An Application of the Pump-to-Fill Policy for Management of Urban Stormwater

We consider the management of urban stormwater in two connected dams. Stormwater generated by local rainfall flows into a capture dam and is subsequently pumped into a similar sized holding dam. We assume random gross inflow and constant demand. If we wish to minimise overflow from the system then the optimal management policy is to pump as much water as possible each day from the capture dam to the holding dam without allowing the holding dam to overflow. We shall refer to this policy as the pump-to-fill policy. The model is based on the Parafield stormwater management system in the City of Salisbury (CoS) but assumes constant demand instead of level dependent outflow. If there is insufficient water in the holding dam to meet the desired daily demand then all water in the holding dam is used and the shortfall is obtained from other sources. CoS, in suburban Adelaide in South Australia, is recognised in local government circles as a world leader in urban stormwater management. The water is supplied to local industry to replace regular mains water and is also used to restore and maintain urban wetlands. In mathematical terms the pump-to-fill policy defines a Markov chain with a large transition matrix and a characteristic regular block structure. We use specialised Matrix Analytic Methods to decompose the event space and find simplified equations for the steady state probability vector. In this way we enable an elementary solution procedure which we illustrate by solving the modified Parafield problem. The optimal nature of the pump-to-fill policy is established in a recent paper by Pearce et al. (JIMO 3(2):313–320, 2007). The purpose of the current study is to find optimal management policies for urban stormwater systems.

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