Kakou, Anastasia; (1997) Point process based models for rainfall. Doctoral thesis (Ph.D), UCL (University College London).

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Abstract

In this thesis, we study the evolution of rainfall at a single site and over a network of sites by generalising existing point process based models. Stochastic models based on clustered point processes, such as the Neyman-Scott and the Bartlett-Lewis processes, have been used recently in the description of the behaviour of rainfall at a fixed point in space. In such models, storms are idealised as cluster origins that arrive in a Poisson process and are followed by a number of rain cell origins, the cluster members. A rectangular pulse is associated with each rain cell origin, having independent random duration and intensity. In this thesis, a class of models with rain cell duration and intensity being dependent random variables has been developed and the main properties have been derived. For the description of the evolution of a rainfall event at many distinct spatial locations, we consider a master clustered point process which is decomposed into subprocesses according to a marking mechanism, depending on the location(s) that are affected by a storm and its rain cells. Each cluster of the sub-processes is randomly translated in time, in order to allow different sites to experience the same event at different times. Some of the model's parameters remain the same at all generated sub-processes, while others vary in a stochastic or deterministic way. We follow two approaches in modelling the probability that a storm or a rain cell affects a particular subset of sites. One is to describe the spatial structure of a rainfall event by assigning to each of its elements a band of random width, location and orientation, that intersects the catchment area. Alternatively, the probability that two sites experience the same event can be expressed as a deterministic function of the distance between the sites. The models are fitted to rain gauge data from the South-West of England.

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