Applying the First-Order Error Analysis in Determining the Margin of Safety for Total Maximum Daily Load Computations
Publication: Journal of Environmental Engineering
Volume 130, Issue 6
Abstract
There are significant uncertainties associated with certain aspects of the total maximum daily load (TMDL) estimation. Selection of the “margin of safety (MOS)” term is typically made by subjectively assigning to it a small percentage (5–10%) of the TMDL load. To introduce some objectivity into the MOS estimation, the first-order error analysis (FOEA) was utilized to quantify the MOS term in the TMDL formulation. A case study, which was based on a previous study entitled “Nitrate TMDL Development for Muddy Creek/Dry River, Virginia,” is presented in this paper. Besides computational efficiency, one of the major advantages of FOEA is its capability of determining the relative importance of the various parameters that contribute to the overall variance of the model output. Precipitation was found by far to be the most dominant source of uncertainty. Furthermore, a relationship was established to link the pollutant loads with the FOEA output concentrations. The results from testing different TMDL allocation scenarios demonstrate that with the increase of relative percentage of nonpoint sources load reduction in the total load reduction, the portion needed to be reserved for MOS increases as well. The MOS term can be related to the variability in rainfall and therefore would be different for different locations in the country. In summary, as a practical, less subjective and reliable approach to TMDL uncertainty analysis, the use of the FOEA is considered as a viable alternative to the current simple explicit and implicit methods in estimating the MOS term for TMDL calculations.
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References
Ang, A. H. S., and Tang, W. H. (1984). Probability concepts in engineering planning and design, Vol. II: Decision, risk and reliability, Wiley, New York.
Beck, M. B.(1987). “Water quality modeling: A review of the analysis of uncertainty.” Water Resour. Res., 23(5), 1393–1441.
Bicknell, B. R., Imhoff, J. C., Kittle, J. L., Jr., and Donigian, A. S., Jr. (1996). Hydrological simulation program—FORTRAN, user’s manual for release 11, Environmental Research Laboratory, U.S. EPA, Athens, Ga.
Bobba, A. G., Singh, V. P., and Bengtsson, L.(1996). “Application of first-order and Monte Carlo analysis in watershed water quality models.” Water Resour. Manage., 10, 219–240.
Bowie, G. L. (1985). “Rates, constants, and kinetic formulation in surface water quality modeling.” Rep. EPA/600/3-85/040, U.S. EPA, Athens, Ga.
Brown, L. C. (2001). “Modeling uncertainty—QUAL2E-UNCAS: A case study.” Water Environment Federation—National TMDL Science Issues Conf., St. Louis.
Brown, L. C., and Barnwell, T. O., Jr. (1987). “The enhanced stream water quality models QUAL2E and QUAL2E-UNCAS: Document and user manual.” Rep. No. EPA 600/3-87/007, Athens, Ga.
Burgers, S. J., and Lettenmaier, D. P.(1975). “Probabilistic methods in stream quality management.” Water Resour. Bull., 11(1), 115–130.
Chadderton, R. A., Miller, A. C., and McDonnell, A. J.(1982). “Uncertainty analysis of dissolved oxygen model.” J. Environ. Eng., 108(5), 1003–1013.
Chen, C. W., Herr, J., Ziemelis, L., Goldstein, R. A., and Olmsted, L.(1999). “Decision support system for total maximum daily load.” J. Water Resour. Plan. Manage., 125(7), 653–659.
Cornell, C. A. (1972). “First-order analysis of model and parameter uncertainty.” Proc., Int. Symp. on Uncertainties in Hydrology and Water Resources Systems, Tucson, Ariz., Vol. 3, 1245–1272.
Culver, T. B., Naperala, T. R., Potts, A., Zhang, X., Neeley, K., and Yu, S. L.(2002a). “Case study of impact of total maximum daily load allocations on nitrate leaching.” J. Water Resour. Plan. Manage., 128(4), 262–270.
Culver, T. B., Neeley, K., Yu, S. L., Zhang, X., Potts, A., and Naperala, T. R. (2002b). “The Muddy Creek/Dry River nitrate total maximum daily load: Leading by example.” Water Resour. Update, March, 5–13.
