Reliability-Based Water Quality Assessment with Load Resistance Factor Design: Application to TMDL
Publication: Journal of Hydrologic Engineering
Volume 23, Issue 12
Abstract
Effective load reduction strategies rely on an accurate Total Maximum Daily Load (TMDL) calculation, which assesses pollutant loading from various sources. Quantification of uncertainty is a critical part of the TMDL process. To account for uncertainty, this paper adapts the load resistance factor design (LRFD), a reliability-based framework, to water quality assessment and the TMDL process. The LRFD replaces the traditional lumped margin of safety (MOS) with design factors that reflect the magnitude and distribution of uncertainty among the various contaminant loads. In addition, it produces load reduction estimates to meet management objectives with a contaminant-specific frequency-based target. The LRFD is computationally efficient and flexible in that, to compute the design factors, the procedure can use measurement data, analytical solutions or model simulation results, as well as full or marginal probability distributions. The applicability of the proposed approach is demonstrated with two case studies.
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Acknowledgments
The authors gratefully acknowledge the National Science Foundation for supporting this research (CBET-1351361 award). The authors thank Dr. A. Safwat for assistance with ArcGIS processing. Algorithms and data used in this paper are publicly available on HydroShare at http://www.hydroshare.org/resource/0fd4e32862fa4097a0d8211b40d5bfef. The USEPA, through its Office of Research and Development, partially funded and collaborated in the research described herein. Any opinions expressed in this paper are those of the authors and do not reflect the views of the Agency, and therefore no official endorsement should be inferred. Any mention of trade names or commercial products does not constitute endorsement or recommendation for use by the USEPA.
References
Ang, A., and W. Tang. 1984. Probability concepts in engineering planning and design. Hoboken, NJ: Wiley.
Ascough, J. C., H. R. Maier, J. K. Ravalico, and M. W. Strudley. 2008. “Future research challenges for incorporation of uncertainty in environmental and ecological decision-making.” Ecol. Modell. 219 (3–4): 383–399. https://doi.org/10.1016/j.ecolmodel.2008.07.015.
Barker, R. M., and J. A. Puckett. 2013. Design of highway bridges: An LRFD approach. Hoboken, NJ: Wiley.
Beven, K., and A. Binley. 1992. “The future of distributed models: Model calibration and uncertainty prediction.” Hydrol. Processes 6 (3): 279–298. https://doi.org/10.1002/hyp.3360060305.
Borsuk, M. E., C. A. Stow, and K. H. Reckhow. 2002. “Predicting the frequency of water quality standard violations: A probabilistic approach for TMDL development.” Environ. Sci. Technol. 36 (10): 2109–2115. https://doi.org/10.1021/es011246m.
Borsuk, M. E., C. A. Stow, and K. H. Reckhow. 2003. “Integrated approach to total maximum daily load development for Neuse River Estuary using Bayesian probability network model (Neu-BERN).” J. Water Resour. Plann. Manage. 129 (4): 271–282. https://doi.org/10.1061/(ASCE)0733-9496(2003)129:4(271).
Camacho, R. A., J. L. Martin, T. Wool, and V. P. Singh. 2018. “A framework for uncertainty and risk analysis in total maximum daily load applications.” Environ. Modell. Software 101 (1): 218–235. https://doi.org/10.1016/j.envsoft.2017.12.007.
Carto. 2018. “Builder.” Accessed August 29, 2018. https://carto.com/builder/.
Chin, D. A. 2009. “Risk-based TMDLs in pathogen-impaired waters.” J. Water Resour. Plann. Manage. 135 (6): 521–527. https://doi.org/10.1061/(ASCE)0733-9496(2009)135:6(521).
CWA (Clean Water Act). 1972. Federal water pollution control amendments. Washington, DC: US Environmental Protection Agency.
Dilks, D. W., and P. L. Freedman. 2004. “Improved consideration of the margin of safety in total maximum daily load development.” J. Environ. Eng. 130 (6): 690–694. https://doi.org/10.1061/(ASCE)0733-9372(2004)130:6(690).
Ellingwood, B. R. 1997. “Probability-based LRFD for engineered wood construction.” Struct. Saf. 19 (1): 53–65. https://doi.org/10.1016/S0167-4730(96)00030-6.
EWRI (Environmental and Water Resources Institute). 2017. Total maximum daily load analysis and modeling: Assessment of the practice. Reston, VA: ASCE.
Fenton, G. A., and D. V. Griffiths. 2008. Risk assessment in geotechnical engineering. Hoboken, NJ: Wiley.
Franceschini, S., and C. W. Tsai. 2008. “Incorporating reliability into the definition of the margin of safety in total maximum daily load calculations.” J. Water Resour. Plann. Manage. 134 (1): 34–44. https://doi.org/10.1061/(ASCE)0733-9496(2008)134:1(34).
Galambos, T. V., and M. K. Ravindra. 1978. “Properties of steel for use in LRFD.” J. Struct. Div. 104 (9): 1459–1468.
