SMAP_10 km is original soil moisture; NDVI, ALB, LST, LAI, SLOPE, VV, and VH are auxiliary data resampled to 10 km resolution.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline  & \multicolumn{2}{c}{**Downscaling to 1 km**} & \multicolumn{2}{c}{**Downscaling to 100 m**} \\ \cline{2-5}  & **RF** & **XGB** & **RF** & **XGB** \\ \hline \multirow{2}{*}{SDR} & MSE & 0.000191 & 0.000197 & 0.000144 & 0.000165 \\  & R\({}^{2}\) & 0.769 & 0.605 & 0.825 & 0.539 \\ \hline \multirow{2}{*}{WDL} & MSE & 0.000465 & 0.000357 & \multirow{2}{*}{} \\  & R\({}^{2}\) & 0.622 & 0.679 & \\ \hline \end{tabular} Notes: SDR: Shandian River; WDL: Wudaoliang; RF: random forest; XGB: extreme gradient boosting.  
\end{table}
Table 3: R\({}^{2}\) and MSE of different downscaling models.