Relationships between Heat Fluxes and Temperature Gradients in a Global Spectral Model

Abstract

Two conceptual paradigms have been used in the past to interpret the observed strength and structure of eddy heat fluxes in the atmosphere. One is the idea of ?adjustment,? whereby the eddies respond efficiently to changes in forcing to maintain the mean isentropic slope. The other is a ?diffusive? paradigm, which assumes that eddy fluxes can be parameterized in terms of the mean flow. The relative merits of these two approaches are examined here with the aid of a two-level primitive equations model on a sphere. In most experiments the model is forced by a completely specified heating field. This eliminates the negative feedback between temperature and forcing that is present in the atmosphere and in idealized formulations such as Newtonian cooling. Thus, any intrinsic relationship that may exist between temperature gradients and the dynamical fluxes can emerge freely. As the specified forcing strength is varied, the net dynamical fluxes vary proportionately in order to maintain an equilibrium climate. There are no constraints, however, on the equilibrium level selected by the mean temperature gradients, beyond those imposed by their dynamical relationship to the fluxes. Our experiments show that, while the dynamical fluxes adjust to the forcing quickly and efficiently to balance the heat budget, the mean temperature gradients can continue to slowly evolve. The mean meridional and vertical temperature gradients can combine in different ways to support the same eddy fluxes. For fixed forcing, the temperature gradients eventually settle to a single climate state (i.e., independent of initial conditions), but the evolution is very slow. The model exhibits elements of both baroclinic adjustment and diffusive behavior. Adjustment operates in the sense that isentropic slopes are relatively independent of the forcing and depend only weakly on the fluxes. Diffusion works in the sense that apparently unique flux-temperature gradient relationships eventually assert themselves, however slowly. Eddy heat flux sensitivity to mean temperature gradients is in broad agreement with recent parameterization theory, given the constraints inherent in the two-level model and the structure of the forcing used in the experiments.