Polar Boundary Conditions in Zonally Averaged Global Climate Models

Abstract

We consider global climate models based on zonally averaged balance relations. Inherent boundary conditions require the meridional fluxes of non-negative properties (temperature, humidity, energy, etc.), as well as the flux of zonal momentum, to vanish at both poles. On the other hand, the meridional divergence of these fluxes does not vanish at either pole. An important exception from this general non-zero polar divergence condition of meridional fluxes is the transport of zonal momentum; the meridional divergence of zonal momentum flux vanishes at the pole because there is neither zonal surface stress nor horizontal wind. These conditions are derived from the balance equations for energy and momentum. Furthermore, they are tested with observed flux data for specific humidity and zonal wind. The closure problem in such models is often overcome by a diffusive parameterization of the fluxes in terms of meridional gradients. It is shown that, due to the above conditions, the exchange coefficient for the energy transport may not vanish at the poles. This has implications for semi-empirical models designed to test climate's stability and transitivity.