Raindrop Interaction in Interrill Erosion: a Probabilistic Approach

Amina Nouhou Bako (1, 2) , Frédéric Darboux (1) , Francois James (2) , Carine Lucas (2)

1 URSols - Unité de Science du Sol (Orléans)
2 MAPMO - Mathématiques - Analyse, Probabilités, Modélisation - Orléans

The main processes involved in interrill erosion are soil particles detachment and transport. Detachment is caused by shear stresses created by the impacts of raindrops. After sediments are lifted in the water layer, they are transported over a distance that depends on their settling velocities and the water flow velocity. This study calculates the probabilities of interactions between raindrops during soil detachment, and between raindrops and particles during their sedimentation. Raindrops are assumed to be consistent with the Poisson process and their densities are described by raindrop size distribution functions (Marshall-Palmer, Gamma and Lognormal laws). Interaction probabilities are calculated based on characteristic time and length scales of the shear stresses and the perturbation created by the raindrop impact inside the water layer. The results show that during soil detachment, raindrops are almost independent. Thus, the total amount of soil detached by a rainfall is practically the sum of soil detached by its individual raindrops. Whereas during sediment transport, the probability of interaction between raindrops and settling particles is very high whatever the rainfall intensity and particle size. The consequences of the settling particles-raindrops interaction need to be further investigated.

Mots clés: Raindrop; Poisson process; shear stress; shallow water flow; detachment; sedimentation; soil erosion

Domaines: Mécanique des fluides [physics.class-ph]; Hydrologie; Science des sols

Amina Nouhou Bako, Frédéric Darboux, Francois James, Carine Lucas. Raindrop Interaction in Interrill Erosion: a Probabilistic Approach. 2016. ⟨hal-01326799v1⟩