Modelling point rainfall occurrences with the Modified Bartlett-Lewis Rectangular Pulses Model

A six parameter stochastic point process model, known as the modified Bartlett-Lewis Rectangular Pulses Model, is applied to fairly long hourly rainfall data recorded at Valentia (relatively a wet location) and Shannon Airport (relatively a dry location), Ireland. Five different sets of statistics of the rainfall data of each month, assuming local stationarity within the month, are used to estimate the parameters and to simulate model output. The problems of parameter stability/sensitivity and identification are discussed and it has been shown that the sensitivity of the model parameters to the choice of six statistics can be avoided by estimating the six parameters by optimization from 16 statistics namely mean, variance, lag-1 autocorrelation coefficient and proportion dry of hourly, 6-hourly, 12-hourly, and 24-hourly rainfalls. Some useful properties of the rainfall depth process are analysed using the notion of event-based statistics. The conditional distributions of rainfall depth and maximum intensity, mean event profiles, and various other features of the rainfall depth process obtained from the model simulated samples compare favourably with the historical ones.