Formula for a baroclinic adjustment theory of climate

Recently, a theory relating baroclinic neutrality and midlatitudes tropopause height has been proposed. However, GCM results have shown that the dependence of the theory on external parameters is not consistent with that displayed by these numerical experiments. In the present paper we suggest an analytic formula for baroclinic adjustment to the neutrality of Eady waves through tropopause modification. This formula extends considerably the abovementioned theory by taking into account both a simple representation of the stratosphere and the topography. These modifications alter the tropopause condition for a baroclinically neutral state and its sensitivity to the external parameters. In particular, the topography introduces a dependence on the tropospheric vertical wind shear of the neutrality condition, This feature is not present in other models that assume a background state with a zero potential vorticity gradient in the troposphere. We show, furthermore, that the modified neutrality condition has sensitivities that may resemble those displayed by GCM simulations, with respect to the parameters defining the background flow.