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Raindrop-impact-induced erosion starts when detachment of soil particles from the surface results from an expenditure of raindrop energy. Hence, rain kinetic energy is a widely used indicator of the potential ability of rain to detach soil. Although it is widely recognized that knowledge of rain kinetic energy plays a fundamental role in soil erosion studies, its direct evaluation is not straightforward. Commonly, this issue is overcome through indirect estimation using another widely measured hydrological variable, namely, rainfall intensity. However, it has been challenging to establish the best expression to relate kinetic energy to rainfall intensity. In this study, first, kinetic energy values were determined from measurements of an optical disdrometer. Measured kinetic energy values were then used to assess the applicability of the rainfall intensity relationship proposed for central Italy and those used in the major equations employed to estimate the mean annual soil loss, that is, the Universal Soil Loss Equation (USLE) and its two revised versions (RUSLE and RUSLE2). Then, a new theoretical relationship was developed and its performance was compared with equations found in the literature.

For the study and modeling of hydrological phenomena, both in urban and rural areas, a proper estimation of the areal reduction factor (ARF) is crucial. In this paper, we estimated the ARF from observed rainfall data as the ratio between the average rainfall occurring in a specific area and the point rainfall. Then, we compared the obtained ARF values with some of the most widespread empirical approaches in literature which are used when rainfall observations are not available. Results highlight that the literature formulations can lead to a substantial over- or underestimation of the ARF estimated from observed data. These findings can have severe consequences, especially in the design of hydraulic structures where empirical formulations are extensively applied. The aim of this paper is to present a new analytical relationship with an explicit dependence on the rainfall duration and area that can better represent the ARF-area trend over the area case of study. The analytical curve presented here can find an important application to estimate the ARF values for design purposes. The test study area is the Lazio Region (central Italy).