## 2 Field Experiment and WRF Model Setup
### Field Measurement and Instrumentation
The linear polarized power was fed through a wave guide and a horn, which represented the feed of an offset paraboloid dish with a 60 cm diameter. The backscattered signal was received with the same antenna assembly. The received signal was detected by a mixing diode mounted in the wave guide between the Gunn oscillator and horn. When operated in continuous wave mode, a voltage appeared at the diode output, which depended on the phase difference between the transmit and receiving signal, and was used for further signal processing. Due to its high sensitivity and fine temporal resolution, light precipitation such as drizzle can be detected by MRR well. In the present study, the observed precipitation was light to moderate; thus, the Rayleigh approximation was applicable. The drop size distributions were retrieved based on the backscatter intensity, and the relation between terminal fall velocity and drop diameter, which was found empirically by [PERSON] and [PERSON] (1977), was put into an analytical form by [PERSON] (1977). The fall velocity of a rain drop is:  
\[v(D)=(9.65-10.3\cdot\exp(-0.6\cdot D))\delta v(h) \tag{1}\]  
\[\delta v(h)=[1+3.68\cdot 10^{-5}h+1.71\cdot 10^{-9}h^{2}] \tag{2}\]  
where \(D\) is the drop diameter, \(h\) is height, and \(\delta v(h)\) is the height-dependent density correction for the fall velocity ([PERSON], 1977). The spectral reflectivity density with respect to the drop diameter (\(\eta\)) can be derived using:  
\[\eta(D,i)=\eta(v,i)\frac{\partial v}{\partial D} \tag{3}\]  
where \(i\) is the number of range gate. Dividing \(\eta(D,i)\) by the single-particle backscattering cross-section \(\sigma(D)\) yields the drop size distribution \(n(D,i)\):  
\[n(D,i)=\frac{\eta(D,i)}{\sigma(D)} \tag{4}\]  
\[\sigma(D)=\frac{\pi^{5}}{\lambda^{4}}|K|^{2}D^{6} \tag{5}\]  
\[K=\frac{m^{2}-1}{m^{2}+1} \tag{6}\]  
where \(\lambda\) is the wavelength and \(m\) is the refractive index. Based on the derived drop size distributions, the drop concentration (\(N\)) and volume mean diameter (VMD) can be calculated using:  
\[N=\int\limits_{0}^{\infty}n(D)dD \tag{7}\]  
\[\text{VMD}=\left[\frac{\int_{0}^{\infty}n(D)D^{3}dD}{N}\right]^{1/3} \tag{8}\]In this study, we only analyze the drop size distributions, concentrations, and VMDs below the melting layer, as the existence of ice particles in the mixed-phase region may result in large uncertainties due to their complex refractive index. The cloud radar used was a Ka-band scanning radar working at 35 GHz deployed on a truck. It generated electromagnetic waves using a solid-state transmitter and received the backscattered signal from targets such as cloud and precipitation particles. The radar could operate in either plan position indicator (PPI) or range-height indicator (RHI) mode with a beam width of 0.5\({}^{\circ}\), providing measurements of reflectivity, Doppler velocity, and spectral width. During the field measurement presented in this study, the cloud radar was located at Ulasitai site, approximately 1 km north of Mushi site (Figure 1b). This was an excellent location for RHI scanning and low-elevation measurement, as it was on a relatively high hummock, with few trees surrounding it. The 0\({}^{\circ}\) elevation angle was unblocked to the north, west, and east, and the radar was able to detect the orographic clouds and precipitation near the surface south of the observational site. In the low-elevation measurements to the south, the return power at many radar gates was suspect because of ground clutter, the anomalous propagation of the radar beam, and other sources of interference with the terrain. However, the ground clutter could be removed because its radial velocity was always close to 0 [34]. To investigate the detailed vertical structures of orographic clouds forming due to the lifting of northerly flows forced by the Tian Shan Mountains, the radar operated on RHI scanning mode along the north-south direction, with 250 range gates and a pulse length of 150 m; thus, the maximum detection range was 37.5 km.