Abstract
A model is developed for annual low flow hydrographs. Its two primary components reflect the fact that hydrologic processes during streamflow rise (function of water input) and recession (function of basin storage) are different. Durations of periods of rise (wet intervals) and recession (dry intervals) are modelled by discrete probability distributions — negative binomial for dry intervals and negative binomial or modified logarithmic series for wet intervals depending on goodness of fit. During wet intervals, the total inflow is modelled by the lognormal distribution and daily amounts are allocated according to a pattern-averaged model. During dry intervals, the flow recedes according to a deterministic-stochastic recession model.
The model was applied to three Canadian basins with drainage area ranging from 2210 to 22000 km2 to generate 50 realizations of low flow hydrographs. The resulting two standard-error confidence band for the simulated probability distribution of annual minimum 7-day flows enclosed the probability distribution estimated from the observed record. A sensitivity analysis for the three basins revealed that in addition to the recession submodel, the most important submodel is that describing seasonality. The state of the basin at the beginning of the low flow period is of marginal importance and the daily distribution of input is unimportant.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
ASCE. 1980: Characteristics of low flows. Task Committee on Low-Flow Evaluation, Methods, and Needs, ASCE J. Hydraul. Div. 105(HY5), 717–731
Astatkie, T. 1994: Modulated time series models with applications in hydrology. Ph.D. Thesis, Queen's University, Kingston, Ontario
Bonser, J.D.; Unny, T.E.; Singhal, K. 1985: A marked Poisson process mode of summer rainfall in Southern Ontario. Can. J. Civ. Eng. 12, 886–897
Buishand, T.A. 1978: Some remarks on the use of daily rainfall models. J. Hydrol. 36, 295–308
Duckstein, L.; Fogel, M.M.; Kisiel, C.C. 1972: A stochastic model of runoff-producing rainfall for summer type storms. Water Resour. Res. 8(2), 410–321
Gabriel, K.R.; Neumann, J. 1962: A Markov chain model for daily rainfall occurrences at Tel Aviv. Q. J. Royal Meteorol Soc. 88, 90–95
Georgakakos, K.P.; Kavvas, L.M. 1987: Precipitation analysis, modelling and prediction in hydrology. Rev. Geophys. 25(2), 163–178
Grace, R.A.; Eagleson. P.S. 1967: A model for generating synthetic sequences of short-time interval depths. Proceedings International Hydrology Symposium, Fort Collins, Colorado, 268–276
Grace, R.A.; Eagleson. P.S. 1966: The synthesis of short-time increament rainfall sequences. Hydrodynamics Lab. Report 91, Dept. Civ. Eng., M.I.T., Cambridge, MA
Grayman, W.M.; Eagleson, P.S. 1969: Streamflow record duration for modelling catchment dynamics. Hydrodynamics Lab. Report 114, Dept. Civ. Eng., M.I.T, Cambridge, MA
Green, J.R.A. 1964: A model for rainfall occurrence. J. Royal Stat. Soc. B 26, 345–353
Haan, C.T.; Allen, M.D.; Street, J. O. 1976: A Markov chain model of daily rainfall. Water Resour, Res. 12(3), 443–449
Horton, R.E. 1914: Discussion of report of committee on yield of drainage-areas. J. New England Water Works Assoc., 538–542
Ison, N.T.; Feyerherm, A.M.; Bark, L.D. 1971: Wet period precipitation and the gamma distribution. J. App. Meteorol. 10, 658–665
Johnson, N.L.; Kotz, S. 1969: Distributions in statistics: discrete distributions. Houghton Mifflin, New York, NY
Kavvas, M.L.; 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
Kirkby, W. 1969: On the random occurrence of major floods. Water Resour. Res. 5(4), 778–784
Kottegoda, N.T. 1972: Stochastic five daily streamflow model. ASCE J. Hydraul. Div. 98(HY9), 1469–1485
Kottegoda, N.T.; Horder, M.A. 1980: Daily flow model based on rainfall occurrences using pulses and transfer function. J. Hydrol. 47, 215–234
Lawal, S.A. 1994: A simulation approach to low flow frequency analysis. Ph.D. Thesis, Queen's University, Kingston, Ontario
Lawrence, A.J.; Kottegoda, N.T. 1977: Stochastic modelling of river flow time series. J. Royal Stat. Sot. A. 140, 1–47
Lettenmaier, D. P. 1993: Application of stochastic modelling in climate change impact assessment Presented at the International Conference on Stochastic and Statistical methods in Hydrology and Environmental Engineering. University of Waterloo, Waterloo, Ontario
Lowry, W.P.; Guthrie, D. 1968: Markov chains of order greater than one. Mon, Weather Rev. 96(11), 798–801
Mills, W.C. 1981: Stochastic modelling of rainfall for deriving distributions of watershed inputs. In: Singh, V.P. (ed.) Statistical analysis of rainfall and runoff, Water Resour. Publications, Littleton, CO, 103–118
Nguyen, V.T.V.; Rousselle J. 1981: A stochastic model for the time distribution of hourly rainfall depth. Water Resour. Res. 17(2), 399–409
O'Connell, P.E.; Jones, D.A. 1979: Some experience with the development of models for the stochastic simulation of daily flows. In: McBean, E.A.; Hipel, K.W.; Unny, T.E. (eds.) Inputs for risk analysis in water systems. Water Resources Bulletin Publications, Littleton, CO
Olason, T. 1990: Developement of adaptive multivariate time series models of river flows. Ph.D. Thesis, Queen's University, Kingston, Ontario
Pilgrim, D.H.; Cordery, I. 1975: Rainfall temporal pattems for design floods. ASCE J. Hydraul. Div. 101(HY1), 81–95
Press, W.H.; Flannery, B.P.; Teukolsky, S.A.; Vetterling, W.T. 1986: Numerical recipes: The art of scientific computing. Cambridge University Press, Cambridge
Rao, A.R.; Chenchayya, B.T. 1984: Depth-duration models of short time increament rainfall. Water Sci. Technology 16, 109–130
Roldan, J.; Woolhiser, D.A. 1982: Stochastic daily precipitation models, 1, a comparison of occurrence processes. Water Resour. Res. 18(5), 1451–1459
Stern, R.D.; Coe, R. 1984: A model fitting analysis of daily rainfall data. J. Royal Stat. Soc. A 147, 1–34
Waymire, E.; Gupta, V.K. 1981a: The mathematical structure of rainfall representations, 1, a review of the stochastic rainfall models. Water Resour. Res. 17(5), 1261–1272
Waymire, E.; Gupta, V.K. 1981b: The mathematical structure of rainfall representations, 2, a review of the theory of point processes. Water Resour. Res. 17(5), 1273–1286
Waymire, E.; Gupta, V.K. 1981c: The mathematical structure of rainfall representations, 3, some applications of the point process theory to rainfail processes. Water Resour. Res. 17(5), 1287–1294
Weisman, R.N. 1977: The effect of evapotranspiration on streamflow recession. Hydro. Sci. Bull. 22(3), 371–377
Yakowitz, S.J. 1973: A stochastic model for daily river flow in an arid region. Water Resour. Res. 9(5), 1271–1285
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Lawal, S.A., Watt, W.E. & Watts, D.G. A stochastic model of low flows. Stochastic Hydrol Hydraul 11, 303–321 (1997). https://doi.org/10.1007/BF02427921
Issue Date:
DOI: https://doi.org/10.1007/BF02427921