Modelling Extremes of the Areal Rainfall Process

Stuart Coles · Jonathan A. Tawn

181 citations0/0 files storedJournal of the Royal Statistical Society Series B (Statistical Methodology)

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Probability and Risk Models Hydrology and Watershed Management Studies Precipitation Measurement and Analysis

Abstract

SUMMARY Risk assessment for many hydrological structures requires an estimate of the extremal behaviour of the rainfall regime within a specified catchment region. In most cases it is the spatially aggregated rainfall which is the key process, though in practice only pointwise rainfall measurements from a network of sites over the region are available. In this paper we address the problem of making inferences about the extremal properties of the aggregated process from the pointwise data. Working within the usual extreme value paradigm, a model is derived in which the resulting distribution is determined by the marginal tail behaviour and spatial dependence at extreme levels of the process. Data collected from a region in the south-west of England are used to illustrate the procedure.

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References

1993Statistics for Spatial Data 1990Models for Exceedances Over High Thresholds 1989Extreme Value Analysis of Environmental Time Series: An Application to Trend Detection in Ground-Level Ozone 1991Modelling Extreme Multivariate Events 1984A Spectral Representation for Max-stable Processes 1994Statistical Methods for Multivariate Extremes: An Application to Structural Design 1994Statistical methods for multivariate extremes: an application to structural design.

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2008Hierarchical modeling for extreme values observed over space and time 2015On spatial extremes: With application to a rainfall problem 2008On spatial extremes: With application to a rainfall problem 1999Spatial Regression Models for Extremes 2000A Comparison of Methods for Estimating the Extremal Index 2018High-dimensional peaks-over-threshold inference 2011Conditional sampling for spectrally discrete max-stable random fields

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