Calibrating and validating bacterial water quality models: A Bayesian approach

Water Research

Volumn 43, Issue 10, 2009, Pages 2688-2698

  Gronewold, Andrew D ^a   Qian, Song S ^a   Wolpert, Robert L ^a,b   Reckhow, Kenneth H ^a  

^a DUKE UNIVERSITY   (United States)

^b Duke University   (United States)

Author keywords

Bacteria die off; Bayesian analysis; MCMC; Parameter estimation; Water quality modeling

Indexed keywords

BACTERIA; BAYESIAN NETWORKS; MARKOV PROCESSES; PARAMETER ESTIMATION; PROBABILITY DISTRIBUTIONS; QUALITY CONTROL; STATISTICAL METHODS; WATER MANAGEMENT; WATER POLLUTION; WATER QUALITY;

BACTERIA DIE-OFF; BAYESIAN ANALYSIS; BAYESIAN APPROACHES; FAECAL INDICATOR BACTERIA; MARKOV CHAIN MONTE CARLO; MARKOV CHAIN MONTE-CARLO; PARAMETERS ESTIMATION; PREDICTIVE PERFORMANCE; UNCERTAINTY; WATER QUALITY MODELLING;

UNCERTAINTY ANALYSIS;

BAYESIAN ANALYSIS; CALIBRATION; EMPIRICAL ANALYSIS; FECAL COLIFORM; MARKOV CHAIN; MODEL VALIDATION; MONTE CARLO ANALYSIS; NUMERICAL MODEL; PUBLIC ACCESS; REGRESSION ANALYSIS; UNCERTAINTY ANALYSIS; WATER MANAGEMENT; WATER POLLUTION; WATER QUALITY; WATER RESOURCE;

ARTICLE; BAYES THEOREM; CALIBRATION; FECES MICROFLORA; MONTE CARLO METHOD; NONHUMAN; POLLUTION TRANSPORT; PRIORITY JOURNAL; STATISTICAL MODEL; VALIDATION PROCESS; WATER QUALITY; WATER SUPPLY;

BACTERIA (MICROORGANISMS);

EID: 65549102480     PISSN: 00431354     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.watres.2009.02.034     Document Type: Article

References (70)

