Exploring the Relations between the Strength of Global Entropy Cycle and Equator-to-Pole Temperature Gradient in an Idealized General Circulation Model

Understanding the temperature difference between the tropics and high latitudes requires knowledge of the poleward eddy heat transport. Some studies on turbulent diffusivity theory for the poleward heat flux have derived an expression for diffusivity D in terms of kinetic energy dissipation ε and planetary vorticity gradient β, D~ε^3/5β^-4/5 (e.g., Held and Larichev, 1996). Estimating ε from the global entropy budget, Barry et al. (2002) tested the diffusivity scaling with a comprehensive global atmospheric model. Despite the level of model complexity, they showed their theory accurately predicts the simulated eddy heat flux over a range of parameters. We have found it also applies to an idealized dry primitive equation model in the Held-Suarez configuration (Held and Suarez, 1994) when rotation rate is increased or meridional temperature gradient at radiative equilibrium is decreased, that is, for those cases where the eddy scale is comparable to or smaller than in the control simulation. This seems to indicate that the strength of global entropy cycle can play an important role in theories for equator-to-pole temperature gradient, deemphasizing the role played by the available potential energy. Here we discuss these relations in the context of idealized dry GCM. With the Held-Suarez model’s diabatic heating formulated as Newtonian relaxation, we can easily calculate the possible range of global entropy destruction subject to different constraints on the equilibrated thermal structure. To the extent that entropy production is mostly caused by kinetic energy dissipation, the global entropy destruction provides a good approximation of ε. It can then be compared to the numerical simulations to study the dependence of ε on external parameters. Based on this analysis, an argument is presented for the joint determination of global entropy cycle strength and equator-to-pole temperature gradient combining thermodynamical and dynamical constraints. We discuss how this approach to eddy closure development highlights the importance of predicting the thermal stratification.