# Real-Time Rain Rate Evaluation via Satellite Downlink Signal Attenuation Measurement
## 1 Introduction
### Weather Radars  
Weather radars are used for monitoring precipitation by most weather services. They are able to detect, quantify and monitor the evolution of precipitation events over a wide area (circular area with a radius ranging from approximately 70 to 200 km, depending on the frequency used) with a high spatial (less than 1 km, although not constant) and temporal (5-10 min) resolution. Furthermore, they can provide a 3D representation of the precipitation event, therefore allowing us to get a deep insight into the characteristics of rainfall and in general of the ongoing microphysical processes governing precipitation. Typically, weather services use radars by arranging them in a networked configuration, in order to obtain seamless coverage of nation-wide areas for meteorological and hydrological applications. However, weather radars perform indirect measurements of rainfall, obtaining precipitation estimates by converting radar measurements into rainfall rate using appropriate conversion algorithms [12]. In the most common configuration, weather radar radiates a train of short duration electromagnetic pulses that, in the presence of precipitation within the radar volume defined by the antenna pattern, is scattered in all directions. The wave's energy backscattered toward the radar receiver (weighted by the inverse of squared distance) is nearly proportional to a weather radar parameter called the radar reflectivity factor (Z), which depends on the number and size distribution of hydrometeors and their absorption and scattering properties related to the density and shape of the hydrometeors, radar wavelength and temperature. Most of the operational weather radars have adopted the dual polarization technology. Such radars are capable of transmitting pulses on both horizontal and vertical planes (following alternate or simultaneous schemes), providing additional information related to the shape and size of the hydrometeors, which can be used to improve the accuracy of the rainfall estimation algorithm and to obtain information on the precipitation microphysics [13; 14]. Quantitative precipitation estimation (QPE) by weather radar can be affected by many sources of errors (see [15; 16] and the references therein), that can be related to (i) errors in radar measurements, such as radar miscalibration, presence of ground clutter, partial beam blocking, propagation effects and precipitation attenuation effects; (ii) errors in the conversion of radar measurements into rainfall rate at ground, due to the vertical variability of the precipitation system and to the assumption made about the drop size distribution (DSD, namely the number of drops per unit of drop diameter interval and per unit volume) used to obtain retrieval algorithms, and (iii) errors that increase with the distance from the radar antenna, such as the broadening of the radar beam (which causes an increase of the radar sampling volume with range), and the time-height ambiguity between the rainfall rate obtained from radar measurement at certain height (that increases with the distance) and the rainfall rate at the ground.