USING MULTIPLE LINEAR REGRESSION TO PREDICT REMOVAL OF COPPER
AND ZINC ON VEGETATIVE BIOFILTER STRIPS TREATING HIGHWAY
STORMWATER RUNOFF
Jessica Marie Wagner
B.S., University of California, Davis, 2001
PROJECT
Submitted in partial satisfaction of
the requirements for the degree of
MASTER OF SCIENCE
in
CIVIL ENGINEERING
at
CALIFORNIA STATE UNIVERSITY, SACRAMENTO
FALL
2011
USING MULTIPLE LINEAR REGRESSION TO PREDICT REMOVAL OF COPPER
AND ZINC ON VEGETATIVE BIOFILTER STRIPS TREATING HIGHWAY
STORMWATER RUNOFF
A Project
by
Jessica Marie Wagner
Approved by:
__________________________________, Committee Chair
John Johnston, Ph.D., P.E.
__________________________________, Second Reader
Dipen Patel, Ph.D.
____________________________
Date
ii
Student: Jessica Marie Wagner
I certify that this student has met the requirements for format contained in the University format
manual, and that this project is suitable for shelving in the Library and credit is to be awarded for
the Project.
__________________________, Graduate Coordinator
Cyrus Aryani, Ph.D., P.E., G.E.
Department of Civil Engineering
iii
________________
Date
Abstract
of
USING MULTIPLE LINEAR REGRESSION TO PREDICT REMOVAL OF COPPER
AND ZINC ON VEGETATIVE BIOFILTER STRIPS TREATING HIGHWAY
STORMWATER RUNOFF
by
Jessica Marie Wagner
This study was conducted to determine if equations could be derived using multiple
linear regression (MLR) to predict the removal of total and dissolved copper and zinc by
vegetated biofilter strips treating highway runoff. The regression analysis was based on
the data set collected during the Caltrans Roadside Vegetative Treatment Site (RVTS)
Study. Eight RVTS study sites distributed across California and storms from several
years were included. The predictors chosen for the MLR analysis were strip slope, strip
width, vegetation coverage, percentage of clay content in the soil, rainfall duration, total
event precipitation, and antecedent dry days. The predictands chosen were effluent
concentration (Ce), concentration reduction (Ci-Ce), and fraction of concentration
remaining (Ce/Ci). In a second analysis, a first order removal model was assumed to fit
the field data, resulting in concentrations that should decline exponentially with strip
width. MLR analysis was used to develop predictive equations for the exponential decay
coefficients based on the same predictors (except width). Regression models were
evaluated using criteria such as the value of the coefficient of determination (R2), whether
iv
or not the sign of the predictor coefficient matched expectations from physical processes
and how well the equations conformed to MLR assumptions. Not all predictors proved to
be statistically significant. Predictive equations were produced for effluent
concentrations of total copper, total zinc, and dissolved zinc based on vegetation
coverage, rainfall duration, total event precipitation, and antecedent dry days. The best
equation for effluent dissolved copper concentrations was based on only vegetation
coverage, rainfall duration, and antecedent dry days. The coefficient of determination
(R2) values for these equations were 0.348 to 0.523. R2 values for the best equations
predicting Ci-Ce and Ce/Ci were much lower. When the predictive Ce equations were
graphed against vegetation coverage, dissolved copper and zinc concentrations are higher
than those for total copper and zinc, thus these equations are unreliable. For the first
order decay coefficient, the best fit equation had a low R2 value and the regression model
could not meet all the assumptions of the MLR. Thus, these equations are also
unreliable.
_______________________, Committee Chair
John Johnston, Ph.D., P.E.
_______________________
Date
v
TABLE OF CONTENTS
Page
List of Tables ............................................................................................................. vii
List of Figures ........................................................................................................... viii
Chapter
1. INTRODUCTION …….………………………………………………………… .1
2. BACKGROUND OF THE STUDY ....................................................................... 4
2.1 Vegetated Biofilter Strips ........................................................................... 4
2.2 Mechanisms ................................................................................................ 7
2.3 Caltrans Roadside Vegetated Treatment Sites (RVTS)……………… .... 11
2.4 Biofilter Strip Performance ....................................................................... 16
3. METHODOLOGY ..........................................................................................…. 18
3.1 RVTS Study Data Analysis ................................……………………….. 18
3.2 Predictors for Multiple Linear Regression ..........……………………….. 20
3.3 Predictands for Multiple Linear Regression .......……………………….. 23
3.4 Using Multiple Linear Regression to Determine First Order Coefficient 23
3.5 Multiple Linear Regression.................................……………………….. 25
4. RESULTS AND DISCUSSION ........................................................................... 32
4.1 Basic Multiple Linear Regression .......................……………………….. 32
4.2 Multiple Linear Regression for First Order Decay .…………………….. 47
4.3 Discussion ...........................................................……………………….. 51
5. CONCLUSION…………………………………………………………….….... 56
Appendix A RVTS Storm Data ................................................................................ 57
Appendix B RVTS Input Data for MLR................................................................... 58
Appendix C Multiple Linear Regression Reports from JMP® ................................ 59
Appendix D MLR Trials ........................................................................................... 76
References ................................................................................................................... 83
vi
LIST OF TABLES
Tables
Page
1.
Table 1 RVTS Study Site Characteristics ... ………….……………………….12
2.
Table 2 Storm Data Qualifiers .......................................................................... 19
3.
Table 3 Predictors for Multiple Linear Regression.. …………………..…….. 22
4.
Table 4a Coefficient Values for Models with R2>0.250 for Total Copper and
Dissolved Copper .............................................................................................. 34
5.
Table 4b Coefficient Values for Models with R2>0.250 for Total Zinc and
Dissolved Zinc .................................................................................................. 35
6.
Table 5 Criteria for Predictor Evaluation of Ce and Ci-Ce ................................ 39
7.
Table 6 Coefficient Values for Total Copper, Dissolved Copper, Total Zinc and
Dissolved Zinc .................................................................................................. 48
vii
LIST OF FIGURES
Figures
Page
1.
Figure 1 Vegetated Biofilter Strip Design…… .……………………………….5
2.
Figure 2 Schematic of RVTS Test Site…… ... .……………………………….14
3.
Figure 3 Dissolved Zinc Removal as a Function of Width (Sacramento) ........ 25
4.
Figure 4 Scatter Plot of Residuals for a Linear and Non-linear Relationship .. 27
5.
Figure 5 Scatter Plot of Residuals Showing Homoscedasticity and
Heteroscedasticity………. ............................ …………………………………29
6.
Figure 6 Total Zinc Residual by Predicted Plot (trial 12 for Ce) .................. …42
7.
Figure 7 Total Zinc Normality Test for ln(Ce) (trial 12)............................... …43
8.
Figure 8 Total Copper Predicted Ce vs. Actual Ce ........................................ …44
9.
Figure 9 Dissolved Copper Predicted Ce vs. Actual Ce ................................ …45
10.
Figure 10 Total Zinc Predicted Ce vs. Actual Ce .......................................... …46
11.
Figure 11 Dissolved Zinc Predicted Ce vs. Actual Ce ................................... …47
12.
Figure 12 Total Zinc Residual by Predicted Plot (trial 8) ............................. …50
13.
Figure 13 Total Zinc Normality Test for ln(k) (trial 8) ................................ …50
14.
Figure 14 Predictive Ce vs. Vegetation Cover (assumed values were antecedent
dry days at 1 day, rainfall duration at 1 hour, and total event precipitation at 24
mm) ............................................................................................................... …52
viii
1
Chapter 1
INTRODUCTION
The purpose of the federal Clean Water Act is to stop pollutants from being
discharged into waterways and to maintain water quality to provide a safe environment
for fishing and swimming. In 1987, the Act was amended to require the Environmental
Protection Agency (EPA) to establish a program to address stormwater discharges. As
part of the Act, the National Pollution Discharge Elimination System (NPDES) permit
program was implemented, which regulates the discharge of pollutants from point
sources to waters. Many California Department of Transportation (Caltrans) properties
and facilities fall under the jurisdiction of the NPDES permitting system. Caltrans
maintains approximately 15,000 miles of highway, 12,000 bridges, and more than
230,000 acres of right-of-way, so the potential for serious pollution problems is elevated.
This is due to water washing materials such as oil, grease, and litter from highways,
streets, and gutters into Municipal Separate Storm Sewer Systems (MS4s) and eventually
into rivers, lakes, and the ocean from every rain event (Brice & Starring, 2002). To meet
the requirements of its NPDES permit, Caltrans created a Storm Water Management Plan
(SWMP) in 2003, which guides all Caltrans activities related to stormwater control and
treatment (Caltrans, 2003).
Caltrans is concerned that chemical constituents in highway stormwater runoff,
particularly copper and zinc, will cause water quality impairments in receiving waters.
Zinc in highway stormwater runoff comes from crankcase and lubricating oils, grease,
2
tire wear, and decorative and protective coatings (Yousef et al., 1985). When zinc
reaches a concentration of 5.6 μg/L or greater in receiving waters, it affects salmon by
altering behavior, blood and serum chemistry, impairing reproduction, and reducing
growth (Sprague, 1968). Copper in highway stormwater runoff comes from bearing
wear, brake lining wear, and decorative and protective coatings (Yousef et al., 1985).
When copper reaches concentrations of 0.18 to 2.1 μg/L in receiving waters, it affects
salmon by disrupting the salmonid smoltification process, interfering with fish sensory
systems, inhibiting their ability to avoid predators and migrate, and slowing juvenile
growth (Hecht et al., 2007). Copper affects the sense of smell in fish by competing with
natural odorants for binding sites in the olfactory tissue, which in turn affects the
activation of the olfactory receptor neurons or intracellular signaling in the neurons
(Solomon, 2009). Fish rely on their sense of smell to find food, avoid predators, and
migrate. In other aquatic organisms, copper causes gills to fray and lose their ability to
regulate the transport of salts such as sodium chloride and potassium chloride into and
out of the fish. These salts are important for the normal functioning of the cardiovascular
and nervous systems. When the salt balance between the body of a copper-exposed fish
and the surrounding water is disrupted, the fish can die (Solomon, 2009). The
reproduction rates of aquatic life such as sea scallops and fathead minnows are also
affected by copper (Solomon, 2009). Thus, contaminating receiving waters with zinc and
copper is a huge concern for not only the salmon population, but also other aquatic
organisms.
3
Vegetative biofilters are a best management practice used to treat stormwater
before it is discharged to natural receiving waters. In laboratory studies, vegetative
biofilters were found to remove heavy metals at rates in excess of 90% (Blecken et al.,
2009). In field studies, the California Department of Transportation (Caltrans) monitored
ten vegetative biofilter sites to evaluate heavy metal removal from highway runoff. Zinc
and copper were removed, but the results varied from site to site. It is not certain which
parameters of biofilter strips and storms are significant in the removal of copper and zinc.
In this project, data collected during the Caltrans’ Roadside Vegetated Treatment Sites
(RVTS) study will be used in a multiple linear regression (MLR) analysis of the biofilter
parameters. The parameters considered are strip width, strip slope, average strip
vegetation coverage, percentage of clay content in the soil, antecedent dry days, total
event precipitation, and rainfall duration. The MLR results will suggest which
parameters are significant in copper and zinc removal. With these parameters, an
equation will be developed to predict the removal of copper and zinc on the vegetative
biofilter strips.
4
Chapter 2
BACKGROUND OF THE STUDY
This chapter provides background information on vegetated treatment systems,
the California Department of Transportation’s Roadside Vegetated Treatment Sites
(RVTS) study and additional studies, which were conducted on vegetative biofilter strips.
2.1
Vegetated Biofilter Strips
As defined by the Environmental Protection Agency (EPA) a vegetated biofilter
strip is a permanent, maintained strip of planted or indigenous vegetation located between
nonpoint sources of pollution and receiving water bodies for the purpose of removing or
mitigating the effects of nonpoint source pollutants (Pennsylvania, 2006). The purpose of
a biofilter strip is to pass water over a vegetated surface, remove pollutants by a variety
of mechanisms, and provide an opportunity for incidental infiltration of runoff. Biofilter
strips function by slowing runoff velocities and filtering out sediment and other pollutants
and by providing some infiltration into underlying soils. Pollutants removed include
nutrients, heavy metals, toxic materials, floatable materials, oxygen demanding
substances, oil, and grease (Ventura, 2009). Biofilters act most effectively when they are
designed to receive sheet flow from paved areas, (e.g. highways), and maximize water
contact within the biofilter vegetation and soil surface (Ventura, 2009).
Various criteria should be considered when designing a vegetated biofilter strip
(see Figure 1). The California Department of Transportation (Caltrans) recommends a
preferred slope of 6% with a width of 5 feet to 150 feet and a flow depth of 1 inch
(Caltrans, 2007). The Washington Department of Transportation suggests a slope of 2%
5
to 15% and states the minimum width is dictated by the runoff treatment design flow
velocity where the maximum flow depth is 1 inch (WSDOT, 2010).
The Texas
Transportation Institute suggests a slope of 1% to 20% with 2% to 6% slope being
preferred, a minimum width of 24 feet with a flow velocity of 0.5 to 1 ft/s, vegetation
density of 80% to 90%, and a flow depth of 1 inch (Storey et al., 2009). Grismer et al.
(2006) suggest a slope of 1% - 3% should have a minimum width of 25 feet, a slope of
4% - 7% should have a minimum width of 35 feet, and a slope of 8% - 10% should have
a minimum width of 50 feet. Grismer et al. (2006) also suggest that sturdy, tall perennial
grasses do the best job of trapping sediment. The Caltrans Roadside Vegetated
Treatment Sites (RVTS) Study (2003) recommends a minimum of 65% vegetation
coverage but observed that a rapid decline in performance occurs below 80% vegetation
coverage.
Figure 1 Vegetated Biofilter Strip Design (Shoemaker et al., 2002)
There are advantages in considering a vegetated biofilter strip as a best
management practice (BMP), including the following:
6

Biofilter strips require minimal maintenance including erosion prevention
and mowing.

Biofilter strips provide reliable water quality benefits in conjunction with
the high aesthetic appeal.

Biofilter strips are cost affective.

Biofilter strips were among the best performers in reducing sediment and
heavy metals in the BMP Retrofit Pilot Program (Caltrans, 2004).

Biofilter strips are well suited to being part of a “treatment train” system
of BMP’s and should be considered whenever siting other BMP’s that
could benefit from pretreatment, especially infiltration basins and
infiltration trenches (Caltrans, 2004).
There are also limitations to biofilter strips, including the following:

Biofilter strips are not appropriate for industrial sites or locations where
spills may occur.

A thick vegetative cover is needed for these practices to function properly,
generally 65% to 80% coverage (Caltrans, 2003).

Sheet flow must be maintained for the strip to be effective.

Biofilter strips are impracticable in watersheds where open land is scarce
or expensive.

