Simplified databased total maximum daily loads, or the world is log-normal

The total maximum daily load (TMDL) approaches that have relied mostly on deterministic modeling have inherent problems with considerations of a margin of safety and estimating probabilities of excursions of water quality standards expressed in terms of magnitude, duration, and frequency. A tiered probabilistic TMDL approach is proposed in this paper. A simple databased Tier I TMDL that uses statistical principles has been proposed for watersheds that have adequate water quality databases enabling statistical evaluations. Studies have shown that for many pollutants, event mean concentrations in runoff, wastewater loads, and concentrations in the receiving waters follow the log-normal probability distribution. Other probability distributions are also applicable. Tier II Monte Carlo simulation, using a simpler deterministic or black box water quality model as a transfer function, can then be used to generate time series of data, which fills the data gaps and allows estimation of probabilities of excursions of chronic standards that are averaged over periods of 4 or 30 days. Statistical approaches, including Monte Carlo, allow replacement of an arbitrary margin of safety by a quantitative estimation of uncertainty and enable linking the model results to the standards defined in terms of magnitude, frequency, and duration.