Mathematical Modeling of Water Quality Data from Constructed Wetlands and Biofilters
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Transcript of Mathematical Modeling of Water Quality Data from Constructed Wetlands and Biofilters
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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