Mawson Lakes is a new suburban housing development, situated 12 kms from the city of Adelaide in South Australia. The developers, the Mawson Lakes Joint Venture (MLJV), and the local council, the City of Salisbury, intend to capture all stormwater entering the site and recondition all wastewater. The water will then be supplied to residents and businesses for non-potable usage. Modelling the behaviour of the Mawson Lakes catchment under extreme conditions such as drought and prolonged periods of high rainfall will allow the project team to determine optimal water management strategies for the catchment. One of the problems facing the team is the prediction of future rainfall patterns and the typical form of extreme events. In this thesis I have used historical records to construct synthetic rainfall data that will allow the project team to investigate a wide range of typical behaviour. The Gamma distribution has been widely used to approximate the probability density function (PDF) of monthly rainfall totals. However, there is no natural way to extend this method directly to obtain a joint PDF for rainfall densities associated with two or more months, unless the monthly totals are independent. I propose a modified method to construct a suitable PDF using parameters from the maximum likelihood estimate for a marginal Gamma distribution and a series of associated Laguerre polynomials. This series of special functions allows us to match the correlation between monthly totals and to match the observed moments with any level of precision needed. The joint PDF for two months is constructed using a sum of products of associated Laguerre polynomials. In order to get an analytic expression for the marginal distributions and the associated cumulative probabilities, it is convenient to use a weighted total and a weighted proportion contributed from the first month. The method makes extensive use of well-known formulae from the theory of special functions. The cumulative marginal probability density for the weighted total and the cumulative conditional probability density for the weighted proportion are used to generate simulated rainfall totals for each month in a two month period. In theory the simulated data is statistically identical to the observed data. In practice we apply standard statistical methods to check that the simulated data is consistent with the observed data. This method can be extended to the general case of any number of months, but computationally is restricted to only three. For this reason an alternative method is proposed to generate synthetic data for more than three months, which uses groups and subgroups of months, but still retains the characteristics of the original PDF. Although the series method could also be used to model a sequence of days, I propose an alternative method using Markov processes. This method will match a sequence of daily totals, generated from a probability transition matrix, to the monthly total generated by the series method. This methodology allows the research team to simulate certain special cases such as droughts and prolonged periods of high rainfall. These unusual events are of great interest in catchment planning and management. / thesis (PhDMathematics)--University of South Australia, 2004.
| Identifer | oai:union.ndltd.org:ADTP/284163 |
| Date | January 2004 |
| Creators | Rosenberg, Kathrine Joan |
| Source Sets | Australiasian Digital Theses Program |
| Language | English |
| Detected Language | English |
| Rights | Copyright 2004 Kathrine Joan Rosenberg |
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