Bayesian Approach for Estimating Biological Treatment Parameters under Flooding Condition
Publication: Journal of Environmental Engineering
Volume 146, Issue 8
Abstract
Wastewater treatment plants (WWTPs) have a significant role in urban system serviceability. Flooding can impact the performance of WWTPs by causing malfunction in its unit operations, which results in releasing partially treated or even untreated effluent into natural water bodies, causing environmental predicaments of significant proportions. In particular, the biological parameters could go through changes that need to be assessed and monitored in order to implement effective adaptation strategies. In this study, the uncertainty analysis and estimation of biological parameters of WWTP modeling under flood conditions is investigated by using Bayesian inference. In the first step, the proper prior distribution is fitted to the important parameters recognized by sensitivity analysis. Next, the effluent parameters in times of wet weather [five-day biochemical oxygen demand (), total suspended solids (TSS), and ammonia and total nitrogen (TN)] are used as new data to update and estimate the value of the parameters. By using the Bayesian inference concept, the posterior distributions of parameters are obtained. Two types of likelihood functions are used: formal, derived from the stochastic error series, and informal, which uses predefined performance criteria to characterize the relationship between the observation and model output. Finally, Markov chain Monte Carlo (MCMC) methods are used to sample from the posterior distribution. Parameter posteriors are summarized using the posterior mean for parameter estimation (in wet weather) and coefficient of variation (CV) for degree of uncertainty. The results show that there are a number of parameters for which the value of CV drops significantly at the time of flood conditions. This means their uncertainty decreases, whereas for some other parameters, it is negligible. Moreover, by using the formal likelihood function, the parameters are pinpointed more precisely, and the range of parameters is narrowed up to 98%. The methodology developed in this study could be used to plan for effective simulation and monitoring of WWTPs in different geographic settings.
Get full access to this article
View all available purchase options and get full access to this article.
Data Availability Statement
All data generated or used during the study appear in the published article.
Acknowledgments
The authors would like to express their gratitude for the MATLAB/Simulink implementation of the BSM2 from the Department of Industrial Electrical Engineering and Automation, Lund University, Lund, Sweden. The authors also wish to thank Zahra Heydari, Reyhaneh Rahimi, and Helia Farzaneh, research assistants at the University of Tehran, for their constructive comments.
References
Alex, J., L. Benedetti, J. Copp, K. V. Gernaey, U. Jeppsson, I. Nopens, and P. Vanrolleghem. 2008. “Benchmark simulation model no. 1 (BSM1).” In IWA taskgroup on benchmarking of control strategies for WWTPs, 19–20. Lund, Sweden: Lund Univ.
Alikhani, J., I. Takacs, A. Al-Omari, S. Murthy, and A. Massoudieh. 2017. “Evaluation of the information content of long-term wastewater characteristics data in relation to activated sludge model parameters.” Water Sci. Technol. 75 (6): 1370–1389. https://doi.org/10.2166/wst.2017.004.
Beven, K., and A. Binley. 1992. “The future of distributed models: Model calibration and uncertainty prediction.” Hydrol. Processes 6 (3): 279–298. https://doi.org/10.1002/hyp.3360060305.
Bloomberg, M. 2013. “A stronger, more resilient New York. City of New York, Chapter 1: Sandy and its impacts and Chapter 6: Water and wastewater, PlaNYC report.” Accessed August 1, 2019. https://www.nycedc.com/resource/stronger-more-resilient-new-york.
Charles, K. J., N. J. Ashbolt, D. J. Roser, R. McGuinness, and D. A. Deere. 2005. “Effluent quality from 200 on-site sewage systems: Design values for guidelines.” Water Sci. Technol. 51 (10): 163–169. https://doi.org/10.2166/wst.2005.0363.
Fearnhead, P., J. Bierkens, M. Pollock, and G. O. Roberts. 2018. “Piecewise deterministic Markov processes for continuous-time Monte Carlo.” Stat. Sci. 33 (3): 386–412. https://doi.org/10.1214/18-STS648.
Gernaey, K. V., X. Flores-Alsina, C. Rosen, L. Benedetti, and U. Jeppsson. 2011. “Dynamic influent pollutant disturbance scenario generation using a phenomenological modelling approach.” Environ. Modell. Software 26 (11): 1255–1267. https://doi.org/10.1016/j.envsoft.2011.06.001.
Gernaey, K. V., M. C. van Loosdrecht, M. Henze, M. Lind, and S. B. Jørgensen. 2004. “Activated sludge wastewater treatment plant modelling and simulation: State of the art.” Environ. Modell. Software 19 (9): 763–783. https://doi.org/10.1016/j.envsoft.2003.03.005.