The width of a biofilter strip must be adequate and flow characteristics
acceptable or water quality performance can be severely limited.
7

Biofilter strips do not provide significant attenuation of the increased
volume and flow rate of runoff during intense rain events.
2.2
Mechanisms
The design of the vegetated biofilter strip should focus on setting up conditions
that facilitate the removal mechanisms for the reduction of total suspended solids (TSS),
hydrocarbons, heavy metals, and nutrients. As water flows through a filter strip,
pollutants are removed by filtering, infiltration, and settling of particulates due to the
slow water velocity. The filter strip has a high sediment trapping efficiency as long as
the flow is shallow and uniform and the filter is only submerged during a rain event
(Dillaha et al., 1986). A pea gravel diaphragm, or a small trench, should be used at the
top of the slope to act as a pretreatment device settling out sediment particles before they
reach the strip and to act as a level spreader establishing sheet flow as runoff enters the
filter strip (see Figure 1). The top and toe of the slope should be as flat as possible to
encourage sheet flow and prevent erosion (US EPA, 2006). To achieve the highest
reduction of pollutants, the biofilter strip should be designed with three layers, a root
zone, a subsoil horizon, and surface vegetation. The root zone will allow high infiltration
rates via macropores that arise with the generally improved soil structure (Grismer et al.,
2006). The subsoil horizon must have moderate permeability and fertility with adequate
organic matter content and sufficient strength to support both plants and the topsoil
(France, 2002). The ideal infiltration rate of the soil is around ½ inch per hour (Cahill et
al., 2011). The vegetation of the filter strip slows the velocity of runoff, stabilizing the
slope, and stabilizing accumulated sediment in the root zone of the plants (Caltrans,
8
2003). Decreasing the flow volume and velocity facilitates sediment deposition on the
filter because of a decrease in transport capacity. As sediment from runoff is deposited in
vegetated zones, sediment-bound nutrients and metals are also removed. Trapping
efficiencies in the Caltrans RVTS study is 14% for zinc and 18% for copper (Caltrans,
2008).
The mechanisms that assist in metal removal are adsorption, ion exchange,
precipitation, complexation, and phytostabilization. Heavy metals are removed initially
by short-term processes, such as adsorption and ion exchange. Adsorption is the
accumulation of ions at the interface between a solid phase and an aqueous phase. The
adsorption of heavy metal ions (e.g. zinc or copper ions), is dependent upon the
properties of the soil including clay and organic fractions, pH, water content, temperature
of soil, and properties of the metal ion. The solid state of soils composes an average of
45% of soil bulk and consists of mineral particles, organic matter, and organic-mineral
particles (Dube et al., 2001). These all play an important role in giving soil the ability to
adsorb metal ions. The inorganic colloidal fraction of soil is the most responsible of
adsorption by it mineral particles including clay minerals, oxides, sesquioxides and
hydrous oxides of minerals (Dube et al., 2001). The clay minerals, montmorillonite,
kaolinite, and iron and manganese oxides in the soil adsorb metals. Clay particles are
usually negatively charged which is an important factor influencing the sorption
properties of the soil. The binding forces between heavy metals and soil fractions are
dependent on pH and ion properties such as charge. The binding forces of metal ions to
soil particles decrease with increasing pH of the environment (Dube et al., 2001).
9
The affinity for binding heavy metals varies between different soil mineral
constituencies and organic material (Dube et al., 2001). There are different types of clay
minerals that can be present in soil including Sepiolite (Orera), Sepiolite (Vallecas),
Bentonite, Palygorskite (Bercimuelle), Palygorskite (Torejon), Illite, and Kaolin. GarciaSanchez, et. al. (1998) found that the adsorptive capacity of these minerals are in the
order of Sepiolite (Orera) > Sepiolite (Vallecas) > Bentonite > Palygorskite (Bercimuelle)
> Illite > Kaolin > Palygorskite (Torejon). The adsorptive capacity of the clay minerals
depends on the inner crystal structure features, as well as the surface area of the particle
where the greatest surface area shows the strongest adsorptive capacity.
Soil organic material consists of living organisms, biochemicals, and insoluble
humic substances. Biochemicals, such as amino acids, proteins, carbohydrates, organic
acids, lignin, etc, and humic substances, such as insoluble polymers of aliphatic and
aromatic substances produced through microbial action, provide sites for metal sorption.
The binding of metals to organic matter involves a continuum of reactive sites ranging
from weak forces of attraction to formation of strong chemical bonds (McLean &
Bledsoe, 1992). Organic matter decreases with depth, so the mineral constituents of soil
will become a more important surface for adsorption.
Ion exchange takes place where there are negatively charged clay or organic
matter in the soil that attract positively charged cations, such as zinc and copper, through
electrostatic forces.
The attractive forces of the positive metal ions to the negatively
charged clay particles are strong enough to hold the metal ions in the soil despite the
passage of water through the soil (McLean & Bledsoe, 1992). In ion exchange, the
10
metals displace other ions of the same valence or multiple ions of lesser valence, thereby
not altering the surface charge.
Another mechanism of metal removal is precipitation. Metals may precipitate to
form inorganic compounds including metal oxides, hydroxides, and carbonates (McLean
& Bledsoe, 1992). Precipitation is pH dependent, occurring mainly when the pH is
greater than 7.5. The precipitates formed will immobilize the metals if the pH drops
below 6.5, however, it has been found that the metals will be released back into the
system (McLean & Bledsoe, 1992).
Complexation changes the adsorptive properties of metals. Metal cations form
soluble complexes with inorganic and organic ligands. Inorganic ligands include SO42-,
Cl-, OH-, PO43-, NO3-, and CO32-. Organic ligands include low molecular weight
aliphatic, aromatic, and amino acids and soluble constituents of fulvic acids. The
presence of complex species in the soil solution can significantly affect the transport of
metals through the soil. With complexation, the resulting metal species may be
positively or negatively charged or be electrically neutral. When metals are complexed
with inorganic ligands, the positive charge on the complexed metal decreases, reducing
its ability to adsorb to a negatively charged surface (McLean & Bledsoe, 1992). In soils
where the organic ligand adsorbs to the soil surface, metal adsorption may be enhanced
by the complexation of the metal to the surface-adsorbed ligand (McLean & Bledsoe,
1992).
Phytostabilization is the immobilization of a contaminant in soil through
adsorption and accumulation by roots, adsorption onto roots, or precipitation within the
11
root zone of plants (Brookhaven National Laboratory, 2008). The metals must be
bioavailable or ready to be adsorbed by roots. Bioavailability depends on metal solubility
in soil solution. Only metals associated as free metal ions, soluble metal complexes, or
adsorbed to inorganic soil constituents at ion exchange sites are readily available for plant
uptake (Lasat, 2000). Metals that are bound to soil organic matter, precipitated as oxides,
hydroxides, or carbonates, and are embedded in the structure of the silicate minerals are
not readily available for plant uptake (Lasat, 2000). The plant species tolerance,
biological cycle, and ability to grow on unvegetated soils are characteristics that may
contribute to the success of the stabilization of plants in soils contaminated with heavy
metals. Plants of biofilters have been shown to accumulate 10% of the metals trapped in
the soil by other mechanisms (Blecken et al., 2009).
2.3
Caltrans Roadside Vegetated Treatment Sites (RVTS)
The Roadside Vegetated Treatment Sites (RVTS) study was an eight-year water
quality monitoring project that was started to evaluate the pollutant removal efficiency of
existing vegetated side slopes adjacent to freeways. The primary objective of this study
was to determine if standard roadway design requirements result in vegetated side slopes
with stormwater treatment capabilities equivalent to biofiltration strips specifically
engineered for water quality performance. The monitoring of the RVTS sites took place
during five wet seasons including October 2001 to April 2002, October 2002 to April
2003, January 2006 to May 2006, October 2006 to April 2007 and October 2007 to April
2008. The ten study sites were located in Sacramento, Redding, Cottonwood, San Rafael,
Yorba Linda, Irvine, San Onofre, Murrieta, and Moreno Valley (two sites: A and B). The
12
study includes 31 strips (Caltrans, 2008). The Murrieta and Moreno Valley B sites were
new for the 2007-2008 monitoring year. Since these sites were not as established as the
other sites and data such as vegetation coverage and clay content were not available,
these sites are not included in the multiple linear regression analysis performed in this
project. The site characteristics of the eight strips included in this project are shown in
Table 1.
Table 1 RVTS Study Site Characteristics (Caltrans, 2008)
Site Location
Cottonwood
Irvine
Sampling
Freeway Location Site ID
I-5, Southbound
2-201
near Cottonwood
2-202
Exit
I-405, Northbound
at Sand Canyon
Ave Exit
SR-60, Eastbound
Moreno Valley A at Frederick St onramp
Redding
SR-99, Eastbound
near Old Oregon
Trail/Shasta
College Exits
Vegetation Clay
Coverage Content
(%)
(%)
Widtha
(m)
Slope
(%)
EOP b
EOP b
EOP b
EOP b
9.3
52
75
14.4
b
EOP
b
EOP b
12-230
EOP
12-231
3.0
11
75
15.2
12-232
6.0
11
63
23.8
12-233
13.0
11
68
33.4
8-201
8-202
EOP b
2.6
EOP b
13
EOP b
7
EOP b
18.2
8-203
4.9
13
19
17.3
8-204
8.0
13
26
24.4
8-205
9.9
13
b
EOP
10
EOP
b
22
b
EOP
88
16.1
b
EOP b
11.6
2-203
2-204
EOP
2.2
2-205
4.2
10
87
10.3
2-206
6.2
10
82
12.5
13
Table 1 (continued)
Site Location
Sacramento
San Onofre
San Rafael
Yorba Linda
Width
(m)
Slope
(%)
3-213
EOP b
EOP b
EOP b
EOP b
3-214
1.1
5c
Sampling
Freeway Location Site ID
I-5, Northbound
between Pocket
and Laguna Exits
I-5, Northbound
near Basilone Exit
I-101, Northbound
at St. Vincent onramp
SR-91, Eastbound
between Weir
Canyon Road and
SR-241 Exits
Vegetation Clay
Coverage Content
(%)
(%)
a
91
11.3
c
3-215
4.6
33
86
31.6
3-216
6.6
33
92
31.0
3-217
8.4
33
90
25.0
11-204
EOP b
EOP b
EOP b
EOP b
11-205
1.3
8
81
17.2
11-206
5.3
10
76
16.1
11-207
9.9
16
b
EOP
73
b
EOP
22.6
b
EOP b
4-213
EOP
4-214
8.3
50
84
20.8
12-225
EOP b
EOP b
EOP b
EOP b
12-226
2.3
14
66
18.5
12-227
12-228
12-229
5.4
7.6
13.0
14
14
14
85
79
79
21.2
22.2
16.2
a
Width is the distance from the edge of pavement to the collection v-ditch
EOP is the edge of pavement, the top of the biofilter slope
c
Slope is 5% for the first 3 meters
b
Figure 2 shows a schematic of the RVTS sites. The collection system at each
location consisted of a concrete v-ditch constructed parallel to the roadway to capture
highway runoff after it passed through existing vegetated slopes of varying widths
perpendicular to the roadway. The concrete v-ditch varied in length from 19 to 30
meters.
14
Figure 2 Schematic of RVTS Test Site (adapted from Caltrans, 2008)
In the 2008 RVTS study, an Analysis of Variance (ANOVA) was performed
using a 95% confidence level on the RVTS data from four locations (Sacramento,
Redding, San Onofre, and Yorba Linda) to determine whether statistically significant
differences exist between concentration levels of constituents at the edge of pavement
and the strips. The results for dissolved copper showed 39.5% significant reduction in
concentration level at the 11-207 strip in San Onofre. The remainder of the strips had a
25% non-significant reduction in concentration for dissolved copper. The results for total
copper showed 52.7% significant reduction in concentration level at the 3-215, 3-216,
and 3-217 strips in Sacramento and the 12-228 and 12-229 strips in Yorba Linda. The
remainder of the strips had a 34% non-significant reduction in concentration for total
copper. ANOVA results for dissolved zinc showed 81% significant reduction in
concentration level at all 4 strips, not including the edge of pavement, for Yorba Linda.
The remainder of the strips had a 37% non-significant reduction in concentration for
15
dissolved zinc. ANOVA results for total zinc showed 68% significant reduction in
concentration level at all the strips, not including the edge of pavement, for Sacramento
and San Onofre and the 2-204 and 2-205 strips in Redding. The remainder of the strips
had a 66% non-significant reduction in concentration for total zinc.
In the 2008 RVTS study, a preliminary Multiple Linear Regression (MLR)
analysis was performed to investigate how various factors affect the performance of the
vegetative strips in terms of concentration. This study tested thirteen constituents,
including copper and zinc. The predictors that were selected for the MLR analysis
included influent concentration, strip width, strip slope, average strip vegetative cover,
hydraulic residence time, infiltration rate, antecedent dry days, total event precipitation
and rainfall duration. A data set was compiled for each of the thirteen constituents,
which included concentration, concentration differences between the edge of pavement
and the strip, and associated site characteristics. The data sets were natural-logarithmtransformed and compiled into an input table for the MLR analysis. The initial
conclusions for this analysis show that the edge of pavement concentration, infiltration
rate, and rainfall duration have a significant impact on strip concentration for total and
dissolved copper and zinc; slope and vegetative cover have a significant impact on
dissolved copper; and antecedent dry days have a significant impact on dissolved zinc.
These are only observations because the MLR analysis lacked a statistical analysis to
validate and verify the assumptions of linearity, normality, collinearity, homoscedasticity,
and constant variance (Caltrans, 2008).
16
2.4
Biofilter Strip Performance
In 2004, Caltrans completed a BMP Retrofit Pilot Program where three
biofiltration strips were monitored in Southern California. Two of the strips were located
at maintenance stations and the other strip was located along a highway (I-605/SR-91).
The design criteria for these strips included a slope of no more than 12 percent (actual
slope obtained was 1% to 3%), a minimum width in the direction of flow of 8 meters, no
gullies or rills that could concentrate overland flow, and a top edge level with the plane of
the adjacent pavement. These biofilter strips removed 85% of total copper, 72% of total
zinc, 65% of dissolved copper, and 53% of dissolved zinc.
Yousef et al. (1985) conducted research on two grass swales in Florida located at
the Maitland/I-4 Interchange and the EPCOT Interchange. The slopes of the sites were
8% to 29% and the areas were predominately covered with Bahia grass. The Maitland
Interchange sampling covered an eight-month period between August 1982 and March
1983 and samples were taken from six stations. A sampling sharp crested 90⁰ v-notch
weir was constructed at 53 m from the pavement. Three experiments were conducted at
the Maitland Interchange at different flow velocities. At a flow velocity of 2.58 m/min,
77% of the dissolved zinc but only about 20% of the dissolved copper were removed. At
a flow velocity of 1.37 m/min, 92% of the dissolved zinc and 60% of the dissolved
copper was removed. Finally, at a flow velocity of 0.90 m/min, 90% of the dissolved
zinc was removed but an accurate analysis of dissolved copper was not achieved in this
experiment. The EPCOT interchange was constructed with two sampling sharp crested
90⁰ v-notch weirs at 90 m and 170 m from the pavement. The grass coverage at this site
17
was about 80%. At the EPCOT interchange site, with a flow velocity of 2.44 m/min and
a distance of 170 meters, 65% of the dissolved zinc was removed but the removal of
dissolved copper was minimal.
18
Chapter 3
METHODOLOGY
Multiple linear regression (MLR) is a method used to model the linear
relationship between a dependent variable (predictand) and one or more independent
variables (predictors). The predictors used in the study are site characteristics of the
biofilter strips analyzed during the Roadside Vegetated Treatments Study (RVTS) and
storm event data. A variety of predictands have been calculated using the RVTS study
data obtained from the Caltrans database. These are described below. The predictors and
predictands were analyzed by means of multiple linear regression (MLR) using the
JMP® 8 statistical program. The method for analyzing the data is described in this
chapter.
3.1
RVTS Study Data Analysis
The data in this study were obtained from the Caltrans database, which contains
information from the Roadside Vegetated Treatments Study (RVTS). From the Caltrans
database, the RVTS study information containing storm information and the amount of
copper and zinc found in the influent and effluent waters were downloaded. These data
can be found in Appendix A. The data were formatted into a spreadsheet and evaluated
for quality assurance to assure that they meet a standard of quality needed to evaluate the
effectiveness of the filter strips in removal of copper and zinc. All storm data were
rejected or deemed unusable if they had one or more of the qualifiers listed in Table 2
(Caltrans, 2008).
19
Table 2 Storm Data Qualifiers (Caltrans, 2008)
Data
Qualifier
Reason for Rejection
U
The analyte was analyzed for, but was not detected above the level of the
reported sample quantitation limit.
J
The result is an estimated quantity. The associated numerical value is the
approximate concentration of the analyte in the sample.
J+
The result is an estimated quantity, but the result may be biased high.
J-
The result is an estimated quantity, but the result may be biased low.
R
The data are unusable. The sample results are rejected due to serious
deficiencies in meeting quality assurance criteria. The analyte may or may
not be present in the sample.
UJ
The analyte was analyzed for, but was not detected. The reported
quantitation limit is approximate and may be inaccurate or imprecise.
In addition to the qualifiers in Table 2, storm data were also rejected for the following
reasons:

The quantity given was based on a "less than" quantity rather than an
"equal to" quantity which means the value of copper or zinc listed is not a
true reading.

