Raindrop erosion of tillage induced microrelief: possible use of the diffusion equation

The purpose of this paper is to evaluate the possibility of using the diffu sion equation for raindrop erosion modelling. We wanted in particular to kn ow if such a model could provide accurate interpolations of microrelief bet ween two known dates. In a theoretical section, we show that the assumption that soil particles follow parabolic trajectories when splashed by raindro p impacts leads to a diffusion equation. This equation suggests a linear re lation between Delta z, the variation of height between two dates, and the Laplacian del(2)z (del(2)z = partial derivative(2)z/partial derivative(2)z/ partial derivative x(2) + partial derivative(2)z/partial derivative y(2)). This relation is confirmed by data from a simulated rainfall experiment car ried out in the sandy soils of the Senegalese groundnut belt. Four square p lots of side 4 m each were used. They were heed with a traditional horse-dr awn three-tined hoe. Three rains of 70 mm h(-1) lasting 30 min each were ap plied. An automated relief meter designed and constructed by the authors wa s used to measure the distribution of heights for every 5 cm before the fir st rain, and after the first and the third rains. The mean correlation coef ficient of the model was 62% for the first rain and 46% for the next two ra ins. Besides raindrop erosion, compaction occurred during the first rain. A dding a crude description of compaction enhanced the mean of the correlatio n coefficients of the model up to 70% for the first rain. Furthermore, the coefficient of variation of the four adjusted total diffusion lessens from 10 to 6%. The simulated surfaces were smoother than the real ones, which wa s an expected result, but the surface storage capacity was overestimated. T he latter result illustrates the role of runoff in shaping the flow paths i t follows and, consequently, in lessening the surface storage capacity. The main conclusion is that the diffusion equation provides a promising frame for further development of models simulating microrelief evolution during r ainfall. Another conclusion is that these models should integrate existing routines for runoff erosion at small scale in order to simulate surfaces wi th realistic hydraulic properties. (C) 2000 Published by Elsevier Science B .V.