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Title: Doubly stochastic Poisson processes in hydrological modelling Authors:  Nadarajah Ramesh - University of Greenwich (United Kingdom) [presenting]
Abstract: The doubly stochastic Poisson process (DSPP) provides a rich class of clustered point process models that can be utilised in rainfall modelling. The purpose is to provide an overview of recent development on models constructed from this class of stochastic point processes and presents the results when they are used to model rainfall collected in different forms. When the rainfall is recorded in the form of rainfall bucket tip time series a class of DSPP models can be constructed whereby the arrival pattern of bucket tip times is viewed as a DSPP whose rate of occurrence varies according to a Markov process. As the likelihood function for this process can be calculated, the maximum likelihood methods can be employed to estimate the parameters. More physically appealing models from the DSPP can be developed, by attaching a pulse or a cluster of pulses to each rain cell, for rainfall collected in the form of accumulated rainfall in discrete intervals of fixed length. Different types of pulses can be employed to extend this model. These models are used to model hourly and sub-hourly rainfall data. The results of our analyses suggest that the proposed class of stochastic models provides useful tools in hydrological modelling.