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Mathematical Modeling of Water Quality Data from Constructed Wetlands and Biofilters

Mathematical Modeling of Water Quality Data from Constructed Wetlands and Biofilters. Maria Castillo Kimberly Duong Edgar Gomez Department of Civil &Environmental Engineering. Background.

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Mathematical Modeling of Water Quality Data from Constructed Wetlands and Biofilters

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  1. Mathematical Modeling of Water Quality Data from Constructed Wetlands and Biofilters Maria Castillo Kimberly Duong Edgar Gomez Department of Civil &Environmental Engineering

  2. Background • In Australia, the UCI Water-PIRE measured many water quality indicators within various wetlands and biofilters • These variables may be correlated • Possible correlations can be revealed through the Multiple Linear Regression (MLR) technique and modeled mathematically

  3. Objective • Evaluate two model formulations for water quality data in wetlands and biofilters [1,5]

  4. Hypothesis • A previous study from the Buffalo Watershed suggests both models are appropriate for determining relationships between turbidity, suspended solids, and bacteria [9] • Power-law models are often appropriate where variables vary over large ranges [1,2,3] • We hypothesize that environmental data from wetlands and biofilters follow the power-law model

  5. Field Work

  6. Data Analysis

  7. Results: Enterococcus vs. TSS Log-Linear Power-Law

  8. Results: Turbidity vs. Chlorophyll Log-Linear Power-Law

  9. Results: Turbidity vs. Phaeophytin Log-Linear Power-Law

  10. Discussion • Power law models explain more data variance than log-linear models. • Pearson’s correlations were significant: • Log(ENT) vs TSS (Log-Linear model) • Log(ENT) vs Log(TSS) (Power-Law model) • Log(Turbidity) vs Log(CHL) (Power-Law model) • Pearson’s correlations not significant: • Log(Turbidity) vs PHAE (Log-Linear model) • Log(Turbidity) vs CHL (Log-Linear model) • Log(Turbidity) vs Log(PHAE) (Power-Law model)

  11. Discussion • Power law models explain more data variance than log-linear models. • Pearson’s correlations were significant: • Log(ENT) vs TSS (Log-Linear model) • Log(ENT) vs Log(TSS) (Power-Law model) • Log(Turbidity) vs Log(CHL) (Power-Law model) • Pearson’s correlations not significant: • Log(Turbidity) vs PHAE (Log-Linear model) • Log(Turbidity) vs CHL (Log-Linear model) • Log(Turbidity) vs Log(PHAE) (Power-Law model)

  12. Discussion • Power law models explain more data variance than log-linear models. • Pearson’s correlations were significant: • Log(ENT) vs TSS (Log-Linear model) • Log(ENT) vs Log(TSS) (Power-Law model) • Log(Turbidity) vs Log(CHL) (Power-Law model) • Pearson’s correlations not significant: • Log(Turbidity) vs PHAE (Log-Linear model) • Log(Turbidity) vs CHL (Log-Linear model) • Log(Turbidity) vs Log(PHAE) (Power-Law model)

  13. Conclusions • The Power-Law model is marginally more successful. • ENT is strongly correlated with TSS [6,9]. • Importance of removing suspended particles. • Future studies during dry and wet-weather periods.

  14. Conclusions

  15. Acknowledgements Thank you to Stan Grant, Megan Rippy, Sunny Jiang, and Andrew Mehring, Nicole Patterson, Alex McCluskey, and Leyla Riley for their guidance, support, and dedication. This project has been funded by the NSF-PIRE. Special thanks to Melbourne Water, Trinity College, The University of Melbourne, and Monash University for their accommodations.

  16. Literature Cited [1] Xiao, X., White, E. P., Hooten, M. B., & Durham, S. L. 2011. On the use of log-transformation vs. nonlinear regression for analyzing biological power laws. Ecology, 92(10):1887-1894. [2] Mitzenmacher, M. 2003. A Brief History of Generative Models for Power Law and Lognormal Distributions. Internet Mathematics, 1(2):226-251. [3] Newman, M.E.J. 2004. Power laws, Pareto distributions, and Zipf's Law. Contemporary Physics, 46(5): 323-351. [4] Bolarinwa, I.A & Bolarinwa, B. T. 2013. Log Linear Modeling. International Journal of Advanced Scientific and Technical Research, 3(1): 587-595. [5] Benoit, K. 2011. Linear Regression Models with Logarithmic Transformations. Methodology Institute, London School of Economics. [6] J. Stephen Fries, G. Characklis, R. Noble. 2006. Attachment of Fecal Indicator Bacteria to Particles in the Neuse River Estuary, N.C. Journal of Environmental Engineering. [7] R. N. Fraser. 1998. Hyperspectral remote sensing of turbidity and chlorophyll a among Nebraska Sand Hills lakes. Remote Sensing, 19:1579-1589. [8] Caroline Andrews, R. Kroger, L. Miranda. Predicting Nitrogen and Phosphorus Concentrations using Chlorophyll-a Fluorescence and Turbidity. Non-Point Source Assessment. [9] K. N. Irvine, E. L. Somogye, G. W. Pettibone. 2002, Turbidity, suspended solids, and bacteria relationships in the Buffalo River Watershed. Middle States Geographer.,35:42-51.

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