The estimation of convective rainfall by area integrals 1. The theoretical and empirical basis

The method is based upon the existence of a well-behaved probability density function (pdf) of rain rate either from the many storms at one instant or from a single storm during its life. In the first method, the lifetime storm rainfall volume is V = [<A(τ)T]S(τ), where <A(τ)> is the average storm area over the life of the storm of duration, T, in which R>τ and the bracketed term is the area time integral. In the second method, the instantaneous areawide rain rate = F(τS(τ), where F(τ) is the fractional observed area with R>τ. In both methods, S(τ) is the climatological rain rate for the regime divided by the relative frequency with which R>τ. For thresholds exceeding some minimum value, S(τ) is essentially linear with τ for the kind of longnormal pdf which characterizes convective rain, and is a constant for specified τ. Thus both the lifetime V of the individual storm and the instantaneous for a multiplicity of storms are linear functions of A(τ) and F(τ), respectively. -from Authors