1. Arega F., and Sanders B.F. Dispersion model for tidal wetlands. Journal of Hydraulic Engineering - ASCE 130 8 (2004) 739-754
2. Auer M.T., and Niehaus S.L. Modeling fecal coliform bacteria-I. Field and laboratory determination of loss kinetics. Water Research 27 4 (1993) 693-701
3. Benham B.L., Baffaut C., Zeckoski R.W., Mankin K.R., Pachepsky Y.A., Sadeghi A.M., Brannan K.M., Soupir M.L., and Habersack M.J. Modeling bacteria fate and transport in watersheds to support TMDLs. Transactions of the ASABE 49 4 (2006) 987-1002
4. Bolstad W.M. Introduction to Bayesian Statistics (2004), Wiley-Interscience, Hoboken, NJ
5. Borsuk M.E., Stow C.A., and Reckhow K.H. Predicting the frequency of water quality standard violations: a probabilistic approach for TMDL development. Environmental Science & Technology 36 10 (2002) 2109-2115
6. Bowie G., Mills W., Porcella D., Campbell C., and Chamberlin C. Rates, Constants, and Kinetics Formulations in Surface Water Quality Modeling. second ed. (1985), United States Environmental Protection Agency Office of Research and Development Environmental Research Laboratory, Washington, DC
7. Brookes J.D., Antenucci J., Hipsey M., Burch M.D., Ashbolt N.J., and Ferguson C. Fate and transport of pathogens in lakes and reservoirs. Environment International 30 5 (2004) 741-759
8. Chambers J.M., and Hastie T.J. Statistical Models in S (1991), CRC Press, Inc., Boca Raton, FL, USA
9. Chapra S.C. Surface Water-quality Modeling. McGraw-hill series in water resources and environmental engineering index (1997), McGraw-Hill, New York
10. Chapra S.C. Engineering water quality models and TMDLs. Journal of Water Resources Planning and Management - ASCE 129 4 (2003) 247-256
11. Chapra, S.C., Pelletier, G.J., Tao, H., 2007. QUAL2K: a Modeling Framework for Simulating River and Stream Water Quality, Version 2.07: Documentation and User's Manual. Tech. rep., Civil and Environmental Engineering Dept., Tufts University.
12. Chigbu P., Gordon S., and Tchounwou P.B. The seasonality of fecal coliform bacteria pollution and its influence on closures of shellfish harvesting areas in Mississippi Sound. International Journal of Environmental Research and Public Health 2 2 (2005) 362-373
13. Chigbu P., Strange T., Gordon S., Jester K., Baham J., Young J., Hughes R., Remata R., Martinolich K., Hilbert K., and Others. A decision support tool for shellfish management in Mississippi Sound. Journal of Shellfish Research 25 3 (2006) 1091-1099
14. Christian R.R., and Pipes W.O. Frequency distributions of coliforms in water distribution systems. Applied and Environmental Microbiology 45 2 (1983) 603-609
15. Darakas E. E. coli kinetics-effect of temperature on the maintenance and respectively the decay phase. Environmental Monitoring and Assessment 78 2 (2002) 101-110
16. DiToro D.M. Probability model of stream quality due to runoff. Journal of Environmental Engineering ASCE 110 3 (1984) 607-628
17. Dufour A.P., Strickland E.R., and Cabelli V.J. Membrane-filter method for enumerating Escherichia coli. Applied and Environmental Microbiology 41 5 (1981) 1152-1158
18. Efron B., and Tibshirani R.J. An Introduction to the Bootstrap (1993), Chapman & Hall/CRC
19. Eisenhart C., and Wilson P.W. Statistical methods and control in bacteriology. Bacteriological Reviews 7 2 (1943) 57-137
20. El-Shaarawi A.H., Esterby S.R., and Dutka B.J. Bacterial density in water determined by Poisson or negative binomial distributions. Applied and Environmental Microbiology 41 1 (1981) 107-116
21. Eleria A., and Vogel R.M. Predicting fecal coliform bacteria levels in the Charles River, Massachusetts, USA. Journal of the American Water Resources Association 41 5 (2005) 1195-1209
22. Ferguson C., Husman A.M.D., Altavilla N., Deere D., and Ashbolt N. Fate and transport of surface water pathogens in watersheds. Critical Reviews in Environmental Science and Technology 33 3 (2003) 299-361
23. Fischer H.B. Mixing in Inland and Coastal Waters (1979), Academic Press, New York
24. Frome E.L., and Checkoway H. Epidemiologic programs for computers and calculators. American Journal of Epidemiology 121 2 (1985) 309-323
