release, as discussed by Gierasch and Conrath (1985). Beyond any uncertainty in the convective heat flux, the constant coefficient scaling the eddy diffusion coefficient is only loosely constrained by observations. For our baseline model we use a coefficient of 1/3 based on previous modeling studies of the Jovian atmosphere (D. M. Hunten 1996, private communication), and consider the sensitivity of our model results to its value in a subsequent section.

For freely convecting atmospheres, the mixing length is typically assumed to be the pressure scale height. However, in stable atmospheric regions, the mixing length will be diminished. We account for this reduction by scaling the mixing length to the local stability: $$\begin{aligned}
\label{L_equals}
L = H \max( \Lambda, \Gamma/\Gamma_{\rm adiab})\end{aligned}$$ where $\Gamma$ and $\Gamma_{\rm adiab}$ are the local and dry adiabatic lapse rates, respectively, and $\Lambda$ is the minimum scaling applied to $L$ (we assume a value of 0.1). In the general case, convective heat fluxes are diminished in radiative regions; hence, we also assume an eddy diffusion coefficient no less than a prescribed minimum value ($K_{\rm min} = 
10^5$ cm$^2$ s$^{-1}$ in our baseline model), which represents residual turbulence due to breaking buoyancy waves (Lindzen 1981) and such. A 