How should trends in hydrological extremes be estimated?

Authors

  • Robin T. Clarke

    Corresponding author
    1. Instituto de Pesquisas Hidraulicas, Universidade Federal do Rio Grande do Sul, Porto Alegre, Brazil
    • Corresponding author: R. T. Clarke, Instituto de Pesquisas Hidraulicas, Universidade Federal do Rio Grande do Sul, Porto Alegre, RS 91501-970, Brazil. (clarke@iph.ufrgs.br)

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Abstract

[1] A comparison of six procedures for estimating the linear trend parameter β in annual maximum 1 day river flows at five sites in southern Brazil showed marked differences between, on the one hand, estimates obtained by incorporating trend into the generalized extreme value (GEV) location parameter with all parameters estimated by maximum likelihood (ML) and on the other hand, estimates found by least squares, trend removal prior to fitting the GEV by ML, boot-strap sampling, and Theil-Sen estimation. ML estimates of trend were considerably smaller than those given by all other procedures. The same was true where trend had been incorporated into the Gumbel location parameter. Where 95% confidence intervals were calculated for the “true” trend β by different procedures, some confidence intervals bracketed zero (indicating that the trend was not “significant” at the 5% level), but there was no consistency between results from different procedures; Theil-Sen confidence intervals always bracketed zero, confidence intervals given by detrending never did. It is concluded that not only do different estimation procedures give different measures of trend uncertainty, as reported elsewhere, but the estimated trends themselves may differ, and the paper suggests an explanation why this may occur. Some philosophical issues relating to estimation of trend in climatological and hydrological extremes are discussed, and it is concluded that selection of a method to estimate trend must depend on context.

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