Balancing Costs and Benefits in Selecting New Information: Efficient Monitoring Using Deterministic Hydro-economic Models

Uncertainty reduces reliability and performance of water system operations. A decision-maker can take action, accepting the present uncertainty and facing its risks, or reduce uncertainty by first obtaining additional information. Information, however, comes at a cost. The decision-maker must therefore efficiently use his/her resources, selecting the information that is most valuable. This can be done by solving the Optimal Design (OD) problem. The OD problem balances the cost of obtaining new information against its benefits, estimated as the added value of better informed actions. Despite its usefulness, the OD problem is not widely applied. Solving the OD problem requires a stochastic hydro-economic model, whereas most of hydro-economic models presently used are deterministic. In this paper we introduce an innovative methodology that makes deterministic hydro-economic models usable in the OD problem. In deterministic models, Least Squares Estimation (LSE) is often used to identify unknown parameters from data, making them, and hence the whole model, de facto stochastic. We advocate the explicit recognition of this uncertainty and propose to use it in risk-based decisions and formulation of the OD problem. The proposed methodology is illustrated on a flood warning scheme in the White Cart River, in Scotland, where a rating curve uncertainty can be reduced by extra gaugings. Gauging at higher flows is more informative but also more costly, and the LSE - OD formulation results in the economically optimal balance. We show the clear advantage of monitoring based on OD over monitoring uniquely based on uncertainty reduction.