The stochastic generation of rainfall time series
The purpose of this project was to propose and validate a stochastic rainfall time series model for the UK, where the model is to be applied to the design of sewer systems. After reviewing the literature, the Neyman-Scott Rectangular Pulses model was selected as being potentially suitable for the project. Some mathematical properties for the model were derived, and used to fit the model to 10 years of hourly rainfall time series. The model performed well, and so could be used with reasonable confidence for the remaining part of the project. A full investigation was carried out to find an optimum combination of historical rainfall statistics to be used to fit the model to hourly rainfall time series. A method of fitting the model to daily rainfall time series was also required. It was found that the hourly rainfall statistics used to fit the model to the hourly rainfall time series could successfully be predicted from daily rainfall statistics. Regression equations were developed so that the mean and variance of the maximum daily rainfalls could be predicted using the parameters of the model. These regression equations were included in the fitting procedure when the model showed a poor fit to the historical daily maxima, so that the model was then able to closely match the historical maxima. The model was fitted to rainfall data taken from 112 sites scattered throughout the UK. The parameters of the model were regressed on site characteristics (e. g. altitude, distance from coast, etc), so that the model could be used to generate hourly rainfall time series at sites lacking in data. Finally, a method of disaggregating the generated hourly rainfall time series to 5 minutely time series was developed and tested.