A statistical model for horizontal mass flux of erodible soil

It is shown that the mass flux of erodible soil transported horizontally by a statistically distributed wind flow has a statistical distribution. Explicit expression for the probability density function of the flux is derived for the case in which the wind speed has a Weibull distribution. The statistical distribution for a mass flux characterized by a generalized Bagnold formula is found to be Weibull for the case of zero threshold speed. Analytic and numerical values for the average horizontal mass flux of soil are obtained for various values of wind parameters by evaluating the first moment of the flux density function.