Guo, L., J. Porro, K. R. Sharma, Y. Amerlinck, L. Benedetti, I. Nopens, A. Shaw, S. W. H. Van Hulle, Z. Yuan, and P. A. Vanrolleghem. 2012. “Towards a benchmarking tool for minimizing wastewater utility greenhouse gas footprints.” Water Sci. Technol. 66 (11): 2483–2495. https://doi.org/10.2166/wst.2012.495.
Helsel, D. R., and R. M. Hirsch. 2002. Vol. 323 of Statistical methods in water resources. Reston, VA: USGS.
Henze, M., C. P. L. Grady, W. Gujer, G. V. R. Marais, and T. Matsuo. 1987. Activated sludge model no. 1. London: IAWPRC.
Henze, M., W. Gujer, T. Mino, T. Matsuo, M. C. Wentzel, G. V. R. Marais, and M. Van Loosdrecht. 1999. “Activated sludge model no. 2d, ASM2d.” Water Sci. Technol. 39 (1): 165–182. https://doi.org/10.2166/wst.1999.0036.
Jeppsson, U., M. N. Pons, I. Nopens, J. Alex, J. B. Copp, K. V. Gernaey, C. Rosen, J. P. Steyer, and P. A. Vanrolleghem. 2007. “Benchmark simulation model no 2: General protocol and exploratory case studies.” Water Sci. Technol. 56 (8): 67–78. https://doi.org/10.2166/wst.2007.604.
Karamouz, M., and Z. Heydari. 2020. “Conceptual design framework for coastal flood’s best management practices (BMPs).” J. Water Resour. Plann. Manage. 146 (6): 04020041. https://doi.org/10.1061/(ASCE)WR.1943-5452.0001224.
Karamouz, M., and M. A. Olyaei. 2019. “A quantitative and qualitative framework for reliability assessment of waste water treatment plants under coastal flooding.” Int. J. Environ. Res. 13 (1): 21–33. https://doi.org/10.1007/s41742-018-0141-8.
Karamouz, M., M. Taheri, P. Khalili, and X. Chen. 2019. “Building infrastructure resilience in coastal flood risk management.” J. Water Resour. Plann. Manage. 145 (4): 04019004. https://doi.org/10.1061/(ASCE)WR.1943-5452.0001043.
Kavetski, D. 2019. “Parameter estimation and predictive uncertainty quantification in hydrological modelling.” In Handbook of hydrometeorological ensemble forecasting, 481–522. Berlin: Springer.
Kenward, A., D. Yawitz, and U. Raja. 2013. Sewage overflows from Hurricane Sandy. Princeton, NJ: Climate Central.
Kuczera, G. 1983. “Improved parameter inference in catchment models, 1. Evaluating parameter uncertainty.” Water Resour. Res. 19 (5): 1151–1162. https://doi.org/10.1029/WR019i005p01151.
Martin, C., I. Eguinoa, N. R. McIntyre, M. García-Sanz, and E. Ayesa. 2007. “ARMA models for uncertainty assessment of time series data: Application to Galindo-Bilbao WWTP.” In Proc., 7th Int. IWA Symp. on Systems Analysis and Integrated Assessment in Water Management (WATERMATEX 2007). London: International Water Association.
McMillan, H., and M. Clark. 2009. “Rainfall-runoff model calibration using informal likelihood measures within a Markov chain Monte Carlo sampling scheme.” Water Resour. Res. 45 (4): W04418. https://doi.org/10.1029/2008WR007288.
Meng, F., G. Fu, and D. Butler. 2016. “Water quality permitting: From end-of-pipe to operational strategies.” Water Res. 101 (Sep): 114–126. https://doi.org/10.1016/j.watres.2016.05.078.
Metropolis, N., A. W. Rosenbluth, M. N. Rosenbluth, A. H. Teller, and E. Teller. 1953. “Equation of state calculations by fast computing machines.” J. Chem. Phys. 21 (6): 1087–1092. https://doi.org/10.1063/1.1699114.
Mugume, S. N., and D. Butler. 2017. “Evaluation of functional resilience in urban drainage and flood management systems using a global analysis approach.” Urban Water J. 14 (7): 727–736. https://doi.org/10.1080/1573062X.2016.1253754.
Niku, S., S. D. Schroeder, and F. J. Samaniego. 1979. “Performance of activated sludge process and reliability-based design.” J. Water Pollut. Control Fed. 51 (12): 2841–2857.
NYCDCP (NYC Department of City Planning). 2007. “The Jamaica Plan—Final environmental impact statement.” Accessed May 1, 2018. https://www1.nyc.gov/site/planning/applicants/env-review/jamaica-plan.page.
Oliveira, S. C., and M. Von Sperling. 2008. “Reliability analysis of wastewater treatment plants.” Water Res. 42 (4): 1182–1194. https://doi.org/10.1016/j.watres.2007.09.001.
