Parsimonious SVD/MAR(1) Procedure for Generating Multisite Multiseason Flows
Publication: Journal of Hydrologic Engineering
Volume 14, Issue 5
Abstract
This paper proposes a stochastic procedure for generating seasonal flows at multiple locations simultaneously. The proposed procedure uses the technique of singular value decomposition (SVD) to transform a historical flow-data matrix into its standardized principal components (SPCs), and then applies the simple Kaiser’s cut-off rule to retain only the significant SPCs (SSPCs) for further fitting the multivariate autoregressive scheme of order one [MAR(1)] to them. It is shown that the Kaiser’s rule is proper for giving the size of the SSPCs of multisite seasonal-flow records because application of the rule yields only a few more SSPCs for each additional site, and its dimension is reasonably definitive. The comparison of the proposed SVD/MAR(1) procedure with the existing one has demonstrated that the proposed procedure has less parameters than the existing one due to taking into consideration the SSPCs only. In addition, the ability of the parsimonious procedure to reproduce adequately the historical key statistics, storage-, and drought-related characteristics at considered monthly and successive aggregation levels, still remains the same as the existing candidate.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
Financial support from the Thailand Research Fund (UNSPECIFIEDPDF24/2542) is acknowledged. The writer is thankful to the Royal Irrigation Department (Thailand) for providing monthly flow records used in this study.
References
Bras, R. L., and Rodriguez-Iturbe, I. (1985). Random functions and hydrology, Addison-Wesley, Reading, Mass.
Camacho, F., McLeod, A. I., and Hipel, K. W. (1985). “Contemporaneous autoregressive-moving average (CARMA) modeling in water resources.” Water Resour. Bull., 21(4), 709–720.
Cavadias, G. S. (1986). “A multivariate seasonal model for streamflow simulation.” La recherche en Hydrologie au Québec, V.-T.-V. Nguyen and Y. Faucher, eds., Les Presses de l’Université du Québec, Quebec, Canada, 58–77.
Chaleeraktrakoon, C. (1999). “Stochastic procedure for generating seasonal flows.” J. Hydrol. Eng., 4(4), 337–343.
Chambers, J. M. (1977). Computational methods for data analysis, Wiley, New York.
Fiering, M. B. (1967). Streamflow synthesis, Harvard Univ. Press, Cambridge, Mass.
Gnanadesikan, R. (1977). Methods for statistical data analysis of multivariate observations, Wiley, New York.
Green, P. E. (1978). Analyzing mutivariate data, Dryden Press, Hinsdale, Ill.
Grygier, J. C., and Stedinger, J. R. (1988). “Condensed disaggregation procedure and conservation correlations for stochastic hydrology.” Water Resour. Res., 24(10), 1574–1584.
Grygier, J. C., and Stedinger, J. R. (1990). “SPIGOT, a synthetic streamflow generation software package.” Technical Description, Ver. 2.5, School of Civil and Environmental Engineering, Cornell Univ., Ithaca, N.Y.
Haltiner, J. P., and Salas, J. D. (1988). “Development and testing of a multivariate, seasonal ARMA(1,1) model.” J. Hydrol., 104, 247–272.
Harms, A. A., and Campbell, T. H. (1967). “An extension to the Thomas-Fiering model for the sequential generation of streamflow.” Water Resour. Res., 3(3), 653–661.
Hipel, K. W., and McLeod, A. I. (1978). “Preservation of the rescaled adjusted range. 2: Simulation studies using Box-Jenkins models.” Water Resour. Res., 14(3), 509–516.
Hoshi, K., Burges, S. J., and Yamaoka, I. (1978). “Reservoir design capacities for various seasonal operational hydrology models.” Proc., Japanese Soc. Civil Eng., 273, 121–134.
Jolliffe, I. T. (1986). “Cumulative percentage of total variation.” Principal component analysis, Springer, New York, 93–94.
Jöreskog, K. G., Klovan, J. E., and Reyment, R. A. (1976). Geological factor analysis, Elsevier, New York.
Kaiser, H. F. (1960). “The application of electronic computers to factor analysis.” Educ. Psychol. Meas., 20, 141–151.
Koutsoyiannis, D. (1992). “A nonlinear disaggregation method with a reduced parameter set for simulation of hydrologic series.” Water Resour. Res., 28(12), 3175–3191.
Lane, W. L. (1982). “Correlated parameter estimates for disaggregation schemes.” Statistical analysis of rainfall and runoff, V. P. Singh, ed., Water Resources, Littleton, Colo., 505–530.
Lane, W. L., and Fervert, D. K. (1990). Applied stochastic techniques: User’s manual, personal computer version, Bureau of Reclamation, Engineering, and Research Center, Denver, Colo.
Loucks, D. P., Stedinger, J. R., and Haith, D. A. (1981). Water resource systems planning and analysis, Prentice-Hall, Englewood Cliffs, N.J.
