Mathematical Model for Rain Drop Distribution and Rainfall Kinetic Energy

Abstract

ABSTRACT AN analytical function is proposed for representing the rain drop size distribution. The function can be easily differentiated to yield the drop size density distribution function and allow two different and rather simple ways of fitting to measured data either by using the observed inflection point or any other two points on the measured distribution curve. A modified weighted regression procedure is developed for best fitting the proposed function to experimental data. Using rain drop distributions measured in Rhodesia and in Washington, DC, it was possible to calibrate the model for each place. Analysis of the results indicates that the dependence of the rain drop distributions upon the rainfall intensity can be modeled very well for both sets of data. Applying the calibrated model together with a continuous function of the terminal velocity versus the drop size, it was possible to predict systematically the kinetic energy per unit mass, dE/dM, and per unit time dE/dt, as a function of rainfall intensity, I. The predicted curves of dE/dM differ significantly from the known empirical functions that were proposed to represent the measured data. The deviation between the predicted curves of dE/dt versus I in Rhodesia and Washington, DC is insignificant at low rainfall intensity but becomes noticable at high values of I.