Estimation of Flood Forecasting Errors and Flow-Duration Joint Probabilities of Exceedance
Publication: Journal of Hydraulic Engineering
Volume 122, Issue 3
Abstract
The conceptual analogy between the impulse response function and the unit hydrograph is applied for the identification of a transfer function model for real-time flood forecasting. The real-time corrections of flood forecasts are obtained from probability distributions of observed and forecasted (without real-time corrections) flows approximated by exponential distributions. The method adds considerable smoothing to error terms. The flood event is defined as the amount of total flow in excess of an alarm level of the flood over its duration. The correlation between the flood flow and its duration is considered to estimate the joint probabilities of exceedance (JPE) of designed flood flow over specified duration using the joint distribution of the flow and duration, given by the Gumbel's bivariate exponential distribution (second type). It is discussed that the univariate analysis (i.e., flow alone) underestimates the exceedance probability of flood flow. The study shows that the JPE increases with the increase of correlation between the flood flow and its duration. The radar-derived rainfall data in the Irwell basin, U.K., are applied in a case study. The method of JPE can be extended to link flood forecasting and flow-duration profile for effective management of flood risk areas.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Bennett, R. J. (1979). Spatial time series. Pion Ltd., London, U.K.
2.
Box, G. E. P., and Jenkins, G. M. (1976). Time series analysis forecasting and control, Second Ed., Holden-Day, San Francisco, Calif.
3.
Chatfield, C. (1989). The analysis of time series an introduction. Chapman and Hall, London, U.K.
4.
Cluckie, I. D., and Yu, P. S. (1989). “Stochastic models for real-time river flow forecasting using radar data.”Int. Symp. on Stochastic Hydr. and Hydrol., Birmingham University, U.K.
5.
Collinge, V. K., and Kirby, C. (eds.). (1987). Weather radar and flood forecasting . John Wiley & Sons Ltd., London, U.K.
6.
Corradini, C., and Molone, F.(1987). “On the structure of semi-distributed adaptive model for flood forecasting.”Hydrological Sci. J., 32, 227–242.
7.
Doviak, R. J.(1983). “A survey of radar rain measurement techniques.”J. Appl. Meteorology, 22, 832–851.
8.
Dracup, J. A., Lee, K. S., and Paulson, E. G.(1980). “On the statistical characteristics of drought events.”Water Resour. Res., 16(2), 289–296.
9.
Gumbel, E. J.(1960). “Bivariate exponential distributions.”J. Am. Statistical Assoc., 55, 698–707.
10.
Jenkins, G. P., and McLeod, G. (1982). Case studies in time series analysis, Vol. 1, Gwilym Jenkins and Partners, Ltd., Jersey, U.K.
11.
Johnson, N. L., and Kotz, S. (1970). Distributions in statistics: Continuous univariate distributions, Vol. 1, 2, John Wiley and Sons, New York, N.Y.
12.
Johnson, N. L., and Kotz, S. (1972). Distributions in statistics: Multivariate distributions, John Wiley and Sons, New York, N.Y.
13.
Lemke, K.(1991). “Transfer function models of suspended sediment concentration.”Water Resour. Res., 27(3), 293–305.
14.
Mukherjee, D. (1989). “Statistical and economic aspects of droughts.” PhD thesis, Birmingham University, U.K.
15.
Mukherjee, D., and Mansour, N.(1991). “A bivariate stochastic approach to estimate reliability of a pumped storage reservoir.”J. Hydrol., 125, 293–310.
16.
Numerical Algorithm Group (NAG). (1988). Manual, Mark 12, FORTRAN Library, Oxford, U.K.
17.
Oslason, T., and Watt, W. E.(1986). “Multivariate transfer function noise model of river flow for hydropower operation.”Nordic Hydrol., 17(3), 185–202.
18.
Rajaram, H., and Georgakakos, P.(1989). “Recursive estimation of hydrological models,”Water Resour. Res., 25(2), 281–294.
19.
Reed, D. W. (1984). “A review of British flood forecasting practice.”Rep. 90, Institute of Hydrology, Wellington, U.K.
20.
Santos, M. A.(1983). “Regional drought: A stochastic characterisation.”J. Hydrol., 66, 183–211.
21.
Sen, Z.(1976). “Wet and dry period of annual flow series.”J. Hydr. Div., ASCE, 49, 193–208.
22.
Snorrason, A., Newbold, P., and Maxwell, W. H. C. (1984). Multiple input transfer function noise modelling of river flow, frontier in hydrology, W. H. C. Maxwell and L. R. Beard, eds., Water Resource Publ., Fort Collins, Colo.
23.
Starosoiszky, O. (1987). Applied surface hydrology . Littleton, Colo.
24.
Szollosi-Nagy, A., and Mekis, E. (1989). “Comparative analysis of three recursive real time river flow models: Deterministic, stochastic and coupled deterministic and stochastic.”Int. Symp. on Stochastic Hydr. and Hydrol., Birmingham University, U.K.
25.
Young, P. C. (1984). Recursive estimation and time series analysis . Springer-Verlag, Berlin, Germany.
Information & Authors
Information
Published In
Copyright
Copyright © 1996 American Society of Civil Engineers.
History
Published online: Mar 1, 1996
Published in print: Mar 1996
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.