## 3 Results
### Interpolation Comparison  
In order to further assess the reliability of satellite-derived precipitation, IMERG data augmented with snowfall not detected by satellite were considered. These data were correlated with interpolations of rainfall data from validated and homogenised neighbouring weather stations at a lower altitude. This made it possible to evaluate the difference between the expected rainfall values and those measured by the satellite and corrected with the actual snowfall data. Backward multiple linear regression, chosen for the statistical analysis, made it possible to exclude independent variables that were not significant for the model. In particular, slope and exposure were excluded using the F-test because they did not add a further explanation of variance to the three considered factors of altitude, distance from the sea and distance from the main ridge. On average, the model annually, from 2010 to 2020, allowed for an explanation of variance of more than 50%, resulting from the adjusted R-squared value, which is a satisfactory value given the high variability of the precipitation parameter. The resulting model equation was used for interpolation at the three investigated weather stations and throughout the neighbouring territory, taking into account the continuous values of the independent variables on which the model is based (Table 5). The IMERG data, to which the snowfall has been added, are much higher than those recorded by the rain gauge for both MB and MP; in fact, on average, the rain gauge records 500 mm less than the satellite data for MB and 400 mm for MP. On the other hand, PB shows a measured value about 160 mm lower than the IMERG satellite data with the addition of the detected snow. The interpolation data are much closer to the IMERG data with the addition of the snow detected than the rain gauges, both for MB and MP; however, for PB, the values from the rain gauge are higher than the interpolation result by about 200 mm and are less distant from the satellite values. In any case, it has to be considered that adding the corrected snowfall value to PB and the increased value in the case of winds above 5 m/s from the N-NW would reach values very similar to those that IMERG increased by the corrected snowfall value. In any case, in order to statistically evaluate the closeness between the IMERG, MLR, and RG data, the standardised root mean square error (RMSSE) was calculated; RMSEE results showed that the IMERG and MLR values were closer than the RG and MLR values for the higher altitude stations MB and MP, whereas the values for the PB rain gauge were almost identical (Table 6). \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & **MB MLR-IMERG** & **MB MLR-RG** & **MP MLR-IMERG** & **MP MLR-RG** & **PB MLR-IMERG** & **PB MLR-RG** \\ \hline RMSSE & 0.03 & 0.41 & 0.08 & 0.52 & 0.49 & 0.53 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Value of the root mean square error standardized (RMSSE) calculated on a monthly basis for Monte Bove Sud (MB), Monte Prata (MP) and Pintura di Bolognola (PB), calculated through interpolation (MLR), IMERG data to which was added the real snowfall data (IMERG) and the data measured by the rain gauge (RG).