Culver, T. B., Zhang, X., Naperala, T., Potts, A., Neeley, K., Yu, S., Froehlich, M., Gregory, R., Martin, C., Bodkin, R., Mizell, C. T., Lazarus, D., Bennett, M., Wade, C., and Schneider, J. (2000). “Nitrate TMDL development for Muddy Creek/Dry River, Virginia.” Final Rep. to Virginia Department of Environmental Quality, and Virginia Department of Conservation and Recreation and EPA Region 3.
Dilks, D. (2002). “Improved methods for calculating the TMDL margin of safety.” Water Environment Federation—National TMDL Science and Policy Conf., Phoenix, Ariz.
Donigian, A. S., Jr., Bicknell, B. R., and Imhoff, J. C. (1995). “Hydrological simulation program—FORTRAN (HSPF).” Computer models of watershed hydrology, V. P. Singh, ed., Water Resources Publication, Littleton, Colo., 395–442.
Garen, D. C., and Burges, S. J.(1981). “Approximate error bounds for simulated hydrographs.” J. Hydraul. Div., Am. Soc. Civ. Eng., 107(11), 1519–1534.
Jacomino, V. M. F., and Field, D. E.(1997). “A critical approach to the calibration of a watershed model.” J. Am. Water Resour. Assoc., 32(1), 143–154.
Johnson, P. A., and Rinaldi, M. (1998). “Uncertainty in stream channel restoration.” Uncertainty modeling and analysis in civil engineering, B. M. Ayyub, ed., CRC Press, Boca Raton, Fla., 425–437.
Lee, H. L., and Mays, L. W.(1986). “Hydraulic uncertainties in flood levee capacity.” J. Hydraul. Eng., 112(10), 928–934.
Lei, J., and Schilling, W.(1994). “Parameter uncertainty propagation analysis for urban rainfall runoff modeling.” Water Sci. Technol., 29(1–2), 145–154.
Malone, R., Bowles, D. S., Windham, M. P., and Grenney, W. J.(1983). “Comparison of techniques for assessing of loading uncertainty upon a long-term phosphorous model.” Appl. Math. Model., 7, 11–18.
Melching, C. S. (1995). “Reliability estimation.” Computer models of watershed hydrology, V. P. Singh, ed., Water Resources Publications, Littleton, Colo., 69–118.
Melching, C. S., and Anmangandla, S.(1992). “Improved first-order uncertainty method for water-quality modeling.” J. Environ. Eng., 118(5), 791–805.
Melching, C. S., and Yoon, C. G.(1996). “Key sources of uncertainty in QUAL2E model of Passaic River.” J. Water Resour. Plan. Manage., 122(2), 105–113.
Morgan, M. G., and Henrion, M. (1990). Uncertainty: A guide to dealing with uncertainty in quantitative risk and policy analysis, Cambridge University Press, Cambridge, U.K.
Muddy Creek TMDL Establishment Workgroup (MCTEW). (1999). Fecal coliform TMDL development for Muddy Creek, Virginia.
National Research Council (NRC). (2001). Assessing the TMDL approach to water quality management, Washington, D.C.
Novotny, V.(1999). “Integrating diffuse/nonpoint pollution control and water body restoration into watershed management.” J. Am. Water Resour. Assoc., 35(4), 717–727.
Scavia, D., Powers, W. F., Canale, R. P., and Moody, J. L.(1981). “Comparison of first-order error analysis and Monte Carlo simulation in time-dependent lake eutrophication models.” Water Resour. Res., 17(4), 1051–1059.
Tang, W. H., Mays, L. W., and Yen, B. C.(1975). “Optimal risk-based design of storm sewer networks.” J. Environ. Eng., 101(3), 381–398.
Tung, Y. K.(1987). “Uncertainty analysis of National Weather Service rainfall frequency atlas.” J. Hydraul. Eng., 113(2), 179–189.
Tung, Y. K., and Hathhorn, W. E.(1988). “Assessment of probability distribution of dissolved oxygen deficit.” J. Environ. Eng., 114(6), 1421–1435.
