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Exploring multi-model atmospheric GCM ensembles with ANOVA

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Abstract

Analysis of variance (ANOVA) is a powerful statistical technique for making inferences about experiments that are influenced by multiple factors. Whilst common in many other scientific fields, its use within the climate community has been limited to date. Here we review the basis for ANOVA and how, in particular, it can be applied to partition the variance in a multi-model ensemble of Atmospheric General Circulation Model simulations. We examine an ensemble of four AGCMs forced with observed twentieth century sea surface temperatures (SST). We show that the dominant contributions to the total variance of seasonal mean sea level pressure arise from between-model differences (the bias term) and internal noise (the noise term). However, which term is most important varies from region to region. Of particular interest is the interaction term, which describes differences between the models in their responses to common SST forcing. The interaction term is found to be largest over the Indian Ocean (in all seasons), and over the subtropical Northwest Pacific in boreal summer. The differences between the model responses in these regions suggest differences in their simulation of atmospheric teleconnections, with potentially important implications, e.g. for seasonal predictions of the South and East Asian Monsoons. Examination of these differences may lead to an understanding of the reasons why models respond differently to common forcing, and ultimately to improvements in the performance of climate models.

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Notes

  1. The analysis can still be performed if the models have a different number of ensemble members, K, but the statistical tests will no longer be exact. See von Storch and Zwiers (2002, p. 178).

  2. It is worth noting at this point, that when t = 2 and m = 1 the ANOVA procedure will reduce exactly to a standard Student's t test between two samples, each of size k. See Scheffe (1959) Appendix 4.

  3. For this test to be accurate, ε tmk must be a normally and independently distributed random variable. For seasonal-mean data, normality is a realistic assumption that follows from the central limit theorem. Additional checks using the estimator of ε tmk , given in Eq. 7 confirmed that ε tmk is independently distributed.

  4. Is is also entirely possible to apply ANOVA to other spatial decompositions—e.g. using expansion coefficients of spatial modes—e.g. empirical orthogonal functions (EOFs), etc.

  5. Other, less common methods also exist that do not rely on the assumption of Gaussian statistics (see for example Anderson and Stern 1996).

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Acknowledgments

This work was supported by European Union Framework 6 ENSEMBLES project (contract number GOCE-CT-2003-505539), DYNAMITE project (contract number 00393 (GOCE)-DYNAMITE), European Union Framework 5 PREDICATE project (contract number EVK2-1999-0020) and by the National Centre for Atmospheric Science (NCAS). R. T. Sutton is supported by research fellowship from the Royal Society. We are grateful to Holger Pohlmann (MPI) for the Echam4 experimental data, Mark Rodwell (ECMWF) for the HadAM3 experimental data, Martin Stendel (DMI) for the Echam5 experimental data, Laurent Terray (CERFACS) for the Arpege experimental data, and to our colleagues at The Met Office Hadley Centre for allowing the use of HadSLP2 and HadISST. We would also like to thank two anonymous reviewers for their suggested improvements to this paper.

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  1. Walker Institute, Department of Meteorology, University of Reading, Reading, RG6 6BB, UK

    D. L. R. Hodson & R. T. Sutton

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  1. D. L. R. Hodson
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  2. R. T. Sutton
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Correspondence to D. L. R. Hodson.

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Hodson, D., Sutton, R. Exploring multi-model atmospheric GCM ensembles with ANOVA. Clim Dyn 31, 973–986 (2008). https://doi.org/10.1007/s00382-008-0372-z

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