American Society of Agricultural and Biological Engineers

Click on “Download PDF” for the PDF version or on the title for the HTML version.

If you are not an ASABE member or if your employer has not arranged for access to the full-text, Click here for options.


Published by the American Society of Agricultural and Biological Engineers, St. Joseph, Michigan

Citation:  Transactions of the ASABE. Vol. 49(4): 1033-1049. (doi: 10.13031/2013.21741) @2006
Authors:   A. Shirmohammadi, I. Chaubey, R. D. Harmel, D. D. Bosch, R. Muñoz-Carpena, C. Dharmasri, A. Sexton, M. Arabi, M. L. Wolfe, J. Frankenberger, C. Graff, T. M. Sohrabi
Keywords:   Latin hypercube sampling, Margin of safety, Monte Carlo simulation, TMDL, Uncertainty

Although the U.S. Congress established the Total Maximum Daily Load (TMDL) program in the original Clean Water Act of 1972, Section 303(d), it did not receive attention until the 1990s. Currently, two methods are available for tracking pollution in the environment and assessing the effectiveness of the TMDL process on improving the quality of impaired water bodies: field monitoring and mathematical/computer modeling. Field monitoring may be the most appropriate method, but its use is limited due to high costs and extreme spatial and temporal ecosystem variability. Mathematical models provide an alternative to field monitoring that can potentially save time, reduce cost, and minimize the need for testing management alternatives. However, the uncertainty of the model results is a major concern. Uncertainty is defined as the estimated amount by which an observed or calculated value may depart from the true value, and it has important policy, regulatory, and management implications. The source and magnitude of uncertainty and its impact on TMDL assessment has not been studied in depth. This article describes the collective experience of scientists and engineers in the assessment of uncertainty associated with TMDL models. It reviews sources of uncertainty (e.g., input variability, model algorithms, model calibration data, and scale), methods of uncertainty evaluation (e.g., first-order approximation, mean value first-order reliability method, Monte Carlo, Latin hypercube sampling with constrained Monte Carlo, and generalized likelihood uncertainty estimation), and strategies for communicating uncertainty in TMDL models to users. Four case studies are presented to highlight uncertainty quantification in TMDL models. Results indicate that uncertainty in TMDL models is a real issue and should be taken into consideration not only during the TMDL assessment phase, but also in the design of BMPs during the TMDL implementation phase. First-order error (FOE) analysis and Monte Carlo simulation (MCS) or any modified versions of these two basic methods may be used to assess uncertainty. This collective study concludes that a more scientific method to account for uncertainty would be to develop uncertainty probability distribution functions and transfer such uncertainties to TMDL load allocation through the margin of safety component, which is selected arbitrarily at the present time. It is proposed that explicit quantification of uncertainty be made an integral part of the TMDL process. This will benefit private industry, the scientific community, regulatory agencies, and action agencies involved with TMDL development and implementation.

(Download PDF)    (Export to EndNotes)