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g LIBRARY
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University

 

 

 

This is to certify that the
dissertation entitled

INFERRING DISSOLVED PHOSPHORUS CYCLING IN A TMDL
WATERSHED USING BIOGEOCHEMISTRY AND MIXED LINEAR
MODELS

presented by
DEAN G. BAAS

has been accepted towards fulﬁllment
of the requirements for the

Doctoral degree in Geological Sciences and
Biosystems and Agricultural Engineering

Mob/Fiﬁ

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5/08 K:IProj/Acc&Pres/ClRC/DateDm.indd

INFERRING DISSOLVED PHOSPHORUS CYCLING IN A TMDL WATERSHED
USING BIOGEOCHEMISTRY AND MIXED LINEAR MODELS
By

Dean G. Baas

A DISSERTATION

Submitted to
Michigan State University
In partial fulﬁllment of the requirements
for the degree of

DOCTOR OF PHILOSOPHY

Geological Sciences and
Biosystems and Agricultural Engineering

2009

ABSTRACT
INFERRING DISSOLVED PHOSPHORUS CYCLING IN A TMDL
WATERSHED USING BIOGEOCHEMISTRY AND MIXED LINEAR
MODELS
By

Dean G. Baas

Eutrophication is a persistent condition of surface waters and a widespread
environmental problem. The current state of aquatic ecosystems reﬂects the
anthropogenic impact on processes, chemistry and hydrology; thus understanding
relationships between land use and stream biogeochemistry is essential to mitigating
eutrophication.

In a two-year study of the Kalamazoo River/Lake Allegan Watershed
(KRLAW), a phosphorus (P) total maximum daily load (TMDL) watershed located in
southwest Michigan, USA, patterns are identiﬁed in suites of chemicals and their
relationship to land use to understand the cycling (sources, pathways, fate) of
chemicals in the watershed. Although this has been done for P, patterns have not been
easily identiﬁed with few and weak relationships. Two reasons are proposed for these
poor relationships. First, multiple and competing effects on P from temporal (climate,
hydrology), catchment (land use, fertilizer application, soil type) and biological (algal
productivity, macro-invertebrate grazing) inﬂuences. Second, structural restrictions
(parameter variance, covariance and correlation) not easily addressed by common
statistical methods. Overcoming these deﬁciencies produces numerous and stronger

relationships providing insight into dissolved P (DP) cycling.

The overall hypothesis is DP, stream biogeochemistry and land use have
unique relationships and patterns that can be quantiﬁed and that DP cycles have
characteristic biogeochemical/land use signatures. If true, biogeochemical/land use
signatures can be used to identify processes that control DP cycling and outcomes
predicted for P mitigation. To test this hypothesis, data is segregated by inﬂuence
based on biological indicators. Mixed linear models, statistical methods that address
parameter covariance and correlation, are used to quantify catchment and biological
temporal trends and site effects. Removing these effects, general linear models and
principal factor analyses produce improved relationships between DP, stream
chemistry and land use.

The catchment inﬂuence relationships identify DP source and process
correlations with land use. An approach for evaluating DP exports based on readily
available land use data is presented. The biological inﬂuence analysis identiﬁes
impoundment serial discontinuity processes that disconnect the stream system from
the landscape, control P cycling and regulate downstream P forms.

Temporal, catchment and biological inferred DP cycling are used to develop an
empirical total P (TP) model, based on historical data, to predict Lake Allegan inlet
concentrations. The TP model predicts a 63% probability of attaining the 2012 TMDL
goal of 72 ug L'l and mean discharge adjusted 2012 concentration of 65.7 pg L".

Results from this study provide insight into the P cycling in a mixed land use
watershed and have implications for watershed assessment, P reduction strategies and

regulatory TMDL policies.

Copyright by
DEAN G. BAAS
2009

DEDICATION

This dissertation is dedicated to my parents, Garry and Verna Baas; my
brother, Duane Baas; my sisters-in-law, nieces, nephew, great-niece; and in memory

of my brother Douglas Baas.

ACKNOWLEDGEMENTS

Thank you to the USDA CSREES and National Water Program for funding
this research, the MSU Aqueous and Environmental Geochemistry Laboratory and the
WK. Kellogg Biological Station for laboratory support; and the MSUE Southwest
Region and MSUE Land & Water Program for providing resources and funding.

Special thanks to Nora Bello for assistance with statistical analyses and David
Week for laboratory analyses and analytical support.

Thank you to my committee of Dr. David T. Long, Dr. Steven 1. Saffennan,
Dr. Theodore L. London and Dr. Phanikumar S. Mantha for their patience and
guidance.

I am especially thankful for the support from my many friends and co-workers,
especially Dale Mutch, Colleen Mclean, Merideth Fitzpatrick, Neville and Dawn

Millar, Danielle Heger, Mike and Cathy McMinn and Drew and Mimi Corbin.

vi

TABLE OF CONTENTS

LIST OF TABLES ......................................................................................................... ix
LIST OF FIGURES ....................................................................................................... xi
CHAPTER 1. INTRODUCTION ................................................................................... 1
Literature Review ........................................................................................................ 6
Research Hypothesis ................................................................................................. 17
Study Site .................................................................................................................. 19
Methods ..................................................................................................................... 21
Research Approach ................................................................................................... 28
Literature Cited ......................................................................................................... 31

CHAPTER 2. IDENTIFYING TEMPORAL TRENDS IN WATERSHED
DISSOLVED PHOSPHORUS USING A MIXED LINEAR MODEL

APPROACH ................................................................................................................. 40
Abstract ..................................................................................................................... 40
Introduction ............................................................................................................... 41
Methods ..................................................................................................................... 44
Results ....................................................................................................................... 49
Discussion ................................................................................................................. 62
Conclusions ............................................................................................................... 65
Literature Cited ......................................................................................................... 67

CHAPTER 3. INFERRING CATCHMENT INFLUENCED DISSOLVED
PHOSPHORUS DYNAMICS USING LAND USE AND STREAM

BIOGEOCHEMISTRY ............................................................................................... 70
Abstract ..................................................................................................................... 70
Introduction ............................................................................................................... 71
Methods ..................................................................................................................... 74
Results ....................................................................................................................... 75
Discussion ................................................................................................................. 90
Conclusions ............................................................................................................... 93
Literature Cited ......................................................................................................... 95

CHAPTER 4. INFERRING DISSOLVED PHOSPHORUS CYCLING ON A RIVER
SYSTEM FROM SERIAL IMPOUNDMENTS USING STREAM

BIOGEOCHEMISTRY ................................................................................................ 98
Abstract ..................................................................................................................... 98
Introduction ............................................................................................................... 99
Methods ................................................................................................................... 101
Results ..................................................................................................................... 103

vii

Discussion ............................................................................................................... 125
Conclusions ............................................................................................................. 128
Literature Cited ....................................................................................................... 130

CHAPTER 5. A MODEL FOR PREDICTTNG THE PHOSPHORUS REDUCTIONS

TO A FLOW THROUGH RIVER IMPOUNDMENT .............................................. 133
Abstract ................................................................................................................... 133
Introduction ............................................................................................................. 134
Methods ................................................................................................................... 136
Model Development ................................................................................................ 137
Results ..................................................................................................................... 149
Discussion ............................................................................................................... 1 56
Conclusions ............................................................................................................. 1 58
Literature Cited ....................................................................................................... 160

APPENDICES ........................................................................................................... l 63

Appendix I: Kalamazoo River/Lake Allegan Watershed Stream Chemistry

Dataset ................................................................................................ 164

Appendix II: Kalamazoo River/Lake Allegan Watershed Stream Trace Element

Dataset 193

Appendix III: Historical Mean Growing Season Data .............................................. 200

Appendix IV: Historical Mean Monthly Discharge Dataset ...................................... 205

Appendix V: Mixed Linear Model Theory ............................................................... 212

Appendix VI: Kalamazoo River/Lake Allegan Subwatershed Land Use and

Land Use Effect Data .......................................................................... 217

BIBLIOGRAPHY ....................................................................................................... 222

viii

LIST OF TABLES

Table 1.1: Site id, name, longitude, latitude, years sampled and % land
use by class level for sampling locations in the Kalamazoo
River/Lake Allegan Watershed .................................................................. 26

Table 1.2: STATSGO soil group distributions representing greater than
90 % of the soils within each sampling site catchment in the
Kalamazoo River/Lake Allegan Watershed .............................................. 27

Table 1.3: Historical data sources by year for P concentrations, point source
loading, discharge at Comstock, MI and discharge at

New Richmond, MI ................................................................................... 29
Table 2.1: Fixed effects results from the catchment inﬂuenced MLM ...................... 55
Table 2.2: Random effects results from the catchment inﬂuenced MLM .................. 56
Table 2.3: Solution for the ﬁxed effects for the biology inﬂuenced MLM ................ 59
Table 2.4: Solution for the random effects for the biology inﬂuenced MLM ............ 59

Table 3.1: The mean and standard deviation (mean :1: standard deviation) by
site for dissolved phosphorus (DP), temporal trend and site adjusted
dissolved phosphorus (DPTSA) and the signiﬁcant (p<0.05) stream
chemistry ﬁxed effects (Mg2+, K+, NO3' ,Na+, pH, alkalinity (Alk)
and speciﬁc conductance (SPC)) and land use percentages for the
signiﬁcant (p<0.05) land use ﬁxed effects (lowland forest,
agricultural and urban) from the catchment inﬂuence MLM ..................... 76

Table 3.2: A comparison of DPTSA category, site, mean DPTSA and the
catchment inﬂuenced MLM lowland forest, agriculture, urban
and total land use effects. Dark highlight compares high lowland
forest effect Sites. Light highlight compares low lowland forest
effect sites ................................................................................................... 78

Table 3.3: Pearson’s correlation coefﬁcients for land use and soil groups for
the Kalamazoo River/Lake Allegan Watershed. See Tables 1.1 and
1.2 for abbreviations. High correlations (>0.75) with lowland forest
(land use class VI) are highlighted ............................................................. 80

ix

Table 3.4: Unrotated factor loading matrix from principal factor analysis for
the stream chemistry dataset from the Kalamazoo River/Lake
Allegan Watershed ...................................................................................... 83

Table 3.5: Un-rotated factor loading matrix from principal factor analysis
for the catchment synoptic trace element dataset from the
Kalamazoo River/Lake Allegan Watershed. Stream biogeochemical
ﬁngerprints: dark highlight = agricultural and DPTSA; medium
highlight = urban only; light highlight = agricultural only;
and box = common agricultural and urban ................................................. 85

Table 4.1: The mean and standard deviation (mean 3: standard deviation)
by site for dissolved phosphorus (DP), temporal trend and site
adjusted dissolved phosphorus (DPTSA) and the signiﬁcant (p<0.05)
stream chemistry ﬁxed effects (PP, NO3', SO42", Cl' and pH) and
land use percentages for the signiﬁcant (p<0.05) land use ﬁxed
effect (urban) from the biological inﬂuenced MLM ................................ 104

Table 4.2: Morrow Lake and Lake Allegan 2005 and 2006 growing season
mean TP, discharge and estimated TP load and Kalamazoo Water
Reclamation Plant TP load ...................................................................... 108

Table 4.3: Varimax-rotated factor loading matrix from principal factor analysis
for the biological inﬂuenced stream chemistry dataset and urban
land use from the Kalamazoo River/Lake Allegan Watershed ................. 110

Table 4.4: Varimax-rotated factor loading matrix from principal component
analysis for the biological inﬂuenced DPTSA, urban land use and
trace element dataset from the Kalamazoo River/Lake Allegan
Watershed ................................................................................................. 111

Table 5.1: GLM output for TPKC = Year for the outlet of Morrow Lake ................. 143
Table 5.2: GLM output for LCAM = Year + MDDs + MBD7 +MD3 for the

growing season catchment input and in-stream inﬂuence TP load
after Morrow Lake ................................................................................... 145

Figure 1.1:

Figure 1.2:

Figure 1.3:

Figure 1.4:

Figure 2.1:

Figure 2.2:

LIST OF FIGURES
Overall research approach ......................................................................... 4

Location and extent of the Kalamazoo River/Lake Allegan
Watershed, major municipalities (Kalamazoo and Battle Creek)
and Lake Allegan ...................................................................................... 5

Aerial view of Lake Allegan, the P impaired waterbody ......................... 5

Sampling locations A in the Kalamazoo River/Lake Allegan
Watershed, and the positions of Morrow Lake and Lake Allegan ......... 22

Comparison of Morrow Lake inﬂow (KM) and outﬂow (KC)

concentrations for alkalinity, calcium and PP, outﬂow discharge
and biological and catchment inﬂuenced dates, 2005 ............................ 51

Comparison of Morrow Lake inﬂow (KM) and outﬂow (KC)
concentrations for alkalinity, calcium, PP and chlorophyll a, outﬂow
discharge and biological and catchment inﬂuenced dates, 2006 ............ 52

Figure 2.3: Comparison of Morrow Lake outﬂow (KC) and biological

Figure 2.4:

Figure 2.5:

Figure 2.6:

Figure 2.7:

Figure 2.8:

Figure 2.9:

inﬂuenced site means (BISM) and Morrow Lake inﬂow (KM) and
catchment inﬂuenced site means (CISM), 2005 ...................................... 53

Comparison of Morrow Lake outﬂow (KC) and biological
inﬂuenced site means (BISM) and Morrow Lake inﬂow (KM) and
catchment inﬂuenced site means (CISM), 2006 ...................................... 53

Data separation into catchment and biological inﬂuenced datasets
by date and site ....................................................................................... 54

Plot of the estimated catchment temporal trend factors (CTTF) by
week from the catchment inﬂuenced MLM.
Note: Week 1 = ﬁrst week of April ....................................................... 57

The catchment inﬂuenced MLM estimates for the 2006 contributions
to total DP from the temporal trend DP and the stream chemistry
and land use DP for the Battle Creek River (site BR). ............................ 58

Plot of the estimated biological temporal trend factors (BTTF) by
week from the biological inﬂuenced MLM.
Note: Week 1 = ﬁrst week of April ....................................................... 60

Actual log(DP) versus predicted log(DP) and linear regressions
for the catchment and biological models on the KRLAW datasets ........ 62

xi

Figure 3.1:

Figure 3.2:

Figure 4.1:

Figure 4.2:

Figure 4.3:

Figure 4.4:

Figure 4.5:

Figure 4.6:

Figure 4.7:

Figure 4.8:

A plot and linear regression of the catchment MLM land use
ﬁxed effects equation versus the mean DPTSA by site ............................ 77

Categories for mean DPTSA for the Kalamazoo River/Lake Allegan
Watershed, HUC 4050003, basin 17, by sub number estimated

using the catchment MLM land use equation and mean DPTSA
relationship (Appendix VI) ...................................................................... 88

Diagram of the biological inﬂuenced region of the KRLAW

depicting 2005 and 2006 sampling sites 0, 2006 sampling sites 0,
impoundments E2, the major point source 0 (Kalamazoo

Water Reclamation Plant) and mean TP, DP and PP concentrations

for the 2005 and 2006 growing seasons and biological inﬂuenced

periods .................................................................................................... 105

Comparison of 2005 and 2006 growing season mean TP, PP and

DP for six Kalamazoo River main stem sites sampled both years

versus distance downstream from the site KE, with Morrow Lake

and Lake Allegan inlets and outlets identiﬁed by vertical lines ............ 107

Discharge hydrographs for the 2005 and 2006 growing seasons
at the outlet of Morrow Lake (Site KC). ................................................ 108

TP changes from Morrow Lake inlet (KM) to outlet (KS and KC)
for the biological inﬂuenced sampling dates. Note: Site KS
sampled in 2006 only ............................................................................ 1 12

Inlet PP (KM PP), outlet PP (KC PP), inlet DP (KM DP) and

outlet DP (KC DP) concentrations for the biological inﬂuenced

dates and the outlet discharge (KC Discharge) for the 2005

and 2006 growing seasons ..................................................................... 114

Morrow Lake inlet (KM) and outlet (KC) PP, DP, NO3' and
chlorophyll a concentrations for the 2006 growing season .................. 115

Historic Morrow Lake outlet mean growing season TP concentrations.
Trend — and range :23: from 1981to 2006 excluding 2003. Data
Sources: 0 USEPA STORET Database; 0 MDEQ; and

O KRLAW study .................................................................................... 117

PP, DP and chlorophyll a concentrations for the 2005 and 2006
biological inﬂuenced dates for locations from the outlet of Morrow

Lake to the inlet of Lake Allegan. Site KK sampled in 2006 only.
Chlorophyll a sampled at sites KC and KA in 2006 only ..................... 119

xii

Figure 4.9:

Figure 4.10:

Figure 5.1:

Figure 5.2:

Figure 5.3:

Figure 5.4:

Figure 5.5:

Figure 5.6:

Figure 5.7:

Figure 5.8:

Lake Allegan inlet (KA) and outlet (KD) chlorophyll a, DP, PP
and NO3' concentrations for the 2005 and 2006 growing seasons ....... 122

Historic Lake Allegan inlet (circles) and outlet (diamonds)

mean growing season TP concentrations from 1998-2006. Outlet

trend — and range 222: Data Sources: o O MDEQ

and c O KRLAW study .......................................................................... 123

Block diagram for the TP model development for KRLAW Lake
Allegan inlet concentration (KA) identi ing inputs and
inﬂuences D and sampling locations .......................................... 138

The relationship between monthly mean discharge at the outlet
of Morrow Lake (DKC) and the inlet of Lake Allegan (DKA) ................. 140

Historic Morrow Lake outlet mean growing season TP concentrations.
Trend— and 95% prediction intervalZZZZ from 1981 to 2006,

excluding 2003. Data Sources: 0 USEPA STORET Database,

0 MDEQ and O KRLAW study ............................................................. 142

GLM relationship for growing season catchment input and in-stream
inﬂuence load. Prediction — and 95% prediction intervalZZZZ for

1998 and 2001-2006. Data Sources: MDEQ and KRLAW study

and KRLAW TMDL point source tracking system ............................... 146

Growing season documented point source TP loads before the

Morrow Lake inlet (LpBM), after the Morrow Lake outlet (LpAM),

total point source load and the KRLAW TMDL point source goal

in 2012. Sources: 1998: (Heaton, 1999) 2001 — 2008: (Kieser &
Associates, 2008) ................................................................................... 147

Histogram of PTPKA in 2012 based on equation 5.14, using 69
years of discharge data at site KC ......................................................... 151

Normal probability plot for PTPKA and the theoretical diagonal
distribution line based on a normal distribution ................................... 151

Figure 5.8: Predicted 2012 contributions to PTPKA of the

modeled P sources at the minimum, mean and maximum

discharge parameters for the period of record at KC. Percentage
contribution to the total listed in bold next to the bars .......................... 155

xiii

CHAPTER 1
INTRODUCTION

Eutrophication (the over-enrichment of aquatic ecosystems with nutrients) is a
persistent condition of surface waters and a widespread environmental problem
(Carpenter, 2005; Smith et al., 2006). Carpenter (2005) states, “Eutrophication has
become a global problem that is likely to intensify in coming decades because of
increases in human population, demand for food, land conversion, fertilizer use and
nitrogen deposition.” These increasing human demands on the environment are
changing ecosystems in unprecedented ways with long lasting consequences
(V itousek, 1997). Consequences of eutrophication include disproportionate plant
production, blooms of harmful algae, increased frequency of anoxic events,
deterioration of ﬁsheries and reductions in the aesthetic and economic quality of water
bodies (Edmondson et al., 1956; Likens et al., 1971). Human demands, associated
with land use and contributing to eutrophication, are reﬂected in stream
biogeochemistry. Understanding land use and stream biogeochemistry relationships
is essential to mitigating the causes of eutrophication.

Excessive phosphorus (P) and nitrogen (N) inputs lead to eutrophication
(Carpenter et al., 1998; Dodd et al., 2003). Of the two, P is the limiting nutrient and
its control is seen as the best means of managing eutrophication (Grobbelaar and
House, 1995). Dissolved P (DP) is readily available for biological uptake associated
with eutrophication (Sharpley, 1999). Relationships between DP, stream
biogeochemistry and land use provide insights into the cycling (sources, transport and

fate) of P within a watershed.

Many studies have demonstrated relationships and patterns between land use,
human disturbance and stream chemistry (Amtson and Tomes, 1985; Boutt et al.,
2001; Fitzpatrick et al., 2007; Wayland et al., 2003; Williams et al., 2005). Although
such work has included P, patterns have been difﬁcult to recognize between P, stream
chemistry and land use (Liu et al., 2000; Momen et al., 1996; Tsegaye et al., 2006;
Zampella et al., 2007). The lack and/or weakness of these patterns is counter-intuitive
in light of the many studies that have identiﬁed agriculture and urban regions as
sources and exporters of P and other chemical solutes (Coulter et al., 2004; Feyereisen
et al., 2007; Lewis et al., 2007; Sharpley et al., 2001; Steuer etal., 1997; Waschbusch
et al., 1999; Withers and Haygarth, 2007). Two reasons are identiﬁed for the lack
and/or weakness of the P, stream chemistry and land use patterns and relationships: (1)
variable temporal catchment and biological inﬂuences, and (2) structural restrictions
that complicate data analysis.

First, catchment inﬂuence changes the DP, stream chemistry and land use
relationships over time with variations in transport pathway (overland, subsurface or
groundwater). Within some stream environments, biological inﬂuence further varies
the catchment inﬂuence relationships over time from high rates of biotic DP uptake
(Mulholland and Hill, 1997). These two inﬂuences introduce different variable
temporal trends in the DP data. The catchment and biological inﬂuences are
addressed by segregating the data by inﬂuence.

Second, there are several common structural restrictions associated with
analyzing land use and chemical indicators in streams. These include collinearity of

land use percentages and spatial autocorrelation of land use and stream data from

nesting of sampling sites and serial dependence of time-series data (King et al., 2005).
These structural restrictions are not easily accounted for with common multivariate
statistical techniques. The structural restrictions are addressed using the mixed linear
model (MLM) that permits the data to exhibit correlation (Taskinen et al., 2008). The
MLM is a generalization of the standard linear model, making it possible to model not
only the means of data but their variances and covariances as well.

Data separation and MLMS are used to quantify the temporal trends and site
effects from catchment and biological inﬂuences and to improve the DP, stream
chemistry and land use relationships. Removing the temporal trends and site effects
from the DP allows further evaluation of the stream chemistry and land use patterns
and relationships using common multivariate statistical techniques (Pearson’s
correlations, general linear models (GLM) and principal factor analyses (PFA)).
Catchment and biological DP cycling are inferred using these techniques. DP cycling
provides insight for watershed P management. These inferences are the basis for
developing a P model using contemporary trends in historical P data to predict future
P levels.

The overall approach for this research is detailed in Figure 1.1. The objectives
of this research are to:

0 Identify patterns in suites of chemicals and their relationship to land use.

0 Infer DP cycling from the chemical and land use relationships.

0 Improve watershed P management using DP cycling insights.

o Predict future P concentrations based on inferred DP cycling.

 

I Study P Data I

 

 

Inﬂuence
I Catchment Inﬂuence I(—-)I Biological Inﬂuence I Separation

 

 

 

 

 

 

 

 

 

Ir J! . I I , ‘l‘_ ‘l' Quantify
Temporal Chemistry Land Use Temporal Chemistry Land Use Temporal Trend
Trend Effects Effects Trend Effects Effects MLM

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Remove 7 7 Remove

 

Identify and
Evaluate
Catchment
Patterns

 

 

Infer Catchment
DP Cycling

 

 

 

 

 

 

 

Identify and
Evaluate
Biological
Patterns

lnfer Biological
DP Cycling

 

 

 

 

 

 

 

 

——-)I Historical P Data I*—- Model

I Statistical
I Predict Future P Levels 7 Trends

 

 

 

 

 

Figure 1.1: Overall research approach.

This study describes a research approach using data separation by inﬂuence
(catchment or biological), MLMS, GLMS, Pearson’s correlations and PFAs to explore
the factors controlling DP cycling in the Kalamazoo River/Lake Allegan Watershed
(KRLAW). The KRLAW (Figure 1.2) is a mixed land use watershed in southwest
Michigan under a P total maximum daily load (TMDL) for Lake Allegan (Figure 1.3),
a P impaired waterbody.

This research is predicated on the hypothesis that unique and signiﬁcant
relationships and patterns between DP, stream biogeochemistry and land use can be
identiﬁed, quantiﬁed and used to provide insight into P sourcing, transport and fate
that lead to eutrophication. If DP cycling is related to stream biogeochemistry and

land use in a predictable manner, the results of this research will facilitate watershed

managers and stakeholders in developing reduction programs to mitigate the
environmental impacts of P. The approach used in this research can be adapted to
other watersheds to improve TMDL development and assessment processes.
Furthermore, results from this research have implications for the effectiveness of

certain P reduction strategies and TMDL policy development.

Lake Allegan

 

 

 

Figure 1.2: Location and extent of the Kalamazoo River/Lake Allegan Watershed,
major municipalities (Kalamazoo and Battle Creek) and Lake Allegan.

 

Fl'glll‘ e 1.3: Aerial view of Lake Allegan, the P impaired waterbody.

