The authors explore the hypothesis that nonlinear eddy interactions in quasigeostrophic turbulence can be parameterized as a stochastic excitation plus an augmented dissipation in a statistically stationary equilibrium. The focus is primarily on models sufficiently simple to be solved analytically. In particular, closed form solutions are obtained for the linear response to stochastic excitation of horizontally uniform baro-tropic and two-layer baroclinic flow. The response of the barotropic model is very simple to understand because the governing equations are mathematically normal. In contrast, the two-layer model is non-normal in the presence of vertical shear and/or vertically asymmetric dissipation and yields rather complicated results. The space-time spectra of the streamfunction and the heat fluxes derived from the two layer model are in qualitative agreement with the corresponding observed quantities at 50°N. The velocity variance predicted from the parameterization is a weaker function of the temperature gradient than indicated by observations. For strong thermal forcing, the parameterized fluxes vary inversely with the difference between a critical temperature gradient and the ambient gradient. This parameterization yields behavior suggestive of baroclinic adjustment but operates by mechanisms fundamentally different from those conventionally associated with instability theory.