Uncertainty in Flood Wave Routing in a Lateral-Inflow-Dominated Stream
Publication: Journal of Hydrologic Engineering
Volume 16, Issue 2
Abstract
Flood wave routing is a common problem in water resources engineering, for example, when a hydrograph enters a stream channel and passes downstream to an observation station. In the past, the problem has been approached by making the best possible estimate of the inflow hydrograph. The channel properties such as geometry and roughness are also estimated, along with any lateral inflow. The best estimates are used with a flood wave routing model to predict the hydrograph at the downstream observation station. Making a prediction by this procedure is full of challenges. It is impossible to exactly know the precise form of the hydrograph that will enter the channel. It is also difficult to select the channel properties from the range of values that may be appropriate. Lateral inflow is notoriously difficult to quantify. Making predictions under these circumstances is full of uncertainties. One approach to analyzing uncertainties is to use Monte Carlo modeling to make quantitative estimates of the uncertainty in flood wave routing results. The best estimates used for boundary conditions and model parameters are replaced by probability estimates. The ensemble of results from the Monte Carlo framework can be analyzed to develop probabilistic estimates of the routed hydrograph at the outlet of the channel reach. While this is a powerful approach, it also requires extensive probability data for the boundary conditions and channel properties. Such input data are rare in the published literature and do not appear to exist at all for lateral-inflow-dominated streams. This study examines the flood wave routing problem in a probabilistic framework using the kinematic wave model. It develops a complete data set for a lateral-inflow-dominated stream that includes a probabilistic description of the inflow hydrograph and lateral inflow. It also includes probability density functions for the parameters used in the kinematic wave model. The resulting data set appears to be the first developed for a lateral-inflow-dominated stream, though data sets do exist for streams without significant lateral inflows. Beyond the development of a new data set, this study seeks to evaluate the relative contributions of uncertainty in boundary conditions and channel parameters to the total uncertainty in the routed flood wave. Results for the lateral-inflow-dominated case developed here are compared to a similar example where lateral inflow is not significant. The results found here suggest that in both cases it is the uncertainty in boundary conditions that is most significant and dominates the total uncertainty in the routed flood wave.
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References
Ajami, N. K., Gupta, H., Wagener, T., and Sorooshian, S. (2004). “Calibration of a semi-distributed hydrologic model for streamflow estimation along a river system.” J. Hydrol., 298, 112–135.
Alley, W. M., and Smith, P. E. (1982). “Distributed routing rainfall-runoff model: Version II.” Open File Rep. 82-344, U.S. Geological Survey, Reston, Va.
Balakrishnan, S., Roy, A., Ierapetritou, M. G., Flach, G. P., and Georgopoulos, P. G. (2005). “A comparative assessment of efficient uncertainty analysis techniques for environmental fate and transport models: Application to the FACT model.” J. Hydrol., 307, 204–218.
Barnes, H. H. (1967). “Roughness characteristics of natural channels.” USGS Water Supply Paper 1849, U.S. Geological Survey, Washington, D.C.
Bates, B. C., and Townley, L. R. (1988). “Nonlinear, discrete flood event models, 3. Analysis of prediction uncertainty.” J. Hydrol., 99, 91–101.
Bonnin, G. M., Martin, D., Lin, B., Parzybok, T., Yekta, M., and Riley, D. (2004). “Precipitation-frequency atlas of the United States.” NOAA atlas 14, Vol. 2, Version 3, NOAA National Weather Service, Silver Spring, Md.
Borah, D. K., and Prasad, S. N. (1980). “Kinematic wave routing incorporating shock fitting.” Water Resour. Res., 16(3), 529–541.
Buhman, D. L., Gates, T. K., and Watson, C. C. (2002). “Stochastic variability of fluvial hydraulic geometry: Mississippi and Red Rivers.” J. Hydraul. Eng., 128(4), 426–437.
Burguete, J., and García-Novarro, P. (2004). “Implicit schemes with large time step for non-linear equations: Application to river flow hydraulics.” Int. J. Numer. Methods Fluids, 46, 607–636.
Chow, V. T. (1959). Open-channel hydraulics, McGraw-Hill, New York.
Copeland, R. R., Biedenarn, D. S., and Fischenich, J. C. (2000). “Channel-forming discharge.” Technical Note ERDC-CHL CHETN-VIII-5, U.S. Army Corps of Engineers, Vicksburg, Miss.
DeGroot, M. H. (1986). Probability and statistics, 2nd Ed., Addison-Wesley, Reading, Mass.
Dorner, S., Shi, J., and Swayne, D. (2007). “Multi-objective modeling and decision support using a Bayesian network approximation to a non-point source pollution model.” Environ. Modell. Software, 22, 211–222.
