POINT AND AREA PRECIPITATION PROBABILITIES

EDWARD S. EPSTEIN Department of Meteorology and Oceanography, The University of Michigan

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Abstract

The relationship between point and area precipitation probabilities is examined on the basis of a simple model in which circular precipitation cells of uniform size are distributed at random over an area that is large compared to the forecast area. From knowledge of the cell size and the number of cells per unit area it is then possible to state both the point and area precipitation probabilities. Formulas and graphs of these relationships are shown. When the cells are large, point and area precipitation probabilities are almost equal, but they differ markedly when the cells are small. Joint and conditional probabilities of precipitation at two or more stations are also examined. An extension of the model is presented in which uncertainty regarding the density of cells is expressed as an elementary probability density, and the effects of this on the expected point and area precipitation probabilities are shown.

Abstract

The relationship between point and area precipitation probabilities is examined on the basis of a simple model in which circular precipitation cells of uniform size are distributed at random over an area that is large compared to the forecast area. From knowledge of the cell size and the number of cells per unit area it is then possible to state both the point and area precipitation probabilities. Formulas and graphs of these relationships are shown. When the cells are large, point and area precipitation probabilities are almost equal, but they differ markedly when the cells are small. Joint and conditional probabilities of precipitation at two or more stations are also examined. An extension of the model is presented in which uncertainty regarding the density of cells is expressed as an elementary probability density, and the effects of this on the expected point and area precipitation probabilities are shown.

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