25. Frome E.L., Kutner M.H., and Beauchamp J.J. Regression analysis of Poisson-distributed data. Journal of the American Statistical Association 68 344 (1973) 935-940
26. Gameson A., and Gould D. Effects of solar radiation on the mortality of some terrestrial bacteria in sea water. International Symposium on Discharge of Sewage from Sea Outfalls vol. 22 (1974), Pergamon Press, London
27. Gelman A. Prior distributions for variance parameters in hierarchical models (comment on article by Browne and Draper). Bayesian Analysis 1 3 (2006) 515-534
28. Gelman A., Carlin J.B., Stern H.S., and Rubin D.B. Bayesian Data Analysis (2004), Chapman & Hall/CRC, Boca Raton, Florida
29. Gelman A., and Hill J. Data Analysis Using Regression and Multilevel/Hierarchical Models (2007), Cambridge University Press, New York, NY
30. Grant S.B., Sanders B.F., Boehm A.B., Redman J.A., Kim J.H., Mrse R.D., Chu A.K., Gouldin M., McGee C.D., Gardiner N.A., Jones B.H., Svejkovsky J., and Leipzig G.V. Generation of enterococci bacteria in a coastal saltwater marsh and its impact on surf zone water quality. Environmental Science & Technology 35 12 (2001) 2407-2416
31. Greenwood M., and Yule G.U. On the statistical interpretation of some bacteriological methods employed in water analysis. The Journal of Hygiene 16 1 (1917) 36-54
32. Gronewold A.D., Borsuk M.E., Wolpert R.L., and Reckhow K.H. An assessment of fecal indicator bacteria-based water quality standards. Environmental Science & Technology 42 13 (2008) 4676-4682
33. Gronewold A.D., and Wolpert R.L. Modeling the relationship between most probable number (MPN) and colony-forming unit (CFU) estimates of fecal coliform concentration. Water Research 42 13 (2008) 3327-3334
34. Haas C.N. Estimation of microbial densities from dilution count experiments. Applied and Environmental Microbiology 55 8 (1989) 1934-1942
35. Haas C.N., and Heller B. Test of the validity of the Poisson assumption for analysis of most-probable-number results. Applied and Environmental Microbiology 54 12 (1988) 2996-3002
36. Habteselassie M., Bischoff M., Blume E., Applegate B., Reuhs B., Brouder S., and Turco R. Environmental controls on the fate of Escherichia coli in soil. Water Air and Soil Pollution 190 (2008) 143-155
37. Houck O.A. The Clean Water Act TMDL Program: Law, Policy, and Implementation. second ed. (2002), Environmental Law Institute, Washington, DC
38. Ihaka R., and Gentleman R. R: a language for data analysis and graphics. Journal of Computational and Graphical Statistics 5 3 (1996) 299-314
39. ISO. Standard Methods for the Examination of Water and Wastewater, ISO 9308-1 (2007), International Organization for Standardization
40. Kashefipour S.M., Lin B., and Falconer R.A. Neural networks for predicting seawater bacterial levels. Proceedings of the Institution of Civil Engineers - Water Management 158 3 (2005) 111-118
41. Kay D., Stapleton C.M., Wyer M.D., McDonald A.T., Crowther J., Paul N., Jones K., Francis C., Watkins J., Wilkinson J., Humphrey N., Lin B., Yang L., Falconer R.A., and Gardner S. Decay of intestinal enterococci concentrations in high-energy estuarine and coastal waters: towards real-time t-90 values for modelling faecal indicators in recreational waters. Water Research 39 4 (2005) 655-667
42. Kelsey H., Porter D.E., Scott G., Neet M., and White D. Using geographic information systems and regression analysis to evaluate relationships between land use and fecal coliform bacterial pollution. Journal of Experimental Marine Biology and Ecology 298 (2004) 197-209
43. Lindley D., and Smith A. Bayes estimates for the linear model. Journal of the Royal Statistical Society, Series B 34 1 (1972) 1-41
44. Lunn D.J., Thomas A., Best N., and Spiegelhalter D. WinBUGS-A Bayesian modelling framework: concepts, structure, and extensibility. Statistics and Computing 10 4 (2000) 325-337
45. Manache G., Melching C.S., and Lanyon R. Calibration of a continuous simulation fecal coliform model based on historical data analysis. Journal of Environmental Engineering 133 7 (2007) 681-691
