Aquifer Response to Sinusoidal or Arbitrary Stage of Semipervious Stream
Publication: Journal of Hydraulic Engineering
Volume 130, Issue 11
Abstract
Analytical expressions for the aquifer responses, viz., groundwater head, rate of flow and cumulative volume of flow, to a generalized sinusoidal stage of semipervious streams considering the stream boundary resistance, are derived. The analytical aquifer responses to a linear stream stage and to a typical analytical flood wave that was used by Cooper and Rorabaugh, are also derived. For a zero-stream resistance, the aquifer responses converge to those for a fully penetrating stream. Also, two analytical methods, a “ramp kernel method” and a “Fourier series method,” for obtaining the aquifer responses to an arbitrary temporal stage of sempervious stream, are developed. The analytical expressions of the ramp kernels for different aquifer responses are developed. The ramp kernel method is found superior to the conventional convolution that uses numerical integration or pulse kernels for obtaining the convolution integral. In the Fourier series method, the aquifer responses to sinusoidal stage are used along with Fourier series. The results obtained using both methods are in close agreement. The new methods are also applicable to fully penetrating streams by assigning a zero value to the stream resistance.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Barlow, P. M., DeSimone, L. A., and Moench, A. F. (2000). “Aquifer response to stream-stage and recharge variations. II: Convolution method and application.” J. Hydrol., 230(3–4), 211–229.
2.
Bouwer, H. (1965). “Theoretical aspect of seepage from open channel.” J. Hydraul. Div., Am. Soc. Civ. Eng., 91(3), 601–608.
3.
Bouwer, H., and Maddock, III, I. (1997). “Making sense of interactions between groundwater and stream flow: Lessons for water masters and adjudicators.” River, 6(1), 19–31.
4.
Carslaw, H.S., and Jaeger, J.C. ( 1959). Conduction of heat in solids, Oxford, New Delhi.
5.
Cooper, H.H., and Rorabaugh, M.I. ( 1963). “Ground-water movement and storage due to flood stages in surface stream.” Geological Survey Water Supply Paper 1536-J, U.S. Dept. of Interior, Washington, D.C., 340–365.
6.
Govindaraju, R. S., and Koelliker, J. K. (1994). “Applicability of linearized Boussinesq equation for modeling bank storage under uncertain aquifer parameters.” J. Hydrol., 157(1–4), 349–366.
7.
Halek, V., and Svec, J. ( 1979). Groundwater hydraulics, Elsevier Science, Amsterdam, The Netherlands, 539–544.
8.
Hall, F. R., and Moench, A. F. (1972). “Application of the convolution equation to stream aquifer relationships.” Water Resour. Res., 8(2), 487–493.
9.
Marino, M. A. (1973). “Water table fluctuation in semipervious stream—Unconfined aquifer systems.” J. Hydrol., 19, 43–52.
10.
Marino, M. A. (1975). “Digital simulation model of aquifer response to stream stage fluctuation.” J. Hydrol., 25, 51–57.
11.
Reynolds, R. J. (1987). “Diffusivity of a glacial-outwash aquifer by the flood wave-response technique. Ground Water, 25(3), 290–299.
12.
Rowe, P. P. (1960). “An equation for estimating transmissibility and coefficient of storage from river level fluctuations.” J. Geophys. Res., 65(10), 3419–3424.
13.
Nielsen, P. (1990). “Tidal dynamics of water table in beaches.” Water Resour. Res., 26(9), 2127–2134.
14.
Singh, S.K. ( 1994). “Semi-pervious stream and aquifer interaction.” Rep. No. TR(BR)-110, National Institute of Hydrology, Roorkee, India.
15.
Singh, S. K. (2003). “Flow depletion of semipervious streams due to pumping.” J. Irrig. Drain. Eng., 129(6), 449–453.
16.
Singh, S. K., Mishra, G. C., Swamee, P. K., and Ojha, C. S. P. (2002). “Aquifer diffusivity and stream resistance from varying stream stage.” J. Irrig. Drain. Eng., 128(1), 57–61.
17.
Swamee, P. K., and Singh, S. K. (2003). “Estimation of aquifer diffusivity from stream stage variation.” J. Hydrologic Eng., 8(1), 20–24.
18.
Workman, S. R., Serrano, S. E., and Liberty, K. (1997). “Development and application of an analytical model of stream/aquifer interaction.” J. Hydrol., 200(1–4), 149–164.
19.
Zlotnik, V., 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.
Information & Authors
Information
Published In
Journal of Hydraulic Engineering
Volume 130 • Issue 11 • November 2004
Pages: 1108 - 1118
Copyright
Copyright © 2004 ASCE.
History
Published online: Oct 15, 2004
Published in print: Nov 2004
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.