[1] From radar observations of rain fields at midlatitudes, a new physical model of rain cells is proposed. It strives to describe optimally the rain rate horizontal distribution within rain cells down to 1 mm h À1 . The approach is similar to that of the well-known EXCELL model. The mathematical definition of the model lies in the combination of a gaussian function and an exponential one, the cells having an elliptic horizontal cross section. Due to its hybrid structure, the new model has been named HYCELL. From a conceptual point of view, the gaussian component describes the convective-like high rain rate core of the cell, while the exponential component accounts for the surrounding stratiform-like low rain rate spreading down to 1 mm h À1 . The modeling of a rain cell with HYCELL then requires the determination of seven parameters. The latter is obtained, cell by cell, by solving a set of five fit-forcing equations completed by two continuity equations. The fit-forcing equations involve radar parameters of integral nature which refer not only to the rain cell geometry (area, ellipticity) but also to the rain rate R distribution inside the cell (mean and root mean square values of R and gradient of R). Their analytical expressions are derived from the model definition, while their values are forced to be those derived from radar measurements. Using this method, thousands of rain cells identified from radar observations in the regions of Bordeaux (southwestern France) and Karlsruhe (southwestern Germany) have been modeled. Though both sites are at midlatitude, the climatic contexts differ: oceanic for Bordeaux and continental for Karlsruhe. Results of rain rate horizontal distribution modeling within cells using HYCELL and EXCELL are compared. It is then suggested that the HYCELL model is a new tool which deserves to be considered by system designers to compute propagation parameters.

[1] A methodology to simulate typical two-dimensional rain rate fields over an observation area A o of a few tens up to a few hundreds of square kilometers (i.e., the scale of a satellite telecommunication beam or a terrestrial Broadband Wireless Access network) is proposed. The scenes generated account for the climatological characteristics intrinsic to the simulation area A o . The methodology consists of the conglomeration of rain cells modeled by HYCELL and of two analytical expressions of the rain cell spatial density, both derived from the statistical distribution of the rain cell size. The scene generating requires, as an input parameter, the local Cumulative Distribution Function (CDF) of the rain rate, a meteorological data commonly available throughout the world. The rain rate field is then generated numerically, according to an iterative scheme, under the constraint of accurately reproducing the local CDF intrinsic to the simulation area A o , and following rigorously the rain cell spatial density. All the potentialities of the HYCELL model are thus used in order to generate a two-dimensional scene having a mixed composition of hybrid, gaussian, and exponential cells accounting for the local climatological characteristics. Various scenes are then simulated throughout the world, showing the ability of the method to reproduce the local CDF, with a mean error, with respect to the rain rate distribution, smaller than 1.86%, whatever the location, that is, whatever the climatology. It is suggested that this statistical modeling of the rain rate field horizontal structure be used as a tool by system designers to evaluate, at any location of the world, diversity gain, terrestrial path attenuation, or slant path attenuation for different azimuth and elevation angle directions.INDEX TERMS: 3354 Meteorology and Atmospheric Dynamics: Precipitation (1854); 3210 Mathematical Geophysics: Modeling; 3360 Meteorology and Atmospheric Dynamics: Remote sensing; 6964 Radio Science: Radio wave propagation; KEYWORDS: propagation in rain, radar meteorology, rain modeling Citation: Féral, L., H. Sauvageot, L. Castanet, and J. Lemorton, HYCELL-A new hybrid model of the rain horizontal distribution for propagation studies: 2. Statistical modeling of the rain rate field,

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A methodology to simulate two-dimensional rain rate fields at large scale (1000 Â 1000 km 2 , the scale of a satellite telecommunication beam or a terrestrial fixed broadband wireless access network) is proposed. It relies on a rain rate field cellular decomposition. At small scale ($20 Â 20 km 2), the rain field is split up into its macroscopic components, the rain cells, described by the Hybrid Cell (HYCELL) cellular model. At midscale ($150 Â 150 km 2), the rain field results from the conglomeration of rain cells modeled by HYCELL. To account for the rain cell spatial distribution at midscale, the latter is modeled by a doubly aggregative isotropic random walk, the optimal parameterization of which is derived from radar observations at midscale. The extension of the simulation area from the midscale to the large scale (1000 Â 1000 km 2) requires the modeling of the weather frontal area. The latter is first modeled by a Gaussian field with anisotropic covariance function. The Gaussian field is then turned into a binary field, giving the large-scale locations over which it is raining. This transformation requires the definition of the rain occupation rate over large-scale areas. Its probability distribution is determined from observations by the French operational radar network ARAMIS. The coupling with the rain field modeling at midscale is immediate whenever the large-scale field is split up into midscale subareas. The rain field thus generated accounts for the local CDF at each point, defining a structure spatially correlated at small scale, midscale, and large scale. It is then suggested that this approach be used by system designers to evaluate diversity gain, terrestrial path attenuation, or slant path attenuation for different azimuth and elevation angle directions.

This paper presents the analysis on two weather radar datasets, collected at Spino d’Adda (Italy) and Bordeaux (France), for the simulation and the performance evaluation of a site diversity system. Results from the two locations are compared and the impact of different factors such as the baseline and link orientation is assessed and related to the local climatologic characteristics. The results obtained are then compared with the model currently recommended by the ITU-R for the estimation of the site diversity performance. A linkage is then established between the preferable baseline orientation and the predominant direction of the rain field advection. The rain field displacement is finally shown to be well approximated by the wind speed and direction relative to the 700 hPa isobar extracted from the ECMWF ERA-40 meteorological database