Models of tropopause height and thermocline depth

We discuss the role of baroclinic eddies in setting the internal deformation radius, L_r=NH/f, of a rotating (f-plane), differentially-heated fluid. We deduce under stated assumptions, and test against numerical and laboratory experiments, that the deformation radius set up by a field of baroclinic eddies fluxing buoyancy vertically at a rate B, is given by:

NH/f=c (L L_rot)^1/2

where H and L are the vertical and horizontal scales of the baroclinic zone, L_rot=(B/f³)^1/2 is the scale that controls rotating convection, f is the Coriolis parameter and c is a constant of order unity.

The ideas are then applied to understand, and derive simple formulae for the height of the tropopause and the statification of the troposphere of the atmosphere and the depth and stratification of the thermocline of the ocean. In the atmosphere we suppose that baroclinic eddies flux buoyancy vertically from the surface at a rate required to offset radiative loss in the upper troposphere. In the ocean we assume that the pumping down of buoyancy from surface Ekman layers is balanced, in an integral sense, by the vertical flux of buoyancy due to eddies. These statements, when combined with the above formula for the deformation radius, allow us to solve for the H and N of the respective fluid. The resulting expressions yield plausible estimates in both atmospheric and oceanic applications.

Finally, we discuss the implications of our results.