Climate Bifurcations in a Schwarzschild Equation Model of the Arctic Atmosphere

Abstract. A column model of the Arctic atmosphere-ocean system is developed including the nonlinear responses of surface albedo and water vapor to temperature. The atmosphere is treated as a gray gas and the flux of longwave radiation is governed by the two-stream Schwarzschild equations. Representative carbon pathways (RCPs) are used to model carbon dioxide concentrations into the future. The resulting nine-dimensional two-point boundary value problem is solved under various RCPs and the solutions analyzed. The model predicts that under the highest carbon pathway, the Arctic climate will undergo an irreversible bifurcation to a warm steady state, which would correspond to an annually ice-free situation. Under the lowest carbon pathway, corresponding to very aggressive carbon emission reductions, the model exhibits only a mild increase in Arctic temperatures. Under the two moderate carbon pathways, temperatures increase more substantially, and the system enters a region of bistability where external perturbations could possibly cause an irreversible switch to a warm, ice-free state.