# Propospheric Attenuation in GeoSurf Satellite Constellations
## 1 The GeoSurf Satellite Constellations  
The GeoSurf satellite constellations belong to the family of Walker Star Constellations [1]. The GeoSurf constellations emulate, for ground stations located at any latitude, the geostationary orbit with zenith paths: any transmitter/receiver, wherever it is located, can be linked to a satellite as if it were at the equator and the satellite at its zenith. The GeoSurf constellations can have most of the advantages of the current GEO (Geostationary), MEO (Medium Earth Orbit), and LEO (Low Earth Orbit) satellite constellations without having most of their drawbacks. For comparing the advantages and disadvantages of a GeoSurf constellation design, see Table 1 in [1].  
In the present paper, our aim is to estimate, globally, the tropospheric attenuation that can be expected in the GeoSurf links at 39.6 GHz--a frequency experimented with the satellites Italsat [2, 3] and Alphasat [4, 5]--due to clear-sky (water vapor, oxygen, and clouds) and to rain, in terms of the probability of annually exceeding a given fade level. For link budgets, this fade level is to be considered as the largest power/coding margin that must be available before link outage. Aside from frequency, of course, clear-sky and rain fades depend on the site and elevation angle under which the satellite is seen from the ground station--practically 90\({}^{\circ}\), i.e., zenith, in the GeoSurf constellations--not on the satellite altitude; therefore, they can be globally applied to any GeoSurf constellation, regardless of orbit altitude.  
For the purpose of illustration, we have studied the tropospheric attenuation predicted for the reference sites listed in Table 1 (Canberra, Holmdel, Pasadena, Robledo, and Spino d'Adda) to show, with some prediction models, the tropospheric attenuation expected there in GeoSurf (zenith) links, in GEO links with satellites located at the same longitude of the site (GEO largest elevation angle), and in LEO links. These specific sites have been chosen because historical radio propagation experiments have been conducted there formany years (Holmdel in New Jersey, Spino d'Adda in Italy) or because they are the seats of important space stations (Canberra in Australia, Robledo in Spain) or space laboratories (Jet Propulsion Laboratory, Pasadena in California).  
These reference sites set the meridian on which we consider sites with latitudes ranging between 60\({}^{\circ}\) N and 60\({}^{\circ}\) S, and report the tropospheric attenuation predicted first for GEO and GeoSurf satellites along the meridian and then for LEO satellites. In other words, we sample Earth longitude along these meridians and sample Earth latitude in a continuous range between 60\({}^{\circ}\) N and 60\({}^{\circ}\) S. The choice of this particular latitude range is just due to the fact that for larger latitudes, the GEO paths would be too low on the horizon to be practical and useful, because they can be obstructed and suffer from large fades, due either to rain or to clear sky, and large scintillations. On the contrary, it is obvious that MEO, LEO, and GeoSurf satellites can always be used at any latitude, with the advantages and disadvantages discussed in [1].  
After this introductory section, Section 2 reports and discusses the probability distributions of rain attenuation at the reference sites in the GEO paths along the meridian; Section 3 reports and discusses the GeoSurf probability distributions of rain attenuation obtained along the meridian of the reference sites in the latitude range of 60\({}^{\circ}\) N to 60\({}^{\circ}\) S; Section 4 reports and discusses the expected tropospheric attenuation affecting LEO satellites; Section 5 reports and discusses similar results but for clear-sky attenuation; and finally, Section 6 reports some final remarks and suggests future work.