A stochastic infilling algorithm for spatial-temporal rainfall data : a thesis presented in partial fulfilment of the requirements for the degree of Master of Science in Statistics at Massey University
The purpose of this thesis is to develop an infilling algorithm for 24-hour (daily) rainfall data. An infilling algorithm replaces missing data within the historical records with sensible estimates, where any appropriate method (prediction from a fitted model, interpolation between points, or random sampling) could be used to select and/or produce the required estimates. The algorithm developed uses simulation data generated using a stochastic point-process model which has been fitted to historical data. In this thesis, the spatial-temporal Neyman-Scott rectangular pulse model as presented in Cowpertwait et al. (2002) is fitted to data provided by Thames Water from 23 sites in the Thames Valley (UK). The model is shown to fit the data reasonably well; however it fails to fit the proportion of dry sites (which is not used in the fitting process). Nevertheless, simulated data is generated using the model and an infilling algorithm is derived. The algorithm is tested by replacing valid historical data with missing values, infilling these missing values, and then comparing relevant statistics for the two samples. Three algorithms are developed in this thesis, of which the final algorithm maintains the statistical characteristics of the historical data, including the proportion of dry sites, while infilling values that are similar to the known historical record.