46. McBride G.B. Using Statistical Methods for Water Quality Management. Issues, Problems and Solutions (2005), John Wiley & Sons Ltd, Chichester, UK
47. Muñoz-Carpena R., Vellidis G., Shirmohammadi A., and Wallender W. Evaluation of modeling tools for TMDL development and implementation. Transactions of the ASABE 49 4 (2006) 961-965
48. National Research Council, 2001. Assessing the TMDL approach to water quality management.
49. Noble R.T., and Fuhrman J.A. Virus decay and its causes in coastal waters. Applied and Environmental Microbiology 63 1 (1997) 77-83
50. Noble R.T., Weisberg S., Leecaster M., McGee C., Dorsey J., Vainik P., and Orozco-Borbon V. Storm effects on regional beach water quality along the Southern California shoreline. Journal of Water and Health (2003) 23-31
51. Novotny V. Water Quality: Diffuse Pollution and Watershed Management. second ed. (2003), John Wiley & Sons, New Jersey
52. Ott W. Environmental Statistics and Data Analysis (1995), Lewis Publishers, Boca Raton
53. Pipes W.O., Ward P., and Ahn S.H. Frequency distributions for coliform bacteria in water. Journal of the American Water Works Association 69 12 (1977) 664-668
54. Press S.J. Subjective and Objective Bayesian Statistics: Principles, Models, and Applications (2003), Wiley-Interscience, Hoboken, NJ
55. Qian S.S., King R., and Richardson C.J. Two statistical methods for the detection of environmental thresholds. Ecological Modelling 166 1-2 (2003) 87-97
56. Qian S.S., Linden K.G., and Donnelly M. A Bayesian analysis of mouse infectivity data to evaluate the effectiveness of using ultraviolet light as a drinking water disinfectant. Water Research 39 17 (2005) 4229-4239
57. Qian S.S., and Richardson C.J. Estimating the long-term phosphorus accretion rate in the Everglades: a Bayesian approach with risk assessment. Water Resources Research 33 7 (1997) 1681-1688
58. R Development Core Team. R: a Language and Environment for Statistical Computing (2006), R Foundation for Statistical Computing, Vienna, Austria. 3-900051-07-0. http://www.R-project.org
59. Reckhow K.H. On the need for uncertainty assessment in TMDL modeling and implementation. Journal of Water Resources Planning and Management - ASCE 129 4 (2003) 245-246
60. Rhodes M.W., and Kator H. Survival of Escherichia coli and Salmonella spp. in estuarine environments. Applied and Environmental Microbiology 54 12 (1988) 2902-2907
61. Salomon J.C., and Pommepuy M. Mathematical-model of bacterial-contamination of the Morlaix estuary (France). Water Research 24 8 (1990) 983-994
62. Sanders B.F., Arega F., and Sutula M. Modeling the dry-weather tidal cycling of fecal indicator bacteria in surface waters of an intertidal wetland. Water Research 39 14 (2005) 3394-3408
63. Shirmohammadi A., Chaubey I., Harmel R.D., Bosch D.D., Munoz-Carpena R., Dharmasri C., Sexton A., Arabi M., Wolfe M.L., Frankenberger J., Graff C., and Sohrabi T.M. Uncertainty in TMDL models. Transactions of the ASABE 49 (2006) 1033-1049
64. Siewicki T., Pullaro T., Pan W., McDaniel S., Glenn R., and Stewart J. Models of total and presumed wildlife sources of fecal coliform bacteria in coastal ponds. Journal of Environmental Management 82 4 (2007) 120-132
65. Sinton L.W., Finlay R.K., and Lynch P.A. Sunlight inactivation of fecal bacteriophages and bacteria in sewage-polluted seawater. Applied and Environmental Microbiology 65 8 (1999) 3605-3613
66. Sjogren R.E. Prolonged survival of an environmental Escherichia coli in laboratory soil microcosms. Water, Air, and Soil Pollution 75 (1994) 389-403
67. Thomann R.V., and Mueller J.A. Principles of Surface Water Quality Modeling and Control (1987), Harper & Row, New York
68. Weisberg S. Applied Linear Regression. third ed. Wiley series in probability and statistics (2005), Wiley-Interscience, Hoboken, NJ
69. Wilkinson G., and Rogers C. Symbolic description of factorial models for analysis of variance. Applied Statistics 22 3 (1973) 392-399
70. Won W.D., and Ross H. Persistence of virus and bacteria in seawater. Journal of the Environmental Engineering Division 99 3 (1973) 205-211