Gren, I.-M., G. Destouni, and R. Tempone. 2002. “Cost effective policies for alternative distributions of stochastic water pollution.” J. Environ. Manage. 66 (2): 145–157. https://doi.org/10.1006/jema.2002.0569.
Gronewold, A. D., and M. E. Borsuk. 2009. “A software tool for translating deterministic model results into probabilistic assessments of water quality standard compliance.” Environ. Modell. Software 24 (10): 1257–1262. https://doi.org/10.1016/j.envsoft.2009.04.004.
Haldar, A. 2008. “Status and recent trends in reliability for civil engineering problems.” In Handbook of performability engineering, 1025–1046. London: Springer.
Haldar, A., and S. Mahadevan. 2000. Probability, reliability and statistical methods in engineering design. New York: Wiley.
Hamed, M. M., and P. B. Bedient. 1997. “On the performance of computational methods for the assessment of risk from ground-water contamination.” Ground Water 35 (4): 638–646. https://doi.org/10.1111/j.1745-6584.1997.tb00129.x.
Hantush, M. M., and A. Chaudhary. 2014. “Bayesian framework for water quality model uncertainty estimation and risk management.” J. Hydrol. Eng. 19 (9): 04014015. https://doi.org/10.1061/(ASCE)HE.1943-5584.0000900.
Hashimoto, T., J. R. Stedinger, and D. P. Loucks. 1982. “Reliability, resiliency, and vulnerability criteria for water resource system performance evaluation.” Water Resour. Res. 18 (1): 14–20. https://doi.org/10.1029/WR018i001p00014.
Jang, Y.-S., N. Sitar, and A. Der Kiureghian. 1994. “Reliability analysis of contaminant transport in saturated porous media.” Water Resour. Res. 30 (8): 2435–2448. https://doi.org/10.1029/93WR03554.
Jia, Y., and T. B. Culver. 2008. “Uncertainty analysis for watershed modeling using generalized likelihood uncertainty estimation with multiple calibration measures.” J. Water Resour. Plann. Manage. 134 (2): 97–106. https://doi.org/10.1061/(ASCE)0733-9496(2008)134:2(97).
Karamouz, M., M. Taheriyoun, M. Seyedabadi, and S. Nazif. 2015. “Uncertainty based analysis of the impact of watershed phosphorus load on reservoir phosphorus concentration.” J. Hydrol. 521 (1): 533–542. https://doi.org/10.1016/j.jhydrol.2014.12.028.
Kay, D., et al. 2008. “Faecal indicator organism concentrations and catchment export coefficients in the UK.” Water Res. 42 (10–11): 2649–2661. https://doi.org/10.1016/j.watres.2008.01.017.
Koltun, G., and M. Whitehead. 2001. Techniques for estimating selected streamflow characteristics of rural, unregulated streams in Ohio. Columbus, OH: USGS.
Langseth, D. E., and N. Brown. 2011. “Risk-based margins of safety for phosphorus TMDLs in lakes.” J. Water Resour. Plann. Manage. 137 (3): 276–283. https://doi.org/10.1061/(ASCE)WR.1943-5452.0000097.
Limpert, E., W. A. Stahel, and M. Abbt. 2001. “Log-normal distributions across the sciences: Keys and clues.” Bioscience 51 (5): 341–352. https://doi.org/10.1641/0006-3568(2001)051[0341:LNDATS]2.0.CO;2.
Loucks, D. P. 1997. “Quantifying trends in system sustainability.” Hydrol. Sci. J. 42 (4): 513–530. https://doi.org/10.1080/02626669709492051.
Maier, H. R., B. J. Lence, B. A. Tolson, and R. O. Foschi. 2001. “First-order reliability method for estimating reliability, vulnerability, and resilience.” Water Resour. Res. 37 (3): 779–790. https://doi.org/10.1029/2000WR900329.
Mayer, A. L., W. Shuster, J. Beaulieu, M. E. Hopton, L. K. Rhea, A. H. Roy, and H. W. Thurston. 2012. “Environmental review and case studies: Building green infrastructure via citizen participation: A six-year study in the Shepherd Creek (Ohio).” Environ. Pract. 14 (1): 57–67. https://doi.org/10.1017/S1466046611000494.
McCormac, J. C., and J. K. Nelson. 2003. Structural steel design: LRFD method. Upper Saddle River, NJ: Prentice Hall.
Miltner, R. J. 2010. “A method and rationale for deriving nutrient criteria for small rivers and streams in Ohio.” Environ. Manage. 45 (4): 842–855. https://doi.org/10.1007/s00267-010-9439-9.
Nowak, A. S. 1995. “Calibration of LRFD bridge code.” J. Struct. Eng. 121 (8): 1245–1251. https://doi.org/10.1061/(ASCE)0733-9445(1995)121:8(1245).
NRC (National Research Council). 2001. Assessing the TMDL approach to water quality management. Washington, DC: National Academies Press.
