Theoretical advancements on a recently proposed method to measure rainfall energy

Soil erosion induced by rainfall is mainly due to the rainfall impact besides the consequent surface runoff. Rainfall kinetic energy is the most used variable to represent its erosivity. The latter represents the weathering attitude to erode soil and is a fundamental variable of the erosion process. Consequently, precise measurements of rainfall erosivity have to perform to develop a reliable prediction model of the erosive phenomenon. Currently, impact energy can be reliably measured only by disdrometers. These instruments measure the Drop Size Distribution (DSD) which, joined with the raindrop falling velocity, allow to calculate, by integration, the impact kinetic energy. However, disdrometers are expensive tools that imply to collect and process a remarkable amount of data, and for these reasons, they are not suitable for land large scale use. Without direct measurements, the rainfall impact energy is currently estimated using only the rainfall intensity, widely detected by the recording rain-gauge network operating all over the country. Recently, an innovative method to measure the rainfall energy, subject of a patent, has been proposed. This method is based on the simultaneous detection, in a given time interval, of the rainfall intensity and the number of raindrops that hit a specific surface. In this paper a theoretical analysis aimed at improving the reliability of this rainfall energy measurement is firstly presented. The developed analysis accounts for the detection of a further variable deriving from the momentum distribution. Then, the reliability of the proposed approach was tested using 44,695 DSDs recorded in Palermo in the period 2006-2014. Using the proposed approach, the reliability of the rainfall energy measurement can significantly improve.