Abstract
Possible climate change caused by an increase ingreenhouse gas concentrations, despite having been asubject of intensive study in recent years, is stillvery uncertain. Uncertainties in projections ofdifferent climate variables are usually described onlyby the ranges of possible values. For assessing thepossible impact of climate change, it would be moreuseful to have probability distributions for thesevariables. Obtaining such distributions is usuallyvery computationally expensive and requires knowledgeof probability distributions for characteristics ofthe climate system that affect climate projections. A fewstudies of this kind have been carried out with energybalance/upwelling diffusion models. Here wedemonstrate a methodology for performing a similarstudy with a 2 dimensional (zonally averaged) climatemodel that reproduces the behavior of coupledatmosphere/ocean general circulation models morerealistically than energy balance models. Thismethodology involves application of the DeterministicEquivalent Modeling Method to derive functionalapproximations of the model's probabilistic response.Monte Carlo analysis is then performed on theapproximations. An application of the methodology isdemonstrated by deriving the uncertainty in surfaceair temperature change and sea level rise due tothermal expansion of the ocean that result fromuncertainties in climate sensitivity and the rate ofheat uptake by the deep ocean for a prescribedincrease in atmospheric CO2 concentration. Wealso demonstrate propagation of correlateduncertainties through different models, by presentingresults that include uncertainty in projected carbonemissions.
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References
Casman, E. A., Morgan, M. G., and Dowlatabadi, H.: 1999, ‘Mixed Levels of Uncertainty in Complex Policy Models’, Risk Anal. 19, 33–42.
Clark, E.: 1961, ‘Importance Sampling in Monte Carlo Analysis’, Operations Res. 9, 603–620.
Clemen, R. T. and Reilly, T.: 1999, ‘Correlations and Copulas for Decision and Risk Analysis’, Manage. Sci. 45, 208–224.
Cubasch, U., Hasselmann, K., Hock, H., Maier-Reimer, E., Mikolajewicz, U., Santer, B. D., and Sausen R.: 1992, ‘Time-Dependent Greenhouse Warming Computations with a Coupled Ocean-Atmosphere Model’, Clim. Dyn. 8, 55–69.
Cubasch, U., Santer, B. D., Hellbach, A., Hegerl, G., Hock, H., Maier-Reimer, E., Mikolajewicz, U., Stossel, A., and Voss, R.: 1994, ‘Monte Carlo Climate Change Forecasts with a Global Coupled Ocean-Atmosphere Model’, Clim. Dyn. 10, 1–19.
Dalkey, N. C.: 1967, ‘DELPHI’, The RAND Corporation, P-30704, Santa Monica, CA.
DeWolde, J. R., Huybrechts, P., Oerlemans, J., and Van deWal, R. S.W.: 1997, ‘Projection of Global Mean Sea Level Rise Calculated with a 2D Energy-Balance Climate Model and Dynamic Ice Sheet Models’, Tellus 49A, 486–502.
Downing, D. J., Gardner, R. H., and Hoffman, F. O.: 1985, ‘Response Surface Methodologies for Uncertainty Analysis in Assessment Models’, Technometrics 27, 151–163.
Forest C. E., Allen, M. R., Stone, P. H., and Sokolov, A. P.: 2000, ‘Constraining Uncertainties in Climate Models Using Climate Change Detection Techniques’, Geophys. Res. Lett., in press.
Genest, C. and Zidek, J. V.: 1986, ‘Combining Probability Distributions: A Critique and Annotated Bibliography’, Stat. Sci. 1, 114–148.
Hansen, J., Lacis, A., Rind, D., Russel, G., Stone, P., Fung, I., Ruedy, R., and Lerner, J.: 1984, ‘Climate Sensitivity: Analysis of Feedback Mechanisms’, in Hansen, J. and Takahashi, T. (eds.), Climate Processes and Climate Sensitivity, Geophysical Monograph Series 29, American Geophysical Union, pp. 130-163.
Hansen, J., Lacis, A., Ruedy, R., Sato, M., and Wilson, H.: 1993, ‘How Sensitive is the World's Climate?’, Natl. Geog. Res. Explor. 9, 142–158.
Hansen, J., Russel, G., Lacis, A., Fung, I., Rind, D., and Stone, P.: 1985, ‘Climate Response Time: Dependence on Climate Sensitivity and Ocean Mixing’, Science 229, 857–859.
