## 4 Results and Performance Evaluation
### Continuous Statistical Scores  
The continuous statistical scores are useful to evaluate the accuracy of the rain rate estimation. To perform a better comparison between the NN technique and PR-OBS3 algorithm, the same PR-OBS3 continuous scores are used [30]: mean error (_ME_), mean absolute error (_MAE_), standard deviation (_SD_), the root mean squared error (_RMSE_), and root mean squared error percent (_RMSE_%). Their definitions are:  
\[ME=\frac{1}{N}\sum(NN-WR), \tag{4}\]  
\[MAE=\frac{1}{N}\sum\lvert NN-WR\rvert,\ SD=\sqrt{\frac{1}{N}\sum\left(NN-WT- ME\right)^{2}} \tag{5}\]  
\[RMSE=\sqrt{\frac{1}{N}\sum\left(NN-WR\right)^{2}},\ RMSE\%=\sqrt{\frac{\frac{ 1}{N}\sum\left(NN-WR\right)^{2}}{WR^{2}}} \tag{6}\]  
where _NN_ is the rain rate retrieved by the data fusion technique and _WR_ is the rain rate from weather radar. The sum is all over the pixels of all 15 min images. * _ME_ provides information on the local behavior of the rain. If the errors compensate with reverse signs the score can be good even with large errors. Range: \(-\infty\) to \(\infty\), perfect score: 0, unit (mm/h). * _MAE_ measures the average magnitude of satellite data respect to radar data; in this way it is a scalar measure of forecast accuracy. It must be used in conjunction with ME. Range: 0 to \(\infty\), perfect score: 0, unit (mm/h). * _SD_ measures how local behavior move away from ME. Range: 0 to \(\infty\), perfect score: 0, unit (mm/h). * _RMSE_ is more sensitive to large errors than the MAE. Range: 0 to \(\infty\), perfect score: 0, unit (mm/h). * _RMSE_% compensates large sensitivity of RMSE to large errors. Range: 0 to \(\infty\), perfect score: 0, unit (\(\times 100\%\)) The product has been evaluated only for the precipitation class for which rain rate is greater than 0.25 mm/h. In Table 12 continuous statistical scores are reported. The interpretation of the continuous statistical scores is less straightforward than the dichotomous ones even when a visual comparison is provided (see below). Globally, looking at ME score, it appears clear that the technique underestimates the amount of precipitation at ground, and this behavior is more pronounced during summer/spring case studies when the precipitation is higher. MAE score confirms this fact. Standard deviation is usually huge compared with ME, in particular for low regime raining. Comparing these results with those of PR-OBS3 it is evident that both products suffer of the same problems but in general the proposed technique provides a significant improved estimation of the rainfall. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Case Studies**} & **ME** & **MAE** & **SD** & **RMSE** & **RMSE**\% \\  & **NN/H03** & **NN/H03** & **NN/H03** & **NN/H03** & **NN/H03** \\ \hline \multicolumn{6}{c}{**Day-Time**} \\
5 June 2015 & \(-1.23/-2.21\) & \(1.12/2.51\) & \(3.11/4.75\) & \(2.07/5.99\) & \(1.28/2.56\) \\
20 February 2016 & \(-1.11/-1.98\) & \(1.48/2.41\) & \(2.54/4.59\) & \(2.39/3.56\) & \(1.34/1.99\) \\
12 October 2015 & \(-1.09/-2.01\) & \(1.23/3.01\) & \(2.11/5.12\) & \(2.25/4.01\) & \(1.31/2.01\) \\
8 July 2015 & \(-1.31/-1.89\) & \(1.57/2.22\) & \(3.09/2.09\) & \(2.48/6.13\) & \(1.43/2.43\) \\
**Night-Time** & & & & & \\
5 June 2015 & \(-1.28/-2.25\) & \(1.64/2.49\) & \(2.99/4.84\) & \(2.89/6.03\) & \(1.62/2.67\) \\
20 February 2016 & \(-1.31/-2.03\) & \(1.23/2.38\) & \(2.77/4.77\) & \(2.37/4.83\) & \(1.33/2.54\) \\
12 October 2015 & \(-1.19/-1.99\) & \(1.85/2.98\) & \(3.23/5.00\) & \(3.15/4.01\) & \(1.87/2.00\) \\ \hline \hline \end{tabular}
\end{table} 
Table 12: Continuous scores for neural network technique (NN) and PR-OBS-3A (H03) algorithm. A visual comparison is presented in Figure 3 that shows precipitation data on 5 June at 17:30 UTC over Belgium. The images confirm the interpretation of the statistical scores. Figure 3a,b represent rain rate of the data-fusion technique and rain rate from radar, respectively. The main path of the precipitation crossing France, Belgium, and North Sea over Holland is well recognized.