M A R IA C A STILLOK IM BER LY D U O N G

ED G A R G O M EZ

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

Mathematical Modeling of Water Quality Data from Constructed Wetlands

and Biofilters

BackgroundIn 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)

HypothesisA 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 multi-colinearity.

•Correlations predicted by MLR were verified using Pearson’s correlation and Bootstrap statistical tests

Results: Enterococcus vs. TSS

0 10 20 30 40 50 60 70 80 901000

0.5

1

1.5

2

2.5

3

3.5

TSS (mg/L)

LO

G10

(Ent

eroc

occu

s) (C

FU/L

)

R² = 0.73*-0.5 0 0.5 1 1.5 2 2.5

0

0.5

1

1.5

2

2.5

3

3.5

LOG10(TSS) (mg/L)

LO

G10

(Ent

eroc

occu

s) (C

FU/L

)

R² = 0.76*

Log-Linear Power-Law

Results: Turbidity vs. Chlorophyll

0 5 10 15 20 25 30 35 400

100

200

300

400

500

600

CHL (µg/L)

Turb

idity

(NTU

)

R² = 0.60

-1 -0.5 0 0.5 1 1.5 20

0.5

1

1.5

2

2.5

3

LOG10(CHL) (µg/L)

LOG

10(T

urbi

dity

) (N

TU)

R² = 0.75*

Log-Linear Power-Law

Results: Turbidity vs. Phaeophytin

Log-Linear Power-Law

0 0.5 1 1.5 2 2.5 30

0.5

1

1.5

2

2.5

3

LOG10(PHAE) (µg/L)

LO

G10

(Tur

bidi

ty) (

NTU

)

R² = 0.64

0 50 1001502002503003504004500

100

200

300

400

500

600

PHAE (µg/L)

Turb

idity

(NTU

)

R² = 0.51

DiscussionPower 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)

DiscussionPower 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)

DiscussionPower 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.

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