Control of Contaminant Releases in Rivers. I: Adjoint Sensitivity Analysis
Publication: Journal of Hydraulic Engineering
Volume 123, Issue 6
Abstract
A mathematical method that determines the sensitivity of solute concentration to real-time changes of the loading intensity at a remote source is developed here. The hydrodynamic and mass transport conditions correspond to flow in rivers and shallow estuaries and numerical simulations are performed by a two-dimensional finite-element model. The sensitivities are evaluated by solution of the adjoint equation of the fate and transport problem, which is shown to produce accurate results with increased efficiency when compared to equivalent perturbations of the loading intensity of the contaminant source. The corresponding reduction in computational effort allows the real-time optimal control of a contaminant release, which cannot be accomplished otherwise. The method is validated by comparisons with perturbation solutions in channels of simple geometry. Results are also presented for a practical application corresponding to the upper Potomac estuary.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Cacuci, D. G.(1981). “Sensitivity theory for nonlinear systems. I: nonlinear functional analysis approach.”J. Math. Phys., 22(12), 2794–2802.
2.
Chavent, G., Dupuy, M., and Lemonnier, P.(1975). “History matching by use of optimal control theory.”Soc. Petr. Engrg. J., 15(1), 74–86.
3.
Dogru, A. H., and Seinfeld, J. H. (1981). “Comparison of sensitivity coefficient calculation methods in automatic history matching.”Soc. Petr. Engrg. J., 21(5).
4.
Hall, M. C. G., and Cacuci, D. G. (1982). “Sensitivity analysis of a radiative-convective model by the adjoint method.”J. Atmospheric Sci., 39(May).
5.
Jarny, Y., Ozisik, M. N., and Bardon, J. P.(1991). “A general optimization method using adjoint equation for solving multidimensional inverse heat conduction.”Int. J. of Heat Mass Transfer, 34(11), 2911–2919.
6.
Kapitza, H. (1991). “Numerical experiments with the adjoint of a nonhydrostatic mesoscale model.”Am. Meteorological Soc. (Apr.).
7.
Katopodes, N. D.(1984). “A dissipative Galerkin scheme for open channel flow.”J. Hydr. Engrg., ASCE, 110(4), 450–466.
8.
Katopodes, N. D. (1987). “Finite element model for hydrodynamics and mass transport in the Upper Potomac Estuary.”Rep. Prepared for Metropolitan Washington Council of Governments.
9.
Marchuk, G. I. (1986). “Mathematical models in environmental problems.”Studies in mathematics and its applications, Vol. 16, North-Holland Publishing Co., Amsterdam, The Netherlands.
10.
Neuman, S. P., and Carrera, J.(1985). “Maximum likelihood adjoint-state finite element estimation of groundwater parameters under steady and non-steady conditions.”Appl. Math. and Computation, 17, 405–432.
11.
Piasecki, M. (1994). “Control of hazardous waste disposals in rivers and estuaries using the adjoint equation solution,” PhD thesis, Dept. of Civ. and Envir. Engrg., Univ. of Michigan, Ann Arbor, Mich.
12.
Sagan, H. (1969). Introduction to the calculus of variations. McGraw-Hill Book Co., Inc., New York, N.Y.
13.
Sinokrot, B. A., and Stefan, H. G. (1994). “Stream water-temperature sensitivity to weather and bed parameters.”J. Hydr. Engrg., 120(6).
14.
Sykes, J. F.(1985). “Sensitivity analysis for steady state ground water flow using adjoint operators.”Water Resour. Res., 21(3), 359–371.
15.
Wilson, J. L., and Metcalfe, D. E.(1985). “Illustration and verification of adjoint sensitivity theory for steady state groundwater flow.”Water Resour. Res., 21(11), 1602–1610.
16.
Yeh, W. W.-G., and Sun, N.-Z.(1990). “Variational sensitivity analysis, data requirements and parameter identification in a leaky aquifer system.”Water Resour. Res., 26(9), 1927–1938.
Information & Authors
Information
Published In
Journal of Hydraulic Engineering
Volume 123 • Issue 6 • June 1997
Pages: 486 - 492
Copyright
Copyright © 1997 American Society of Civil Engineers.
History
Published online: Jun 1, 1997
Published in print: Jun 1997
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.