Skip to main content
Log in

A univariate model for long-term streamflow forecasting

1. Development

  • Originals
  • Published:
Stochastic Hydrology and Hydraulics Aims and scope Submit manuscript

Abstract

This paper, the first in a series of two, employs the principle of maximum entropy (POME) via maximum entropy spectral analysis (MESA) to develop a univariate model for long-term streamflow forecasting. Three cases of streamflow forecasting are investigated: forward forecasting, backward forecasting (or reconstruction) and intermittent forecasting (or filling in missing records). Application of the model is discussed in the second paper.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  • Beck, M.B. 1978: A comparative study of dynamic models for DO-BOD-Algae interaction in a freshwater river. International Institute of Applied Systems Analysis, Report No. RR-78-19

  • Bergman, M.J.; Delleur, J.W. 1985a: Kalman filter estimation and prediction of daily streamflows, I. Review, algorithm and simulation experiments. Water Resources Bulletin 21 (5), 815–825

    Google Scholar 

  • Bergman, M.J.; Delleur, J.W. 1985b: Kalman filter estimation and prediction of daily streamflows, II. Application to the Potomac River. Water Resources Bulletin 21 (5), 826–832

    Google Scholar 

  • Box, G.E.P.; Jenkins, G. 1976: Time series analysis, forecasting and control. 2nd edition. San Francisco, California: Holden Day

    Google Scholar 

  • Bras, R.L.; Rodriguez-Iturbe, I. 1985: Random functions and hydrology. Reading, Massachusetts: Addison-Wesley Publishing Company

    Google Scholar 

  • Brazil, L.E.; Hudlow, M.D. 1981: Calibration procedures used with the National Weather Service river forecast system. In: Haimes, Y.Y.; Kindler, J. (eds.) Water and related resource systems, pp. 457–466. New York: Pergamon Press

    Google Scholar 

  • Burden, R.L.; Faires, J.D.; Reynolds, A.C. 1979: Numerical analysis. Boston, Massachusetts: Prindle, Weber and Schmidt

    Google Scholar 

  • Burg, J.P. 1975: Maximum entropy spectral analysis. Ph.D. Thesis, Stanford University, 123 p., Palo Alto, California, University Microfilms, pp. 75–25, 499

    Google Scholar 

  • Carlson, R.F.; MacCornick, A.J.A.; Watts, D.G. 1970: Application of linear models to four annual stream-flow series. Water Resources Research 6 (4), 1070–1088

    Google Scholar 

  • Chang, T.J.; Kavvas, M.L.; Delleur, J.W., 1982: Stochastic daily precipitation modeling and daily stream-flow transfer processes. Tech. Report No. 746, Water Resources Research Center, Purdue University, West Lafayette, Indiana

    Google Scholar 

  • Chatfield, C. 1984: The analysis of time series: An introduction. London, U.K.: Chapman and Hall

    Google Scholar 

  • Christensen, R.A. 1981: An exploratory application of entropy minimax to weather prediction: estimating the likelihood of multi-year droughts in California. In: Christensen, R.A. (ed.) Entropy minimax source book, Vol. IV: Applications, pp. 495–544. Lincoln, Massachusetts: Entropy Limited

    Google Scholar 

  • Copper, D.M.; Wood, E.F. 1982a: Identification of multivariate time series and multivariate input-output models. Water Resources Research 18 (4), 937–946

    Google Scholar 

  • Cooper, D.M.; Wood, E.F. 1982b: Parameter estimation of multiple input-output time series models: Application to rainfall-runoff processes. Water Resources Research 10 (5), 1352–1364

    Google Scholar 

  • Eilbert R.F.; Christensen, R.A. 1983: Performance of the entropy hydrological forecasts for California water years 1948–1977. Journal of Climate and Applied Meteorology 22, 1654–1657

    Google Scholar 

  • Georgakakos, K.P.; Bras, R.L. 1980: A statistical linearization approach to real time nonlinear flood routing. Technical Report 256, Ralph M. Parsons Laboratory, Dept. of Civil Engineering, MIT, Cambridge, Massachusetts

    Google Scholar 

  • Georgakakos, K.P.; Bras, R.L. 1982: Real-time, statistically linearized adaptive flood routing. Water Resources Research 18 (3), 513–524

    Google Scholar 

  • Gosain, A.K. 1984: Intercomparison of real-time highflow forecasting models for Yamuna catchment. Unpublished Ph.D. dissertation, Indian Institute of Technology, Delhi, India

    Google Scholar 

  • Hino, M. 1970: Runoff forecasts by linear predictive filter. Journal of Hydraulics Division, ASCE 96 (HY 3), 681–707