Ewen, J., O’Donnell, G., Burton, A., and O’Connell, E. (2006). “Errors and uncertainty in physically-based rainfall-runoff modeling of catchment change effects.” J. Hydrol., 330, 641–650.
Faulkner, H. (1992). “Simulation of summer storms of differing recurrence intervals in a semiarid environment using a kinematic routing scheme.” Hydrol. Process., 6, 397–416.
Fiener, P., and Auerswald, K. (2005). “Measurement and modeling of concentrated runoff in grassed waterways.” J. Hydrol., 301, 198–215.
Fishman, G. S. (1996). Monte Carlo: Concepts, algorithms, and applications, Springer, New York.
Franchini, M., and Lamberti, P. (1994). “A flood routing Muskingum type simulation and forecasting model based on level data alone.” Water Resour. Res., 30(7), 2183–2196.
Gates, T. K., and Al-Zahrani, A. (1996). “Spatiotemporal stochastic open-channel flow: Model and its parameter data.” J. Hydraul. Eng., 122(11), 641–651.
Gaur, M. L., and Mathur, B. S. (2003). “Modeling event-based temporal variability of flow resistance coefficient.” J. Hydrol. Eng., 8(5), 266–277.
Geer Mountain Software. (2001). Stat:Fit version 2 user’s manual, South Kent, Conn.
Guganesharajah, K., Lyons, D. J., and Lloyd, B. J. (2006). “Influence of uncertainties in the estimation procedure of floodwater level.” J. Hydraul. Eng., 132(10), 1052–1060.
Haltas, I., and Kavvas, M. L. (2009). “Modeling the kinematic wave parameters with regression methods.” J. Hydrol. Eng., 14(10), 1049–1058.
Henderson, F. M. (1966). Open channel flow, Macmillan, New York.
Hession, W. C., Storm, D. E., and Haan, C. T. (1996). “Two-phase uncertainty analysis: An example using the universal soil loss equation.” Trans. ASAE, 39(4), 1309–1319.
Huang, J., and Song, C. C. S. (1985). “Stability of dynamic flood routing schemes.” J. Hydraul. Eng., 111(12), 1497–1505.
Hydrologic Engineering Center (HEC). (1993). “Introduction and application of kinematic wave routing techniques using HEC-1.” Training Document 10, U.S. Army Corps of Engineers, Davis, Calif.
Hydrologic Engineering Center (HEC). (2004). Pistol Creek, Tennessee model study report: Hydrologic and hydraulic analysis of the Pistol Creek watershed above Maryville, Tennessee, U.S. Army Corps of Engineers, Davis, Calif.
Hydrologic Engineering Center (HEC). (2005). HEC-DSS Vue HEC data storage system visual utility engine: User’s manual, U.S. Army Corps of Engineers, Davis, Calif.
Hydrologic Engineering Center (HEC). (2006). Hydrologic modeling system HEC-HMS: User’s manual, U.S. Army Corps of Engineers, Davis, Calif.
Iwagaki, Y. (1955). “Fundamental studies on the runoff analysis by characteristics.” Bulletin 10, Kyoto Univ. Disaster Prevention Research Institute, Kyoto, Japan.
Jacquin, A. P., and Shamseldin, A. Y. (2007). “Development of a possibilistic method for the evaluation of predictive uncertainty in rainfall-runoff modeling.” Water Resour. Res., 43, W04425.
Jakeman, A. J., and Letcher, R. A. (2003). “Integrated assessment and modeling: Features, principles and examples for catchment management.” Environ. Modell. Software, 18, 491–501.
Krzysztofowicz, R. (2001). “The case for probabilistic forecasting in hydrology.” J. Hydrol., 249, 2–9.
Kunstmann, H., and Kastens, M. (2006). “Direct propagation of probability density functions in hydrological equations.” J. Hydrol., 325, 82–95.
Lapedes, D. N. (1978). McGraw-Hill dictionary of scientific and technical terms, 2nd Ed., McGraw-Hill, New York.
Law, G. S., and Tasker, G. D. (2000). “Flood-frequency prediction methods for unregulated streams of Tennessee, 2000.” Water Resource Investigations Rep. 03-4176, U.S. Geological Survey, Nashville, Tenn.
Lian, Y., and Yen, B. C. (2003). “Comparison of risk calculation methods for a culvert.” J. Hydraul. Eng., 129(2), 140–152.
Lighthill, M. J., and Whitham, G. B. (1955). “On kinematic waves: 1. Flood movement in long rivers.” Proc. R. Soc. London, Ser. A, 229, 281–316.
Mailhot, A., and Villeneuve, J. (2003). “Mean-value second-order uncertainty analysis method: Application to water quality modeling.” Adv. Water Resour., 26, 491–499.
