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Simple Estimates of Polar Amplification in Moist Diffusive Energy Balance Models

Diffusive energy balance models (EBMs) that use moist static energy, rather than temperature, as the thermodynamic variable to determine the energy transport provide an idealized framework to understand the pattern of radiatively forced surface warming. These models have a polar amplified warming pattern that is quantitatively similar to general circulation model simulations. Even without surface albedo changes or other spatially varying feedbacks, they simulate polar amplification that results from increased poleward energy transport with warming. Here, two estimates for polar amplification are presented that do not require numerical solution of the EBM governing equation. They are evaluated relative to the results of numerical moist EBM solutions. One estimate considers only changes in a moist thermodynamic quantity (assuming that the increase in energy transport results in a spatially uniform change in moist static energy in the warmed climate) and has more polar amplification than the EBM solution. The other estimate uses a new solution of a truncated form of the moist EBM equation, which allows for a temperature change that is consistent with both the dry and latent energy transport changes, as well as radiative changes. The truncated EBM solution provides an estimate for polar amplification that is nearly identical to that of the numerical EBM solution and only depends on the EBM parameters and climatology of temperature. This solution sheds light on the dependence of polar amplification on the climatological temperature distribution and offers an estimate of the residual polar warming in solar radiation management geoengineered climates.