• Armour, K. C., C. M. Bitz, and G. H. Roe, 2013: Time-varying climate sensitivity from regional feedbacks. J. Climate, 26, 45184534, https://doi.org/10.1175/JCLI-D-12-00544.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Bowman, K. W., N. Cressie, X. Qu, and A. Hall, 2018: A hierarchical statistical framework for emergent constraints: Application to snow-albedo feedback. Geophys. Res. Lett., 45, 13 05013 059, https://doi.org/10.1029/2018GL080082.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Brient, F., 2020: Reducing uncertainties in climate projections with emergent constraints: Concepts, examples and prospects. Adv. Atmos. Sci., 37, 115, https://doi.org/10.1007/s00376-019-9140-8.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Brient, F., and T. Schneider, 2016: Constraints on climate sensitivity from space-based measurements of low-cloud reflection. J. Climate, 29, 58215835, https://doi.org/10.1175/JCLI-D-15-0897.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Brient, F., T. Schneider, Z. Tan, S. Bony, X. Qu, and A. Hall, 2016: Shallowness of tropical low clouds as a predictor of climate models’ response to warming. Climate Dyn., 47, 433449, https://doi.org/10.1007/s00382-015-2846-0.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Caldwell, P. M., C. S. Bretherton, M. D. Zelinka, S. A. Klein, B. D. Santer, and B. M. Sanderson, 2014: Statistical significance of climate sensitivity predictors obtained by data mining. Geophys. Res. Lett., 41, 18031808, https://doi.org/10.1002/2014GL059205.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Caldwell, P. M., M. D. Zelinka, and S. A. Klein, 2018: Evaluating emergent constraints on equilibrium climate sensitivity. J. Climate, 31, 39213942, https://doi.org/10.1175/JCLI-D-17-0631.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Cess, R. D., and Coauthors, 1989: Interpretation of cloud-climate feedback as produced by 14 atmospheric general circulation models. Science, 245, 513516, https://doi.org/10.1126/science.245.4917.513.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Cox, P. M., C. Huntingford, and M. S. Williamson, 2018: Emergent constraint on equilibrium climate sensitivity from global temperature variability. Nature, 553, 319322, https://doi.org/10.1038/nature25450.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Eaton, M. L., 1983: Multivariate Statistics: A Vector Space Approach. Institute of Mathematical Statistics, 512 pp.

  • Gregory, J. M., and T. Andrews, 2016: Variation in climate sensitivity and feedback parameters during the historical period. Geophys. Res. Lett., 43, 39113920, https://doi.org/10.1002/2016GL068406.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Hall, A., and X. Qu, 2006: Using the current seasonal cycle to constrain snow albedo feedback in future climate change. Geophy. Res. Lett., 33, L03502, https://doi.org/10.1029/2005GL025127.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Hall, A., P. Cox, C. Huntingford, and S. Klein, 2019: Progressing emergent constraints on future climate change. Nat. Climate Change, 9, 269278, https://doi.org/10.1038/s41558-019-0436-6.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Hoerl, A. E., 1962: Application of ridge analysis to regression problems. Chem. Eng. Prog., 58, 5459.

  • IPCC, 2013: Summary for policymakers. Climate Change 2013: The Physical Science Basis, T. F. Stocker et al., Eds., Cambridge University Press, 3–29, http://www.climatechange2013.org/images/uploads/WGI_AR5_SPM_brochure.pdf.

  • Klein, S. A., and A. Hall, 2015: Emergent constraints for cloud feedbacks. Curr. Climate Change Rep., 1, 276287, https://doi.org/10.1007/s40641-015-0027-1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Knutti, R., D. Masson, and A. Gettelman, 2013: Climate model genealogy: Generation CMIP5 and how we got there. Geophys. Res. Lett., 40, 11941199, https://doi.org/10.1002/grl.50256.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Knutti, R., M. A. A. Rugenstein, and G. C. Hegerl, 2017: Beyond equilibrium climate sensitivity. Nat. Geosci., 10, 727736, https://doi.org/10.1038/ngeo3017.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Lipat, B. R., G. Tselioudis, K. M. Grise, and L. M. Polvani, 2017: CMIP5 models’ shortwave cloud radiative response and climate sensitivity linked to the climatological Hadley cell extent. Geophys. Res. Lett., 44, 57395748, https://doi.org/10.1002/2017GL073151.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Masson, D., and R. Knutti, 2011: Climate model genealogy. Geophys. Res. Lett., 38, L08703, https://doi.org/10.1029/2011GL046864.

  • Qu, X., A. Hall, S. A. Klein, and P. M. Caldwell, 2013: On the spread of changes in marine low cloud cover in climate model simulations of the 21st century. Climate Dyn., 42, 26032626, https://doi.org/10.1007/s00382-013-1945-z.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Read, W. G., and Coauthors, 2007: Aura Microwave Limb Sounder upper tropospheric and lower stratospheric H2O and relative humidity with respect to ice validation. J. Geophys. Res., 112, D24S35, https://doi.org/10.1029/2007JD008752.

