Surface Turbulent Flux Formulation in Stable Conditions for Atmospheric Circulation Models

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Abstract
The forty-day Wangara data set is used to discuss the applicability of the traditional formulations for the surface fluxes for atmospheric circulation models. It is shown that, while in unstable conditions the surface layer relationships can be applied to the whole boundary layer with little modification, the use of the log-linear equations in stable stratification should be restricted to very near the surface. The alternative of using resistance laws for models which do not resolve the boundary layer down to a few tens of meters above ground is found to be impractical. Instead a new formulation is proposed for the surface stress in the stable case which avoids the problem of having to position the lowest level of a model close to the surface. This formulation depends explicitly on a near surface temperature and on wind and temperature at a height which can be several hundred meters above the surface. Though our expression for the surface stress is independent of the formulation of the surface beat flux, an expression for the heat flux derived from surface layer theory is found to be adequate over the same domain. The angle between the surface stress and the wind is given as a function of height and stability. The effect of baroclinity is also discussed. The benefit of the new formulation, which requires a near-surface temperature (the topic of a forthcoming paper), is to allow the calculation of surface fluxes of appropriate quality in a model regardless of its vertical resolution.

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