What determines the height of the tropopause?

The tropopause may be regarded as the boundary between a dynamically active troposphere and a stratosphere that is more nearly in radiative equilibrium. In the extra-tropics the dynamical activity is predominantly in the form of baroclinic eddies that transport heat polewards and upwards and the height of the tropopause is largely determined by the vertical extent of the isentropic mass flux, and so is closely related to the vertical extent of the baroclinic eddies themselves. The vertical extent of the boundary layer is influenced both by the adiabatic dynamics of the baroclinic eddies and by diabatic effects, and therefore both dynamical and radiative constraints must be satisfied (with radiative constraints being a statement of energy conservation). For some idealized constructions of the adjusted state this implies a relation between tropospheric stratification and tropopause height. However, in practice the radiative constraint need not necessarily provide a tight constraint on tropopause height. As regards dynamical constraints, various theories have been proposed ranging from baroclinic adjustment and its relatives to diffusive closures. In a vertically homogeneous, unbounded fluid the only height scale is the Charney height and the radiative constraint does not introduce any additional height scale. In that limit one would expect the tropopause height to scale as the Charney height, which leads to a baroclinic adjustment closure. In the opposite limit one might conceive a radiative constraint so tight that it would not allow the tropopause height to depart much from some radiative scale height.

We have studied the extent to which the radiative constraint and the baroclinic adjustment dynamical constraint are in fact useful in simulations with a continuously-stratified primitive equation model. It is found that there are effectively two limits depending on whether the vertical heat transport is large or small. When the vertical heat transport is large the idealized radiative constraint is a good approximation and does not allow the tropopause height to move much. In that limit, the baroclinic adjustment condition is violated. In contrast, when the vertical heat transport is small the idealized radiative constraint is only loosely satisfied, the tropopause is freer to move, and there is a tendency to produce a baroclinically adjusted stated. Finally, we will try to relate these results to the real atmosphere.