Effect of Input and Parameter Uncertainties in Rainfall-Runoff Simulations
Publication: Journal of Hydrologic Engineering
Volume 4, Issue 3
Abstract
The uncertainty or reliability of model simulation results produced by rainfall-runoff models is a function of uncertainties in model parameters, input data, and model structure. The present study considers a stochastic instantaneous unit hydrograph (SIUH) model describing the catchment as a single linear reservoir with input and transfer functions treated as random processes. Errors in runoff predictions caused by errors in input data and model parameters are analyzed by solving the governing stochastic differential equation (SDE) analytically, thus quantifying—in a general way—the error propagation structure and the relative importance of input errors and parameter errors. The result shows that the SIUH parameter variance has a direct bearing on the runoff variance, whereas the error contribution from the effective rainfall variance depends on the parameter mean value and the ratio between effective rainfall and simulated runoff. Data from 34 rainstorms are selected to verify the analytical SDE approach. The selected events represent varying: (1) rainfall intensity and duration; (2) single/multiple peak events; and (3) catchment initial losses. The results from the simulations are compared with observed runoff peaks and flood volumes. It is concluded that: (1) the SIUH model is a simple yet robust method, for which the parameter uncertainty can be realistically assessed; (2) the application of a theoretical SDE to estimate the prediction variance is supported by the statistical analysis of simulated and observed runoff; and (3) the estimation of flood peak variance can improve the design of flood control measures.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Berndtsson, R., Teng, W., Jia, S., Høybye, J., and Svensson, C. (1997). “Introduction and general space-time properties of rainfall.” Tech. Rep., Lund University, Lund, Sweden.
2.
Bodo, B. A., and Unny, T. E. ( 1987). “On the output of stochastisized Nash-Dooge linear reservoir cascades.” Stochastic hydrology, I. B. MacNeil and G. I. Umphrey, eds., Reidel, Dordrecht, The Netherlands, 131–137.
3.
Bras, R. L. (1990). “Hydrology.” An introduction to hydrologic science, Addison-Wesley, Reading, Mass.
4.
Bras, R. L., and Rodriguez-Iturbe, I. (1985). Random functions and hydrology. Addison-Wesley, Reading, Mass.
5.
Chong, S. K., and Green, R. E. (1983). “Sorptivity measurement and its application.” Advances in infiltration, ASAE Publ. No. 11-83, American Society of Agricultural Engineers, St. Joseph, Mich., 82–91.
6.
Chow, V. T., Maidment, D. R., and Mead, L. W. (1988). Applied hydrology. McGraw-Hill, New York.
7.
Dooge, J. C. I. (1977). “Problems and methods of rainfall-runoff modelling.” Mathematical models for surface water hydrology, T. A. Ciriani, U. Maione, and J. R. Wallis, eds., Wiley, New York.
8.
Dyhr-Nielsen, M. (1972). “Loss of information by discretizing hydrologic series.” Hydrology Papers No. 54, Fort Collins, Colo.
9.
Eagleson, P. S. (1970). Dynamics hydrology. McGraw-Hill, New York.
10.
Eagleson, P. S. (1972). “Dynamics of flood frequency.” Water Resour. Res., 8(4), 878–898.
11.
Fujia, T., and Yumei, L. ( 1994). “Reconstruction of the Banqiao and Shimantan dams.” Hydropower and dams, July, 49–53.
12.
Gelhar, L. W. (1986). Stochastic subsurface hydrology. Prentice-Hall, Englewood Cliffs, N.J.
13.
Goodrich, D. C., Faures, J., Woolhiser, D. A., Lane, L. J., and Sorooshian, S. (1995). “Measurement and analysis of small-scale convective storm rainfall variability.” J. Hydro., Amsterdam, 173, 283–308.
14.
Hjelmfelt, A., and Wang, Y. M. (1994). “General stochastic unit hydrograph.”J. Irrig. and Drain. Engrg., ASCE, 120(1), 138–148.
15.
Høybye, J. ( 1998). “Uncertainty modelling in hydrological applications. Error propagation properties of random linear systems,” PhD thesis, Lund University, Lund, Sweden.
16.
Høybye, J., and Iritz, L. (1997). “Analysis of extreme hydrological events in a monsoon climate catchment: The Hongru River, China.” Hydrological Sci. J., 42(3), 343–355.
17.
Jenkins, G. M., and Watts, D. G. (1968). Spectral analysis and its applications. Holden-Day, Oakland, Calif.
