Investigating regime shifts and the factors controlling Total Inorganic Nitrogen concentrations in treated wastewater using non-homogeneous Hidden Markov and multinomial logistic regression models

Total Inorganic Nitrogen (TIN) in treated wastewaters: the sum of effluent ammonia-, nitrate- and nitrite-nitrogen, is a common regulatory measure of nitrogen removal. In many parts of the United States, regulatory agencies have reduced discharge limits for TIN, recognizing the environmental and health impacts of these species. However, many permit limits are based on annual average or median values, and because temporal variability in effluent TIN is common, may not achieve water quality goals. We created a performance-based modeling approach using Hidden Markov Models and multinomial logistic regression using weekly effluent water quality data from an operating wastewater treatment facility in the US, over the period of January 1, 2010–March 31, 2014. In the two-step modeling approach, Hidden Markov Models capture temporal regime shifts in effluent TIN and multinomial logistic regression identifies prominent factors associated with the regime shifts. Simulations from the proposed Hidden Markov Model and multinomial logistic regression indicate that climate factors (temperature and precipitation), seasonality, effluent total ammonia nitrogen (TAN), and prior weeks' levels of effluent TIN are predictive of effluent TIN concentrations. The hybrid HMM-regression model correctly predicted the states of compliance (state 1) and non-compliance (state 2) with TIN limits with 84% accuracy. Further analysis using model simulations suggest that although annual average or median limits for TIN are met, this plant had a >30% probability of exceeding the annual limit on a weekly time scale, and therefore may not be reliably effective in protecting receiving water quality.