Chapter 9
Model Uncertainty Analysis and the Margin of Safety
Publication: Total Maximum Daily Load Development and Implementation: Models, Methods, and Resources
Abstract
This chapter covers the state-of-the-practice on the selection of margin of safety (MOS) in total maximum daily loads (TMDL) and the state-of-the-art on model uncertainty estimation and risk-based MOS determination. It provides a summary of sources of uncertainty, approaches for MOS, a survey of MOS types implemented in practice, and advanced probabilistic methods that practitioners may find helpful in future TMDL development. Uncertainty analysis quantifies predictive capability of a model and therefore a necessary step after calibration and validation of the model. An explicit inclusion of the MOS is performed by setting aside a fraction of the calculated assimilative loading capacity to account for uncertainty in the TMDL study. Several TMDL studies have considered statistical models including linear regression. Bayesian methods utilize Bayes theorem to formally modify the prior assumptions on model parameters and to update the probability distributions of the parameters and model outputs as additional information becomes available.
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Total Maximum Daily Load Development and Implementation: Models, Methods, and Resources
Pages: 271 - 306
Editors: Harry X. Zhang, Ph.D., Nigel W.T. Quinn, Ph.D. https://orcid.org/0000-0003-3333-4763, Deva K. Borah, Ph.D. https://orcid.org/0000-0002-2107-9390, and G. Padmanabhan, Ph.D. https://orcid.org/0000-0002-3209-1379
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- Deva K. Borah, Harry X. Zhang, Moira Zellner, Ebrahim Ahmadisharaf, Meghna Babbar-Sebens, Nigel W. T. Quinn, Saurav Kumar, Vamsi Krishna Sridharan, Navaratnam Leelaruban, Craig Lott, Advances in Total Maximum Daily Load Implementation Planning by Modeling Best Management Practices and Green Infrastructures, Journal of Environmental Engineering, 10.1061/JOEEDU.EEENG-7578, 150, 7, (2024).
- Harry X. Zhang, John J. Ramirez-Avila, Deva K. Borah, Zhonglong Zhang, Advancing Watershed Modeling for TMDL and Holistic Watershed Management Including Climate Change Impacts, World Environmental and Water Resources Congress 2023, 10.1061/9780784484852.112, (1227-1241), (2023).