Hansen, J., Russel, G., Rind, D., Stone, P., Lacis, A., Lebedeff, S., Ruedy, R., and Travis, L.: 1983, ‘Efficient Three Dimensional Global Models for Climate Studies: Models I and II’, Mon. Wea. Rev. 111, 609–662.
Henrion, M. and Fischhoff, B.: 1986, ‘Assessing Uncertainty in Physical Constants’, Amer. J. Phys.
Holian, G. L.: 1998, ‘Uncertainty in Atmospheric CO2 Concentrations from a Parametric Uncertainty Analysis of a Global Ocean Carbon Cycle Model’, Report No. 39, Joint Program on the Science and Policy of Global Change, MIT, Cambridge, MA.
Intergovernmental Panel on Climate Change: 1996, Climate Change 1995-The Science of Climate Change, Contribution of Working Group I to the Second Assessment Report of the Intergovernmental Panel on Climate Change, Houghton, J. T., Meira Filho, L. G., Callander, B. A., Harris, N., Kattenberg, A., and Maskell, K. (eds.), Cambridge University Press, Cambridge and New York.
Jacoby, H. D., Eckaus, R. S., Ellerman, A. D., Prinn, R. G., Reiner, D. M., and Yang, Z.: 1997, ‘CO2 Emissions Limits: Economic Adjustments and Distribution of Burdens’, Energy J. 18 (3), 31–58.
Keen, A. B. and Murphy, J. M.: 1997, ‘Influence of Natural Variability and the Cold Start Problem on the Simulated Transient Response to Increasing CO2’, Clim. Dyn. 13, 847–864.
Keith, D. W.: 1996, ‘When Is It Appropriate to Combine Expert Judgements?’, Clim. Change 33, 139–143.
Manne, A. S. and Richels, R. G.: 1992, Buying Greenhouse Insurance: The Economic Costs of Carbon Dioxide Emission Limits, MIT Press, Cambridge, MA.
McKay, M. D., Conover, W. J., and Beckman, R. J.: 1979, ‘A Comparison of Three Methods for Selecting Values of Input Variables in the Analysis of Output from a Computer Code’, Technometrics 21, 239–245.
Morgan, M. G.: 1997, ‘Quantitative Expert Subjective Judgement: Does It Have a Role in Future IPCC Assessments?’, in Hassol, S. J. and Katzenberger, J. (eds.), Elements of Change 1996, Aspen Global Change Institute, Aspen, CO.
Morgan, M. G. and Keith, D. W.: 1995, ‘Subjective Judgements by Climate Experts’, Environ. Sci. Technol. 29 (10), 468A–476A.
Moss, R. H. and Schneider, S. H.: 1997, ‘Characterizing and Communicating Scientific Uncertainty: Building on the IPCC Second Assessment Report’, in Hassol, S. J. and Katzenberger, J. (eds.), Elements of Change 1996, Aspen Global Change Institute, Aspen, CO.
Murphy, J. M.: 1995, ‘Transient Response of the Hadley Center Coupled Ocean-Atmosphere Model to Increasing Carbon Dioxide III: Analysis of Global-Mean Responses Using Simple Models’, J. Climate 8, 496–514.
Murphy, J. M. and Mitchell, J. F. B.: 1995, ‘Transient Response of the Hadley Centre Coupled Ocean-Atmosphere Model to Increasing Carbon Dioxide II: Spatial and Temporal Structure of Response’, J. Climate 8, 57–80.
Nordhaus, W. D.: 1994, Managing the Global Commons, MIT Press, Cambridge, MA.
Nordhaus, W. D. and Popp, D.: 1997, ‘What Is the Value of Scientific Knowledge? An Application to Global Warming Using the PRICE Model’, Energy J. 18, 1–45.
Paté-Cornell, E.: 1996, ‘Uncertainties in Global Climate Change Estimates’, Clim. Change 33, 145–149.
Paté-Cornell, E.: 1997, ‘Different Levels of Treatment of Uncertainty in Risk Analysis and Aggregation of Expert Opinions’, in Hassol, S. J. and Katzenberger, J. (eds.), Elements of Change 1996, Aspen Global Change Institute, Aspen, CO.
Press, W. H., Teukolsky, S. A., Vetterling, W. T., and Flannery, B. P.: 1992, Numerical Recipes in C, Cambridge University Press, New York.
