## 2 Materials and Methods
### Brief Description of the Study Area  
The study area is a rectangular region of 360 \(\times\) 240 km around Switzerland. Figure 1 shows a digital elevation map (using the Swiss conformal mapping, CH1903) of this 86,400 km\({}^{2}\) area, which is roughly twice the size of the Switzerland. It is straightforward and intuitive to have an idea of the minimum height of visibility from space, which is several hundred meters above the highest mountain within the ~20 km\({}^{2}\) GPM circular pixel. To derive the actual height of visibility (see [5], Section 2.2, p. 2238 for a detailed definition) of ground based radars, one needs a digital elevation model (DEM), the exact scan strategy, and a radar simulator like [6] or [41]. Figure S1 in the Supplementary Material shows the height of visibility (geometric optics approach) for the MeteoSwiss network based on four radars (we make the simplification that exactly four radars were available during the whole study period). As a consequence of the simplifying geometric optics approach (according to which the angular resolution is much better than the DEM pixel, which is not the case in reality), there is an abundance of narrow radial features, so that it is easy to identify the location of the four radars. Figure 1 also shows the gauge locations, all of which are inside Switzerland. In the present note, the qualitative comparison (see Section 4 and figures in the Supplementary Material) refers to the whole rectangular area: it involves RADAR, GPM, and CombiPrecip. The quantitative comparison is based on 221 sites inside the Swiss territory (see Section 3) and involves GAUGE precipitation products, too. Figure 1: Digital Elevation Map of the (360 \(\times\) 240 km\({}^{2}\)) Alpine study area centered around Switzerland. The black (red) dots show the locations of the “complex (“non-complex) terrain” rain gauges (for more details see Section 4 and [25], Section 2.d, p. 1253). The displayed Cartesian grid is coincident with the Swiss national coordinate system (CH1903), which results from a conformal mapping from the Bessel reference ellipsoid onto a longitudinal cylinder. The Swiss coordinates of the four corners (bottom-left, top-left, top-right, bottom-right) are: (473; 62), (473; 302); (833; 302), (833; 62). The corresponding Lat-Long coordinates (WGS84 datum) are: (45.6978\({}^{\circ}\); 5.8083\({}^{\circ}\)), (47.8561\({}^{\circ}\); 5.7416\({}^{\circ}\)), (47.8269\({}^{\circ}\); 10.5509\({}^{\circ}\)), (45.6698\({}^{\circ}\); 10.8083\({}^{\circ}\)). Integration in Time, Areal Average Precipitation, and Spatial Distribution of 2-Year Amounts in Switzerland  
As stated in the introduction, integration in time is a possible remedy to smooth out the huge differences among the various precipitation products described in detail in Sections 2.1-2.4. For GPM, this simply means adding (and counting) all available observations over each gauge. For the MeteoSwiss products, we add (and count) the measured values for the acquisition times that contain the overpasses; note that the GAUGE temporal resolution is 10 min, while the RADAR temporal resolution is 5 min. The hourly accumulations of CombiPrecip are disaggregated in twelve 5 min maps using the temporal information of RADAR, as described in [22] (Section 4.4, p. 1108); then, the corresponding nearest in time 5 min estimate is used. The total rainfall accumulation derived in such a way is based on the assumption of a constant precipitation rate in 5 min. Regarding the spatial support, which is an important cause of difference among the various devices for estimating precipitation amounts, the half-power-beam wide GPM cells at the nadir have an area of roughly 20 km\({}^{2}\). Only GPM cells that contain a gauge are considered, and the rest are discarded. For upscaling, RADAR and CombiPrecip pixels are simply averaged (in linear units of precipitation amounts) over the 25 km\({}^{2}\) area centered on each gauge (i.e., approximately matching the GPM measurements in spatial scale).