The Probability Density Function of Rain Rate and the Estimation of Rainfall by Area Integrals

Abstract

A database on the rain rate collected with disdrometers at various sites located from the middle to tropical latitudes is used to analyze the variations of the parameters of the probability density function of rain rate P(R). Experimental evidence shows that ?R?, the area-average rain rate, and F(τ), the fractional area occupied by rain rate exceeding a fixed threshold τ, are highly linearly related; that is, ?R? = S(τ)F(τ), with R > τ. From the values of P(R), the variations of the proportionality factor S(τ) are computed. The P(R) can be represented by a lognormal distribution; the parameters of that distribution, the average mR and the variance σ2R, are shown to be very tightly linked by the relation σ2R = 5m2R. This is one of the reasons for the stability of S(τ). Using this relation, analytical expressions of P(R) and S(τ) as functions of mR only are proposed. Varying the integration time used for R measurements between 1 and 5 min does not significantly modify the parameters of P(R) or the computed S(τ) values.