Scaling Laws in Aeolian Sand Transport Under Low Sand Availability

Previous studies of wind-blown sand have considered either fully erodible or non-erodible soils, but the transport over sparsely sand-covered soils is still poorly understood. The quantitative modeling of this transport is important for parameterizing Aeolian processes under low sand availability. Here we show, by means of numerical simulations, that the sand transport rate Q scales with the wind shear velocity u(*) as Q = a center dot [1 + b center dot(u(*)/u(*)t - 1)]center dot root d/g center dot rho(f)center dot(u(*)(2) - u(*t)(2)), where u(*t) is the minimal threshold u(*) for sustained transport, d is particle size, g is gravity and rho(f) is air density, while u(*t) and the empirical parameters a and b depend on the sand cover thickness. Our model explains the transition from the quadratic to cubic scaling of Q with u(*) as soil conditions change from fully erodible to rigid and provides constraints for modeling Aeolian transport under low sand availability. Plain Language Summary The transport of sand by wind shapes the Earth's surface and constitutes one major factor for the emission of dust aerosols. The accurate modeling of wind-blown sand transport is thus important to achieve reliable climate simulations and to make predictions about the propagation of desertification. Previous models of wind-blown sand were designed to compute sand transport rates over a thick sand layer, such as the surface of large, active sand dunes. However, natural soils encompass a broad range of low sand availability conditions, such as crusted or bare soils. It has been a long-standing open question how wind-blown sand transport rates respond to wind velocity when the bare ground is covered by a thin layer of sand. Here we calculate the trajectories of wind-blown sand grains and find that sand transport rates increase faster with wind speed under low sand availability conditions than over sand dunes. The reason for this behavior is elucidated in our simulations: The hopping sand grains fly higher the less sand is covering the hard surface. We obtain mathematical expressions for the sand transport rates as a function of the thickness of sand covering the bare soil, which will be important to improve climate models