5

Literature Review
Eutrophication and its eﬂects
Surface water eutrophication resulting from nonpoint source P and N inputs is
the most common water quality problem in the United States (USEPA, 1996). The
trophic state of surface waters ranges from unproductive (oligitrophic) through
intermediate productivity (mesotrophic) to highly productive (eutrophic). Developed
most extensively for lakes, factors relating to primary plant production include algal
biomass, water column nutrients and water transparency (Dodds, 2007).
Consequences of eutrophication include disproportionate plant production, blooms of
harmful algae, increased frequency of anoxic events, deterioration of ﬁsheries and
reductions in the aesthetic and economic quality of water bodies (Edmondson et al.,
1956; Likens et al., 1971). Carpenter (2005) states, “Economic losses attributed to
eutrophication include costs of water puriﬁcation for human use, losses of ﬁsh and
wildlife production, and loss of recreational amenities.”
The adverse effects of eutrophication result from anthropogenic activities in

urban and agricultural environments that are major sources of excessive nutrients P
and N to aquatic ecosystems (Carpenter et al., 1998; Dodd et al., 2003). P is the
limiting nutrient and controlling P concentrations in aquatic systems is a means of
controlling aquatic productivity and hence eutrophication (Grobbelaar and House,

1995). Point sources of pollution, including P, from industrial discharges and
municipal waste water treatment plants are easily identiﬁed and quantiﬁed. Point
Source P loading to surface waters has been greatly reduced since the implementation

of the 1972 Federal Clean Water Act (Brett et al., 2005b). However, control of diffuse

nonpoint source pollution has been less successful and is considered the main cause of
eutrophication in lakes, streams and coastal areas in the United States (National
Research Council, 1992; USEPA, 1996).

Sources of eutrophication

Agricultural and urban land uses as sources of P to the environment have been
extensively studied. Agriculture has evolved from a net sink of P (e.g., deﬁcits of P
limit crop production) to net sources of P (e.g., P inputs in feed and mineral fertilizer
can exceed outputs in farm produce) (Sharpley et al., 2001). Continued application of
manures and fertilizers in many areas has led to the buildup of soil P concentrations
above those required for optimum plant grth (Beauchemin and Simard, 2000;
Carpenter et al., 1998; Inamdar et al., 2001; Kleinman et al., 2000; McDowell et al.,
2001; McDowell and Sharpley, 2001; Nelson, 1999; Withers and Haygarth, 2007). In-
stream concentrations and catchment export of N and P tend to increase with
increasing agricultural land use (Bemot et al., 2006; Coulter et al., 2004; Dodds and
Oakes, 2006; McDowell et al., 2003).

Compared to rural streams, urban streams often have elevated concentrations
of solutes, such as NO3', SO42} PO43} Cl' and base cations (Lewis et al., 2007). The
expansion of urban land areas alters land use, which increases impervious surfaces,
decreases inﬁltration, produces higher peak discharge and increases point source
inputs from industry and wastewater treatment (Brett et al., 2005a; Brezonik and
Stadelmann, 2002; Coulter et al., 2004; Hatt et al., 2004; Lewis et al., 2007; Steuer et

al., 1997; Waschbusch et al., 1999). Urban development factors (increases in storm

drains, dry wells, impermeable surfaces, etc.) may be responsible for higher P inputs

to the stream in urbanizing areas of the Johnson Creek watershed in northern Oregon
(Sonoda et al., 2001).

Regulatory requirements

Section 303d of the Federal Clean Water Act requires all states to submit a list

of water bodies that do not meet water quality standards to the United States
Environmental Protection Agency (USEPA). In addition, the states must identify the
impairment, specify the impairment cause and develop and prioritize TMDLs or other
watershed restoration approaches for the impaired water bodies (Haggard et al., 2003).
As of 2008 in the United States, 5707 water bodies are listed with nutrient impairment
and 5084 of those include P (U SEPA, 2008b). The proliferation of TMDLS has lead
to extensive studies of the relationships between land use change, human disturbance
and surface water chemistry, including P.

Land use and surface water chemistry studies

The inﬂuence of development, urbanization, agriculture and industrialization,

manifested through land use, on surface and groundwater quality is well documented
in the literature (Amtson and Tomes, 1985; Boutt et al., 2001; Fitzpatrick et al., 2007;
Wayland et al., 2003; Williams et al., 2005). In a study of the Twin Cities
metropolitan area (MN), Amston and Tomes (1985) found the highest concentration
of metals, Cl', dissolved solids and suspended sediment for the most urbanized site.

Rural sites had low concentrations of metals but the highest concentrations of many
nutrients. Solute concentrations of Cl', 8042', N03” and base cations had signiﬁcant,
positive relationships with the percentage of urban plus agricultural land use in 43

ﬁrst-order catchments in the Ipswich sub-basins in northeastern Massachusetts

(Williams et al., 2005). Wayland et a1. (2003) found elevated levels of Ca“, Mg” and
alkalinity and frequently K+, SO42' and N03' were associated with agricultural activity
while higher concentrations of Na+, K+ and Cl' were associated with urban areas.

Land use changes are known to inﬂuence the biogeochemistry of watersheds
(Boutt et al., 2001; Fitzpatrick et al., 2007; Tsegaye et al., 2006; Wayland et al., 2003;
Williams et al., 2005; Zampella et al., 2007). Fitzpatrick et a1. (2007), in a study of
the Muskegon River Watershed in Michigan, found all major cations (N a+, Mg”, K+
and Ca2+), anions (HCO3', Cl', SO42", NOx and F') and most trace elements (V, Co, Cu,
Se, Rb, Sr, Mo, Cd, Ba and U) are higher in both agricultural and urban streams than
reference forested streams. Cr and Pb were elevated in urban as compared to
agricultural and forested sites. Regression analysis of ﬁrst-order catchment data
indicated a positive and exponential relationship between NO3', acid neutralizing
capacity, Cl', 8042' and base cations and the increasing extent of urban plus
agricultural area (Williams et al., 2005).

Land use patterns and their contribution to P exports and loads is also well
documented (Glandon et al., 1980; Lehrter, 2006; Lewis et al., 2007; Ontkean et al.,
2005; Sonoda and Yeakley, 2007; Tsegaye et al., 2006; Winter and Duthie, 2000).
Glandon et a1. (1980), in a study of P and N loading from urban, agricultural and
wetland sources, found annual P loadings of 0.595 kg ha", 0.180 kg ha'1 and 0.023 kg
ha'1 for agricultural, urban and wetland land use, respectively. Fewer studies quantify
DP exports and their relationship to land use. One such study by Coulter et al. (2004)

documented armual orthophosphate ﬂuxes of 0.28 kg ha", 0.12 kg ha'1 and 0.07 kg ha”

I . . . .
for agricultural, mlxed and urban land uses, respectively, In eastern Kentucky.

Researchers have found large variations in subwatershed stream DP concentrations
within the same watershed and attribute this variability to various factors, including
seasonal inﬂuences, landscape characteristics, hydrology and wetland processes
(Novak et al., 2004; Novak et al., 2003; Ontkean et al., 2005).

Lack/weakness of phosphorus relationships

Many studies have demonstrated relationships between land use, human

disturbance and surface water chemistry (Liu et al., 2000; Momen et al., 1996;
Tsegaye et al., 2006; Zampella et al., 2007). Although such work has included P,
patterns have been difﬁcult to recognize between P, stream chemistry and land use by
commonly used multivariate statistical techniques (e. g., factor analysis, analysis of
variance (ANOVA), multiple regression and cluster analysis). Liu etal. (2000) used
factor analysis on 14 subwatersheds throughout the Chesapeake drainage basin to
identify the related chemistry variables and their relationship with land cover and
physiography. They found DP and PO43' had high loadings on a single factor
unrelated to other variables which they termed the P factor. Further, for the P factor,
regression analyses suggested no signiﬁcant inﬂuence of land cover on P. In a study
of the Wheeler Lake Basin of northern Alabama and southern Tennessee, Tsegaye et
al. (2006) used ANOVA to identify differences in stream water quality properties in
response to seasonal variation, land use practices and location. No signiﬁcant
relationships were found for DP land use, season or the interaction between land use
and season. Zampella et a1. (2007) used ANOVA and multiple regression in a study
of the Mullica River Basin, a major New Jersey Pinelands watershed, to describe the

relationship between water quality and land use patterns. In this study, total P (TP)

10

did not appear to vary in relation to land use intensity. Momen et a1. (1996) applied
multivariate statistics in detecting temporal and spatial patterns in water chemistry
from Lake George, New York. Their cluster analysis identiﬁed a linear component,
which included organic P, which explained a small percentage (10 — 23%) of the total
TP variation.

Contributors to phosphorus relationships

Deﬁning the relationship between land use and solute concentrations in large
urban and agricultural watersheds is confounded by landscape complexity combining
a large variety of human activities, land cover types, topography, geology, soils and
vegetation (Herlihy et al., 1998; Norton and Fisher, 2000; Williams et al., 2005).
Despite the general trend of higher nutrient exports from disturbed watersheds, it
remains difﬁcult to predict ﬂux rates even if land use patterns are well-characterized
(Puckett, 1995; Vanni et al., 2001). Several factors can potentially account for
variation in nutrient ﬂux rates from watersheds of Similar land use, including
watershed area, spatial patterns within a landscape, areas which are sources or sinks
for nutrients, soil characteristics and the distribution and extent of riparian buffers
(Dillon and Kirchner, 1975; Gburek and Sharpley, 1998; Puckett, 1995; Sharpley,
1995; Soranno et al., 1996; Vanni et al., 2001).

In addition to the spatial and physical complexities of large mixed use
watersheds, numerous studies have identiﬁed temporal effects associated with season
hydrological and biological processes. In the Wheeler Lake Basin of northern

Alabama, total N (TN), particulate P (PP) and TP concentrations peaked during the

Summier, TN concentration was lowest in the fall and PP and TP were low in the

11

spring (Tsegaye et al., 2006). Yuan et a1. (2007) studied chemical species as
i ndi cators for the tracking and apportionment of P within the Table Rock Lake
Watershed, Missouri. They found no chemical species had consistent concentration
ratios to P due to high seasonal variation of P concentrations. In sub-basins of three
d i fret-em watersheds emptying into an estuary in Mobile Bay, Alabama, P
concentrations were strongly regulated by land use/land cover, discharge and
seasonality (Lehrter, 2006). A seasonal trend in the daily P dataset was more evident
Wi th lower concentrations during intermediate ﬂows than during base ﬂow in the
Ki vet Kennet, England (Evans and Johnes, 2004). Dorioz et a1. (1998) state, “Within
the hydrological context of a watershed many physical, biological and chemical
processes function to determine the patterns of storage and transport of P.” Nonpoint
inputs of nutrients are derived from activities dispersed over wide areas of land and
are variable in time due to effects of weather (Carpenter et al., 1998).
Mulholland and Hill (1997) found two general modes of control of stream
IllJtI’ient concentrations: (1) catchment inﬂuence via seasonal variation in the
dominant hydrologic pathway, and (2) in-stream biological inﬂuence via high rates of
biotic nutrient uptake during the spring and autumn.

Ca 1‘ Chment inﬂuence

For catchment control, studies by Mulholland (1993) and Mulholland and Hill

( 1 997) indicate variation in the relative importance of different ﬂow paths. In
particular, deep ﬂow permits geochemical interaction with bedrock and shallow lateral
ﬂ OW through the upper soils results in substantial temporal variation in stream water

:1 -
utrl ent concentrations. Such hydrological processes helped explain the temporal

12

vari ation within, and spatial variation between, two streams in southeastern Minnesota
with regard to NO3':TP ratios (Green et al., 2007).

B i0 logical inﬂuence

For biological inﬂuence, surveys and experiments have shown increases in P

concentrations lead to increases in algal biomass as chlorophyll a in lakes
(Edmondson and Lehman, 1981; Smith, 1982), reservoirs (Havel and Pattinson, 2004)
311d streams (Morgan et al., 2006). Morgan et a1. (2006) observed that in high-nutrient
agricultural streams, timing and density of algal mats can vary signiﬁcantly among

y e ars and between streams. Biological effects are more prevalent in lakes and

re servoirs because they often provide gradients in light and nutrients and retention

time for primary production (Kimmel et al., 1990; Knoll et al., 2003).

Restrictions for data analysis

In addition to spatial, physical and temporal complexities, several structural
prOblems have been identiﬁed in relating land use to ecological indicators in streams.
These include collinearity of land use percentages and spatial autocorrelation of land
“Se and stream data from nesting of sites and serial dependence of time-series data
(King et al., 2005; Momen et al., 1996; Zampella et al., 2007). The unidirectional
ﬂ 0W of a stream system is such that data from some sampling locations may not be
independent observations from other sampling locations. The values at a downstream
l Ocation are related and correlated to values at the upstream locations. Also, repeated

IIz'leasures over time are not independent from previous sampling dates. Watershed

l':‘<'=ll‘aeterlstlcs such as land use have overlapping reglons when sampling Sltes are

13

Mixed linear model

The MLM provides a method that overcomes these restrictions by permitting
the data to exhibit correlation and heteroscedasticity (Taskinen et al., 2008). A MLM
i s a generalization of the standard linear model, making it possible to model not only
the means of data but their variances and covariances as well. Covariance parameters
are required when the experimental units can be grouped and the data within a group is
c orrelated and repeated measurements are taken on the same experimental unit and are
c o rrelated or exhibit variability that changes (Taskinen et al., 2008).

MLM studies in the biogeochemical sciences are rare but have been used in
some environmental applications. Taskinen et al. (2008) used the MLM to study the
effects of spatial variation in the saturated hydraulic conductivity on the variation of
Over] and ﬂow in southern Finland. Lehrter (2006) determined station differences in
O bserved constituent concentrations using a MLM with station as a ﬁxed variable and
time as a random variable in a study in the Dog River watershed in Alabama. MLMS
Were used to identify land cover classes that exhibited signiﬁcant relationships with
in- Stream nutrient concentrations in a prairie stream in the Mill Creek Watershed in
I(Eltlsas (Dodds and Oakes, 2006). In that study, spatial autocorrelation was accounted
for using MLM for nested sampling locations. Incorporating temporal variables in the
MLM analyses with appropriate covariance parameters can identify and quantify the
S'3rclsonal effects attributable to catchment and biological inﬂuences. The remaining

8 i gniﬁcant ﬁxed effects can be evaluated using various statistical methods to develop

3 land use, stream chemlstry and trace element relationships.

14

Catchment inﬂuenced DP cycling

Researchers have found large variations in subwatershed stream DP
concentrations within the same watershed and attribute this variability to various
factors (Novak et al., 2004; Novak et al., 2003; Ontkean et al., 2005). Some of these
inc lude seasonal inﬂuences, landscape characteristics, hydrology and wetland
processes. In the Herrings Marsh Run Watersheds (Duplin County, North Carolina),
N ovak et a1. (2003) conclude higher DP mass loads were exported during base ﬂow
than during storm conditions.
They found that mean stream DP concentrations varied throughout the watershed. The
percentage of TP as DP was affected by land cover in all sub-basins in the Crowfoot
Creek Watershed (Wheatland County, Alberta, Canada) (Ontkean et al., 2005). In that
Study, the percentage of TP as DP decreased with increased cropped land and
increased where grassland acted as a buffer.
Catchment inﬂuenced stream segments are connected to the landscape
t1'11‘()11gh a system of hydrologically active ﬁelds linked to an outlet through a
hydrologic network (Jordan-Meille et al., 1998). P is retained and transformed at the
Watershed-scale through this network. P and N availability vary with seasonal
fertilizer application. Their supply, modiﬁcation and transport through different ﬂow

paths produces the greatest variability in nutrient delivery to the stream system

C Mulholland and Hill, 1997).
BiOIOgical inﬂuenced DP cycling

Biological inﬂuenced stream segments have been associated with increased

1) I—ltri ent availability for biological activity. TN, TP and benthic and total chlorophyll

15

concentrations were positively correlated to the percentage of upstream land covered
[33/ impervious surfaces in the Malibu Creek Watershed, California (Busse et al.,

2 o ()6). In a study of six streams in Indiana and Michigan, Bemot et a1. (2006)

demonstrated that biological activity in agriculturally inﬂuenced streams is high

re 1 ative to more pristine streams. This increase likely inﬂuences nutrient retention and

transport to downstream ecosystems.

The biological activity in streams (Figueroa-Nieves et al., 2006; Morgan et al.,

2 O 06; Mulholland, 2004; Stevenson et al., 2006), lakes (French and Petticrew, 2007;
Grover and Chrzanowski, 2004; Hékanson, 2005; Reed-Andersen et al., 2000; Yuan et
a1 - , 2007) and reservoirs (Havel and Pattinson, 2004; Reed-Andersen et al., 2000;
S clneiber and Rausch, 1979) has been shown to regulate many variables, including
concentrations of P, suspended solids, many water quality variables and water clarity.
Stevenson et al. (2006) state that many measures of algal biomass and nutrient
avai lability were positively correlated in a study of Michigan and Kentucky streams.
Lakes are the most extensively studied biologically inﬂuence waterbodies.
Re Searchers have identiﬁed relationships between chlorophyll a, TP and DP (French
atld Petticrew, 2007; Hakanson, 2005; Momen et al., 1996) in lake systems.
Described as “river-lake hybrids,” reservoirs or impoundments represent a transition
Zone from lotic to lentic ecosystems. They encompass intermediate characteristics that
deﬁne both lakes and rivers (Kimmel et al., 1990; Wall et al., 2005). Kelly (2001), in
a Study in the Rio Grande and Colorado basins, found that the connectivity of the
ac] uatic system with the landscape is apparently disrupted by processes within

Servorr systems. This concept of process disruption by reservons has been termed

16

Serial discontinuity (SDC) and results in large changes in solutes (Ward and Stanford,
1 9 9 5 3. These changes persist downstream in the absence of signiﬁcant additional
so 1 ute inputs. Reservoir processes may be linked for upstream/downstream reservoirs
that are located relatively close in a series (Kelly, 2001; Stanford and Ward, 2001).
Pre dieting future P concentrations
It has long been recognized that P transports in and from catchments are

(:0 ntrolled by climate, geology, topography and anthropogenic inﬂuences (Dillon and

Kirchner, 1975). Models of P transfers range from simple conceptual models to more
complex process-based models. Scientists use both theoretical and empirical
approaches to prediction. Theoretical predictions are based on a theory of a process or
mechanism. However, because of the complexity of catchment systems, the spatial
Variation of characteristics that control P loss hampers the performance of these
models (van der Perk et al., 2007). Empirical predictions are based on curve ﬁtting or
pattern recognition without an attempt to represent underlying mechanisms. These
mOdels are frequently developed by predicting the contemporary value of a variable
from simultaneous values of other variables. Then, by assuming contemporary

relationships hold across time, scientist use contemporary models to make future

predictions (Carpenter, 2002).

Research Hypothesis

The goal of this research is to use stream biogeochemistry to enhance the

thlderstanding of P dynamics (e. g. sourcing, fate and transformation) in a mixed land

use Watershed under regulatory pressure from a P TMDL. The working hypothesis is

17

that DP, stream biogeochemistry and land use have unique relationships and
patterns that can be quantiﬁed, and that certain DP processes have characteristic
biogeochemical/land use signatures. If true, these biogeochemical/land use
signatures can be used to identify processes that control DP cycling at various
locations within the watershed, and the outcome of P mitigation efforts can be
predicted.

A crucial assumption of this research is that temporal trends in DP change DP,
biogeochemical and land use patterns over time. By quantifying and removing the
underlying DP temporal trends, more and stronger correlations are anticipated between
DP, stream biogeochemistry and watershed land use.

Quantifying DP temporal trend from catchment inﬂuences should result in
strong correlations between DP and stream chemistry parameters derived from the
same sources as P. NO3' and K+ are applied with P as fertilizers for agricultural
production and are also susceptible to loss to surface and groundwaters. Changes in
pH, alkalinity and speciﬁc conductance associated with urban inputs should relate to
DP exported from these environments. Urban and agricultural land uses, as sources of
P, are expected to relate to DP. Other land uses contributing to transformations in P
form may also be identiﬁed.

For biological inﬂuenced regions of the watershed, quantifying the DP
temporal trends should produce strong correlations between DP, stream solutes and
stream chemistry that are modiﬁed by biological nutrient uptake and release. DP and
N03' concentrations should be highly correlated as essential nutrients for biological

activity. Exchanges are expected between PP and DP fractions as DP is removed from

18

the water column and assimilated into biotic biomass. Biomass PP should be released
as DP through macroinvertebrate consumption. Photosynthetic effects on pH,
alkalinity and Ca2+ precipitation from primary productivity may also be evident.
Inferences about the P cycling in the KRLAW should be possible from the
relationships and patterns between DP, stream biogeochemistry and land use. DP
cycling inferences and historical KRLAW P data can be used to develop an empirical
model for predicting future growing season mean P concentration at the inlet of Lake
Allegan, the impaired waterbody. This model and the inferred P cycling should

provide insight into the effectiveness and outcome of various P reduction strategies.

Study Site

The Kalamazoo River/Lake Allegan Watershed (KRLAW) is a 4200 km2
watershed located in the southwestern portion of Michigan’s Lower Peninsula (Figure
1.2) beginning at the headwaters of the Kalamazoo River and ending at the outlet of
Lake Allegan. The Kalamazoo River drains into Lake Michigan approximately 35 km
downstream from the outlet of the study area. The geology of the KRLAW is
dominated by superﬁcial glacial deposits overlying a bedrock stratigraphy that
progresses from Saginaw Formation in the upper northeast through Bayport Limestone
and Michigan and Marshall Formations in the central portion. The southeast,
northwest and central portions progress from Marshall Formation to Coldwater Shale.
Coldwater Shale dominates the southwest and west regions of the KRLAW (Westjohn
and Weaver, 1997). Characteristic of Michigan’s Lower Peninsula, the Kalamazoo

River is predominantly composed of Ca-HCO3 waters (Wahrer et al., 1996).

19

The Kalamazoo River has a legacy of serious industrial and nutrient pollution
(Heaton, 1999). Largely rural, the watershed is dominated by agriculture and forests.
Land use consists of agriculture (46%), upland forest (21%), urban (9%), upland open
(9%), non-forested wetlands (8%), lowland forest (5%) and open water (2%). Morrow
Lake and Lake Allegan are two large ﬂow-through reservoirs created for electrical
generation within the KRLAW.

Lake Allegan is a 6.4 km2 impoundment formed in 1936 by the building of the
Caulkins hydroelectric darn. TheUSEPA conducted a National Eutrophication Study
of Lake Allegan in 1972 and classiﬁed it as hypereutrophic (USEPA, 1975). The
limiting nutrient contributing to eutrophication is P. Additional Michigan Department
of Natural Resources (MDNR) studies in 1988, 1994, 1996 and 1997 indicated that
Lake Allegan had improved since the 19705. However, it was still hypereutrophic,
with high nutrient and chlorophyll 0 levels, excessive turbidity, periodic nuisance algal
blooms, low dissolved oxygen levels and an unbalanced ﬁsh community (Heaton,
1999). Lake Allegan was listed in the 1996 and 1998 reports required by section
305(b) of the Clean Water Act as a waterbody not attaining water quality standards
(Kosek, 1997; Wycheck, 1998) and was included on Michigan’s 303(d) list of
impaired surface waters requiring development of a TMDL for P. The USEPA
approved the Lake Allegan/Kalamazoo River P TMDL in 2001, setting a TP goal in
Lake Allegan of 60 pg L'1 and an inlet goal of 72 pg L'1 (Heaton, 2001). Morrow
Lake was used as the reference impoundment to determine Lake Allegan TMDL

goals.

20

Formed in 1939 for the Bryce E. Morrow Power Plant, Morrow Lake is a 4.0
km2 impoundment. Lake Allegan and Morrow Lake share similar land use
characteristics, size and average depth. Morrow Lake has desirable water quality
characteristics, including no reported algae blooms, low chlorophyll a concentrations,
transparency over three feet and a balanced ﬁsh community (Bohr and Liston, 1987;
Heaton, 2001). These attributes are the basis for the Lake Allegan/Kalamazoo River
TMDL goals.

From its inception in 1998, the Lake Allegan/Kalamazoo River TMDL effort
has been community based, including landowners, industries, government, community
organizations and citizens. These stakeholders collaborated to develop the TMDL
goals and P reduction implementation plan. The KRLAW was chosen for this study
because of its diverse landscape for examining patterns in P, stream chemistry and
land use; regional P reduction challenges; and the TMDL stakeholder interest in P
cycling. Furthermore, some biogeochemical data are available from past Michigan
Department of Environmental Quality (MDEQ) and MDNR studies for selected

locations in the watershed.

Methods
Sample collection and in-stream measurements
Weekly samples were taken from the thalwag portion of the streams in the
KRLAW (Figure 1.4). Thirteen and 15 locations (Table 1.1) were sampled during the
2005 and 2006 growing seasons (April through September), respectively. Water

samples were collected using a Van Dom-style horizontal sampler. Filtered samples

21

were ﬁltered through a 0.45 pm Millipore disposable ﬁlter. Unﬁltered and
unpreserved 50 mL samples were retained for TP. Filtered and unpreserved 50 mL
samples were retained for DP. Filtered and preserved by acidiﬁcation with HN03 to
pH < 2, 50 mL samples were collected for cation and anion analysis. Samples were
kept on ice in the ﬁeld and stored at 4 °C until analysis. TP and DP analyses were
performed typically within three to seven days of collection. Filtered, unpreserved
and unrefrigerated 30 mL samples were collected for alkalinity and analyzed the day
of collection. One liter samples were collected at seven locations (BR, WC, KM, KC,
KS, KA and KD) in 2006 for chlorophyll a and refrigerated and maintained in a dark

environment until analysis, typically less than two weeks.

