Optimal stormwater management with two dams: the dynamics of the pump-to-fill policy

We consider the management of water in two connected dams. Stormwater generated by rainfall flows into a large capture dam and is subsequently pumped to a smaller supply dam. Recently it was shown that the twin objectives of minimizing overflow and maximizing the amount of demand met are both achieved by the pump-to-fill policy, in which as much water as possible is pumped each day from the capture dam to the supply dam without allowing the supply dam to overflow. We present a simplifying reparameterization for this case and study the dynamics of the system.