A Neyman-Scott model with continuous distributions of storm types

Abstract

In previous studies, different types of precipitation (for example convective and stratiform) were modelled using superposed Poisson cluster processes. When the underlying processes are independent, statistical properties, up to third order, are obtained by aggregation of the properties of each independent point process. However, each superposition introduces further parameters, which can result in too many parameters. A continuum of storm types $z$ is proposed, where $z$ comes from a continuous probability distribution, and selected model parameters are taken to be functions of $z$. This has the effect of allowing for different types of storms through superposition whilst retaining a moderate number of model parameters. Using a uniform distribution for $z$, properties up to third order are re-derived for the Neyman--Scott model, and used to fit the model to a sixty year record from Wellington, New Zealand. The parameterization enables the exploration of whether storms with fewer cells, on average, tend to have heavier or lighter rainfall. References

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