 

 

Figure 1.4: Sampling locations A in the Kalamazoo River/Lake Allegan Watershed,
and the positions of Morrow Lake and Lake Allegan.

22

ln-stream measurements were taken for temperature, pH, speciﬁc conductance,
dissolved oxygen and percent dissolved oxygen using a Hydrolab Surveyor 4a and
Minisonde 4a sonde.

The KRLAW was synoptically sampled for trace metals on four dates (June 9,
2005, September 13, 2005, August 8, 2006 and September 12, 2006) corresponding to
weekly sampling and in-stream measurement dates. Synoptic sampling was
performed at or near stream baseﬂow conditions. Clean sampling techniques detailed
by Fitzpatrick et al. (2007) and Wayland et al. (2003) were used to minimize possible
trace element contamination. Trace element samples were ﬁltered through a 0.45 um
Aquaprep disposable ﬁlter and acidiﬁed with Optima grade HN03 to pH < 2 and were
stored at 4 °C.
Chemical analysis

TP and DP samples were digested using persulfate digestion (Langner and
Hendrix, 1982; Valderrama, 1981) and were analyzed by UV/V IS spectrometer
(Therrno) using an ammonium molybdate/ascorbic acid method to measure
absorbance at 885 nm (Wetzel and Likens, 2000). PP was calculated from the
difference between TP and DP. Chlorophyll a was analyzed by ﬂuorometer (Sequoia-
Tumer) aﬁer ﬁltering and ethanol extraction (Welschmeyer, 1994). Ca2+ and Mg2+
were measured using ﬂame atomic adsorption spectroscopy (Perkin-Elmer). Na+, K+,
Cl', NO3' and 8042' were analyzed using ion chromatography (Dionex). Alkalinities
were determined by Gran titration with H2804. Analytical accuracy was checked
using the charge balance method (Freeze and Cherry, 1979). For charge balance

errors greater than 10% the source of the error was identiﬁed (e. g., recording errors or

23

analysis errors) and corrected, including reanalysis if required. For the ﬁnal dataset,
all sample charge balance errors were less than 8%. The weekly sampled stream
chemistry dataset is given in Appendix 1.

Trace elements (B, A1, Sc, Ti, V, Cr, Mn, Fe, Co, Ni, Cu, Zn, As, Se, Rb, Sr,
Cd, Sn, Ba, Pb, U and M0) were quantiﬁed using a Micromass Platform Hexapole
inductively coupled plasma-mass spectrometer. Results below the detection limits for
each element were eliminated from the data. This eliminated all results for Cu and
some of the results for Co, Ni, Cd, Sn and Pb. The trace element dataset is given in
Appendix 11.
Land use identification

Land use was quantiﬁed for the catchment draining to each sampling location
from geographic information system (GIS) data obtained from the Michigan
Geographic Data Library (MiGDL). The 2001 Lower Peninsula Land Cover/Use
Theme (MiGDL, 2007), derived from classiﬁcation of Landsat Thematic Mapper
imagery was clipped by the sample watersheds delineated from the Kalamazoo River
Watershed Theme (MiGDL, 2007) using ArcView GIS (Environmental Systems
Research Institute, Inc., 1992 — 1999).

Land use percentages were summarized for each sample catchment at the class
levels of (I) urban, (II) agricultural, (III) upland openland, (IV) upland forest, (V)
water, (VI) lowland forest, (V II) non-forested wetlands and (VIII) bare/sparsely

vegetated (Table 1.1).

24

Soil group identification

Soil groups were quantiﬁed for the catchment draining to each sampling
location from GIS data obtained from the MiGDL (MiGDL, 2007). The 1994 State
Soil Geographic (STATSGO) database for Michigan Theme was clipped by the
sample watersheds delineated from the Kalamazoo River Watershed Theme using
ArcView GIS (Environmental Systems Research Institute, Inc., 1992 — 1999).

Twenty soil groups identiﬁed by map unit ID (MUID) were represented in the
KRLAW. The 13 MUIDs and their corresponding soil group common to all sampled
catchments that reﬂect at least 90% of individual catchment soil groups is given in
Table 1.2.
Historical data sources

In addition to P concentration data from this KRLAW study, historical data
from other sources were obtained (Table 1.3, Appendices III and IV). P concentration
data collected by the MDEQ for the Kalamazoo River was acquired from MDEQ
reports (Heaton, 1999; Heaton, 2003), STORET, the EPA’s Computerized
Environmental Data System (USEPA, 2008a) and through personal communications.
Point source loading data were obtained from the Kalamazoo River TMDL Point
Source Tracking System (Kieser & Associates, 2008) and an MDEQ report (Heaton,
1999). Discharge information for gaging stations 04106000, Kalamazoo River at
Comstock, MI, and 04108670, Kalamazoo River at New Richmond, M1, were

obtained from the USGS Annual Water Data Reports (U SGS, 2008a; USGS, 2008b).

25

 

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27

Research Approach

The working hypothesis is that DP, stream biogeochemistry and land use have
unique relationships and patterns that can be quantiﬁed and that certain DP processes
have characteristic biogeochemical/land use signatures. This hypothesis will be
explored for the KRLAW through intensive sampling, various statistical analyses,
geographic information system land use/land cover databases and historical data.
While other research has linked a limited number of stream chemistry and land use
parameters to DP, this research is the ﬁrst to separate temporal trends in DP to
increase the number and strength of correlated stream chemistry and land use
parameters. The approach in this proposal is unique in the use of MLMS to overcome
structure restrictions in longitudinal, time-series data. The analysis presented provides
an approach for inferring P cycling using stream biogeochemistry and land use
information that leads to a better understanding of the interaction between competing
processes and their potential effect on the outcome of P mitigation strategies.

Chapter 2 develops methods to quantify the temporal trends in DP to increase
and strengthen the relationships between DP, stream chemistry and land use. An
approach is presented for separating data by catchment or biological inﬂuence and
uses MLMs to quantify DP temporal trends. The results of these analyses are used to
remove temporal trends and site effects from the DP data, allowing the investigation
of DP cycling using other common statistical methods.

Chapter 3 explores DP cycling in the catchment inﬂuenced MLM results and
analyzes the temporal and site adjusted DP and land use relationships. A DP source

component associated with agricultural and urban land use and a catchment DP

28

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29

process represented by lowland forest land use are identiﬁed. An approach for
evaluating the susceptibility of KRLAW subwatersheds to low, medium and high DP
exports based on readily available land use data is presented. To explore the existence
and interaction of P source and P process dynamics, Pearson’s correlation coefﬁcients
and principal factor analyses are used to identify patterns in temporal and site adjusted
DP, land use, stream chemistry, trace elements and soil groups. The implications of P
management practices on DP are considered in light of the inferred P cycling.

Chapter 4 evaluates DP cycling in the biological inﬂuenced MLM results and
analyzes the temporal and site adjusted DP and stream chemistry relationships. Large
serial ﬂow-through impoundments are identiﬁed as environments for biological
inﬂuence including algal productivity. Impoundment processes are explored that
disconnect the stream system from the landscape, control P cycling and regulate
downstream P forms. The compensatory nature of these processes to offset P
reduction efforts and delay the downstream response is discussed.

Chapter 5 uses inferences into DP cycling developed in Chapters 2 through 4
to develop an empirical TP model for the KRLAW based on contemporary trends in
historical TP and discharge data. The model is used to predict the future growing
season mean TP concentration to Lake Allegan. Dependencies between TP
concentration and various discharge parameters are identiﬁed through this model.
Probabilities are predicted for attaining the 72 pg L'1 TMDL P goal in 2012 without
discharge adjustments. Discharge adjusted inlet concentration to Lake Allegan is
forecasted for 2012. The effectiveness and outcome of various point and nonpoint P

reduction strategies in the KRLAW are presented.

30

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38

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39

CHAPTER 2
IDENTIFYING TEMPORAL TRENDS IN WATERSHED DISSOLVED
PHOSPHORUS USING A MIXED LINEAR MODEL APPROACH
Abstract

Patterns in suites of chemicals and their relationship with land use can provide
insight into the processes inﬂuencing eutrophication. In a two-year study of the
KRLAW, these patterns are used to understand the cycling (sources, pathways, fate) of
chemicals in the watershed. Although such work is being done for P, patterns and
relationships of P to stream chemistry and land use are not easily identiﬁed because of
temporal effects and structural restrictions in the data. Two temporal effects are
identiﬁed: a catchment inﬂuence and a biological inﬂuence. Structural restrictions
are produced by autocorrelation of the test series, correlation between factors and
nesting of sample locations. To address these issues, mixed linear models (MLM) are
applied to watershed data segregated by inﬂuence.

The catchment MLM identiﬁed a temporal trend by year and week-within-year
and correlations between DP and Mg“, K+, NO3', Na+, pH, alkalinity, speciﬁc
conductance and lowland forest, agricultural and urban land uses. The biological
MLM identiﬁed a temporal trend by year and correlations between DP, PP, NO3',
SO42} Cl', pH and urban land use.

Results conclude temporal trends in DP are identiﬁable, differ by inﬂuence,
vary and change patterns over time. Quantifying temporal trends improves the
number and strength of correlated chemistry and land use parameters. Further studies

of these correlations advances the understanding of DP cycling within the watershed.

40

Introduction

Cultural eutrophication (anthropogenic nutrient loading to aquatic ecosystems)
is a persistent condition of surface waters and a widespread environmental problem
(Carpenter, 2005). Stream chemistry reﬂects the cumulative effects of
biogeochemical and hydrological processes occurring throughout the watershed
(Mulholland, 2004). However, nonpoint inputs of nutrients are derived from activities
dispersed over wide areas of land and are variable in time due to effects of weather
(Carpenter et al., 1998). Many studies have demonstrated relationships between land
use/land cover, human disturbance and surface water chemistry (Liu et al., 2000;
Momen et al., 1996; Tsegaye etal., 2006; Zampella et al., 2007). Although such work
has included P, patterns have been difﬁcult to recognize between P, stream chemistry
and land use by commonly used multivariate statistical techniques. Previous studies
have used factor analysis (Liu et al., 2000), analysis of variance (Tsegaye et al., 2006),
multiple regression (Zampella et al., 2007) and multivariate statistics (Momen et al.,
1996), ﬁnding few and/or weak correlations between P and watershed parameters.

The lack and/or weakness of statistical relationships between P, stream
chemistry and land use is counter-intuitive in light of the many studies that have
identiﬁed agriculture and urban regions as sources and exporters of P and other
chemical solutes (Coulter et al., 2004; Lewis et al., 2007). This inconsistency has led
us to propose two potential sources that obscure the existing P, stream chemistry and
land use relationships: (1) two distinct and variable temporal effects, and (2) structural
restrictions in the data not easily addressed with common multivariate statistical

techniques.

41

First, Mulholland and Hill (Mulholland, 1993; 1997) found two general modes
of control of stream nutrient concentrations: catchment control via seasonal variation
in the dominant hydrologic pathway, and in-stream control via high rates of biological
nutrient uptake during the spring and autumn. They found that variation in the relative
importance of different ﬂow paths and in-stream biological modiﬁcation of catchment
delivered nutrients can result in substantial temporal variation in stream water nutrient
concentrations. In the context of this study, catchment inﬂuence is exhibited through
landscape control of stream chemistry and biological inﬂuence is an observable
modiﬁcation of catchment controlled stream chemistry resulting from biomass
production or consumption.

Second, several common structural problems have been identiﬁed in relating
land use to ecological indicators in streams. These include collinearity of land use
percentages and spatial autocorrelation of land use and stream data from nesting of
sites and serial dependence of time-series data (King et al., 2005; Momen et al., 1996;
Zampella et al., 2007). The mixed linear model (MLM) provides a statistical method
that overcomes these problems by permitting the data to exhibit correlation and
heteroscedasticity. A MLM is a generalization of the standard linear model that
makes it possible to model not only the means of data but their variances and
covariances as well. Covariance parameters are required when the experimental units
can be grouped, the data within a group is correlated and repeated measurements are
taken on the same experimental unit and are correlated or exhibit variability that

changes (Taskinen et al., 2008).

42

Mixed linear model studies in the biogeochemical sciences are rare, but they
have been used in some environmental applications (Dodds and Oakes, 2006; Lehrter,
2006; Taskinen et al., 2008). For example, Taskinen et al. (2008) used the mixed
linear model to study the effects of spatial variation in the saturated hydraulic
conductivity on the variation of the overland ﬂow in southern Finland. The MLM has
been identiﬁed as a statistical method that addresses the various structural restrictions
within the data. Using the MLM, variable temporal trends are quantiﬁed that
previously obscured the relationships and patterns between P, stream chemistry and
land use.

The hypothesis is that DP concentrations are correlated to land use and stream
chemistry, but the speciﬁc patterns change over time. To test the hypothesis, stream
chemistry and land use data are separated by catchment or biological inﬂuence and
MLMS are used to identify temporal trends and the relationships between DP, stream
chemistry and land use.

For this study, the segregation of catchment and biological inﬂuenced data and
their separate analysis using MLMS that include temporal variables in the ﬁxed effects
provides a unique approach for identifying temporal trends in watershed DP. The
approach develops a method to characterize the catchment and biological inﬂuenced
temporal trends in DP. Quantifying temporal trends improves the number and strength
of DP correlations between stream chemistry and land use variables. Results indicate
temporal trends are responsible for changing the relationships over time between DP,
stream chemistry and land use. This supports the hypothesis that DP concentrations

are correlated to land use and stream chemistry, but the speciﬁc patterns change over

43

time. Accounting for temporal DP trends allows further evaluation of the remaining
ﬁxed and random effects to improve our understanding of anthropogenic impacts on

DP cycling.

Methods

Temporal trends in DP were investigated using the KRLAW stream chemistry
dataset (Appendix I) and land use description (Table 1.1.). The study site, sampling
locations, sampling methods and chemical analyses are described in Chapter 1.
Catchment and biological inﬂuence separation

Temporal trends in DP are derived from catchment inﬂuences (climate, land
use inputs and hydrology) and biological inﬂuences (algal production and macro-
invertebrate grazing). Catchment inﬂuences are assumed to drive temporal trends
unless biological inﬂuence is identiﬁed. PP, chlorophyll a, alkalinity and Ca2+
concentrations are used to indicate sampling dates and locations under biological
inﬂuence.

Biological indicators are most evident at reservoirs because reservoirs often
provide gradients in light and nutrients and retention time for primary production
(Kimmel et al., 1990; Knoll et al., 2003). Nutrient uptake, primarily P and N, occurs
from inﬂow to outﬂow during productivity (Kennedy and Walker, 1990). Since N is
not the limiting nutrient, surplus NO3' is available early in the growing season and
does not provide a clear pattern for biological inﬂuence. In a study of 12 Ohio
reservoirs, a high correlation was found between primary productivity, TP and

chlorophyll a (Knoll et al., 2003). Chlorophyll a was used as an indicator of

44

biological activity in 2006 when measurements were taken. There is a strong link
between algae and PP, but the relationship between algae and DP forms is weak (Neal
et al., 2006). The comparison of PP from inlet to outlet provided a clearer signal of
algal activity than TP or DP and was used as another biological indicator.

While chlorophyll a and PP provide indication of biological productivity, they
are associated with the particulate, not dissolved fraction and are not sufficient to
determine the transition between the stream chemistry produced by catchment
inﬂuence and biological inﬂuence. The alkalinity of most fresh waters is imparted by
the presence of bicarbonates and carbonates, and the COz—HCO3—C032' equilibrium
system is the major buffering mechanism in those waters (Wetzel, 2001). The C02 in
water can be substantially inﬂuenced by photosynthesis and respiration by aquatic
organisms, leading to a decrease in alkalinity (Wetzel and Likens, 2000). In a solution
where calcium bicarbonate is in equilibrium with C02, H2CO3 and CO32' , CO;
assimilated by photosynthetic organisms will precipitate calcite to reestablish
equilibrium (House, 2003; Wetzel, 2001). Precipitation of calcite is indicated by a
decrease in dissolved Ca2+ concentration. Decreases in alkalinity and Ca2+ from
reservoir inﬂow to outﬂow are also used as biological indicators. The biological
indicators are evaluated for the ﬁrst large reservoir (Morrow Lake) in the Kalamazoo
River system with a retention time greater than seven days.

Reservoirs with retention times greater than seven days provide an
environment for phytoplankton production, and upstream reservoirs have been
demonstrated to inﬂuence downstream systems (Kimmel et al., 1990; Straskrabova et

al., 1973). TP concentrations at locations upstream and downstream are compared to

45

Morrow Lake concentrations to determine if they are also under biological inﬂuence
on the same sampling dates. TP was used for this evaluation because two biological
processes, algal productivity and macro-invertebrate grazing, have opposite effects on
PP, chlorophyll a, alkalinity and Ca2+ concentrations. Locations that maintained the
trend in TP seen at the outlet of Morrow Lake were included as biological inﬂuenced
locations for the same dates as the outlet of Morrow Lake.
Statistical analysis

The catchment and biological datasets present some unique challenges that
cannot be addressed with commonly used statistical analyses such as ANOVA,
general linear models and factor and cluster analyses. The physical locations sampled
in the stream system result in collinearity of land-cover percentages and spatial
autocorrelation of land cover and stream data from nesting of sites and serial
dependence of time-series data. This scenario occurs in longitudinal studies where
repeated measurements are taken over time and the repeated measures could be spatial
or multivariate in nature (SAS, 1999). The MLM, a generalization of the standard
linear model, makes it possible to model not only the means of data, but also the
variances and covariances that exist due to nesting and serial dependence (Taskinen et
al., 2008). The separation of the data by dates and locations yields unbalanced
designs. The MLM also accommodates unbalanced designs (Milliken and Johnson,
1984; University of Oregon, 2007). A detailed description of mixed linear model
theory and its application can be found in the literature (Littel etal., 2006; Milliken

and Johnson, 1984; SAS, 1999; Searle, 1971) and is summarized in Appendix V.

46

In general, the standard GLM can be written as

y = XB + a (2.1)
In contrast, the MLM takes into account correlations and heterogeneities between the
terms of 8 and is written as (Searle, 1971)

y=XB+Zy+s (2.2)
where y is a vector of observations, B is a vector of unknown ﬁxed effects, X and Z
are known design matrices that relate observations to ﬁxed effects and random effects,
7 is a vector of unkown random effect predictors and 8 is a vector of residuals. y and 8
are assumed to be normally distributed with a zero mean and variance-covariance
matrices G and R respectively.

The matrix G can be conceptualized as a between-location variance-covariance
matrix and R as a within-location variance-covariance matrix (University of Oregon,
2007). Since 1 and 8 are assumed to be independent, the variance-covariance matrix
of the vector of observations y (denoted by V) from each location has the form (SAS,
1999)

V = ZGZ' + R (2.3)
Unlike the GLM, where only B requires estimation through the least squares method,
the MLM has B, 7, V, G and R as unknowns. An estimate for V using equation 2.3 is
obtained by the generalized least squares method minimization. G and R are
estimated using the maximum likelihood method (ML) incorporating a ridge-stabilized
Newton-Raphson algorithm (SAS, 1999) that can handle multi-collinearity problems.

Finally, to obtain estimates for B and y the mixed model equations are solved:

47

[xii-1x x'fz-lxz ] [ii]

2' ii-lx z' fz-Iz+f;~l 7

[x' “I
1' ﬁdy (2.4)
where the symbolsé, R, B and 7 denote estimates.

The statistical methods for this study were implemented using SAS 9.1.3
(SAS, 2007). The SAS PROC MIXED procedure uses the methods brieﬂy described
above and detailed in Appendix V to solve the MLM and to provide estimates for the
ﬁxed (B) and random effects (7). When the number of ﬁxed effects is greater than
one, a general F -statistic is constructed, allowing inferences about the ﬁxed effects
which account for the variance-covariance model (SAS, 1999).

The model is speciﬁed with repeated measures by week-within-year (Week)
because the 2005 and 2006 datasets were not contiguous. The ﬁrst week of both the
2005 and 2006 growing seasons (ﬁrst week in April) is designated as Week = 1 and
weeks are sequentially numbered through the end of the growing season, Week = 26.
The structure of the R matrix speciﬁed in the repeated statement is a direct product of
unstructured (SAS designation UN) by year and first order autoregressive (SAS
designation AR(1)) by Week input as UN@AR(1). UN is used because no deﬁned
structure is expected to exist between years. However, the nature of a stream system
in which the current value of a parameter is not independent of but related to the
previous values led to the choice of the AR(l) for the week to week structure. The
general deﬁnition of an AR(l) process indicates that the current value of the process
(tk) can be expressed as a ﬁnite linear aggregate of previous values of the process plus

a residual (8k) (Wade and Quaas, 1993).

48

In addition to the repeated measures, the model is speciﬁed with a random
effect by site. This accounts for unknown random effects between sample locations.
The structure of the G matrix is speciﬁed as variance components (SAS designation of
VC). VC speciﬁes standard variance components and a distinct variance component is
assigned to each random effect (SAS, 1999).

Separate catchment and biological MLMs model the log of DP (log(DP)) as
the dependent variable. Stream chemistry, in-stream measurements, land use and
temporal variables for Year, Week, Week2 and Week3 are the independent variables.
Log transforming DP provides a normal distribution for the dependent variable. The
forward substitution method is used where each ﬁxed effect is analyzed independently
and the most signiﬁcant effect is retained and added to the model. This iterative
process continues, evaluating the individual remaining ﬁxed effects with the
signiﬁcant effects retained from the previous iterations until none of the remaining
effects are signiﬁcant as tested through the F -statistic (p < 0.05).

Normality was tested using the Shapiro-Wilk statistic. This statistic, W, tests
the null hypothesis of normality, ranging from greater than zero to less than or equal to
one (0 < W S 1). Small values of W lead to rejecting the null hypothesis. The

Shapiro-Wilk test was performed using SAS software (SAS, 2007).

Results
Catchment and biological inﬂuence separation
The onset of the biologically inﬂuenced periods were indicated on June 7,

2005, and July 1 1, 2006, by the coincidence of a decrease in alkalinity and calcium

49

concentrations and an increase in PP from the Morrow Lake inﬂow (site KM) to the
outﬂow (site KC) (Figures 2.1 and 2.2). In 2006, chlorophyll a concentrations
conﬁrmed increasing algal activity as early as May 30, 2006 however, catchment
inﬂuences continued to dominate until July 11, 2006 as shown by the similarity in
inlet and outlet alkalinity, calcium and PP concentrations (Figure 2.2). The biological
inﬂuenced period, ended on September 27, 2005, and September 19, 2006 as some of
the biological indicators were no longer separated (Figures 2.1 and 2.2). On three
dates —June 14, 2005, July 19, 2005, and August 29, 2006— Morrow Lake reverted to
catchment inﬂuence due to runoff events on or near those dates (Figures 2.1 and 2.2).
This was most evident in the loss of the decrease in alkalinity from the inlet to the
outlet site. The outﬂow stream chemistry of Morrow Lake (site KC) provides the
reference for identifying the temporal distribution (sampling dates) of biological and
catchment inﬂuences.

The outﬂow TP of Morrow Lake (site KC) is the reference location for the
spatial distribution (sampling sites) under biological inﬂuence. Catchment inﬂuence is
referenced to the Morrow Lake inﬂow (site KM). TP concentrations at the upstream
and downstream sites are compared to sites KM and KC. The TP for sites upstream
(WC, BR, BC, KE, KG and FC) and downstream tributary sites (PC, GR and SB) have
patterns similar to site KM and are under catchment inﬂuence throughout the study
periods. The TP for sites downstream on the Kalamazoo River (KS, KK, KP, KA and
KD) have similar patterns to site KC and are under biological or catchment inﬂuence

on the same dates as site KC. The TP means of the catchment inﬂuenced sites (CISM)

50

and the biologically inﬂuenced sites (BISM) are compared to sites KM and KC in

 

 

 

 

 

 

    

 

 
      

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 
 
 
 

 

 

 

 

  

 

 

Figures 2.3 and 2.4.
40
30 ‘
0
g5: 20 ‘
5 V 0 I
I ' ' j
325 l f .L i
A E I I g
5. 300 - PT? .51 1?
go : . I:
'c I 275 ‘ P
= q, . I
3 " Onsetof ‘ :
'2 'I' 250 . . I
3', Biological \' :
g 225 - Inﬂuence E I . g
g I I ‘I
200 4 L I 4 T I i | r I I PI 9 I I I I
o I '
80 i I t g
' I
I a I
75 ' El ' I ~ I
A ~ ELI B-
SE: 70‘ 51.x IE] 135’ a a 3'5
5;; a: ' I “fl I [3’ l
o 3 65 ‘ Revertto A .;f E
60 . Catchment "’ ., " j 1
Influence (p l
55 ‘ II II
ll 1 l}
50 ‘ ‘ 1‘1 ‘ i ‘ 4 i ! i4 I J i ‘ ' i ‘ ' i ‘ i
l; . '
100 . . I
End of f l
3 8° ‘ Biological E
Inﬂuence I
.8 so I l
in =
E :1 40 ‘ I
§ 3
3
.2
E
°- 3/29 4/19 5/10 5/31 6/21 7/12 8/2 8/23 9/13 10/4

------I3 KM + KC 0 Biological . Catchment

Figure 2.1: Comparison of Morrow Lake inﬂow (KM) and outﬂow (KC)
concentrations for alkalinity, calcium and PP, outﬂow discharge and biological and
catchment inﬂuenced dates, 2005.

