# Propospheric Attenuation in GeoSurf Satellite Constellations
## 2 GEO Probability Distributions of Rain Attenuation at the Reference Sites  
Let us consider Spino d'Adda. In the countryside of this town, there is a small space station of Politecnico di Milano where, since the 1970s, the Italian National Research Council (CNR) first, and the Italian Space Agency (ASI) later, with the experts of Politecnico di Milano, have conducted radio propagation and telecommunication experiments at Ku and Ka frequency bands, with the satellites SIRIO [6], ITALSAT [7], and currently Alphasat, within the framework of the Aldo Paraboni experiment [4; 5]. In Figure 1, we show the annual probability distributions (%) of exceeding rain attenuation (dB) in the slant path in Spino d'Adda to a geostationary satellite on the meridian (elevation angle 37.7\({}^{\circ}\), see Table 1) at 39.6 GHz and a circular polarization. Rain attenuation is calculated by using, as input, the rain rate probability distribution recorded locally--with rain rate expressed in millimeters per hour--in the years 1993\(-\)2002 (10 years of continuous observation). In other words, we simulate links towards GEO satellites with the highest elevation angle. The prediction models applied are those known in the literature as \"Brazil\" [8], Bryant [9], Excell [10], Flavin [11], [PERSON] [12], Global Synthetic Storm Technique (SST glo) [13], Svyatogor [14], and the current ITU\(-\)R model [15]. The choice of these particular prediction models is mainly due to their global applicability for later calculations. For predictions at low latitudes, we have not considered the ITU\(-\)R model because it predicts doubtful results at these latitudes when the slant path elevation angle is large. We consider \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Station** & **Latitude** & **Longitude** & **Altitude (m)** &
\begin{tabular}{c} **GEO Elevation** \\ **Angle (\({}^{\circ}\)) on the** \\ **Local Meridian** \\ \end{tabular} \\ \hline Canberra (Australia) & 35.30\({}^{\circ}\) S & 149.10\({}^{\circ}\) E & 597 & 49.0 \\ \hline Holmdel (New Jersey) & 40.40\({}^{\circ}\) N & 74.10\({}^{\circ}\) W & 23 & 43.3 \\ \hline Pasadena (California) & 34.15\({}^{\circ}\) N & 118.00\({}^{\circ}\) W & 352 & 50.3 \\ \hline Robledo (Spain) & 40.87\({}^{\circ}\) N & 4.25\({}^{\circ}\) W & 987 & 42.8 \\ \hline Spino d’Adda (Italy) & 45.40\({}^{\circ}\) N & 9.50\({}^{\circ}\) E & 82 & 37.7 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Reference sites. this model later because at the latitudes of the reference sites listed in Table 1, with the slant paths elevation angles indicated there, its predictions are reliable (see Section 4). Finally, note that it is not the aim of this paper to test the various models, an activity that has been carried out several times (e.g., [16]). They are only used to show the possible range of predictions, although we observe that the Svyatogor model predicts largely pessimistic values, just at the largest probabilities where most direct user applications are envisaged at the Ka band. In Figure 1, the full Synthetic Storm Technique (SST) prediction is also reported (red solid curve). This is the classical SST [17], which transforms the rain rate time series into the rain attenuation time series and gives very reliable predictions of both first-order statistics, i.e., probability distributions of rain attenuation [18; 19; 20; 21; 22; 23], and second-order statistics (parameters dependent on the time evolution of rain attenuation, such as, for example, fade durations) [24; 25; 26; 27]. Therefore, its probability distribution should be the closest to real measurements. The full SST should always be used whenever rain rate time series are locally available. The global SST (SST glo in Figure 1) only mimics the probability distribution of the full SST, and similar to the other models mentioned, it only needs, as input, the annual probability distribution of rain rate, expressed in millimeters per hour, either given by local measurements or by the ITU\(-\)R [28]. Let us now consider the other reference sites.