TECHNICAL PAPERS
Jan 1, 1996

Chebyshev Model for Water-Quality Management

Publication: Journal of Water Resources Planning and Management
Volume 122, Issue 1

Abstract

A Chebyshev criterion is used to develop robust direct regulation water-quality management models. The reserve capacity of the stream, in terms of the excess capacities above the water-quality goal at the most critical water-quality checkpoints, is used as a measure of robustness of the management solutions to uncertainties in the water-quality input information. The models maximize the minimum reserve capacity along the river. They are applied to the control of biochemical oxygen–demanding waste in an example river basin based on the Willamette River in Oregon. The addition of a robustness measure in the model formulation gives additional insight into the management system. Although the mathematical formulation of the application is simple, the results provide important information for decision makers, such as identifying polluters with high waste-treatment cost per unit dissolved oxygen improvement at the critical stream locations. Such information is often useful for screening alternative options and making sophisticated water-quality policy and management decisions, based on detailed dynamic water-quality simulation.

Get full access to this article

View all available purchase options and get full access to this article.

References

1.
Ambrose, R. B. Jr., Fitzpatrick, T. A., Connoly, J. P., and Schanz, R. W. (1991). WASP5.x A hydrodynamic and water quality model theory, user manual, and programmer's guide . Envir. Res. Lab., Office of Res. Development, U.S. Envir. Protection Agency, Athens, Ga.
2.
Arikol, A. M., and Basak, N.(1985). “Equity approach to stream water quality management.”Eur. J. Operational Res., 20(2), 182–189.
3.
Baumol, W. J., and Oates, W. E. (1988). The theory of environmental policy, 2nd Ed., Cambridge University Press, Cambridge, England.
4.
Beavis, B., and Walker, M.(1979). “Interactive pollutants and joint abatement costs: achieving water quality standards with effluent charges.”J. Envir. Econ. Mgmt., 6(4), 275–286.
5.
Brill, E. D. Jr., Eheart, J. W., Kshirsagar, S. R., and Lence, B. J.(1984). “Water quality impacts of biochemical oxygen demand under transferable discharge permit programs.”Water Resour. Res., 20(4), 445–455.
6.
Brill, E. D. Jr., Liebman, J. C., and ReVelle, C. S.(1976). “Equity measures for exploring water quality management alternatives.”Water Resour. Res., 12(5), 845–851.
7.
Brown, L. C., and Barnwell, T. O. Jr. (1987). “The enhanced stream water quality models QUAL2E and QUAL2E-UNCAS: Documentation and user manual.”Rep. EPA/600/3-87/007, U.S. Envir. Protection Agency, Athens, Ga.
8.
Burn, D. H., and Lence, B. J.(1992). “Comparison of optimization formulations for waste load allocations.”J. Envir. Engrg. Div., ASCE, 118(4), 597–612.
9.
Burn, D. H., and McBean, E. A.(1985). “Optimization modeling of water quality in an uncertain environment.”Water Resour. Res., 21(7), 934–940.
10.
Burn, D. H., and McBean, E. A.(1986). “Linear stochastic optimization applied to biochemical oxygen demand—dissolved oxygen modelling.”Can. J. Civ. Engrg., 13(2), 249–254.
11.
Camp, T. R. (1963). Water and its impurities. Rheinhold Publishing, New York, N.Y.
12.
Chadderton, R. A., and Kropp, I. S.(1985). “Evaluation of eight wasteload allocation methods.”Water Resour. Bull., 21(5), 833–839.
13.
Dobbins, W. E.(1964). “BOD and oxygen relationships in streams.”J. Sanitary Engrg. Div., ASCE, 90(3), 53–78.
14.
Eheart, J. W.(1980). “Cost efficiency of transferable discharge permits for the control of BOD discharges.”Water Resour. Res., 16(6), 980–986.
15.
Eheart, J. W., Brill, E. D. Jr., Lence, B. J., Kilgore, J. D., and Uber, J. G.(1987). “Cost efficiency of time-varying discharge permit programs for water quality management.”Water Resour. Res., 23(2), 245–251.
16.
Eheart, J. W., Joeres, E. F., and David, M. H.(1980). “Distribution methods for transferable discharge permits.”Water Resour. Res., 16(5), 833–843.
17.
Ellis, J. H.(1987). “Stochastic water quality optimization using imbedded chance constraints.”Water Resour. Res., 23(12), 2227–2238.
18.
Johnson, E. L.(1967). “A study in the economics of water quality management.”Water Resour. Res., 3(2), 291–305.
19.
Kilgore, J. D. (1985). “Seasonal static transferable discharge permits for the control of biochemical oxygen demand in the Willamette River.”Working Paper No. 2, NSF Award PRA 81-21692, Dept. of Civ. Engrg., University of Illinois, Urbana, Ill.
20.
Lence, B. J., Eheart, J. W., and Brill, E. D. Jr.(1990). “Risk equivalent seasonal discharge programs for multidischarger streams.”J. Water Resour. Plng. and Mgmt. Div., ASCE, 116(2), 170–186.
21.
Lence, B. J., and Takyi, A. K.(1992). “Data requirements for seasonal discharge programs: an application of a regionalized sensitivity analysis.”Water Resour. Res., 28(7), 1781–1789.
22.
Liebman, J. C. (1965). “The optimal allocation of stream dissolved oxygen resources,” PhD thesis, Cornell University, Ithaca, N.Y.
23.
Liebman, J. C., and Lynn, W. R.(1966). “Optimal allocation of stream dissolved oxygen resources.”Water Resour. Res., 2(3), 581–591.
24.
Lohani, B. N., and Thanh, N. C.(1978). “Stochastic programming model for water quality management in a river.”J. Water Pollution Control Fed., 50(9), 2175–2182.
25.
Lohani, B. N., and Thanh, N. C.(1979). “Probabilistic water quality control policies.”J. Envir. Engrg. Div., ASCE, 105(4), 713–725.
26.
Loucks, D. P., ReVelle, C. S., and Lynn, W. R. (1967). “Linear programming for water pollution control.”Mgmt. Sci., 14(4), B166–B181.
27.
Michels, C. M. (1987). “Incorporating reserve capacity in the waste load allocation process,” MSc thesis, University of Illinois, Urbana, Ill.
28.
Montgomery, W. D.(1972). “Markets in licenses and efficient pollution control programs.”J. Econ. Theory, 5, 395–418.
29.
ReVelle, C. S., Loucks, D. P., and Lynn, W. R.(1968). “Linear programming applied to water quality management.”Water Resour. Res., 4(1), 1–9.
30.
Roberts, M. J. (1976). “Environmental protection: the complexities of real policy choice.”Managing the water environment, N. A. Swainson, ed., University of British Columbia Press, Vancouver, Canada, 157–235.
31.
Rose-Ackerman, S.(1977). “Market models for water pollution control: their strengths and weaknesses.”Public Policy, 25(3), 383–406.
32.
Sobel, M. J.(1965). “Water quality improvement programming problems.”Water Resour. Res., 1(4), 477–487.
33.
Sobel, M. J.(1969). “Chebyshev optimal waste discharges.”Operations Res., 19(2), 308–322.
34.
Takyi, A. K. (1991). “Uncertainty analysis for environmental management models: Application of the generalized sensitivity analysis,” MSc thesis, University of Manitoba, Winnipeg, Canada.
35.
Worley, J. L. (1963). “A system analysis method for water quality management by flow augmentation,” MSc thesis, Oregon State University, Corvllis, Oreg.

