A fast analytical approximated method <strong>of</strong> solution for RTE,based on the generalization <strong>of</strong> the Ed<strong>di</strong>ngton approximationand capable to unfold the azimuthal dependence <strong>of</strong> thera<strong>di</strong>ance field, has been developed [17], [18]. Performances <strong>of</strong>this new ra<strong>di</strong>ative model, named GERM (GeneralizedEd<strong>di</strong>ngton Ra<strong>di</strong>ative Model), in simulating the backscattered(reflected) and forwarded (transmitted) intensity field due to aplane- parallel homogeneous me<strong>di</strong>um, have been evaluated bycomparison with the “exact” DISORT numerical model. Themain theoretical limitations <strong>of</strong> GERM are related to theassumption <strong>of</strong>: i) stratified me<strong>di</strong>um geometry; ii) unpolarizedra<strong>di</strong>ation. A way to apply GERM to a 3-D problem is to resortto a 1-D slant geometry along the viewing angle, that is toconstruct an equivalent 1-D problem from the given 3-D one.The limitation due to the hypothesis <strong>of</strong> unpolarized ra<strong>di</strong>ancecan be only removed if the elements <strong>of</strong> the rotated phasematrix can be approximated by means <strong>of</strong> a Sobolev phasefunction [16]. The vali<strong>di</strong>ty <strong>of</strong> this approximation would, <strong>of</strong>course, depend on the properties <strong>of</strong> the particle <strong>di</strong>stributionPreliminary GERM numerical results are shown in Fig. 6 interms <strong>of</strong> percentage fractional error, with respect to DISORToutputs, as a function <strong>of</strong> optical thickness and volumetricalbedo for asymmetry scattering factor g. The percentageerror is less than 10% on average, being higher for largeralbedo and optical thickness.IV. PRELIMINARY MEASUREMENTSPreliminary measurements, carried out in Rome using the<strong>FSO</strong> link illustrated in Sect. II, are shown here. The temporaltrend <strong>of</strong> temperature and humi<strong>di</strong>ty for an event with moderatestratiform rain with some embedded convection is shown inFig. 7. The coupled <strong>FSO</strong>/meteorological measurements spanbetween December 14 and 15, 2010 and clearly evidences theanti-correlation between thermal and wet characteristics <strong>of</strong> theatmosphere.For the considered winter event Fig. 8 shows the sametemporal trend <strong>of</strong> Fig. 7, but for the measured rainfall andreceived power at 1550 nm. The received power is anticorrelatedwith rain intensity: when the latter increases, thereceived power decreases and viceversa. Fig. 9 shows themeasured path attenuation, derived from the received power inFig. 8, and the pre<strong>di</strong>cted rain specific attenuation, derivedfrom the semi-empirical model (3). There is a good agreementin terms <strong>of</strong> value range, even though a certain <strong>di</strong>spersion isnoted probably due to the raingauge sensitivity (about 0.2mm/h). Further analysis is needed to investigate themeasurement quality and test attenuation pre<strong>di</strong>ction models.2520Precipitationrain [mm/h]1510500 5 10 15 20 25 30 35 40 45 50time [h]90Received power [W]80706050403020100 5 10 15 20 25 30 35 40 45 50time [h]Fig. 8. Same as in Fig. 7, but for rain (mm/h) and received power (W).Fig. 7. Temporal trend <strong>of</strong> temperature (K) and relative humi<strong>di</strong>ty (%) overa period <strong>of</strong> 50 hours on Dec. 14-15, 2010 in Rome (Italy).V. CONCLUSIONSThe activity devoted to the deployment <strong>of</strong> a new free spaceoptics (<strong>FSO</strong>) link set up in Rome (Italy) has been illustrated.
The two-way optical link at 1550 nm is about 1 km long andcan operate with a transmission rate up 1.5 Gbps. Among dust,precipitation, turbulence, fog, and any flying objects affectingthe capacity <strong>of</strong> the optical channel, a focus has been placed onwater particle effects (fog and rain). A numerical evaluation <strong>of</strong>these atmospheric effects has been illustrated, together with apreliminary <strong>FSO</strong> channel modelling based on semi-empiricalpre<strong>di</strong>ction models and the ra<strong>di</strong>ative transfer theory. The latterframework can, in principle, take into account multiplescattering effects along the <strong>FSO</strong> path.Further activity will be devoted to assess data quality,collect long time series in various meteorological scenariosand optimize the attenuation pre<strong>di</strong>ction models.Path attenuation [dB]Specific attenuation Rain[dB/km]54.543.532.521.510.5<strong>FSO</strong> Measured average path attenuation at 1550 nm00 5 10 15 20 25 30 35 40 45 50time [h]654321Rain specific attenuation pre<strong>di</strong>ction at 1550 nm00 5 10 15 20 25 30 35 40 45 50time [h]Fig. 9. Same as in Fig. 7, but for <strong>FSO</strong> measured path attenuation (dB) andrain pre<strong>di</strong>cted specific attenuation (dB/km), from expression (3).ACKNOWLEDGMENTThe authors deeply thank the staff <strong>of</strong> CommunicationsDepartment ISCTI (Italy) for the technical support. 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