Comparison of dynamic and steady-state models for determining water quality based national pollutant discharge elimination system limits for toxics

Current U.S. Environmental protection Agency guidance allows water quality based effluent limits for toxic substances to be based on one of two types of water quality models: steady state and dynamic. The intention of both ty pes of models is to limit occurrence of instream toxicity to a frequency of no greater than once in 3 years. Steady-state models are used to predict c oncentrations for a single critical (i.e., almost worst-case) combination o f effluent and environmental conditions. These models assume that effluent limits that are protective for critical conditions will also be in complian ce with the less than once-in-3-year frequency of toxicity objective. Dynam ic (or probabilistic) models explicitly consider the variability in all mod el inputs and define effluent limits that will be in direct compliance with the once-in-3-year goal. Essentially all published comparisons of steady-s tate and dynamic model results have indicated that steady-state models are more protective than dynamic models, leading to the commonly held assumptio n that steady-state models are always overprotective. This assumption was evaluated by comparing steady-state and dynamic wastelo ad allocation model results with 10 different sites across the United State s. At 8 of the 10 sites, steady-state modeling resulted in more lenient eff luent limits. The primary factor that determines which wasteload allocation model produces the more stringent result was found to be the variation in receiving water assimilative capacity. Steady-state analyses are less strin gent than dynamic models for cases when there is a small variability in rec eiving water assimilative capacity. For systems with more variable assimila tive capacity, the steady-state model may be more stringent, depending on t he severity of the critical condition selected. Equations are derived that allow a direct comparison of the two methods for simple single-discharge si tuations.