The amount of precipitation is missing due to equipment malfunctioning.

There were edge of pavement readings with no corresponding strip
readings or there were corresponding strip readings with no edge of
pavement readings.

The entries that were duplicates.

Dissolved metal concentrations were higher than total metal
concentrations.
20
After analyzing the data for quality assurance, 17 complete storms out of 233
storms (7%) were rejected for dissolved copper. For total copper, 14 complete storms out
of 153 storms (9%) were rejected. For dissolved zinc, 30 complete storms out of 233
storms (13%) were rejected. Finally, for total zinc, 8 complete storms out of 153 storms
(5%) were rejected.
3.2
Predictors for Multiple Linear Regression
Multiple linear regression (MLR) is a method used to model the linear
relationship between a predictand and one or more predictors. In general, the predictand
is a variable that is affected by the predictors.
The site characteristic predictors chosen to be included in this MLR are strip
slope, strip width, vegetation cover, and percentage of clay content in the soil. Table 3
provides a list of the predictors and the metals removal mechanisms that are affected by
each predictor. The slope of the vegetative biofilter strip influences the velocity at which
the water passes through the strip. The flow velocity affects contact time, which in turn
affects filtration, sedimentation, ion exchange, adsorption, and precipitation of the metals.
The lower the flow velocity is, the more contact time the water has with the vegetation
and soil. Increased contact time allows for more filtration, sedimentation, adsorption, ion
exchange, and precipitation to take place. The width of the strip is important because it
also influences contact time. The amount of vegetation cover that is present on the strip
slows down the flow of water thus increasing contact time. With the decrease in the
flow, sediment deposition is facilitated on the filter due to a decrease in transport
capacity. The decaying vegetation cover can also provide more adsorption sites and aid
21
in sediment deposition. The decaying vegetation is known as a humic substance and has
been found to strongly influence the adsorption of metals (Dube et al., 2000). The
percentage of clay in the soil is important because it indicates the relative number of
negatively charged sites for ion exchange. Clay also provides sites for adsorption.
The storm event predictors include total event precipitation, rainfall duration, and
antecedent dry days. The total event precipitation is important when considering the
amount of copper or zinc flushed from the roadway during a storm. In the Statewide
Discharge Characterization Study (Caltrans, 2003), it was observed that pollutant
concentrations tend to be higher for smaller rainfall events and lower for larger events,
which implies that pollutants tend to become diluted in larger storms. This observation is
consistent with the existence of an event first flush effect where concentrations tend to be
highest in the initial portion of runoff events and are diluted as the storm event continues
(Caltrans, 2003).
This could affect adsorption, ion exchange, and precipitation
negatively because the sites for these reactions become occupied during the first flush of
a storm event limiting the removal of copper and zinc during the remainder of a storm
event. If equilibrium is achieved in the high concentration first flush, when the cleaner
water passes over the soil, adsorbed metals may desorb. Whether desorption cancels the
adsorption can be seen in the event mean concentration data. In addition, if the total
event precipitation is high due to a large amount of rainfall in a short period, the water
will flow faster and deeper over the vegetated biofilter strip limiting the amount of water
that comes in contact with the soil and vegetation of the strip for filtration and
sedimentation. However, if total event precipitation is high due to a long rainfall
22
duration, this should not be an issue. Thus, event volume is an imperfect measure of
storm size. The rainfall duration is important for copper and zinc removal because the
longer it rains, the more water that will be on the filter strip saturating the soil. Once the
soil is saturated, the strips infiltration capacity has been reached and overland flow will
occur. The water now relies on the vegetation to slow it down so that sedimentation and
adsorption can take place. The antecedent dry days are the number of dry days prior to
the start of a storm event. Kim et al. (2003), found the longer the period of antecedent
dry days, the higher the concentration of metals that will be at the edge of pavement.
With longer antecedent dry days, the soil becomes dry, which will increase infiltration
allowing for more adsorption and ion exchange within the soil particles. Longer
antecedent dry days could cause further reactions, like precipitation, that would sequester
the metals and maybe regenerate the adsorptive capacity of the soil.
Table 3 Predictors for Multiple Linear Regression
Predictor
Strip Slope
Strip Width
Metals Removal Mechanism Affected in the
Biofilter Strip
Adsorption, Ion Exchange, Precipitation, Filtration,
Sedimentation
Adsorption, Ion Exchange, Precipitation, Filtration,
Sedimentation
Vegetation Cover
Adsorption, Ion Exchange, Filtration, Sedimentation
Clay Content
Adsorption, Ion Exchange
Adsorption, Ion Exchange, Precipitation, Filtration,
Sedimentation
Adsorption, Ion Exchange, Precipitation, Filtration,
Sedimentation
Total Event Precipitation
Rainfall Duration
Antecedent Dry Days
Adsorption, Ion Exchange, Precipitation, Filtration
23
3.3
Predictands for Multiple Linear Regression
Several predictands were considered in the multiple linear regression model.
When looking at possible predictands, the natural logarithm (ln) was used to be consistent
with the early multiple linear regression analysis in the 2008 RVTS study. Natural
logarithms were used because the Discharge Characterization Study (Caltrans, 2003)
found that the natural logarithm transformations were needed to satisfy the statistical
assumptions of the analyses. The predictands used for the multiple linear regression are
the natural logarithm of the effluent concentration (ln(Ce)), change of concentration
(ln(Ci-Ce)), and fraction of concentration remaining (ln(Ce/Ci)). Appendix B contains the
values of the above listed predictands for each study site, as well as the values for the
predictors mentioned in Section 3.2.
3.4
Using Multiple Linear Regression to Determine First Order Coefficient
Kadlec (1999) defined a first-order decay equation that summarizes the
performance of a wide range of pollutants in wetlands. This two-parameter model
includes k, the area-based removal rate constant, and C*, the irreducible background
concentration of the pollutant in the wetland, and assumes plug flow kinetics. The
resulting equation is,
Cout = C* + (Cin - C* )e-kt
(1)
where Cout is the effluent concentration, C* is the irreducible background concentration,
Cin is the influent concentration, k is the first order decay constant, and t is the detention
time.
24
The Environmental Protection Agency (EPA) defines a removal mechanism using
first order decay as
C = Co e-kt
(2)
where C is the effluent concentration, Co is the initial concentration, k is the first order
decay constant, and t is the hydraulic detention time (Huber et al., 2006).
Based on Kadlec’s and EPA’s studies, it was decided to try an alternate approach
with multiple linear regression. In this approach, the first-order model would be assumed
and MLR would be used to predict the first order decay coefficient. To evaluate a first
order decay equation the following equation was used,
Ce = Ci e-kw
(3)
where Ce is the effluent concentration, Ci is the influent concentration, k is the first order
decay constant, and w is the filter strip width. To use this equation, the relationship
between the effluent concentration and the strip width should be exponential in nature.
Such a relationship is shown in Figure 3 where the Sacramento RVTS dissolved zinc data
is graphed with the effluent concentration on the y-axis and the width on the x-axis.
To find the k values from the above equation, the slope function was used in
Excel with the natural logarithm of Ce as the dependent (y) variable and strip width as the
independent (x) variable. The multiple linear regression was run using the natural
logarithm of k values as the predictand against the various predictors mentioned above
with the exception of width, which is used to calculate the k value.
25
80
70
60
Ce (ug/L)
50
40
30
20
10
0
0
1
2
3
4
5
6
7
8
9
Width (m)
Figure 3 Dissolved Zinc Removal as a Function of Width (Sacramento)
3.5
Multiple Linear Regression
Multiple linear regression is a method used to model the linear relationship
between a dependent variable (predictand) and one or more independent variables
(predictor). In MLR the model is fit such that the sum-of-squares of differences of
observed and predicted values is minimized. MLR expresses the value of a predictand
variable as a linear function of one or more predictor variables and an error term:
y = b0 + b1 x1 + b2 x2 +…+ bm xm + ε
(4)
where y is the predictand variable, b0 , b1 , …, bm are unknown parameters, x1 , x2 , …, xm
are the predictor variables, and ε is a random error term (Freund & Littell, 2003). Least
squares is a technique used to estimate the unknown parameters. The goal is to find
estimates of the parameters, b0 , b1 ,…,bm, that minimize the sum of the squared
26
differences between the actual y values and the values of y predicted (ŷ ) by the equation.
The estimates are the least-square estimates and the quantity minimized is the error sum
of squares (Freund & Littell, 2003).
The principle of least squares is applied to a set of n observed values of y and the
associated xj to obtain estimates, b̂ 0 , b̂ 1 ,…,b̂ m, of the respective parameters b0 , b1 , …, bm.
The method of ordinary least squares minimizes the sum of squared vertical distances
between observed predictors and the predictors predicted by the linear approximation.
The resulting estimated values are expressed in the estimating equation
ŷ = b̂ 0 + b̂ 1 x1 + b̂ 2 x2 +…+ b̂ m xm
(5)
The MLR model is based on several assumptions, which, if satisfied, show that
the regression estimators are optimal in the sense that they are unbiased, efficient, and
consistent. An unbiased estimator means its expected value is equal to the true value of
the predictor. An efficient estimator has a smaller variance than any other estimator has.
A consistent estimator has a bias and variance that approach zero as the sample size
approaches infinity (Meko, 2011).
The basic assumptions for MLR are linearity, collinearity, zero mean, constant
variance, and normality. Multiple linear regression can only accurately estimate the
relationship between the predictand and predictors if the relationships are linear in nature.
If the relationship between the predictand and predictors is not linear, the results of the
regression analysis will under-estimate the predictor and over-estimate other predictors
that share the same variance. A method of checking for linearity is examination of
27
residual scatter plots showing the studentized residuals as a function of predicted values
(Osborne & Waters, 2002). The residual represents unexplained variation after fitting a
regression model. It is the difference between the observed value of the variable and the
value suggested by the regression model. The studentized residual is the residual divided
by its estimated standard deviation. The residuals are assumed to be uncorrelated with
the predicted values of the predictand. A violation of linearity is indicated by a
noticeable pattern of dependence in the scatter plot by a flare out with increasing value of
the predictand or curvature in the plot. Figure 4 shows examples of linear and nonlinear
relationships of residuals.
Figure 4 Scatter Plot of Residuals for a Linear (left plot) and Non-Linear (right plot)
Relationship (Osborne & Waters, 2002)
Collinear variables are a major problem with MLR modeling. Two variables are
said to be collinear if they are approximately (or exactly) linearly dependent or if there is
a high correlation between them. When collinearity between variables is present, it does
not invalidate the regression model in the sense that the predictive value of the equation
may still be good as long as the prediction is based on combinations of predictors within
28
the same multivariate space used to calibrate the equation (Meko, 2011). However, there
are various negative effects of collinearity to consider. The variance of the regression
coefficients can be inflated so much that individual coefficients are not statistically
significant even though the overall regression equation is strong and the predictive ability
good. The relative magnitudes and even the signs of the coefficients may defy
interpretation. Finally, the values of the individual regression coefficients may change
radically with the removal or addition of a predictor variable in the equation. The
Variance Inflation Factor (VIF) is a statistic that is used by the JMP statistical program to
identify collinearity amongst the predictor variables. VIF provides an index that
measures how much the variance of an estimated regression coefficient increases as a
result of collinearity. VIF is based on the multiple coefficient of determination in
regression of each predictor in multivariate linear regression on all the other predictors
VIFi 
1
1  R i2
(6)
where R2i is the multiple coefficient of determination in a regression of the ith predictor on
all other predictors, and VIFi is the variance inflation factor associated with the ith
predictor. Collinearity can be a problem when the variance inflation factor of one or
more predictors is greater than five (Meko, 2011).
Zero mean assumes the expected value of the residuals is zero. Zero mean is
generally not a problem because the least squares method of estimating regression
equations guarantees that the mean of the residuals is zero.
29
Constant variance assumes the variance of the residuals is constant. The method
of least squares used to find the line of best fit assumes that each data point is equally
reliable. In some cases, it is known that the predictand is more variable and hence less
predictable for certain values of predictors. An example of a violation of this assumption
is a scatter plot, which shows a pattern of residuals whose variance increases over time
(Meko, 2011).
The assumption of homoscedasticity means that the variance of errors is the same
across all levels of predictors. Heteroscedasticity is indicated when the variance of errors
differs at different values of the predictors. When heteroscedasticity is present, it can
lead to distortion of the findings and weaken the analysis thus increasing the possibility
of over-estimation of significance. Homoscedasticity can be checked by visual
examination of a scatter plot of the studentized residuals by the regression predicted
value (Osborne & Waters, 2002). Figure 5 shows examples of a homoscedasticity and
heteroscedasticity scatter plot of studentized residuals.
Figure 5 Scatter Plot of Residuals Showing Homoscedasticity and Heteroscedasticity
(Osborne & Waters, 2002)
30
Multiple linear regression assumes that the residuals are normally distributed.
Non-normally distributed residuals can distort relationships and significance tests.
Normality can be tested by using the Shapiro-Wilks test where the hypothesis is that the
data are from a normal distribution. Using a confidence interval of 0.05, a P-value
greater than 0.05 accepts the hypothesis whereas a P-value less than 0.05 rejects the
hypothesis.
The coefficient of determination (R2) is the proportion of variance accounted for,
explained, or described by regression. The relative sizes of the sums-of-squares terms
indicate how “good” the regression is in terms of fitting the calibration data. If the
regression is “perfect”, all residuals are zero and R2 is one. If the regression is a total
failure, the sum-of-squares of residuals equals the total sum-of-squares (sum-of-squares
of regression plus sum-of-squares of errors), no variance is accounted for by regression,
and R2 is zero (Meko, 2011).
The MLR modeling in this study was evaluated using JMP®, Version 8, SAS
Institute Inc., Cary, NC, 1989-2011. All the data for the MLR were calculated by the
author using Microsoft Excel and transferred into a table within the JMP® program.
Once the data were in a table in JMP®, the MLR was calculated using the Analyze Data
Fit Model where the personality used was “standard least squares” and the emphasis used
was “effect leverage”. The predictand (ln(Ce), ln(C-Ci), etc.) was graphed on the y-axis
while the predictors (strip slope, strip width, vegetation cover, etc.) were placed on the xaxis in combinations of two to seven predictors. Refer to Appendix C for a sample report
from JMP® showing the MLR results along with a description of the results shown.
31
After several regression models were produced, the models with R2 values greater than
0.250 were evaluated to make sure the results made physical sense, the predictors were
significant, and the assumptions were valid.
32
Chapter 4
RESULTS AND DISCUSSION
In this chapter the results from multiple linear regression are presented, which
includes the testing of the assumptions and the formulation of predictive equations.
4.1
Basic Multiple Linear Regression
Multiple linear regression (MLR) was performed using the three predictands,
