# GNSS-IR Soil Moisture Retrieval Using Multi-Satellite Data Fusion Based on Random Forest
## 5 Discussion  
### Reliability Analysis of MDI Algorithms  
In the training process, the RF model utilizes a method based on MDI to measure the contribution of each arc, and quantifies this as arc importance. Specifically, the Random Forest model consists of multiple decision trees. In each tree, the decision tree is constructed by recursively splitting nodes. At each node split, the MDI algorithm calculates the reduction in impurity for each segment involved in the split. The segment that maximizes the reduction in impurity is selected as the partition point. After building the tree, the reduction in impurity for each segment at every split is accumulated, and then the reductions across all trees are averaged to obtain the average decrease in impurity for each segment. For ease of comparative analysis, the importance of segments is normalized using min-max normalization, which allows for the adaptive allocation of segment weights. In the MDI algorithm, MSE serves as the criterion for measuring impurity, reflecting the average of the squared differences between model predictions and actual values. MSE directly assesses the predictive error at a node. A feature that consistently reduces MSE across multiple nodes in several trees is frequently selected as the splitting feature, thereby increasing its weight. The use of MSE in regression problems provides a standardized measurement for segment weights, enabling comparability among different segments. Phase feature parameters can indicate changes in soil moisture, and the stronger their correlation, the more accurate the soil moisture retrieval. However, the correlation between phase data from different satellite segments and soil moisture varies significantly. Identifying and utilizing segments with strong correlations is key to enhancing the accuracy of soil moisture retrievals. The Random Forest's MDI algorithm adaptively identifies high \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Station** & **Model** & **R** & **RMSE** & **MAE** \\  & & & **cm3/cm3** & **cm3/cm3** \\ \hline \multirow{4}{*}{P041} & RF & 0.94 & 0.032 & 0.025 \\  & SVM & 0.89 & 0.048 & 0.037 \\  & RBF & 0.81 & 0.072 & 0.059 \\  & CNN & 0.83 & 0.062 & 0.049 \\ \hline \multirow{4}{*}{P037} & RF & 0.95 & 0.028 & 0.022 \\  & SVM & 0.89 & 0.033 & 0.026 \\  & RBF & 0.85 & 0.036 & 0.028 \\  & CNN & 0.84 & 0.038 & 0.029 \\ \hline \multirow{4}{*}{LM} & RF & 0.98 & 0.003 & 0.002 \\  & SVM & 0.95 & 0.007 & 0.005 \\ \cline{1-1}  & RBF & 0.95 & 0.005 & 0.004 \\ \cline{1-1}  & CNN & 0.91 & 0.009 & 0.007 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: R, RMSE, and MAE between inverted soil moisture and reference values for each model at sites P041, P037, and LM. correlation satellite segments by calculating the decrease in impurity at splitting nodes, thereby assigning weights and establishing a reliable retrieval model. To validate the appropriateness of segment weight assignment based on MDI in the RF model, this study compared the importance of various segments, as output by the RF model, with the correlation coefficients between phase and reference soil moisture values. Figure 14 illustrates the relationship between segment importance and correlation coefficients at stations P041 and P037. As shown in Figure 14, for ease of comparative analysis, the importance of segments and their correlation coefficients were normalized using min-max normalization. There is a significant positive correlation between the segment importance calculated by the RF model and their correlation coefficients. Segments with lower correlation coefficients at the two sites also demonstrated lower segment importance, displaying consistent trends overall.