A refined model for the Earth’s global energy balance

A commonly-used model of the global radiative budget assumes that the radiative response to forcing, R, is proportional to global surface air temperature T, R=λT\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$R=\lambda T$$\end{document}. Previous studies have highlighted two unresolved issues with this model: first, the feedback parameter λ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\lambda$$\end{document} depends on the forcing agent; second, λ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\lambda$$\end{document} varies with time. Here, we investigate the factors controlling R in two atmosphere–slab ocean climate models subjected to a wide range of abrupt climate forcings. It is found that R scales not only with T, but also with the large-scale tropospheric stability S (defined here as the estimated inversion strength area-averaged over ocean regions equatorward of 50∘\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$^\circ {}$$\end{document}). Positive S promotes negative R, mainly through shortwave cloud and lapse-rate changes. A refined model of the global energy balance is proposed that accounts for both temperature and stability effects. This refined model quantitatively explains (1) the dependence of climate feedbacks on forcing agent (or equivalently, differences in forcing efficacy), and (2) the time evolution of feedbacks in coupled climate model experiments. Furthermore, a similar relationship between R and S is found in observations compared with models, lending confidence that the refined energy balance model is applicable to the real world.