Olyaei, M. A., M. Karamouz, and R. Farmani. 2018. “Framework for assessing flood reliability and resilience of wastewater treatment plants.” J. Environ. Eng. 144 (9): 04018081. https://doi.org/10.1061/(ASCE)EE.1943-7870.0001422.
Petersen, B., P. A. Vanrolleghem, K. Gernaey, and M. Henze. 2002. “Evaluation of an ASM1 model calibration procedure on a municipal–industrial wastewater treatment plant.” J. Hydroinf. 4 (1): 15–38. https://doi.org/10.2166/hydro.2002.0003.
Ramin, E., X. Flores-Alsina, G. Sin, K. V. Gernaey, U. Jeppsson, P. S. Mikkelsen, and B. G. Plósz. 2014a. “Influence of selecting secondary settling tank sub-models on the calibration of WWTP models—A global sensitivity analysis using BSM2” Chem. Eng. J. 241 (Apr): 28–34. https://doi.org/10.1016/j.cej.2013.12.015.
Ramin, E., G. Sin, P. S. Mikkelsen, and B. G. Plósz. 2014b. “Significance of settling model structures and parameter subsets in modelling WWTPs under wet-weather flow and filamentous bulking conditions.” Water Res. 63 (Jun): 209–221. https://doi.org/10.1016/j.watres.2014.05.054.
Rodríguez, J. P., N. McIntyre, M. Díaz-Granados, S. Achleitner, M. Hochedlinger, and C. Maksimovi. 2013. “Generating time-series of dry weather loads to sewers.” Environ. Modell. Software 43 (May): 133–143. https://doi.org/10.1016/j.envsoft.2013.02.007.
Rukovets, R. B., and B. J. Mitchell. 2010. Impact of wet-weather peak flow blending on disinfection and treatment: A case study at three wastewater treatment plants. Washington, DC: USEPA.
Schoups, G., and J. A. Vrugt. 2010. “A formal likelihood function for parameter and predictive inference of hydrologic models with correlated, heteroscedastic, and non-Gaussian errors.” Water Resour. Res. 46 (10): W10531. https://doi.org/10.1029/2009WR008933.
Sharifi, S., S. Murthy, I. Takács, and A. Massoudieh. 2014. “Probabilistic parameter estimation of activated sludge processes using Markov chain Monte Carlo.” Water Res. 50 (Mar): 254–266. https://doi.org/10.1016/j.watres.2013.12.010.
Sherri, M., I. Boulkaibet, T. Marwala, and M. I. Friswell. 2019. “A differential evolution Markov chain Monte Carlo algorithm for Bayesian model updating.” In Vol. 5 of Special topics in structural dynamics, 115–125. Cham, Switzerland: Springer.
Sin, G., K. V. Gernaey, M. B. Neumann, M. C. van Loosdrecht, and W. Gujer. 2011. “Global sensitivity analysis in wastewater treatment plant model applications: Prioritizing sources of uncertainty.” Water Res. 45 (2): 639–651. https://doi.org/10.1016/j.watres.2010.08.025.
Smith, P., K. J. Beven, and J. A. Tawn. 2008. “Informal likelihood measures in model assessment: Theoretic development and investigation.” Adv. Water Resour. 31 (8): 1087–1100. https://doi.org/10.1016/j.advwatres.2008.04.012.
Sweetapple, C., G. Fu, and D. Butler. 2013. “Identifying key sources of uncertainty in the modelling of greenhouse gas emissions from wastewater treatment.” Water Res. 47 (13): 4652–4665. https://doi.org/10.1016/j.watres.2013.05.021.
Talebizadeh, M., E. Belia, and P. A. Vanrolleghem. 2016. “Influent generator for probabilistic modeling of nutrient removal wastewater treatment plants.” Environ. Modell. Software 77 (Mar): 32–49. https://doi.org/10.1016/j.envsoft.2015.11.005.
Tung, Y. K., B. C. Yen, and C. S. Melching. 2006. Hydrosystems engineering reliability assessment and risk analysis. New York: McGraw-Hill Education.
Vanderhasselt, A., A. Fuchs, P. Vanrolleghem, G. Staudinger, and W. Verstraete. 1999. “Monitoring of the effects of additives on sludge separation properties by using sensors.” Water Environ. Res. 71 (3): 355–362. https://doi.org/10.2175/106143099X148211.
Information & Authors
Information
Published In
Journal of Environmental Engineering
Volume 146 • Issue 8 • August 2020
Copyright
©2020 American Society of Civil Engineers.
History
Received: Sep 29, 2019
Accepted: Mar 9, 2020
Published online: May 30, 2020
Published in print: Aug 1, 2020
Discussion open until: Oct 30, 2020
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.