51

 

Discharge
(may)
3 o 8 8 8 8

 

§§§“’

AlkaIInIty
(mg L:1 as H003)
'8
0|

 

N

Bsaaaeass

 

Calcium
(mg L1 )

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1
In
g 100 Revertto
ﬁ Catchment
é’ : 3° Influence
.'_I
it c» 6°
16 3:
3 40
.9
g 20
n.
0
25
End of
20 . .
g BIologIcal
3:315 Influence
3;
D)
g 3 10
o
5
El
0 = v '

 

 

3/28 4/18 5/9 5/30 6/20 7/11 8/1 8/22 9/12 10/3
3 KM +KC 0 Biological 0 Catchment

Figure 2.2: Comparison of Morrow Lake inﬂow (KM) and outﬂow (KC)
concentrations for alkalinity, calcium, PP and chlorophyll a, outﬂow discharge and
biological and catchment inﬂuenced dates, 2006.

52

 

140
120 . 2005 A
100 ‘
80 ‘

60‘

(119 L" )

40‘

Total Phosphorus

 

20‘

 

 

0 A]AAAIIAAAJLLAIAJAILlijgkg
l I I I I

3/29 4/19 5/10 5/31 6/21 7/12 8/2 8/23 9/13 10/4

 

—e—Kc "-ﬁ-"BISM +KM “*CISM

Figure 2.3: Comparison of Morrow Lake outﬂow (KC) and biological inﬂuenced site
means (BISM) and Morrow Lake inﬂow (KM) and catchment inﬂuence site means
(CISM), 2005.

 

140

2006

120 -
100 '
80 -
60 ‘

Total Phosphorus
(I19 L"1 )

40‘

 

20‘

 

 

 

IIIIII l I l I A l I I l l I l A I I .l l I I
v 7 l l I v TI I

3/28 4/18 5/9 5/30 6/20 7/11 8/1 8/22 9/12 10/3

+Kc "-ﬁr-"BISM +KM ----'*CISM

Figure 2.4: Comparison of Morrow Lake outﬂow (KC) and biological inﬂuenced site
means (BISM) and Morrow Lake inﬂow (KM) and catchment inﬂuence site means
(CISM), 2006.

53

The stream chemistry, in-stream measurements and land use data were
separated into catchment and biological datasets by the dates and sites determined
from the inﬂuence analysis. Figure 2.5 shows the sites and sampling dates in each

dataset.

 

JP

wc —-~

 

 

 

 

Site

 

 

 

 

 

 

 

KP 1:? 3333 333333333 3.33303 33
KA <3 3333 33.303333 3.30033 33
KD 3333 333333333 3333333 33
PC
GR
SB
; ; I 01" A $ é I. —r'%r I I I I r n I T
ss§ssss§Date§§§§§§§§§§
O -I d M Q (4) e -b -‘ N 0) co .5 0| 0| 0| 0)
B a B B o o o B 8 g a a B a 8 E5 5 g
OI 0| 0| OI OI 0| 0| 01 O) O) O) O) O) O) O) O)
c Catchment Inﬂuenced Data 0 Biological Influenced Data

Figure 2.5: Data separation into catchment and biological inﬂuenced datasets by date
and site.

Catchment influence model

The catchment inﬂuenced MLM yielded signiﬁcant relationships between
log(DP) and Mg2+, K+, NO3', Na+, pH, alkalinity (Alk), speciﬁc conductance (SPC),
lowland forest land use, agricultural land use, urban land use, Year, Week, Week2 and
Week3 (Table 2.1). Signiﬁcance is tested using the F -statistic with the criteria of p <

0.05 (Table 2.1). The estimates (coefﬁcients) for the ﬁxed effects and variable

54

groupings by category are given Table 2.1. The results, including the estimates, for

the random effects by site are given in Table 2.2. The general form of the model is:
log(DP) = int + SC + LU + IT + SE + a (2.5)

where: int = intercept, SC = stream chemistry, LU = land use, TI = temporal trend,

SE = site effect and 8 = residual error.

Table 2.1: Fixed effects results from the catchment inﬂuenced MLM.

 

 

 

 

 

 

 

 

Fixed Effect Year Estimate F'Stat's‘" Em“
p value Category
Intercept 2.4932 Intercept (int)
Mg2+ -0.01365 0.0145
16 0.05108 0.0003
NO3' 0.04687 <.0001 Stream
Na+ 0.006301 0.0046 Chemistry
pH -0.3136 <.0001 (SC)
Alk 0.002215 <.0001
spc -0001 1 0.0001
Lowland Forest 13.4145 <.0001
Agricultural 0.6828 0.0001 ”23386
Urban 1 .9947 0.0003
2005 -1.2438
Year <.0001
2006 0
w k 2005 0.27 <0001
ee .
2006 0.01034 Temporal
2005 0 01467 Trend
Week2 - ' <.0001 (IT)
2006 0.002318
3 2005 0.000245
Week <.0001
2006 0.00009

 

55

Table 2.2: Random effects results from the catchment inﬂuenced MLM.

 

 

Random Estimate Effect
Effect Category
BC -0.04909
BR 0.1077
F C 0.01627

GR 0.07224
KA 0.1394

KB 0.06732

KC 0.06304

KD 0.0991 1 Site
KE 0.07914 Effect
KG 0.00616 (SE)
KK 0.06564

KM 0.01322

KP 0.171

KS -0.08243

PC 0.02585

SB 0.09083

wc 0.05962

 

The temporal variables Year, Week, Week2 and Week3 estimate the temporal trend in
the log(DP). Including these variables, equation 2.5 for the 2005 sampling period is:
log(DP) = int + SC + LU + [ -1.2348 + 0.27(Week) - 0.01467(Week)2 +
0.000245(Week)3] + $13 + e (2.6)
and for the 2006 sampling period is:
log(DP) = int + SC + LU + [ 0.01034(Week) + 0.002318(Week)2 —

0.00009(Week)3] + SE + e (2.7)

56

Transforming equation 2.4 back to DP yields
DP = (1 01"‘)(105C)(10L”)(10")(1055)(1 0") (2.8)

Equation 2.7 shows that the estimate for DP is derived from the product of the
exponential terms for the ﬁxed and random effects. Therefore, temporal trends will
amplify or diminish the combination of the random and other ﬁxed effects. Using the
equation 2.8 and the temporal trend variables in equations 2.6 and 2.7, the catchment

temporal trend factors (CTTF) for 2005 and 2006 can be represented as follows:

[-1.2348 + 0.27(Week) - 0.01467(Week)2 + 0.000245(Week)3]
CTTonos = 10 (2.9)

[0.01034(Week) + 0.002318(Week)2 - 0.00009(Week)3]
CTTF2006 = 10 (2.10)

The plot of the CTTFs by week of the growing season is given in Figure 2.6.

 

 

3 4
2.5 3
A 2 A
In
C)
a
E
g 1.5 -4
IL
I-
l-
O
1 4
0.5 -
0 I T I " I' ‘l _ 1 ’T "‘T I 1’" " I” I"'"]" ' 1' "1"" "I ' I I "z ‘I I I F " .Y 1 1"" "T
012 3 4 5 6 7 8 9101112131415161718192021222324252627
Week
—2005 --- 2006

Figure 2.6: Plot of the estimated catchment temporal trend factors (CTTF) by week
from the catchment inﬂuenced MLM. Note: Week 1 = ﬁrst week of April.

57

The CTTFs are watershed-wide factors that apply equally to all sites.
However, the other ﬁxed and random effects vary by site and are ampliﬁed or
diminished by the temporal effect. This is demonstrated by the 2006 MLM estimated
contributions to total DP from the temporal effect DP and other ﬁxed effects for the

Battle Creek River location (site BR) ( Figure 2.7).

Total DP

 

 

‘4 m
0 O
- ~J
' a
h
«I.
’
p
’
\
\
\
I
I
\
.I
0‘.
.&

 

 

 

60 . \ c- ‘ \
I 0 ‘ I I , \ I '
r: = . I‘ ' - Stream ChemIstry . - \
L. 50 4‘ "‘ ‘ e ’.\ \ I
U) : l,‘ ; -’ and LandUse DP . ,
1 f ' . . ‘
I 40 g "1 I. II' ‘1‘ Contributlon
D ; " Q. ’ VI. 1 IX
‘ ‘\' "'" l ‘t I’ \ s
. o ..... ' \
30 . V “so"\ ‘ ------ ‘ “"‘s l’
l SOO"-~ ’
20 ‘§~l

 

TemporaITrend DP

 

 

A
O
..1.. ..1

 

Contribution
0...,
§§§§§§§§§§§§§§§§§§§§§§§§§§
$23SSEeS§E§S$§s§$§S§SSS§SS
‘I‘IegmmaSmwaSSFngwwaggmaaS
Date

Figure 2.7: The catchment inﬂuenced MLM estimates for the 2006 contributions to
total DP from the temporal trend DP and the stream chemistry and land use DP for the
Battle Creek River (site BR).
Biological inﬂuenced model

The biological inﬂuenced MLM yielded signiﬁcant (F -statistic, p<0.05)
relationships between log(DP) and PP, NO3', 8042', Cl', pH, urban land use and Year
(Table 2.3). No Week variables were signiﬁcant. The estimates (coefﬁcients) for the

ﬁxed effects and variable groupings by category are given Table 2.3. The results,

including the estimates, for the random effects by site are given in Table 2.4.

58

Table 2.3: Solution for the ﬁxed effects for the biology inﬂuenced MLM.

 

 

 

 

 

Fixed Effect Year Estimate F::::::ic (3:33;;
Intercept 3.4486 Intercept (int)
PP -0.00138 0.0054
NO3' 0.1426 0.0004 Stream
8042' 001444 <.0001 Chemistry
Cl' 0.003959 0.0060 (SC)
pH -0.2856 <.0001
Urban 7.4666 0.0452 Land Use (LU)
Year 2005 -0.1041 0.0020 Temporal
2006 0 Trend (TT)

 

Table 2.4: Solution for the random effects for the biology inﬂuenced MLM.

 

 

Random Estimate Effect
Effect Category
KA 0.08775
KC 0.0185
KD -0.1334 Slte
ffect

KK 0.007106 (SE)
KP 0.02753
KS -0.00752

 

Following the form of equation 2.8, for the 2005 sampling period:

DP = (1OintXlOSCXlOLUXlO-O.1041)(IOSE)(103) =

(10‘"‘)(103C)(10L“)(0.787)(1055)(108) (2.1 1)
and for the 2006 sampling period:
DP = (1o‘"‘)(105C)(10L”)(10°)(105500“) =
(10‘"‘)(105C)(10L”)(1 .000)(1oSE)(108) (2.12)

59

From equations 2.11 and 2.12, the biological temporal trend factor (BTTF) for 2005 is
BTTonos = 0.787 and for 2006 is BTTF2006 = 1.000. The intercept and land use terms
are equal in equations 2.10 and 2.11 on a given date for a given site. The plot of the
B'ITFs for 2005 and 2006 by week of the growing season are given in Figure 2.8. The
biological inﬂuence is zero prior to establishing the level of productivity required to
control the stream chemistry —week 10 in 2005 and week 15 in 2006. The biological
inﬂuence reverts to zero during runoff events that return stream chemistry control to
the catchment inﬂuence. The variability in DP is a combination of variations in

stream chemistry and season (year to year).

 

 

o

a)

_.L_
j

l

BTTF (unitless)
.0
O)

.0
4;

l

 

 

 

 

 

 

 

 

 

 

 

0.24}
i
01
012 3 4 5 6 7 8 9101112131415161718192021222324252627
Week
—2005 ---2006

Figure 2.8: Plot of the estimated biological temporal trend factors (BTTF) by week
from the biological inﬂuenced MLM. Note: Week 1 = ﬁrst week of April.

60

Catchment and biological model assessment

To assess the suitability of the catchment and biological MLMS for identifying
relationships between DP and watershed variables, the normality of the residuals and
the correlation between actual and predicted log(DP) were evaluated. Both the MLM
and the GLM have the key assumption that the residuals are zero-mean and normally
distributed (SAS, 1999). Normality was evaluated using the Shapiro-Wilk statistic, W.
For the catchment MLM residuals, W= 0.9837 (p < 0.0001) and for the biological
model residuals, W = 0.9729 (p < 0.0194). The Shapiro-Wilk statistics for both
indicate a high probability that the residuals are normally distributed.

The actual log(DP) and the catchment and biological model predicted log(DP)
were correlated from the model outputs using linear regression. The catchment and
biological MLMS estimate the log(DP) based on the stream chemistry, land use,
temporal trend and site effect using equation 2.5 and the estimates from Tables 2.1 and
2.2 for the catchment model and Tables 2.3 and 2.4 for the biological model.

The plots of actual log(DP) versus the predicted log(DP) from the catchment and
biological MLMS and the linear regression analysis are shown in Figure 2.9. The
square of the correlation coefﬁcient, R2, represents the fraction of the variation in the
actual log(DP) explained by the MLM predicted log(DP). The catchment model (R2 =
0.8658) explained 87 percent of the variation and the biological model (R2 = 0.8455)
explained 85 percent of the variation in actual log(DP). In environmental studies, an

R2 > 0.75 is considered highly correlated.

61

 

 

 

 

 

2.0 ~ 0
A 0 O """
L 1.8 2 Catchment Model .80 “2.2%
a, y = 0.8567x + 0.1934 8 ,2. T 3“ a o
31.6 2 R2 = 03658 ° . » o"2 o
% . ”2:922: o .

,.,°'-°f(~°' .‘ ‘ ’.' ’ o

5 1 4 322-13220" ° 0
2 - IMQ. o 0 0
3 12 " ° Biological Model
ft} ’ y=0.8815x+0.158
3 1.0 - R2=0.8455
E

0.8

0.6 2 . . 2 2 2 r

0 6 0.3 1 0 1.2 1.4 1.6 1.8 2.0 2.2

Actual log(DP (ugL'1))

<> CatchmentModel 0 Biological Model
----- Linear (Catchment Model) — Linear (Biological Model)

Figure 2.9: Actual log(DP) versus predicted log(DP) and linear regressions for the
catchment and biological models on the KRLAW datasets.

Discussion

MLMS provide estimates for the signiﬁcant relationships between DP and
temporal trends, stream chemistry and land use for catchment and biological
inﬂuenced datasets from the KRLAW. The data are segregated by date and location
using PP, alkalinity, Ca2+ and chlorophyll a, and are separted into catchment and
biological inﬂuenced datasets. While chlorophyll a and PP may be reliable indicators
of primary productivity, they were not sufﬁcient for determining when the biological
processes are the dominant inﬂuences on stream chemistry. In 2006, as the
chlorophyll a and PP concentrations elevated, alkalinity and calcium were similar

from the inlet to the outlet of Morrow Lake, indicating continued catchment inﬂuence

62

for an additional six weeks. Also, the inﬂuence of the primary producers on stream
chemistry could not overcome the catchment inﬂuence during runoff events.
Particular attention should be given to multiple indicators when separating data by
dominant inﬂuence. The catchment and biological models produced different
temporal variations and different stream chemistry and land use relationships.

The catchment model estimated a cubic expression for the temporal trend on
log(DP) as a function of Year, Week, Week2 and Week3. While both the 2005 and
2006 temporal trends were modeled by a cubic expression, the coefﬁcients varied
between years. Therefore, the CTTFs varied week to week within year and also varied
for the same week in different years. The CTTF2005 varied from 0.76 to 2.16 and
peaked week 14 (the ﬁrst week in July). The CT'I‘F2006 varied from 1.03 to 2.61 and
peaked week 19 (the ﬁrst week in August).

The catchment MLM showed a signiﬁcant relationship between the log(DP)
and Mg”, K+, NO3', Na+, pH, alkalinity, speciﬁc conductance and lowland forest,
agricultural and urban land uses. These relationships will be further explored to
provide insight into DP cycling within the watershed.

The biological model estimated a year to year temporal effect, but no week to
week effect on the log(DP). The BTTonos was 0.80 compared to a BTTonm; of 1.00.
The lack of week to week effect may result from the level of primary productivity,
near the maximum, required to alter the catchment inﬂuenced stream chemistry. The
2006 chlorophyll a data indicate that once the maximum productivity is reached, that
level is maintained until the end of the growing season unless disturbed. This is

consistent with the concept of biological thresholds put forth by Grover and

63

Chrzanowski (2004) where minimum nutrient and maximum light thresholds at
varying times limit phytoplankton productivity to a maximum threshold unless
disturbed. The disturbances of runoff events did not impact the biological model
because they were included in the catchment dataset as the system reverted to
catchment inﬂuence. The limitation in 2005 of the temporal trend to 79 percent of the
2006 value is probably due to a lower nutrient threshold, particularly P, in 2005 and
will be investigated in a separate study. Similar to the catchment model, identifying
the year to year temporal trend resulted in the identiﬁcation of signiﬁcant relationships
between log(DP) and stream chemistry and land use parameters.

The biological MLM showed signiﬁcant relationships between log(DP) and
PP, NO3', SO42} Cl', pH and urban land use. These relationships will be further
evaluated to provide insight into biological processes affecting the sources, fate and
transport of DP within the watershed.

The temporal trends apply equally to all locations, but produce greater effects
in high DP watersheds than in low DP watersheds. Although this study is
inconclusive as to the source of the catchment temporal and biological inﬂuences,
Mulholland and Hill’s (1997) catchment and biological control, warrant further
investigation. As a ﬁrst step, the identiﬁcation of temporal trends, regardless of the
source, generates more signiﬁcant relationships with stream chemistry and land use
variables than statistical methods where a temporal component is not included.

We propose data separation by inﬂuence and statistical analysis using the
MLM as a method to identify temporal trends and the relationships between DP and

stream chemistry and land use in the KRLAW to test our hypothesis. Temporal trends

64

in DP are identiﬁed from both catchment and biological inﬂuences and from
establishing relationships among DP, stream chemistry and land use variables. These
results support the hypothesis that DP concentrations are related to land use and
stream chemistry, but that the speciﬁc patterns change over time. These MLMS show
that the changes in land use and stream chemistry patterns over time are the result of
temporal trends from the dominant inﬂuence, year-to-year and week-within-year for
catchment inﬂuence and year to year for biological inﬂuence. The variability '
associated with these temporal trends changes the patterns and relationships among

DP, land use and stream chemistry.

Conclusions

The approach described in this study develops a method using data separation
by inﬂuence and MLMS to characterize the temporal effects on DP by catchment and
biological inﬂuences. Stream biological indicators —alkalinity, Ca2+ concentration, PP
and chlorophyll a— allow us to segregate the KRLAW data into catchment and
biological datasets by locations and dates. From separate MLMS used to evaluate the
catchment and biological data, we conclude for the KRLAW that: 1) temporal trends
in DP are identiﬁable, 2) temporal trends for catchment and biological inﬂuences are
different, 3) temporal trends exhibit variation over time, 4) DP, land use and stream
chemistry are correlated, and (5) speciﬁc land use and stream chemistry patterns
change over time due to temporal trends.

Results from this study support our hypothesis that DP concentrations are

correlated to land use and stream chemistry, but that the speciﬁc patterns change over

65

time. Data separation and including temporal variables in MLMS improve the number
and strength of the signiﬁcant ﬁxed effect relationships for stream chemistry and land
use to DP compared to studies using traditional statistical techniques. These
signiﬁcant land use and stream chemistry ﬁxed effects and the random effects by site

provide a basis for additional studies to provide inferences into watershed DP cycling.

66

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69

CHAPTER 3
INFERRING CATCHMENT INFLUENCED DISSOLVED PHOSPHORUS
DYNAMICS USING LAND USE AND STREAM BIOGEOCHEMISTRY
Abstract

Patterns in suites of chemicals and their relationships to land use can provide
insight into catchment processes inﬂuencing eutrophication. In a two-year study of
the KRLAW, these patterns are used to understand the catchment cycling (sources,
pathways, fate) of chemicals. These types of studies are being done for DP, but
temporal trends are obsuring the catchment patterns. To address this issue, a MLM is
used to quantify the temporal trend, improving the relationships between DP, stream
chemistry and land use. The MLM results are used to remove the temporal trend, and
patterns are explored using common multivariate statistical techniques.

MLM and PFA land use and stream chemistry relationships provide evidence
that agricultural and urban land uses represent P sources, but lowland forest does not.
Lowland forest land use indicates watershed characteristics that provide DP processes
that dissolve and/or release P supplied from other sources. From these results an
approach is developed to estimate subwatershed DP contributions using readily
available land use information. The implications for some common P management
practices are considered in light of the inferred DP cycling.

The approaches developed in this paper advance the knowledge of the stream
DP response to catchment anthropogenic P inputs, land use and management practices.
These insights have implications for watershed P assessment and bring into question

the long term effectiveness of some common management practices for P remediation.

70

Introduction

The use of the world’s water resources has intensiﬁed in the last 100 years,
hastened by the subtle and direct consequences of unprecedented human population
growth (Turner et al., 2003). A consequence of increased anthropogenic inﬂuence is
excessive inputs of N and P, often resulting in eutrophication, impairing the physical
and biologic integrity of surface waters (Carpenter et al., 1998; Dodds et al., 2002).
Among the important constituents of aquatic ecosystems leading to eutrophication is
DP. How human activity affects changes in water quality and chemistry, including
DP, deserves increasing attention as water quality management becomes more
complex, if not more uncertain (Turner et al., 2003).

This study attempts to identify patterns and relationships between DP, land
use, stream chemistry, trace elements and soil groups to infer the inﬂuence of
catchment DP cycling on eutrophication. In Chapter 2, a MLM was used to identify a
temporal trend that changes the catchment DP, stream chemistry and land use
relationships. By removing these effects, temporal trend and site adjusted DP (DPTSA)
increases and strengthens the stream chemistry and land use relationships. Patterns
and relationships between DPTSA, biogeochemistry and land use are analyzed using
MLM results and common univariate and multivariate statistical techniques.

Land use changes derived from human activity are known to inﬂuence the
biogeochemistry of watersheds ((Boutt et al., 2001; Fitzpatrick et al., 2007; Tsegaye et
al., 2006; Wayland et al., 2003; Williams et al., 2005; Zampella et al., 2007).
Fitzpatrick et al. (2007), in a study of the Muskegon River Watershed in Michigan,

found all major cations (Na+, Mg2+, K+ and Ca2+), anions (HCO3', Cl', 8042', NO)( and

71

F') and most trace elements (V, Co, Cu, Se, Rb, Sr, Mo, Cd, Ba and U) are higher in
both agricultural and urban streams than reference forested streams. Cr and Pb were
elevated in urban as compared to agricultural and forested sites.

Land use patterns and their contribution to P exports and loads is also well
documented (Glandon et al., 1980; Lehrter, 2006; Lewis et al., 2007; Ontkean et al.,
2005; Sonoda and Yeakley, 2007; Tsegaye et al., 2006; Winter and Duthie, 2000).
Glandon et a1. (1980), in a study of P and N loading from urban, agricultural and
wetland sources, found annual P loadings of 0.595 kg ha", 0.180 kg ha'1 and 0.023 kg
ha", respectively. Few studies quantify DP exports and their relationship to land use.
One such study, by Coulter et al. (2004), documented annual orthophosphate ﬂuxes of
0.28 kg ha", 0.12 kg ha'1 and 0.07 kg ha'1 for agricultural, mixed and urban land uses,
respectively, in eastern Kentucky.

Researchers have found large variations in subwatershed stream DP
concentrations within the same watershed, and attribute this variability to various
effects (Novak et al., 2004; Novak et al., 2003; Ontkean et al., 2005). Including
seasonal inﬂuences, landscape characteristics, hydrology and wetland processes. This
study explores the variability in DP cycling through stream biogeochemistry and land
use patterns and relationships.

The hypothesis is that catchment inﬂuenced DP, land use and stream chemistry
patterns identify sources and processes that affect DP cycling. To test this hypothesis
MLM quantiﬁed ﬁxed temporal trend and random site effects are removed from the

DP. DPTSA, stream chemistry, trace element, soil type and land use pattern and

72

relationship results from MLM, PFA, GLM and Pearson correlation coefﬁcient
analyses provide inferences about catchment DP cycling.

Results show land use coefﬁcient ratios are consistent with published P export
ratios for urban to agricultural (approximately 3:1) land use (Glandon et al., 1980).
However, lowland forest to agricultural (19.5:1) land use and lowland forest to urban
(6.8: 1) land use coefficient ratios are considerably higher than published export ratios
(0.13:1 and 0.04:1, respectively) (Glandon et al., 1980). The high degree of inﬂuence
and relatively low percentage of lowland forest land use suggests that lowland forest
does not represent a P source. Instead, lowland forest is a proxy for watershed
characteristics (% wetlands and soil types) that provide processes that dissolve and/or
release P from other sources. Additional evidence for the P source, DP process and
land use relationships is presented from the stream biogeochemical ﬁngerprints
identiﬁed for agricultural, urban and mixed agricultural/urban land uses.

