## 3 Results
### Impact of Vertical Wind Shear on Clouds as Interpreted from Model Simulation
#### 3.2.2 The Impact of Vertical Wind Shear on Clouds  
Figure 12 shows the modeled cross-section of equivalent potential temperature, wind vectors, and water vapor mixing ratio along the east black line (same as the RHI scan of cloud radar shown in Figure 10a). At 8:00 UTC, low-level convective instability was present, as seen from the decrease in potential temperatures with height in some areas, such as 30 km south of the radar, and we can see there was updraft due to the convergence between the cross-ridge flow and the northerly upslope wind. The vapor mixing ratio was high in the convergence zone, providing favorable conditions for convective cloud formation. The updraft was weakened at 8:30 UTC, and the convergence zone moved northward (Figure 12b,c), consistent with the cloud radar observation. Strong vertical wind shear persisted at approximately 4-5 km during this case, and most of the time, the convection was limited to beneath the shear level. The low-level humidity kept increasing during the precipitation process (Figure 12a-f), probably due to the evaporation of rain drops, while the upper-level humidity showed no significant change. The small-scale gravity waves forced by the terrain provided weak updrafts near the surface and were responsible for the generation of weak convergences, which contributed to the formation of low-level warm clouds. Figure 12: Modeled cross–section of equivalent potential temperature (contours), wind field (gray vectors), and water vapor mixing ratio (colored) along the east black line in Figure 10 for (**a–d**) segment 1, (**e**) segment 2, and (**f**) segment 3. S and N below each panel indicate south and north of the cloud radar. Another feature seen from the figure is that lee waves from the southernly cross-ridge flow were present. For example, at 10:00 and 11:00 UTC, there were clear lee waves at heights of about 5-6 km above the observational site, generating updraft and downdraft (Figure 12e,f). Below the lee waves, a weak northernly flow was found, forming vertical wind shear. This explains the formation of the observed stratiform clouds at this level (Figures 7a and 8c). The wind near the surface at 11:00 UTC turned to a southerly direction; thus, two wind shear levels were present, consistent with radar observation. Convective instability still can be seen near surface, and the high relative humidity provided good conditions for forming low-level warm clouds, but no strong updraft was seen at 11:00 UTC; thus, the precipitation seen in Segment 3 was determined to be light. To investigate the impact of vertical wind shear on the convection, we analyzed the tendency of the convective stability, which can be expressed using:  
\[\frac{d}{dt}\bigg{(}\frac{\partial\theta_{e}}{\partial z}\bigg{)}=m_{1}+m_{2} \tag{9}\]  
\[m_{1}=-\frac{\partial u}{\partial z}\frac{\partial\theta_{e}}{\partial x}- \frac{\partial v}{\partial z}\frac{\partial\theta_{e}}{\partial y} \tag{10}\]  
\[m_{2}=\bigg{(}\frac{\partial u}{\partial x}+\frac{\partial v}{\partial y} \bigg{)}\frac{\partial\theta_{e}}{\partial z} \tag{11}\]  
where \(m_{1}\) is the vertical wind shear term and \(m_{2}\) is the divergence term. Positive values of \(m_{1}\) and \(m_{2}\) result in an enhancement in convective stability, while negative values of \(m_{1}\) and \(m_{2}\) indicate a decline in convective stability (i.e., a more unstable atmosphere) due to the vertical wind shear and divergence. Figure 13 shows the convective stability, the vertical wind shear term, and the divergence term of the convective stability tendency modeled by WRF at 9:00, 10:00, and 11:00 UTC, respectively. It can be seen from the figure that the tendency of convective stability was highly variable because of the high spatial variability of the potential temperature (Figure 12c). The overall tendency (left panels) was dominated by the vertical wind shear term (middle panels) at most of the heights, and impacted by both the vertical wind shear and divergence term near the surface.