18.
Klemeš, V. ( 1982). “Empirical and causal models in hydrology.” Scientific basis of water-resource management, National Research Council (United States), Geophysics Study Committee, National Academy Press, Washington, D.C., 95–104.
19.
Lin, G. F., and Wang, Y. M. (1996). “General stochastic instantaneous unit hydrograph.” J. Hydro., Amsterdam, 182, 227–238.
20.
Linsley, R. K., Kohler, M. A., and Paulhus, J. L. H. (1982). Hydrology of engineers. 2nd Ed., McGraw-Hill, New York.
21.
Lund University and Ministry of Water Resources of China. (1996). “Development of optimal flood control systems for China, Part one: Basin flood analysis and water balance.” Rep. No. 3187, Department of Water Resources, Lund University, Lund, Sweden.
22.
Melching, C. S. (1992). “An improved first-order reliability approach for assessing uncertainties in hydrologic modelling.” J. Hydrol., Amsterdam, 132, 157–177.
23.
Moran, P. A. P. (1971). “Dams in series with a continuous release.” J. Appl. Prob., 4, 380–388.
24.
Niemczynowicz, J. (1986). “A non-linear rainfall-runoff simulation model applicable to a desk calculator.” Urban drainage modelling, C. Maksimovic and M. Radojkovic, eds., Pergamon, Tarrytown, N.Y.
25.
Novotny, V., and Zheng, S. (1994). “Hydrologic considerations and precipitation-runoff relationship.” Water quality prevention, identification, and management of diffuse pollution, Novotny and Olem, eds., Van Nostrand Reinhold, New York.
26.
O'Connell, P. E., and Todini, E. (1996). “Modeling of rainfall, flow and mass transport in hydrological systems: An overview.” J. Hydrol., Amsterdam, 175, 3–16.
27.
Philip, J. R. (1969). “Theory of infiltration.” Adv. Hydroscience, 5, 216–296.
28.
Quimpo, R. G. (1973). “Link between stochastic and parametric hydrology.”J. Hydr. Div., ASCE, 99, 461–470.
29.
Raudkivi, A. J. (1979). Hydrology. Pergamon, Tarrytown, N.Y.
30.
Rosbjerg, D., and Madsen, H. ( 1998). “Design with uncertain design values.” Hydrology in a changing environment, H. Wheater and C. Kirby, eds., Vol. III, Wiley, Chichester, U.K., 155–163.
31.
Sarino, and Serrano, S. E. ( 1990). “Development of the instantaneous unit hydrograph using stochastic differential equations.” Stoch. Hydrol. and Hydraul., 4, 151–160.
32.
Singh, V. P., and Woolhiser, D. A. (1976). “Sensitivity of linear and nonlinear surface runoff models to input errors.” J. Hydrol., Amsterdam, 29, 243–249.
33.
Sorooshian. (1983). “Surface water hydrology: On-line estimation.” Rev. Geophysics Space Phys., 21, 706–721.
34.
Storm, B., Høgh Jensen, K., and Refsgaard, J. C. (1989). “Estimation of catchment rainfall uncertainty and its influence on runoff prediction.” Nordic Hydro., 19, 77–88.
35.
Svensson, C. ( 1998). “Properties of heavy rainfall in an East Asian monsoon catchment,” PhD thesis, Lund University, Lund, Sweden.
36.
Troutman, B. M. (1983). “Runoff prediction errors and bias in parameter estimation induced by spatial variability of precipitation.” Water Resour. Res., 19(3), 791–810.
37.
Troutman, B. M. (1985). “Errors and parameter estimation in precipitation-runoff modeling, 1. Theory.” Water Resour. Res., 21(8), 1195–1213.
38.
UN. (1983). “Flood damage prevention and control in China.” Natural Resour./Water Ser. No. 11, United Nations, N.Y.
39.
Unny, T. E. (1984). “Numerical integration of stochastic differential equations in catchment modeling.” Water Resour. Res., 20, 360–368.
40.
Yevjevich, V. (1972). Probability and statistics in hydrology. Water Resources Publications, Littleton, Colo.
Information & Authors
Information
Published In
Journal of Hydrologic Engineering
Volume 4 • Issue 3 • July 1999
Pages: 214 - 224
History
Received: Jul 20, 1998
Published online: Jul 1, 1999
Published in print: Jul 1999
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.