# Rainfall Estimation from Tropospheric Attenuation Affecting Satellite Links
## 1 Introduction  
The observation, monitoring, and estimation of rainfall are matters of major concern for a number of reasons. For instance, public administrators aim at guaranteeing an adequate level of security for people living and operating on a given territory: for this purpose, rainfall forecasting is key for the assessment of hydrogeological risks due to landslides and floods. An accurate measurement of total rainfall amount is also critical in climatological studies, since it represents one of the main climate indices. Moreover, the knowledge of the real-time rain rate during precipitation events is useful in urban areas to estimate water runoff from the drainage system.  
A very high spatial and temporal variability characterizes rainfall [1; 2; 3]: it is then difficult to obtain accurate measurements with proper spatial density and temporal detail. Several instruments and techniques have been developed to gauge this quantity (e.g., the use of weather radars, rain gauges, infrared satellite imagery, microwave links, etc.). Each of them presents advantages and limitations [4]: for example, remote sensing measurements aim at estimating the precipitation field over wide areas, but typically with limited spatial resolution and accuracy; on the contrary, point observations, e.g., collected by rain gauges and disdometers, deliver precise local measurements, but they hardly provide large and dense coverage.  
Recently, increasing attention has been paid to the exploitation of satellite downlink signals for the estimation of rainfall, as most of the commercial satellite communication systems currently operate in the Ku band (12-18 GHz) and the K band (18-26 GHz): in fact, in such a frequency range, rain significantly impairs the propagation of electromagnetic waves [5; 6]. Some approaches have been developed for estimating the intensity of precipitation on a large scale from space-borne signals, with a spatiotemporal resolution between that of rain gauges and of weather radars. In fact, the opportunisticuse of satellite downlink signals to estimate rainfall combines the benefit of covering areas where ground instrumentation or radar networks are not available, and the requirement of high temporal resolution measurements, which is in the order of one minute [7]: this approach would allow providing two-dimensional maps of the rain intensity, even across continental regions (e.g., Europe) by using a sufficiently dense network of ground receivers.  
The methodologies that are currently available to assess rainfall rate via satellite links are of limited accuracy and reliability and, in some cases, of complex implementation [8; 9; 10; 11]: as a consequence, it becomes necessary to investigate alternative estimation methods, which only require few measurable physical parameters as input.  
This contribution presents a novel estimation methodology that aims to estimate the rain rate by opportunistically exploiting local downlink satellite communication signals and by making use of local ancillary meteorological data, namely the hourly zero-degree isotherm height and the monthly connectivity index. The model also includes different expressions to take the different impact of stratiform and convective rain events on the link into due account. More specifically, the remainder of the paper is structured as follows. Section 2 presents the Earth-space propagation experiment carried out at Politecnico di Milano, along with the experimental setup used in this work. Section 3 describes the experimental datasets. Section 4 describes the proposed prediction methodology in detail, while Section 5 summarizes the full procedure for rain rate estimation. Lastly, Section 6 discusses the performance of the proposed model (as well as of other methodologies that are available in the literature) and Section 7 draws some conclusions.