Statistical distribution of the fractional area affected by rain

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Abstract

[1] The knowledge of the fraction of an area that is affected by rain (or fractional area) is of prime interest for hydrologic studies or for rainfall field modeling. Up to now, the statistical distribution of this parameter has been poorly studied. In the present paper, a model of the statistical distribution of the fraction of an area affected by rain over a given rainfall rate is proposed. It takes into account at the same time the size of the area and the local climatology. The analytic formulation of the distribution is established, considering that rainfall fields can be obtained from a nonlinear filtering of a Gaussian random field. As the analytic derivation of the distribution lies on some assumptions, the model accuracy is first evaluated from numerical simulations. It is then shown that the model reproduces accurately the distribution of fractional areas derived from radar observations of rain fields for various rain thresholds, sizes of area, and climatologies. A generic parameterization is then proposed for areas ranging from 100 × 100 to 300 × 300 km2.

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