The apparent roughness of a sand surface blown by wind from an analytical model of saltation

We present an analytical model of aeolian sand transport. The model quantifies the momentum transfer from the wind to the transported sand by providing expressions for the thickness of the saltation layer and the apparent surface roughness. These expressions are derived from basic physical principles and a small number of assumptions. The model further predicts the sand transport rate (mass flux) and the impact threshold (the smallest value of the wind shear velocity at which saltation can be sustained). We show that, in contrast to previous studies, the present model's predictions are in very good agreement with a range of experiments, as well as with numerical simulations of aeolian saltation. Because of its physical basis, we anticipate that our model will find application in studies of aeolian sand transport on both Earth and Mars.