|
This work develops a unified theory for the estimation of both total rainfall from an individual convective storm over its lifetime and the areawide instantaneous rainfall from a multiplicity of such storms by use of measurements of the areal coverage of the storms within a threshold rain intensity isopleth or the equivalent threshold radar reflectivity. 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(&tgr;)⟩T>S(&tgr;), where ⟨A(&tgr;)⟩ is the average storm area over the life of the storm of duration, T, in which R>&tgr; and the bracketed term is the area time integral. In the second method, the instantaneous areawide rain rate, ⟨R⟩=F(&tgr;)S(&tgr;), where F(&tgr;) is the fractional observed area with R>&tgr;. In both methods, S(&tgr;) is the climatological rain rate for the regime divided by the relative frequency with which R>&tgr;. For thresholds exceeding some minimum value, S(&tgr;) is essentially linear with &tgr; for the kind of lognormal pdf which characterizes convective rain, and is a constant for specified &tgr;. Thus both the lifetime V of the individual storm and the instantaneous, R, for a multiplicity of storms are linear functions of A(&tgr;) and F(&tgr;), respectively. This is in accord with the observations of Doneaud et al. (1984) and Chiu (1988a, b). Because the autocorrelation time of the areawide rain rate of convective storms in areas in excess of 104 km2 is about 5--6 hours, the snapshot, R, is representative of the rain for a few hours. This enhances the accuracy of snapshot measurements for climate purposes and also extends their utility to smaller time/space problems such as hydrology and numerical weather prediction. We also discuss ways of obtaining climatologically valid and unbiased values of S(&tgr;) and means of establishing its values from aircraft and space. ¿ American Geophysical Union 1990 |
