Hydraulics of Stream Flow Routing with Bank Storage
Publication: Journal of Hydrologic Engineering
Volume 7, Issue 1
Abstract
Bank storage is a process in which volumes of water are temporarily retained by alluvial stream banks during storm events and gradually released to partially sustain baseflow. This process has important hydrologic and ecological implications. In this paper, analytical solutions are developed for routing stream flow, lateral stream-aquifer interactions, and aquifer storage. In effect, the stream-flow routing Muskingum method is modified for bank storage. The analysis is based on one-dimensional lateral groundwater flow in semiinfinite homogeneous unconfined aquifers, which are in contact with streams through semipervious bed sediments. Impulse response and unit step response functions are derived for the stream-aquifer system, using Laplace transformations. These response functions relate stream outflow, stream-aquifer flow, bank storage, and cumulative reach discharge volume to discrete-time inflow hydrographs through convolution integrals. The impulse response function decreases with increasing aquifer hydraulic conductivity at earlier times, but increases with the conductivity and persists at later times. The unit step response function decreases with aquifer conductivity uniformly in time. The dependence of stream flow and bank storage on aquifer hydraulic conductivity, streambed leakance, stream width, and aquifer diffusivity is investigated. The analysis is extended to discrete input data, and modification of the methodology to route discrete-time inflow hydrographs of general form is achieved, using discrete-time kernels. The presented analysis establishes the time domain for validity of the analytical solutions in terms of the Muskingum parameters and an aquifer-related parameter.
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References
Chow, V. T., Maidment, D. R., and Mays, L. W. (1988). Appl. hydrology. McGraw-Hill, New York.
Cooper, H. H., and Rorabaugh, M. I. (1963). “Ground-water movements and bank storage due to flood stages in surface streams.” U.S. Geol. Surv. Water Supply Pap. 1536-J, 343–366.
Cunge, J. A.(1969). “On the subject of a flood propagation method (Muskingum method).” J. Hydraul. Res., 7(2), 205–230.
Domenico, P. A., and Schwartz, F. W. (1990). Physical and chemical hydrogeology. Wiley, New York.
Govindaraju, R. S., and Kavvas, M. L.(1991). “Dynamics of moving boundary overland flows over infiltrating surfaces at hillslopes.” Water Resour. Res., 27(8), 1885–1898.
Govindaraju, R. S., and Koelliker, J. K.(1994). “Applicability of linearized Boussinesq equation for modeling bank storage under uncertain aquifer parameters.” J. Hydrol., Amsterdam, 157, 349–366.
Hall, F. R., and Moench, A. F.(1972). “Application of the convolution equation to stream aquifer relations.” Water Resour. Res., 8(2), 487–493.
Hantush, M. S.(1965). “Wells near streams with semipervious beds.” J. Geophys. Res., 70(12), 2829–2838.
Harada, M., Hantush, M. M., and Mariño, M. A. (2000). Hydraulic analysis on stream-aquifer interaction by storage function models. Proc., Groundwater Updates IAHR International Symposium, Tokyo, 229–234.
Hornberger, G. M., Ebert, J., and Remson, I.(1970). “Numerical solution of the Boussinesq equation for stream-aquifer interaction.” Water Resour. Res., 6(2), 601–608.
Hunt, B.(1990). “An approximation for the bank storage effect.” Water Resour. Res., 26(11), 2769–2775.
Mariño, M. A.(1973). “Water table fluctuation in semipervious stream-unconfined aquifer systems.” J. Hydrol., Amsterdam, 19, 43–52.
Mariño, M. A.(1975). “Digital simulation model of aquifer response to stream stage fluctuation.” J. Hydrol., Amsterdam, 25, 51–58.
Moench, A. F., and Barlow, P. M.(2000). “Aquifer response to stream-stage and recharge variations. I: Analytical step-response functions.” J. Hydrol., Amsterdam, 230, 192–210.
Moench, A. F., Sauer, V. B., and Jennings, M. E.(1974). “Modification of routed streamflow by channel loss and base flow.” Water Resour. Res., 10(5), 963–968.
Perkins, S. P., and Koussis, A. D.(1996). “Stream aquifier interaction model with diffusive wave routing.” J. Hydraul. Eng., 122(4), 210–218.
Pinder, G. F., and Sauer, S. P.(1971). “Numerical simulation of flood wave modification due to bank storage effects.” Water Resour. Res., 7(1), 63–70.
Serrano, S. E., and Workman, S. R.(1998). “Modeling transient stream/aquifer interaction with the non-linear Boussinesq equation and its analytical solution.” J. Hydrol., Amsterdam, 206, 245–255.
Todd, D. K. (1955). “Ground-water in relation to a flooding stream.” Proc. American Society of Civil Engineers, 81, pp. 1–20, separate 628.
Viessman, W., Jr., and Lewis, G. L. (1996). Introduction to hydrology. Harper Collins, New York.
Workman, S. R., Serrano, S. E., and Liberty, K.(1997). “Development and application of an analytical model of stream/aquifer interaction.” J. Hydrol., Amsterdam, 200, 149–164.
Wylie, C. R., and Barrett, L. C. (1982). Advanced engineering mathematics. McGraw-Hill, New York.
Yeh, W. W.-G.(1970). “Nonsteady flow to a surface reservoir.” J. Hydraul. Eng., 96(3), 609–618.
Zitta, V. L., and Wiggert, J. M.(1971). “Flood routing in channels with bank storage.” Water Resour. Res., 7(5), 1341–1345.
Zlotnik, V. A., and Huang, H.(1999). “Effect of shallow penetration and streambed sediments on aquifer response to stream stage fluctuations (analytical model).” Ground Water, 37(4), 599–605.
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Published In
Journal of Hydrologic Engineering
Volume 7 • Issue 1 • January 2002
Pages: 76 - 89
Copyright
Copyright © 2002 American Society of Civil Engineers.
History
Received: Nov 14, 2000
Accepted: Apr 20, 2001
Published online: Jan 1, 2002
Published in print: Jan 2002
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