| Summary: | The seasonal mean of a climate variable is considered to consist of: (a)~slow-external; (b)~slow-internal; and (c)~intraseasonal components. Using an Analysis of Variance-based method, the interannual variability of the seasonal mean from an ensemble of coupled atmosphere-ocean general circulation model realisations is separable into these components. Here, we propose a method for analysing the covariability of these components between pairs of climate variables. In particular, the method allows for an estimate of the covariability of the projected time series of the modes of variability of one climate variable with the time series of another. To illustrate this, the relationship between time series of the modes of variability of 500\,hPa geopotential height and sea surface temperature is examined for an ensemble of coupled general circulation model realisations. The method is applicable to other atmospheric climate variables and datasets. References C. S. Frederiksen and X. Zheng. Coherent structures of interannual variability of the atmospheric circulation: the role of intraseasonal variability. Frontiers in Turbulence and Coherent Structures, World Scientific Lecture Notes in Complex Systems, Vol. 6, Eds Jim Denier and Jorgen Frederiksen, World Scientific Publications, 87--120, 2007. C. E. Leith. The standard error of time-average estimates of climatic means. J. Appl. Meteor., 12:1066--1069, 1973. doi:10.1175/1520-0450(1973)012<1066:TSEOTA>2.0.CO;2 X. Zheng and C. S. Frederiksen. Variability of seasonal-mean fields arising from intraseasonal variability. Part 1, methodology. Climate Dynamics, 23:177--191, 2004. doi:10.1007/s00382-004-0428-7 X. Zheng and C. S. Frederiksen. Validating interannual variability in an ensemble of AGCM simulations. J. Climate, 12:2386--2396, 1999. doi:10.1175/1520-0442(1999)012<2386:VIVIAE>2.0.CO;2 C. S. Frederiksen and X. Zheng. Variability of seasonal-mean fields arising from intraseasonal variability. part 2, application to nh winter circulations. Climate Dynamics, 23:193--206, 2004. doi:10.1007/s00382-004-0429-6 C. S. Frederiksen and X. Zheng. Variability of seasonal-mean fields arising from intraseasonal variability. Part 3: Application to SH winter and summer circulations. Climate Dynamics, 28:849--866, 2007. doi:10.1007/s00382-006-0214-9 S. Grainger, C. S. Frederiksen and X. Zheng. A method for evaluating the modes of variability in general circulation models. ANZIAM J., 50:C399--C412, 2008. http://anziamj.austms.org.au/ojs/index.php/ANZIAMJ/article/view/1431 X. Zheng, M. Sugi and C. S. Frederiksen. Interannual variability and predictability in an ensemble of climate simulations with the MRI-JMA AGCM. J. Meteor. Soc. Jap., 82:1--18, 2004. doi:10.2151/jmsj.82.1 S. Grainger, C. S. Frederiksen, X. Zheng, D. Fereday, C. K. Folland, E. K. Jin, J. L. Kinter, J. R. Knight, S. Schubert and J. Syktus. Modes of variability of Southern Hemisphere atmospheric circulation estimated by AGCMs. Climate Dynamics, 36:473--490, 2011. doi:10.1007/s00382-009-0720-7 H. von Storch and F. W. Zwiers. Statistical Analysis in Climate Research. Cambridge University Press, 484pp, 1999. G. A. Meehl, C. Covey, T. Delworth, M. Latif, B. McAvaney, J. F. B. Mitchell, R. J. Stouffer and K. E. Taylor. The WCRP CMIP3 multimodel dataset: A new era in climate change research. Bull. Amer. Meteor. Soc., 88:1383--1394, 2007. doi:10.1175/BAMS-88-9-1383 E. Kalnay, M. Kanamitsu, R. Kistler, W. Collins, D. Deaven, L. Gandin, M. Iredell, S. Saha, G. White, J. Woollen, Y. Zhu, A. Leetmaa, R. Reynolds, M. Chelliah, W. Ebisuzaki, W. Higgins, J. Janowiak, K. C. Mo, C. Ropelewski, J. Wang, R. Jenne and D. Joseph. The NCEP/NCAR 40-year reanalysis project. Bull. Amer. Meteor. Soc., 77:437--471, 1996. doi:10.1175/1520-0477(1996)077<0437:TNYRP>2.0.CO;2 N. A. Rayner, D. E. Parker, E. B. Horton, C. K. Folland, L. V. Alexander, D. P. Rowell, E. C. Kent and A. Kaplan. Global analyses of sea surface temperature, sea ice, and night marine air temperature since the late nineteenth century. J. Geophys. Res., 108(D14):4407, 2003. doi:10.1029/2002JD002670 J. M. Arblaster and G. A. Meehl. Contributions of external forcings to Southern Annular Mode trends. J. Climate, 19:2896--2905, 2006. doi:10.1175/JCLI3774.1
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