Stochastic point process modelling of rainfall .1. Single-site fitting and validation

A Neyman-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 derided 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.