Tung, Y. K., and Mays, L. W.(1980). “Risk analysis for hydraulic design.” J. Hydraul. Div., Am. Soc. Civ. Eng., 106(5), 893–913.
Tung, Y. K., and Mays, L. W.(1981). “Risk models for levee design.” Water Resour. Res., 17(4), 833–841.
U.S. EPA. (1986). “Methodology for analysis of detention basins for control of urban runoff quality.” EPA 440/5-87-001, Washington, D.C.
U.S. EPA. (1991). “Guidance for water quality-based decisions: The TMDL process.” EPA 440/4-91-001, Washington, D.C.
U.S. EPA. (1996). TMDL background paper #2: Criteria for EPA approval of state/tribal TMDLs, 〈http://www.epa.gov/OWOW/tmdl/nov96mtg/back2.html〉
U.S. EPA. (1999a). “Draft guidance for water quality-based decisions: The TMDL process (second edition).” EPA Rep. 841-D-99-001, Washington, D.C.
U.S. EPA. (1999b). “Protocol for developing nutrient TMDLs (first edition).” Rep. EPA 841-B-99-007, Washington, D.C.
U.S. EPA. (2000). Joseph Piotrowski, Acting Director, Water Protection Division, U.S. EPA, Letter of Approval for the Muddy Creek, Rockingham County TMDL for Nitrate to Mr. Larry Lawson, VADEQ, April 27, 2000.
U.S. EPA. (2002). “The twenty needs report: How research can improve the TMDL program.” EPA Rep. 841-B-02-002, Washington, D.C.
Wagner, R. A., Tisdale, T. S., and Zhang, J.(1996). “A framework for phosphorus transport modeling in the Lake Okeechobee Watershed.” Water Resour. Bull., 32(1), 57–73.
Walker, W. W.(1982). “A sensitivity analysis and error analysis framework for lake eutrophication modeling.” Water Resour. Bull., 18, 53–60.
Warwick, J. J.(1997). “Use of first-order uncertainty analysis to optimize successful stream water quality simulation.” J. Am. Water Resour. Assoc., 33(6), 1173–1185.
Yeh, K. C., and Tung, Y. K.(1993). “Uncertainty and sensitivity analyses of pit-migration model.” J. Hydraul. Eng., 119(2), 262–283.
Yen, B. C., Cheng, S. T., and Melching, C. S. (1986). “First order reliability analysis.” Stochastic and risk analysis in hydraulic engineering, B. C. Yen, ed., Water Resources Publications, Littleton, Colo., 1–36.
Yen, B. C., and Tang, W. H.(1976). “Risk-safety factor relation for storm sewer design.” J. Environ. Eng., 102(2), 509–516.
Yu, S. L., Hamilton, P. A., and Kent, C. E. (1984). “Temporal distribution of rainfall in Virginia.” Final Rep. VTRC 85-R29, Virginia Transportation Research Council, Charlottesville, Va.
Zhang, H. X. (2000). “The critical flow-storm approach and uncertainty analysis for the TMDL development process.” PhD dissertation, Department of Civil Engineering, University of Virginia, Charlottesville, Va.
Zhang, H. X., and Fillmore, L. A. (2003). “Is the TMDL on target: Rigorous uncertainty analysis can help ensure that a TMDL includes a reasonable margin of safety.” Water Envir. Tech., June, 27–31.
Zhang, H. X., and Yu, S. L. (2002). “Uncertainty analysis of margin of safety in a nutrient TMDL modeling and allocation.” Water Environment Federation—Watershed’02, Fort Lauderdale, Fla.
Zhang, H. X., Yu, S. L., and Culver, T. B. (2001). “The critical flow-storm approach for nitrate TMDL development in the Muddy Creek Watershed, Virginia.” WEFTEC’01, Atlanta.
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Information
Published In
Journal of Environmental Engineering
Volume 130 • Issue 6 • June 2004
Pages: 664 - 673
Copyright
Copyright © 2004 American Society of Civil Engineers.
History
Received: Jan 2, 2003
Accepted: Jun 30, 2003
Published online: May 14, 2004
Published in print: Jun 2004
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