Prinn, R., Jacoby, H., Sokolov, A., Wang, C., Xiao, X., Yang, Z., Eckhaus, R., Stone, P., Ellerman, D., Melillo, J., Fitzmaurice, J., Kicklighter, D., Holian, G., and Liu, Y.: 1999, ‘Integrated Global System Model for Climate Policy Assessment: Feedbacks and Sensitivity Studies’, Clim. Change 41, 469–546.
Raper, S. C. B. and Cubasch, U.: 1996, ‘Emulation of the Results from a Coupled General Circulation Model Using a Simple Climate Model’, Geophys. Res. Lett. 23, 1107–1110.
Senior, C. A. and Mitchell, J. F. B.: 1993, ‘Carbon Dioxide and Climate: The Impact of Cloud Parameterization’, J. Climate 6, 393–418.
Sokolov, A. P. and Stone, P. H.: 1998, ‘A Flexible ClimateModel for Use in Integrated Assessments’, Clim. Dyn. 14, 291–303.
Sokolov, A., Wang, C., Holian, G., Stone, P., and Prinn, R.: 1998, ‘Uncertainty in the Oceanic Heat and Carbon Uptake and its Impact on Climate Projections’, Geophys. Res. Lett. 25, 3603–3606.
Stone, P. H. and Yao, M.-S.: 1987, ‘Development of a Two-Dimensional Zonally Averaged Statistical-Dynamical Model. II: The Role of Eddy Momentum Fluxes in the General Circulation and Their Parameterization’, J. Atmos. Sci. 44, 3769–3536.
Stone, P. H. and Yao, M.-S.: 1990, ‘Development of a Two-Dimensional Zonally Averaged Statistical-Dynamical Model. III: The Parameterization of the Eddy Fluxes of Heat and Moisture’, J. Climate 3, 726–740.
Tatang, M. A., Pan, W., Prinn, R. G., and McRae, G. J.: 1997, ‘An Efficient Method for Parametric Uncertainty Analysis of Numerical Geophysical Models’, J. Geophys. Res. 102 (D18), 21,925–21,932.
Titus, J.: 1997, ‘Probabilities in Sea Level Rise Projections’, in Hassol, S. J. and Katzenberger, J. (eds.), Elements of Change 1996, Aspen Global Change Institute, Aspen, CO.
Titus, J. G. and Narayanan, V. K.: 1995, ‘The Probability of Sea Level Rise’, Environmental Protection Agency, Washington, D.C.
Titus, J. G. and Narayanan, V. K.: 1996, ‘The Risk of Sea level Rise’, Clim. Change 33, 151–212.
Wang, C., Prinn, R. G., and Sokolov, A. P.: 1998, ‘A Global Interactive Chemistry and Climate Model: Formulation and Testing’, J. Geophys. Res. 103 (D3), 3399–3418.
Webster, M. D.: 1997, ‘Exploring the Uncertainty in Future Carbon Emissions’, Report No. 30, Joint Program on the Science and Policy of Global Change, MIT, Cambridge, MA.
Webster, M., Tatang, M. A., and McRae, G. J.: 1996, ‘Application of the Probabilistic Collocation Method for an Uncertainty Analysis of a Simple Ocean Model’, Report No. 4, Joint Program on the Science and Policy of Global Change, MIT, Cambridge, MA.
Wigley, T. M. L. and Raper, S. C. B.: 1993, ‘Future Changes in Global Mean Temperature and Sea Level’, in Warrick, R. A., Barrow, E. M., and Wigley, T. M. L. (eds.), Climate and Sea Level Change: Observations, Projections, and Implications, Cambridge University Press, Cambridge, U.K.
Winkler, R. L.: 1986, ‘Expert Resolution’, Manage. Sci. 32, 298–303.
Yang, Z., Eckaus, R. S., Ellerman, A. D., and Jacoby, H. D.: 1996, ‘The MIT Emissions Prediction and Policy Analysis (EPPA) Model’, Report No. 6, Joint Program on the Science and Policy of Global Change, MIT, Cambridge, MA.
Yao, M.-S. and Stone, P. H.: 1987, ‘Development of a Two-Dimensional Zonally Averaged Statistical-Dynamical Model. I: The Parameterization of Moist Convection and its Role in the General Circulation’, J. Atmos. Sci. 44, 65–82.
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Webster, M.D., Sokolov, A.P. A Methodology for Quantifying Uncertainty in Climate Projections. Climatic Change 46, 417–446 (2000). https://doi.org/10.1023/A:1005685317358
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DOI: https://doi.org/10.1023/A:1005685317358