Water management is a critical issue around the world. In South Australia, and throughout Australia, demand for water has increased beyond the capacity of existing water supply systems. For this reason there is great interest in optimal management of water resources at both a national and local level. / In this thesis I discuss the capture and treatment of urban stormwater and suggest practical strategies for water storage in a sequence of dams. My primary motivation was a proposal for the capture, treatment and storage of all stormwater and wastewater on a new suburban housing estate at Mawson Lakes in South Australia, while minimising overflow. / A discrete state mathematical model for the management of water in a system of two connected dams is described in detail, through the use of stochastic matrices. I assume random inputs and regular demand. The system is controlled by pumping water from the first to the second dam. Only practical policies are considered. My initial analysis was restricted to a class of policies that depends only on the content of the first dam. The steady state of the system can be determined for each particular control policy. To determine the steady state I have used Gaussian elimination to reduce the problem of solving a large set of linear equations to a much smaller set. The steady state is an invariant measure that determines the long-term expected overflow. The systematic state reduction procedure subsequently allowed me to consider more complex policies that depend on the content of both dams. One such policy that I analyse in detail is to pump to fill the second dam. Though it is not yet proven this policy is possibly the optimal policy from among the classes considered. I also extend the discrete state model to a system of two connected dams with continuous input into the first dam. The stochastic matrices are replaced by integral operators on a space of bounded probability measures. / An alternative general analysis is described for the policy of pumping to fill the second dam. By using the characteristic pattern of the steady state equations I can define new variables and equations to reduce the problem to a much smaller system of equations. This method was also applied to policies in which I overfill or underfill the second dam. All three solutions are closely related. Yet another method uses a set of superstates. Each superstate is a set of states for which the particular control policy defines a common outcome. Once again the invariant measure is found by solving a reduced order matrix equation. I have also illustrated this method in a particular example. It is entirely possible that my various solution methodologies can be directly related. Although no analysis has yet been done further research into general reduction procedures would be certainly worthwhile. / For each class of controls a computer simulation was used to confirm the theoretical results. The simulation of the two dam system was extended to a system with many dams that is similar to the one proposed at Mawson Lakes. Future investigations include the development of mathematical models and theoretical solutions for the recently revised stormwater storage system at Mawson Lakes. / Thesis (PhDMathematics)--University of South Australia, 2004.
| Identifer | oai:union.ndltd.org:ADTP/267659 |
| Creators | Piantadosi, Julia |
| Source Sets | Australiasian Digital Theses Program |
| Language | English |
| Detected Language | English |
| Rights | copyright under review |
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