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Modeling risk attributes of wastewater treatment plant violations of total ammonia nitrogen discharge limits in the United States

Suchetana, Bihu, Rajagopalan, Balaji, Silverstein, JoAnn
Stochastic environmental research and risk assessment 2019 v.33 no.3 pp. 879-889
Poisson distribution, ammonium nitrogen, compliance, linear models, prediction, regression analysis, risk, wastewater treatment, United States
A performance-based modeling framework is developed to estimate three attributes of the risk of Total Ammonia Nitrogen (TAN) permit limit violations: probability, magnitude and frequency of violations. Discharge Monthly Report data from a sample of 106 US municipal treatment plants for the period of 2004–2008 is used for the analysis. A Generalized Linear Model regression produces estimates for the probability and frequency of TAN discharge violations, using logistic and Poisson distributions, respectively. The expected magnitude of violations is modeled as a non-stationary Generalized Pareto Distribution (GPD), using Extreme Value Theory. Regression covariates are plant inflow, fractional use of design hydraulic capacity, seasonality and previous month’s performance. The logistic regression model of the probability of a TAN violation has a median Brier Skill Score of 0.25, while the Poisson regression model of violation frequency has a median of 65% correct prediction in validation. The GPD model has equivalent model and empirical quantiles. Model predictions of probability and frequency are combined to obtain two composite risk indices—the Estimated Violation Index (EVI), which is the product of the average probabilities of violation and frequency at each location, and the Estimated Severity Index (ESI) which is the product of the EVI and the predicted 2-year return value of discharge TAN concentrations above the regulatory limit. Spatial maps of ESI and EVI provide visual guides for regulatory agencies to identify risks and prioritize compliance and enforcement efforts.