Preprints
https://doi.org/10.5194/npg-2022-2
https://doi.org/10.5194/npg-2022-2
 
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19 Jan 2022
19 Jan 2022
Status: a revised version of this preprint was accepted for the journal NPG and is expected to appear here in due course.

Climate Bifurcations in a Schwarzschild Equation Model of the Arctic Atmosphere

Kolja L. Kypke1, William F. Langford2, Gregory M. Lewis3, and Allan R. Willms2 Kolja L. Kypke et al.
  • 1Niels Bohr Institute, University of Copenhagen, Copenhagen, Denmark
  • 2Dept. of Mathematics & Statistics, University of Guelph, Guelph, Canada
  • 3Faculty of Science, Ontario Tech University, Oshawa, Canada

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.

Kolja L. Kypke et al.

Status: closed

Comment types: AC – author | RC – referee | CC – community | EC – editor | CEC – chief editor | : Report abuse
  • RC1: 'Comment on npg-2022-2', Anonymous Referee #1, 17 Feb 2022
  • RC2: 'Comment on npg-2022-2', Marek Stastna, 31 Mar 2022
  • AC1: 'Comment on npg-2022-2', Allan Willms, 20 Apr 2022

Status: closed

Comment types: AC – author | RC – referee | CC – community | EC – editor | CEC – chief editor | : Report abuse
  • RC1: 'Comment on npg-2022-2', Anonymous Referee #1, 17 Feb 2022
  • RC2: 'Comment on npg-2022-2', Marek Stastna, 31 Mar 2022
  • AC1: 'Comment on npg-2022-2', Allan Willms, 20 Apr 2022

Kolja L. Kypke et al.

Kolja L. Kypke et al.

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Climate change is causing rapid temperature increases in the polar regions. A fundamental question is whether these temperature increases are reversible. If we control carbon dioxide emissions will the temperatures revert, or will we have passed a tipping point beyond which return to the present state is impossible? We address this question with a column model of the Arctic atmosphere based on mathematical representations of the primary physical features, including the Schwarzschild two-stream equations for the long wave radiation, the Clausius-Clapeyron equation for water vapour concentrations, atmosphere absorption characteristics dependent on carbon dioxide and water vapour concentration levels, and nonlinear albedo response to surface temperature. We analyzed solutions of our model under four representative carbon pathways (RCPs) extending into the future. Under the strongest mitigation pathway (which represents far swifter carbon emission reductions than presently seen), the Arctic shows a mild increase in temperature that is reversible. Under the highest carbon pathway (which represents a continuation of the status quo with regard to emissions), the Arctic climate undergoes an irreversible bifurcation to a warm steady state, corresponding to annually ice-free conditions, prior to the end of this century. Under the two intermediate pathways, temperatures increase substantially and the system enters a state of bi-stability where an external perturbation could possible cause an irreversible switch to warm, ice-free state.
Short summary
Climate change is causing rapid temperature increases in the polar regions. A fundamental question is whether these temperature increases are reversible. If we control carbon dioxide emissions will the temperatures revert, or will we have passed a tipping point beyond which return to the present state is impossible? Our mathematical model of the Arctic climate indicates that under present emissions the Arctic climate will change irreversibly to a warm climate before the end of the century.