Use of Monte Carlo Techniques in the Design and Operation of a Multipurpose Reservoir System

Abstract

The output from most analytical procedures used to set firm .output levels for water projects is not associated with any given probability of failure to meet those output objectives. As a result, such output cannot always be used with confidence in the design and operation of water resource systems. A simple procedure is proposed that uses Monte Carlo techniques in deriving the optimum contract levels for a multipurpose system subject to constraints imposed by stated maximum permissible probabilities of failure to meet firm contract deliveries. The procedure is tested by analyzing a particular reservoir system. Similar procedures can be designed to handle multireservoir, multipurpose systems with a large number of such constraints and can be used to choose between alternative designs and fix optimum contract levels and release rules. Probability tables derived from such analyses can be used to improve the operational efficiency of water resource systems.By using Monte Carlo techniques to generate long or multiple streamflow records and then analyzing the output of a water resource system with these records as inputs, one can test the system's response to periods that are longer and contain greater extremes than the historical record. In addition, one can obtain an estimate of the probability of failure associated with any design or operational criteria. This method of analysis originated with work such as Hazen's [1914], but it was not until the digital computer was perfected that its application became practical on a large scale. More recently Fiering [1961] and Hu•schrnidt and Fiering [1966] described an application of the method to the design of a single purpose reservoir and pointed out its simplicity in interpreting and analyzing the results.At present computers are widely available, and yet in recent years an increasing percentage of research has been directed toward the use of various programing techniques and much less has been done with regard to Monte Carlo analysis. Linear and dynamic programing [Hall and Shephard, 196,7] have been shown to be very powerful tools for the optimum planning and design of water resource systems for * Now with the World Meteorological Organization, Geneva, Switzerland. cases in which the inflows and demands are deterministic or can be treated as random sets 819

Hydrology Handbook

“…This technique has led to several proposals for generating synthetic stream flow sequences. Although the general objective is to produce stream flow sequences that preserve the statistical characteristics of the historical data, there is no general agreement on how many and which of these characteristics should be preserved (Askew et al, 1971).…”

Runoff, Stream Flow, Reservoir Yield, and Water Quality

“…Although the general objective is to produce stream flow sequences that preserve the statistical characteristics of the historical data, there is no general agreement on how many and which of these characteristics should be preserved (Askew et al, 1971).…”

Evaluation of dam overtopping probability induced by flood and wind

“…In earlier studies (Askew et al 1971;Cheng et al 1982;Afshar and Marino 1990;Meon 1992;Pohl 1999;Kwon and Moon 2006;Kuo et al 2007Kuo et al , 2008, dam overtopping probability was assessed without considering the possible errors arising from adopting a particular distribution model for flood data or the uncertainty of estimated flood quantiles. Therefore, this study takes into account the two types of errors and proposes a sampling scheme that combines the importance sampling (IS) and the Latin hypercube sampling (LHS) for generating random floods and wind speeds in dam safety evaluation.…”

“…Yeh and Tung (1993) applied the FOSM method to evaluate the uncertainty and sensitivity of a pit-migration model for sand and gravel mining from riverbed. Askew et al (1971) used Monte Carlo sampling (MCS) technique to evaluate the design of a multi-object reservoir system. McKay (1988) developed the LHS method, and it was proved to achieve a convergence in system performance more quickly with less samples than the MCS by various studies (Hall et al 2005;Khanal et al 2006;Manache and Melching 2004;Salas and Shin 1999;Smith and Goodrich 2000).…”