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.

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Hydrologic and water quality (H/WQ) models are being used with increasing frequency to devise alternative pollution control strategies. It has been recognized that such models may have a large degree of uncertainty associated with their predictions, and that this uncertainty can significantly impact the utility of the model. In this study, ARRAMIS (Advanced Risk & Reliability Assessment Model) software package was used to analyze the uncertainty of the SWAT2000 (Soil and Water Assessment Tool) outputs concerning nutrients and sediment losses from agricultural lands. ARRAMIS applies Monte Carlo simulation technique connected with Latin hypercube sampling (LHS) scheme. This technique is applied to the Warner Creek watershed located in the Piedmont physiographic region of Maryland, and it provides an interval estimate of a range of values with an associated probability instead of a point estimate of a particular pollutant constituent. Uncertainty of model outputs was investigated using LHS scheme with restricted pairing for the model input sampling. Probability distribution functions (pdfs) for each of the 50 model simulations were constructed from these results. Model output distributions of interest in this analysis were stream flow, sediment, organic nitrogen (organic-N), organic phosphorus (organic-P), nitrate, ammonium, and mineral phosphorus (mineral-P) transported with water. Developed probability distribution functions for the model provided information with desirable probability. Results indicate that consideration of input parameter uncertainty produces 64% less mean stream flow along with approximately 8.2% larger sediment loading than obtained using mean input parameters. On the contrary, mean of outputs regarding nutrients such as nitrate, ammonia, organic-N, and organic-P (but not mineral-P) were almost the same as the one using mean input parameters. The uncertainty in predicted stream flow and sediment loading is large, but that for nutrient loadings is the same as that of the corresponding input parameters. This study concluded that using a best possible distribution for the input parameters to reflect the impact of soils and land use diversity in a small watershed on SWAT2000 model outputs may be more accurate than using average values for each input parameter.

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One of the important factors in fertilizer application efficiency in surface fertigation is the shape of inflow hydrographs. In this research, a fertigation model is developed to analyse the effect of surge flow on furrow fertigation. Saint-Venant equations and the advection-dispersion equation were used to estimate water flow and solute transport characteristics, respectively. The field experiments, including different fertigation treatments with surge flow, were conducted to calibrate and evaluate the developed model. Most of the water and nitrate losses occurred through runoff; water losses through runoff ranged from 13.8 to 33.4%, while fertilizer losses varied between 5.1 and 47%. Water and nitrate losses in the second fertigation experiments were higher than those in the first due to the reduction of the surge effect. A comparison between simulated and observed data shows appropriate accuracy of the developed model; the root mean squared error (RMSE) index for nitrate and water runoff losses was 8.4 and 12.1%, respectively. Fertigation during all advance surges was recognized as the desirable option in furrow irrigation with a surge flow.