A Heuristic Investigation to Evaluate the Feasibility of Developing a Desert Dust Prediction Model

Abstract

A boundary layer model, to investigate various aspects of desert circulation, has been devised. The planetary boundary layer is divided into a surface (constant flux) layer, a transition layer and an inversion layer. The basic equations (motion, continuity, first law of thermodynamics, dust concentration equation)are integrated with respect to height from the bottom of the transition layer up to the top of the boundary layer. It is assumed that this height coincides with that of the inversion, which is allowed to vary in space and time. Interface conditions are derived by integration of the equations across the inversion layer. These may be used to eliminate the momentum, moisture and dust concentration turbulent fluxes from the vertically integrated equations. The turbulent beat flux is eliminated from the first law by a closure assumption, relating the turbulent flux at the base of the inversion to that at the bottom of the transition layer. Modelling assumptions, specifying the variation with height of wind, temperature and dust concentration, are used in the vertically integrated equations. The resulting equations predict the horizontal wind components at a ?mean? level, and the temperature and dust concentration at the bottom of the transition layer. A simplified version of the model, in which advective terms are neglected, couples the dust concentration and inversion height equations. In the former, the time variation of the dust concentration depends upon the difference between sedimentation and turbulent diffusion of dust, and upon the time variation of the inversion height. The latter depends upon the turbulent transport of heat from the ground, upon the difference between the initial temperature and temperature at a later time, and upon the vertical velocity of the larger scale motions at interface height. A numerical integration of this system describes the evolution of the inversion height, its effect on the dust concentration evolution, as well as the evolution of the dust concentration itself.