ln(Ce), ln(Ci-Ce), ln(Ce/Ci), and the seven predictors, strip slope, strip width, vegetation
coverage, clay content, rainfall duration, total event precipitation, and antecedent dry
days, described in Chapter 3. The dissolved zinc regression trials were used to narrow
down which combinations of predictors would be used for the regression trials of total
zinc and total and dissolved copper. The regression trials for dissolved zinc started by
using all seven predictors and then removing one predictor randomly so that only six
predictors were used and then five predictors and so on. First each predictor was
eliminated one at a time. Then the predictors which were not significant (P-value >0.05),
were eliminated. (The MLR was tested with a 95% confidence level so the significant
predictors are those with a t- statistic P-value less than the 0.05, which rejects the null
hypothesis that the predictors have values of zero.) The effect the eliminated predictors
had on the significance of the other predictors dictated which predictors were chosen
until numerous combinations had been tried. After several trials with dissolved zinc were
completed, only the significant predictors were evaluated in different combinations.
Then only the predictor combinations that produced R2 values greater than 0.200 were
applied to total zinc and total and dissolved copper. Appendix D contains the regression
33
model results for total and dissolved copper and total and dissolved zinc showing the tstatistic P-value and whether or not a predictor is significant in the model, which is
indicated by the asterisk (*) next to the P-value.
Of the predictands, only ln(Ce) and ln(Ci-Ce) produced results that were worthy of
further evaluation, as determined by the value of the coefficient of determination (R2).
The MLR trial results did not produce any R2 values greater than 0.55, so trials with R2
values of 0.250 or greater were evaluated further. Linear associations between ln(Ce/Ci)
and the predictors were not observed. R2 values were less than 0.150. Table 4a presents
the predictor coefficients of the regression model trials with R2 values of 0.250 or greater
for total copper and dissolved copper while Table 4b presents the predictor coefficients
for total zinc and dissolved zinc.
34
Dissolved Copper
Total Copper
Table 4a Coefficient Values for Models with R2 > 0.250 for Total Copper and Dissolved
Copper
Trial
No. Predictand ln slope
1
ln Ce
(0.212)*
2
ln Ce
3
ln Ce
(0.302)*
4
ln Ce
(0.279)*
5
ln Ce
0.030
6
ln Ce
(0.223)*
7
ln Ce
(0.202)*
8
ln Ce
0.077
9
ln Ce
(0.290)*
10
ln Ce
(0.033)
11
ln Ce
12
ln Ce
1
ln Ci-Ce
0.219
2
ln Ci-Ce
3
ln Ci-Ce
0.392*
4
ln Ci-Ce
0.208
5
ln Ci-Ce
0.333
6
ln Ci-Ce
0.215
7
ln Ci-Ce
0.233
9
ln Ci-Ce
0.223
10
ln Ci-Ce
0.572*
12
ln Ci-Ce
0.359*
ln Ci-Ce
13
1
2
3
4
5
6
7
8
9
10
11
12
1
5
6
ln Ce
ln Ce
ln Ce
ln Ce
ln Ce
ln Ce
ln Ce
ln Ce
ln Ce
ln Ce
ln Ce
ln Ce
ln Ci-Ce
ln Ci-Ce
ln Ci-Ce
(0.320)*
(0.294)*
(0.420)*
(0.119)
(0.334)*
(0.299)*
(0.077)
(0.414)*
(0.078)
0.514*
0.550*
0.518*
ln
ln width vegetation ln % clay
(0.131)
(0.416)*
0.965*
(0.221)* (0.436)*
0.805*
(0.404)*
0.933*
(0.092)
1.079*
(0.083)
(0.469)*
(0.131)
(0.422)*
1.041*
(0.162)* (0.421)*
0.957*
(0.141)
(0.510)*
(0.154)
1.278*
(0.460)*
(0.429)*
0.569*
(0.599)*
0.258
(0.122)
0.671
0.370*
(0.102)
0.796*
(0.147)
0.766
0.267
0.694*
0.314
(0.159)
0.255
(0.113)
0.730*
0.232
(0.163)
0.653
0.200
0.832*
(0.197)
0.904*
0.373*
0.810*
ln rainfall
duration
(0.189)*
(0.194)*
(0.189)*
(0.199)*
(0.251)*
0.037
(0.123)*
(0.107)
(0.128)*
(0.107)
(0.127)*
(0.159)*
0.107
0.056
0.039
0.013
0.004
0.061
0.288
0.308
0.288
(0.543)*
(0.584)*
(0.548)*
(0.578)*
(0.549)*
(0.535)*
(0.580)*
0.731*
0.473*
0.735*
0.838*
0.775*
0.722*
(0.337)*
(0.250)*
(0.200)*
(0.287)*
(0.129)
(0.125)
(0.126)
(0.124)
(0.180)
(0.222)
(0.185)
(0.121)
ln
ln event Antecedent
rain
Dry Days R2 value
(0.264)*
0.324*
0.523
(0.260)*
0.346*
0.513
(0.275)*
0.316*
0.517
(0.270)*
0.379*
0.457
(0.260)*
0.369*
0.452
(0.367)*
0.302*
0.506
0.312*
0.489
0.282*
0.305
0.298*
0.334
(0.267)*
0.362*
0.450
(0.283)*
0.348*
0.488
(0.269)*
0.427*
0.523
(0.166)
0.421*
0.283
(0.178)
0.394*
0.278
(0.133)
0.447*
0.273
(0.186)
0.437*
0.282
(0.153)
0.442*
0.267
(0.249)*
0.408*
0.280
0.416*
0.278
0.398*
0.257
(0.109)
0.479*
0.251
0.425*
0.250
(0.194)
0.409*
0.276
(0.134)*
(0.108)
(0.129)*
(0.108)
(0.125)*
(0.198)*
(0.185)*
0.942*
(0.585)*
(0.577)*
(0.753)*
(0.360)*
(0.371)*
(0.361)*
* Predictors are significant
() Coefficient of the predictor is negative
0.346*
0.250
0.235
(0.160)*
(0.134)*
(0.212)*
0.022
(0.010)
(0.118)
(0.122)*
(0.330)*
(0.318)*
(0.317)*
0.296*
0.330*
0.297*
0.358*
0.333*
0.286*
0.292*
0.298*
0.325*
0.336*
0.335*
0.322*
0.423*
0.436*
0.427*
0.445
0.420
0.445
0.340
0.400
0.440
0.437
0.351
0.308
0.399
0.412
0.348
0.256
0.254
0.256
35
Table 4b Coefficient Values for Models with R2 > 0.250 for Total Zinc and Dissolved
Zinc
Dissolved Zinc
Total Zinc
Trial
No. Predictand ln slope
1
2
3
4
5
6
7
8
10
11
12
1
2
3
4
5
6
7
8
9
10
11
ln Ce
ln Ce
ln Ce
ln Ce
ln Ce
ln Ce
ln Ce
ln Ce
ln Ce
ln Ce
ln Ce
ln Ci-Ce
ln Ci-Ce
ln Ci-Ce
ln Ci-Ce
ln Ci-Ce
ln Ci-Ce
ln Ci-Ce
ln Ci-Ce
ln Ci-Ce
ln Ci-Ce
ln Ci-Ce
1
2
3
4
5
7
8
10
12
13
14
15
18
19
20
21
ln Ce
ln Ce
ln Ce
ln Ce
ln Ce
ln Ce
ln Ce
ln Ce
ln Ce
ln Ce
ln Ce
ln Ce
ln Ce
ln Ce
ln Ce
ln Ce
(0.208)
(0.266)*
(0.302)*
(0.028)
(0.224)*
(0.188)
0.018
(0.061)
(0.302)
(0.135)
(0.376)*
(0.048)
(0.324)
(0.274)
0.009
(0.369)*
0.205
0.015
0.042
(0.131)
(0.001)
0.027
0.132
0.143
0.157
(0.052)
(0.031)
(0.044)
0.105
(0.500)
(0.036)
(0.143)
(0.051)
ln
ln rainfall ln event
ln width vegetation ln % clay duration
rain
(0.085)
(0.171)*
(0.034)
(0.042)
(0.079)
(0.122)
(0.097)
0.251
0.124
0.279*
0.334*
0.263
0.202
0.265
0.198
(0.551)*
(0.571)*
(0.544)*
(0.592)*
(0.551)*
(0.553)*
(0.605)*
(0.587)*
(0.566)*
(0.863)*
(0.472)*
(0.497)*
(0.484)*
(0.536)*
(0.473)*
(0.477)*
(0.563)*
0.829*
0.746*
0.414*
1.195*
0.988*
1.283*
1.347*
1.284*
1.191*
(0.203)*
(0.211)*
(0.200)*
(0.202)*
(0.248)*
(0.246)*
(0.238)*
(0.256)*
(0.249)*
(0.242)*
(0.360)*
(0.346)*
(0.246)*
(0.212)*
(0.258)*
(0.267)*
(0.279)*
(0.275)*
(0.269)*
(0.330)*
(0.247)*
(0.260)*
(0.307)*
(0.291)*
(0.277)*
(0.258)*
(0.298)*
(0.288)*
(0.439)*
(0.433)*
1.556*
(0.559)*
(0.496)*
(0.100)
(0.120)
(0.020)
(0.090)
(0.121)
(0.070)
(0.093)
(0.085)
(0.083)
(0.096)
(0.097)
(0.054)
0.753*
0.602*
0.729*
0.920*
(0.487)*
(0.489)*
(0.605)*
(0.487)*
(0.477)*
(0.522)*
(0.519)*
(0.516)*
1.127*
0.502*
0.437*
0.643*
0.561*
0.556*
0.668*
0.606*
0.716*
(0.484)*
(0.483)*
(0.603)*
(0.471)*
0.475*
0.402*
0.636*
0.521*
ln
Antecedent
Dry Days R2 value
0.315*
0.336*
0.310*
0.375*
0.348*
0.292*
0.311*
0.280*
0.345*
0.337*
0.411*
0.520*
0.550*
0.537*
0.571*
0.577*
0.485*
0.521*
0.491*
0.489*
0.605*
0.550*
0.445
0.437
0.442
0.340
0.410
0.429
0.421
0.299
0.409
0.424
0.483
0.416
0.408
0.407
0.378
0.375
0.403
0.400
0.294
0.311
0.359
0.405
0.455
0.424
0.270
0.446
0.365
0.433
0.407
0.337
0.353
0.320
0.266
0.287
0.451
0.418
0.270
0.359
(0.348)*
(0.280)*
(0.243)
(0.259)*
(0.131)*
(0.262)*
(0.168)*
(0.232)*
0.316*
0.317*
(0.308)*
0.300*
0.273*
0.332*
0.331*
0.288*
0.365*
0.364*
0.322*
0.389*
0.307*
0.307*
(0.167)*
(0.282)*
(0.211)*
(0.131)
(0.250)*
(0.218)*
(0.279)*
(0.126)*
(0.262)*
(0.169)*
(0.240)*
0.264*
36
Table 4b Continued
Dissolved Zinc
Trial
No. Predictand ln slope
30
31
32
33
36
37
38
40
41
42
4
5
6
9
10
12
21
22
24
26
ln Ce
ln Ce
ln Ce
ln Ce
ln Ce
ln Ce
ln Ce
ln Ce
ln Ce
ln Ce
ln Ci-Ce
ln Ci-Ce
ln Ci-Ce
ln Ci-Ce
ln Ci-Ce
ln Ci-Ce
ln Ci-Ce
ln Ci-Ce
ln Ci-Ce
ln Ci-Ce
ln
ln rainfall ln event
ln width vegetation ln % clay duration
rain
(0.094)
(0.103)
(0.074)
(0.110)
(0.486)*
(0.485)*
(0.622)*
(0.474)*
(0.488)*
(0.486)*
(0.476)*
(0.508)*
0.513*
0.465*
0.556*
0.575*
0.419*
0.362*
0.465*
(0.131)* (0.232)*
(0.261)*
(0.167)*
(0.128)* (0.238)*
(0.263)*
0.572*
1.04*
1.02*
0.990*
1.14*
1.11*
1.10*
0.635*
0.637*
0.628*
0.717*
(0.687)*
(0.651)*
(0.619)*
(0.663)*
(0.629)*
(0.588)*
(0.630)*
(0.748)*
(0.783)*
(0.766)*
(0.774)*
(0.807)*
(0.794)*
(0.782)*
(0.804)*
(0.788)*
(0.807)*
0.457
0.412
0.501
0.319
0.270
0.351
(0.150)* (0.286)*
(0.198)
(0.111)
(0.241)
(0.225)
(0.257)*
(0.094)
(0.127)
(0.203)
(0.162)
ln
Antecedent
Dry Days R2 value
0.314*
0.313*
0.271*
0.311*
0.310*
0.267*
0.275*
0.323*
0.341*
0.493*
0.482*
0.439*
0.510*
0.496*
0.454*
0.426*
0.423*
0.389*
0.401*
0.455
0.424
0.265
0.365
0.450
0.418
0.359
0.329
0.258
0.470
0.325
0.317
0.302
0.319
0.313
0.296
0.276
0.272
0.261
0.258
* Predictors are significant
() Coefficient of the predictor is negative
The regression models presented in this table were then examined to determine
whether the coefficients make physical sense and whether the model is a good
representation of the data based on the corresponding leverage plots. Then, the
regression models were examined to make sure that all the assumptions presented in
Chapter 3 were valid. From this process, the best predictive equation was chosen.
One way to check whether a model is consistent with the physical and chemical
processes on the ground is to examine the signs of the predictor coefficients. To
determine which sign a predictor coefficient should have, it is important to think back to
37
the removal mechanisms and how they are affected by the predictors and how they affect
the predictands. When considering Ce, the slope coefficient should be positive whereas
the width, vegetative cover, percentage of clay content, and antecedent dry days
coefficients should be negative. As the slope increases, the effluent concentration should
increase because the runoff will be flowing faster over the biofilter strip, which will not
allow for much infiltration and will decrease contact time, which in turn limits filtration,
sedimentation, adsorption, ion exchange, and precipitation. Thus, the slope predictor
coefficient sign should be positive. As the width increases, the effluent concentration
should decrease because the wider biofilter strip will allow for more filter area and
contact time, which should provide more adsorption and ion exchange sites and more
vegetation contact area for particle removal. Therefore, the width predictor coefficient
sign should be negative. As vegetative cover increases, the effluent concentration should
decrease because the vegetation will slow down the flow of water allowing for more
contact time and provide more sites for adsorption. Therefore, the sign of the vegetative
coverage predictor coefficient should be negative. As the percentage of clay increases,
the effluent concentration should decrease because more adsorption and ion exchange
sites are available for the uptake of metals. Thus, the sign of the clay predictor
coefficient should be negative. When considering Ci-Ce, smaller Ce values lead to larger
Ci-Ce values, so all the expected predictors signs should be reversed from what is
expected for Ce.
For both effluent concentration and concentration reduction, it is difficult to
determine the expected sign for antecedent dry days, rainfall duration and total event
38
precipitation. As the antecedent dry days increase, the effluent concentration should
decrease because during the non-rain inter-event time, the ground dries out which
increases infiltration in the following storm allowing for more contact with the adsorptive
and ion exchange sites within the soil particles. On the other hand, between storms more
pollutants build up on the road, which might increase influent concentrations, which may
lead to higher effluent concentrations. Thus, the sign of the antecedent dry days predictor
coefficient is not obvious. Although rainfall duration is a good measure of how long it
rains and the total event precipitation is a good measure of rainfall volume, neither is a
good measure of the intensity of the rain event. If the total event precipitation is high due
to a large volume storm with short rainfall duration, water will flow faster and deeper
over the strip limiting the amount of water that comes in contact with soil and vegetation
for filtration and sedimentation. From this argument, the sign for the total event
precipitation predictor coefficient should be positive and the rainfall duration predictor
coefficient should be negative for effluent concentration. However, if the total event
precipitation is high due to long rainfall duration, runoff will have sufficient contact with
soil and vegetation and the total event precipitation and rainfall duration coefficients
should be positive for effluent concentration. Thus, without further knowledge of the
storm event, it is difficult to determine whether the predictor coefficients for rainfall
duration and total event precipitation should be positive or negative. Table 5 shows the
sign that is expected of the coefficient for each of the predictors.
39
Table 5 Criteria for Predictor Evaluation of Ce and Ci-Ce
Criteria for Equation Evaluation
Ce
Ci-Ce
Slope
+
-
Width
-
+
Veg. Cover
-
+
% Clay
-
+
Rainfall Duration
?
?
Total Event Rain
?
?
Antecedent Dry Days
?
?
The set of regression models was narrowed down by eliminating the trials which
had two or more coefficient signs that did not match the expected signs and which
included insignificant predictors. It was decided not to eliminate those trials that had
only one coefficient sign that did not match the expected signs because in only three trials
did all coefficient signs match the expected signs. By this process, 17 trials were
eliminated for total copper, 14 for dissolved copper, 16 for total zinc, and 34 for
dissolved zinc. The predictors were then evaluated for significance. The significance
level was evaluated using the P-value of each predictor and examination of the leverage
plot. The equations that contained a predictor with P-values greater than 0.05 were recast
with the elimination of the insignificant predictor(s). Different combinations were
generated for each metal. For example, in trial 5 for Ce of total copper, strip slope and
strip width were insignificant (see Appendix D) and strip slope was insignificant in trial
10. Upon eliminating strip slope and strip width, the MLR was run again and the result is
40
shown as trial 12. A second example is Ci-Ce of total copper. Trial 2 showed
insignificant strip vegetation, rainfall duration, and total event precipitation and trial 13
showed insignificant rainfall duration and total event precipitation. After eliminating
these insignificant predictors, the MLR was run again (Trial 14) with only predictors strip
width, clay content, and antecedent dry days as predictors. An R2 value of less than
0.250 was produced, so these results are not shown in Table 4a, although the P-values are
shown in Appendix D. Total copper had only one equation for Ci-Ce (trial 12) in which
all predictor coefficient signs matched the expected values and all predictors were
significant. For Ce of dissolved copper, only one equation (trial 12) has only significant
predictors. For Ci-Ce of dissolved copper, there were no equations with two or fewer
unexpected coefficient signs and all predictors being significant. For Ce of total zinc,
only in trial 12 were all predictors significant and all signs matched expectations. For CiCe of total zinc, trials 4 and 11 have all significant predictors, but trial 4 has 3 unexpected
signs while trial 11 has only two. For Ce of dissolved zinc, six trials had all significant
predictors, but only trial 42 had no unexpected coefficient signs. For Ci-Ce of dissolved
zinc, there were no equations with two or fewer unexpected coefficient signs and all
significant predictors.
In the end, only seven equations were produced in which all the predictors were
significant. These regression models were then checked for outliers, which are data
points that are distant from the remainder of the data and can skew the results of a
predictive equation. The outlier analysis was performed in JMP® by using the
Multivariate function. Mahalanobis distance, which is a distance measure based on
41
correlations between predictors by which different patterns can be identified and
analyzed, was used to find outliers. By using the Mahalanobis distance, outliers with a
distance greater than 3.25 were eliminated and the models were re-run. For Ci-Ce of total
copper, the R2 value for trial 12 dropped below 0.250 when outliers were removed so this
equation was eliminated. For Ci-Ce of total zinc, the rainfall duration in trial 11 was no
longer significant and slope, width, and rainfall duration in trial 4 were no longer
significant once the outliers were removed.
The remaining four regression models were evaluated to verify the MLR
assumptions described in Chapter 3. For the assumption of linearity, constant variance,
and homoscedasticity, the residual versus predicted plot was visually inspected. Figure 6
shows the residual versus predicted plot for total zinc trial 12 with the ln(Ce) predictand
and the vegetation coverage, rainfall duration, total event rain, and antecedent dry days
predictors. The evenly scattered data points about the line at zero and good dispersal of
the data points show that the linearity, constant variance, and homoscedasticity
assumptions have been met. All of the regression models checked in this way had
residual versus predicted plots with evenly scattered data points about the line at zero and
good dispersal of the data points, thus verifying the assumptions.
42
Figure 6 Total Zinc Residual by Predicted Plot (trial 12 for Ce)
The assumption of zero mean for residuals was not an issue because the least
squares method of estimating regression equations guarantees that the mean of the
residuals is zero.
The remaining four equations were then checked for collinearity. The Variance
