Quasigeostrophic Dynamics of the Tropopause

Abstract

The dynamical properties of potential temperature anomalies on the tropopause are analyzed for quasigeo-strophic flow on an f plane. The potential vorticity is taken to he piecewise constant, with a single discontinuity at the tropopause. The tropopause potential temperature, on scales too small to feel the lower boundary, is found to be proportional to the tropopause geopotential height. The constant of proportionality is the geometric mean of the stratospheric and tropospheric lapse rates. Results from a general circulation model are found to be in agreement with this prediction. The streamfunction associated with a combination of anomalies on the lower boundary and tropopause is also derived. The solution, determined completely by the potential temperature distributions, in general has a nonzero velocity at the lower boundary. Applying the theory to the time-mean zonal-mean jets, which must have a near-zero velocity at the ground, imposes a constraint on parameters defining the jet. The dynamical properties of the system are further elucidated using the scaling argument previously applied by Charney to geostrophic turbulence. Charney's assumption of vertical homogeneity is replaced by the assumption that the dynamics is concentrated around the tropopause. In the nonlinear cascade to small scales the Rossby number is predicted to increase with horizontal wavenumber, leading to an eventual breakdown of geostrophic balance.