# On the Use of Bright Scatterers for Monitoring Doppler, Dual-Polarization Weather Radars
## 4 Discussion  
From the values of the statistical parameters that characterize the radar observables presented in Section 3, it is easy to conclude that, on a daily basis, the BS signals acquired over the five selected clear sky days are statistically similar. This is why they were merged to derive a more representative 5-day data set (see the last line in Tables 2-4 and 8). Our strategy is that of trying to set up preliminary thresholds for warnings. The focus is on five (out of six) radar observables presented in Section 2.2, \begin{table}
\begin{tabular}{c c c c c c} \hline  & **Minimum** & **Average** & **Median** & **90\%tile** & **MAX.** \\ \hline
5 January 2015 & 0.9870 & 0.9944 & 0.9950 & 0.9971 & 0.9984 \\
9 February 2015 & 0.9925 & 0.9984 & 0.9985 & 0.9994 & 0.9998 \\
10 February 2015 & 0.9939 & 0.9976 & 0.9978 & 0.9994 & 0.9995 \\
13 October 2016 & 0.9882 & 0.9939 & 0.9941 & 0.9957 & 0.9976 \\
18 January 2017 & 0.9890 & 0.9966 & 0.9972 & 0.9983 & 0.9994 \\ \hline \end{tabular}
\end{table} 
Table 7: Values of five location parameters for the copolar correlation coefficient. \begin{table}
\begin{tabular}{c c c} \hline  & \((\rho^{HV}_{84}-\rho^{HV}_{16})/2\) & \(\pm\{\sigma\rho^{HV}\}\}\) \\ \hline
5 January 2015 & 0.0025 & 0.0023 \\
9 February 2015 & 0.0007 & 0.0009 \\
10 February 2015 & 0.0008 & 0.0009 \\
13 October 2016 & 0.0012 & 0.0014 \\
18 January 2017 & 0.0017 & 0.0019 \\ \hline
5 days above & 0.0024 & 0.0024 \\ \hline \end{tabular}
\end{table} 
Table 8: Values of spread and standard deviation for the copolar correlation coefficient. because a warning based on the differential phase shift of an individual radar bin is considered too risky. As far as the Doppler spectrum width is concerned, since all 1440 values were DN = 1, a different value from DN = 1 would cause a warning. The reference framework for the Doppler velocity (1 st Doppler moment) consists of 578 values with DN = 128 (zero velocity) and of 862 values with DN = 127. A different value would cause a warning. As far as radar reflectivity is concerned, the median value results to be 81.5 (80.5) dBZ for the horizontal (vertical) polarization. The horizontal polarization shows a smaller standard deviation (\(\pm\)0.90 dB) than the vertical one (\(\pm\)1.21 dB). Hence, a rough monitoring of both polarizations is feasible. As a conservative rule of thumb, it can be decided that if the horizontal and vertical daily median reflectivity values were outside the [79.5-83.5] or [77.5-82.5] dBZ intervals (a little more than \(\pm\)2\(\sigma\)), a warning would be raised. Regarding the relative dispersion of linear Z a threshold of 0.30 (0.35) for the horizontal (vertical) polarization could be selected (see Table 4). As far as the differential reflectivity is concerned, the 5-day mean and median values are 1.20 dB and 1.18 dB, respectively. The standard deviation and spread are 0.89 and 0.99 dB, respectively. Such dispersion is too large for monitoring purposes (see Section 2.4.4 and [19])  
As far as the copolar correlation coefficient is concerned, the 5-day median (mean) value is 0.9968 (0.9962); the standard deviation and spread are both 0.0024 (last row of Table 8). Hence, the daily median of the copolar correlation coefficient could be expected to be larger than 0.994. Anyhow, if the median were smaller than 0.990 (conservative threshold) a warning would be raised. We have tested the above-defined empirical intervals, using, as an example, data from another eleven clear sky days. In all cases, the spectrum width was always the same (DN = 1), while the average radial velocity DN equaled 128 or 127 in all the cases but one (out of 3456 5-min samples). Four warnings occurred on 28 September 2016. These were related to the following observables: Radial velocity (DN = 129 once) and the coefficient of variation of both the horizontal (CoV = 0.31) and vertical (CoV = 0.48) reflectivity polarizations. On 22 February 2017, the CoV for the vertical polarization was as large as 0.50 (the standard deviation of \(Z^{dr}\) was as large as 1.9 dB).