From these results, a method is developed to estimate the DPTSA contribution
using only readily available agricultural, urban and lowland forest land use
information. Insights into the contributions to mean DPTSA from different land use
effects provided by this approach are described. Finally, the implications of P
management practices on DP in light of the inferred P cycling are considered.

The approaches developed in this paper advance the knowledge of the stream
DP response to catchment anthropogenic P inputs, land use and management practices.
These insights have implications for watershed P assessment and bring into question

the long term effectiveness of some common management practices for P remediation.

73

Methods

Catchment inﬂuenced DP cycling was investigated using the KRLAW stream
chemistry dataset (Appendix I), KRLAW trace element dataset (Appendix 11), land use
descriptions (Table 1.1.) and STATSGO soil group distribution (Table 1.2). The study
site, sampling locations, sampling methods and chemical analyses are described in
Chapter 1. The catchment inﬂuenced MLM ﬁxed stream chemistry, land use and
temporal trend effects (Tables 2.1) and random effects (Table 2.2) detailed in Chapter
2 were used for this study. The sites and dates that constitute the catchment
inﬂuenced datasets are shown in Figure 2.5
Temporal trend and site adjusted DP

Temporal trends and site effects from the catchment MLM were removed from
the catchment inﬂuenced DP to improve the number and strength of the DP, stream
chemistry and land use relationships. DPTSA is determined by rearranging equation
2.5 as follows:

log(DP)TSA = log(DP) — TT — SE = int + SC + LU (3.1)

Equation 3.1 and the estimates from Table 2.1 were used to calculate log(DP)1~5A.
DPTSA was calculated by back transforming log(DP)TSA.
Statistical Analysis

MLM, Pearson correlation coefﬁcients, GLM and PFA are the statistical
methods used to identify patterns among DPTSA, suites of chemicals and land use to
infer catchment inﬂuenced DP cycling. MLMs are described in Chapter 2 and
Appendix V. Pearson correlation coefﬁcients are nonparametric measures and

probabilities of association between two variables (SAS, 1999). GLM uses the least

74

squares method to ﬁt a general linear model relating continuous dependent variables to
independent variables (SAS, 1999). PF A detects structure in variables identifying a
common factor that explains the variability between variables. The common factor is
an unobservable, hypothetical variable that contributes to the variance of at least two
observed variables (SAS, 1999). The statistical methods for this study were
implemented using SAS 9.1.3 (SAS, 2007), including PROC MIXED, PROC CORR,
PROC GLM and PROC FACTOR procedures.
Results

The MLM temporal trend and random site effects (Tables 2.1 and 2.1) were
removed from the DP, using eq. 3.1, providing a dependent variable, DPTSA, related to
stream chemistry and land use that can be analyzed using common univariate and
multivariate statistical techniques. The signiﬁcant (p<0.05) ﬁxed effects for stream
chemistry (Mg2+, K+, Na+, NO3', pH, alkalinity and speciﬁc conductance, Table 2.1)
and land use (lowland forest, agricultural and urban, Table 2.1) from the catchment
inﬂuenced MLM were evaluated with respect to DPTSA. The mean and standard
deviation by site for DP, DPTSA, and the signiﬁcant stream chemistry, and the percent
by site for each signiﬁcant land use are given in Table 3.1.
Land use relationships

The relationship, between the land use variables and mean DPTSA was

analyzed by plotting the result of the MLM land use ﬁxed effects (Table 2.1) equation
(13.414Slowland forest + 0.6828agricultural + 1.9947urban) against the mean DPTSA

by site (Figure 3.1).

75

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76

A linear regression of these data shows a good ﬁt with R2 = 0.84. This relationship
exhibits three clusters that have been assigned the categories low, medium and high
mean DPTSA. Further inspection of the individual land use ﬁxed effect contribution to
DPTSA category (Table 3.2) indicates that no individual land use contribution directly

relates to DPTSA.

 

 

 

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0.80 0.90 1.00 1.10 1.20 1.30 1.40 1.50 1.60
Land Use Fixed Effects
(13.4145lowland forest + 0.6828agrlcultural + 1.9947urban)

Figure 3.1: A plot and linear regression of the catchment MLM land use ﬁxed effects
equation versus the mean DPTSA by site.

High lowland forest contribution exists in all three DPTSA categories (indicated by the
dark highlight) while low lowland forest contribution exists in the medium and low
DPTSA categories (indicated by the light highlight). The high DPTSA category does not
include a low lowland forest contribution. The agricultural and urban contributions

are similar among DPTSA categories with the exception of sites FC and PC.

77

The ﬁxed effect coefﬁcients provide insight into the relative contributions of
each land use. Urban has a 2.9:1 ratio of impact compared to agricultural land use.
This is consistent with the ratio between published P loading values for urban and
agricultural land use. Glandon et al. (1980), in a study of P and N loading from urban,
wetland and agricultural sources, found P loading from urban sources at 0.595 kg ha'1
and from agricultrual at 0.180 kg ha", a ratio of 3.3:1 urban to agricultural land use.
The ﬁxed effect coefﬁcients for urban and agricultural land use reﬂect their
contributions as sources of P. However, lowland forest land use and its coefﬁcient are
inconsistent with this explanation.

Table 3.2: A comparison of DPTSA category, site, mean DPTSA and the catchment
inﬂuenced MLM lowland forest, agriculture, urban and total land use effects. Dark

highlight compares high lowland forest effect sites. Light highlight compares low
lowland forest effect sites.

 

 

 

 

 

 

 

 

 

 

 

Land Use Effect
DPTSA ite Mean DPTSA Lowland Forest Agricultural Urban Total
Category (pglﬂ) (13.285 x %) (0.6824 x %) (1.9588 x %)

“ 087 0539‘ 7506 055'":

0.52 0. 32 7 0.11 0.95

0.53 0.40 0.10 1.03

0.71 0.31 0.17 1.19

0.70 0.37 0.12 1.20

0.45 0.12 ' 0.60 1.17

KC 13.57 0.79 0.33 0.13 1.25

KA 13.87 0.72 0.32 0.17 1.20

Medium KS 14.00 0.79 0.33 0.13 1.26

KB 14.51 0.80 0.36 0.12 1.29

14.98 0.80 0.33 0.13 1.26
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K 18.86 0.75 0.32 0.18 1.25

23.20 1.00 0.35 0. 10 1.45

High 23.74 0.98 0. 32 0.08 1.38

 

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78

to agricultural land use of 0.13:1 and wetland to urban land use of 0.04:1. The ﬁxed
effects coefﬁcients indicate ratios for wetland (lowland forest) to agricultural land use
of 19.5:1 and wetland (lowland forest) to urban land use of 6.8: 1. This large
inconsistency suggests that lowland forest land use represents something other than a
P source. Lowland forest land use is low, ranging from 3.4 to 7.6% for the study area,
yet it exerts a large inﬂuence in the land use component of the MLM. It does not seem
reasonable that this inﬂuence is solely from the small percentage of lowland forest.

Instead, lowland forest land use percentage indicates watersheds that have
processes that promote the dissolution and release of P. While urban and agricultural
land use indicates the level of P sources, lowland forest land use indicates the level of
P dissolution/release processes. If other watershed characteristics also promote the
dissolution/release of P they should be related lowland forest land use.

The Pearson correlation coefﬁcients for land use and soil group were
calculated to identify these relationships (Table 3.3). Non-forested wetland has a high
positive correlation (0.87) with lowland forest land use. Both are lowland systems,
deﬁned as areas that have hydric soils and are permanently or temporarily inundated,
with high water tables (Paciﬁc Meridian Resources, 2001). These lowland systems
are buffers to the stream system, retarding the movement of water and collecting PP
transported via surface runoff from upland portions of the catchment. These areas
provide an environment and time for the processes that dissolve, adsorb and desorb P
(Novak et al., 2004). In addition to a correlation with similar environments, lowland

forest land use is correlated with three soil groups.

79

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80

Lowland forest is highly, positively correlated with M1024, Boyer-Oakville-
Cohoctah (0.84) and M1035, Marlette-Capac-Parkhill (0.81) soil groups and highly,
negatively correlated with M1011, Coloma-Spinks-Oshtemo (-0.76). The positively
correlated soil groups increase in percentage with lowland forest land use. The Boyer-
Oakville-Cohoctah and Marlette-Capac—Parkhill groups consist of two types of soils:
1) rapidly-permeable sandy or loamy, gravelly soils, and 2) slowly-permeable loamy
soils (USDA, 1990; USDA, 1997). Soil P adsorption capacity has been shown to
increase with increasing surface area and clay content (Penn et al., 2005). The ﬁrst
soil type has coarse particles, low surface area and a low capacity for P retention (high
release), and drains water and DP rapidly into hydrologic pathways. The second has
less coarse particles and a higher P retention, but drains slower, providing additional
time for P desorption to occur. The negatively correlated soil group increases with
decreasing lowland forest land use. The Coloma-Spinks—Oshtemo group consists of
moderately-slow permeable loamy to loamy silt soils (USDA, 1990; USDA, 1997).
These ﬁner soils, more prevalent in watersheds low in lowland forest, have a higher
capacity to retain P, resulting in the inverse relationship.

These soil groups and non-forested wetland correlations to lowland forest are
examples of watershed characteristics that contribute to P dissolution and release that
are identiﬁable from this data. It is anticipated that other characteristics (6. g. depth to
water table, runoff lag time, hydrology) potentially correlated to lowland forest land
use but not measured in this study are also contributing to the strength of the lowland

forest relationship to DP.

81

Using the land use MLM coefﬁcients and lowland forest as an indicator of P
processes and urban/agricultural as an indicator of P sources, it is evident from Table
3.4 that both source and process are required to produce high mean DPTSA. Site FC
has a high lowland forest effect (high process) and low urban and agricultrual effects
(low source), resulting in low mean DPTSA. Site BR has high lowland forest effect
(high process) and high agricultural effect (high source), producing high mean DPTSA.
Site GR has low lowland forest effect (low process) and high agricultural effect (high
source), resulting in low mean DPTSA. Additional insights into these dynamics
between land use, P sources and P processes are inferred from the stream chemistry
and trace element relationships.

Stream chemistry relationships

An un-rotated PFA was performed on the catchment inﬂuenced stream
chemistry, land use and DPTSA data. The results are given in Table 3.4 and explain
79.6% of the variance in the data with four factors. Factor 1, unrelated to DPTSA, is
the urban inﬂuence on stream chemistry, reﬂecting strong and moderate loadings of
urban land use, alkalinity, Mg2+, speciﬁc conductance and Na“, most likely from the
high level of road salt loss to streams in urban environments. Factor 2 has strong
positive lowland forest and agricultural loadings, a moderate negative urban and
moderate positive DPTSA, K+ and alkalinity loadings. This factor is interpreted as
reﬂecting the source effect of agricultural nutrients in the DPTSA and K+ and the
lowland forest process effect in DPTSA and alkalinity. Urban land use is inversely
correlated to both agricultural and lowland forest land use (Table 3.3), leading to the

inverse relationship in this factor. Factor 3 is the inverse relationship between

82

agricultural and lowland forest with DPTSA loading directionally, with lowland forest
indicating that DPTSA levels relate to process when source is present. The strong
loading of N03' directly to agricultural land use but inversely to DPTSA and lowland
forest indicates a short ﬂow path and lack of process for N conversion in low lowland
forest watersheds. The opposing situation of factor 2, the direct relationship between
agricultural and lowland forest land use, has low loading for N03' as the environment
and processes indicated by lowland forest convert N03' to other N forms.

Table 3.4: Un-rotated factor loading matrix from principal factor analysis for the
stream chemistry dataset from the Kalamazoo River/Lake Allegan Watershed.

 

Factor 1 Factor 2 Factor 3 Factor 4

 

DPTSA 0.6448 .0.5504

Lowland Forest 0.7343 -0. 4453
Agricultural 0.7620 0.44 73

Urban 0.671 7 -0. 6121

Mg2+ 0. 6162 —0. 4524
K+ 0.4466 0.6494
NO3' 0.7044 0.4307
Na" 0.8615

pH 0.5 750

Alk 0. 6313 0. 4497 -0.5096
SPC 0.9248

Percent of total variance explained
0.2808 0.2306 0.1520 0.1325
Total percentage of variance explained: 79.6%

Strong loadings (Z 0.70) are indicated by bold type.
Moderate loadings (>0.40 and <0.70) are indicated by italics.

 

Factor 4 is unrelated to DPTSA and relates Mg”, K+, NO3' and alkalinity. The
catchment stream chemistry PFA demonstrates patterns and relationships in land use

and stream chemistry that supports the P source and P process dynamics discussed

83

l;

Tll

5U

earlier. The catchment trace element PF A provides further evidence of these
dynamics.
Trace element relationships

The catchment trace element PFA (Table 3.5) has four factors explaining
99.6 % of the variance in the data. Factor 1 is the DP factor with strong and moderate
loadings on DPTSA, lowland forest, agricultural, many trace metals (Mn, As, Cd Ni,
Sn, Sr, Co, Pb, V, Se, Ti, Ba, Cr, Sc, Zn and Mo) and inverse loading on urban.
Lowland forest and undeveloped land uses are not known to be a source of trace
elements, and their strong positive loadings are contrary to previous studies
(Fitzpatrick et al., 2007; Williams et al., 2005). This factor suggests that the processes
indicated by lowland forest that dissolve P also result in the dissolution of many trace
metals if a source of those, agricultural land use in this case, is present. As in the
stream chemistry PFA, urban land use is inversely correlated to both agricultural and
lowland forest land use, leading to the inverse relationship in this factor. Factor 4 is
the lowland forest only factor and the lack of or inverse loading on DPTSA and trace
metals reinforces the need for source along with process. Factor 2 is urban land use
and associated trace element loadings. Factor 3 is direct and inverse agricultural,
urban and trace element loading.

Further inspection of the patterns across factors 1, 2 and 3 in the PFA provides
insight into stream biogeochemical ﬁngerprints of agricultural and urban land use.
Trace elements that load only with agricultural land use and DPTSA are Mn, As, Cd,

Ni, Sn, Sr, and Co (dark highlight in Table 3.5). Boron loads only with urban land

84

 

’ (ﬂ
0

Rb
Al

Peres:

Total
\
sifting
“Cain

use and is not related to DPTSA (medium highlight in Table 3.5). Iron loads only with

agricultural land use and is not related to DPTSA (light highlight in Table 3.5).

Table 3.5: Un-rotated factor loading matrix from principal factor analysis for the
catchment synoptic trace element dataset from the Kalamazoo River/Lake Allegan
Watershed. Stream biogeochemical ﬁngerprints: dark highlight = agricultural and
DPTSA; medium highlight = urban only; light highlight =agricultural only; and box =
common agricultural and urban.

 

Factor 1 Factor 2 Factor 3 Factor 4

 

Lowland Forest 0.7721 0.4678
Urban -0. 438 7 0. 5201 0.6398

Agricultural 0.4 727 -0.7173

.4

 

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-0. 4126
T1 0 6714 -0 7075
Ba 0 6168 —0 5233
Se 0 5607 -0 7853
Pb 0.7467 0.4950 -0. 4048
v 0.7343 0.4384 0. 4049
Se 0 6880 0 5885
Cr 0.6031 0.4931
U -0. 6486
Zn 0.4652
Mo 0.4378
Fe -0. 5080 -0. 6969
Rb -0.7822 0.5040
A]

Percent of total variance explained
0.5158 0.2520 0.1381 0.0896
Total percentage of variance explained: 99.6%
Strong loadings (Z 0.70) are indicated by bold type.
Moderate loadings (>0.40 and <0.70) are indicated by italics.

 

85

Common trace element loadings to agricultural and urban land uses with some
relationships to agricultural and DPTSA are Ti, Ba, Sc, Pb, V, Se, Cr, U, Zn and Mo
(box in Table 3.5). Rubidium inconsistently loads with urban, inversely in Factor 2
and directly in Factor 3. Aluminum does not load with any land use, DPTSA or other
trace elements. These biogeochemical ﬁngerprints show promise for relating DPTSA to
agricultural inputs and the anthropogenic inﬂuence on stream chemistry of urban and
agricultrual land uses. The catchment trace element PFA demonstrates patterns and
relationships in biogeochemical ﬁngerprints, supporting agricultural and urban land
use as P sources and high loadings with lowland forest land use indicating P process
dynamics.

The DPTSA, land use and stream chemistry patterns and relationships examined
through stream chemistry and trace element PFAs lead to the identiﬁcation of a P
source and P process dynamic that is quantiﬁable through MLM land use coefﬁcients
and lowland forest, agricultural and urban land use percentages, providing a method to
assess watershed DP.

Watershed DP assessment

Stream chemistry and trace metal patterns support the DPTSA and land use
dynamics and provide additional insights into sources and processes. However, stream
chemistry and trace element sampling and analysis is time consuming and expensive
for a large number of subwatersheds. Identifying agricultural and urban land uses as
measures for P sources and lowland forest as a proxy for P processes provides a
method for assessing the land use contribution to DPTSA throughout the watershed

using readily available land use data. The relationship developed in Figure 3.1 using

86

N._“
R“\J

l‘tr.
d:«ld

the MLM land use coefﬁcients and land use percentages was applied to 78
subwatersheds in the KRLAW to estimate their mean DPTSA category as low, medium
or high (Figure 3.2 and Appendix VI).

The estimated categories depicted in Figure 3.2 identify subwatershed
susceptibility to DP, a consideration when developing P reduction strategies. The
adjacency of low, medium and high DPTSA subwatersheds indicates that a single P
reduction strategy within a region may not be appropriate. A beneﬁt of this approach
is that individual land use effects identify the P source and DP process dynamics
contributing to these differences, demonstrated by the following examples.

The Pine Creek Watershed (sub 73), with high mean DPTSA, is near the Gun
River Watershed (sub 70), with low mean DPTSA. Pine Creek and Gun River were
sampled by the Michigan Department of Environmental Quality (MDEQ) in 1998.
From unpublished MDEQ results, the mean DP concentrations were 34 ugL'l and 9
ugL'l for Pine Creek and Gun River, respectively. With nearly four times the level of
DP in Pine Creek as compared to Gun River, these results are consistent with the
estimates made here. Comparing the land use effects in Appendix 11, Gun River has a
greater P source dynamic (0.510) than Pine Creek (0.443), but a much less DP process
dynamic (0.379 versus 1.383). The difference in mean DPTSA is due to Pine Creek’s
higher level of watershed characteristics that promote the dissolution and release of P,

indicated by the higher lowland forest land use effect.

87

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Process

The high mean DPTSA levels in sub 63, the city of Kalamazoo, and sub 41, the city of
Battle Creek, are due to high urban source effects (1.078 and 1.154, respectively) with
low process effects (0.579 and 0.479). Agricultural subwatersheds exhibit from low to
high mean DPTSA with similar agricultural land use effect contributions. Subs 32 and
34 have high mean DPTSA with medium high agricultural source effects (0.333 and
0.344), but high process effects (1.234 and 1.024, respectively). Subs 69 and 70 have
low mean DPTSA with medium high agricultural source effects (0.350 and 0.390,
repectively), but low process effects (0.559 and 0.379).

These examples illustrate how the combination of P source and DP process
dynamics inﬂuence the estimated subwatershed mean DPTSA. The P source and DP
process dynamics inferred by these results have implications for watershed P
management practices.

Phosphorus management implications

Agricultural and urban environments have long been recognized as sources of
excess P to surface waters (Lewis et al., 2007; Sharpley, 1999). Common practices for
controlling agricultural inputs are ﬁlter strips, buffer strips and minimum tillage
(McDowell et al., 2003). Common urban P control practices are aimed at breaking the
direct linkage between impervious areas and receiving waters through low impact
designs (Hatt etal., 2004). All of these practices are “at source measures” intended to
retain soil and associated P at the source location and out of surface waters. In light of
the P source and DP process dynamics inferred from this research, an unintended
consequence of these practices is to increase P source potential while increasing DP

process potential. These practices, while reducing sediment delivery, also retard

89

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runoff delivery to surface waters (Hatt etal., 2004; Sharpley et al., 2000), producing
the time and environment for DP dissolution and release processes.

These measures may have the short term effect of reducing total P (TP), but
may result in a long term return to near previous TP concentrations consisting of
higher DP and lower particulate P (PP) fractions when a new steady state is reached.
Inamdar et al. (2001) studied the Nomini Creek Watershed after seven years of best
management practice (BMP) implementation including no-till, ﬁlter strips and nutrient
management. At one location, they found the TP load was reduced by 4 % with a PP
reduction of 30% offset by dissolved orthophosphate and dissolved organic P
increases of 92 and 83%, respectively. A second location exhibited a TP load
reduction of 24% with 41% PP reduction offset by increases of 123% in dissolved
orthophosphate and 55% in dissolved organic P.

The Inamdar et al. study, others (Hickey and Doran, 2004; Schippers et al.,
2006; Sharpley et al., 2000; Uusi-Kamppa et al., 2000) and this research bring into
question the long term effectiveness of P management practices that alter P dynamics

in lieu of reducing P inputs.

Discussion
In a previous study of the KRLAW examining temporal trends in DP, data
were separated by catchment and biological inﬂuence and were analyzed using
MLMS. This study focuses on the land use, stream chemistry and trace element
relationships in the catchment inﬂuenced data. The temporal trend and site effects

were removed from the DP data —referred to as DPTSA — using the relationships

90

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developed in the previous study. Patterns among DPTSA, land use, stream chemistry
and trace elements are used to infer catchment inﬂuenced DP dynamics.

A plot and linear regression of the equation for the signiﬁcant land use
variables (lowland forest, agricultural and urban) from the MLM and the mean DPTSA
by site exhibited a strong relationship, and three clusters were divided into categories
representing low, medium and high mean DPTSA. The ratios of the land use
coefﬁcients from this relationship were consistent with published P export ratios for
agricultural to urban land uses, but were much higher for lowland forest to agricultural
and lowland forest to urban land uses. The large inﬂuence contributed by lowland
forest land use in the equation is inconsistent with other studies that have found
lowland forest to be a low source of P. From these results it is proposed that
agricultural and urban land uses represent P sources and that lowland forest is an
indicator of watershed characteristics that promote DP dissolution and release
processes.

Further evidence for these P source and DP process dynamics was gained by
analyzing patterns in land use, stream chemistry, trace elements and soil groups using
Pearson’s correlation coefﬁcients and PF A. Pearson’s correlation coefﬁcients
identiﬁed another wetland land use —non-forested wetlands- and three soil groups that
impact the dissolution time for and the release of P. The PFA of stream chemistry and
trace element data that supports lowland forest as an indicator of watershed DP
process dynamics. Direct lowland forest, DPTSA and trace elements are unrelated, but

lowland forest in combination with a P source land use has numerous strong and

91

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moderate loadings. These results support that lowland forest land use does not
indicate a P source dynamic, but a DP process dynamic when P sources are present.

The PFAs also provide insight into the P source dynamics of agricultural and
urban land uses. The strong and moderate loading patterns for DPTSA, stream
chemistry and trace elements provide biogeochemical ﬁngerprints related to P source
land uses. The biogeochemical ﬁngerprint of agricultural sources includes DPTSA,
Mn, As, Cd, Ni, Sn, Sr and Co. Not related to DPTSA, a combine agricultural and
urban source biogeochemical ﬁngerprint includes Ti, Ba, Sc, Pb, V, Se, Cr, U, Zn and
M0. The agricultural land use ﬁngerprint may include DPTSA because trace elements
associated with agrichemicals are applied proportionately to P for crop production.
The lack of DPTSA in the urban and mixed agricultural/urban ﬁngerprint indicates that
those trace elements have variable sources not linked P application or use.

The PFAs, mean DPTSA and land use relationships and Pearson’s correlations
reinforce the association of the combination of the P source and DP process dynamics
with DPTSA levels. A low P source (indicated by low agricultural and/or urban land
use) and a high DP process (indicated by high lowland forest land use) result in low
DPTSA. A high P source (high agricultural and/or urban land use) and a low process
(low lowland forest land use) produce low DPTSA. A high P source (high agricultural
and/or urban land use) and a high process (high lowland forest land use) provide high
DPTSA. Both P source and DP processes are required for increased DPTSA levels.

The inferences into the P source and DP process dynamics indicated by the
three land use relationships allows development of a watershed DP assessment method

to estimate and categorize subwatershed mean DPTSA using only readily available land

92

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use information for the‘KRLAW. Underlying individual land use effects that can be
evaluated to understand the P source and DP process contributions to DPTSA levels are
described. This approach has the potential improve P reduction strategies at both the
watershed and subwatershed levels.

The watershed DP assessment and inferences about P source and DP process
dynamics have implications for P management. Common P agricultural and urban
management practices are aimed at preventing PP from entering surface waters. These
practices are believed to have the potential to increase the watershed characteristics
that promote the dissolution and release of P. While a short-term improvement in TP
should result, long-term TP levels may increase as a new steady state is achieved and
reduced PP is replaced by increased DP. Agricultural watershed studies have
conﬁrmed this phenomenon (Inamdar et al., 2001). Studies have not been found that
evaluate urban P management practices and associate DP increases, but speculation is
that the P source and DP process dynamics apply to urban environments as well. This
research along with that of others raises questions about the lOng term effectiveness of

common P management practices in lieu of P input reductions.

