## 1 Introduction  
With the introduction of a precipitation radar on board the Tropical Rainfall Measuring Mission (TRMM) satellite, meteorological radar applications could be expanded to the oceans and lands between \(\pm 35^{\circ}\) latitude on Earth. The Global Precipitation Measurement (GPM) mission _Core Observatory_ satellite, launched on 27 February 2014 [1], has extended the TRMM coverage to \(\pm 65^{\circ}\) latitude, hence including the Alps. Because of the roughly 5 km diameter footprint of the GPM dual-frequency precipitation radar (DPR), clutter contamination will typically limit GPM measurements to areas above the mountains, except where very broad valleys are present. The DPR adds significant new coverage to orographically complex areas, especially in poorly instrumented regions of the world. Precipitation in orographically complex regions like the Alps is inherently complex because of the interactions between the mountainous terrain and the atmosphere. The resultant effects have been the subject of extensive research (e.g., [2]). Additionally, the higher altitudes (and hence lower temperatures) mean that a large proportion of precipitation falls in solid phase, resulting in significant amounts of water being stored in the Alps as snow. This makes the mountains a vital water source in many parts of the world. Better knowledge of precipitation fields in the Alps is necessary in weather, nowcasting, and climate research, and more accurate precipitation measurements, especially in orographically complex catchments, are essential to develop reliable warnings. However, the same complex orography and colder temperatures that make the Alpine environment an important water reservoir in Europe, also make the measurement of precipitation challenging not only for spaceborne radars, but also for ground-based weather radars. The rough and complex orography together with cold and windy conditions make the installation of large radar antennas difficult [3]; the terrain may cause partial or almost total shielding of the radar beam, restricting measurements to high altitudes (e.g., [4; 5; 6]). Unfortunately, the well-known sources of error that affect radar estimations (e.g., [7; 8; 9; 10]) become particularly severe in mountainous terrain (e.g., [11; 12]). Rain gauges are usually considered to provide accurate \"point\" measurements. In this context, \"point\" means a gauge cross section that is usually 200 cm\({}^{2}\) (and a sampling volume of the order of \(\sim\)60 m\({}^{3}\) every 10 min, assuming, for instance, an average terminal fall velocity of 4 m/s). Consequently, it is well known that gauge observations represent local effects and not areal quantities. For hydrological applications, areal precipitation estimates are required, and, therefore, their main drawback is undersampling [13], i.e., there will not be enough observations to describe the variability of the field. Because of the spatial variability of rainfall (especially during intense, convective events), it is obvious that point measurements would undersample the precipitation fields, even though the measurements themselves were correct. Radar measurements can add the desired information on the areal distribution of precipitation. There are enormous differences between remotely sensed radar observations and in situ point measurements by the rain gauges. On the one hand, the small-scale variability of precipitation is such that even three decades ago [PERSON] [14] wrote that \"the spatial variability of rainfall is so pronounced that a single gauge often does not sample representatively over any area, even as small as 4 km\({}^{2}\)\". On the other hand, spatial smoothing by the main Gaussian lobe of the radar antenna radiation pattern, as well as post-detection integration over many pulses reduce the variability of the distribution of precipitation rate in space. Even in the liquid phase, when radar data are compared with \"instantaneous\" point rainfall rate, a random error and a bias are introduced by the smoothing [15].