## 3 Results and Discussions
### Simulations of Other Crucial Elements in the Water Cycle  
#### 3.2.1 Temporal Variation of the Water Cycle Elements  
In addition to evaluating the spatiotemporal patterns of the rainfall, the spatiotemporal distribution variables of the other elements in water cycle were analyzed to understand the fully coupled system. These variables included evapotranspiration, runoff (the sum values of infiltration excess and saturated groundwater), water storage, and surface temperature. The basin water balance theory [22; 51] was used in the calculation of the water storage change. This calculation can be expressed as follows:  
\[Dw=P-R-Et, \tag{8}\]  
Figure 8: Spatial distributions of the 24 h accumulative rainfall for the three storm events in the Zijingguan catchment, from left to right: gauge observation; (**a**) WRF-only; (**b**) the fully coupled WRF/WRF-Hydro; (**c**) the fully coupled WRF/WRF-Hydro minus WRF-only. where \(Dw\) is the water storage change within 24 h for each flood event in the two catchments, and \(P\), \(R\), and \(Et\) are the rainfall, the generated runoff, and the evapotranspiration within the same time period, respectively. For the analysis of the variables in the grid area, the 24 h changes can be seen in Figure 9. There were small amounts differed of the elements between WRF-only and the fully coupled WRF/WRF-Hydro as a short duration of 24 h. The \(R\) values of the fully coupled WRF/WRF-Hydro for the six events were less than that in WRF-only. In general, the fully coupled system increased the soil moisture and decreased the \(R\). Note that the largest difference in \(R\) is Event 4 among all rainstorms, where the fully coupled WRF/WRF-Hydro was only 1.1 mm less than that of WRF-only. Compared to WRF-only, the coupled system \(Et\) values exhibited a decreasing trend, except for Event 2, which rose by only 0.001 mm. The amount of water storage slightly decreased in Type 1 and Type 2, while the water storage in the Type 3 events increased. At the same time, the change of the surface temperature within 24 h was not obvious, and the fluctuation range was quite narrow. Figure 10 shows the graphs for the temporal variations of the grid average values of the crucial water cycle elements within 24 h. The \(Et\) trend was nearly the same as that of the Ts. During the period with high rainfall intensity, the \(Dw\) in the two catchments rose and \(Et\) increased until a stabilization in the later period. When the rainfall had gradually stopped, the \(Et\) increased with rising Ts (excepted for Event 1 and Event 6 with decreasing Ts), triggering the \(Dw\) decreasing to negative. For Event 4, and Event 6, the \(P\) and the \(Dw\) values generated by the fully coupled WRF/WRF-Hydro were slightly higher than those from WRF-only before and after the peak period. A number of studies (e.g., [PERSON] and [PERSON] (2018), and [PERSON] et al. (2019)) have argued that local soil moisture changes significantly in arid and semiarid regions dominated by convective rainfall, and such changes can affect the accuracy of a model simulation and reflect the \(Dw\) change to a certain extent. Figure 11 displays the hourly grid averaged soil moisture of the four soil layers (S1 to S4 with soil thickness ranges: 0-10 cm, 10-40 cm, 40-100 cm, 100-200 cm, respectively) simulated by the fully coupled WRF/WRF-Hydro and WRF-only, which are expressed in terms of the volumetric water content. That is, the values showed the average of the soil moisture in three dimensions including the grid, time, and layer number. For the soil layers in semi-humid watershed, due to the low soil moisture in the early stage and the short duration of the rainfall and infiltration processes, thinner S1 and S2 had a rapid soil moisture decrease due to high surface temperature and surface evaporation. Among 4 soil layers, soil moisture follows the rule that the attenuation gradually decreases with increasing layers. For S3 and S4, they have larger thickness and slower response. This could be reflected in Event 1, Event 3, and Event 5.