Inflation Factor (VIF) must be less than five to say that there is no collinearity within the
predictors. In all the regression models, the VIF values were less than two.
Normality was tested using the Distribution function in JMP® in which the
residuals of ln(Ce) were evaluated using the Shapiro-Wilks test. Only the residuals of
ln(Ce) were used since the remaining equations are all for Ce. To show normal
distribution, the Shapiro-Wilks P-value must be greater than 0.05, which accepts the null
hypothesis that the data are from a normal distribution. All of the regression models
evaluated have P values greater than 0.05, so all exhibit normality. Figure 7 shows
normality test results for total zinc trial 12.
43
Goodness-of-Fit Test
Shapiro-Wilk W Test
W
Prob<W
0.988357
0.0736
Figure 7 Total Zinc Normality Test for ln(Ce) (trial 12)
The final four equations, all using the ln(Ce) predictand are trial 12 for total
copper, trial 12 for dissolved copper, trial 12 for total zinc, and trial 42 for dissolved zinc.
The predictive equations produced from these trials are shown below. In these equations
V is the strip vegetation coverage (%), RD is the rainfall duration (hours), EP is the total
event precipitation (mm), and DD is the antecedent dry days (days). Equation 8
(dissolved copper) varies from the others in that it does not contain total event
precipitation. This is discussed further in Section 4.3. Also shown below are plots of
predicted Ce vs. actual Ce plots, which show how well the predicted values match the
actual values. The JMP® reports for the chosen equations can be found in Appendix C.
44
Total Copper:
5.846(DD) 0.427
Ce 
(V) 0.599 (RD) 0.287 (EP) 0.269
(R2 = 0.523)
(7)
100
90
Actual Ce (μg/L)
80
70
60
50
MLR Results
40
30
Ce Predicted = Ce
Actual
20
10
0
0
50
100
150
Predicted Ce (μg/L)
Figure 8 Total Copper Predicted Ce vs. Actual Ce
200
45
Dissolved Copper:
5.075(DD) 0.322
Ce 
(V) 0.753 (RD) 0.212
(R2 = 0.348)
(8)
80
70
Actual Ce (μg/L)
60
50
40
MLR Series
30
20
Ce Predicted = Ce
Actual
10
0
0
50
100
150
200
250
Predicted Ce (μg/L)
Figure 9 Dissolved Copper Predicted Ce vs. Actual Ce
300
46
Total Zinc:
9.130(DD) 0.457
Ce 
(V) 1.062 (RD) 0.265 (EP) 0.363
(R2 = 0.483)
500
MLR Series
450
400
Actual Ce (μg/L)
(9)
Ce Predicted = Ce
Actual
350
300
250
200
150
100
50
0
0
200
400
600
800
1000
Predicted Ce (μg/L)
Figure 10 Total Zinc Predicted Ce vs. Actual Ce
1200
47
Dissolved Zinc:
6.277(DD) 0.341
Ce 
(V) 0.630 (RD) 0.150 (EP) 0.286
(R2 = 0.470)
(10)
200
180
Actual Ce (μg/L)
160
140
120
100
80
MLR Series
60
40
Ce Predicted = Ce
Actual
20
0
0
50
100
150
200
Predicted Ce (μg/L)
Figure 11 Dissolved Zinc Predicted Ce vs. Actual Ce
In all of the chosen equations, the predictor exponent signs match the signs
expected from the physical mechanisms (Table 5).
4.2
Multiple Linear Regression for First Order Decay
Multiple linear regression (MLR) was performed using the natural logarithm of
the first order decay coefficient (ln(k)) as the predictand. The predictors investigated
include strip slope, vegetation coverage, clay content, rainfall duration, total event
precipitation, and antecedent dry days. The strip width was not used in the MLR since it
was used in the calculation of the k value. Table 6 presents the estimate coefficients of
the regression model trials for total copper, dissolved copper, total zinc, and dissolved
48
zinc. The highest coefficient of determination (R2) value obtained was 0.227 with most
of the values being less than 0.150. The R2 value of 0.227 means that only 22.7% of the
variation in ln(k) can be attributed to the linear model.
Total Zinc
Dissolved Copper
Total Copper
Table 6 Coefficient Values for Total Copper, Dissolved Copper, Total Zinc, and
Dissolved Zinc
Trial
ln
ln rainfall
No. Predictand ln slope vegetation ln % clay duration
1
ln k
0.165
0.609* (0.934)* 0.031
2
ln k
0.622* (0.736)* 0.037
3
ln k
0.223
(1.117)* 0.046
4
ln k
(0.105)
0.665*
0.092
5
ln k
0.166
0.610* (0.947)*
6
ln k
0.158
0.608* (0.942)* (0.053)
7
ln k
(0.115)
0.665*
8
ln k
0.213
(1.105)*
9
ln k
0.618* (0.733)*
1
ln k
0.281*
0.278* (0.769)* 0.268*
2
ln k
0.307* (0.401)* 0.293*
3
ln k
0.308*
(0.829)* 0.280*
4
ln k
0.058
0.317*
0.323*
5
ln k
0.311*
0.293* (0.879)*
6
ln k
0.295*
0.314* (0.803)* 0.016
7
ln k
0.060
0.358*
8
ln k
0.329*
(0.884)*
9
ln k
0.345* (0.432)*
1
ln k
(0.103)
0.894*
(0.252) 0.279*
2
ln k
0.885*
(0.373) 0.275*
3
ln k
(0.004)
(0.548) 0.285*
4
ln k
(0.174)
0.909*
0.295*
5
ln k
(0.087)
0.896*
(0.358)
6
ln k
(0.113)
0.896*
(0.289) (0.015)
7
ln k
(0.195)
0.914*
8
ln k
(0.015)
(0.580)
9
ln k
0.905*
0.304*
ln event
rain
(0.147)
(0.143)
(0.143)
(0.155)
(0.130)
(0.424)*
(0.431)*
(0.441)*
(0.435)*
(0.264)*
(0.503)*
(0.504)*
(0.507)*
(0.506)*
(0.350)*
(0.513)*
ln
Antecedent
Dry Days R2 value
0.153*
0.156
0.135*
0.151
0.068
0.07
0.106
0.116
0.156*
0.155
0.145*
0.149
0.098
0.108
0.052
0.063
0.119
0.144
0.040
0.133
0.005
0.113
0.006
0.114
0.000
0.100
0.064
0.110
0.025
0.750
(0.008)
0.037
(0.012)
0.051
(0.007)
0.053
0.170*
0.227
0.180*
0.226
0.062
0.076
0.157*
0.225
0.203*
0.211
0.156*
0.172
0.142*
0.169
0.045
0.02
0.168*
0.218
49
Dissolved Zinc
Table 6 (continued)
Trial
ln
ln rainfall ln event
No. Predictand ln slope vegetation ln % clay duration
rain
1
ln k
0.009
(0.144)
0.157
0.182
0.117
2
ln k
(0.144)
0.169
0.183
0.116
3
ln k
(0.004)
0.191
0.171
0.135*
4
ln k
0.054
(0.152)
0.169
0.127*
5
ln k
0.040
(0.126)
0.071
0.141*
6
ln k
0.026
(0.094)
0.120
(0.017)
0.121
7
ln k
0.059
(0.102)
0.125*
8
ln k
0.013
0.155
0.129*
ln
Antecedent
Dry Days R2 value
(0.335)*
0.061
(0.335)*
0.061
(0.318)*
0.055
(0.332)*
0.059
(0.230)*
0.050
0.023
0.022
0.021
Even though the R2 values are low, the regression models were evaluated for the
validity of the assumptions. For the assumptions of linearity, constant variance, and
homoscedasticity, the residual versus predicted plots were visually inspected. These
plots do not show a good dispersal of the data as seen in Figures 4 and 5, meaning the
linearity, constant variance, and homoscedasticity assumptions cannot be verified as valid
for this model. Figure 12 shows the residual versus predicted plot for total zinc with the
ln(k) predictand and strip slope, vegetation coverage, clay content, rainfall duration, total
event precipitation, and antecedent dry days predictors. The assumption of zero mean is
not a problem because the least squares method of estimating regression equations
guarantees that the mean of the residuals is zero. As before, the Variance Inflation Factor
(VIF) must be less than five to say that there is no collinearity amongst the predictors and
in all the ln(k) regression models, the VIF values were less than two. Normality was
checked using the same process as previously mentioned. All of the regression models
for ln(k), have Shapiro-Wilks P-values less than 0.05 with least being less than 0.001.
50
Thus, normality cannot be validated for these regression models. Figure 13 shows the
normality test results for total zinc.
Figure 12 Total Zinc Residual by Predicted Plot (trial 8)
Goodness-of-Fit Test
Shapiro-Wilk W Test
W
0.871170
Prob<W
<.0001*
Figure 13 Total Zinc Normality Test for ln(k) (trial 8)
With the low R2 values and all assumptions being rejected except for zero mean
and collinearity, it was determined that even though equation (3) may be a valid
representation of first order decay for a vegetated biofilter strip, multiple linear regression
is not a useful tool for predicting the first order decay coefficient, k.
51
4.3
Discussion
There are several conceptual difficulties with the chosen predictive equations.
Although equations (7) thru (10) were found to be the best fit regression models based on
R2 values, expected sign of the predictor coefficients, and validity of the assumptions, the
highest R2 value was only 0.55 which is the proportion of variability in the data set that is
accounted for by the model. One factor that could affect the goodness-of-fit is variability
in the raw data collected at the RVTS sites. These are field measurements made under
storm conditions at different locations over several years. In a multiple linear regression
analysis of Caltrans highway runoff data from edge of pavement, Kayhanian et al. (2003)
concluded that regression models are generally limited to the region or site from which
the original data used to develop the model were collected and tend to be unreliable when
applied to conditions beyond the range of the original data set. Since the MLR in this
study combined study sites from different regions of California, regional variabilities may
be a factor affecting the R2 values.
Another problem with the predictive equations is their apparent conflict with
physical process. Although formulated and mathematically correct based on MLR
assumptions, when predictive values of effluent concentration calculated from equations
(7) thru (10) are graphed (Figure 14) against vegetative cover of the strip, dissolved
copper and dissolved zinc show higher effluent concentrations than total copper and total
zinc. One possible cause could be the exclusion of influent concentration from this study,
which may change the MLR results enough to give higher dissolved metals than total
metals. The dissolved metals would be expected to be more sensitive to influent quality
52
because the strips provide less treatment for them. Because the total values include the
dissolved values, these results cannot be accurate.
1
Total Copper
0.9
Dissolved Copper
Predicted Ce (μg/L)
0.8
0.7
Total Zinc
0.6
Dissolved Zinc
0.5
0.4
0.3
0.2
0.1
0
0
20
40
60
80
100
Vegetation Cover (%)
Figure 14 Predicted Ce vs. Vegetation Cover (assumed values were antecedent dry days
at 1 day, rainfall duration at 1 hour, and total event precipitation at 24 mm)
Additionally, antecedent dry days were found to have a positive coefficient; the
strip slope, strip width, and clay content predictors are not included in any of the
equations; and the total event precipitation predictor is not included in the equation for
dissolved copper. The positive antecedent dry days coefficient means as antecedent dry
days goes up, the effluent concentration also goes up. Antecedent dry days were usually
a significant predictor in the equations with P-values of <0.0001, which is highly
indicative of a coefficient that is not zero. In most cases when the antecedent dry days
predictor was removed from the regression model, a lower R2 value was obtained and
other predictors that were significant became non-significant. Thus, even though the
result seems counter-intuitive, it seemed fitting to include antecedent dry days in the
53
predictive equation. Kayhanian et al. (2003) found that longer antecedent dry periods
tend to result in higher pollutant concentrations in storm runoff, which is consistent with
the “buildup” of pollutants during dry periods. This could be the cause of the positive
coefficient seen in equations (7) thru (10).
Strip slope and strip width were not included in the predictive equations because
they surprisingly did not often prove to be significant predictors. In those regression
models, where they were significant predictors, their coefficients had the opposite sign
from what was expected. The effluent concentration was expected to have a positive
strip slope coefficient because as the slope gets steeper, the runoff moves more quickly
over the strip minimizing the contact time and treatment. It does not make physical sense
for the effluent concentration to go down as slopes get steeper. Conversely, the effluent
concentration was expected to have a negative strip width coefficient because as the strip
gets wider, the runoff contact time increases. Thus, it would not make physical sense that
the strip width coefficient would be positive. The strips may be acting oddly with respect
to strip slope and width due to the water films being shallow and moving so fast because
of steep slopes that only minimal treatment is occurring. Thus, the effects of slope and
width are not apparent. In Chapter 2 various references were cited suggesting that
biofilter slopes should be between 2% and 15% and that the minimum width should be 24
feet. In the Caltrans RVTS study, three sites have slopes of 33%, 50%, and 52% and 14
of the 23 strips have widths less than 24 feet. In a future study, the regression models
should be based only on strip slopes and widths that are within the recommended ranges.
54
The clay content was a significant predictor in most of the regression models, but
it always had the opposite sign from what was expected. Possibly, if the clay content is
too great, the runoff will not be able to infiltrate well and the water film on the surface
will be thicker, providing less contact with vegetation and soil and less treatment. This is
speculation. Nevertheless, when clay content was eliminated from the predictive
equation, the R2 of the revised model did not change substantially. For this reason, it was
decided to exclude this predictor from the predictive equation.
The total event precipitation was not a significant predictor in the equation for
dissolved copper. When it was excluded from the regression model for dissolved copper,
the R2 value did not decrease by much and the P-value of predictors that were significant,
got closer to 0.05 meaning predictors became less significant. Dissolved copper
consistently had the most data variability and the fewest number of regression models
with R2 values greater than 0.250. If data variability is higher in dissolved copper than
the other metals, this could cause one or more predictors such as total event precipitation
to drop out of the dissolved copper predictive equation even though it remained a
significant predictor in the predictive equations for the other metals.
One factor that might be an important influence on equation performance is
influent concentration. There is an intuitive sense that effluent concentration may be
directly related to influent concentration. When Caltrans performed the preliminary
MLR study, influent concentration was included as a predictor and was consistently
found to be a significant one (Caltrans, 2008). Although influent concentration was not
included as a predictor in this project, it was included as a predictand in Ci-Ce and Ce/Ci.
55
The regression models for Ce/Ci produced R2 values that were all less than 0.250
thus they were not further evaluated. For the models of Ci-Ce, very few produced
predictor coefficients with the expected signs. When the regression models that did
follow the sign convention were analyzed and outliers were eliminated, two or more of
the predictors were no longer significant. One possibility for the relatively poor fit from
Ce/Ci and Ci-Ce models is that they rely on two accurately measured concentrations. As
noted earlier, there is much variation in the original data. Because Ce models rely on only
one concentration measurement, there may be less error in the predictand values.
With regards to the first order model, although Kadlec (1999) was able to define a
first-order decay equation for the performance of pollutants in wetlands, multiple linear
regression did not prove to be an effective tool in predicting the first order decay
coefficient for metal removal in vegetative biofilter strips. The first-order decay model
assumes plug flow conditions on the vegetated slopes. In reality there is significant
potential for channelized flow caused by motor vehicle tracks from maintenance
equipment or vehicles leaving the pavement. Burrowing wildlife can also disrupt plug
flow conditions on the slopes (Caltrans, 2004). The assumption in this MLR study was
that all the data fit a first-order model, was not always the case as seen in total copper
where 53% of R2 values for the first-order decay value were below 0.85. In further
studies, only those cases where the R2 for the first-order fit is greater than a specified
value should be used in MLR studies. This may cause the MLR fit to be considerably
better.
56
Chapter 5
CONCLUSION
Based on the Caltrans RVTS study data, MLR was used to formulate equations
that might be used in vegetated biofilter strip designs to predict copper and zinc removal
rates or effluent concentrations using design parameters such as strip slope, strip width,
vegetation cover, percentage of clay content in the soil, rainfall duration, total event
precipitation, and antecedent dry days. Predictive equations were formulated for effluent
concentration (Ce) for total and dissolved copper and total and dissolved zinc. Although
these equations are mathematically correct because they meet the MLR assumptions, the
R2 values are relatively low, meaning they are explaining only a part of the observed
variation in the data. In addition, these equations predict that the dissolved metals
concentrations will be greater than total metals concentrations, which is physically
impossible. Consequently, these equations are unreliable predictors of effluent
concentration.
MLR was also used to predict first-order decay coefficients derived from the same
data set. The predictand was Ce/Ci and the same predictors, except slope width, were
used. None of the MLR equations produced R2 values above 0.23, and the MLR
assumptions were violated. These equations are also unreliable.
Further research should be conducted to determine if including influent
concentrations as a predictor in the MLR would improve the resulting equations.
57
APPENDIX A
RVTS Storm Data
This appendix contains the RVTS storm data that were obtained from the Caltrans
database and used in the calculations found in Appendix B. The storm data includes the
following:

