# Real-Time Rain Rate Evaluation via Satellite Downlink Signal Attenuation Measurement
## 4 Direct Method for the Estimation of the Rain Rate
### Rain Height  
Rain height is a key parameter for both direct and statistical models. Through weather radar data, one can estimate the actual height and width of the melting layer. Different signatures of radar measurements can be used, depending on the available measures and the observation geometry. The most known signature is the \"bright band\", a layer of enhanced reflectivity below the 0 \({}^{\circ}\)C isotherm that is due to large and wet snowflakes that melt during their fall. This signature can be observed both at vertical incidence and in the quasi-horizontal scan performed by operational radar systems, where it appears as a circular band with greater reflectivity. The Doppler velocity signature reflects the increase of velocity that takes place during melting: In vertically pointing measurements, Doppler velocity exhibits a sudden increase that ends where melting of particles is complete [30]. Therefore, the position where such enhanced reflectivity ends indicates the height where melting is complete. Such a feature is observable only at vertical incidence. Dual polarization measurements present specific signatures of the melting layer, the most evident being the dip in the copolar correlation coefficient, which is determined by the heterogeneity of scatterers (iced, liquid or partially melted) within a radar resolution volume during the melting process. In quasi-horizontal scans, such a signature results in a circular band of lower values which is thinner than the bright band. Criteria to identify the melting layer have been incorporated into operational products that are provided by some radar networks [38]. Such products fail in some situations and become less accurate at an increasing distance from the radar. When radar data are not sufficient to determine melting layer characteristics, melting layer estimates are obtained from models or other inputs. Although based on empirical observations, there is extensive literature [30; 39; 40; 41; 42] that links the actual rain height with the altitude of the 0 \({}^{\circ}\)C isotherm. According to ITU-R P.839-4 model [43], the mean annual rain height above mean sea level (\(h_{R}^{m}\)) is obtained from the mean annual height of the 0 \({}^{\circ}\)C isotherm (\(h_{0}^{m}\)) as  
\[h_{R}^{m}=h_{0}^{m}+0.36\ \text{km}. \tag{3}\]  
For the direct model presented in this paper, we instead resort to the more accurate instantaneous rain height \(h_{R}\), which is calculated from the instantaneous height of the 0 \({}^{\circ}\)C isotherm \(h_{0}\) as\[h_{R}=h_{0}-\Delta h, \tag{4}\]  
where \(\Delta h\) is an empirical parameter [44; 45; 46], whose value depends on many different variables. In the remainder of the paper we have set \(\Delta h=400\) m. Clearly, being based upon current height values, (4) reveals more accurate than (3) which instead relies on just a fixed annual average. In the perspective of a practical implementation, the instantaneous value of \(h_{0}\), needed for the estimation of the rain rate can be obtained in two different manners. The first approach is to extract the information relevant to a short-term forecast for the 0 \({}^{\circ}\)C isotherm height from the numerical weather prediction (NWP) weather research and forecasting (WRF) model data, which are obtained by mixing either real data (observations and analyses) with idealized atmospheric conditions [47]. Alternatively, we can resort to the modern-era retrospective analysis for research and applications (MERRA) [48] global re-analysis database that provides, over very long periods, modelled data relevant to the 0 \({}^{\circ}\)C isotherm height. Since the 0 \({}^{\circ}\)C isotherm height shows a very strong periodicity over seasons, averaged data may provide sufficient approximation for the daily values [39]. For example, Figure 7 shows, for each day of the year, the average value over 35 consecutive years of the 0 \({}^{\circ}\)C isotherm height over the city of Florence, Italy, obtained from the MERRA database.