## 5 Results and Discussion
### TWSA Data Preprocessing  
In the data resolution process, the spherical harmonic data released by the three data centers are arithmetically averaged, with the mean solution serving as the resolved data for this section of the study. The advantage of this approach is that the standard deviation of the average monthly solution is smaller than the standard deviation of the data from any single institution. If the standard deviations of the monthly solutions from the three institutions relative to the true terrestrial water storage are denoted as \(\sigma_{\text{CSR}},\sigma_{\text{GSFC}},\sigma_{\text{JPL}}\). This formula is derived based on the Variance Sum Law. Assuming that the three datasets are independent, the standard deviation of their mean is expressed as follows [49]:  
\[m_{std}=\frac{\sqrt{\sigma_{\text{CSR}}^{2}+\sigma_{\text{GSFC}}^{2}+\sigma_{ \text{JPL}}^{2}}}{3} \tag{12}\]  
where \(m_{std}\) denotes the standard deviation of the mean solution. Using multiple datasets enhances the accuracy of TWSA estimates and offers a broader perspective on water storage changes in the basin. By averaging across the three sources, this method mitigates potential biases or errors inherent in individual datasets, thereby offering a more accurate representation of terrestrial water dynamics. Assuming uniform accuracy among the products from these institutions, the standard deviation of the mean solution is expressed as \(\sigma/3\). This mathematical simplification indicates that the overall variability in the mean solution is effectively reduced by approximately 42% compared to the standard deviation associated with data from a single institution. Such a reduction in standard deviation is crucial, as it enhances the reliability and stability of the resolved TWSA data, making it more robust for subsequent analyses. Figure 5 displays the mean TWSA in the PRB from March 2022 to November 2022.  
Figure 4: Terrestrial water storage anomaly estimates from CSR, GSFC, and JPL in the PRB with precipitation from GPM.  
Figure 5 visually conveys the temporal dynamics of TWSA, highlighting fluctuations in water storage across the specified period. The spatial distribution of TWSA in the PRB exhibits significant spatial heterogeneity and temporal variability. Pronounced changes are observed in the upstream and midstream regions, while downstream areas display relatively smaller fluctuations, reflecting the influence of regional hydrological processes and climatic conditions. Alternating patterns of positive and negative anomalies highlight periods of water surplus and deficit, which can be attributed to seasonal precipitation, evapotranspiration, and anthropogenic activities. Over time, regions transition between positive and negative anomalies, indicating dynamic water storage changes influenced by both natural and human factors. The magnitude of anomalies varies across the basin, with some areas exhibiting significant deviations, while others remain relatively stable, suggesting uneven impacts of hydrological processes and water management practices. These findings underscore the complex interactions between climatic drivers, hydrological dynamics, and human interventions.