Rainfall modelling using Poisson-cluster processes: a review of developments

Abstract

Over a decade ago, point rainfall models based upon Poisson cluster processes were developed by Rodriguez-Iturbe, Cox and Isham. Two types of point process models were envisaged: the Bartlett±Lewis and the Neyman±Scott rectangular pulse models. Recent developments are reviewed here, including a number of empirical studies. The parameter estimation problem is addressed for both types of Poisson-cluster based models. The multiplicity of parameters which can be obtained for a given data set using the method of moments is illustrated and two approaches to ®nding a best set of parameters are presented. The use of a proper ®tting method will allow for the problems encountered in regionalisation to be adequately dealt with. Applications of the point process model to¯ood design are discussed and ®nally, results for a model with dependent cell depth and duration are given. Taking into account the spatial features of rainfall, three multi-site models are presented and compared. They are all governed by a master Poisson process of storm origins and have a number of cell origins associated with each storm origin. The three models differ as to the type of dependence structure between the cell characteristics at different sites. Analytical properties are presented for these models and their ability to represent the spatial structure of a set of raingauge data in the South-West of England is examined. Continuous spatial-temporal models are currently being developed and results are presented for a model in which storm centres arrive in a homogeneous Poisson process in

A doubly stochastic rainfall model with exponentially decaying pulses

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Incorporating parameter dependencies into temporal downscaling of extreme rainfall using a random cascade approach

“…For canonical models, the probability distribution of weights is typically a log-normal, log-Poisson or log-Levy distribution (Onof et al 2000, Molnar and Burlando 2005, Sivakumar and Sharma 2008, Lovejoy and Schertzer 2013 with the parameters estimated using a theoretically derived relationship with the scaling properties of the rainfall moments. The weights for adjacent sub-intervals at each cascade level (W 1 and W 2 in the case of dividing into two sub-intervals) are sampled independently from the same distribution so that their sum may be greater than 1.0; in other words the canonical models do not aim to conserve volume when sub-dividing R, except in the trivial case of dividing a zero volume.…”

“…An attraction of the MDRC approach is its simplicity -the model development only involves the identification of suitable probability distributions for the W values at each cascade level. Alternative statistical approaches to developing continuous-time sub-daily rainfall series, while having their own strengths, have more complicated model identification procedures (Onof et al 2000).…”

La méthode SHYREG débit—application sur 1605 bassins versants en France métropolitaine

“…Les résultats de ces travaux montrent de bons résultats, quel que soit le pas de temps étudié (Rodriguez-Iturbe et al 1987, Onof et al 2000, Blazkova et Beven 2004. Afin de reproduire au mieux les valeurs extrêmes, des études prennent en compte la dépendance entre certaines variables comme la durée et l'intensité des pluies à l'aide des copules (De Michele et Salvadori 2003, Cantet et al 2011, Vandenberghe et al 2011.…”