Mays, L. W. (2005). Water resources engineering, Wiley, Hoboken, N.J.
Melone, F., Corradini, C., and Singh, V. P. (2002). “Lag prediction in ungauged basins: An investigation through actual data of the upper Tiber River valley.” Hydrol. Process., 16, 1085–1094.
Natural Resources Conservation Service (NRCS). (1986). “Urban hydrology for small watersheds.” Technical Release 55, USDA Natural Resources Conservation Service, Conservation Engineering Div., Washington, D.C.
Natural Resources Conservation Service (NRCS). (1995). “Soil survey geographic (SSURGO) Data base: Data use information.” Miscellaneous Publication No. 1527, USDA Natural Resources Conservation Service, National Soil Survey Center, Fort Worth, Tex.
Natural Resources Conservation Service (NRCS). (2001). National engineering handbook, part 630 hydrology, USDA Natural Resources Conservation Service, Washington, D.C.
Newton, D. W. and Herrin, J. C. (1982). “Assessment of commonly used flood frequency methods.” Transportation Research Record. 896, Transportation Research Board, Washington, D.C.
O’Donnell, T. (1985). “A direct three-parameter Muskingum procedure incorporating lateral inflow.” J. Hydrol. Sci., 30(4), 479–496.
Odai, S. N. (1999). “Nonlinear kinematic-wave model for predicting open-channel flow rate.” J. Hydraul. Eng., 125(8), 886–889.
Oreskes, N., Shrader-Frechette, K., and Belitz, K. (1994). “Verification, validation, and confirmation of numerical models in the earth sciences.” Science, 263, 641–646.
Pappenberger, F., et al. (2005). “Cascading model uncertainty from medium range weather forecasts (10 days) through a rainfall-runoff model to flood inundation predictions within the European flood forecasting system (EFFS).” Hydrology Earth Syst. Sci., 9(4), 381–393.
Pappenberger, F., and Beven, K. J. (2006). “Ignorance is bliss: Or seven reasons not to use uncertainty analysis.” Water Resour. Res., 42, W05302.
Pappenberger, F., Matgen, P., Beven, K. J., Henry, J., Pfister, L., and deFraipont, P. (2006). “Influence of uncertain boundary conditions and model structure on flood inundation predictions.” Adv. Water Resour., 29, 1430–1449.
Ponce, V. M., Li, R., and Simons, D. B. (1978). “Applicability of kinematic and diffusion models.” J. Hydr. Div., 104(3), 353–360.
Resource Analysis, Inc. (1975). MITCAT catchment simulation model: Description and user’s manual, Cambridge, Mass.
Shirmohammadi, A., et al. (2006). “Uncertainty in TMDL models.” Trans. ASABE, 49(4), 1033–1049.
Singh, V. P. (1996). Kinematic wave modeling in water resources: Surface-water hydrology, Wiley, New York.
Stedinger, J. R., and Tasker, G. D. (1985). “Regional hydrologic regression: 1. Ordinary, weighted and generalized least squares compared.” Water Resour. Res., 21(9), 1421–1432.
Stewardson, M. (2005). “Hydraulic geometry of stream reaches.” J. Hydrol., 306, 97–111.
Takeuchi, K. (2004). “Hydrology as a policy-relevant science.” Hydrol. Process., 18, 2967–2976.
Tsai, C. W. (2003). “Applicability of kinematic, noninertia, and quasi-steady dynamic wave models to unsteady flow routing.” J. Hydraul. Eng., 129(8), 613–627.
Tseng, M. H., Hsu, C. A., and Chu, C. R. (2001). “Channel routing in open-channel flows with surges.” J. Hydraul. Eng., 127(2), 115–122.
Wong, S. W., and Zhou, M. C. (2006). “Kinematic wave parameters for trapezoidal and rectangular channels.” J. Hydrol. Eng., 11(2), 173–183.
Yen, B. C. (2002). “Open channel flow resistance.” J. Hydraul. Eng., 128(1), 20–40.
Yu, P. S., Yang, T. C., and Chen, S. J. (2001). “Comparison of uncertainty analysis methods for a distributed rainfall-runoff model.” J. Hydrol., 244, 43–59.
Zheng, Y., and Keller, A. A. (2006). “Understanding parameter sensitivity and its management implications in watershed-scale water quality modeling.” Water Resour. Res., 42, W05402.
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Published In
Journal of Hydrologic Engineering
Volume 16 • Issue 2 • February 2011
Pages: 165 - 175
Copyright
© 2011 ASCE.
History
Received: Oct 15, 2009
Accepted: Jul 21, 2010
Published online: Jan 14, 2011
Published in print: Feb 2011
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