Abstract
Rainfall kinetic energy has been linked to linear, exponential, logarithmic, and power-law functions using rainfall intensity as an independent variable. The power law is the most suitable mathematical expression used to relate rainfall kinetic energy and rainfall intensity. In evaluating the rainfall kinetic energy, the empirical power laws have shown a larger deviation than other functions. In this study, universal power law between rainfall kinetic energy and rainfall intensity was proposed based on the rainfall power theory under an ideal assumption that drop-size is uniformly distributed in constant rainfall intensity. An exponent of the proposed power law was 11/9 and coefficient was estimated at 10.3 from the empirical equations of the existing power-law relation. The rainfall kinetic energy calculated by universal power law showed >95% concordance rate in comparison to the average values calculated from exponential and logarithmic functions used in soil erosion model such as USLE, RUSLE, EUROSEM, and SEMMA and <5% relative difference as compared to the average rainfall kinetic energies calculated by other empirical functions. Therefore, it is expected that power law of ideal assumption may be utilized as a universal power law in evaluating rainfall kinetic energy.
Highlights
Soil erosion is a natural process in all landform evolution and soil degradation along with various environmental problems
We compared the relationship between existing empirical equations and the ideal equation of rainfall power to evaluate the availability as the universal power law
The time-specific rainfall kinetic energy equation based on the power theory was derived through the ideal assumption that the drop-size is uniformly distributed under the constant rainfall intensity
Summary
Soil erosion is a natural process in all landform evolution and soil degradation along with various environmental problems. The empirical equations for the rainfall kinetic energy in various mathematical expressions have been developed in the form of power-law, exponential, logarithmic, and linear functions. Under the assumption based on the DSD measurements [18], EUROSEM [15], the representative soil erosion model in Europe, used a logarithmic function presented by Brandt [19]. Van Dijk et al [20] proposed a general equation of the exponential type from the measured data through a literature review on the relationship between rainfall kinetic energy and rainfall intensity. The empirical power-law relation from the observation of rainfall intensity and radar reflectivity factors using a statistical model of the DSD was presented by Smith and de Veaux [26]. Our newly proposed power law is evaluated through comparing with existing empirical equations
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