Drop size distributions and kinetic energy rates in variable intensity rainfall

Abstract

Rainfall kinetic energy is a key factor in soil erosion processes. It is determined by rainfall intensity, related drop size distribution (DSD), and the drops' terminal velocity. Temporal variability in rainfall intensity is reflected in the DSD and affects the rainfall kinetic energy during the event. Smith et al. (2009) reported on 1‐min interval rainfall intensity and corresponding DSD variability during a storm on 22 July 2006 at Princeton, New Jersey. They reported also on DSD characteristics of heavy convective rainfall events during the whole summer. It is shown that (1) a similar relationship between the mean drop size and the rainfall intensity characterized the local rainfall at both the seasonal and the single‐storm scale, and (2) using the mean drop size as a scaling factor of the DSD removes the rainfall intensity dependence also at the intrastorm scale, providing a powerful tool to deal with temporal variability of rainfall rates during rainfall events. For a given storm characterized by a specific temporal variability of rates, three different ways of evaluating kinetic energy per unit mass or time were applied. By comparison to estimates accounting for rainfall temporal variability and related full DSDs, representing the storm by mean intensity and drop diameter tends to overestimate kinetic energy for low intensities and underestimate it for the higher ones. The relative error for the kinetic energy per unit of mass is ±45% and shifts from negative to positive sign for I > 25 mm/h. For the kinetic energy per unit of time, the relative error ranges from −100% to +210% and changes sign from negative to positive for I > 45 mm/h. When temporal variation of intensity is accounted for but drops are characterized by their mean values instead of the full DSD, kinetic energy is underestimated by 20% on average. Consequently, accounting for temporal variability in rainfall intensity during a storm has a notable impact on the erosive power of the rainfall.