Bayesian approach to estimating margin of safety for total maximum daily load development

Area of Science:

• Environmental Science
• Water Quality Management
• Statistical Modeling

Background:

• Total Maximum Daily Load (TMDL) calculations require accurate estimation of the Margin of Safety (MOS).
• Conventional MOS methods may not fully capture the total uncertainty in water quality parameters.
• Accurate assessment of dissolved oxygen is critical for aquatic ecosystem health.

Purpose of the Study:

• To present a Bayesian-updating approach for estimating total uncertainty-based MOS in TMDL calculations.
• To compare the Bayesian approach with conventional methods for dissolved oxygen reserve estimation.
• To demonstrate the application of the Bayesian approach in a real-world case study.

Main Methods:

• Utilized a Bayesian-updating framework to incorporate probability distributions for likelihood, prior, and posterior probabilities.
• Applied the method to a case study on the Lower Amite River, Louisiana, focusing on dissolved oxygen.
• Compared results with two conventional MOS estimation techniques (fixed percentage and standard deviation).

Main Results:

• The Bayesian approach updated the standard deviation of summer dissolved oxygen from 1.88 mg/L to 2.10 mg/L, reflecting total uncertainty.
• The Bayesian method yielded a dissolved oxygen reserve of 38,614.43 kg/Day (μ-σ MOS), indicating a deficit.
• Increasing MOS levels (μ-2σ, μ-3σ) in the Bayesian approach resulted in larger dissolved oxygen reserve deficits.

Conclusions:

• The Bayesian-updating approach provides a more comprehensive estimation of MOS by accounting for total uncertainty.
• This method offers a valuable tool for TMDL development and water quality management in various river systems.
• The study highlights the importance of considering total uncertainty for robust environmental decision-making.