Paikowsky, S. G., et al. 2004. Load and resistance factor design (LRFD) for deep foundations. Washington, DC: Transportation Research Board.
Patil, A., and Z. Q. Deng. 2011. “Bayesian approach to estimating margin of safety for total maximum daily load development.” J. Environ. Manage. 92 (3): 910–918. https://doi.org/10.1016/j.jenvman.2010.10.049.
Reckhow, K. H. 2003. “On the need for uncertainty assessment in TMDL modeling and implementation.” J. Water Resour. Plann. Manage. 129 (4): 245–246. https://doi.org/10.1061/(ASCE)0733-9496(2003)129:4(245).
Riasi, M. S., A. Teklitz, B. Shuster, C. Nietch, and L. Yeghiazarian. 2018. “Reliability-based water quality assessment with LRFD.” HydroShare, in press.
Robertson, D. M., and D. A. Saad. 2011. “Nutrient inputs to the Laurentian great lakes by source and watershed estimated using SPARROW watershed models.” J. Am. Water Resour. Assoc. 47 (5): 1011–1033. https://doi.org/10.1111/j.1752-1688.2011.00574.x.
Roy, A. H., H. Cabezas, M. P. Clagett, N. T. Hoagland, A. L. Mayer, M. A. Morrison, and H. W. Thurston. 2006. “Retrofit stormwater management: Navigating multidisciplinary hurdles at the watershed scale.” Stormwater 7: 16–29.
Roy, A. H., L. K. Rhea, A. L. Mayer, W. D. Shuster, J. J. Beaulieu, M. E. Hopton, M. A. Morrison, and A. St Amand. 2014. “How much is enough? Minimal responses of water quality and stream biota to partial retrofit stormwater management in a suburban neighborhood.” PLOS One 9 (1): 1–14. https://doi.org/10.1371/journal.pone.0085011.
Saka, M. P., and Z. W. Geem. 2013. “Mathematical and metaheuristic applications in design optimization of steel frame structures: An extensive review.” Math. Prob. Eng. 2013 (1): 1–33. https://doi.org/10.1155/2013/271031.
Sandoval-Solis, S., D. C. McKinney, and D. P. Loucks. 2011. “Sustainability index for water resources planning and management.” J. Water Resour. Plann. Manage. 137 (5): 381–390. https://doi.org/10.1061/(ASCE)WR.1943-5452.0000134.
Shirmohammadi, A., et al. 2006. “Uncertainty in TMDL models.” Trans. ASABE 49 (4): 1033–1049. https://doi.org/10.13031/2013.21741.
Shuster, W., and L. Rhea. 2013. “Catchment-scale hydrologic implications of parcel-level stormwater management (Ohio USA).” J. Hydrol. 485 (1): 177–187. https://doi.org/10.1016/j.jhydrol.2012.10.043.
Stow, C. A., K. H. Reckhow, S. S. Qian, E. C. Lamon, G. B. Arhonditsis, M. E. Borsuk, and D. Seo. 2007. “Approaches to evaluate water quality model parameter uncertainty for adaptive TMDL implementation.” J. Am. Water Resour. Assoc. 43 (6): 1499–1507. https://doi.org/10.1111/j.1752-1688.2007.00123.x.
Teklitz, A., W. Shuster, and L. Yeghiazarian. 2014. “Hydrologic network fault trees help understand patterns of water contamination.” In AGU Annual Meeting. Washington, DC: American Geological Union.
USEPA. 2007. An approach for using load duration curves in the development of TMDLs. Washington, DC: USEPA.
USEPA. 2008. Handbook for developing watershed TMDLs. Washington, DC: USEPA.
Van Buren, M. A., W. E. Watt, and J. Marsalek. 1997. “Application of the log-normal and normal distributions to stormwater quality parameters.” Water Res. 31 (1): 95–104. https://doi.org/10.1016/S0043-1354(96)00246-1.
Wymer, L., and T. J. Wade. 2007. “The lognormal distribution and use of the geometric mean and the arithmetic mean in recreational water quality measurement.” In Statistical framework for recreational water quality criteria and monitoring, edited by L. Wymer. Chichester, UK: Wiley.
Zhang, H. X., and S. L. Yu. 2004. “Applying the first-order error analysis in determining the margin of safety for total maximum daily load computations.” J. Environ. Eng. 130 (6): 664–673. https://doi.org/10.1061/(ASCE)0733-9372(2004)130:6(664).
Zheng, Y., W. Wang, F. Han, and J. Ping. 2011. “Uncertainty assessment for watershed water quality modeling: A probabilistic collocation method based approach.” Adv. Water Resour. 34 (7): 887–898. https://doi.org/10.1016/j.advwatres.2011.04.016.
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Published In
Journal of Hydrologic Engineering
Volume 23 • Issue 12 • December 2018
Copyright
©2018 American Society of Civil Engineers.
History
Received: Sep 30, 2017
Accepted: Jul 10, 2018
Published online: Oct 5, 2018
Published in print: Dec 1, 2018
Discussion open until: Mar 5, 2019
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