Maass, A., Hufschmidt, N. M., Dorfman, R., Thomas, H. A., Jr., Marglin, S. A., and Fair, G. M. (1962). Design of water resource systems, Harvard University Press, Cambridge, Mass.
Matalas, N. C. (1967). “Mathematical assessment of synthetic hydrology.” Water Resour. Res., 3(4), 937–945.
Mejia, J. M., and Rousselle, J. (1976). “Disaggregation models in hydrology revisited.” Water Resour. Res., 12(2), 185–186.
O’Connell, P. E. (1974). “Stochastic modeling of long-term persistence in streamflow sequences.” Ph.D. thesis, Imperial College, Univ. of London.
Oliveira, G. C., Kelman, J., Pereira, M. V. F., and Stedinger, J. R. (1988). “A representation of spatial cross correlations in large stochastic seasonal streamflow models.” Water Resour. Res., 24(5), 781–785.
Pegram, G. G. S., and James, W. (1972). “Multilag multivariate autoregressive model for the generation of operational hydrology.” Water Resour. Res., 8(4), 1074–1076.
Press, W. H., Flannery, B. P., Teukolsky, S. A., and Verttering, W. T. (1993). Numerical recipes in C: The art of scientific computing, Cambridge University Press, Cambridge, U.K.
Salas, J. D., Delleur, J. W., Yevjevich, V., and Lane, W. L. (1980). Applied modelling of hydrologic time series, Water Resources, Littleton, Colo.
Salas, J. D., and Pegram, G. G. S. (1977). “A seasonal multivariate multilag autoregressive model in hydrology.” Proc., 3rd Int. Symp. of Theoretical and Applied Hydrology, Colorado State Univ., Fort Collins, Colo., 125–145.
Salas, J. D., Sevinsson, O. G., Lane, W. L., and Frevert, D. K. (2006). “Stochastic streamflow simulation using SAMS-2003.” J. Irrig. Drain. Eng., 132(2), 112–122.
Salas, J. D., Tabios, G. Q., III, and Bartolini, P. (1985). “Approaches to multivariate modeling of water resources time series.” Water Resour. Bull., 21(4), 683–708.
Santos, E. G., and Salas, J. D. (1992). “Stepwise disaggregation scheme for synthetic hydrology.” J. Hydraul. Eng., 118(5), 765–784.
Srikanthan, R., and McMahon, T. A. (2001). “Stochastic generation of annual, monthly and daily climate data: A review.” Hydrology Earth Syst. Sci., 5(4), 653–670.
Stedinger, J. R. (1980). “Fitting log normal distributions to hydrologic data.” Water Resour. Res., 16(3), 481–490.
Stedinger, J. R., Lettenmaier, D. P., and Vogel, R. M. (1985). “Multisite ARMA(1,1) and disaggregation models for annual streamflow generation.” Water Resour. Res., 21(4), 497–509.
Stedinger, J. R., and Vogel, R. M. (1984). “Disaggregation procedures for generating serially correlated flow vectors.” Water Resour. Res., 20(1), 47–56.
Stedinger, J. R., Vogel, R. M., and Foufoula-Georgiou, E. (1993). “Frequency analysis of extreme events.” Handbook of hydrology, D. R. Maidment, ed., McGraw-Hill, New York.
Tao, P. C., and Delleur, J. W. (1976). “Multistation multiyear synthesis of hydrologic time series by disaggregation.” Water Resour. Res., 12(6), 1303–1312.
Tarboton, D. G., Sharma, A., and Lall, U. (1998). “Disaggregation procedures for stochastic hydrology based on nonparametric density estimation.” Water Resour. Res., 34(1), 107–120.
Valencia, D. R., and Schaake, J. C. (1973). “Disaggregation processes in stochastic hydrology.” Water Resour. Res., 9(3), 580–585.
Wallis, J. R., and O’Connell, P. E. (1973). “Firm reservoir yield—How reliable are hydrological records?” Hydrol. Sci. Bull., 18, 347–365.
Yevjevich, V. (1965). “The application of surplus, deficit and range in hydrology.” Hydrology Paper 10, Colorado State Univ., Fort Collins, Colo.
Yevjevich, V. (1967). “An objective approach to definitions and investigations of continental hydrologic droughts.” Hydrology Paper 23, Colorado State Univ., Fort Collins, Colo.
Young, G. K., and Jettmar, R. U. (1976). “Modeling monthly hydrologic persistence.” Water Resour. Res., 12(5), 829–835.
Young, G. K., and Pisano, W. C. (1968). “Operational hydrology using residuals.” J. Hydr. Div., 94(4), 909–923.
Information & Authors
Information
Published In
Copyright
© 2009 ASCE.
History
Received: Jun 18, 2007
Accepted: Jul 9, 2008
Published online: Feb 18, 2009
Published in print: May 2009
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.