statistics to the kinds of problems considered in the present report has been limited. For the univariate case, methods exist for determining trends in extreme event probabilities based on observational data and, by combining observations with climate models, for extrapolating these trends forward in time. However, we are not aware of published results that directly address the question of a 10-year time frame, which has been the main focus of the present report. There is no reason in principle that existing statistical methods could not be used to produce such estimates, and we recommend pursuing that.

For the bivariate case, the main question of interest is one of dependence: whether some underlying process creates a reliable association between the occurrence of an extreme event in one climate variable in one place and the probability of an extreme event in another variable or place. The relatively short length of most observational series limits the extent to which this question can be answered based on observational data. It would be valuable to conduct studies using longer series generated from climate models. Another question concerns the time-scale of dependence, e.g., if one extreme does indeed raise the probability of another, then for what period of time does this elevated probability of an extreme event remain valid?

More broadly, there is a need for research on clusters of extreme events. It is possible that an extreme value of one climate variable is systematically associated with extreme events in several related variables. Extensions of extreme value theory to multivariate data, to time series and spatial processes (see, e.g., Cooley et al., 2012), could in principle be used to answer such questions, but there is a need for more extensive practical development of these methods.

REFERENCES

Brockwell, P.J., and Davis, R.A. 2002. Introduction to time series and forecasting (2nd edition). New York: Springer Verlag.

Coles, S.G. 2001. An introduction to statistical modeling of extreme values. New York: Springer Verlag.

Coles, S.G., and J.A. Tawn. 1991. Modeling extreme multivariate events. Journal of the Royal Statistical Society, Series B 53:377–392.

Coles, S., J. Heffernan, and J. Tawn. 1999. Dependence measures for extreme value analysis. Extremes 2(4):339–365.

Cooley, D., J. Cisewski, R.J. Erhardt, S. Jeon, E. Mannshardt, B.O. Omolo, and Y. Sun. 2012. A survey of spatial extremes: Measuring spatial dependence and modeling spatial effects. Revstat 10:135–165.

Dole, R., M. Hoerling, J. Perlwitz, J. Eischeid, P. Pegion, T. Zhang, X.-W. Quan, T. Xu, and D. Murray. 2011. Was there a basis for anticipating the 2010 Russian heat wave? Geophysical Research Letters 38:L06702. doi:10.1029/2010GL046582.

Gumbel, E.J., and C.K. Mustafi. 1967. Some analytical properties of bivariate exponential distributions. Journal of the American Statistical Association 62:569–588.



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