Kinetic energy of rain and its functional relationship with intensity

Abstract

The rain kinetic energy (KE) is a widely used indicator of the potential ability of rain to detach soil. However, rain kinetic energy is not a commonly measured meteorological parameter. Therefore, empirical laws linking the rain kinetic energy to the more easily available rain intensity (I) have been proposed based on drop-size and drop-velocity measurements. The various mathematical expressions used to relate rain kinetic energy and rain intensity available from the literature are reported in this study. We focus our discussion on the two expressions of the kinetic energy used: the rain kinetic energy expended per volume of rain or volume-specific kinetic energy (KEmm, Jm−2mm−1) and the rain kinetic energy rate or time-specific kinetic energy (KEtime, Jm−2h−1). We use statistical and micro-physical considerations to demonstrate that KEtime is the most appropriate expression to establish an empirical law between rain kinetic energy and rain intensity. Finally, considering the existing drop-size distribution models from literature, we show that the most suitable mathematical function to link KE and I is a power law. The constants of the power law are related to rain type, geographical location and measurement technique.