Station Name

Station ID

Collection Date

Fraction (Total or Dissolved)

Constituent (Copper or Zinc)

Reported Value (concentration)

Precipitation Start Date

Precipitation Start Time

Precipitation End Date

Precipitation End Time

Event Rain (mm)

Antecedent Dry Days
Due to the quantity of storm data, this information can be found on the attached
CD.
58
APPENDIX B
RVTS Input Data for MLR
This appendix contains the calculations used to prepare the inputs used in the
multiple linear regression. These include the predictands and predictors and their natural
logarithm values. The following predictands were calculated in Excel and are included in
this appendix:

Ce is equal to the reported value of concentration.

Ci-Ce is calculated by using the edge of pavement reported value of
concentration as Ci subtracting the reported value of concentration for the
strip of interest.

Ce/Ci is the reported value of concentration for the strip of interest divided
by the edge of pavement reported value as Ci.

First order decay coefficient, k, is the slope of the line with ln(Ce) on the
y-axis and strip width on the x-axis. This value was calculated by using
the slope function in Excel.
Due to the quantity of storm data, this information can be found on the attached
CD.
59
APPENDIX C
Multiple Linear Regression Reports from JMP®
The JMP® reports in the printer part of this appendix coincide with equations (7), (8), (9)
and (10), respectively. The remainder of the JMP® reports coinciding with the MLR
trials summarized in Appendix D, can be found on the attached CD. To provide a better
understanding of the various data and plots shown on the JMP® reports, an explanation
of the different components is presented below.
Summary of Fit Table

“R Square” (R2) is the coefficient of determination, which is the proportion of
variance accounted for, explained, or described by the regression model. If the
regression is perfect, the R2 value is one. If the regression is a failure and the sum
of squares of errors equals the total sum of squares, no variance is accounted for
by regression and R2 is zero.

“R Square Adj” is the adjusted R2 value, which measures the proportion of the
variation in the predictand accounted for by the predictors. Adjusted R2 allows
for the degrees of freedom associated with the sums of squares.

“Root Mean Square Error” is the square of the differences between values
predicted by a model and the observed values being modeled.

“Mean of Response” is the values of the predictand calculated from the regression
parameters and a given value of the predictor. This is an estimate of the mean of
60
the predictand associated with an explanatory value of the predictor. The mean of
response is used in the plots as a horizontal reference point.

“Observations” are the number of data points used in the regression model.
Analysis of Variance Table

“Source” has three rows, one for total variability and one for each of the two
pieces comprising the total, Model or Regression, and Error or Residual. The “C”
in “C Total” stands for corrected.

“DF” is the degrees of freedom. For the Model, the number of degrees of
freedom is the number of predictors used for the regression. For the Error, the
degrees of freedom is the number of observations minus the number of predictors
minus 1. The degrees of freedom for C Total is the sum of the degrees of freedom
for the Model and the Error.

“Sum of Squares” is a way to find the function which best fits (least varies) from
the data. It is the total variability in the response which is calculated from ∑(yy̅ )2 , where y̅ is the sample mean. The “Corrected” in “C Total” refers to
subtracting the sample mean before squaring. The amount of variation in the data
that cannot be accounted for by this simple method of prediction is given by the
total sum of squares. When the regression model is used for prediction, the
2
uncertainty that remains is the variability about the regression line, ∑ (y-ŷ ) ,
where ŷ is the predicted value of the predictand. This is the Error sum of squares.
61
The difference between the Total sum of squares and the Error sum of squares is
2
the Model sum of squares, which is equal to ∑ (ŷ -y̅ ) .

“Mean Squares” are the sum of squares divided by the corresponding degrees of
freedom.

“F Ratio” is the test statistic used to decide whether a model as a whole has a
statistically significant predictive capability, that is, whether the regression sum of
squares is big enough, considering the number of variables needed to achieve it.
F is the ratio of the Model mean square to the Error mean square.

“Prob>F” is the probability that the null hypothesis for the full model is true. The
null hypothesis is that all of the regression coefficients are zero. The lower the
value of Prob>F, the more likely the null hypothesis will be rejected which means
that some of the regression coefficients are not zero and that the regression
equation does have validity in fitting the data (i.e. the predictors are not purely
random with respect to the predictand).
Parameter Estimates Table

‘Term” is the predictor.

“Estimate’ is the regression coefficients in the regression equation.

“Standard Error” is an estimate of the standard deviation of the regression
coefficients.
62

“t ratio” tests the hypothesis that a population regression coefficient is 0 when the
other predictors are in the model. It is the ratio of the sample regression
coefficient to its standard error.

‘Prob>|t|” or “P”-value labels the observed significance levels for the t statistics.
The P value indicates whether a predictor has statistically significant predictive
capability in the presence of the other predictors. If the p value is less than the
confidence level, in this case 0.05, then the null hypothesis that the predictors
have values of 0, is rejected. The asterisk (*) next to this value indicates a
significant value.

“VIF” is the Variance Inflation Factor. This statistical measure is used to identify
collinearity amongst the predictor variables. If the VIF is greater than five, one or
more predictors are said to be collinear.
Plots

“Whole Model Actual by Predicted Plot” shows the observed values of y versus
its predicted values for the hypothesis that all the predictors for the model are 0.
The plot portrays the observation-by-observation composition of the regression
sum of squares. This plot can be used to detect linearity, constant variance, or
homoscedasticity within the regression model as shown in Chapter 3.

“Residual by Predicted Plot” shows the actual residual values of y versus its
predicted values in reference to 0. This plot is used to detect linearity, constant
variance, or homoscedasticity within the regression model as shown in Chapter 3.
63

