The Role of Diffusivity Changes on the Pattern of Warming in Energy Balance Models

Abstract

Abstract Atmospheric macroturbulence transports energy down the equator-to-pole gradient. This is represented by diffusion in energy balance models (EBMs), and EBMs have proven valuable for understanding and quantifying the pattern of surface temperature change. They typically assume climate-state-independent diffusivity, chosen to well represent the current climate, and find that this is sufficient to emulate warming response in general circulation models (GCMs). Meanwhile, model diagnoses of GCM simulations have shown that the diffusivity changes with climate. There is also ongoing development for diffusivity theories based on atmospheric dynamics. Here, we examine the role that changes in diffusivity play in the large-scale equator-to-pole contrast in surface warming in EBMs, building on previous analytic EBM theories for polar-amplified warming. New analytic theories for two formulations of climate-state-dependent diffusivity capture the results of numerical EBM solutions. For reasonable choices of parameter values, the success of the new analytic theories reveals why the change of diffusivity is limited in response to radiative forcing and does not eliminate polar-amplified warming.