Soil detachment caused by divided rain power from raindrop parts splashed downward on a sloping surface

In modelling interrill erosion caused by raindrops splashed on the soil surface, the parameters most frequently considered are the kinetic energy of the raindrops, the rain power and the rainfall intensity. The present paper presents arguments supporting the inclusion among these parameters of that part of the raindrops' kinetic energy that is expended to splash the soil downslope and introduces a theoretical mathematical equation for a dimensionless function of the kinetic energy distribution fd. The fd function depends on the raindrop angle of incidence θ and is derived from an appropriate division of a falling raindrop into two parts. The multiplication product of the dimensionless function fd and the rain power R (W m− 2) yields the divided rain power Rd (W m− 2). An experiment on loess soil with simulated rainfall at intensities of 19, 33 and 54 mm h− 1 and slopes of 4%, 12% and 25% allowed measurement not only of the soil particle detachment rate ψ (g m− 2 s− 1) caused by surface runoff but also the values of soil splash determined in three directions (upslope, downslope and lateral to the direction of the soil slope). The data obtained were used to estimate α and β coefficients of the power function (ψ = αRβ and ψ = αRdβ) that links the soil particle detachment rate (ψ) caused by surface runoff with the rain power (R) and with the divided rain power (Rd). The determination coefficients R2 were 0.52 and 0.64, respectively. The use of the Rd improved the correlation with the soil particle detachment rate ψ because of the standardisation of trends over a wide range of input values. Additionally, two 3-factor multiple regression analyses were conducted using a main-effect model. Apart from initial soil moisture and density, the predictors R or Rd were used, and the determination coefficients R2 were 0.49 and 0.64, respectively. The results demonstrated the benefit of using the dimensionless function of the kinetic energy distribution fd in empirical models of interrill erosion caused by raindrops.

► The dimensionless function of the kinetic energy distribution fd was introduced.
► The use of the fd improved the correlation with the interrill soil erosion.
► This study supports the division of raindrops into their upper and lower parts.