## 3 Methods
### Calculation of Calibration Bias in \(Z_{\text{H}}\) Based on SC Principle  
The calibration bias in \(Z_{\text{H}}\) was calculated by comparing the power-related observations with the phase-related observations. \(Z_{\text{H}}\) can be contaminated by several error sources, such as bright bands, partial beam blockages, and rainfall attenuation. The following criteria were suggested to avoid the effects of observational error sources.  
1. The data from the third to the last elevation angles with a pulse width of 2 \(\upmu\)s were selected to minimize the impact of the GC.
2. The contamination by the bright band was removed based on the statistics of the monthly averaged bright band [30] and \(\rho_{\text{HV}}\).
3. The partial beam blockage region was identified based on beam blockage simulation (BBF). The BBF is calculated by assuming the beam propagation in the standard atmosphere and the Gaussian beam pattern using digital elevation model (DEM) data with a horizontal resolution of 30 m [31; 32]. The azimuth angle, where the BBF was greater than 10%, was excluded.
4. The relationship between \(Z_{\text{H}}\) and specific attenuation (A = 3.348 \(\times\) 10\({}^{-}\)6 ZH0.\({}^{755}\)) was used to correct the \(Z_{\text{H}}\) loss caused by rain attenuation [33]. The \(Z_{\text{H}}\)-A relationship was derived from Precipitation Occurrence Sensor System (POSS) disdrometer data collected at Busan (35.12\({}^{\circ}\)N, 129.10\({}^{\circ}\)E), South Korea.
5. Azimuth angles containing \(Z_{\text{H}}\) above 45 dBZ were excluded to avoid the presence of hail.
6. If the mean \(Z_{\text{H}}\) near the radar was above 30 dBZ, the scan was excluded to avoid wet radome attenuation.  
The relationship between \(Z_{\text{H}}\) and the specific differential phase (\(Z_{\text{H}}\) = 7.33 \(\times\) 10\({}^{4}\) K\({}_{\text{DP}}\)\({}^{1.1}\)) suggested by [PERSON] et al. [13] was used. The calculated \(\Phi_{\text{DP}}\) (\(\Phi_{\text{DP},\text{cal}}\)) was obtained by  
Figure 3: Example of ground clutter map (GCM) for GSN radar constructed at 0000 KST 1 May 2020.  
accumulating the specific differential phase (\(\text{K}_{\text{DP}}\)) along the radial direction. The measured \(\Phi_{\text{DP}}\) (\(\Phi_{\text{DP\_meas}}\)) is defined as the change in \(\Phi_{\text{DP}}\) from the start to the end of the rain path. A finite impulse response (FIR) filter was repeatedly applied to reduce the noise in the measured \(\Phi_{\text{DP}}\). In addition, the rain path was carefully selected. The successive rain segment, where \(\Phi_{\text{DP}}\) is greater than \(3^{\circ}\), was selected, and the rain path should be at least 10 km. The calibration bias (\(\varepsilon_{\text{SC}}\)) is calculated from the slope (tan\(\theta\)) of the \(\Phi_{\text{DP}}\) pairs, as shown in the following equation:  
\[\begin{array}{c}\tan\theta\ =\sum\Phi_{\text{DP\_cal}}\Phi_{\text{DP\_meas}}/ \sum\Phi_{\text{DP\_meas}}{}^{2}\\ \varepsilon_{\text{SC}}(\text{dB})=(10\times\text{b})\log(\tan\theta)\end{array} \tag{5}\]  
where b is the exponent (=1.1) of the \(Z_{\text{H}}\)-\(\text{K}_{\text{DP}}\) relationship. A positive calibration bias means that \(Z_{\text{H}}\) was over-measured, while a negative calibration bias means that \(Z_{\text{H}}\) was under-measured. Figure 4 shows the scatterplot of \(\Phi_{\text{DP\_cal}}\) and \(\Phi_{\text{DP\_meas}}\) for the GSN radar on 3 July 2020. The slope (tan\(\theta\)) of the \(\Phi_{\text{DP}}\) pairs was 0.80 in Figure 4. In addition, the calibration bias of GSN radar was \(-1.08\) dB for this case.