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Statistical Methods for Nonstationary Extremes

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Extremes in a Changing Climate

Part of the book series: Water Science and Technology Library ((WSTL,volume 65))

Abstract

There is a long tradition of the use of methods based on the statistical theory of extreme values in hydrology, particular for engineering design (e.g., for the proverbial “100-yr flood”). For the most part, these methods are based on the assumption of stationarity (i.e., an unchanging climate in a statistical sense). The focus of this chapter is on how the familiar distributions that arise in extreme value theory, namely the generalized extreme value (GEV) and generalized Pareto (GP) distributions, can be retained under nonstationarity. But now the extremal distribution is allowed to gradually shift by introducing time as a covariate; that is, expressing one or more of the parameters of the distribution as a function of time. At least for the parameter estimation technique of maximum likelihood, it is straightforward to fit such statistical models. Some detailed examples are provided of how the proposed methods can be applied to the detection and statistical modeling of trends in hydrologic extremes, such as for stream flow and precipitation.

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Acknowledgments

I gratefully acknowledge the comments of one anonymous reviewer. The Mercer Creek stream flow time series was obtained from the U.S. Geological Survey (USGS) web site (http://nwis.waterdata.usgs.gov/usa/nwis/peak). I thank Yun Li (CSIRO, Perth, Australia) for providing the daily precipitation data for southwest Western Australia. This research was partially supported by the National Center for Atmospheric Research (NCAR) Weather and Climate Impacts Assessment Science Program. NCAR is sponsored by the National Science Foundation.

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Authors and Affiliations

  1. Institute for Mathematics Applied to Geosciences, National Center for Atmospheric Research, Boulder, CO, USA

    Richard W. Katz

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  1. Richard W. Katz
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Correspondence to Richard W. Katz .

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Editors and Affiliations

  1. , Dept. of Civil and Env. Engineering, University of California, Irvine, Engineering Gateway E/4130, Irvine, 92697, California, USA

    Amir AghaKouchak

  2. NOAA's National Climatic Data Center, Patton Avenue 151, Asheville, 28801-5001, North Carolina, USA

    David Easterling

  3. , Dept. of Civil and Env. Engineering, University of California, Irvine, Engineering Gateway E/4130, Irvine, 92697, California, USA

    Kuolin Hsu

  4. NASA/Goddard Space Flight Center, Greenbelt Road 8800, Greenbelt, 20771, USA

    Siegfried Schubert

  5. , Dept. Civil & Environmental Engineering, University of California, Irvine, Engineering Gateway E/4130, Irvine, 92697, California, USA

    Soroosh Sorooshian

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Katz, R.W. (2013). Statistical Methods for Nonstationary Extremes. In: AghaKouchak, A., Easterling, D., Hsu, K., Schubert, S., Sorooshian, S. (eds) Extremes in a Changing Climate. Water Science and Technology Library, vol 65. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-4479-0_2

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