Identifying effective forecast horizon for real-time reservoir operation under a limited inflow forecast

The use of a streamflow forecast for real-time reservoir operation is constrained by forecast uncertainty (FU) and limited forecast horizon (FH). The effects of the two factors are complicating since increasing the FH usually provides more information for decision making in a longer time framework but with increasing uncertainty, which offsets the information gain from a longer FH. This paper illustrates the existence of an effective FH (EFH) with a given forecast, which balances the effects of the FH and FU and provides the maximum information for reservoir operation decision making. With the assumption of a concave objective function, a monotonic relationship between current operation decision and ending storage is derived. Metrics representing the error resulting from a limited forecast relative to a perfect forecast are defined to evaluate reservoir performance. Procedures to analyze the complicating effect of FU and FH and to identify EFH are proposed. Results show that: (1) when FH is short, FH is the dominating factor for determining reservoir operation, and reservoir performance exhibits a quick improvement as FH increases; (2) when FH is long, the inflow information may be too uncertain to guide reservoir operation decisions and FU becomes the dominating factor; and (3) at a medium FH, reservoir performance depends on the complicating effects of FU and FH and EFH locates with a certain balanced level of FU and FH. The statistical characteristics of EFH are illustrated with case studies with deterministic forecast and ensemble forecast. Moreover, the impacts of temporal correlation of FU, inflow variability, evaporation loss, and reservoir capacity on EFH are explored.