Generalized storage-reliability-yield relationships

Abstract Traditionally water resource engineers have employed Rippl's mass curve approach or its automated equivalent sequent peak alogrithm, in conjunction with the historical streamflow sequence to obtain a single estimate of the design capacity of a storage reservoir. More recently stochastic streamflow models have been recommended for use in deriving the probability distribution of the required capacity of a storage reservoir to maintain a prespecified release. The use of stochastic streamflow models in conjunction with the sequent peak algorithm leads to a storage-reliability-yield (S-R-Y) relationship. This study develops approximate but general expressions which describe the over-year S-R-Y relationship when annual streamflows are log normal and follow a first-order autoregressive model. These expressions were developed for three reasons: (1) to provide preliminary design capacity or yield estimates for storage reservoirs governed by over-year storage requirements; (2) to improve our understanding of the S-R-Y relationship; and (3) to facilitate Monte-Carlo experiments which examine the sampling properties of reservoir design capacity and/or yield estimates.

[1]  Dennis P. Lettenmaier,et al.  Operational assessment of hydrologic models of long-term persistence , 1977 .

[2]  Brent M. Troutman.  Reservoir storage with dependent, periodic net inputs , 1978 .

[3]  N. T. Kottegoda,et al.  Stochastic Modelling of Riverflow Time Series , 1977 .

[4]  Guillermo J. Vicens,et al.  Bayesian generation of synthetic streamflows , 1975 .

[5]  Jery R. Stedinger,et al.  The value of stochastic streamflow models in overyear reservoir design applications , 1988 .

[6]  Norman R. Draper,et al.  Applied regression analysis (2. ed.) , 1981, Wiley series in probability and mathematical statistics.

[7]  W. Rippl.  The capacity of storage reservoirs for water supply , 1883 .

[8]  Daniel P. Loucks,et al.  Some Comments on Linear Decision Rules and Chance Constraints , 1970 .

[9]  Jery R. Stedinger,et al.  Synthetic streamflow generation: 1. Model verification and validation , 1982 .

[10]  N. C. Matalas,et al.  Autocorrelation of rainfall and streamflow minimums , 1963 .

[11]  R. Srikanthan,et al.  Long-memory flow models in reservoir analysis: What is their practical value? , 1981 .

[12]  K. Potter.  Sequent Peak Procedure: Minimum Reservoir Capacity Subject to Constraint on Final Storage , 1977 .

[13]  Range and deficit analysis using Markov chains , 1975 .

[14]  Allen Hazen,et al.  Storage to be Provided Impounding Reservoirs for Municipal Water Supply , 1913 .

[15]  Jery R. Stedinger,et al.  A condensed disaggregation model for incorporating parameter uncertainty into monthly reservoir simulations , 1985 .

[16]  V. Klemeš.  Storage mass‐curve analysis in a systems‐analytic perspective , 1979 .

[17]  Ideal reservoir capacity as a function of yield and risk , 1982 .

[18]  V. Klemeš,et al.  Applied Stochastic Theory of Storage in Evolution , 1981 .

[19]  David T. Howell,et al.  Effects of serially correlated inflows on reservoir behavior , 1972 .

[20]  Robert M. Hirsch,et al.  Synthetic hydrology and water supply reliability , 1979 .

[21]  Richard M. Vogel,et al.  The Probability Plot Correlation Coefficient Test for the Normal, Lognormal, and Gumbel Distributional Hypotheses , 1986 .

[22]  J. Filliben.  The Probability Plot Correlation Coefficient Test for Normality , 1975 .

[23]  R. K. Linsley,et al.  Some Factors Influencing Required Reservoir Storage , 1971 .

[24]  N. Draper,et al.  Applied Regression Analysis. , 1967 .

[25]  Jery R. Stedinger,et al.  Synthetic streamflow generation: 2. Effect of parameter uncertainty , 1982 .

[26]  D. Lettenmaier,et al.  An operational approach to preserving skew in hydrologic models of long‐term persistence , 1977 .

[27]  Jery R. Stedinger,et al.  Fitting log normal distributions to hydrologic data , 1980 .

[28]  J. R. Wallis,et al.  Sensitivity of reservoir design to the generating mechanism of inflows , 1972 .

[29]  H. Thomas.  Mathematical synthesis of streamflow sequences for the analysis of river basin by simulation , 1962 .

[30]  T. McMahon,et al.  Reservoir capacity and yield , 1978 .

[31]  J. Stedinger,et al.  Water resource systems planning and analysis , 1981 .

[32]  N. Draper,et al.  Applied Regression Analysis , 1966 .

[33]  Harold A Thomas,et al.  OPERATIONS RESEARCH IN WATER QUALITY MANAGEMENT. , 1963 .