HYCELL—A new hybrid model of the rain horizontal distribution for propagation studies: 1. Modeling of the rain cell

Abstract

[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.

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

“…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].…”

“…[12] Féral et al [2003] proposed to describe the rain rate horizontal distribution (RRHD) within rain cells having an elliptic horizontal cross section by combining a gaussian component with an exponential one (Figure 1), so that the analytical expression of the RRHD becomes, in the horizontal plane (Oxy):…”

“…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).…”

“…[10] The object of this paper is to propose a new methodology for generating, over an observation area A o , a two-dimensional rain rate field composed of hybrid cells, that is to say modeled by HYCELL [Féral et al, 2003], so that the simulated scene accounts for the climatological characteristics of the simulation area A o . The mathematical definition of the HYCELL model is reviewed in Section 2.…”