Research Letters in the Information and Mathematical Sciences
Permanent URI for this collectionhttps://mro.massey.ac.nz/handle/10179/4332
Research Letters welcomes papers from staff and graduate students at Massey University in the areas of: Computer Science, Information Science, Mathematics, Statistics and the Physical and Engineering Sciences. Research letters is a preprint series that accepts articles of completed research work, technical reports, or preliminary results from ongoing research. After editing, articles are published online and can be referenced, or handed out at conferences.
Copyright remains with the authors and the articles can be used as preprints to academic journal publications or handed out at conferences.
Editors Dr Elena Calude Dr Napoleon Reyes The guidelines for writing a manuscript can be accessed here.
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Item 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.Item 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.Item 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.Item A continuous stochastic disaggregation model of rainfall for peak flow simulation in urban hydrologic systems(Massey University, 2001) Cowpertwait, Paul S.P.In the paper by Durrans et al. (1999), an algorithm proposed by Ormsbee (1989) is recommended for the stochastic disaggregation of hourly rainfall in continuous flow simulation studies of urban hydrologic systems. However, Durrans et al. found that the method produced a “severe negative bias” in the maximum rainfall intensity of the disaggregated series, so that peak flows in urban systems are likely to be under-estimated by the model. Here we develop a method for disaggregating hourly data to 5min series, which addresses the problem of negative bias. A regression equation is derived for the ratio of the maximum 5min depth to the total depth in the hour. Thus, for any given hourly depth this ratio can be simulated and multiplied by the hourly depth to obtain a 5min maximum. The temporal location of the maximum within the hour can be randomly placed using an appropriate distribution function, e.g. based on a geometrical construction as developed by Ormsbee (1989). The model is developed and tested using 5min rainfall data taken from Lund (1923-39) and Torsgatan (1984-93), Sweden. The results support the use of the model in urban drainage applications.Item A renewal cluster model for the inter-arrival times of rainfall events(Massey University, 2000) Cowpertwait, Paul S.P.A statistical model, based on a renewal cluster point process, is proposed and used to infer the distributional properties of dry periods in a continuous-time record. The model incorporates a mixed probability distribution in which inter-arrival times are classified into two distinct types, representing cyclonic and anticyclonic weather. This results in rainfall events being clustered in time, and enables objective probabilistic statements to be made about storm properties, e.g. the expected number of events in a storm cluster. The model is fitted to data taken from a gauge near Wellington, New Zealand, by maximising the likelihood function with respect to the parameters. The Akaike Information Criteria is used to select the best fitting distributions from a range of candidates. The log-Normal distribution is found to provide the best fit to the times between successive storm clusters, whilst the Weibull distribution is found to provide the best fit to the times between successive events in the same storm cluster. Harmonic curves are used to provide a parsimonious parameterisation, allowing for the seasonal variation in precipitation. Under the fitted model, the interval series is transformed into a residual series, which is assessed to determine overall goodness-of-fit.
