Reexamination of Critical Period for Reservoir Design and Operation Jiing-Yun You 1 and Ximing Cai 2 Abstract: Reservoir operating rules are often based on deterministic models using critical period CP analysis, which results in very conservative decisions. CP is defined as the historical hydrologic period that includes the lowest flow or the most severe drought, which represents functionally as the full-empty cycle of reservoir storage under a given firm yield. This paper compares CP with another time scale, the forecast horizon FH underlying hedging rule policies for reservoir operation. When the decisions in the initial few periods are not affected by forecast data beyond a certain period, the period is known as FH, and the number of the initial periods is known as the decision horizon. When a reservoir operation policy follows the concept of CP, CP is used as FH and the optimal yield generated within the FH is the firm yield. FH as long as the CP is not realistic because in the real world data for a such a long future period is unavailable; and using CP as FH is not effective either, because CP—the longest FH-involving the most severe drought leads to very conservative release decisions, i.e., the “near-zero-risk” decision and the time preference of utility diminishes the influence of hedging for over long periods. DOI: 10.1061/ASCE0733-94962009135:5392 CE Database subject headings: Water supply; Reservoir operation; Optimization; Planning. Introduction The concept of critical period CP, which was interpreted as a historical hydrologic period that included the lowest flow or the most severe drought, was systematically studied by Hall et al. 1969 for reservoir design and operation. They defined CP func- tionally as the full-empty cycle of reservoir storage under a given firm yield. Following Hall et al. 1969, McMahon and Mein 1986, Oguz and Bayazit 1991, and Montaseri and Adeloye 1999 elaborated the concept of CP and provided different tech- niques for estimating the value of CP, using either historical records or synthesized data. CP was primarily determined by the sequent peak algorithm i.e., Rippl’s method with consideration of the combination of demand and critical hydrologic conditions USACE 1997. Once CP is determined, it can be used for several purposes of reservoir design and operations: 1 determining the minimum required res- ervoir storage capacity using the CP hydrologic inflow series for a target delivery and 2 determining the maximum delivery that can be always produced during the CP, known as the firm yield, given the storage capacity of a reservoir. Following the U.S. Army Corps of Engineers USACE 1997, besides determining the firm yield, CP has also been used to derive the operation curves that are regularly used by reservoir managers. An opera- tion curve establishes a tentative plan of operation which consid- ers the hydrologic date, flood control, and reservoir sedimentation as well as conservation requirements that can be undertaken by performing detailed sequential routing of the CP and several other periods of low flow. Once the operation curve is developed, “ad- ditional sequential routings for the entire period of flow record are then made using the rule curve developed in the CP studies” USACE 1997. The operational rules developed with CP are usually extended to deal with drought events. CP is supposed to represent the most severe situation for reservoir operation, but it is based on histori- cal hydrological records and it assumes that the most severe hy- drological condition in the future will repeat the observed severe event experienced in the history Loucks et al. 1981. This as- sumption forms a limitation for the CP-based method since the future hydrological conditions can differ from the historical record. The CP-based method also leads to very conservative res- ervoir management only suitable for very risk adverse decision makers Draper 2001 because the probability of the “most se- vere” drought is very low theoretically, it should be zero. In general, since the CP-based method assumes fully known deter- ministic information, it facilitates the traditional linear decision rules or standard operating policies which ensure an optimal op- eration under a static situation with a given demand Shih and ReVelle 1994. Thus, the method is not suitable for deriving de- cision rules, such as hedging rules, regarding stochastic utility or cost optimization under incomplete information. With these concerns in mind, this paper examines the rationale of the CP-based rules considering the imperfect forecast of future periods. The question to address is: When the CP-based rules are applied to real world reservoir operations that face future inflow uncertainty, what limitations are imposed? In the following, we first introduce hedging rules and the time scale of hedging for stochastic reservoir operations considering inflow uncertainty. We then show that CP is a special time scale for hedging and discuss 1 Ph.D. Candidate, Dept. of Civil and Environmental Engineering, Univ. of Illinois, Urbana-Champaign, IL 61801. 2 Associate Professor, Dept. of Civil and Environmental Engineering, Univ. of Illinois, Urbana-Champaign, IL 61801 corresponding author. E-mail: xmcai@uiuc.edu Note. This manuscript was submitted on October 22, 2007; approved on December 11, 2008; published online on August 14, 2009. Discussion period open until February 1, 2010; separate discussions must be submit- ted for individual papers. This paper is part of the Journal of Water Resources Planning and Management, Vol. 135, No. 5, September 1, 2009. ©ASCE, ISSN 0733-9496/2009/5-392–396/$25.00. 392 / JOURNAL OF WATER RESOURCES PLANNING AND MANAGEMENT © ASCE / SEPTEMBER/OCTOBER 2009 Downloaded 25 Aug 2009 to 140.112.4.234. Redistribution subject to ASCE license or copyright; see http://pubs.asce.org/copyright