On the Diffusivity of Moist Static Energy and Implications for the Polar Amplification Response to Climate Warming

Abstract

Energy balance models (EBMs) have been widely used in a range of climate problems, but the assumption of constant diffusivity in the parameterization of the moist static energy (MSE) flux can hardly be justified. We demonstrate in this study that the diffusive MSE flux can be derived from the basic energy balance equation with a few tolerable assumptions. The estimated diffusivity is both spatially and seasonally dependent, and its midlatitude average is then tested against several scaling theories for the midlatitude eddy diffusivity. The result supports the diffusivity theory of Held and Larichev modified for the moist atmosphere, affording a dynamics-based parameterization of MSE diffusivity. The implementation of the parameterization in an EBM leads to an interactive MSE diffusivity that accounts for the midlatitude eddy response to climate forcing perturbations. Under a uniform radiative forcing, the EBM with a diffusivity so parameterized produces a weakening of the midlatitude diffusivity and a modestly polar-amplified surface temperature response as an inevitable outcome under the dual constraints of the nonlinear Clausius–Clapeyron relation and the temperature gradient-dependent diffusivity, even in the absence of any poleward-amplifying radiative feedbacks. As the consequence of more isothermal temperature and reduced diffusivity, the variance of the midlatitude surface temperature also decreases with warming.