The Role of the Nonlinearity of the Stefan-Boltzmann Law on the Structure of Radiatively Forced Temperature Change

The role of the Stefan-Boltzmann law’s nonlinearity on the structure of temperature change is investigated. It is expected to give rise to larger temperature change where the mean climate is colder. We linearize the radiative transfer scheme in a gray-radiation atmospheric General Circulation Model (GCM) with an interactive hydrological cycle. Contrary to expectations, climate change simulations with linearized radiation do not always have reduced polar amplification of surface air warming relative to the standard GCM configuration. However, the simulations with linearized radiation consistently show less warming in the upper troposphere and more warming in the lower troposphere across latitudes. The effect of the nonlinearity of the Stefan-Boltzmann law is to therefore systematically make the lapse rate feedback more stabilizing across latitudes. A hierarchy of GCM configurations (radiative equilibrium, radiative convective equilibrium, and full GCM) with linearized radiation is used to show the key role radiation plays in setting the vertical structure of temperature change, particularly in polar regions. We also show using both the idealized GCM and comprehensive estimates for Earth's climate that the combination of the spatial structure of the radiative forcing from an increase in well-mixed greenhouse gases and the Planck feedback structure, which arises from the Stefan-Boltzmann nonlinearity, produce a tropically-amplified warming.