A general model for the exact computation of yield from a rainwater tank

The models presented in the literature for the computation by simulation of yield from a rainwater tank are either incorrect or approximate at best. In this paper a general, exact, continuous time model of the operation of rainwater tanks is presented. The operation of a tank is determined by the rainfall runoff and demand distribution functions and the capacity of the tank. The runoff and demand distributions are assumed to satisfy certain reasonable conditions which are satisfied in all cases of practical interest, e.g. when the distributions are described by piecewise constant functions. The yield, spill and volume functions are characterized by equations which, by means of a constructive proof involving mathematical induction, can be shown to have unique solutions. This model can be used to compute the exact yield and spill over any period and the volume at any time during the operation of the tank. Correct discrete time simulation models are derived in the special cases of demand before rain (DBR) or demand after rain (DAR).