**The ESA-ANISAP Study: Retrieval of Tropospheric Water Vapour Fields by Using co-rotating LEO Satellites**
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Argenti, Fabrizio ^{1}; Facheris, Luca^{1}; Cuccoli, Fabrizio^{2}; Lapini, Alessandro^{1}
^{1}University of Florence, Information Engineering Dept., ITALY; ^{2}CNIT - National RASS Laboratory, ITALY
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The atmospheric water vapour (WV) content can be estimated from Normalized Differential Spectral Attenuation (NDSA) measurements, as demonstrated by the first two authors in 2001. The method is based on the different attenuation encountered on a radio path at closely spaced frequencies. It can be demonstrated that such measurements are strongly correlated with the water vapour content along the path. By using a couple of counter-rotating LEO (Low Earth Orbit) satellites (one carrying a transmitter, the other a receiver) operating in the Ku/K bands, a vertical profile of the WV can be achieved from the total content of water vapour (Integrated Water Vapour, IWV) along the propagation path between the two LEO satellites. The rationale for using the NDSA approach is that of combating the severe impact of scintillation due to tropospheric turbulence on the water vapour estimates. The present study analyses the possibility of applying the NDSA measurement approach to the estimation of a 2-D atmospheric field. We consider, in this case, a geometry of co-rotating (CO-RO) satellites. The CO-RO case assumes that one (or more) transmitting (TX) satellites follow, in the same orbit and in the same direction, one (or more) receiving (RX) satellites. The propagation links cross the troposphere yielding a set of integral attenuation measures along paths that belong to the orbital plane. Like in the counter-rotating case, from the attenuation measurement a spectral sensitivity (SS) - and from this an integral water vapour content - can be achieved. The objective is the estimation of a 2-D field lying on the orbital plane of the satellites and is formulated as the solution of an inverse problem. The following issues are at the basis of the proposed solution. The integral measurement obtained in the CO-RO case contains information about the local attenuation encountered by the propagating wave in points of the orbital plane. Such an attenuation is a function of the local WV content. For the sake of simplicity, we have assumed circular orbits and circular Earth's shape. Let h be the altitude of the satellites and Hm be the maximum altitude of the annular region we would like to sound. We assume that one transmitting satellite and a number nR of receiving satellites are deployed. The geometry of the constellation can be set such that the radio paths have a minimum distance from the Earth's surface between 0 and Hm (possibly equispaced in this range). During satellites movement, the paths span a annular area in the orbital plane so that, in principle, the reconstruction of the WV field in this region can be formulated as an inverse problem. A similar problem is encountered in the tomographic reconstruction of images. In our case, however, unlike in classical tomographic methods used in biomedical imaging, powerful mathematical tools such as the radon transform can not be applied. In order to verify the feasibility of the CO-RO approach, we have implemented a simulator that permits to reconstruct, starting from a set of integral measurements, the unknown WV field. Such a tool allows us to evaluate the accuracy of the inverse problem solution when the different parameters are varied (e.g., number and altitude of satellites). We have also analysed various parameters that may influence the computation of the spectral sensitivity and its accuracy. One of the basic parameters that influences measurements is the receiver SNR, due basically to thermal noise. The SNR increases if the integration time used to estimate the received power and the attenuation over the propagation path increases. The SNR improvement contrasts with the spatial resolution of the WV field that can be reconstructed. In fact, a higher SNR (higher integration time) means a lower number of measurements that can be obtained in a given area, so that a compromise between the maximum SNR and the maximum spatial resolution must be achieved. In the paper, some results obtained form the simulations with different operating parameters will be shown in order to assist the design of the constellation geometry and to assess the overall performance of the NDSA approach in the CO-RO case.