A Neyman-Scott model with continuous distributions of storm types

Paul Cowpertwait


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.

  • Burton, A., Kilsby, C., Fowler, H., Cowpertwait, P., and O'Connell, P. (2008). RainSim: A spatial-temporal stochastic rainfall modelling system. Environmental Modelling and Software, 23:1356--1369.
  • Cowpertwait, P. (1998). A Poisson-cluster model of rainfall: High order moments and extreme values. Proceedings of the Royal Society of London, Series A, 454:885--898.
  • Cowpertwait, P. (2004). Mixed rectangular pulses models of rainfall. Hydrology and Earth System Sciences, 8:993--1000.
  • Cowpertwait, P. (2009). Spatial-temporal poisson cluster models of rainfall: Applications and further developments. 9th Engineering Mathematics and Applications Conference, Adelaide 6--9 December.
  • Cox, D. and Isham, V. (1980). Point Processes. Chapman and Hall.
  • R Development Core Team (2009). R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna, Austria. {ISBN} 3-900051-07-0.
  • Rodriguez-Iturbe, I., Cox, D., and Isham, V. (1987). Some models for rainfall based on stochastic point processes. Proc. R. Soc. Lond. A, 410:269--288.
  • Wheater, H., Chandler, R., Onof, C., Isham, V., Bellone, E., Yang, C., Lekkas, D., Lourmas, G., and Segond, M.-L. (2005). Spatial-temporal rainfall modelling for flood risk estimation. Stochastic Environmental Research and Risk Assessment, 19:403--416.


Stochastic Processes; Point Processes; Rainfall Time Series; Poisson Cluster Models; Urban Hydrology

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DOI: http://dx.doi.org/10.21914/anziamj.v51i0.3025

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