Statistical Modelling 3 (2003), 7998
Extensions of the Bartlett-Lewis model for rainfall processes
A. Salim
Department of Statistics,
University College Cork,
Republic of Ireleand.
eMail: agus@stat.ucc.ie
Y. Pawitan
Department of Medical Epidemiology,
Karolinska Institutet,
Stockholm, Sweden.
Abstract:
While the Bartlett-Lewis model has been widely used for modelling
rainfall processes at a fixed point in space over time, there are
observed features, such as longer-scale dependence, which are not
well fitted by the model. In this paper, we study an extension where
we put an extra layer in the clustered Poisson process of storm
origins. We also investigate the Pareto inter-arrival time for the
storm origins, which has been used to model web-traffic data. We
derive the theoretical first and second-order properties of the
multi-layer clustered Poisson processes, but generally we have to
rely on Monte Carlo techniques. The models are fitted to hourly
rainfall data from Valentia observatory in southwest Ireland,
where the extensions are shown to improve on the standard models.
We generalize these models further by allowing some parameters of
the models to be a function of some covariates. An application
using data from Valentia observatory and Belmullet shows how to
use this class of models to analyze the association between the
rainfall pattern and the North Atlantic Oscillation (NAO) index.
Keywords:
RAINFALL; BARTLETT-LEWIS MODELS; LONG-RANGE DEPENDENCE;
MULTI-LAYER STRUCTURE; NAO INDEX.
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