## 3 Results  
### Spatial-Temporal Dynamics of Soil Moisture from Inversion of the Water Cloud Model  
In this study, soil moisture content, based on field measurements, was used to calibrate the water cloud model parameters. The values of parameters A, B, C, and D are shown in Table 1. It is noteworthy that, in the water cloud model, the value of the polarization of VV from Sentinel-1 represents the \(o_{pq}^{0}\), while Veg is replaced by NDVI calculated from Sentinel-2.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Date** & **A** & **B** & **C** & **D** \\ \hline
1 April & \(-\)7.12 & \(-\)1.56 & 0.02 & \(-\)5.71 \\
7 May & \(-\)1.28 & \(-\)2.83 & 0.0015 & \(-\)0.91 \\
1 June & \(-\)23.37 & \(-\)3.57 & 0.06 & \(-\)6.84 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Parameter values used in the water cloud model for the study area.  
Figure 3: Flowchart for the winter wheat yield estimation using the EnKF-based assimilation algorithm.  
Soil moisture maps retrieved from the water cloud model from three dates and the retrieved soil moisture content of 22 measured sites over the three dates are shown in Figure 4, respectively. From both figures, we can see that the soil moisture is relatively higher on 1 April and 7 May than 1 June in most areas. Soil moisture in most areas was more than 20% on 1 April and 7 May, while soil moisture was mostly less than 20%, or even less than 10%, on 1 June. This is primarily due to the different irrigation on different dates. Based on our field experiment, we found that the farmers in this area usually irrigate the winter wheat 2-4 times during the whole growing season and the irrigation dates are mainly concentrated in the jointing stage, the heading stage, and the grain filling stage, which are generally from early March to mid-May, while 1 April and 7 May generally belong to the jointing stage and heading stage, respectively. Figure 5 shows the validation of the water cloud model soil moisture inversion results. The validation of 7 May has the best precision among the three dates, followed by 1 June and 1 April, and the R\({}^{2}\) is 0.53, 0.49, and 0.45, respectively. RMSE is 7.43%, 8.53%, and 9.16%, respectively. In general, the trend of soil moisture inversion is consistent with the ground measurements. Usually, the accuracy of soil moisture retrieval should be higher with less vegetation, due to less disturbance of the vegetation. However, the precision of the soil moisture retrieved with the water cloud model on 1 April is not the best among the three periods. We think that there are two possible reasons. The first is the effect of vegetation. We can see from Figure 2 that the study area was at the jointing stage of winter wheat on 1 April. We found that the plant height of winter wheat was approximate 17-33 cm, LAI ranged from 0.7-2.0 m\({}^{2}\)/m\({}^{2}\), and the vegetation coverage was higher than 75% when we performed the field experiments. We think the vegetation influence of this period is not much different from the other two periods. Second is the impact of irrigation. From the end of March to early April in Hengshui city is a common irrigation period and the irrigation has a certain impact on the accuracy of field measurements, which brings errors to the retrieval and validation of soil moisture.