    Google Scholar 

  • Hosking, J.R.M. 1984: Modeling persistence in hydrologic time series using fractional differencing. Water Resources Research 20, 1898–1908

    Google Scholar 

  • Jaynes, E.T. 1982: On the rationale of maximum entropy methods. Proceedings of IEEE 70 (9), 939–952

    Google Scholar 

  • Karlsson, M.; Yakovitz, S. 1987a: Rainfall-runoff forecasting methods, old and new. Stochastic Hydrology and Hydraulics 2 (4), 303–318

    Google Scholar 

  • Karlsson, M.; Hakovitz, S. 1987b: Nearest-neighbor methods for non-parametric rainfall-runoff forecasting. Water Resources Research 23 (7), 1300–1308

    Google Scholar 

  • Kitanidis, P.K.; Bras, R.L. 1979: Colinearity and stability in the estimation of rainfall-runoff model parameters. Journal of Hydrology 42, 91–108

    Google Scholar 

  • Kitanidis, P.K.; Bras, R.L. 1980: Real-time forecasting with a conceptual hydrologic model, 2. Applications and results. Water Resources Research 16 (6), 1034–1044

    Google Scholar 

  • Kitanidis, P.K.; Lara, O.G.; Lane, R.W. 1984: Evaluation of streamflow data collection strategies for alluvial rivers. Journal of Hydrology 72, 85–103

    Google Scholar 

  • Klemes, V. 1974: The Hurst phenomenon: A puzzle? Water Resources Research 10 (4), 675–688

    Google Scholar 

  • Klemes, V.; 1982: Empirical and causal models in hydrology. In: Fiering, M.B. (ed.) Scientific basis of water resources management, pp. 95–104. Washington, D.C.: National Academy Press

    Google Scholar 

  • Krstanovic, P.F.; Singh, V.P. 1987: A multivariate stochastic flood analysis using entropy. In: Singh, V.P. Hydrologic frequency modeling, pp. 515–539. Dordrecht, Holland: D. Reidel Publishing Co.

    Google Scholar 

  • Krstanovic, P.F.; Singh, V.P. 1988: Application of entropy theory to multivariate hydrologic analysis. Technical Report WRR9, Dept. of Civil Engineering, Louisiana State University, Baton Rouge, Louisiana

    Google Scholar 

  • Krzysztofowitz, R. 1983: A Bayesian Markov model of the flood forecast process. Water Resources Research 19 (6), 1455–1465

    Google Scholar 

  • Krzysztofowitz, R. 1985: Bayesian models of forecasted time series. Water Resources Bulletin 21 (5), 805–814

    Google Scholar 

  • Krzysztofowitz, R.; Davis, D.R. 1983: A methodology for evaluation of flood forecasts-response systems. Water Resources Research 19 (6), 1423–1454

    Google Scholar 

  • Lawrence, A.J.; Kottegoda, N.T. 1977: Stochastic modeling of riverflow time series (with discussion). Journal Royal Statistical Society, Series A 140, 1–47

    Google Scholar 

  • Levinson, N. 1946: The Wiener rms criterion in filter design and prediction. Journal of Mathematical Physics 25, 261–278

    Google Scholar 

  • Mandelbrot, B.B.; Wallis, J.R. 1968: Noah, Joseph and operational hydrology. Water Resources Research 4, 908–918

    Google Scholar 

  • Mandelbrot, B.B.; Wallis, J.R. 1969: Computer experiments with fractional Gaussian noises. Water Resources Research 5, 321–340

    Google Scholar 

  • McLeod, A.J.; Hipel, K.W. 1978: Preservation of the rescaled adjusted range, 1. A reassessment of the Hurst phenomenon. Water Resources Research 14 (3), 491–508

    Google Scholar 

  • Nemec, J. 1986: Design and operation of forecasting operational real-time hydrological systems (FORTH). In: Kraijenhoff, D.A.; Moll, J.R. (eds.) River flow modeling and forecasting, pp. 299–327. Dordrecht, Holland: D. Reidel Publishing Co.

    Google Scholar 

  • O'Connell, P.E. 1974: Stochastic modeling of long-term persistence in streamflow sequences. Ph.D. Thesis, Dept. of Civil Engineering, Imperical College, London, U.K.

