## 3 Methods
### Ground Clutter (GC) Monitoring  
The \(Z_{\rm C}\) was monitored by calculating the relative calibration adjustment (RCA), which is defined as the change in \(Z_{\rm C}\) relative to the baseline. The procedures for calculating RCA were divided into three steps: (1) construction of the GC map (GCM), (2) determination of the baseline, and (3) calculation of the RCA.  
The GCM was constructed by counting the frequency of reflectivity (FOR) over a predefined threshold (50 dBZ) for a short period (an hour) on a clear day. The bin with a FOR of 100% was defined as GC. [PERSON] et al. [23] accumulated \(Z_{\rm H}\) above 55 dBZ during a single precipitation-free day (24 h) and selected the bin with FOR \(\geq\) 50% within 1-5 km range from the radar to minimize AP effects. In this study, a GC above 50 dBZ within a 1-10 km or 1-15 km range from the radar was selected because no sufficient GC above 55 dBZ was captured within a 1-5 km range due to the surrounding geography. The statistics of \(Z_{\rm C}\) were stable despite a short period and somewhat far range (will be shown in the next section). We constructed the GCM of individual radar at the first time of the analysis period (0000 KST 1 May 2020). Figure 3 is an example of GCM for GSN radar located at low altitudes and in the western part of Jeju Island. The total number of GCs was 1584 within 1-10 km, and most GCs were in the eastern part of the GSN radar due to the Halla Mountain.  
The RCA depends on the baseline. To determine the baseline, the \(Z_{\rm C}\) was extracted from the data used to construct the GCM. The 95 th (\(Z_{\rm baseline,95 th}\)) and 50 th percentile (\(Z_{\rm baseline,50 th}\)) of \(Z_{\rm C}\) were defined as the baseline from the probability distribution of \(Z_{\rm C}\). We determined the baseline using the data when the calibration value was unknown. In other words, the RCA reflects the change in calibration status with respect to a baseline. Therefore, it is important to check the change in RCA, not the absolute value of RCA.  
In this study, the hourly RCA was calculated from the \(Z_{\rm C}\) statistics. We used hourly RCA to identify the changes in the radar system as quickly as possible and to figure out when the calibration bias changed during the non-precipitation period. The RCA and azimuth and/or elevation slip indicator (dMedian) were calculated using the following equations:  
\[\rm RCA(dB)=Z_{baseline,95 th}-Z_{\rm C,95 th} \tag{1}\]  
\[\rm dMedian=|Z_{baseline,50 th}-Z_{\rm C,50 th}| \tag{2}\]  
Figure 2: Concepts of calculating and monitoring of calibration bias in the \(Z_{\rm H}\) measurements in real time.  
where \(Z_{\text{C},95\text{th}}\) and \(Z_{\text{C},50\text{th}}\) are the 95 th and 50 th percentiles of \(Z_{\text{C}}\), respectively. The \(Z_{\text{baseline},50\text{th}}\), was not used in previous studies [7; 23; 26]. In this study, the \(Z_{\text{baseline},50\text{th}}\), was used to determine the change in antenna pointing.  
To estimate the calibration bias from RCA, the change in RCA (\(\Delta\)RCA, Equation (3)) was defined as the difference between the most recent RCA (\(\text{RCA}_{\text{recent}}\)) and RCA at the current time (\(\text{RCA}_{\text{current}}\)). The calibration bias (\(\epsilon_{\text{GC}}\)) was estimated using the following equations:  
\[\Delta\text{RCA}(\text{dB})=\text{RCA}_{\text{current}}-\text{RCA}_{\text{ most recent}} \tag{3}\]  
\[\epsilon_{\text{GC}}=\epsilon_{\text{SC}}-\Delta\text{RCA} \tag{4}\]  
where, \(\epsilon_{\text{SC}}\) is the calibration bias estimated from the SC of previous rainfall events.