The Vertical Scale of an Unstable Baroclinic Wave and Its Importance for Eddy Heat Flux Parameterizations

Linear, quasi-geostrophic waves destabilized by a surface temperature gradient produce eddy potential vorticity fluxes which characteristically extend above the surface to a height where the vertical shear ∂u¯/∂z, static stability N2 and potential vorticity gradient ∂q/∂y of the zonal flow are evaluated at the surface. Utilizing this result and a simple scaling analysis, we argue that the time averaged, vertically integrated, poleward eddy heat flux is proportional to the fifth power of the meridional temperature gradient when h0 is much less than the scale height of the atmosphere.