A statistical rainfall‐runoff mixture model with heavy‐tailed components

“…This approach is unavoidable when the data do not cover the same period, but the model is potentially open to inference from data from the same events as in the method of Carreau et al (2009). Another possibility is to fit rainfall and runoff distributions jointly and not only with one-way dependence.…”

Section: Discussionmentioning

confidence: 97%

A model capable of changing the heaviness of the tail of a probability distribution function

Leviandier¹

2010

Hydrological Sciences Journal

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A model capable of changing the heaviness of the tail of a probability distribution function. Hydrol. Sci. J. 55(6), 992-1001.Abstract Exceptional events may be declared exceptional due to underestimation of extreme values. We focus on the uncertainties associated with the transformation of extreme variables by a rainfall-runoff model, or by a catchment. Conditional probabilities provide a simple model that accounts for the modification of the extreme value index due to the rainfall-runoff transformation. In its original form, this model can only decrease the value of this index, but a modified form yields a family of distributions resilient to exponentially distributed perturbations, not subject to this restriction. The behaviour of these distributions in extreme values is related to the intensity of the perturbation versus the intensity of the relationship with the independent variable (rainfall). The tails of the rainfall and runoff distributions are not necessarily parallel. A case study is presented with positive -but not very differentvalues of the extreme value indexes. Complementary investigations are performed on synthetic data. As the model exhibits the same behaviour as a more detailed model, the transformation of the extreme value index clearly depends on the transfer function. Hydrological or hydraulic knowledge is therefore necessary to improve estimation of the upper tail of flood distributions.Un modèle capable de modifier l'épaisseur de la queue d'une fonction de distribution de probabilité Résumé La qualification d'événements comme exceptionnels peut être due à une sous-estimation des valeurs extrêmes. Nous portons notre attention sur les incertitudes associées à la transformation de valeurs extrêmes par un modèle pluie-débit, ou un bassin versant. Un modèle simple rendant compte de cette transformation est bâti sur les probabilités conditionnelles. Dans sa forme originale, il ne peut que diminuer l'indice de valeurs extrêmes, mais cette restriction disparaît dans une variante qui définit des distributions de probabilité stables sous l'effet de perturbations, que nous appelons distributions exponentielles-résilientes. Leur comportement dépend de l'intensité de la perturbation par rapport à la variable indépendante initiale, et ne force pas de parallélisme entre la distribution des pluies et celle des débits. Une application sur données réelles est étudiée, présentant une (faible) différence des indices de valeurs extrêmes pour ces deux distributions. Des simulations complémentaires établissent la similitude de comportement de ce modèle simplifié avec un modèle stochastique pluie-débit et montrent que l'indice de valeurs extrêmes est influencé par le paramètre de la fonction de transfert. Une connaissance de l'hydrologie et de l'hydraulique est donc nécessaire pour améliorer les estimations de queue de distributions de débits.

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“…To model marginal distributions in this case, a GPD tail model can be coupled with a model for non-exceedances, which can be empirical [47], non-parametric [49] or parametric [50]. To give spatial simulations, empirical estimates of spatial dependence can be used together with a suitable interpolation scheme.…”

Section: Discussionmentioning

confidence: 99%

A geostatistical extreme-value framework for fast simulation of natural hazard events

Youngman¹,

Stephenson²

2016

Proc. R. Soc. A.

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We develop a statistical framework for simulating natural hazard events that combines extreme value theory and geostatistics. Robust generalized additive model forms represent generalized Pareto marginal distribution parameters while a Student's t-process captures spatial dependence and gives a continuous-space framework for natural hazard event simulations. Efficiency of the simulation method allows many years of data (typically over 10 000) to be obtained at relatively little computational cost. This makes the model viable for forming the hazard module of a catastrophe model. We illustrate the framework by simulating maximum wind gusts for European windstorms, which are found to have realistic marginal and spatial properties, and validate well against wind gust measurements.

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A statistical rainfall‐runoff mixture model with heavy‐tailed components

Cited by 37 publications

References 12 publications

On the emergence of heavy-tailed streamflow distributions

On the emergence of heavy-tailed streamflow distributions

A model capable of changing the heaviness of the tail of a probability distribution function

A geostatistical extreme-value framework for fast simulation of natural hazard events

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