## 5 Results and Discussion
### Retrieval of SM  
After completing the selection of the satellite phases, the MRER model entered the processing stage. Following the results in the previous section, 12 satellites were selected for the experiment: PRN 19, PRN 24, PRN 01, PRN 16, PRN 30, PRN 23, PRN 07, PRN 13, PRN 32, PRN 09, PRN 04, and PRN 14. In this experiment, two methods were used to build the MRER model: method 1, i.e., a single-satellite model, and method 2, i.e., a  
Figure 8: Values of \(r\) between phases of the initially selected satellites and SM. The ascending (**left panel**) and descending (**right panel**) segments are shown. Figure 9: Linear regression analysis of the phases of the certain initially selected satellites and SM. In the graph, the solid line represents the linear regression trend. The results are shown for a total of 12 satellites, and these satellites were characterized by different cross-correlation threshold ranges. multi-satellite combination model according to the gradually increasing threshold range of \(r_{n}\). For method 1, the MRER model was built directly using a single satellite, and the model test results from 12 satellites were calculated and are shown in scheme 1. Method 2 combined the satellites corresponding to the different ranges of \(r_{n}\); the specific scheme settings are shown in Table 6. After completing the modeling training, the testing set was input into the model to retrieve SM. The retrieval errors of SM for the different methods are shown in Figure 10.  
In Figure 10, it can be seen that whatever the modeling or the testing stages, accurately grasping the variation trend of SM when using a single satellite was difficult, and the retrieval error fluctuated obviously. Especially, for satellites with \(r_{n}\) less than 0.600, such as PRN16 and PRN32, the retrieval effect was poor, and the retrieval process was highly prone to abnormal jumps. It can also be seen from Figure 10 that the retrieval errors of schemes 2 to 5 generally tended to be stable, and the errors mainly fluctuated within the range of \(-0.070\)-\(0.100\). Compared with scheme 1, the model was significantly improved. For example, as the cross-correlation coefficients of schemes 4 and 5 were greater than 0.600, the number of combined satellites was reduced. However, the retrieval errors of the models still tended to be stable, but the errors fluctuated less. Additionally, as shown in Figures 2 and 10, the retrieval error of a single satellite gradually increased during the period of continuous precipitation. Especially for the periods of sudden precipitation, such as DOY98-DOY99, DOY116, DOY161-DOY162, and DOY249, the retrieval error values suddenly increased, which might be due to the existence of a certain delay in the SM of \begin{table}
\begin{tabular}{c c c} \hline \hline
**Scheme** & \(r_{n}\) & **Method 2** \\ \hline
2 & \(>\)0.4 & PRN 19, 24, 01, 16, 30, 23, 07,13, 32, 09, 04, 14 \\
3 & \(>\)0.5 & PRN 24, 01, 16, 30, 23, 07, 13, 32, 09, 04, 14 \\
4 & \(>\)0.6 & PRN 30, 23, 07, 09, 04, 14 \\
5 & \(>\)0.7 & PRN 30, 23, 07, 14 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Modeling scheme for the multisatellite combination of method 2. Figure 10: SM retrieval errors of the different methods. Top and left bottom panels: single-satellite model corresponding to method 1. Right bottom panel: multisatellite combination model corresponding to method 2.  
single-satellite retrieval. In comparison, the retrieval errors of multisatellite combinations tended to be smooth and basically undisturbed by a sudden or persistent precipitation. To further assess the performance of each scheme, \(r\), RMSE, MAE, and Max were used, as shown in Figure 11. It can be seen that in the single-satellite scheme, \(r\) of the model was low, with a Max generally greater than 0.131, and the ranges of RMSE and MAE were 0.057-0.167 and 0.062-0.155, respectively.