A Simple Model for the Interaction between Vertical Eddy Heat Fluxes and Static Stability

Abstract

A model designed for studying the interaction between vertical eddy beat fluxes and the vertical temperature structure in midlatitudes is presented. A temperature profile is obtained for the model by computing an equilibrium among heating rates from simplified representations of the large-scale vertical eddy heat flux, moist convection and radiation. In particular, the eddy flux profile is obtained from the quasi-geostrophic, linear baroclinic instability of a single wave, and the eddy amplitude is either specified or else obtained from a closure assumption. Tests using a variety of input conditions indicate that the most appropriate single wave to use is the most unstable mode of the instability problem. The model's temperature and Brunt-Väisälä frequency profiles am compared with observed profiles. The most unstable mode computations, in particular, reproduce well the observed profiles for both winter and summer conditions. Model runs with various eddy amplitudes show that particular aspects of the observed profiles, such as the strong decrease of Brunt- Väis?lä frequency with height in the lower troposphere, can be understood in terms of the vertical eddy flux's influence on temperature structure. Also, the eddy flux tends to alter the lapse rate more than the tropopause height as its strength varies. This particular influence is part of a negative feedback between temperature structure and the eddy flux strength: an increase in flux strength causes the lapse rate to decrease, which in turn causes the flux to weaken. The lapse rate alteration occurs primarily in the lower troposphere, indicating that the eddy flux places a significant constraint on how the vertical temperature structure in midlatitudes change when the climate changes.