## 2 Materials and Methods
### Brief Description of the Study Area
In [42] (Figure 4, p. 1004) it is shown that an upscaling based on the convolution between the Gaussian antenna radiation pattern of the spaceborne radar and the 1 km precipitation field would give better agreement; hence, we know that the scores relating GPM to RADAR and CombiPrecip are slightly pessimistic because the upscaling technique is based on the simple average of 25 pixels centered on the gauge, rather than on matching the GPM cells. GAUGE measurements are point measurements, and, as stated, the gauge cross section is 200 cm\({}^{2}\). Once these 2 year amounts have been derived, it is straightforward to compare the bias of GPM to that of other products. By looking at the first line of Table A1 in [25], one clearly expects a relatively large GPM underestimation with respect to RADAR (in [25] a \"double-conditional\" bias is presented: only estimates simultaneously larger than 0.15 mm/h from both radars are taken into account). Here we present the \"overall bias\", which means that all available observations (including null values of one product while the other one was reporting precipitation, and vice versa) are taken into account. GPM overall underestimation with respect to RADAR results to be \(-\)3.0 dB, which means that, above the 221 selected pixels, only half of the total precipitation estimated by the RADAR product was estimated by GPM. Knowing that RADAR underestimation with respect to GAUGE during the whole 2014 and 2015 period was on the order of \(-\)0.9 dB, one expects a larger GPM underestimation with respect to GAUGE. This is in fact the case: GPM overall underestimation with respect to GAUGE was found to be \(-\)3.4 dB. Note that the \(-\)0.9 dB figure is based on 288 (144) RADAR (GAUGE) observations per day. If the temporal resolution of GPM were 10 min, we would have approximately 105 thousand samples in two years; instead, there are just 528 overpasses. Using the GAUGE network as a reference, one can evaluate whether 528 overpasses are representative, at least to characterize the average annual precipitation in Switzerland. Using all 105 thousand samples, one gets an average annual precipitation of approximately 1200 mm/a (GAUGE network); using only the 528 nearest in time GAUGE observations and averaging the 221 rain gauge values, one gets approximately 1100 mm/a. In this paper, the annual estimates are simply derived by multiplying the sum of the instantaneous amounts (expressed in mm/h) by 24 \(\times\) 365 and dividing the result by the number of available overpasses over the 221 sites. However, it is important to remark that the focus of this study is not on the estimate of the average precipitation in the country, but on its spatial variability. Consequently, in Section 3, the agreement is not evaluated in terms of the mean error, but rather in terms of the dispersion of the error around the mean (Section 3.2), as well as of the correlation among the various precipitation products (Section 3.1). As will be seen in Sections 2.7 and 3, the scores used to evaluate the agreement are independent of any multiplicative compensation factor; however, for visualization purposes (scatter plots in Sections 3 and 4; GPM, RADAR and CombiPrecip maps in the Supplementary Material file), GPM precipitation values will be multiplied by a factor of 1.6, which corresponds approximately to a 2 dB compensation.