Conclusions
This study uses patterns in land use, stream chemistry, trace element and soil
group data to infer catchment inﬂuenced DP dynamics in the KRLAW aﬁer the
removal of seasonal trend and site effects. The combination of and interaction
between a P source dynamic —related to agricultural and urban land use— and a DP

process dynamic —indicated by lowland forest land use as a proxy for watershed

93

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characteristics, were inferred from this research. These results support the hypothesis
that catchment inﬂuenced DP, land use and stream chemistry patterns identify P
sources and processes that affect DP cycling.

PFAs and Pearson’s correlations provide evidence of P sources, DP processes
and land use relationships. The PFA results show potential for identifying stream
biogeochemical ﬁngerprints for agricultural, urban and mixed agricultural/urban land
uses in the KRLAW.

From the evidence of P dynamics, mean DPTSA and land use relationships it is
concluded that three land use relationships (agricultural, urban and lowland forest) can
be used to estimate and categorize subwatershed mean DPTSA concentrations. From
this approach, individual land use effects show promise for additional insight into P
sources and DP processes contributing to elevated mean DPTSA concentrations.

The interaction between P sources and DP processes described here leads to
consideration of the unintended consequences toward DP levels of some common P
management practices. These practices, while reducing PP to surface waters, may
result in long term increases in DP. The inferences into catchment inﬂuenced DP
cycling identiﬁed here provide insights that can be use to improve watershed P

assessment and management strategy development.

94

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Literature Cited

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potential land use-derived solute sources to stream baseﬂow using ground
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Carpenter, S.R., Caraco, N.F., Correll, D.L., Howarth, R.W., Sharpley, AN. and
Smith, V.H., 1998. Nonpoint Pollution of Surface Waters with Phosphorus and
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Coulter, C.B., Kolka, R.K. and Thompson, J.A., 2004. Water quality in agricultural,
urban, and mixed land use watersheds. Journal of the American Water
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Dodds, W.K., Smith, V.H. and Lohman, K., 2002. Nitrogen and phosphorus
relationships to benthic algal biomass in temperate streams. Canadian Journal
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Fitzpatrick, M.L., Long, D.T. and Pijanowski, BC, 2007. Exploring the effects of
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Glandon, R.P., Payne, F .C., McNabb, CD. and Batterson, T.R., 1980. A comparison
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Hatt, B.E., Fletcher, T.D., Walsh, C.J. and Taylor, S.L., 2004. The inﬂuence of urban
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Hickey, M.B.C. and Doran, B., 2004. A review of the efﬁciency of buffer strips for the
maintenance and enhancement of riparian ecosystems. Water Quality Research
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Inamdar, S.P., Mostaghimi, S., McClellan, P.W. and Brannan, K.M., 2001. BMP
impacts on sediment and nutrient yields from an agricultural watershed in the
coastal plain region. Transactions of the Asae, 44(5): 1191-1200.

Lehrter, J .C., 2006. Effects of land use and land cover, stream discharge, and
interannual climate on the magnitude and timing of nitrogen, phosphorus, and
organic carbon concentrations in three coastal plain watersheds. Water
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Lewis, G.P., Mitchell, J .D., Andersen, C.B., Haney, D.C., Liao, MK. and Sargent,
K.A., 2007. Urban inﬂuences on stream chemistry and biology in the Big
Brushy Creek watershed, South Carolina. Water Air and Soil Pollution, 182(1-
4): 303-323.

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McDowell, R.W., Sharpley, AN. and F olmar, G., 2003. Modiﬁcation of phosphorus
export from an eastern USA catchment by ﬂuvial sediment and phosphorus
inputs. Agriculture Ecosystems & Environment, 99(1-3): 187-199.

Novak, J.M., Stone, K.C., Szogi, A.A., Watts, D.W. and Johnson, M.H., 2004.
Dissolved phosphorus retention and release from a coastal plain in-stream
wetland. Journal of Environmental Quality, 33(1): 394-401.

Novak, J.M., Stone, K.C., Watts, D.W. and Johnson, M.H., 2003. Dissolved
phosphorus transport during storm and base ﬂow conditions from an
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the Asae, 46(5): 1355-1363.

Ontkean, G.R., Chanasyk, D.S. and Bennett, DR, 2005. Snowmelt and growing
season phosphorus ﬂux in an agricultural watershed in south-central Alberta,
Canada. Water Quality Research Journal of Canada, 40(4): 402-417.

Paciﬁc Meridian Resources, 2001. Integrated forest monitoring assessment and
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project, 2nd Revision. Report for the Michigan DNR. On the web at

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and+Cover+2001 .

     

Penn, C.J., Mullins, G.L. and Zelazny, L.W., 2005. Mineralogy in relation to
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Schippers, P., van de Weerd, H., de Klein, J ., de Jong, B. and Scheffer, M., 2006.
Impacts of agricultural phosphorus use in catchments on shallow lake water
quality: About buffers, time delays and equilibria. Science of the Total
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Sharpley, A., 1999. Agricultural phosphorus, water quality, and poultry production:
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control of agricultural phosphorus losses to water: An overview. Journal of
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dissolved N, P and Si in large rivers. Biogeochemistry, 64(3): 297-317.

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Buffer zones and constructed wetlands as ﬁlters for agricultural phosphorus.
Journal of Environmental Quality, 29(1): 151-158.

Wayland, K.G., Long, D.T., Hyndman, D.W., Pijanowski, B.C., Woodhams, SM. and
Haack, SK, 2003. Identifying relationships between baseﬂow geochemistry
and land use with synoptic sampling and R-mode factor analysis. Journal of
Environmental Quality, 32(1): 180-190.

Williams, M., Hopkinson, C., Rastetter, E., Vallino, J. and Claessens, L., 2005.
Relationships of land use and stream solute concentrations in the Ipswich River
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loading in an urban watershed. Journal of the American Water Resources
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basin. Journal of the American Water Resources Association, 43(3): 594-604.

97

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CHAPTER 4
INFERRING DISSOLVED PHOSPHORUS CYCLING ON A RIVER SYSTEM
FROM SERIAL IMPOUNDMENTS USING STREAM BIOGEOCHEMISTRY
Abstract

Patterns in suites of chemicals can be used to provide insight into the
biological cycling (sources, pathways, fate) of P resulting from serial impoundments.
Biological activity in streams, lakes and impoundments has been shown to regulate
many abiotic variables (P concentrations, suspended solids, water quality variables
and clarity). The role of serial impoundments in the biological cycling (sources,
pathways, fate) of P in stream systems has been difﬁcult to discern from other
watershed inﬂuences (temporal trends and catchment inﬂuence).

To address this issue, in a two-year study of the KRLAW, a MLM is used to
quantify the temporal trend, improving the relationships between DP, stream
chemistry and land use. The MLM results are used to remove the temporal trend, and
patterns are explored using common multivariate statistical techniques.

Results show that for stream systems containing serial impoundments the
aquatic system connectivity with the landscape is disrupted by processes within
theimpoundment systems that control P and delay eutrophic recovery. Additionally,
impoundment processes are linked for upstream/downstream impoundments.

The inferences into biological impoundment DP cycling have implications for
watershed P assessment and management. The inlet P status to Lake Allegan, the
impaired waterbody, is largely determined by the downstream effect of Morrow Lake

impoundment processes.

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Introduction

The USEPA (1996) identiﬁed accelerated eutrophication as the most
ubiquitous water quality problem in the United States (McDowell and Sharpley,
2003). Eutrophication can be reversed by decreasing input rates of P and N, but rates
of recovery are highly variable among waterbodies and often the eutrophic state is
persistent and recovery is slow (Carpenter et al., 1998).

The biological activity in streams (Figueroa-Nieves et al., 2006; Morgan et al.,
2006; Mulholland, 2004; Stevenson et al., 2006), lakes (French and Petticrew, 2007;
Grover and Chrzanowski, 2004; Hakanson, 2005; Reed-Andersen et al., 2000; Yuan et
al., 2007) and reservoirs (Havel and Pattinson, 2004; Reed-Andersen et al., 2000;
Schreiber and Rausch, 1979) has been shown to regulate many variables associated
with eutrophication. These include concentrations of P, suspended solids, many water
quality variables and water clarity. Stevenson et al. (2006) state that many measures
of algal biomass and nutrient availability were positively correlated in a study of
Michigan and Kentucky streams. Researchers have identiﬁed relationships between
chlorophyll a, total P (TP) and DP in lake systems (French and Petticrew, 2007;
Hakanson, 2005; Momen et al., 1996).

Reservoirs or impoundments represent a transition zone from lotic to lentic
ecosystems, and given that they encompass intermediate characteristics that deﬁne
both lakes and rivers, they have been described as ‘river-lake hybrids’ (Kimmel et al.,
1990; Wall et al., 2005). Kelly (2001), in a study of the Rio Grande and Colorado
basins, found that the connectivity of the aquatic system with the landscape is

apparently disrupted by processes within reservoir systems and that these processes

99

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result in large changes in characteristics for solute transport that persist downstream in
the absence of signiﬁcant inputs. Additionally, reservoir processes may be linked for
upstream/downstream reservoirs that are located relatively close in a series. This
concept of process disruption by reservoirs -termed serial discontinuity (SDC)— has
also been explored by Ward and Stanford (2001; 1995).

The role of serial impoundments in the biological cycling of P in stream
systems has been difﬁcult to discern from other watershed inﬂuences such as temporal
trends and catchment inﬂuence. The hypothesis is that patterns in biological
inﬂuenced DP, land use and stream chemistry correlate to impoundment SDC
processes. To test this hypothesis, biological inﬂuenced data are separated ﬁ'om
catchment inﬂuenced data and the MLM, used to quantify the ﬁxed temporal trend
and random site effects (see Chapter 2). By removing these effects, temporal trend
and site adjusted DP (DPTSA) increase and strengthen the stream chemistry and land
use relationships. DPTSA, stream chemistry, trace element and land use patterns and
relationships are analyzed using MLM, PFA and GLM to provide inferences about
impoundment DP cycling and stream system response to impoundment SDC.

Patterns and relationships in DPTSA, PP and chlorophyll a are shown to
correlate to biological inﬂuenced impoundment DP cycling. Changes in P forms and
chlorophyll a are identiﬁed for two impoundments and for the stream segment ﬂowing
between them. This study provides evidence for biological inﬂuence and the
regulation of P from the impoundment SDC of the ﬁrst impoundment on the

downstream river and impoundment. Impoundment P sourcing and sinking processes

100

are identiﬁed as contributors to DP cycling. Historical P data is explored to evaluate
impoundment regulation of P outlet concentrations.

The approaches developed in this study advance the knowledge of the stream
DP response to the biological inﬂuence of impoundment SDC. These insights have
implications for P management strategies and expectations. Results indicate that
current P reduction strategies of TP and PP management should be refocused on DP
for serial impoundment systems. DP reductions at impoundment inlets should
accelerate the rate of decline in outlet P concentrations. The expectations for
watershed recovery should be based on this rate of decline in outlet concentrations as

opposed to reductions in catchment TP inputs.

Methods

Impoundment biological inﬂuenced DP cycling was investigated using the
KRLAW stream chemistry dataset (Appendix I), KRLAW trace element dataset
(Appendix 11), land use descriptions (Table 1.1.), historical mean growing season data
(Appendix III) and historical mean monthly discharge data (Appendix IV). The study
site, sampling locations, sampling methods and chemical analyses are described in
Chapter 1. The biological inﬂuenced MLM ﬁxed stream chemistry, land use and
temporal trend effects (Tables 2.3) and random effects (Table 2.4) detailed in Chapter
2 were used for this study. The sites and dates that constitute the biological inﬂuence

datasets are shown in Figure 2.5.

101

Temporal trend and site adjusted DP

The temporal trend and site effects were removed from the biological
inﬂuenced DP to improve the number and strength of the DP, stream chemistry and
land use relationships. DPTSA is determined by rearranging equation 2.5 as follows:

log(DP)r5A = log(DP) — TT — SE = int + SC + LU (4.1)

Equation 4.1 and the estimates from Table 2.3 were used to calculate
log(DP)TSA. DPTSA was calculated by back transforming log(DP)T3A.
Load estimation

Constituent loads were estimated by multiplying the period mean daily
discharge by the period mean weekly constituent concentrations by the period of
interest. Mean daily discharge for the outlet of Morrow Lake was calculated from
USGS gaging station data for the Kalamazoo River at Comstock, Michigan, station
number 04106000. Morrow Lake inlet mean daily discharge was calculated by
adjusting the outlet mean daily discharge by the ratio of the catchment area at the inlet,
divided by the catchment area at the outlet (0.96). Lake Allegan inlet and outlet daily
mean discharge was calculated from USGS gaging station data for the Kalamazoo
River near New Richmond, Michigan, station number 04108670. Lake Allegan outlet
mean daily discharge was calculated by adjusting the New Richmond gaging station
daily mean discharge by the ratio of the catchment area at the outlet, divided by the
catchment area at New Richmond (0.81). Lake Allegan inlet mean daily discharge
was calculated by adjusting the New Richmond gaging station daily mean discharge
by the ratio of the catchment area at the inlet, divided by the catchment area at New

Richmond (0.78).

102

Statistical analysis

MLM, GLM and PF A are the statistical methods used to identify patterns
among the DPTSA, suites of chemicals and land use to infer impoundment inﬂuenced
DP cycling. MLMs are described in Chapter 2 and Appendix V. GLM uses the least
squares method to ﬁt a general linear model relating continuous dependent variables to
independent variables (SAS, 1999). PF A detects structure in variables identifying a
common factor that explains the variability between variables. The common factor is
an unobservable, hypothetical variable that contributes to the variance of at least two
observed variables (SAS, 1999). Rotations are used with PFA analyses to achieve a
simple structure having a few high loadings and many zero or near-zero loadings
(Reyment and Joreskog, 1993). The statistical methods for this study were
implemented using SAS 9.1.3 (SAS, 2007), including PROC MIXED, PROC GLM

and PROC FACTOR procedures.

Results

The MLM temporal trend and random site effects (Tables 2.3 and 2.4) were
removed from the DP using equation 4.1, providing a dependent variable —DPT5A—
related to stream chemistry and land use that can be analyzed using common
univariate and multivariate statistical techniques. The signiﬁcant (p<0.05) ﬁxed
effects for stream chemistry (PP, NO3', 8042', C1' and pH; Table 2.3) and land use
(urban; Table 2.3) from the catchment inﬂuenced MLM were evaluated with respect
DPTSA. The mean and standard deviation by site for DP, DPTSA, and signiﬁcant stream

chemistry, and the percent by site for each signiﬁcant land use are given in Table 4.1.

103

Table 4.1: The mean and standard deviation (mean :1: standard deviation) by site for
dissolved phosphorus (DP), temporal trend and site adjusted dissolved phosphorus
(DPTSA) and the signiﬁcant (p<0.05) stream chemistry ﬁxed effects (PP, NOg', SO42}
Cl' and pH) and land use percentages for the signiﬁcant (p<0.05) land use ﬁxed effect
(urban) from the biological inﬂuenced MLM.

 

 

 

SITE DPTSA PP Cl'
on") 04L") ogr') (mgL">
KS 14.15 :1: 2.23 14.39 :1: 2.26 72.87 1 20.64 53.33 3: 4.81
KC 15.37 :1: 3.17 17.33 :1: 4.57 67.38 4 17.85 54.45 :1: 6.82
K 35.60 :t 12.49 35.02 :L- 12.29 80.78 :L- 20.44 84.42 :1: 11.82
KP 46.74 i 19.90 49.45 :t 17.47 51.00 :t 25.69 87.34 :1: 19.61
KA 33.94 :E 16.47 30.65 :t 11.98 47.81 :h 27.07 74.16 :1: 8.64
KD 14.81 :1: 2.38 23.52 :1: 4.64 52.80 3: 10.82 71.60 i 9.28
SITE so.,"-'l N03:l pH Urban
(mgr) (mgL ) (pH) %
KS 45.30 :b 2.27 0.40 :1: 0.18 8.08 :1: 0.17 6.7
KC 45.43 :t 2.84 0.32 :t 0.19 8.06 :1: 0.16 6.8
K 49.89 :t 3.02 1.00 :1: 0.24 7.90 4: 0.16 9.1
KP 48.49 :t 6.46 1.36 i 0.40 7.72 :h 0.19 9.0
KA 491232.89 1.12i0.31 8.063015 8.5
KD 48.33 :1: 2.62 0.45 i 0.20 7.98 :t 0.20 8.5

 

A block diagram of the system with KM, the site upstream, and biological
inﬂuenced sites (KS, KC, KK, KP, KA and KD), is shown in Figure 4.1. The mean
growing season (April through September) and mean biological inﬂuenced (data from
dates under biological inﬂuence) TP, DP and PP concentrations for 2005 and 2006 are
plotted in Figure 4.1.

General trends in mean TP concentrations through this region for both 2005
and 2006 are typiﬁed by an increase from in TP the inlet to the outlet of Morrow Lake;
an increase in TP from the Kalamazoo Water Reclamation Plant (KWRP); a decrease
in TP at sites (KP in 2005, K in 2006) following the KWRP to the inlet of Lake

Allegan; and a decrease in TP from the inlet to the outlet of Lake Allegan. For both

104

VF“
El .

CUT:

lllll Ill, ll.

2005 and 2006, trends in DP and PP are the same from the Morrow Lake inlet to after
the KWRP, but these fractions differ for the remainder of the system. The mean
growing season TP concentrations follow the mean TP concentrations of the biological
inﬂuenced dates. Although under biological inﬂuence for a only portion of the

growing season, this biological inﬂuence provides the greatest control on mean TP

 

 

 

 

 

 

 

 

 

 

 

 
     
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

concentrations.
Mean Concentration (ng‘)
l
3‘”: "9 2005 2000
0‘” om GrowinqSeason Biological Inﬂuenced Growing Season Biologicallnﬂuenced
DP PP TP DP PP , TP DP PP TP DP f PP TP
0 36 10 10510 35 70 105 0 36 70 106 0 3.5 10 100
. n, . 1 j , .
T I Q\ " Q3
lt‘ ‘( ’s
l 1 l“ I ‘
l ‘\ l l l
‘ \
l ‘ l \ I
\
1 1 (1
3 r - - t 1 _
,1 1'. . ‘ '
r r r . Q
1 1 g \
1, 1 _ g ‘ _
l , l 1 \C“
1 ‘ l
l t g
l, l, l 4
1' r 1: , . 1
I ’ l 1
1 I '_ 1 1
it t l 4
l l i ‘1
Lake ' 1' f ,‘E
Allegan : , '. 1
. I
t ,- l 3 ' 1
:I: [DP - — - - PP ------- TP |

Figure 4.1: Diagram of the biological inﬂuenced region of the KRLAW depicting

2005 and 2006 sampling sitesO, 2006 sampling sites 0 , impoundments: , the
major point source (Kalamazoo Water Reclamation Plant) and mean TP, DP and

PP concentrations for the 2005 and 2006 growing seasons and biological inﬂuenced
periods.

A closer inspection of growing season mean TP, DP and PP for the six
Kalamazoo River main stem locations (Figure 4.2) shows similar concentrations at the

105

outlets of the impoundments (KC and KD) in 2005 and 2006. Prior to the Morrow
Lake outlet (KB and KM), differences exist between 2005 and 2006 in all three P
forms that are associated with variable catchment inﬂuences (sources and ﬂow paths).
Impoundment processes within Morrow Lake compensate for these differences,
producing similar concentrations for all three P forms at the outlet. Therefore,
Morrow Lake processes disrupt the connection of the downstream system from the
upstream catchment inﬂuence. Similar mean TP concentrations after the outlet of
Morrow Lake show the persistence of the impoundment biological inﬂuence
downstream and the linkage with the downstream impoundment (Lake Allegan).
While the mean TP concentrations are comparable year to year downstream of
Morrow Lake, the DP and PP forms vary for the sites (KP and KA) between the
impoundment outlets. This indicates impoundment processes control TP, PP and DP,
but additional processes downstream change the DP and PP fractions without
changing the TP relationship year to year.

For the impoundment processes to produce similar outlet P forms, Morrow
Lake sourced an additional 8000 kg P (2005) and 3900 kg P (2006) and Lake Allegan
sinked 6100 kg P (2005) and 5900 kg P (2006) between the inlet and outlet (Table
4.2). Similar mean outlet P concentrations are attained with yearly variable mean inlet
P concentrations and under differing yearly climatic conditions evident in the
discharge hydrographs (Figure 4.3). The consistent increase in TP concentration from
KC to KP is the result of the similar loading in 2005 and 2006 by the point source

input of the KWRP (Table 4.2).

106

— Morrow Lake Inlet

Morrow Lake Outlet

Lake Allegan Outlet —ﬁ
Lake Allegan Inlet -

 

 

 

 

 

 

 

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L 80 -
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4° <r""

20 7

0 ‘1 t r I
0 20 40 60 80 100 120
KE KM KC KP KA KD

Distance Downstream from KE (km)
Sampling Location

"9"2005 +2006

Figure 4.2: Comparison of 2005 and 2006 growing season mean TP, PP and DP for
six Kalamazoo River main stem sites sampled both years versus distance downstream

from the site KE, with Morrow Lake and Lake Allegan inlets and outlets identiﬁed by
vertical lines.

107

Table 4.2: Morrow Lake and Lake Allegan 2005 and 2006 growing season mean TP,
discharge and estimated TP load and Kalamazoo Water Reclamation Plant TP load.

 

 

 

2005 2006
Mean Mean
Mean TP . TP Load Mean TP . TP Load
Drscharge Drscharge

my") 011’s") (kg) 0%") (m3s") (kg)
Morrow Lake Inlet 48.3 19.4 14,794 62.4 22.9 22,611
Morrow Lake Outlet 71.6 20.1 22,758 70.4 23.8 26,485
Difference (Outlet-Inlet) 7,964 3,875
Lake Allegan Inlet 79.5 33.1 41,666 78.1 38.3 47,283
Lake Allegan Outlet 65.9 34.1 35,527 66.4 39.4 41,407
Difference (Outlet-Inlet) -6,139 -5,876
Kalamazoo Water 8,209 8,341

Reclamation Plant“
*Source: (Kieser & Associates, 2008)

 

70

 

 

 

 

2005 i l 2006

J JALALAA

A 01
O 0

Discharge (m3s'1)
O)
O

 

N
O

103

 

 

 

 

 

 

Figure 4.3: Discharge hydrographs for the 2005 and 2006 growing seasons at the
outlet of Morrow Lake (site KC).

Prior to discussing the P cycling of these individual systems, the overall

system will be considered. Patterns and relationships among DPTSA and stream

108

chemistry, land use and trace elements are investigated using the MLM results (Table
2.3) and PFA to provide insight into DP cycling due to impoundment biological
inﬂuences.

Stream chemistry and land use relationships

A varimax-rotated PF A was performed on the biological inﬂuenced stream
chemistry, land use and DPTSA data (Table 4.1). The results are given in Table 4.3 and
explain 90.4% of the variance in the data with three factors. Factor 1 is interpreted as
the urban inﬂuence indicated by a strong DPTSA loading directly with moderate urban
land use, NO3' and Cl' and inversely with moderate pH. Factor 2, unrelated to DPTSA,
is another urban factor with the stream chemistry reﬂecting strong and moderate
loadings of urban land use to DPTSA, NO3', 8042' and Cl'. Inspection of the mean
NO3', SO42} Cl' and pH (Table 4.1) reveals the greatest change in these parameters
occur after the KWRP (site KK). Urban relationships of Factors 1 and 2 reﬂect the
point source input of the KWRP as a source for DP, NO3', 8042' and Cl' and as a
modiﬁer of pH. Factor 3 is interpreted as the biological inﬂuence with moderate
inverse loading between DPTSA and PP and moderate direct loading between DPTSA
and N03".

Factor 3 relationships are consistent with changes in DP, PP and NO3' with an
increase associated with algal productivity and macro-invertebrate grazing. N03' is
confounded with Factor 1, and changes could be from the KWRP, biological inﬂuence
or a combination of both. PP is unique in loading with DPTSA in Factor 3, indicating

PP is the best parameter to use when inferring DP cycling associated with biological

109

inﬂuence. Patterns in the biological trace element PFA were investigated for
relationships between DPTSA, urban land use and trace elements. -
Table 4.3: Varimax-rotated factor loading matrix from principal factor analysis for the

biological inﬂuenced stream chemistry dataset and urban land use from the
Kalamazoo River/Lake Allegan Watershed.

 

 

Factor 1 Factor 2 Factor 3
DPTSA 0.7708 0.5339
PP -0. 5253
NO; 0. 4877 0.4190 0.5490
sof' 0.8472
Cl' 0.4763 0.8011
pH -0. 6664
Urban 0.5691 0. 4801

Percent of total variance explained
0.3613 0.3461 0.1963
Total percentage of variance explained: 90.4%
Strong loadings (Z 0.70) are indicated by bold type.
Moderate loadings (>0.40 and <0.70) are indicated by italics.

Trace element relationships

The varimax-rotated biological trace element PF A (Table 4.4) has four factors
explaining 82.3% of the variance in the data. Factor 2 is the only DP factor with
strong loadings on DPTSA, urban land use, B, V, Mo and Cr. The inclusion of urban
land use in this factor suggests that the DPTSA, B, V, Mo and Cr relationship results
from the KWRP and does not relate DP to biological inﬂuence. Factors 1, 3 and 4 are
unrelated to DPTSA with strong and moderate loadings between suites of trace
elements. Due to the lack of relationships with DPTSA in Factors 1, 3 and 4, as well as
the interaction with urban land use in Factor 2, the trace element PFA does not provide

additional information for inferring biological inﬂuenced DP cycling.

