Stochastic point process modelling of rainfall. I. Single-site fitting and validation

doi:10.1016/S0022-1694(96)80004-7

Journal of Hydrology

Volume 175, Issues 1–4, February 1996, Pages 17-46

https://doi.org/10.1016/S0022-1694(96)80004-7 Get rights and content

Abstract

A Newman-Scott clustered point process model for rainfall is developed for use in storm sewer rehabilitation studies in the UK, where predictions are needed of the frequency of system overloading for existing and upgraded conditions. In the first part of this two-part paper, a flexible model fitting procedure is presented which involves matching approximately a chosen set of historical rainfall statistics, which exceeds in number the set of parameters. In fitting the model to hourly data, it is found that wet and dry spell transition probabilities should be included in the chosen set of statistics rather than lag 1 autocorrelations, as they improve the model's fit to the historical dry spell sequences. In fitting the model to daily data, estimates of the variances of sub-daily rainfall totals derived from regional regression relationships are used to ensure that sub-daily totals generated by the fitted model exhibit the desired statistical behaviour. A number of validation checks are carried out on simulated time series, which include visual comparisons with historical series, and comparisons of crossing properties and of the distributions of daily annual maximum rainfalls. Overall, the results support the use of the model for its intended application.

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Since the fundamental structure was formalized in the late 1980s by Rodriguez-Iturbe et al. (1987); (1988;), developments of the Poisson cluster model have focused on improving the estimation of key summary statistics such as auto-correlation or proportion of dry periods (Rodriguez-Iturbe et al., 1988); improving the simulation of convective and stratiform events (Cowpertwait, 1994, Onof and Wang, 2020); reproducing long- and short-term rainfall persistence (Kim et al., 2013a; Park et al., 2019; Kim and Onof, 2020); extending the temporal to a spatial–temporal model (Cowpertwait, 1995; Northrop, 1998; Burton et al., 2008); regionalizing the parameters (Kim et al., 2013a; 2016); and extending the model to represent for the non-stationarity of the precipitation process (Burton et al., 2010; Evin and Favre, 2013; and Kaczmarska et al., 2015). A longstanding limitation of the Poisson cluster rainfall models has been their tendency to underestimate rainfall extremes at fine (e.g. sub-hourly) temporal scales (Cowpertwait et al., 1996; Verhoest et al., 1997; Cameron et al., 2000c; Onof et al., 2000; Kaczmarska et al., 2014; Cross et al., 2018). Cowpertwait (1998) included the third central moment in the fitting statistics to better capture the skewness of the rainfall intensity.
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¹: Present address: National Rivers Authority, Northumbria Region, Newcastle upon Tyne NE1 7RU, UK.

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Stochastic point process modelling of rainfall. I. Single-site fitting and validation

Abstract

J. Hydrol.

Review of rainfall data application for design analysis

Water Sci. Technol.

Analysis of the structure of precipitation patterns in New England

J. Appl. Meteorol.

Further developments of the Neyman-Scott clustered point process for modelling rainfall

Water Resour. Res.

The stochastic generation of rainfall time series

A generalized point process model for rainfall

Proc. R. Soc. London

Clustering population means under heterogeneity of variance with an application to a rainfall time series problem

Statistician