### Mathematical Modeling of Empirical Data from - UCI Water-PIRE

```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
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