    Google Scholar 

  • Padmanabhan, G.; Rao, A.R. 1986: Maximum entropy spectra of some rainfall and river flow time series from southern and central India. Theoretical and Applied Climatology 37, 63–73

    Google Scholar 

  • Padmanabhan, G.; Rao, A.R. 1988: Maximum entropy spectral analysis of hydrologic data. Water Resources Research 24 (9), 1519–1533

    Google Scholar 

  • Potter, K.W. 1976: Evidence for nonstationarity as a physical explanation of the Hurst phenomenon. Water Resources Research 12, 1047–1052

    Google Scholar 

  • Puente, C.E.; Bras, R.L. 1987: Application of nonlinear filtering in the real-time forecasting of river flows. Water Resources Research 23 (4), 675–682

    Google Scholar 

  • Salas, J.D.; Delleur, J.W.; Yevjevich, V.; Lane, W.L. 1980: Applied modeling of hydrologic times series. Water Resources Publications, Littleton, Colorado

    Google Scholar 

  • Schultz, G.A. 1986: Introduction. In: Kraijenhoff, D.A.; Moll, J.R. (eds.) River flow modeling and forecasting, pp. 1–10. Dordrecht, Holland: D. Reidel Publishing Company

    Google Scholar 

  • Sorooshian, S. 1983: Surface water hydrology: on line estimation. Reviews of Geophysics and Space Physics 21 (3), 706–721

    Google Scholar 

  • Sorooshian, S.; Gupta, V.K.; Fulton, Y.L. 1982: Parameter estimation of conceptual rainfall-runoff models assuming autocorrelated streamflow data errors — a case study. In: Singh, V.P. (ed.) Statistical analysis of rainfall and runoff, pp. 491–504. Water Resources Publications, Littleton, Colorado

    Google Scholar 

  • Souza, R.C. 1978: A Bayesian entropy approach to forecasting. Ph.D. Thesis, University of Warwick, Coventry, U.K.

    Google Scholar 

  • Souza, R.C. 1981: A Bayesian entropy approach to forecasting: the multistate model. In: Anderson, O. D. and Perryman, M. R. (eds.) Time series analysis, pp. 535–542. Amsterdam, Holland: North Holland Publishing Company

    Google Scholar 

  • Souza, R.C. 1982: A Bayesian entropy approach to forecasting: the Binomial Beta model. In: Anderson, O. D. and Perryman, M. R. (eds.) Time series analysis, pp. 475–486. Amsterdam, Holland: North Holland Publishing Company

    Google Scholar 

  • Souza, R.C. 1983: A general Bayesian formulation for the steady-state model. In: Anderson, O.D. (ed.) Time series analysis: Theory and practice III, pp. 43–50. Amsterdam, Holland: North Holland Publishing Company

    Google Scholar 

  • Van den Boss, A. 1971: Alternative interpretation of maximum entropy spectral analysis. IEEE Transactions on Information Theory IT-17, 493–494

    Google Scholar 

  • Thomas, H.A.; Fiering, M. B. 1962: Mathematical synthesis of streamflow sequences for the analysis of river basins by simulation. In: Mass, M. et al. (eds.) Design of water resources systems, pp. 459–463. Cambridge, Massachusetts: Harvard University Press

    Google Scholar 

  • Wiener, N. 1950: Extrapolation, interpolation and smoothing of stationary time series with engineering application. New York, New York: John Wiley and Sons, Inc.

    Google Scholar 

  • WMO. 1974: International glossary of hydrology. UNESCO and WMO, Geneve, Switzerland

    Google Scholar 

  • WMO, 1975: Intercomparison of conceptual models used in operational hydrologic forecasting. Operational Hydrology Report No. 7, Secretariat of WHO, Geneva, Switzerland

    Google Scholar 

  • WMO, 1983: Guide to hydrological practice. WMO, No. 168, 4th edition, WMO, Geneve, Switzerland

    Google Scholar 

  • Yakowitz, S. 1979: A nonparametric Markov model for daily river flow. Water Resources Research 15 (5), 1035–1043

    Google Scholar 

  • Yakowitz, S. 1985: Markov flood models and the flood warning program. Water Resources Research 21 (1), 81–88

    Google Scholar 

  • Yevjevich, V. 1963: Fluctuations of wet and years (Part I), Research data assembly and mathematical models. Hydrology Paper I, Colorado State University, Fort Collins, Colorado

    Google Scholar 

  • Young, P.C. 1974: Recursive approaches to time series analysis. Bulletin Institute Math. Application 10, 209–224

    Google Scholar 

  • Young, P.C. 1986: Time series methods and recursive estimation of hydrological system analysis. In: Kraijenhoff, D.A. and Moll, J.R. (eds.) River flow modeling and forecasting, pp. 129–180. Dordrecht, Holland: D. Reidel Publishing Company

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Krstanovic, P.F., Singh, V.P. A univariate model for long-term streamflow forecasting. Stochastic Hydrol Hydraul 5, 173–188 (1991). https://doi.org/10.1007/BF01544056

Download citation

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01544056

Key words

Navigation