“Leverage Plot” shows a point-by-point composition of the sum of squares for a
hypothesis test. The leverage plot is useful for identifying likely candidate points
that might be influential to the hypothesis. This plot shows the confidence limits
for the expected value as a function of the predictor. The hyperbola has
properties, which make it a useful significance-measuring instrument. If the slope
predictor is significantly different from 0, the confidence curve will cross the
horizontal line of the response mean. If the slope predictor is not significantly
different from 0, the confidence curve will not cross the horizontal line of the
response mean. If the t test for the slope predictor is sitting right on the margin of
significance, the confidence curve will have the horizontal line of the response
mean as an asymptote.
64
JMP® report coinciding with equation (7) for total copper:
Response ln Ce
Whole Model
Actual by Predicted Plot
Summary of Fit
RSquare
RSquare Adj
Root Mean Square Error
Mean of Response
Observations (or Sum Wgts)
0.523064
0.51398
0.608854
2.592512
215
Analysis of Variance
Source
Model
Error
C. Total
DF
4
210
214
Sum of Squares
85.37685
77.84759
163.22444
Mean Square
21.3442
0.3707
F Ratio
57.5777
Prob > F
<.0001*
Parameter Estimates
Term
Intercept
ln Vegetation
ln Rainfall Duration
ln Event Rain
ln Antecedant Dry Days
Estimate
5.8459517
-0.598525
-0.286517
-0.268827
0.4265024
Std Error
0.47692
0.099502
0.067715
0.067373
0.041584
t Ratio
12.26
-6.02
-4.23
-3.99
10.26
Prob>|t|
<.0001*
<.0001*
<.0001*
<.0001*
<.0001*
VIF
.
1.0938455
1.7214278
1.6478328
1.2043856
65
Residual by Predicted Plot
ln Vegetation
Leverage Plot
ln Rainfall Duration
Leverage Plot
66
ln Event Rain
Leverage Plot
ln Antecedant Dry Days
Leverage Plot
67
JMP® report coinciding with equation (8) for dissolved copper:
Response ln Ce
Whole Model
Actual by Predicted Plot
Summary of Fit
RSquare
RSquare Adj
Root Mean Square Error
Mean of Response
Observations (or Sum Wgts)
0.348001
0.341831
0.682306
1.912928
321
Analysis of Variance
Source
Model
Error
C. Total
DF
3
317
320
Sum of Squares
78.76837
147.57668
226.34505
Mean Square
26.2561
0.4655
F Ratio
56.3991
Prob > F
<.0001*
Parameter Estimates
Term
Intercept
ln vegetation
ln rainfall duration
ln antecedent dry days
Estimate
5.0749741
-0.752602
-0.212181
0.3223368
Std Error
0.462135
0.099201
0.049144
0.040169
t Ratio
10.98
-7.59
-4.32
8.02
Prob>|t|
<.0001*
<.0001*
<.0001*
<.0001*
VIF
.
1.0598281
1.0316266
1.090435
68
Residual by Predicted Plot
ln vegetation
Leverage Plot
ln rainfall duration
Leverage Plot
69
ln antecedent dry days
Leverage Plot
70
JMP® report coinciding with equation (9) for total zinc:
Response ln Ce
Whole Model
Actual by Predicted Plot
Summary of Fit
RSquare
RSquare Adj
Root Mean Square Error
Mean of Response
Observations (or Sum Wgts)
0.483113
0.473883
0.715722
3.705415
229
Analysis of Variance
Source
Model
Error
C. Total
DF
4
224
228
Sum of Squares
107.24801
114.74567
221.99369
Mean Square
26.8120
0.5123
F Ratio
52.3409
Prob > F
<.0001*
Parameter Estimates
Term
Intercept
ln Vegetation
ln Rainfall Duration
ln Event Rain
ln Antecedent Dry Days
Estimate
8.167073
-0.863429
-0.257729
-0.307068
0.4108706
Std Error
0.534948
0.110869
0.080265
0.077382
0.046002
t Ratio
15.27
-7.79
-3.21
-3.97
8.93
Prob>|t|
<.0001*
<.0001*
0.0015*
<.0001*
<.0001*
VIF
.
1.0530361
1.6785512
1.608196
1.1338568
71
Residual by Predicted Plot
ln Vegetation
Leverage Plot
ln Rainfall Duration
Leverage Plot
72
ln Event Rain
Leverage Plot
ln Antecedent Dry Days
Leverage Plot
73
JMP® report coinciding with equation (10) for dissolved zinc:
Response ln Ce
Whole Model
Actual by Predicted Plot
Summary of Fit
RSquare
RSquare Adj
Root Mean Square Error
Mean of Response
Observations (or Sum Wgts)
0.470214
0.461119
0.606438
3.008192
238
Analysis of Variance
Source
Model
Error
C. Total
DF
4
233
237
Sum of Squares
76.05412
85.68959
161.74371
Mean Square
19.0135
0.3678
F Ratio
51.7000
Prob > F
<.0001*
Parameter Estimates
Term
Intercept
ln Strip Vegetation
ln rainfall duration
ln total event precipitation
ln antecedent dry days
Estimate
6.2769443
-0.630037
-0.150002
-0.285506
0.3406691
Std Error
0.445724
0.09109
0.063755
0.064922
0.037233
t Ratio
14.08
-6.92
-2.35
-4.40
9.15
Prob>|t|
<.0001*
<.0001*
0.0195*
<.0001*
<.0001*
VIF
.
1.0957188
1.6422912
1.5883739
1.1712607
74
Residual by Predicted Plot
ln Strip Vegetation
Leverage Plot
ln rainfall duration
Leverage Plot
75
ln total event precipitation
Leverage Plot
ln antecedent dry days
Leverage Plot
76
APPENDIX D
MLR Trials
This appendix contains the results obtained from the multiple linear regression
models. The tables presented below contain the predictand in the left column with the
predictors listed across the top of the table. For each predictor that was used in a
particular MLR model, the box contains the probability that is calculated from each tratio. This value comes from the JMP® reports in Appendix C and is listed in the
Parameter Estimates table as Prob>t. If this value is significant as defined in Appendix
C, it has an asterisk (*) next to it. In the far right column is the associated coefficient of
determination (R2) value, which is the proportion of variability in a data set that is
accounted for by the statistical model.
77
D-1
TOTAL COPPER
Trial
No. Predictand ln slope ln width
0.0842
0.0282*
ln Ce
1
0.0007*
ln Ce
2
0.0003*
ln Ce
3
0.2524
0.0065*
ln Ce
4
0.3008
0.743
ln Ce
5
0.0885
0.0234*
ln Ce
6
0.0426* 0.0385*
ln Ce
7
0.117
0.4595
ln Ce
8
0.0804
0.0101*
ln Ce
9
0.6413
ln Ce
10
ln Ce
11
ln Ce
12
0.1265
0.2552
ln Ci-Ce
1
0.0072*
ln Ci-Ce
2
ln Ci-Ce 0.0129*
3
0.1119
0.2776
ln Ci-Ce
4
0.0608
0.0717
ln Ci-Ce
5
0.1296
0.2648
ln Ci-Ce
6
0.1641
0.2258
ln Ci-Ce
7
0.1284
ln Ci-Ce 0.0420*
8
0.231
0.248
ln Ci-Ce
9
ln Ci-Ce <0.0001*
10
ln Ci-Ce
11
ln Ci-Ce 0.0228*
12
0.0066*
ln Ci-Ce
13
0.0128*
ln Ci-Ce
14
0.4005
0.0032*
ln C/Ci
1
0.0046*
ln C/Ci
2
ln C/Ci <0.0001*
3
0.576
0.0011*
ln C/Ci
4
0.3712
0.0005*
ln C/Ci
5
0.4
0.0033*
ln C/Ci
6
0.4291
0.0030*
ln C/Ci
7
0.4263
0.0004*
ln C/Ci
8
0.6419
0.0011*
ln C/Ci
9
ln C/Ci <0.0001*
10
ln C/Ci
11
ln C/Ci <0.0001*
12
0.2382
ln k
1
ln k
2
0.1252
ln k
3
0.3595
ln k
4
0.2319
ln k
5
0.257
ln k
6
0.3174
ln k
7
0.1419
ln k
8
ln k
9
ln vegetation
<0.0001*
<0.0001*
<0.0001*
<0.0001*
<0.0001*
<0.0001*
<0.0001*
<0.0001*
<0.0001*
<0.0001*
0.5217
0.591
0.4418
0.4038
0.553
0.3832
0.1985
0.3034
0.5309
0.0031*
0.0010*
0.0037*
0.0033*
0.0031*
0.0031*
0.0040*
.0042*
0.0016*
0.0049*
<0.0001*
<0.0001*
<0.0001*
<0.0001*
<0.0001*
<0.0001*
<0.0001*
ln event ln Antecedent
R2 value
Dry Days
rain
0.523
<0.0001*
<0.0001*
0.513
<0.0001*
0.0001*
0.517
<0.0001*
<0.0001*
0.457
<0.0001*
0.0001*
0.452
<0.0001*
0.0002*
0.506
<0.0001*
<0.0001*
0.489
<0.0001*
0.305
<0.0001*
0.334
<0.0001*
<0.0001*
0.45
<0.0001*
0.0004* 0.0002*
0.488
<0.0001*
<0.0001* 0.0036* <0.0001*
0.523
<0.0001*
<0.0001* <0.0001*
0.283
<0.0001*
0.2811
0.3695
0.0587
0.278
<0.0001*
0.2483
0.3861
0.0186*
0.273
<0.0001*
0.3846
0.3838
0.0291*
0.282
<0.0001*
0.2182
0.3867
0.0488*
0.267
<0.0001*
0.3251
0.2062
0.28
<0.0001*
0.0428*
0.0363*
0.278
<0.0001*
0.053
0.0653
0.238
<0.0001*
0.257
<0.0001*
0.0171*
0.251
<0.0001*
0.4813
0.1973
0.245
<0.0001*
0.4193
<0.0001* 0.4534
0.25
<0.0001*
0.0088*
0.276
<0.0001*
0.1987
0.3999
0.0161*
0.243
<0.0001*
0.0162*
0.168
0.0004*
0.5819
0.6521
0.6677
0.136
0.0043*
0.5379
0.7385
0.0606
0.166
0.0003*
0.6391
0.6525
0.6001
0.135
0.0043*
0.6221
0.7154
0.9505
0.168
0.0002*
0.5844
0.5974
0.168
0.0004*
0.3346
0.6102
0.167
0.0005*
0.362
0.6715
0.163
0.0004*
0.132
0.0062*
0.8323
0.165
0.0001*
0.6467
0.5867
0.105
0.0054*
0.7498
0.7969
0.0005*
0.161
0.0002*
0.156
0.0274*
0.1891
0.7855
0.0012*
0.151
0.0454*
0.2031
0.7447
0.0016*
0.07
0.3328
0.2223
0.7018
0.0002*
0.116
0.1244
0.1749
0.4242
0.155
0.0211*
0.1606
0.0008*
0.149
0.0361*
0.5773
0.0011*
0.108
0.1392
0.063
0.4289
0.0002*
0.144
0.0649
0.0014*
ln rainfall
ln % clay duration
<0.0001* 0.0046*
<0.0001* 0.0038*
<0.0001* 0.0048*
<0.0001* 0.0051*
0.0004*
<0.0001*
<0.0001* <0.0001*
78
D-2
DISSOLVED COPPER
Trial
No. Predictand ln slope
1
2
3
4
5
6
7
8
9
10
11
12
1
2
3
4
5
6
7
8
9
10
11
12
13
1
2
3
4
5
6
7
8
9
10
11
12
1
2
3
4
5
6
7
8
9
ln Ce
ln Ce
ln Ce
ln Ce
ln Ce
ln Ce
ln Ce
ln Ce
ln Ce
ln Ce
ln Ce
ln Ce
ln Ci-Ce
ln Ci-Ce
ln Ci-Ce
ln Ci-Ce
ln Ci-Ce
ln Ci-Ce
ln Ci-Ce
ln Ci-Ce
ln Ci-Ce
ln Ci-Ce
ln Ci-Ce
ln Ci-Ce
ln Ci-Ce
ln Ce/Ci
ln Ce/Ci
ln Ce/Ci
ln Ce/Ci
ln Ce/Ci
ln Ce/Ci
ln Ce/Ci
ln Ce/Ci
ln Ce/Ci
ln Ce/Ci
ln Ce/Ci
ln Ce/Ci
ln k
ln k
ln k
ln k
ln k
ln k
ln k
ln k
ln k
0.0001*
<0.0001*
<0.0001*
0.1165
<0.0001*
0.0003*
0.3223
<0.0001*
0.1506
0.0024*
<0.0001*
0.0081*
0.0008*
0.0020*
0.0004*
0.0001*
0.0019*
<0.0001*
ln width ln vegetation ln % clay
0.5927
0.0317*
0.1535
0.4355
0.5739
0.8502
0.9587
0.4185
0.0743
<0.0001*
0.0411*
0.0521
0.0726
0.1654
0.1954
0.1628
<0.0001*
<0.0001*
<0.0001*
<0.0001*
<0.0001*
<0.0001*
<0.0001*
0.0158*
0.0190*
0.0167*
0.0144*
<0.0001*
<0.0001*
<0.0001*
<0.0001*
<0.0001*
<0.0001*
<0.0001*
<0.0001*
0.2164
0.3137
0.2205
0.2852
0.4269
0.3373
<0.0001*
0.0066*
0.0030*
0.4821
0.0028*
0.0057*
0.4772
0.0021*
0.0686
0.0318*
0.067
0.0473*
0.0081*
0.0247
0.0736
0.0283*
0.0933
0.0420*
<0.0001*
0.0001*
0.0023*
0.4517
0.1017
0.2855
0.3356
0.4581
0.6428
0.0075*
0.0429*
<0.0001*
0.8764
0.5649
0.8282
0.8097
0.9403
0.0526
0.0249*
0.0144*
0.0023*
0.0294*
0.0122*
0.0173*
0.0034*
0.1068
0.2423
<0.0001*
<0.0001*
0.2239
<0.0001*
<0.0001*
<0.0001*
ln event
rain
<0.0001*
<0.0001*
<0.0001*
<0.0001*
0.0197*
0.0723
0.0112*
0.0075*
0.0692
<0.0001*
<0.0001*
0.0002*
<0.0001*
<0.0001*
ln rainfall
duration
0.9485
0.3546
0.8252
0.7768
0.933
0.9931
0.7436
0.0005*
0.1568
0.0869
0.0003*
0.6287
0.0004*
0.0003*
0.0003*
0.0003*
0.9134
0.2684
0.0410*
0.0069*
0.5508
0.6505
0.863
0.6368
0.6478
0.8588
0.0024*
0.2972
0.089
0.387
0.2974
0.2632
0.1031
0.1831
0.0005*
0.8801
0.5383
0.8282
0.0084*
0.0039*
0.0030*
0.0060*
0.0039*
0.0011*
0.0016*
0.0110*
0.0005*
0.0215*
0.0002*
<0.0001*
0.0004*
<0.0001*
0.0149*
0.8791
0.652
0.33
0.3237
