## 4 Results and Performance Evaluation
### Dichotomous Statistical  
The dichotomous statistical scores help to evaluate the accuracy of rain detection of the technique and then of the classifier. Six scores are used: probability of detection (\(POD\)), false alarm rate (\(FAR\)), critical success index (\(CSI\)), the frequency bias index (\(BIAS\)), probability of false detection (\(POFD\)), and the percentage of corrects (\(PC\)). The rain/no rain threshold was set to 0.2 mm/h. Their definitions are:  
\[POD=\frac{s1}{s1+s3},\ FAR=\frac{s2}{s1+s2},\ CSI=\frac{s1}{s1+s2+s3}, \tag{2}\] \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Date** & **Total Pixels** & **Training Pixels** & **Validation Pixels** & **Testing Pixels** \\ \hline
5 June 2015 & 7913 & 5934 & 1186 & 1186 \\
20 February 2016 & 75,322 & 56,491 & 11,298 & 11,298 \\
12 October 2015 & 18,693 & 14,019 & 2803 & 2803 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Rain rate estimation dataset-night-time. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Date** & **Images** & \begin{tabular}{c} **Pixels Classified** \\ **Day** \\ \end{tabular} & \begin{tabular}{c} **Pixels Classified** \\ **Night** \\ \end{tabular} & \
\begin{tabular}{c} **Pixels Retrieved** \\ **Day** \\ \end{tabular} &
\begin{tabular}{c} **Pixel Retrieved** \\ **Night** \\ \end{tabular} \\ \hline
5 June 2015 & 37 & 48,7547 & 658,634 & 57,097 & 49,732 \\
20 February 2016 & 89 & 1,777,737 & 2,914,099 & 376,591 & 272,805 \\
12 October 2015 & 37 & 739,551 & 409,922 & 34,193 & 19,412 \\
8 July 2015 & 17 & 342,565 & – & 52,542 & – \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Number of pixels processed for performance evaluation. \[BIAS=\frac{s1+s2}{s1+s3},\ POFD=\frac{s2}{s2+s4},\ PC=\frac{s1+s4}{N}. \tag{3}\]  
where \(s1\), \(s2\), \(s3\), \(s4\) are defined according to the contingency Table 10.  
* POD measures the fraction of observed events that were correctly identified, the best value is one. * FAR measures the fraction of estimated rainy pixels that were not raining, its best value is zero. * CSI measures the fraction of estimated events that were correctly identified, its best value is one. * BIAS measures the overestimation or underestimation of the method, then a BIAS greater than one indicates an overestimation, while a BIAS lower than one indicates an underestimation. * POFD indicates the fraction of pixels incorrectly identified by the satellite and its optimal value is zero. * PC is the percentage of correct estimations and its best value is one. A pixel is considered \"rainy\" if the rain rate is greater than 0.2 mm/h. In Table 11 the statistical results are listed. According to the values in Table 11, globally, the fraction of raining cloud detected by the proposed technique is quite consistent with the one detected by weather radars. Indeed, high POD values go always together with very low POFD and low FAR. Bias values show a more complex situation. During spring/summer case studies the technique seems to overestimate raining area and the opposite in autumn/winter. As it appears clearly, the data fusion technique is always much better the PR-OBS3 product which has performance consistent with results of its validation report [31]. Performance during day time are usually better, showing that the use of visible channel has a measurable impact on the algorithm. As suggested in [46] it seems that information on CWP (provided by VIS0.6 and NIR1.6) helps to identify precipitation area better. This behavior is not present for PR-OBS3 product because it only uses 10.8 \(\upmu\)m infrared channel during day and night.