Information & Authors

Information

Published In

Go to Journal of Water Resources Planning and Management
Journal of Water Resources Planning and Management
Volume 122Issue 1January 1996
Pages: 40 - 48

History

Published online: Jan 1, 1996
Published in print: Jan 1996

Permissions

Request permissions for this article.

Authors

Affiliations

Andrews K. Takyi
Lect., Dept. of Civ. and Bldg. Engrg., Victoria Univ. of Tech., Box 14428 MMC, Melbourne, VIC 3000, Australia; formerly, Grad. Student, Dept. of Civ. and Geol. Engrg., Univ. of Manitoba, 15 Gillson Street, Winnipeg, MB, Canada, R3T-5V6.
Barbara J. Lence
Assoc. Prof., Dept. of Civ. and Geol. Engrg., Univ. of Manitoba, 15 Gillson Street, Winnipeg, MB, Canada, R3T-5V6.

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.

Cited by

View Options

Get Access

Access content

Please select your options to get access

Log in/Register Log in via your institution (Shibboleth)
ASCE Members: Please log in to see member pricing

Purchase

Save for later Information on ASCE Library Cards
ASCE Library Cards let you download journal articles, proceedings papers, and available book chapters across the entire ASCE Library platform. ASCE Library Cards remain active for 24 months or until all downloads are used. Note: This content will be debited as one download at time of checkout.

Terms of Use: ASCE Library Cards are for individual, personal use only. Reselling, republishing, or forwarding the materials to libraries or reading rooms is prohibited.
ASCE Library Card (5 downloads)
$105.00
Add to cart
ASCE Library Card (20 downloads)
$280.00
Add to cart
Buy Single Article
$35.00
Add to cart

Get Access

Access content

Please select your options to get access

Log in/Register Log in via your institution (Shibboleth)
ASCE Members: Please log in to see member pricing

Purchase

Save for later Information on ASCE Library Cards
ASCE Library Cards let you download journal articles, proceedings papers, and available book chapters across the entire ASCE Library platform. ASCE Library Cards remain active for 24 months or until all downloads are used. Note: This content will be debited as one download at time of checkout.

Terms of Use: ASCE Library Cards are for individual, personal use only. Reselling, republishing, or forwarding the materials to libraries or reading rooms is prohibited.
ASCE Library Card (5 downloads)
$105.00
Add to cart
ASCE Library Card (20 downloads)
$280.00
Add to cart
Buy Single Article
$35.00
Add to cart

Media

Figures

Other

Tables

Share

Share

Copy the content Link

Share with email

Email a colleague

Share