110

Phosphorus forms

The biological MLM and stream chemistry PFA provide an association
between DP and PP. Changes in PP concentrations are the result of biological PP and
DP exchanges and sediment PP settling and resuspension. The analysis for PP in the
study does not discriminate between biological and sediment PP forms. When
exploring DP exchanges, these forms will be described as DP, sediment PP and algae
bound PP. Morrow Lake, Lake Allegan and the connecting stream segment will be
evaluated to infer DP cycling from biological and impoundment inﬂuences.
Table 4.4: Varimax-rotated factor loading matrix from principal component analysis

for the biological inﬂuenced DPTSA, urban land use and trace element dataset from the
Kalamazoo River/Lake Allegan Watershed.

 

 

Factor 1 Factor 2 Factor 3 Factor 4
DPTSA 0.8389
Urban 0.7506
B 0.9633
V 0.8713
Mo 0.8033
Cr 0.7197 0.4356
Se 0.7128
Rb -0.7612
Mn 0.8694
Fe 0.9030
As 0.8844
Ba 0.9383
U -0.9489
Sr -0.7811 0.4218
Al 0.6922
Sc 0.8872
Ti 0.9205
Percent of total variance explained

0.3052 0.2543 0.1706 0.0927

Total percentage of variance explained: 82.3%
Strong loadings (2 0.70) are indicated by bold type.
Moderate loadings (>0.40 and <0.70) are indicated by italics.

111

Morrow Lake — A phosphorus sourcing impoundment

The Morrow Lake impoundment is the ﬁrst impoundment in the Kalamazoo
River system with a residence time greater than seven days. Reservoirs with retention
times greater than seven days provide an environment for primary productivity
(Kimmel et al., 1990; Straskrabova et al., 1973). TP concentrations increase from the
inlet (KM) to the outlet (KS and KC) of Morrow Lake during the biological inﬂuenced
sampling dates (Figure 4.4). TP loads were increased by 8000 and 3900 kg per
growing season from inlet to outlet in 2005 and 2006, respectively (Table 4.2). These
TP load increases reﬂect growing season exports of 0.76 and 0.31 kg ha", which are
much greater than the growing season exports ranging ﬁ'om 0.03 to 0.17 ha'1 estimated

during this study for other catchments in the KRLAW.

 

 

 

 

 

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Figure 4.4: TP changes from Morrow Lake inlet (KM) to outlet (KS and KC) for the
biological inﬂuenced sampling dates. Note: Site KS sampled in 2006 only.

112

The increase in TP concentrations and P loads are believed to be sourced from
within Morrow Lake. Impoundment biological inﬂuences are proposed as part of the
P release process. Before examining the Morrow Lake inﬂuence, the catchment
surrounding and draining into Morrow Lake was considered as a potential source for
these increases.

An industrial P input the size of the KWRP located in the Morrow Lake
catchment would be required to supply the 2005 P load increase, yet there are no
industries located in the Morrow Lake catchment, thus eliminating industry as the
source. The DP concentration decreases while the PP concentration increases from the
Morrow Lake inlet (KM) to the outlet (KC) (Figure 4.5). The discharge hydrograph in
Figure 4.5 shows that the PP increase occurs during lower ﬂows and therefore is not
associated with runoff transporting catchment PP. Chlorophyll a was sampled in 2006
to determine if algal productivity contributed to TP loading, mean DP decreases and
mean PP increases. Increases in chlorophyll a correspond to increases in PP,
decreases in DP and decreases in dissolved NO3' from the inlet (KM) to the outlet
(KC) of Morrow Lake (Figure 4.6). TP, chlorophyll a, NOg' and primary productivity
have been shown to be highly correlated (Knoll et al., 2003). From these chemistry
associations with primary productivity and the lack of industry present, it is assumed
that the increases in TP and PP at the outlet of Morrow Lake are sourced from within
the impoundment, not from catchment inﬂuences.

Mass balances of inlet to outlet P fractions and the accounting for exchanges
between DP and algae bound PP are used to provide insight into DP cycling from

biological and impoundment processes within Morrow Lake. Mass balances of the P

113

fractions show that the increase in PP is 8000 kg greater than the decrease in DP for
the 2005 growing season and 3900 kg greater for 2006. This additional P comes from
within Morrow Lake —most likely from P stores in the bottom sediments— to support
algal productivity. More DP was available from the inlet in 2006 compared to 2005
(mean DP concentrations of 27.4 ugL'l and 23.0 ugL", respectively), resulting in less

P required from the Morrow Lake bottom sediments to support similar algal

 

 
 
  

 

 

 

 

productivity.

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+KM PP +KC PP 'G'KM DP 'G'KC DP ——KC Discharge

Figure 4.5: Inlet PP (KM PP), outlet PP (KC PP), inlet DP (KM DP) and outlet DP
(KC DP) concentrations for the biological inﬂuenced dates and the outlet discharge
(KC Discharge) for the 2005 and 2006 growing seasons.

114

 

120
100 7
80 7

PP (119 L-1 1
a

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20 7

 

 

 

 

 

DP (149 L" )
(,0
O

 

 

 

 

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P
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Chlorophyll 3 (mg L‘1 )

 

 

 

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3/28 4/18 5/9 5130 6/20 7/11 8/1 8/22 9/12 1013
---a--- KM + KC

Figure 4.6: Morrow Lake inlet (KM) and outlet (KC) PP, DP, NO3' and chlorophyll a
concentrations for the 2006 growing season.

115

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The similarity in mean outlet TP concentrations between 2005 and 2006
implies a comparable annual algal productivity that controls outlet TP levels. The
deﬁcit between inlet P and the P required for algal productivity is supplied from
Morrow Lake bottom sediments. Historical P data (Appendix III) of mean growing
season outlet TP concentrations indicate impoundment biological processes have
controlled mean growing season outlet TP since 1981 (Figure 4.7). From 1981 to
2006 the outlet TP concentrations and variability have reduced from pre-1981 levels
with the exception of 2003 (Figure 4.7). Data were not available to assess 1973, 1995,
1996 or1997. Late season discharge in 2003 was at consecutively low levels from
July through September. Increased water residence time and decreased algae ﬂushing
under these conditions probably led to higher than normal productivity within Morrow
Lake and to higher TP concentrations. The 2003 growing season data was excluded
from the analyses. Outlet TP levels and variability prior to 1981 suggest that inlet P
levels were in excess of biological needs and that the impoundment was sinking P.
Industrial control of P due to regulations in the 19705 may have reduced P
concentrations at the inlet below biological requirements, leading to a switch to P
s ourcing to maintain productivity.

The trend line indicates a decrease in mean growing season outlet TP
concentrations since 1981. This suggests that the release rate of P stored in the bottom
sediments of the lake may be declining. The biological inﬂuenced DP cycling

Morrow Lake processes decreases DP and converts DP and stored P to algae bound

116

PP. These processes control outlet mean TP, DP and PP concentrations,

compensating for inlet differences across both years of the study.

180

 

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80

 

 

 

60 -

4O -

Mean Total Phosphorus (ng'1)

20 ~

 

 

 

0 f - r r r
1965 1970 1975 1980 1985 1990 1995 2000 2005 2010

Year

ﬂ r

Figure 4.7: Historic Morrow Lake outlet mean growing season TP concentrations.
Trend — and range 1:: from 1981to 2006 excluding 2003. Data Sources: 0 USEPA
STORET Database; 0 MDEQ; and O KRLAW study.
Morrow Lake outlet to Lake Allegan inlet

The changes in mean TP, DP and PP for the 2005 and 2006 growing seasons
are given in Figure 4.1 for the sampling sites from the Morrow Lake outlet to the Lake
Allegan inlet (KC, KK, KP and KA). The KWRP is located between sampling sites
KC and KP. Mean TP concentrations were similar at sites KC, KP and KA in 2005

and 2006. Growing season TP loadings reported for the KWRP were comparable at

8209 kg in 2005 and 8341 in 2006 (Kieser & Associates, 2008).
117

In 2006, sampling site KK, downstream of the KWRP, was added to better
understand the impact of the KWRP. The 2006 mean TP data show that the KWRP
load increases the Morrow Lake outlet mean TP concentration by 25.4 ugL'l by site
KK. Lower TP concentrations from catchment inputs, typically 36 to 60 ugL", mix
with higher stream concentrations, reducing concentrations at sites KP and KA. The
2006 growing season mean DP and PP increases at site K are attributed to the
KWRP point source input. After the KWRP, changes occur in the DP and PP
fractions. Chlorophyll a, PP and DP relationships at sites KC and KA (Figure 4.8)
indicate a conversion of PP to DP associated with algal consrunption. The stream
segment from K to KP contains substrates to support macroinvertebrate populations
(Cooper, 2005) that graze on algae and convert DP to PP.

Without chlorophyll a data and sampling site KK, only DP and PP data are
available to assess the macroinvertebrate conversion of algae bound PP to DP in 2005
(Figure 4.8). The DP and PP patterns seen in 2006 are not present in 2005. The
KWRP increase between sites KC and KP is evident. However, the conversion
between DP and PP does not appear to occur until later in the season and in much
lower levels. Cooper (2005) noted in the 2004 bioassessment that macroinvertebrate
densities were low due to an unusually wet spring that created multiple high water
events. Discharge conditions were similar in 2005, with multiple high water events
that may have reduced macroinvertebrate communities, grazing populations and the
conversion of algal PP to DP. Speculation is that in 2005 higher levels of PP
—consisting partially of algae that were not consumed after exiting Morrow Lake—

reached the Lake Allegan inlet.

118

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119

The DP cycling ﬁ'om the Morrow Lake outlet to the Lake Allegan inlet is
variable between years. DP concentrations decreased after the KWRP in 2005 and
increased in 2006. Variation in DP and PP forms appears to be caused by climatic
effects on the integrity of the macroinvertebrate community. TP concentrations were
comparable from 2005 to 2006 through this stream segment supporting the minimal
effect of catchment inputs and the dominance of biological inﬂuences on P. Morrow
Lake control of DP and PP mean concentrations is disrupted by variable downstream
biological inﬂuences that determine the concentrations reaching Lake Allegan.

Lake Allegan — A phosphorus sinking impoundment

The Lake Allegan mean inlet TP concentrations were similar for the growing
seasons in 2005 and in 2006 (Figure 4.1). The P cycling within Lake Allegan
produced similar, but lower mean outlet TP concentrations (Figure 4.1). The TP load
estimations show sinking of TP within Lake Allegan of 61 00 kg in 2005 and 5900 kg
in 2006 (Table 4.2).

The TP load retention and outlet mean TP, DP and PP concentrations were
comparable in 2005 to 2006, with differences in mean inlet DP and PP concentrations
(Figure 4.1). As with Morrow Lake, the year to year consistency of the P forms
exiting Lake Allegan suggests that productivity limits the biological processes. In
2006, when chlorophyll a data are available, the biological inﬂuence in Lake Allegan
is evident through the increase in chlorophyll a corresponding to a decrease in DP, an
increase in PP and a decrease in N03' from the inlet (KA) to the outlet (KD) (Figure

4.9). Compared to Morrow Lake, Lake Allegan PP changes are smaller for similar

120

chlorophyll a changes. Since Lake Allegan is sinking P, the exchange of sediment PP
for algae PP in the water column may account for this difference.

Without chlorophyll a data in 2005, the DP, PP and N03' patterns are used to
provide insight into DP cycling (Figure 4.9). The inlet PP concentrations are higher
and the DP and N03' concentrations lower in 2005 than 2006, which supports the
previous speculation that algae survived transport to Lake Allegan as multiple high
water events reduced macroinvertebrate communities in 2005. This algal load
produced in Morrow Lake contributes to the total algae populations in Lake Allegan
but reduces the algae produced within the impoundment. The reduction in N03'
within Lake Allegan should result in a larger than observed increase in PP and a
decrease in DP, would suggest that a portion of the algae produced in Lake Allegan
may die and remain there. As in 2006, the P fractions are rebalanced as a portion of
the inlet PP as sediment P settles out and is replaced algal PP.

Comparing the 2005 and 2006, the Lake Allegan outlet mean DP and PP
concentrations are similar indicating similar productivity. HoweVer, because of the
differences between 2005 and 2006 in inlet mean DP and PP, this productivity was
achieved by different pathways. Productivity is limited by the combination of
incoming algae as PP and DP. In 2005, algae PP was high and DP low. The low DP
was reduced from a mean concentration of 21 ugL'l to 13 1.1gL'l by additional algal
uptake. In 2006, algae PP was low and DP high. The high DP was reduced from a

mean concentration of 41 ugL'l to 14 ugL'l by algal uptake.

121

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122

In both years, approximately 6000 kg of TP were retained in Lake Allegan.
The settling of sediment PP was probably responsible for a large portion of this TP,
but algae —produced in either Morrow Lake or Lake Allegan— dying, settling and
burying in Lake Allegan may also contribute to this load.

Available historic mean TP data (Figure 4.10) show that Lake Allegan P
dynamics have produced a relatively stable range of outlet concentrations with large
ﬂuctuations in inlet concentrations since 1998. 2005 and 2006 produced similar inlet
TP concentrations, leading to the retention of similar TP loads. The large differences
in inlet to outlet TP in previous years would require the amount of P retained within

Lake Allegan to vary substantially year-to-year to produce this outlet TP stability.

 

 

 

 

 

 

 

 

 

 

 

140
0
120 “ ’ I ’ \\
.1." I ’0' \\ , ’ ®\\
I I
31004 (9’ \ ,I‘O’ \\
a I
g ...... b' 9‘ ~
.2 80 . h ' A ‘0 - - - .
3' 7Wv\- A """
O *‘“ V VV=Q
3
n. 60 """
'3
...
c 40 .
3
E
20 1
0 - r . ' r ‘ ' ‘~
1998 1999 2000 2001 2002 2003 2004 2005 2006

Year

Figure 4.10: Historic Lake Allegan inlet (circles) and outlet (diamonds) mean
growing season TP concentrations from 1998-2006. Outlet trend — and range 33::
Data Sources: 0 O MDEQ and o O KRLAW study.

123

Since] 998, a downward trend in outlet TP is observed. This decline
corresponds to the downward trend previously discussed in the outlet TP
concentrations exiting Morrow Lake, one major source of DP and algal PP depending
on the condition of the downstream macroinvertebrate community.

The DP cycling from processes in Lake Allegan modiﬁes DP and PP
concentrations and controls TP outlet concentrations. Available DP is taken up by
algae growth down to minimum levels of 9 tolO ugL". The distribution of DP and PP
is a function of Morrow Lake impoundment processes, upstream/downstream linkage
of serial impoundments and macroinvertebrate grazing upstream of the Lake Allegan
inlet. Lake Allegan is a P sink retaining approximately 6000 kg of TP for both years
of the study. The P cycling produces similar outlet mean TP, DP and PP
concentrations, regardless of inlet concentrations across both years of the study.
Impoundment phosphorus sourcing and sinking dynamics

This study has inferred biological inﬂuenced P dynamics occurring within
large ﬂow-through impoundments that produce major modiﬁcations to the P forms
between the inlet and the outlet. Within the same watershed, one impoundment
(Morrow Lake) is sourcing P and one (Lake Allegan) is sinking P. While evaluating
inlet and outlet stream chemistry supports the existence of P sourcing and sinking, the
exact nature of the processes that produce these results cannot be determined without
extensive in-lake water and sediment sampling. Regardless, the impoundment
processes have a controlling effect on the P status of the downstream system that has
not been previously identiﬁed and was not anticipated at the beginning of the study.

Knowledge of the release and accumulation of P is important to watershed P recovery.

124

The ability to compesate for variable incoming P conditions to produce a similar
narrow range of outlet conditions year to year has signiﬁcant implications for P
management strategy.
Phosphorus management implications

The control exerted on P forms by ﬂow-through impoundments such as
Morrow Lake and Lake Allegan compensates for changes in P delivered by the
upstream system. In a P stressed watershed like the KRLAW, P reduction efforts
upstream of these impoundments will be compensated for by this natural process. It
is encouraging that recent historical evidence shows a decline in mean yearly TP
concentrations being produced by these processes. Intervention to modify these
impoundment processes is limited to accelerating the rate of this decline. Reductions
in DP at the inlet should accelerate the decline in mean yearly TP at the outlet of these
impoundments. In the meantime, upstream P reductions will be will be compensated
for with remaining stored P by impoundment processes. The overall watershed

response to P reductions will be delayed by those processes.

Discussion
By removing the temporal trend and site effects from biological inﬂuenced DP data,
patterns between DPTSA and land use, stream chemistry and trace elements are used to
provide insight into DP cycling associated with ﬂow-through impoundment processes.
MLM results and PF As develop DP and PP relationships associated with biological

processes. Other DP, stream chemistry and trace element relationships relate to urban

125

land use, including industrial inputs. The urban inﬂuence prevents their use as
indicators for biological inﬂuence.

Biological inﬂuences are identiﬁed through the changes in and exchanges
between DP and PP for Morrow Lake, Lake Allegan and the stream segment ﬂowing
between them. Impoundment SDC processes and biological inﬂuences are shown to
regulate P concentrations and forms on a watershed scale. Morrow Lake compensates
for deﬁcits in incoming DP by internally sourcing additional DP to support biological
productivity. This process releases previously stored P from within the impoundment,
reduces inlet P variability and regulates outlet mean P forms from growing season to
growing season. Morrow Lake is a natural control on the P delivered from the
upstream landscape and from industrial inputs (approximately 64% of the KRLAW
catchment area). Exchanges between the pools of DP and PP are shown to be variable
depending on climatic conditions and the integrity of the macroinvertebrate
community. The total DP represented by these two forms —largely determined by
Morrow Lake and the point source input of the KWRP— establish the inlet conditions
for processes within Lake Allegan. Lake Allegan processes provide a regulating effect
similar to Morrow Lake but as a P sink. The apparent productivity in the Lake
Allegan system is similar from year to year. The actual productivity differs depending
on the amount of algae that survives the transport from Morrow Lake and the amount
produced internally. Data from 2005 and 2006 exhibit similar outlet P forms from
growing season to growing season. The total productivity in Lake Allegan is

controlled by Morrow Lake and the industrial inputs after Morrow Lake, while the

126

actual productivity is controlled by the macroinvertebrate community exchanges
between DP and PP.

Impoundments processes exert the greatest control and regulation within this
system. Sourcing or sinking P, the impoundments produced comparable mean TP, DP
and PP concentrations for both years of the study. The ﬁrst impoundment (Morrow
Lake) in the KRLAW study system is the primary control. The sinking of P in Lake
Allegan accounts for excess P delivered to the inlet beyond the needs for biological
productivity. Until inlet TP is reduced below productivity needs, Lake Allegan
responds to Morrow Lake and industrial inputs by accumulating P. Reducing inlet DP
and algae PP concentrations below the levels required for productivity will force Lake
Allegan to switch to sourcing P to meet productivity requirements.

The biological inﬂuence and inferences about P sourcing, P sinking and DP
cycling have implications for P management. Common P agricultural and urban
management practices are aimed at preventing catchment PP from entering surface
waters. However, biological inﬂuenced systems are governed by DP, not catchment
supplied sediment PP. Moreover, the P compensation and regulation imposed by
impoundment processes overrides the inlet conditions to produce similar outlet
conditions from growing season to growing season. Managing impoundment DP
cycling is limited to reducing inlet concentration to accelerate the depletion of P stored
in lake-bottom sediments. Reducing the catchment inputs of DP to the inlet of a P
sourcing impoundment will have minimal immediate impact, but should accelerate the
of decline outlet P concentrations over time. Reducing DP inputs to P sinking

impoundments will accelerate the decline in the rate of P accumulation. The ultimate

127

goal of these reductions should be to transition the P sinking impoundment to P
sourcing conditions. Once P is being removed from the system, recovery from
anthropogenic P degradation and the long-term reversal of eutrophication will begin.
Results from this study support the hypothesis that patterns among biological
inﬂuenced DP, stream chemistry and land use correlate to impoundment SDC
processes. Prior to this study the extent of the control imparted by ﬂow-through
impoundments in the KRLAW on P levels was not understood. Fortunately, historical
data indicate a downward trend in mean TP concentrations exiting these
impoundments, suggesting progress towards recovery. In light of these ﬁndings,
watershed managers should recognize impoundment P dynamics, target reductions in
DP and gauge the watershed response by the rate of decline in impoundment mean TP

concentrations.

Conclusions

This study uses patterns among land use, stream chemistry and trace element
data to infer biological inﬂuenced DP cycling in the KRLAW. These results support
the hypothesis that patterns among biological inﬂuence DP, stream chemistry and land
use correlate to impoundment SDC processes.

MLM results and stream chemistry PF A provide evidence of the biological
inﬂuence on DP cycling through DP and PP relationships. The trace element PFA
identiﬁed the association of DP, Cl', SO42”, NO3’, pH and trace elements urban land

use, not biological inﬂuence.

128

From the DP dynamics inferred for the biological inﬂuenced segments of the
KRLAW, it is concluded that: 1) impoundment processes disrupt the connection
between the landscape and the stream system; 2) processes in Morrow Lake —the ﬁrst
large impoundment— are sourcing P and are regulating P forms delivered downstream;
3) the KWRP P input is additive to the Morrow Lake P outputs; 4) DP and PP —but
not TP— are altered by biological processes and diluted by catchment inputs after the
KWRP; and 5) the processes in Lake Allegan —the second large impoundment— are
linked to the processes in Morrow Lake, sinking P and regulating P forms
downstream.

The inferences into biological inﬂuenced DP dynamics identiﬁed here have
implications for watershed P assessment and management strategy development. The
regulatory processes resulting from impoundment SDC are a natural control on outlet
P concentrations. The compensatory nature of impoundment processes will offset P
reduction efforts and delay the downstream response. Current P reduction strategies
that promote conservation practices such as reducing PP inputs should be reconsidered
and redirected towards DP reductions. The downstream effects of Morrow Lake
impoundment processes and the point source inputs of the KWRP are largely
responsible for the inlet P concentrations to Lake Allegan, the impaired waterbody.
Two control points exist in the KRLAW which affect and assess P concentrations at
the inlet to Lake Allegan: the Morrow Lake outlet TP concentrations and the industrial

point source loading after Morrow Lake.

129

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Figueroa-Nieves, D., Royer, T.V. and David, M.B., 2006. Controls on chlorophyll-a in
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French, TD. and Petticrew, EL, 2007. Chlorophyll a seasonality in four shallow
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132

CHAPTER 5
A MODEL FOR PREDICTING THE PHOSPHORUS REDUCTIONS TO A
FLOW THROUGH RIVER IMPOUNDMENT
Abstract

The Federal Clean Water Act Section 303(d) requires all states to identify
water quality impaired waterbodies and develop Total Maximum Daily Loads
(TMDLs) or other watershed restoration approaches to correct impairments. Models
using historical data can be used to predict TMDL recovery and guide P reduction
strategies. Historical data is oﬁen limited and difﬁcult to use in a modeling
framework. To address this, intensive sampling is used to provide insight into the
cycling (sources, pathways and fate) of chemicals and to simplify model development.

A two-year study of stream chemistry in the KRLAW identiﬁed DP cycling
within impoundments that regulate P concentrations downstream. Using this
knowledge, an empirical model developed for Lake Allegan’s (the KRLAW impaired
waterbody) inlet TP concentration is reduced to three terms. The model is used to
predict progress toward TMDL goals and to understand the effects of reduction
efforts.

The model predicts with 95% conﬁdence that the Lake Allegan inlet TP goal
will be achieved when adjusted to mean discharge. TP and discharge relationships are
identiﬁed that inﬂuence Lake Allegan inlet TP. P recovery and timing for various
management and reduction strategies are estimated using the model. This research has

broader implications for P TMDL development and assessment.

133

Introduction

The Federal Clean Water Act Section 303(d) requires all states to identify
streams and rivers that do not attain water quality standards and to submit a list of
these streams to the US. Environmental Protection Agency (USEPA) (U SEPA,
2008b). For listed streams, the Act requires that states must develop Total Maximum
Daily Loads (TMDLs) or other watershed restoration approaches. TMDLs are an
estimation of the amount of a constituent that streams can receive and still meet water
quality standards (Haggard et al., 2003). Models using historical data can be used to
predict TMDL recovery and guide P reduction strategies. In general, developing these
models involves using historical data amassed by federal, state and local monitoring
programs. These data are collected on a fairly regular schedule (oﬁen at monthly or
bimonthly intervals) but with varying periods of record by location. While such
limited data can form the basis for water quality characterization, they are oﬁen
difﬁcult to use in a modeling framework. Model studies oﬁen require intensive
sampling for a reliable assessment (Litwack et al., 2006).

Intensive sampling can provide insight into processes that control constituent
sourcing, fate and transformation. These insights simplify modeling and trend
analysis by reducing the model to fewer terms that describe constituent loading at a
point of interest. By individually analyzing model terms, the maximum historical data
available from associated locations can be used to improve the reliability of that term’s
prediction. Improving the reliability of individual terms should improve the capability

of the ﬁnal model combining those terms.

134

Scientists use both theoretical and empirical approaches to prediction.
Theoretical predictions are based on a theory of a process or mechanism, while
empirical predictions are based on curve ﬁtting or pattern recognition without an
attempt to represent underlying mechanisms (Carpenter, 2002). Empirical models are
developed by predicting the contemporary value of a variable from simultaneous
values of other variables. Then, assuming that contemporary relationships hold across
time, scientist use empirical models to make future predictions (Carpenter, 2002).

