Data and theory for a new model of the horizontal structure of rain cells for propagation applications

Abstract

A large population of radar-measured ground rain cells is used to devise and assess a rain cell model for use in some of the future telecommunication applications. The model is based on cells of exponential profile (which is shown to reproduce best the point rain rate CDF); both rotational and biaxial symmetries are considered for the horizontal cross sections. Furthermore, the proposed model contains analytical expressions for the joint probability densities of the parameters which define the cell, i.e., peak rain intensity, cell size and axial ratio. Finally, an algorithm is given for adapting the model to the characteristics of any given site: this algorithm requires as input the local cumulative distribution of point rainfall and provides the spatial number densities (i.e., the average number of cells per square kilometer and per unit range of the parameters) which this distribution would produce. The model offers the possibility of predicting the statistics of many propagation parameters (such as attenuation or interference by rain scattering) which are determined by the rain cell characteristics and their frequency of occurrence. assumption is made that the same types of precipi-during 1980 near Milan, Italy. tation occur in different locations' what varies is the The model is based on a distribution of cells each frequency of their occurrence. Yet propagation pre-one characterized by an exponential profile of the diction models become a powerful tool in predicting rain rate (in the following referred to as "model statistics of the quantities of interest only if the model cells"). parameters can be derived from local meteorological The statistical properties of the population of data [Rogers, !976]. "model cells" are presented and discussed together with the procedure for linking the parameters of the •Dipartimento di Elettronica, Centro di Studio per le Telecom-model to the meteorological data. rnunicazioni Spaziali CNR Politeenico di Milano, Milano, Italy. A rain cell is defined as any connected region of aFondazione Ugo Bordoni, Rome, Italy. space composed of points where the rain rate exceeds aCentro di Studio per le Telecomunicazioni Spaziali CNR Poli-a given intensity threshold. tecnico di Milano, Milano, Italy. The "model cell" is identified by forcing some of Copyright 1987 by the American Geophysical Union. its integral parameters to correspond with those of Paper number 6S0709. the observed cell. 0048-6604/87/006s-0709508.00 Two models of cell are dealt with' a monoaxial 395 in the range 6-150 mm/h is given by (19). Konrad, T. G., Statistical models of summer rainshowers derived rom fine-scale radar observations, J. Appl Meteorol., 17(2), 171-4. No(R•t ), the number density of R u, in Figure 199,1978. 8, is given in the form of a cumulative distribution Lane, S. O., and W. L. Stutzman, Spatial rain rate distribution normalized to the total number of cells exceeding 5 modeling for earth-spaoe link propagation calculations, paper 404 CAPSONI ET AL.: RAIN CELL MODELING FOR PROPAGATION APPLICATIONS pr...

HYCELL—A new hybrid model of the rain horizontal distribution for propagation studies: 2. Statistical modeling of the rain rate field

“…[59] The methodology developed by Goldhirsh [2000] to generate two-dimensional rain rate fields lies on the description of the rain rate horizontal distribution within the cells by the EXCELL model [Capsoni et al, 1987b]. Considering its monoaxial formulation, the analytical expression of the rain rate distribution within a cell is then given by:…”

“…Considering a database of 213 112 rain cells identified at t = R 2 = 1 mm h À1 from the radar of Météo-France at Bordeaux in 1996 (southwestern France, midlatitude oceanic climate), and another database composed of 701 882 cells observed at the same threshold from the radar of Karlsruhe in 1999 (southwestern Germany, midlatitude continental climate), Féral et al [2003] have shown that, whatever the climatology, the HYCELL model enables one to improve the description of the rain rate horizontal distribution within the cells with respect to the well-known EXCELL model [Capsoni et al, 1987b].…”

“…However, how is it possible to generate a rain rate field over an observation area A o so that the simulated scene should account for the local climatology, that is, for the local CDF? [7] As it is difficult to describe and, a fortiori, to model a rain rate field by considering it as a single entity, it might be possible to split up the field into individual areas, the rain cells, defined as the closed contours over which the rain rate R exceeds a threshold value t. This cellular approach is all the more interesting as deterministic models of rain cells are available, allowing one to describe the inner structure of the cells from a small number of parameters, such as those proposed by Capsoni et al [1987b] or Féral et al [2003]. Whatever the model considered, the two-dimensional generation of a rain rate field from modeled cells requires the determination of a key parameter: the spatial density of the cells, expressed as a function of the model parameters.…”

“…First, HYCELL [Féral et al, 2003] now provides a new model of the rain cell which describes the rain cell horizontal structure more accurately than EXCELL. Secondly, the analytical expression of the cell spatial density has been derived by Capsoni et al [1987b] from the radar observation of 6215 cells in the region of Milan (Italy, midlatitude area). Hence the question: ''can the same expression of cell spatial density be used when generating, for instance, a rain field in tropical regions?''…”

“…The method relies on the rain cell modeling by EXCELL [Capsoni et al, 1987a[Capsoni et al, , 1987b and allows one to fill in the observation area A o with a population of cells having exponential profiles and rotational symmetry. To determine the rain cell spatial density over A o , Goldhirsh [2000] uses the analytic formulation of Capsoni et al [1987b], slightly corrected by Awaka [1989]. The cell density involves the EXCELL parameters and the local CDF intrinsic to the simulation area A o .…”