Bootstrap Position Analysis for Forecasting Low Flow Frequency
Publication: Journal of Water Resources Planning and Management
Volume 123, Issue 6
Abstract
A method of random resampling of residuals from stochastic models is used to generate a large number of 12-month-long traces of natural monthly runoff to be used in a position analysis model for a water-supply storage and delivery system. Position analysis uses the traces to forecast the likelihood of specified outcomes such as reservoir levels falling below a specified level or streamflows falling below statutory passing flows conditioned on the current reservoir levels and streamflows. The advantages of this resampling scheme, called bootstrap position analysis, are that it does not rely on the unverifiable assumption of normality, fewer parameters need to be estimated directly from the data, and accounting for parameter uncertainty is easily done. For a given set of operating rules and water-use requirements for a system, water managers can use such a model as a decision-making tool to evaluate different operating rules.
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References
1.
Cover, K. A., and Unny, T. E. (1986). “Application of computer intensive statistics to parameter uncertainty in streamflow synthesis.”Water Resour. Bull. 22(3), 495–507.
2.
Day, G. N.(1985). “Extended stream flow forecasting using NWSRFS.”J. Water Resour. Plng. and Mgmt., ASCE, 111(2), 157–170.
3.
Dunne, P., and Tasker, G. (1996). “Computer model of the Raritan River basin water-supply system in central New Jersey.”USGS Open-file Rep. No. 96-360.
4.
Efron, B.(1979). “Bootstrap methods: another look at the jackknife.”Ann. of Statistics, 7(1), 1–26.
5.
Efron, B. (1982). The jackknife, the bootstrap and other resampling plans. Society for Industrial and Applied Mathematics, Philadelphia, Pa.
6.
Haltiner, J. P., and Salas, J. D.(1988). “Development and testing of a multivariate seasonal ARMA(1,1) model.”J Hydro., Amsterdam, The Netherlands, 104, 247–272.
7.
Hirsch, R. M.(1978). “Risk analysis for a water-supply system—Occoquan Reservoir, Fairfax and Prince William counties, Virginia.”Hydro. Sci. Bull., 23(4), 476–505.
8.
Hirsch, R. M. (1979). “Synthetic hydrology and water supply reliability.”Water Resour. Res., 15(6) 1603–1615.
9.
Hirsch, R. M.(1981). “Stochastic hydrologic model for drought management.”J. Water Resour. Plng. and Mgmt. Div., ASCE, 107(2), 303–313.
10.
Hirsch, R. M.(1982). “A comparison of four streamflow record extension techniques.”Water Resour. Res., 18(4), 1081–1088.
11.
Hirsch, R. M., Helsel, D. R., Cohn, T. A., and Gilroy E. (1993). “Statistical analysis of hydrologic data.”Handbook of hydrology, D. R. Maidment, ed. McGraw-Hill, Inc., New York, N.Y. 17.1–17.55.
12.
Kunsch, H. R.(1989). “The jackknife and the bootstrap for general stationary observations.”Ann. of Statistics, 17(3), 1217–1241.
13.
Lall, U., and Sharma, A. (1996). A nearest neighbor bootstrap for resampling hydrologic time series.”Water Resour. Res., 32(3), 679–693.
14.
Loucks, D. P., Stedinger, J. R., and Haith, D. A. (1981). Water Resour. Syst. Plng. and Anal. Prentice-Hall, Inc., Englewood Cliffs, N.J.
15.
Moss, M. E., and Tasker, G. D.(1991). “An intercomparison of hydrological network-design technologies.”Hydrological Sci. J., Oxford, U.K., 36(3), 209–221.
16.
Northeast Regional Climate Center. (1996). Northeast climate impacts. Northeast Regional Climate Center, Cornell University, Ithaca, N.Y.
17.
Oliverira, C. G., Kelman, J., Pereira, M. V. F., and Stedinger, J. R.(1988). “A representation of spatial correlations in large stochastic seasonal streamflow models.”Water Resour. Res., 24(5), 781–785.
18.
Pereira, M. V. F., Oliverira, G. C., Costa, C. G., and Kelman, J. (1984). Stochastic streamflow models for hydroelectric systems.”Water Resour. Res., 20(3), 379–390.
19.
Rasmussen, P. F., Salas, J. D., Fagherazzi, L., Rassam, J., and Bobee, B.(1996). “Estimation and validation of contemporaneous PARMA models for streamflow simulation.”Water Resour. Res., 32(10), 3151–3160.
20.
Salas, J. D. (1993). “Analysis and modeling of hydrologic time series.”Handbook of hydrology, D. R. Maidment, ed. McGraw-Hill, Inc., New York, N.Y., 19.1–19.72.
21.
Salas, J. D., Boes, D. C., and Smith, R. A. (1982). “Estimation of ARMA models with seasonal parameters.”Water Resour. Res., 18(4) 1006–1010.
22.
Salas, J. D., Dellur, J. W., Yevjevich, V., and Lane, W. L. (1980). Applied modeling of hydrologic time series. Water Resources Publications, Littleton, Colo.
23.
Salas, J. D., Tabios, Guillermo Q., and Bartolini, P.(1985). “Approaches to multivariate modeling of water resources time series.”Water Resour. Bull., 21(4), 683–708.
24.
Sharma, A., Tarboton, D. G., and Lall, U.(1997). “Streamflow simulation: a nonparametric approach.”Water Resour. Res., 33(2), 291–308.
25.
Stedinger, J. R., and Taylor, M. R.(1982). “Synthetic streamflow generation, 2. Effect of parameter uncertainty.”Water Resour. Res., 18(4), 919–924.
26.
Tasker, G. D.(1987). “Comparison of methods for estimating low flow characteristics of streams.”Water Resour. Bull., 23(6), 1077–1083.
27.
Thombs, L. A., and Schucany, W. R.(1990). “Bootstrap prediction intervals for autoregression.”J. Am. Statistical Assoc., 85(410), 486–492.
28.
Valencia, D. R., and Schaake, J. C. (1973). “Disaggregation process in stochastic hydrology.”Water Resour. Res., 9(3) 580–585.
29.
Vecchia, A. V.(1985a). “Maximum likelihood estimation for periodic autoregressive moving average models.”Technometrics, 27(4), 375–384.
30.
Vecchia, A. V.(1985b). “Periodic autoregressive-moving average (PARMA) modeling with applications to water resources.”Water Resour. Bull., 21(5), 721–730.
31.
Vecchia, A. V., Obeysekera, J. T. B., Salas, J. D., and Boes, D. C.(1983). “Aggregation and estimation for low-order periodic ARMA models”Water Resour. Res., 19(5), 1297–1306.
32.
Vogel, R. M., and Stedinger, J. R.(1985). “Minimum variance streamflow augmentation procedures.”Water Resour. Res., 21(5), 715–723.
33.
Vogel, R. M., and Shallcross, A. L.(1996). “The moving blocks bootstrap versus parametric time series models.”Water Resour. Res., 32(6), 1875–1882.
34.
Woo, M. K.(1989). “Confidence intervals of optimum risk-based hydraulic design parameters.”Can. Water Resour. J., 14(2), 10–16.
35.
Zucchini, W., and Adamson, P. T.(1989). “Bootstrap confidence intervals for design storms from exceedence series.”Hydrological Sci. J., Oxford, U.K., 34(1), 41–48.
Information & Authors
Information
Published In
Journal of Water Resources Planning and Management
Volume 123 • Issue 6 • November 1997
Pages: 359 - 367
Copyright
Copyright © 1997 American Society of Civil Engineers.
History
Published online: Nov 1, 1997
Published in print: Nov 1997
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