Analytical calculation of the minimum wind speed required to sustain wind-blown sand on Earth and Mars

The wind-driven hopping motion of sand grains, known as saltation, forms dunes and ripples and ejects fine dust particles into the atmosphere on both Earth and Mars. While the wind speed at which saltation is initiated, the fluid threshold, has been studied extensively, the wind speed at which it is halted, the impact threshold, has been poorly quantified for Mars conditions. We present an analytical model of the impact threshold, which we show to be in agreement with measurements and recent numerical simulations for Earth conditions. For Mars conditions, we find that the impact threshold is approximately an order of magnitude below the fluid threshold, in agreement with previous studies. Saltation on Mars can thus be sustained at wind speeds an order of magnitude less than required to initiate it, leading to the occurrence of hysteresis. These results confirm earlier simulations with a detailed numerical saltation model, and have important implications for the formation of sand dunes, ripples, and dust storms on Mars.