# Real-Time Rain Rate Evaluation via Satellite Downlink Signal Attenuation Measurement
## 3 Earth-Space Radio Links in the Presence of Rain
### Effects of Rain on Earth-Space Radio Links
The smart-LNB provides the total attenuation (in dB) along the radio path between satellite and the ground. As mentioned before, the attenuation due to frozen hydmeteors can be neglected, and the majority of the attenuation is due to rain (namely along the path called \(l^{(r)}\) in Figure 6). During operations, two different reference precipitation regimes may show up, namely, convective rain and stratiform rain, which are associated with different environmental conditions and precipitation growth mechanisms. Several different definitions of stratiform and convective rain can be found in the literature. However, for the scope of the present study, we can say that convective rain is associated with the presence of vertical wind (up or down-draft) and high rainfall rates. Furthermore, it usually covers a small area and has a huge vertical extension, without a well-defined separation layer between frozen and liquid hydmeteors as sketched in Figure 6b. Instead, in stratiform precipitation, the vertical wind is almost absent, the precipitation covers an extended area and is fairly homogeneous on the horizontal level, as shown in Figure 6a. Finally, along the vertical, three different layers characterized by the presence of different types of hydmeteors are typically well identifiable. At the cloud top, frozen particles are present that start to melt when the environmental temperature approaches 0 \({}^{\circ}\)C. The melting layer has a thickness of few hundreds of meters [30], and below its bottom border there are hydmeteors in liquid phase. Figure 5: Specific attenuation in dB/km vs. carrier frequency in GHz (from recommendation ITU-R P.838-3 [29]), with the rain rate (mm/h) as the parameter. Solid lines and dashed lines refer to horizontal and vertical polarization, respectively. Conventional Statistical Models for Attenuation Prediction in Earth-Space Radio Links in the Presence of Rain  
The two most used statistical models [31] for the prediction of the attenuation affecting a satellite link are the ITU-R (see recommendation ITU-R P.618-11 [32]) and the Crane Global [33] models. Furthermore, the technical literature presents a plenty of models that exhibit good prediction accuracy performance, such as those introduced in [34; 35; 36]. For any geographical location, as a starting point, all the models take the statistical information about the local precipitation expressed as the complementary cumulative distribution function (CCDF) of the rain rate \(R\) as \(F_{R}(x)=\Pr(R>x)\) (see e.g., recommendation ITU-R P.837-6 [37]). This information is then analytically used for a prevision of the statistics of the signal attenuation \(A\) (dB) that will be experienced on the satellite link. Summarizing, both models yield a relationship \(\Phi\) between a given threshold value \(\overline{R}\) of the rain rate \(R\), together with the associated probability \(p=F_{R}(\overline{R})=\Pr(R>\overline{R})\), and a threshold value \(\overline{A}\) of the signal attenuation \(A\) having the same probability of being exceeded, i.e.,  
\[\text{given }\overline{R}:p=F_{R}\big{(}\overline{R}\big{)}=\Pr\big{(}R> \overline{R}\big{)},\text{ the model yields }\overline{A}=\Phi(\overline{R},p):p=F_{A}(\overline{A})=\Pr(A> \overline{A}). \tag{2}\]  
Figure 6: Geometry of an Earth-space radio link in two different meteorological conditions: (**a**) stratiform precipitation and (**b**) convective precipitation.