Gridsize induced error in the discretization of exchange processes at the tropopause

Abstract

We study the accuracy of the finite differences discretization scheme for a 2-D simplified model of global tracer transport, in the case that the diffusion coefficients relating flux to the gradient of the mixing ratio have discontinuity jumps at the tropopause. We analyze the conventional box method for a typical downward flow with chemical reaction and for a typical upward flow, comparing the approximations of the solutions, for different discretization gridsizes. It turns out that the jumps may introduce remarkable errors in the discrete solutions, in the case of a typical downward flow; these errors propagate mainly into the troposphere. A noticeable improvement is achieved by reducing the gridsize. However, a typical upward flow is rather insensitive to the chosen gridsizes.