Applying the first-order error analysis in determining the margin of safety for total maximum daily load computations

There are significant uncertainties associated with certain aspects of the total maximum daily load (TMDL) estimation. Selection of the margin of safety (MOS) term is typically made by subjectively assigning to it a small percentage (5-10%) of the TMDL load. To introduce some objectivity into the MOS estimation, the first-order error analysis (FOEA) was utilized to quantify the MOS term in the TMDL formulation. A case study, which was based on a previous study entitled Nitrate TMDL Development for Muddy Creek/Dry River, Virginia, is presented in this paper. Besides computational efficiency, one of the major advantages of FOEA is its capability of determining the relative importance of the various parameters that contribute to the overall variance of the model output. Precipitation was found by far to be the most dominant source of uncertainty. Furthermore, a relationship was established to link the pollutant loads with the FOEA output concentrations. The results from testing different TMDL allocation scenarios demonstrate that with the increase of relative percentage of nonpoint sources load reduction in the total load reduction, the portion needed to be reserved for MOS increases as well. The MOS term can be related to the variability in rainfall and therefore would be different for different locations in the country. In summary, as a practical, less subjective and reliable approach to TMDL uncertainty analysis, the use of the FOEA is considered as a viable alternative to the current simple explicit and implicit methods in estimating the MOS term for TMDL calculations.