## 3 Results
### Wind Analysis  
It was assumed that the failure to detect part of the snow or liquid precipitation could be due to errors induced by wind intensity, as highlighted in the literature [5,6]. Therefore, the difference in precipitation was assessed from both satellite data (IMERG) and rain gauges, in relation to different wind speeds. The wind speed variable was classified by merging contiguous integer values of speed in m/s, based on the statistical method \"sample size for one sample, continuous outcome\" to define the correct sample size to achieve the chosen objectives, which were 95% significance with an error of no more than 0.3 mm of rain. At the same time, the sample size between the two sets of IMERGs and rain gauges was evaluated using the \"sample size for matched samples, continuous outcome\" method with a 95% significance level, as well as a maximum error value of 0.2 mm of rain. Both sample size conditions were satisfied, so that differences between IMERG and rain gauges could be evaluated significantly at certain wind speed intervals. Table 4 shows the common behaviour of the investigated mountain rain gauges as a function of different wind speeds. In particular, it is possible to observe that the trend of the IMERG data compared to those of the rain gauges is very similar, more pronounced in the case of MB and PB and less pronounced for MP. It can be observed from the graph (Figure 2) that in the range from 7 to 20 m/s wind speed, the IMERG precipitation data increases, while those of the rain gauges increase less or even decrease. The differences seem to be very well correlated between the various measuring points; in fact, the Pearson correlation coefficient shows the following values: MB-MP is equal to about 0.85; MB-PB is equal to about 0.96 and MP-PB is equal to about 0.81. Thus, it can be seen that the pattern of the variation between the IMERG data and the rain gauge data is very similar between the three weather stations. In order to better understand the differences affecting the investigated weather stations, wind was also taken into account by observing the annual distribution of wind in percentage. The prevailing direction is similar for MP and MB, correlation coefficient 0.67, while it seems to be significantly different for PB, which has approximately 0 correlation with the other two weather stations (Figure 3). In particular, the two prevailing directions for PB are W-SW and E-NE, while for MB and MP they are W-NW and S-SE. These differences are probably due to the exposure, which is equal to 278\({}^{\circ}\) for MP, 230\({}^{\circ}\) for MB and 246\({}^{\circ}\) for PB, \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Wind Speed m/s**} & **MB** & **MB RG** & **MP** & **MP RG** & **PB IMERG** & **PB RG** & **MBIMERG-** & **MPIMERG-** & **PB IMERG-** & **PG\%** \\  & **IMERG** & **mm** & **mm** & **mm** & **mm** & **mm** & **RG\%** & **RG\%** & **RG\%** \\ \hline
0–2 & 3.2 & 3.0 & 3.7 & 3.7 & 4.6 & 8.6 & 0.1 & 0.0 & \(-\)3.9 \\
2–3 & 3.7 & 4.3 & 3.7 & 3.8 & 4.7 & 7.9 & \(-\)0.5 & \(-\)0.1 & \(-\)3.2 \\
3–4 & 4.8 & 5.3 & 4.2 & 4.6 & 5.3 & 9.1 & \(-\)0.5 & \(-\)0.4 & \(-\)3.7 \\
4–5 & 5.6 & 7.1 & 6.0 & 6.4 & 8.6 & 14.7 & \(-\)1.5 & \(-\)0.4 & \(-\)6.1 \\
5–7 & 7.4 & 6.5 & 6.9 & 6.3 & 8.0 & 10.8 & 0.9 & 0.6 & \(-\)2.8 \\
7–20 & 11.3 & 6.6 & 10.3 & 9.7 & 8.2 & 6.8 & 4.7 & 0.6 & 1.3 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Average annual difference (2010–2020) between snow level water equivalents (SLWE) and IMERG data and average annual difference (2010–2020) between SLWE and rain gauges data (RG); the values are given in mm (MB mm; MP mm; PB mm) and as a percentage of the annual average rainfall 2010–2020 (MB%; MP%; PB%).