Institute of Natural and Mathematical Sciences

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Browsing Institute of Natural and Mathematical Sciences by Author "Cowpertwait, P.S.P."

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    Mixed rectangular pulses models of rainfall
    (Massey University, 2003) Cowpertwait, P.S.P.
    In a recent paper ((3)) a fitting procedure for the Neyman-Scott rectangular pulses (NSRP) spatial-temporal model of rainfall was developed. In that paper, the NSRP third moment function was fitted to the equivalent sample value taken at one-hour time intervals. In this paper, the fitting and modelling procedure are extended to ensure a close fit is obtained to further sample properties over a range of time scales. The stochastic model is a ‘mixed’ model obtained as the superposition of two independent NSRP processes. The model is fitted to hourly data from Auckland, New Zealand, where a good fit to sample properties is obtained. It is found that a special case arises (the superposition of an NSRP process and a Poisson rectangular pulses process) for data over the summer period. A simulation study of extremes over a range of time scales supports the use of the model in hydrological applications.
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    A model of rainfall based on finite-state cellular automata
    (Massey University, 2004) Munroe, D.R.; Mills, B.I.; Cowpertwait, P.S.P.
    The purpose of this paper is to demonstrate that a finite state cellular automata model is suitable for modeling rainfall in the space-time plane. The time-series properties of the simulated series are matched with historical rainfall data gathered from Whenuapai, NZ. The spatial scale of the model cells in related to land-area by optimizing the cross-correlation between sites at lag 0 relative to rainfall data collected from Auckland, NZ. The model is shown to be adequate for simulation in time, but inadequate in spatial dimension for short distances.
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    A stochastic spatial-temporal disaggreation model for rainfall
    (Massey University, 2004) Cowpertwait, P.S.P.; Lockie, T.; Davis, M.D.
    A stochastic model for disaggregating spatial-temporal rainfall data is presented. In the model, the starting times of rain cells occur in a Poisson process, where each cell has a random duration and a random intensity. In space, rain cells have centres that are distributed according to a two dimensional Poisson process and have radii that follow an exponential distribution. The model is fitted to seven years of five-minute data taken from six sites across Auckland City. The historical five-minute series are then aggregated to hourly depths and stochastically disaggregated to five-minute depths using the fitted model. The disaggregated series and the original five-minute historical series are then used as input to a network flow simulation model of Auckland City’s combined and wastewater system. Simulated overflow volumes predicted by the network model from the historical and disaggregated series are found to have equivalent statistical distributions, within sampling error. The results thus support the use of the stochastic disaggregation model in urban catchment studies.