Increasing atmospheric carbon dioxide concentration is expected to cause substantial changes in climate1. Recent model studies suggest that the equilibrium warming for a CO2 doubling (Δ T2×) is about 3–4°C2–4. Observational data show that the globe has warmed by about 0.5°C over the past 100 years5,6. Are these two results compatible? To answer this question due account must be taken of oceanic thermal inertia effects, which can significantly slow the response of the climate system to external forcing. The main controlling parameters are the effective diffusivity of the ocean below the upper mixed layer (κ) and the climate sensitivity (defined by Δ T2×). Previous analyses of this problem have considered only limited ranges of these parameters. Here we present a more general analysis of two cases, forcing by a step function change in CO2 concentration and by a steady CO2 increase. The former case may be characterized by a response time which we show is strongly dependent on both κ and Δ T2×. In the latter case the damped response means that, at any given time, the climate system may be quite far removed from its equilibrium with the prevailing CO2 level. In earlier work this equilibrium has been expressed as a lag time, but we show this to be misleading because of the sensitivity of the lag to the history of past CO2 variations. Since both the lag and the degree of disequilibrium are strongly dependent on κ and Δ T2×, and because of uncertainties in the pre-industrial CO2 level, the observed global warming over the past 100 years can be shown to be compatible with a wide range of CO2-doubling temperature changes.
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Carbon Dioxide Assessment Committee, Board on Atmospheric Sciences and Climate, National Research Council Changing Climate (National Academy Press, Washington, DC, 1983).
Washington, W. M. & Meehl, G. A. J. geophys. Res. 89, 9475–9503 (1984).
Hansen, J. E. et al. Geophys. Monogr. 29, Maurice Ewing Vol. 5, 130–163 (1984).
Schlesinger, M. E., Gates, W. L. & Han, Y.-J. in Coupled Atmospheric-Ocean Models (ed. Nihoul, J. C. J.) (Elsevier, Amsterdam, in the press).
Jones, P. D., Wigley, T. M. L. & Kelly, P. M. Mon. Weath. Rev. 110, 59–70 (1982).
Folland, C. K., Parker, D. E. & Kates, F. E. Nature 310, 670–673 (1984).
Hoffert, M. I., Callegari, A. J. & Hsieh, C.-T. J. geophys. Res. 85, 6667–6679 (1980).
Cess, R. D. & Goldenberg, S. D. J. geophys. Res. 86, 498–502 (1981).
Siegenthaler, U. & Oeschger, H. Ann. Glaciol. 5, 153–159 (1984).
Dickinson, R. E. J. atmos. Sci. 38, 2112–2120 (1981).
Augustsson, T. & Ramanathan, V. J. atmos. Sci. 34, 448–451 (1977).
Manabe, S. Adv. Geophys. 25, 39–82 (1983).
Abramowitz, M. & Stegun, I. A. (eds) Handbook of Mathematical Functions (Dover, New York, 1965).
Report of the WMO(CAS) Meeting of Experts on the CO2 Concentrations from Pre-Industrial Times to IGY, WCP-55 (WMO, Geneva, 1983).
Keeling, C. D. in Proc. Carbon Dioxide Res. Conf. Carbon Dioxide, Science and Consensus, CONF-820970, II. 3–II. 62 (US Department of Energy, Washington, DC, 1983).
Weller, G. et al. in Changing Climate, 292–382 (National Academy Press, Washington, DC, 1983).
Lacis, A. et al. Geophys. Res. Lett. 8, 1035–1038 (1981).
Wigley, T. M. L. Climate Monitor 13, 133–148 (1985).
Neftal, A. Nature 315, 45–47 (1985).
Madden, R. A. & Ramanathan, V. Science 209, 763–768 (1980).
Wigley, T. M. L. & Jones, P. D. Nature 292, 205–208 (1981).
Broecker, W. S., Peng, T. H. & Engh, R. Radiocarbon 22, 565–598 (1980).
Bryan, K., Komro, F. G. & Rooth, C. Geophys. Monogr. 29, Maurice Ewing Vol. 5, 29–38 (1984).
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Wigley, T., Schlesinger, M. Analytical solution for the effect of increasing CO2 on global mean temperature. Nature 315, 649–652 (1985). https://doi.org/10.1038/315649a0
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