## 2 Model Description and Experimental Design  
### Numerical Framework  
In the study, the Advanced Research WRF (ARW) version 3.5 [59] is utilized. To simulate ideal front system, the mode control equations were improved by using [PERSON] et al. [60] method to bring large scale meridional geostrophic wind forces into the momentum equation. We assume that Mei-Yu front is east-west direction and is forced by the meridional geostrophic wind \(V_{g}\), which is only a function of vertical displacement \(z\). To keep balance, geostrophic potential temperature advection term is introduced in thermodynamic equation, and water vapor advection term is introduced in water vapor equation accordingly. This gives  
\[\frac{du}{dt}=-\frac{1}{\rho}\frac{\partial p^{\prime}}{\partial x}+f(v-V_{g} )+\mathcal{D}_{u} \tag{1}\]  
\[\frac{dv}{dt}=-\frac{1}{\rho}\frac{\partial p^{\prime}}{\partial y}-fu+ \mathcal{D}_{v} \tag{2}\]  
\[\frac{dw}{dt}=-\frac{1}{\rho}\frac{\partial p^{\prime}}{\partial z}-g\frac{p ^{\prime}}{\rho}+\mathcal{D}_{w} \tag{3}\]  
\[\frac{d\theta}{dt}=S_{\theta}-u\bigg{(}\frac{\partial\theta_{g}}{\partial x} \bigg{)}_{LS}+\mathcal{D}_{\theta} \tag{4}\]  
\[\frac{dq_{v}}{dt}=S_{q_{w}}-u\bigg{(}\frac{\partial q_{vg}}{\partial x} \bigg{)}_{LS}+\mathcal{D}_{q_{v}} \tag{5}\]  
\[\frac{dq_{m}}{dt}=S_{q_{m}}+\mathcal{D}_{q_{m}} \tag{6}\]  
\[\frac{d\rho_{d}}{dt}+\rho_{d}(\frac{\partial u}{\partial x}+\frac{\partial v}{ \partial y}+\frac{\partial w}{\partial z})=0 \tag{7}\]  
where \(u\), \(v\), and \(w\) are zonal velocity (along the frontal boundary), meridional velocity (perpendicular to the frontal boundary), and vertical velocity in the \(z\) direction, respectively. \(V_{g}\) is meridional geostrophic wind velocity, \(f\) is Coriolis parameter, \(\theta\) is the potential temperature of dry air, \(\rho_{d}\) is the density of dry air, \(D\). expresses the dissipation term of the physical property, \(q_{v}\) is the mixing ratio of water vapor, \(q_{m}=q_{c}\), \(q_{r}\), \(q_{i}\), \(q_{s}\), \(q_{g}\) represent the mixing ratio of cloud water, rainwater, cloud ice, snow, and graupel, respectively, \(\rho=p_{d}\) (\(1+q_{v}+q_{c}+q_{r}+q_{i}+q_{s}+q_{g}\)) is the total mass density, \(S_{\theta}\) represents the heating/cooling effect associated with cloud microphysical processes, \(S_{q_{v}}\) is the source/sink term for water vapor, and \(S_{q_{m}}\) is the source/sink term for hydrometeors. The superscript' represents deviations from the dry, static equilibrium basic-state \(\overline{p}(z)\) and \(\overline{\rho}(z)\).  
The model domain is \(L_{x}=1000\) km, \(L_{y}=2000\) km, \(L_{z}=20\) km in the \(f\) plane, using \(f=10^{-4}\) s\({}^{-1}\). The lateral boundaries are periodic in \(x\) (west-east) and open in \(y\) (south-north). The lower boundary is flat without terrain. To inhibit gravity wave reflection from the upper boundary, Rayleigh damping is applied to the vertical velocity in the uppermost 5 km of the domain [61; 62]. Horizontal grid resolution is \(\Delta x=\Delta y=5\) km. The number of the vertical levels was 81, with a nearly constant vertical spacing of \(\Delta z\approx 250\) m. Time step is \(\Delta t=20\) s. [PERSON] double-moment cloud microphysics scheme [63] is used and depicted in Section 2.2. Cumulous cloud parameterization is not considered. The radiative effect of clouds is considered, but the direct radiative effect of aerosol is not. The simulations are integrated for 48 h and model output data is available every 5 min.