Report

Mathematical Modeling of Water Quality Data from Constructed Wetlands and Biofilters MARIA CASTILLO K I M B E R LY D U O N G EDGAR GOMEZ D E PA RT M E N T O F C I V I L & E N V I R O N M E N TA L E N G I N E E R I N G 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 Objective Evaluate two model formulations for water quality data in wetlands and biofilters [1,5] 1.) Log-linear model • Assume that a log-transformed dependent variable depends linearly on one or more independent variables • log(y) = mx + b 2.) Log-log (or power-law) model • Assume a log-transformed dependent variable depends linearly on one or more log-transformed independent variables • y=axb ↔ log(y) = log(a) + b·log(x) 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 Field Work Data was collected from 3 biofilters and 3 wetlands in Melbourne, Australia Turbidity and pH were measured using a Horiba multi-probe; dissolved oxygen (DO) was measured using a DO meter Water samples filtered for chlorophyll (CHL), phaeophytin (PHAE), total suspended solids (TSS), and microbial concentrations (Enterococcus; ENT and Escherichia coli; EC) Data Analysis • Multiple Linear Regression (MLR) performed using Virtual Beach. • Dependent variables: EC, ENT, DO, Turbidity, pH, Nitrate, Phosphate • Independent variables: EC, ENT, DO, Turbidity, pH, Nitrate, Phosphate, CHL, PHAE, TSS • Candidate models ranked according to their Corrected Akaike Information Criteria (AICc). • Variable Inflation Factor used to reduce multicolinearity. • Correlations predicted by MLR were verified using Pearson’s correlation and Bootstrap statistical tests Results: Enterococcus vs. TSS Power-Law LOG10(Enterococcus) (CFU/L) 3.5 3 2.5 2 1.5 1 R² = 0.73* 0.5 0 0 50 TSS (mg/L) 100 LOG10(Enterococcus) (CFU/L) Log-Linear 3.5 3 2.5 2 1.5 1 R² = 0.76* 0.5 0 -0.5 0 0.5 1 1.5 LOG10(TSS) (mg/L) 2 2.5 Results: Turbidity vs. Chlorophyll Log-Linear 600 3 LOG10(Turbidity) (NTU) R² = 0.60 500 Turbidity (NTU) Power-Law 400 300 200 100 2.5 2 1.5 1 0.5 0 R² = 0.75* 0 0 10 20 30 CHL (µg/L) 40 -1 -0.5 0 0.5 1 LOG10(CHL) (µg/L) 1.5 2 Results: Turbidity vs. Phaeophytin Log-Linear Power-Law 3 Turbidity (NTU) 500 400 300 R² = 0.51 200 100 0 LOG10(Turbidity) (NTU) 600 2.5 2 1.5 1 R² = 0.64 0.5 0 0 200 400 PHAE (µg/L) 600 0 1 2 LOG10(PHAE) (µg/L) 3 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) 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) 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) 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. Conclusions 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. 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.