Stable Schemes for Nonlinear Vertical Diffusion in Atmospheric Circulation Models

Abstract

The intensity of vertical mixing in atmospheric models generally depends on wind shear and static stability, making the diffusion process nonlinear. Traditional implicit numerical schemes, which treat the variables to be diffused implicitly but the diffusion coefficients explicitly, are shown to be only conditionally stable. Instability arises in statically stable conditions with an increase of the vertical resolution or of the time step. Stable schemes are derived whose principal characteristic is to take into account the variation of the diffusion coefficient with respect to the basic variables. One scheme looks like a traditional scheme in which the parameter that determines how implicit the calculations are done is made to vary locally instead of being a constant. This insures stability and at the same time provides optimum accuracy. This scheme did remove spurious oscillations found in the Canadian spectral weather forecasting model.