lthough sampling to assess transport of water quality constituents in runoff has been conducted for many years, relatively little information is available on the uncertainty of measured data. The need to understand uncertainty in measured water quality data has recently increased because of the adverse impact of diffuse or nonpoint-source pollution on rivers, lakes, and coastal waters (USEPA, 2000) and the intensified disputes regarding relative contributions of diffuse and point-source pollution (e.g., McFarland and Hauck, 2001). The issue of uncertainty is particularly important in water quality modeling because models are increasingly used to guide decisions regarding water resource policy, management, and regula-
Three different models of tipping bucket rain gauges (TBRs), viz. HS-TB3 (Hydrological Services Pty Ltd), ISCO-674 (Isco, Inc.) and TR-525 (Texas Electronics, Inc.), were calibrated in the lab to quantify measurement errors across a range of rainfall intensities (5 mm.h-1 to 250 mm.h-1) and three different volumetric settings. Instantaneous and cumulative values of simulated rainfall were recorded at 1, 2, 5, 10 and 20-min intervals. All three TBR models showed a substantial deviation (α = 0.05) in measurements from actual rainfall depths, with increasing underestimation errors at greater rainfall intensities. Simple linear regression equations were developed for each TBR to correct the TBR readings based on measured intensities (R 2 > 0.98). Additionally, two dynamic calibration techniques, viz. quadratic model (R 2 > 0.7) and T vs. 1/Q model (R 2 =>0.98), were tested and found to be useful in situations when the volumetric settings of TBRs are unknown. The correction models were successfully applied to correct field-collected rainfall data from respective TBR models. The calibration parameters of correction models were found to be highly sensitive to changes in volumetric calibration of TBRs. Overall, the HS-TB3 model (with a better protected tipping bucket mechanism, and consistent measurement errors across a range of rainfall intensities) was found to be the most reliable and consistent for rainfall measurements, followed by the ISCO-674 (with susceptibility to clogging and relatively smaller measurement errors across a range of rainfall intensities) and the TR-525 (with high susceptibility to clogging and frequent changes in volumetric calibration, and highly
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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