    • Search Google Scholar
    • Export Citation
  • Reynolds, R. W., N. A. Rayner, T. M. Smith, D. C. Stokes, and W. Wang, 2002: An improved in situ and satellite SST analysis for climate. J. Climate, 15, 16091625, https://doi.org/10.1175/1520-0442(2002)015<1609:AIISAS>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Rossow, W., and R. A. Schiffer, 1991: ISCCP cloud data products. Bull. Amer. Meteor. Soc., 72, 220, https://doi.org/10.1175/1520-0477(1991)072<0002:ICDP>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Sanderson, B. M., R. Knutti, and P. Caldwell, 2015: A representative democracy to reduce interdependency in a multimodel ensemble. J. Climate, 28, 51715194, https://doi.org/10.1175/JCLI-D-14-00362.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Santosa, F., and W. W. Symes, 1986: Linear inversion of band-limited reflection seismograms. SIAM J. Sci. Statist. Comput., 7, 13071330, https://doi.org/10.1137/0907087.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Shapiro, S. S., and M. B. Wilk, 1965: An analysis of variance test for normality (complete samples). Biometrika, 52, 591611, https://doi.org/10.1093/biomet/52.3-4.591.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Sherwood, S. C., S. Bony, and J.-L. Dufresne, 2014: Spread in model climate sensitivity traced to atmospheric convective mixing. Nature, 505, 3742, https://doi.org/10.1038/nature12829.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Siler, N., S. Po-Chedley, and C. S. Bretherton, 2018: Variability in modeled cloud feedback tied to differences in the climatological spatial pattern of clouds. Climate Dyn., 50, 12091220, https://doi.org/10.1007/s00382-017-3673-2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Strutz, T., 2016: Data Fitting and Uncertainty: A Practical Introduction to Weighted Least Squares and Beyond. Springer, 244 pp.

  • Su, H., J. H. Jiang, C. Zhai, T. J. Shen, J. D. Neelin, G. L. Stephens, and Y. L. Yung, 2014: Weakening and strengthening structures in the Hadley circulation change under global warming and implications for cloud response and climate sensitivity. J. Geophys. Res. Atmos., 119, 57875805, https://doi.org/10.1002/2014JD021642.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Tian, B., 2015: Spread of model climate sensitivity linked to double-intertropical convergence zone bias. Geophys. Res. Lett., 42, 41334141, https://doi.org/10.1002/2015GL064119.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Volodin, E. M., 2008: Relation between temperature sensitivity to doubled carbon dioxide and the distribution of clouds in current climate models. Izv. Atmos. Ocean. Phys., 44, 288299, https://doi.org/10.1134/S0001433808030043.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Wagman, B. M., and C. S. Jackson, 2018: A test of emergent constraints on cloud feedback and climate sensitivity using a calibrated single-model ensemble. J. Climate, 31, 75157532, https://doi.org/10.1175/JCLI-D-17-0682.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Williamson, D. B., and P. G. Sansom, 2019: How are emergent constraints quantifying uncertainty and what do they leave behind? Bull. Amer. Meteor. Soc., 100, 25712588, https://doi.org/10.1175/BAMS-D-19-0131.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Zhai, C., J. H. Jiang, and H. Su, 2015: Long-term cloud change imprinted in seasonal cloud variation: More evidence of high climate sensitivity. Geophys. Res. Lett., 42, 87298737, https://doi.org/10.1002/2015GL065911.

    • Crossref
    • Search Google Scholar
    • Export Citation
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Combining Emergent Constraints for Climate Sensitivity

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  • 1 University of Washington, Seattle, Washington
  • 2 Lawrence Livermore National Laboratory, Livermore, California
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Abstract

A method is proposed for combining information from several emergent constraints into a probabilistic estimate for a climate sensitivity proxy Y such as equilibrium climate sensitivity (ECS). The method is based on fitting a multivariate Gaussian PDF for Y and the emergent constraints using an ensemble of global climate models (GCMs); it can be viewed as a form of multiple linear regression of Y on the constraints. The method accounts for uncertainties in sampling this multidimensional PDF with a small number of models, for observational uncertainties in the constraints, and for overconfidence about the correlation of the constraints with the climate sensitivity. Its general form (Method C) accounts for correlations between the constraints. Method C becomes less robust when some constraints are too strongly related to each other; this can be mitigated using regularization approaches such as ridge regression. An illuminating special case, Method U, neglects any correlations between constraints except through their mutual relationship to the climate proxy; it is more robust to small GCM sample size and is appealingly interpretable. These methods are applied to ECS and the climate feedback parameter using a previously published set of 11 possible emergent constraints derived from climate models in the Coupled Model Intercomparison Project (CMIP). The ±2σ posterior range of ECS for Method C with no overconfidence adjustment is 4.3 ± 0.7 K. For Method U with a large overconfidence adjustment, it is 4.0 ± 1.3 K. This study adds confidence to past findings that most constraints predict higher climate sensitivity than the CMIP mean.

Corresponding author: Christopher S. Bretherton, breth@uw.edu

Abstract

A method is proposed for combining information from several emergent constraints into a probabilistic estimate for a climate sensitivity proxy Y such as equilibrium climate sensitivity (ECS). The method is based on fitting a multivariate Gaussian PDF for Y and the emergent constraints using an ensemble of global climate models (GCMs); it can be viewed as a form of multiple linear regression of Y on the constraints. The method accounts for uncertainties in sampling this multidimensional PDF with a small number of models, for observational uncertainties in the constraints, and for overconfidence about the correlation of the constraints with the climate sensitivity. Its general form (Method C) accounts for correlations between the constraints. Method C becomes less robust when some constraints are too strongly related to each other; this can be mitigated using regularization approaches such as ridge regression. An illuminating special case, Method U, neglects any correlations between constraints except through their mutual relationship to the climate proxy; it is more robust to small GCM sample size and is appealingly interpretable. These methods are applied to ECS and the climate feedback parameter using a previously published set of 11 possible emergent constraints derived from climate models in the Coupled Model Intercomparison Project (CMIP). The ±2σ posterior range of ECS for Method C with no overconfidence adjustment is 4.3 ± 0.7 K. For Method U with a large overconfidence adjustment, it is 4.0 ± 1.3 K. This study adds confidence to past findings that most constraints predict higher climate sensitivity than the CMIP mean.

Corresponding author: Christopher S. Bretherton, breth@uw.edu
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