# Propospheric Attenuation in GeoSurf Satellite Constellations
## 3 Global GeoSurf Probability Distributions of Rain Attenuation  
In this section, we consider the meridian of the reference sites and run the prediction models along each meridian in the latitude range 60\({}^{\circ}\) N to 60\({}^{\circ}\) S. Our aim is to compare the GEO links with the GeoSurf links, as we have done for the reference sites. The input to the models is again the rain rate probability distribution given by the ITU\(-\)R. In particular, we show the difference \(A_{GEO}-A_{Z}\) (dB), calculated at selected annual probabilities, between the rain attenuation exceeded in the GEO path, \(A_{GEO}\) (dB), and the rain attenuation exceeded in the GeoSurf path, \(A_{Z}\) (dB), i.e., at the zenith. Figure 3 shows the results for the longitude of Spino d'Adda, 9.5\({}^{\circ}\) E (see Table 1), for probabilities exceeded for 1%, 0.1%, and 0.01% of an average year. The difference obtainable specifically at Spino d'Adda can be read at the latitude of 45.4\({}^{\circ}\) N.  
We can observe some interesting findings:  
1. At 1% probability (Figure 3, left panel), rain attenuation is due to low values of rain rate; therefore, we expect it is produced by a rather uniform rain rate spatial field. This yields limited differences between GEO and GeoSurf paths for GEO high elevation angles (close to 90\({}^{\circ}\)), as is the case for latitudes between 30\({}^{\circ}\) N and 30\({}^{\circ}\) S, the range in which there are no significant differences between Northern and Southern Hemispheres. 2. Significant differences are found for latitudes greater than 30\({}^{\circ}\) N or 30\({}^{\circ}\) S. Now, the GeoSurf (90\({}^{\circ}\) path) and the GEO paths intersect tracts of rain cells which can be significantly diverse. At these latitudes, the GeoSurf paths are less attenuated than the GEO paths. For example, at 60\({}^{\circ}\) N, the average difference \(A_{GEO}-A_{Z}\) predicted is about 5 dB at 1% probability, 11 dB at 0.1% (middle panel), and 20 dB at 0.01% (right panel). 3. In the low latitude range of \(\sim\) 20\({}^{\circ}\) N to \(\sim\)20\({}^{\circ}\) S (GEO elevation angle along the meridian is larger than about 67\({}^{\circ}\)), the difference \(A_{GEO}-A_{Z}\) is quite small and even negative for some models at probability 0.01%, especially for Excell and Global SST. This latter model retains, in fact, some spatial features of the full SST, which at high elevation angles, such as those found in this latitude range (>67\({}^{\circ}\)), samples the small high-intensity rain cells differently compared to the zenith path (see [13]). In this range, desert areas, such as the Sahara Desert, also affect the results, of course. 4. Notice that in the low latitude range of \(\sim\) 20\({}^{\circ}\) N to \(\sim\)20\({}^{\circ}\) S, the difference \(A_{GEO}-A_{Z}\) predicted by the ITU\(-\)R model is extremely large. 5. Northern and Southern Hemispheres show significant differences as probability decreases, especially for the larger latitudes. Figures 4-7 show similar results concerning the longitude of the other reference sites. However, it is very interesting to notice the large negative difference (5 to 8 dB) found at  
Figure 3: The difference \(A_{GEO}-A_{Z}\) (dB), calculated at fixed annual probabilities 1% (**a**) 0.1% (**b**), and 0.01%, (**c**) between the rain attenuation exceeded in the GEO path, \(A_{GEO}\) (dB), and the rain attenuation exceeded in the GeoSurf path, \(A_{Z}\) (dB), i.e., at the zenith in Spino d’Adda; 39.6 GHz, circular polarization. a probability of 0.01% for sites along the meridian of Holmdel (74.1\({}^{\circ}\) W) in the latitude range of \(\sim\)10 to \(\sim\)30\({}^{\circ}\) N, a region that includes Florida and the Carebbean Islands. Similar observations can be done at a probability of 0.01% for the longitudes, such as the longitudes of Pasadena (118\({}^{\circ}\) W) and Canberra (149.1\({}^{\circ}\) E), which include desert areas and the ocean.