## 4 Discussion
In fact, by eliminating GSB, the correlation coefficient between GAUGE and GPM increases from 0.403 to 0.411 (Log values) and from 0.290 to 0.312, and the scatter decreases from 2.84 dB to 2.78 dB using GAUGE as a reference. As expected, the elimination of the GSB site does not influence the agreement of GPM with RADAR or with CombiPrecip. Figure 3: As in Figure 2, but using a linear (instead of logarithmic) scale for both axes and displaying GAUGE (instead of GPM) amounts on the abscissa. The performance of the various precipitation products can also be evaluated using additional scores, like the Root Mean Square Error (RMSE), the Heidke skill score (HSS), and the Nash-Sutcliffe (NS) efficiency. Table 3 shows the values of the root mean square difference (\"error\") between GPM and the three MeteoSwiss precipitation products. The results are identical to those obtained with the correlation coefficient (Table 1) and the scatter (Table 2): the best agreement is observed with CombiPrecip, followed by the ground-based radar, and finally the gauge network. Note that the RMSE can be decomposed in two orthogonal contributions: the square of the mean difference and the variance of the differences. Original GPM values give a significant mean error component because of the large underestimation. Therefore, in the second row of Table 3 we also show the values after a posterior adjustment of +2 dB, which is the same factor used in Figures 1 and 2. However, due to the relatively poor correlations (see Table 1, line 2) between GPM and the three products, this causes not only a reduction of the squared mean difference, but also an increase of the variance of the difference. Nevertheless, a compensation of 2 dB still gives a better RMSE than the one obtained with the original GPM estimates, as can be seen by comparing the values in the two lines of Tables 3 and 4. An adjustment of 3 dB brings the square of the mean difference to zero, but causes an enormous increase of the variance of the difference, so that the RMSE becomes even larger than the one obtained with the original (underestimated) GPM estimates. Similar results can be seen in Table 4, with a slight improvement when using the new version of the GPM-DPR level-2 data, namely, V05A. Table 5 shows the values of the Heidke Skill Score in the case of a polychoric metrics; in particular, we have opted for a 4 \(\times\) 4 contingency table, with the GPM estimates augmented by 2 dB along the columns, and (alternatively) the three MeteoSwiss products along the rows. The three thresholds used to define the four categories are: 650, 850, and 1250 mm/a. These are exactly the same values used in Figures S2 (GPM estimates), S3 (RADAR estimates), and S4 (CombiPrecip estimates). The HSS values confirm the results obtained using correlation, scatter, MADM, and RMSE: the best agreement is observed between GPM and CombiPrecip, followed by RADAR and GAUGE. In all cases, the GPM version V05A performs better than the V04A. \begin{table}
\begin{tabular}{l c c c} \hline  & **CombiPrecip** & **RADAR** & **GAUGE** \\ \hline Original annual GPM precipitation estimates & 597.9 mm/a & 675.1 mm/a & 770.8 mm/a \\ Annual GPM estimates augmented by 2 dB & 462.4 mm/a & 552.1 mm/a & 639.3 mm/a \\ \hline \end{tabular}
\end{table} 
Table 4: Root Mean Square Error (in mm/a) between the GPM estimates (version V05A) above 221 Swiss sites and the estimates derived from three different MeteoSwiss precipitation products. \begin{table}
\begin{tabular}{l c c c} \hline  & **CombiPrecip** & **RADAR** & **GAUGE** \\ \hline \hline GPM product version V04A augmented by 2 dB & 0.266 & 0.223 & 0.087 \\ GPM product version V05A augmented by 2 dB & 0.277 & 0.262 & 0.122 \\ \hline \end{tabular}
\end{table} 
Table 5: Values of the Heidke Skill Score between the GPM estimates (versions V04A and V05A) augmented by 2 dB and the estimates derived from three different MeteoSwiss precipitation products above 221 Swiss sites. Four classes were used for deriving a 4 \(\times\) 4 contingency table.