Measurement method of rainfall energetic characteristics using the Weibull drop size distribution

Rainfall kinetic energy is a critical variable in assessing rainfall erosivity, that is the capability of rainfall to erode soil. Accurate measurements of rainfall erosivity are essential for predicting soil loss and refining soil erosion models. Currently, rainfall energy is derived from measurements of raindrop size distribution (DSD) and raindrop terminal velocity. However, traditional disdrometers, which measure DSD, face limitations related to both the produced large datasets and the high costs associated with their deployment, especially over large areas, limiting their use to experimental installations for scientific research. Recent advancements have introduced a patented method to measure rainfall energy, relying on the simultaneous detection of rainfall intensity and the number of raindrops impacting a surface within a specific time interval. This paper presents advances in the theoretical measurement method of rainfall kinetic power and momentum by using Weibull distribution and rainfall momentum distribution. The developed theoretical analysis aimed at enhancing the reliability of this innovative approach for measuring rainfall kinetic power and momentum, by the detection of the rainfall intensity, number of the raindrops and the mean raindrop diameter calculated by the raindrop momentum distribution. This analysis developed by using measured DSDs demonstrates that the proposed approach provides accurate estimates of rainfall kinetic power and momentum, but also of the shape and the scale parameters of the DSD. Furthermore, the results suggest that the momentum distribution-based estimates of rainfall momentum are more accurate than those of kinetic power, due its reduced sensitivity to uncertainties in terminal velocity calculations. Implementing direct measurements of rainfall erosivity, this method could significantly improve the accuracy of erosion models and contribute to more effective large-scale monitoring of soil erosion risk.