## 3 Results  
### The Impact of Soil Moisture Retrieval Uncertainty  
The impact of satellite soil moisture retrieval uncertainty was detected by comparing estimates obtained using soil moisture from different sources but with the same sampling interval (i.e., SMAP_X vs. OBS_X) as input to SM2 RAIN. Figures 6-9 illustrate the estimated precipitation from SMAP_X and OBS_X compared to the rain gauge observations and the corresponding evaluation metrics. Notably, the substantial amount of missing SMAP ascending retrievals resulted in a significant reduction in precipitation estimates during the period from 2015 to 2016, as depicted in Figure 6.  
Taking ascending orbit as an example, SM2 RAIN-derived precipitation based on SMAP_A captures almost all precipitation events, except for days with missing soil moisture retrievals (i.e., days colored with gray background in Figure 6(a1)). However, obvious underestimation is observed on some days, especially on the days with intense precipitation (i.e., days around July 2018, and August 2018 in Figure 6(a1)). This may attribute to the fact that when precipitation intensity is high, the soil becomes saturated and difficult to record more information about precipitation. In terms of accumulated precipitation, the SM2 RAIN estimates is 801 mm, which is lower than that of the rain gauge observed (i.e., 812 mm). For the quantiles, it tends to exhibit slightly larger values in the lower quantiles but much smaller values in the upper quantiles than the rain gauge observations, indicating that SM2 RAIN-derived precipitation based on SMAP_A tends to slightly overestimate low intensity precipitation but largely underestimate extreme high intensity precipitation. In terms of evaluation metrics, it yields statistical metrics of \(R\), _RMSE_, and _BIAS_ to be 0.66, 10.77 mm/5 d, and \(-0.26\) mm/5 d, respectively, while categorical metrics of _POD_, _FAR_, and \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Metric Classes** & **Metrics** & **Equation** & **Range** \\ \hline Statistical & \(R\) & \(R=\frac{cov(P_{\text{obs}},P_{\text{obs}})}{\sigma(P_{\text{obs}},P_{\text{ obs}})}\) & \([-1,1]\) \\ metrics & _BIAS_ (mm/5 d) & \(BIAS=\frac{\sum P_{\text{obs}}-P_{\text{obs}}}{N}\) & \([-\infty,+\infty]\) \\  & _RMSE_ (mm/5 d) & \(RMSE=\sqrt{\frac{\sum(P_{\text{obs}}-P_{\text{obs}})^{2}}{N}}\) & \([0,+\infty]\) \\  & _POD_ & \(POD=\frac{H}{H^{2}}\) & \([0,1]\) \\ Categorical & _FAR_ & \(FAR=\frac{H^{2}}{H^{2}}\) & \([0,1]\) \\ metrics & _TS_ & \(TS=\frac{H^{2}}{H+M+F}\) & \([0,1]\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: List of precipitation evaluation metrics. Pobs and Pest represent the observed and SM2 RAIN estimated 5 -day accumulated precipitation. TS_ to be 0.45, 0.02, and 0.44, respectively (Figure 7a). Nevertheless, as would be expected, the SM2 RAIN estimate is improved with OBS_A, as evidenced by alleviated underestimation in accumulated precipitation amount (Figure 6) and more favorable evaluation metrics (i.e., \(R\), \(RMSE\), and \(BIAS\) in Figure 7a). Figure 6: Lineplots and scatterplots of 5-day accumulated precipitation estimated by SM2 RAIN (P\({}_{\text{est}}\)) versus the corresponding rain gauge observations (P\({}_{\text{obs}}\)) during JJAS 2015–2018. (**a1,a2**) are the results with SMAP_A as input. (**b1,b2**) are the results with OBS_A as input. Grey background in the lineplots indicates failed precipitation estimates due to missing satellite soil moisture retrievals. The sPest and sPobs in the scatterplots indicate the total estimated and observed precipitation, respectively. N indicates the number of successful SM2 RAIN estimation. Figure 7: Evaluation metrics of SM2 RAIN with regard to input of (**a**) ascending, (**b**) descending, and (**c**) combined soil moisture datasets, respectively, during JJAS 2015–2018.