0.0032*
0.0014*
0.0023*
0.0004*
<0.0001*
<0.0001*
<0.0001*
<0.0001*
0.0004*
0.8288
ln Antecedent
Dry Days
R2 value
<0.0001*
<0.0001*
<0.0001*
<0.0001*
<0.0001*
<0.0001*
<0.0001*
<0.0001*
<0.0001*
<0.0001*
<0.0001*
<0.0001*
<0.0001*
0.0002*
<0.0001*
<0.0001*
<0.0001*
<0.0001*
<0.0001*
<0.0001*
<0.0001*
<0.0001*
0.0019*
<0.0001*
<0.0001*
<0.0001*
0.0009*
<0.0001*
<0.0001*
<0.0001*
<0.0001*
<0.0001*
<0.0001*
<0.0001*
<0.0001*
0.0052*
<0.0001*
0.4785
0.9316
0.9168
0.9993
0.2639
0.6664
0.8917
0.8355
0.9066
0.445
0.420
0.445
0.340
0.400
0.440
0.437
0.351
0.308
0.399
0.412
0.348
0.256
0.221
0.244
0.236
0.254
0.256
0.234
0.220
0.203
0.240
0.156
0.195
0.209
0.247
0.142
0.243
0.247
0.216
0.246
0.244
0.213
0.240
0.214
0.046
0.211
0.133
0.113
0.114
0.100
0.110
0.750
0.037
0.051
0.053
79
D-3
TOTAL ZINC
Trial
No.
1
2
3
4
5
6
7
8
9
10
11
12
1
2
3
4
5
6
7
8
9
10
11
1
2
3
4
5
6
7
8
9
10
11
1
2
3
4
5
6
7
8
9
Predictand
ln Ce
ln Ce
ln Ce
ln Ce
ln Ce
ln Ce
ln Ce
ln Ce
ln Ce
ln Ce
ln Ce
ln Ce
ln Ci-Ce
ln Ci-Ce
ln Ci-Ce
ln Ci-Ce
ln Ci-Ce
ln Ci-Ce
ln Ci-Ce
ln Ci-Ce
ln Ci-Ce
ln Ci-Ce
ln Ci-Ce
ln C/Ci
ln C/Ci
ln C/Ci
ln C/Ci
ln C/Ci
ln C/Ci
ln C/Ci
ln C/Ci
ln C/Ci
ln C/Ci
ln C/Ci
ln k
ln k
ln k
ln k
ln k
ln k
ln k
ln k
ln k
ln slope
0.0645
0.0053*
0.0129*
0.7865
0.0481*
0.1
0.873
0.0193*
0.4437
0.0808
0.3585
0.0337*
0.7724
0.063
0.116
0.9599
0.0463*
0.1084
0.4991
0.4789
0.4873
0.9346
0.4993
0.5457
0.9684
0.5151
0.0368*
0.4962
0.9828
0.1594
0.5661
0.4692
0.126
0.9304
ln width
0.3257
0.0212*
0.7139
0.6324
0.3688
0.1648
0.306
0.322
0.068
0.2884
0.0489*
0.0177*
0.0584
0.1408
0.0711
0.1764
0.0167*
0.0160*
0.0157*
0.0095*
0.0164*
0.0249*
0.0162*
0.0263*
ln
vegetation ln % clay
<0.0001* 0.0001*
<0.0001* 0.0009*
<0.0001* 0.0002*
<0.0001*
<0.0001*
<0.0001* <0.0001*
<0.0001* 0.0002*
<0.0001*
<0.0001*
<0.0001*
<0.0001* 0.0105*
<0.0001*
0.0002*
0.0001*
<0.0001* 0.0007*
0.0002* <0.0001*
<0.0001*
<0.0001*
0.0002* <0.0001*
0.0002*
0.0002*
<0.0001*
<0.0001*
<0.0001*
0.0001* <0.0001*
0.9254
0.1492
0.8567
0.2007
0.7621
0.0806
0.1418
0.7799
0.9251
0.1458
0.9202
0.154
0.7562
0.1038
0.5811
0.8123
0.0085*
<0.0001*
0.4152
<0.0001*
0.1396
0.1018
<0.0001*
<0.0001*
0.2452
<0.0001*
0.365
<0.0001*
0.0863
<0.0001*
ln rainfall
duration
0.0103*
0.0078*
0.0111*
0.0187*
0.0021*
<0.0001*
0.0022*
0.0082*
0.0015*
0.0314*
0.0247*
0.0270*
0.0350*
0.0094*
<0.0001*
0.0067*
0.0241*
0.9615
0.9927
0.9834
0.9613
0.8647
0.4008
0.7679
0.9882
0.0268*
0.0287*
0.0384*
0.0179*
0.8886
0.0147*
ln event ln Antecedent
rain
Dry Days
R2 value
0.0016*
<0.0001*
0.445
0.0023*
<0.0001*
0.437
0.0009*
<0.0001*
0.442
0.0033*
<0.0001*
0.34
0.0025*
<0.0001*
0.41
<0.0001*
<0.0001*
0.429
<0.0001*
0.421
<0.0001*
0.299
<0.0001*
0.248
0.0018*
<0.0001*
0.409
0.0009*
<0.0001*
0.424
<0.0001*
<0.0001*
0.483
0.0171*
<0.0001*
0.416
0.0236*
<0.0001*
0.408
0.0332*
<0.0001*
0.407
0.0177*
<0.0001*
0.378
0.0219*
<0.0001*
0.375
<0.0001*
<0.0001*
0.403
<0.0001*
0.4
<0.0001*
0.294
<0.0001*
0.311
0.0525
<0.0001*
0.359
0.0321*
<0.0001*
0.405
0.1972
0.0006*
0.121
0.2093
0.0002*
0.119
0.3314
0.0002*
0.099
0.1961
0.0004*
0.121
0.2041
0.0002*
0.113
0.1234
0.0004*
0.121
0.0006*
0.115
0.0003*
0.103
0.0006*
0.112
0.3594
<0.0001*
0.088
0.3371
0.0002*
0.098
<0.0001*
0.0220*
0.227
<0.0001*
0.0132*
0.226
0.0002*
0.79
0.076
<0.0001*
0.0298*
0.225
0.0006*
0.0055*
0.211
0.0413*
0.172
0.0490*
0.169
0.5562
0.02
<0.0001*
0.0200*
0.218
80
D-4
DISSOLVED ZINC
Trial
No. Predictand ln Slope
1
0.8685
ln Ce
2
0.6515
ln Ce
3
0.2014
ln Ce
4
0.9916
ln Ce
5
0.7815
ln Ce
6
0.2277
ln Ce
7
0.1207
ln Ce
8
0.0994
ln Ce
9
0.9191
ln Ce
10
0.0866
ln Ce
11
0.7361
ln Ce
12
0.6
ln Ce
13
0.7541
ln Ce
14
0.6714
ln Ce
15
0.2652
ln Ce
16
0.5106
ln Ce
17
0.6518
ln Ce
18
0.5202
ln Ce
19
0.6545
ln Ce
20
0.1047
ln Ce
21
0.5411
ln Ce
22
0.1093
ln Ce
23
0.5163
ln Ce
24
0.9468
ln Ce
25
0.2618
ln Ce
26
0.8573
ln Ce
27
0.0209*
ln Ce
28
0.0259*
ln Ce
29
0.0148*
ln Ce
30
ln Ce
31
ln Ce
32
ln Ce
33
ln Ce
34
ln Ce
35
ln Ce
36
ln Ce
37
ln Ce
38
ln Ce
39
ln Ce
40
ln Ce
41
ln Ce
42
ln Ce
ln rainfall ln Antecedent ln Event
ln Strip
R2 Value
Rain
Dry Days
ln Width Vegetation ln % Clay duration
0.1776
0.1104
0.81
0.2274
0.1261
0.7292
0.3469
0.2203
0.7354
0.2877
0.7844
0.3043
0.2411
0.2532
0.5129
0.2503
0.2822
<0.0001*
<0.0001*
<0.0001*
<0.0001*
<0.0001*
<0.0001*
<0.0001*
<0.0001*
<0.0001*
<0.0001*
<0.0001*
<0.0001*
<0.0001*
<0.0001*
<0.0001*
<0.0001*
<0.0001*
0.0016*
0.0070*
0.0004*
0.0004*
0.0010*
0.0001*
0.0346*
<0.0001*
0.0032*
0.0077*
<0.0001*
0.0009*
0.0002*
<0.0001*
<0.0001*
<0.0001*
<0.0001*
<0.0001*
<0.0001*
<0.0001*
0.0009*
<0.0001*
0.0533
0.0001*
0.0005* <0.0001*
<0.0001*
<0.0001*
0.0094*
<0.0001*
<0.0001*
<0.0001*
<0.0001*
0.0014*
0.0425*
<0.0001*
0.0031*
<0.0001*
<0.0001*
0.0001*
0.0026*
0.0125*
0.0004*
0.0018*
0.0001*
<0.0001*
0.0102*
<0.0001*
0.0007*
0.7378
0.8119
0.1371
0.11
0.3049
0.1038
0.2686
0.5363
<0.0001*
<0.0001*
<0.0001*
<0.0001*
<0.0001*
<0.0001*
<0.0001*
<0.0001*
<0.0001*
<0.0001*
<0.0001*
<0.0001* 0.0303*
<0.0001*
<0.0001*
0.0004* 0.0348*
0.0017* <0.0001*
0.0009* 0.0035*
0.0002*
0.0002*
0.0014*
0.0068*
0.0008*
0.0003*
0.0383*
<0.0001*
0.0001*
<0.0001*
0.0195*
<0.0001*
<0.0001*
0.0002*
<0.0001*
<0.0001*
<0.0001*
<0.0001*
<0.0001*
<0.0001*
<0.0001*
0.0001*
<0.0001*
0.455
0.424
0.270
0.446
0.365
0.245
0.433
0.407
0.233
0.337
0.198
0.353
0.320
0.266
0.287
0.031
0.005
0.451
0.418
0.270
0.359
0.244
0.198
0.026
0.217
0.044
0.107
0.090
0.090
0.455
0.424
0.265
0.365
0.240
0.198
0.450
0.418
0.359
0.237
0.329
0.258
0.470
81
D-4
Trial
ln Strip
ln rainfall ln Antecedent
No. Predictand ln Slope ln Width Vegetation ln % Clay duration
Dry Days
1
ln Ce/Ci <0.0001* 0.0020*
0.0177*
0.394
0.8424
0.0037*
2
ln Ce/Ci <0.0001* 0.0021*
0.0122*
0.3394
0.8658
0.0043*
3
ln Ce/Ci <0.0001* 0.0073*
0.0022*
0.606
0.6368
4
ln Ce/Ci <0.0001* 0.0019*
0.0174*
0.3653
0.4865
5
ln Ce/Ci <0.0001* 0.0020*
0.0122*
0.346
0.0038*
6
ln Ce/Ci <0.0001* 0.0075*
0.0019*
0.5593
7
ln Ce/Ci <0.0001* 0.0014*
0.0233*
0.7187
0.4392
8
ln Ce/Ci <0.0001* 0.0013*
0.0171*
0.9813
0.0059*
9
ln Ce/Ci <0.0001* 0.0053*
0.0025*
0.5854
10
ln Ce/Ci <0.0001* 0.0013*
0.0168*
0.0049*
11
ln Ce/Ci <0.0001* 0.0054*
0.0022*
12
ln Ce/Ci <0.0001* 0.0030*
0.6371
0.8363
0.5477
13
ln Ce/Ci <0.0001* 0.0035*
0.5851
0.9355
0.0008*
14
ln Ce/Ci <0.0001* 0.0167*
0.9142
0.4802
15
ln Ce/Ci <0.0001* 0.0035*
0.5885
0.0006*
16
ln Ce/Ci <0.0001* 0.0178*
0.9909
17
ln Ce/Ci <0.0001* 0.0026*
0.9997
0.0010*
18
ln Ce/Ci <0.0001* 0.0158*
0.4833
19
ln Ce/Ci <0.0001* 0.0025*
0.0007*
20
ln Ce/Ci <0.0001* 0.0163*
21
ln Ce/Ci <0.0001*
0.0268*
0.2433
0.6859
0.0162*
22
ln Ce/Ci <0.0001*
0.0212*
0.1932
0.8771
0.0176*
23
ln Ce/Ci <0.0001*
0.0049*
0.3722
0.7021
24
ln Ce/Ci <0.0001*
0.0211*
0.1952
0.0161*
25
ln Ce/Ci <0.0001*
0.0043*
0.3417
26
ln Ce/Ci <0.0001*
0.0065*
27
ln Ce/Ci <0.0001*
0.7147
28
ln Ce/Ci <0.0001*
0.5178
29
ln Ce/Ci <0.0001*
0.0048*
30
ln Ce/Ci <0.0001*
31
ln Ce/Ci
0.9724
0.1061
0.0981
0.4985
0.1162
32
ln Ce/Ci
0.9775
0.092
0.1241
0.9551
0.1252
33
ln Ce/Ci
0.9766
0.0909
0.1212
0.1122
34
ln Ce/Ci
0.9391
0.0340*
0.1007
35
ln Ce/Ci
0.9491
0.0378*
0.0931
0.6896
36
ln Ce/Ci
0.3764
0.0189*
37
ln Ce/Ci
0.0903
0.0822
0.1106
38
ln Ce/Ci
0.0337*
0.0621
39
ln Ce/Ci
0.0546
0.0935
40
ln Ce/Ci
0.0498*
0.0417*
1
ln Ci-Ce
0.2772
0.0301*
2
ln Ci-Ce
0.0035*
0.0813
0.7324
3
ln Ci-Ce
0.0032*
0.0836
4
ln Ci-Ce <0.0001* 0.0006*
<0.0001*
0.2452
0.1932
<0.0001*
ln Event
Rain
0.4957
0.0026*
0.0048*
0.0007*
0.3204
0.6603
0.244
0.4643
R2 Value
0.165
0.162
0.135
0.165
0.162
0.135
0.163
0.159
0.134
0.159
0.133
0.146
0.141
0.103
0.141
0.101
0.140
0.103
0.140
0.101
0.133
0.130
0.110
0.130
0.110
0.107
0.081
0.082
0.108
0.082
0.049
0.044
0.044
0.036
0.036
0.025
0.044
0.036
0.033
0.034
0.058
0.049
0.049
0.325
82
D-4
Trial
ln Strip
ln rainfall ln Antecedent
No. Predictand ln Slope ln Width Vegetation ln % Clay duration
Dry Days
5
ln Ci-Ce <0.0001* 0.0010*
<0.0001*
0.2942
0.0599
<0.0001*
6
ln Ci-Ce <0.0001* 0.0019*
<0.0001*
0.203
<0.0001*
7
ln Ci-Ce
0.0035* 0.0252*
<0.0001*
0.0771
8
ln Ci-Ce
0.0036* 0.0233*
<0.0001*
0.0907
0.4719
9
ln Ci-Ce <0.0001* 0.0009*
<0.0001*
0.1365
<0.0001*
10
ln Ci-Ce <0.0001* 0.0014*
<0.0001*
0.0435*
<0.0001*
11
ln Ci-Ce
0.0002* 0.0413*
<0.0001*
0.3814
12
ln Ci-Ce <0.0001* 0.0029*
<0.0001*
<0.0001*
13
ln Ci-Ce
0.0002* 0.0465*
<0.0001*
14
ln Ci-Ce <0.0001* 0.0005*
0.092
0.2448
<0.0001*
15
ln Ci-Ce
0.0001* 0.0011*
0.1079
0.124
<0.0001*
16
ln Ci-Ce
0.0479* 0.0356*
0.0144*
0.8759
17
ln Ci-Ce
0.0002* 0.0018*
0.0743
<0.0001*
18
ln Ci-Ce
0.0469* 0.0355*
0.0134*
19
ln Ci-Ce <0.0001* 0.0019*
0.085
<0.0001*
20
ln Ci-Ce <0.0001* 0.0034*
<0.0001*
21
ln Ci-Ce
0.0017*
<0.0001*
0.4294
0.4157
<0.0001*
22
ln Ci-Ce
0.0016*
<0.0001*
0.5019
0.1207
<0.0001*
23
ln Ci-Ce
0.0388*
<0.0001*
0.1716
0.5493
24
ln Ci-Ce
0.0020*
<0.0001*
0.38
<0.0001*
25
ln Ci-Ce
0.0368*
<0.0001*
0.1507
26
ln Ci-Ce <0.0001*
<0.0001*
<0.0001*
27
ln Ci-Ce
0.0015*
<0.0001*
28
ln Ci-Ce
0.0189*
0.8163
29
ln Ci-Ce
0.0003*
<0.0001*
30
ln Ci-Ce
0.0163*
31
ln Ci-Ce
0.2322
0.0001*
0.0033*
0.4366
0.0004*
32
ln Ci-Ce
0.2618
<0.0001*
0.0052*
0.1383
0.0004*
33
ln Ci-Ce
0.3394
<0.0001*
0.0045*
0.4815
34
ln Ci-Ce
0.3025
<0.0001*
0.0033*
0.0011*
35
ln Ci-Ce
0.3586
<0.0001*
0.0035*
36
ln Ci-Ce
0.796
<0.0001*
37
ln Ci-Ce
<0.0001*
0.0057*
0.0012*
38
ln Ci-Ce
<0.0001*
0.0052*
39
ln Ci-Ce
<0.0001*
0.0013*
40
ln Ci-Ce
0.0031*
<0.0001*
1
ln k
0.9364
0.2072
0.5253
0.0731
0.0588
2
ln k
0.2072
0.3851
0.0676
0.0524
3
ln k
0.9756
0.4392
0.0915
0.0262*
4
ln k
0.5509
0.1809
0.0884
0.0352*
5
ln k
0.7259
0.2691
0.7708
0.0215*
6
ln k
0.8272
0.4113
0.633
0.8436
0.0557
7
ln k
0.5225
0.3699
0.0378*
8
ln k
0.9117
0.5261
0.0302*
ln Event
Rain
0.5333
0.5822
0.3
0.4004
0.3138
0.0009*
0.0008*
0.0014*
0.0009*
0.0049*
R2 Value
0.317
0.302
0.215
0.218
0.319
0.313
0.204
0.296
0.200
0.243
0.226
0.082
0.215
0.082
0.214
0.200
0.276
0.272
0.194
0.261
0.192
0.258
0.182
0.032
0.160
0.037
0.238
0.234
0.178
0.224
0.175
0.134
0.219
0.171
0.183
0.139
0.061
0.061
0.055
0.059
0.050
0.023
0.022
0.021
83
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