Hybrid, Markov Chain-Based Model for Daily Streamflow Generation at Multiple Catchment Sites
Publication: Journal of Hydrologic Engineering
Volume 11, Issue 3
Abstract
A hybrid, seasonal, Markov chain-based model is formulated for daily streamflow generation at multiple sites of a watershed. Diurnal increments of the rising limb of the main channel hydrograph were stochastically generated using fitted, seasonally varying distributions in combination with an additive noise term, the standard deviation of which depended linearly on the actual value of the generated increment. Increments of the ascension hydrograph values at the tributary sites were related by third- or second-order polynomials to the main channel ones, together with an additive noise term, the standard deviation of which depended nonlinearly on the main channel’s actual increment value. The recession flow rates of the tributaries, as well as of the main channel, were allowed to decay deterministically in a nonlinear way. The model-generated daily values retain the short-term characteristics of the original measured time series (i.e., the general shape of the hydrograph) as well as the probability distributions and basic long-term statistics (mean, variance, skewness, autocorrelation structure, and zero-lag cross correlations) of the measured values. Probability distributions of the annual maxima, means, and minima of the measured daily values were also well replicated.
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Acknowledgments
This work has been supported by the Hungarian Research and Development Project: “Flood Risk Analysis,” Grant No. UNSPECIFIEDNKFP 3/067/2001 by the Hungarian American Joint Research Fund (MAKA). The writers are grateful to Charles Flowerday for his editorial help and to Margit Horosz-Gulyas for her help with the figures. The views, conclusions, and opinions expressed in this paper are solely those of the writers and not the University of Nebraska, State of Nebraska, or any political subdivision thereof. This paper is a contribution of the University of Nebraska Agricultural Research Division, Lincoln, NE 68583, Journal Series No. 14518.
References
Aksoy, H. (2003). “Markov chain-based modeling techniques for stochastic generation of daily intermittent streamflows.” Adv. Water Resour., 26, 663–671.
Aksoy, H., Bayazit, M., and Wittenberg, H. (2001). “Probabilistic approach to modeling of recession curves.” Hydrol. Sci. J., 46(2), 269–285.
Bernier, J. (1970). “Inventaire des modeles de processus stochastiques applicable a la description des debits journaliers des riveres.” Int. Statist. Rev., 38(1), 49–61.
Bierkens, M. F. P., and Puente, C. E. (1990). “Analytically derived runoff models based on rainfall point processes.” Water Resour. Res. 26(11), 2653–2659.
Brutsaert, W., and Nieber, J. L. (1977). “Regionalized drought flow hydrograph from a mature glaciated plateau.” Water Resour. Res., 13(3), 637–643.
Cowpertwait, P. S. P., and O’Connell, P. E. (1992). “A Neymann–Scott shot noise model for the generation of daily streamflow time series.” Advances in theoretical hydrology—A tribute to James Dooge, J. P. O’Kane, ed., Elsevier, New York.
DeBarry, P. A. (2004). Watersheds: Processes, assessment, and management, Wiley, Hoboken, N.J.
Engle, R. F. (1982). “Autoregressive conditional heteroscedasticity with estimates of the variance of UK inflation.” Econometrica, 50, 987–1007.
Kavvas, M. L., and Delleur, J. W. (1984). “A statistical analysis of the daily streamflow hydrograph.” J. Hydrol., 71, 253–275.
Kelman, J. (1980). “A stochastic model for daily streamflow.” J. Hydrol., 47, 235–249.
Koch, R. W. (1985). “A stochastic streamflow model based on physical principles.” Water Resour. Res., 21(4), 545–553.
Kottegoda, N. T., and Horder, M. A. (1980). “Daily flow model based on rainfall occurrences using pulses and a transfer function.” J. Hydrol., 47, 215–234.
McGinnis, D. F., and Sammons, W. H. (1970). “Discussion of ‘Daily streamflow simulations.’” J. Hydraul. Div., Am. Soc. Civ. Eng., 96(5), 1201–1206.
Murrone, F., Rossi, F., and Claps, P. (1997). “Conceptually-based shot noise modelling of streamflows at short time interval.” Stochastic Hydrol. Hydr., 11(6), 483–510.
Payne, K., Neumann, W. R., and Kerri, K. D. (1969). “Daily streamflow simulation.” J. Hydraul. Div., Am. Soc. Civ. Eng., 95(4), 1163–1180.
Quimpo, R. G. (1968). “Stochastic analysis of daily river flows.” J. Hydraul. Div., Am. Soc. Civ. Eng., 94(1), 43–57.
Sargent, D. M. (1979). “A simplified model for the generation of daily streamflows.” Hydrol. Sci. Bull., 24(4), 509–527.
Sharma, A., Tarboton, D. G., and Lall, U. (1997). “Streamflow simulation: a nonparametric approach.” Water Resour. Res., 33(2), 291–308.
Szilagyi, J. (1999). “On the use of semi-logarithmic plots for baseflow separation.” Ground Water, 37(5), 660–662.
Szilagyi, J. (2004). “Heuristic continuous baseflow separation.” J. Hydrologic Eng., 9(4), 1–8.
Treiber, B., and Plate, E. J. (1977). “A stochastic model for the simulation of daily flows.” Hydrol. Sci. Bull., 22(1), 175–192.
Weis, G. (1973). “Shot noise models for synthetic generation of multisite daily streamflow data.” IAHS Publ., 108, 457–467.
Weis, G. (1977). “Shot noise models for the generation of synthetic streamflow data.” Water Resour. Res., 13(1), 101–108.
Xu, Z. X., Schumann, A., and Brass, C. (2001). “Markov autocorrelation pulse model for two sites daily streamflow.” J. Hydrologic Eng., 6(3), 189–195.
Xu, Z. X., Schumann, A., and Li, J. (2003). “Markov cross-correlation pulse model for daily streamflow generation at multiple sites.” Adv. Water Resour., 26, 325–335.
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© 2006 ASCE.
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Received: May 27, 2004
Accepted: Jul 18, 2005
Published online: May 1, 2006
Published in print: May 2006
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