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Natural Hazards and Earth System Sciences An interactive open-access journal of the European Geosciences Union
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Volume 6, issue 3
Nat. Hazards Earth Syst. Sci., 6, 459–470, 2006
https://doi.org/10.5194/nhess-6-459-2006
© Author(s) 2006. This work is licensed under
the Creative Commons Attribution-NonCommercial-ShareAlike 2.5 License.

Special issue: Mediterranean Storms (Plinius 2004)

Nat. Hazards Earth Syst. Sci., 6, 459–470, 2006
https://doi.org/10.5194/nhess-6-459-2006
© Author(s) 2006. This work is licensed under
the Creative Commons Attribution-NonCommercial-ShareAlike 2.5 License.

  06 Jun 2006

06 Jun 2006

The effect of scale in daily precipitation hazard assessment

J. J. Egozcue1, V. Pawlowsky-Glahn2, M. I. Ortego1, and R. Tolosana-Delgado2 J. J. Egozcue et al.
  • 1Dept. de Matemàtica Aplicada III, Universitat Politècnica de Catalunya, Barcelona, Spain
  • 2Dept. d’Informàtica i Matemàtica Aplicada, Universitat de Girona, Girona, Spain

Abstract. Daily precipitation is recorded as the total amount of water collected by a rain-gauge in 24 h. Events are modelled as a Poisson process and the 24 h precipitation by a Generalised Pareto Distribution (GPD) of excesses. Hazard assessment is complete when estimates of the Poisson rate and the distribution parameters, together with a measure of their uncertainty, are obtained. The shape parameter of the GPD determines the support of the variable: Weibull domain of attraction (DA) corresponds to finite support variables as should be for natural phenomena. However, Fréchet DA has been reported for daily precipitation, which implies an infinite support and a heavy-tailed distribution. Bayesian techniques are used to estimate the parameters. The approach is illustrated with precipitation data from the Eastern coast of the Iberian Peninsula affected by severe convective precipitation. The estimated GPD is mainly in the Fréchet DA, something incompatible with the common sense assumption of that precipitation is a bounded phenomenon. The bounded character of precipitation is then taken as a priori hypothesis. Consistency of this hypothesis with the data is checked in two cases: using the raw-data (in mm) and using log-transformed data. As expected, a Bayesian model checking clearly rejects the model in the raw-data case. However, log-transformed data seem to be consistent with the model. This fact may be due to the adequacy of the log-scale to represent positive measurements for which differences are better relative than absolute.

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