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Estimating the probability of simultaneous rainfall extremes within a region: a spatial approach

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  • Lee Fawcett
  • David Walshaw

Abstract

In this paper we investigate the impact of model mis-specification, in terms of the dependence structure in the extremes of a spatial process, on the estimation of key quantities that are of interest to hydrologists and engineers. For example, it is often the case that severe flooding occurs as a result of the observation of rainfall extremes at several locations in a region simultaneously. Thus, practitioners might be interested in estimates of the joint exceedance probability of some high levels across these locations. It is likely that there will be spatial dependence present between the extremes, and this should be properly accounted for when estimating such probabilities. We compare the use of standard models from the geostatistics literature with max-stables models from extreme value theory. We find that, in some situations, using an incorrect spatial model for our extremes results in a significant under-estimation of these probabilities which -- in flood defence terms -- could lead to substantial under-protection.

Suggested Citation

  • Lee Fawcett & David Walshaw, 2014. "Estimating the probability of simultaneous rainfall extremes within a region: a spatial approach," Journal of Applied Statistics, Taylor & Francis Journals, vol. 41(5), pages 959-976, May.
    • Handle: RePEc:taf:japsta:v:41:y:2014:i:5:p:959-976
    DOI: 10.1080/02664763.2013.856872
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    References listed on IDEAS

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    1. Lee Fawcett & David Walshaw, 2006. "A hierarchical model for extreme wind speeds," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 55(5), pages 631-646, November.
    2. Lee Fawcett & David Walshaw, 2012. "Estimating return levels from serially dependent extremes," Environmetrics, John Wiley & Sons, Ltd., vol. 23(3), pages 272-283, May.
    3. Cristiano Varin, 2008. "On composite marginal likelihoods," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 92(1), pages 1-28, February.
    4. Jonathan Atyeo & David Walshaw, 2012. "A region‐based hierarchical model for extreme rainfall over the UK, incorporating spatial dependence and temporal trend," Environmetrics, John Wiley & Sons, Ltd., vol. 23(6), pages 509-521, September.
    5. Janet E. Heffernan & Jonathan A. Tawn, 2004. "A conditional approach for multivariate extreme values (with discussion)," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 66(3), pages 497-546, August.
    6. Jennifer L. Wadsworth & Jonathan A. Tawn, 2012. "Dependence modelling for spatial extremes," Biometrika, Biometrika Trust, vol. 99(2), pages 253-272.
    7. D. R. Cox, 2004. "A note on pseudolikelihood constructed from marginal densities," Biometrika, Biometrika Trust, vol. 91(3), pages 729-737, September.
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    Cited by:

    1. Gloria Buriticá & Philippe Naveau, 2023. "Stable sums to infer high return levels of multivariate rainfall time series," Environmetrics, John Wiley & Sons, Ltd., vol. 34(4), June.

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