# GNSS-IR Soil Moisture Retrieval Using Multi-Satellite Data Fusion Based on Random Forest
## 4 Results  
### Experimental Methods and Results  
To verify the feasibility and effectiveness of the soil moisture retrieval method based on Random Forest and multi-satellite data fusion GNSS-IR, this study used phase datasets extracted from all available satellite arcs at the P041, P037, and LM stations to establish soil moisture retrieval models based on Random Forest. The Random Forest model is capable of handling high-dimensional data and large datasets. It constructs multiple decision trees by randomly sampling subsets of the phase dataset and uses the MDI algorithm to assess the importance of each arc, demonstrating strong generalization performance. Additionally, it offers robust handling of missing and anomalous values, and its performance is not compromised by local node failures, making it highly suitable for soil moisture retrieval based on multi-satellite data. 1. Construction of the Random Forest Regression Model  
The TreeBagger class is utilized to build a Random Forest regression model, comprising datasets with input and output variables. The input variables consist of phase data from all satellite arcs at each site, while the output variables are soil moisture reference data from the P041 station in 2012, the P037 station in 2017, and the LM station in 2014. During model construction, the number of decision trees and the minimum number of leaves are crucial parameters affecting the MDI calculation. The quantity of trees influences the robustness of MDI calculations, with more counts providing more opportunities for segmentation, and thus a more accurate reflection of the importance of each arc segment. However, too many trees can cause diminishing marginal effects. The minimum number of leaves affects the  
Figure 6: (a) Variation curve of DOY 57–59 soil moisture with rainfall histogram in 2012 at P041; (b) variation curve of soil moisture with rainfall histogram for DOY 29–302 in 2017 at station P037. complexity of the decision trees; reducing the minimum number of leaves increases the depth of the trees, which helps capture features of the arcs beneficial for retrieval, but too few leaves can increase the risk of overfitting, thus reducing the model's generalization ability. Therefore, selecting the appropriate parameters is particularly crucial. In this study, grid search is employed for parameter tuning to minimize training errors and avoid overfitting on the test set. Specific parameter settings are provided in Table 1.  
2 Model Training  
To train the model for optimal performance, the dataset is divided into two parts, with the first 70% of the data and the soil moisture reference values simultaneously input into the model. Figure 7 shows the error variation of the trained Random Forest model. From the graph, it is evident that the model's error tends to stabilize when the number of decision trees reaches about 250. The error is minimized, and the performance is optimized when the number reaches 300 trees. 3 Model Validation  
The remaining 30% of the phase data from the dataset were input into the trained Random Forest model to retrieve soil moisture values using multi-satellite data fusion. The study also incorporated an RBF, SVM, and CNN model for precision comparative analysis to demonstrate the feasibility and accuracy of the proposed model. Based on the principles and methods discussed, soil moisture retrieval models were constructed using four algorithms: RF, SVM, RB, and CNN. Figures 8 and 9 display the correlations between the retrieval results of these models using the datasets from P041 and P037 stations, respectively, and the soil moisture reference values provided by the PBO. Figure 10 shows the correlation for the models built using the LM station dataset with the in situ soil moisture reference values. The observations from the graphs indicate \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Station** & **P041** & **P037** & **LM** \\ \hline Decision tree & 300 & 300 & 150 \\ Minimum leaves & 3 & 2 & 2 \\ \hline \hline \end{tabular}
\end{table}