An empirical model is developed that uses statistical trends and relationships
as the basis for predicting TP from the KRLAW at the inlet to Lake Allegan. An
empirical model was chosen because KRLAW historical data —although limited to TP,
discharge and a few locations— could provide trends that could be used for model
predictions. To address data limitations, intensive sampling over two growing seasons
provided insight into temporal (Chapter 2), catchment (Chapter 3) and biological
(Chapter 4) inﬂuences on DP cycling in the KRLAW. Impoundment processes were
identiﬁed that control DP cycling in Morrow Lake (Chapter 2). These processes
reduce the model to three terms: 1) the Morrow Lake outlet; 2) point source inputs
after Morrow Lake; and 3) catchment and in-stream inﬂuences aﬁer Morrow Lake.
Historical TP and discharge data are available to model these three terms.

The model is developed for the mean growing season (April to September).

TP concentration is predicted for the inlet to Lake Allegan in 2012, the year for
achieving the TMDL P goal of 72 pg L". Sixty-nine years of discharge data are used
to assess the probability of attaining the TMDL P goal under various discharge

conditions. The TP concentration is forecast below the 2012 TMDL goal at the mean

135

discharge parameters from the 69 year period of record. The short- and long-term
effectiveness of reduction strategies targeted at catchment and point source P inputs
based on the model terms are discussed.

The results of this study have implications for evaluating the progress toward
TMDL goals in the KRLAW relevant to stakeholders and the regulatory agency.
Implications for current and future P reduction strategies with respect to maximizing
short-term P reduction potential in the KRLAW are presented. Finally, the broader

implications for P TMDL development and assessment are considered.

Methods

The empirical KRLAW TP model was developed using the KRLAW stream
chemistry dataset (Appendix 1), historical mean growing season data (Appendix III)
and historical mean monthly discharge data (Appendix IV). The study site, sampling
locations, sampling methods, chemical analyses and historical data sources are
described in Chapter 1. Insights and inferences into catchment and biological
inﬂuenced DP cycling developed in Chapters 3 and 4 were used to develop the model
system.
Statistical analysis

The general linear model (GLM) was the method used to identify trends in TP.
GLM uses the least squares method to ﬁt a general linear model relating continuous
dependent variables to independent variables (SAS, 1999). A 95%
conﬁdence/prediction interval for individual predictions is used for the statistical
analysis to account for the variability within the data. The 95% individual prediction

interval is given by the equation (Ott and Longnecker, 2001):

136

 

x —x
Yn+lita/2 S§\/1+'Ill‘+£'il (5-1)

SXX

where to); is the Student’s t for a/2 = 0.05/2 = 0.025 and n —- 2 degrees of freedom.
Prediction equations and conﬁdence/prediction intervals were developed from the
GLM output. Standard statistical methods were used to develop frequency
distributions and probability plots. Normality was tested using the Shapiro-Wilk
statistic. This statistic —W—, tests the null hypothesis of normality, ranging from
greater than zero to less than or equal to one (0 < W S 1). Small values of W lead to
rejecting the null hypothesis. The statistical methods for this study were implemented
using SAS 9.1.3 (SAS, 2007), including PROC GLM and PROC UNIVARIATE

procedures.

Model Development

Impoundment processes that control DP cycling were identiﬁed in Chapter 2
which disconnects the upstream landscape from the Kalamazoo River at the Morrow
Lake outlet. Variations in Morrow Lake inlet TP concentration are compensated for
by interaction between biological activity and the storage and release of sediment
phosphorus regulating outlet TP concentration. These processes simplify modeling
the TP concentrations at the inlet to Lake Allegan by eliminating approximately two-
thirds of the catchment (the area upstream of the Morrow Lake outlet) from the model.

Available historical P data from the KRLAW project, the MDEQ and the

KRLAW TMDL point source tracking system is separated into three model terms to

137

predict the Lake Allegan inlet concentration: I) the Morrow Lake outlet; 2) point
source inputs aﬁer Morrow Lake; and 3) the combined catchment and in-stream
inﬂuences aﬁer Morrow Lake. KRLAW sampling cannot discriminate between
catchment (sources, climate, hydrology, etc.) and in-stream inﬂuences (settling,
resuspension, adsorption, desorption, etc.). The combined effects of catchment and in-
stream inﬂuences are modeled in term 3. A block diagram of the system showing the
model terms is given in Figure 5.1.
Concentration, load and discharge considerations

Available historical P data have been reported as TP concentrations (pg L")
from stream sampling locations, and TP load (kg month") has been reported for point
source inputs. The model is developed based on growing season TP loading.

<-1 r")

 

 

Before Morrow Lake outlet is After Lake Allegan inlet is
System Model

disconnected from the system disconnected from the system
Point Source

 

 

 

 

 

has been designated at 72 pg L"

POIIII Source at sampling site KA.

 

 

 

l
I
by impoundment SDC. l by impoundment SDC.
I The TMDL concentration goal
I
Inputs :
I

Inputs

 

 

 

 

 

 

    

w-@ o a

 

 

 

 

 

 

 

 

I I

Catchment : Catchment :

and ' and |

ln-stream : In-stream :

Inﬂuences I Inﬂuences I
<-J L->

Figure 5.1: Block diagram for the TP model development for KRLAW Lake Allegan
inlet concentration (KA) identifying inputs and inﬂuences D and sampling
locations .

138

TP loading is calculated by multiplying mean TP concentration by total
discharge volume as follows:

Lsma (kg gs") = TPSITE (pg L") 135...; (m3s"><o.0864 kg L s m‘3 d")<183 d gs") (5.2)
or

LsrrE = 15-311TPSITEDSITE (53)
where: Lsmg = growing season TP load, TPsm; = growing season mean TP
concentration, Dsm; = growing season mean daily discharge and SITE is the location
designation.

Load calculation using 5.3 requires discharge. The USGS gaging station for
the Kalamazoo River at Comstock, Michigan —station number 04106000 at sampling
site KC- has discharge records dating back to 1931. The discharge at KC (DKC) was
used as the reference discharge for the model because of this extensive record.
Discharge is required site KA (DKA). The relationship between DKA and DKC is
developed using data from the USGS gaging station for the Kalamazoo River near
New Richmond, Michigan —station number 04108670— downstream from KA. DKA is
estimated by adjusting the discharge at New Richmond by the ratio of the catchment
area at site KA to the catchment area at New Richmond (0.81). The correlation
between the growing season monthly means for DKA and DKC for the period of record
for New Richmond (1994, 1995 and 2003 to 2007) is shown in Figure 5.2. DKA and
DKC are highly correlated (R2 = 0.97) and their relationship is represented by the
equation:

DKA = 1.7765DKC +1.5568 (5.4)

139

Growing season mean monthly discharge (MDKC) at Site KC is available from
USGS gaging data. In addition, MDKC was separated into mean monthly direct
discharge (MDDKC) and mean monthly base ﬂow discharge (MBDKC). The recursive
digital ﬁlter method was used for base ﬂow separation. The digital ﬁlter method is
used in signal analysis and processing to separate high frequency signal from low
frequency signal and has been used in base ﬂow separation because high frequency
waves can be associated with direct runoff and low frequency waves with base ﬂow
(Eckhardt, 2005; Lim et al., 2005). The Web-based Hydrograph Analysis Tool
(WHAT) (Lim etal., 2004) was used to generate mean monthly direct and base ﬂow

separated data directly from the USGS data for the period of record at KC.

 

90

on
O
L
O

 
 

y = 1.7765x - 1.5568

 

N
O
l

O)
0

U1
0

 

h
0
-.LL .--

Monthly Mean Du (m3s4)
03
O

N
O
I

O

10*

 

 

 

0 10 2o 30 40 so 60
Monthly Mean DKc (mite-1)

Figure 5.2: The relationship between monthly mean discharge at the outlet of Morrow
Lake (DKC) and the inlet of Lake Allegan (DKA).

140

All of the discharge data are summarized in Appendix IV. TP concentration, TP
loading and various discharge parameters were used to create a TP load model for the
inlet to Lake Allegan.

The goal is to produce a model that can be used to predict the inlet
concentration to Lake Allegan with 95% conﬁdence and thus predict the ﬁiture
potential to attain the TMDL goal.

TP load model

The TP load model is the summation of the growing season TP loads to the
inlet of Lake Allegan shown in Figure 5.1 and is represented by the equation:

LKA = LKC + LCAM + LPAM (55)
where LKA = TP load at the inlet to Lake Allegan (KA), LKC = TP load at the outlet of
Morrow Lake (KC), LCAM = TP load from catchment inputs and in-stream inﬂuences
after Morrow Lake, and LpAM = TP load from the point sources after Morrow Lake.
Each term is considered individually and recombined to create the ﬁnal model.

T P load from Morrow Lake (LKC)

The available historical Morrow Lake outlet mean growing season TP
concentration data by year is given in Figure 5.3. Visual inspection of this plot shows
a shift after 1981 —with the exception of 2003— where the growing season mean TP
concentrations appear to be regulated by the processes within the Morrow Lake
system to a narrower range of values. Late season discharges in 2003 were at
consecutively low levels compared the period of record from July through September.

Increased residence time and lack of ﬂushing under these conditions probably allowed

141

for higher than normal productivity and outlet TP concentrations. As an outlier for the

period, the 2003 growing season was excluded from the analyses.

 

 

 

 

 

 

 

 

 

180

160 *
.1.“ Outlying data point
.51, 140 ' Removedfortrendanalysis
5
a 120
E
2
a 100 ~
in
2
a- 80 7
:3
|_ 60
c
3 40 . y=-0.4794x+1029.6
E R2 = 0.3139

20 ,4

0 . . . . . . . . f . .
1968 1972 1976 1980 1984 1988 1992 1996 2000 2004 2008 2012 2016
Year

Figure 5.3: Historic Morrow Lake outlet mean growing season TP concentrations.
Trend — and 95% prediction interval 33:: from 1981 to 2006, excluding 2003. Data
Sources: 0 USEPA STORET Database, 0 MDEQ and O KRLAW study.

The data from 1981 to 2006 —excluding 2003— was analyzed using a GLM
(Table 5.1). Year was the only signiﬁcant variable (p = 0.0067). All discharge
parameters including DKC, MDKC, MDDKC and mean MBDKC were evaluated and
none were signiﬁcant for explaining the remaining variability. The equation for the

trend line shown in Figure 5.4 from the GLM model output is:

TPKC = -0.4794Year + 1029.6 (5.6)

142

Table 5.1: GLM output for TPKC = Year for the outlet of Morrow Lake.

 

 

 

 

 

 

 

Source df SS MS F Value Pr > F
Model 1 307.6146 307.615 9.15 0.0067
Error 20 672.5105 33.6255
Total 21 980.1251
Parameter Estimate S.E t Value Pr > M
Intercept 1029.6 315.863 3.26 0.0039
Year -O.4794 0.1585 -3.02 0.0067
n = 22
x = 1993.73
7 = 74.259

£=5.7987

SXX = 672.5105

 

The upper and lower 95% prediction limits from equation 5.1 are shown in
Figure 5.4 using tags/2 = 2.086 and the model output from Table 5.1. The range of the
95% predicted mean growing season TP values is approximately i 12.5 to 15.8 pg L",
the result of a low R2 (0.31) and the unexplained variability remaining in the data.
Combining equations 5.4 and 5.6 —substituting TPKC for yn+1, Year for xw, and using
the values for the GLM output— the equation for predicting growing season mean
TPKC with a 95% prediction interval is:
TPKC = (-0.4796Year + 1029.6) 8: (152.96 + (0.4664Year — 929.48)2)°'5 (5.7)
Incorporating the growing season discharge volume to produce the equation for
predicting the TP load at the outlet of Morrow Lake using equation 5.3 yields:
Lxc = TDKC((-7.583Year + 16,2790) i (38,2381 + (7.374Year - 14,696.0)2)°'5 (5.8)

Equation 5.8 provides the 95% conﬁdence statistical prediction for LKC for the ﬁnal

model.

143

T P load ﬁom catchment and in-stream inﬂuences after Morrow Lake (LC/1M)

The TP load from the catchment and in-strearn inﬂuence (LCAM) after Morrow
Lake and before the inlet to Lake Allegan was not measured directly. Growing season
LCAM was calculate as the remaining load after the subtracting the Morrow Lake outlet
load (LKA) and the point source load after Morrow Lake (LpAM) from the load at the
inlet to Lake Allegan (LKA), or LCAM = LKA - LKC - LpAM. Historical data were
available for 1998 and 2001 to 2006 to calculated LCAM. The calculated values for
LCAM are given in Appendix III.

Year and the distribution of discharge for the growing season are used to
account for the variability in LCAM. Green et al. (2007) found that TP concentrations
were more variable in a watershed with a higher contribution from overland ﬂow.
Moog and Whiting (2002) concluded that stream ﬂow tended to dominate the other
explanatory variables in explaining load variation, including TP load. A GLM was
used to evaluate Year and various discharge parameters to estimate LCAM. Year,
monthly direct discharge in May (MDDs), monthly base discharge in July (MDB7) and
monthly total discharge in August (MDg) were signiﬁcantly (p < 0.05) related to LCAM
(Table 5.2). The equation for the prediction from the GLM output in Table 5.2 and
shown in Figure 5.4 is:

LCAM= -176l .7Year + 316.9MDD5 - 1113.4MBD7 + 2753.6MTD3

+ 3,518,413.0 (5.9)
The upper and lower 95% prediction limits from equation 5.4 are given in Figure 5.4

using 1005/2 = 2.571 and the model output from Table 5.2.

144

Table 5.2: GLM output for LCAM = Year + MDD5 + MBD7 +MD3 for the growing
season catchment input and in-stream inﬂuence TP load after Morrow Lake.

 

 

 

 

 

 

 

Source df SS MS P Value Pr > F
Model 4 790,048,419.3 197,512,104.8 7184.4 0.0001
Error 2 54,983 .4 27,491.7

Total 6 790,103,402.7

Parameter Estimate S.E t Value Pr > |t|
Intercept 3,518,413.011 65,455.87555 53.75 0.0003
Year -1761.69 32.55766 -54.1 1 0.0003
MDDS 316.939 15.97918 19.83 0.0025
MBD7 -1113.4l 33.80229 -32.94 0.0009
MDs 2753.553 33.53644 82.11 0.0001
n = 7

i = 25,206.07

3' = 25,206.07

s, =165.8062

sxx = 790,048,419.3

 

Combining equations 5.4 and 5.9 —substituting for y... and xn+1, and including the
values from the GLM output—— the equation for predicting growing season mean LCAM
with a 95% prediction interval is:
LCAM = -1761.7Year + 316.9MDD5 - 1113.4MBD7 + 2753.6 MDg +
3,518,413.0 i: ((207,613.5 + (—26.7Year + 4.8MDD5 —
16.9MBD7 + 41 .8MD3 + 52,969.9)2)°‘5 (5.10)
Equation 5.10 provides a strong correlation (R2 = 0.99) between Low and Year,
MDD5, MBD7 and MDg. This is a statistical relationship where in addition to Year, a
combination of mean growing season monthly direct, base ﬂow and total monthly
discharges in May, July and August, respectively, estimate LCAM. The association of

TP loading with the amount and timing of discharge parameters is consistent with the

145

results of other research (Green et al., 2007; Moog and Whiting, 2002). Equation 5.10

provides the 95% conﬁdence statistical prediction for LCAM for the ﬁnal model.

 

45.000 .
1

40.000
1

35.000

30,000 *

    

R2 = 0.9999
15.000 1

LC”. (kg growing season")
N N
0 0'1
0 O
O O
O 0

10.000 1

5,000 1

 

 

0 g . a? . —.— , 4 .—-— ———4
0 5.000 10.000 15.000 20.000 25,000 30,000 35.000 40.000 45.000
-1761.692Year + 316.939MDD5 - 11 1 3.408MBD7 +

2753.553MD. + 3,518,413.011
(kg growing season")

 

 

Figure 5.4: GLM relationship for growing season catchment input and in-stream
inﬂuence load. Prediction — and 95% prediction interval:::: for 1998 and 2001-
2006. Data Sources: MDEQ and KRLAW study and KRLAW TMDL point source

tracking system.
T P load from point sources after Morrow Lake (LpAM)

Thirty-seven industrial and municipal point sources that discharge into the
KRLAW system were signatories of the Kalamazoo River/Lake Allegan Watershed
Cooperative Agreement for the Reduction of Phosphorus Loading (known as
the“Cooperative Agreement”) (Molloy et al., 2002). As part of the Cooperative
Agreement, their monthly loading is reported and tracked on the Web-based

Kalamazoo River/Lake Allegan TMDL Point Source Tracking System (Kieser &

146

Associates, 2008). The growing season point source loading before Morrow Lake,
after Morrow Lake and the total are shown in Figure 5.5. Under the Cooperative
Agreement, the point sources have committed to maintaining 1998 loading levels for
April through June and to reducing 1998 loading levels by 23 % for July through
September. This amounts to an overall reduction goal of 11.5 % for the growing
season by 2012 (Figure 5.5). As of 2008, total point source loading has been reduced

by over 40%, aided by the closure of manufacturing facilities between 1998 and 2001.

 

30,000

23.449

25.000 7

20.956

20.000 3

15,000 3

10.000 -

Growing Season TP Load (kg)

5,000 ‘

 

 

 

 

o 4 . . . '
1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2012
Goal

Year

I Before Morrow Lake I After Morrow Lake

Figure 5.5: Growing season documented point source TP loads before the Morrow
Lake inlet (LPBM), after the Morrow Lake outlet (LpAM), total point source load and the
KRLAW TMDL point source goal in 2012. Sources: 1998: (Heaton, 1999) 2001 —
2008: (Kieser & Associates, 2008).

Morrow Lake impoundment processes disconnect the point source loads from

the model system before the impoundment. However, the point source loads after

147

Morrow Lake (LpAM) contribute to the loading at the Lake Allegan inlet. Since the
decline before 2001, the LPAM has ranged from 8,516 kg to 10,256 kg. Industrial and
municipal TP loading is demand driven and does not lend itself to statistical prediction
using watershed parameters. For the ﬁnal model, LPAM will be retained and estimates
assumed for this loading will be used for prediction purposes.

Final model for TP loading at the Lake Allegan inlet (L 101)

Statistical inferences with 95 % prediction intervals for the trends in LKC
(equation 5.7) and LCAM (equation 5.9) have been developed. LPAM remains to be
estimated based on assumptions for future point source loading after Morrow Lake.
Combining these terms into the load model (equation 5.5) produces the ﬁnal model
equation:

L KC estimate

 

I I
LKA = [DKc(-7.583Year + 16,279.0)] (5.11)

LCAM estimate
1

+l [-1761.7Year + 316.9MDD5 - 1113.4MBD7 + 2753.6 MDs + 3,518,413.0l
LpAM estimate

PAM

LKC 95 % prediction interval

 

:tl [DKC(38,238.1 + (7.374Year - 14,696.0)2)°'5]|

LCAM 95 % prediction interval

 

F l
i [(207,613.5 + (-26.7Year + 4.8MDD5 - 16.9MBD7 + 41 .8MD3 + 52,969.9)2)°'5]
Equation 5.11 represents a model for the 95% conﬁdence prediction of the TP load at

the inlet to Lake Allegan (LKA) based on statistical inferences of the trends in the

148

Morrow Lake outlet TP load (LKC) and the catchment input and in-stream inﬂuenced
load after Morrow Lake (LCAM) and an estimate for the point source inputs after

Morrow Lake (LPAm).

Results

The goal in producing the loading model for the inlet to Lake Allegan is to
estimate the short-term TP recovery prospects for Lake Allegan and the implications
to TP reduction strategies based on recent trends in watershed characteristics. The use
of any model to forecast future values comes with assumptions. The assumptions
made in forecasting LKA and thereby TPKA are: 1) the statistical trends inferred for LKc
and LCAM will continue, and 2) the estimate for LpAM is reasonable for the prediction
year. The year 2012 was chosen for the prediction year because it is the year
designated for attaining the TMDL goal.
Recovery prospects by 2012

The KRLAW TMDL produced an implementation plan (Molloy et al., 2002)
for P reductions to attain a Lake Allegan inlet growing season mean TP concentration
of less than or equal to 72 pg L”1 by 2012. Given a value for TPKA for a target year, an
estimate for LpAM is required to evaluate the model equation. As previously discussed,
the point source load is demand driven. The highest recorded loading (10,256 kg)
since 2001 was increased by 10% to estimate LpAM (11,282 kg) in 2012.

The load model (equation 5.11) is used to evaluate TPKA S 72 pg L'1
—attainment of the TMDL goal. Using equation 5.3, TPKA is represented by:

LKA =15.811TPKADKA (5.12)

149

DKC is the reference discharge location. Substituting equation 5.4 for DKA and
rearranging equation 5.12 yields:
TPKA = (LU/15.8112)(1.7765DKC + 1.5568) (5.13)

To ensure 95% conﬁdence in the prediction, LKC and LCAM must be less than their
upper prediction limits, so these are used from equation 5.11 when substituting for
LKA. Substituting equation 5.11 for LKA, Year = 2012, and LpAM = 11,282 kg in
equation 5.13 creates the following model equation predicting TPKA (PTPKA) S 72 pg
L" in 2012:
PTPKA S 72 pg L'IS [1262.43DKC - 11,282 + 316.9MDD5 - 1113.4MBD7 +

2753.6 MDg + ((207,613.5 + (-750.5 + 4.8MDD5 —

16.9MBD7 + 41 .8MD3)2)°'5)] / [(280881)KC + 246149)] (5.14)
Equation 5.14 describes the combination of discharge conditions for DKC, MDDs,
MBD7 and MDg that predict PTPKA in 2012. Discharge conditions in 2012 were
estimated based on the probability of the discharge conditions from the period of
record for DKC. Equation 5.14 was evaluated for each of the 69 years of growing
season discharge data (1933 to 1979 and 1985 to 2006) to generate the frequency
distribution for PTPKA based on historical discharge at KC (Figure 5.6).

For the distribution of PTPKA, the Shapiro-Wilk statistics (W = 0.9535, p <
0.0119) indicate that the distribution of PTPKA is normal and can be used to estimate
the probability of discharge conditions that may occur in 2012. The probability plot
for PTPKA and the theoretical diagonal distribution line based on a normal distribution

are given in Figure 5.7.

150

 

50

45

(a)
U'I

0)
O

 

Frequency (percent)
N N
O 0'!

_A
01

 

 

 

 

 

PTPKA (11814")

Figure 5.6: Histogram of PTPKA in 2012 based on equation 5.14, using 69 years of
discharge data at site KC.

 

 

    

 

 

 

 

120 ‘
+
+
100 ‘
+
+ +
80 ‘ +"
5;" .12 ...........................
_l b
D
3.- 60 ‘
i
n.
I- 40 7
n.
20 - 70.1
I I I I I I I I I I I
0.1 l 5 10 25 50 75 90 95 99 99.9

Normal Percentiles

Figure 5.7: Normal probability plot for PTPKA and the theoretical diagonal
distribution line based on a normal distribution.

151

Based on the 69 years of discharge recorded at KC, the probability that the
combination of discharge conditions for DKC, MDD5, MBD7 and MDs will satisfy
PTPKA S 72 ug L'1 is 70.1%. However, LKC and LCAM are predicted at 95% prediction
intervals. The probability of multiple events occurring is the product of the
probability of those events. Therefore, the probability of meeting the TMDL goal in
2012 is:

Prob(TPKA S 72 1.1g L") = Prob(PTPKA) Prob(LKc)Prob(LCAM)

= (0.701)(0.950)(0.950) = 0.633 or 63.3%

The probability of meeting the TMDL goal in 2012 is 63.3% assuming the
Morrow Lake outlet concentration trend continues, the loading trend from the
catchment and in-stream processes after Morrow Lake continues and the point source
loading is not greater than 11,282 kg.

Discharge dependencies

The load model (equation 5.11) shows the dependency of the outcome of LKA
and therefore TPKA on discharge and discharge distribution during the growing season.
In developing the TMDL goal, the MDEQ recognized this dependency and
“normalized” the 1998 nonpoint source monthly load data to monthly mean discharge
for the period of record (1931 to 1997) (Heaton, 1999). The mean values for the
current period of record through 2006 are 24.3, 6.6, 15.4 and 16.4 m3s’l for DKC,
MDD5, MBD7 and MDs, respectively. Using these mean values in equation 5.14, the
predicted value for the growing season mean TP concentration at the inlet to Lake

Allegan —PTPKA— in 2012 is 65.7 ng", below the 72 ng" goal.

152

Implications for reduction strategies
Since the inception of the KRLAW P TMDL in 2000, various P reduction
strategies have been implemented in the watershed. This research and the load model
provide insight into the potential effectiveness of these efforts in different parts of the
watershed. P reductions upstream of the outlet of Morrow Lake, by point sources after
Morrow Lake and from the catchment after Morrow Lake will be considered.
Reductions upstream of the Morrow Lake outlet
Morrow Lake processes disconnect the outlet TP concentrations from the
catchment and point source inputs upstream of the inlet. While these processes
regulate the outlet TP concentrations, they are not totally unrelated to the inlet
concentration. The declining trend in the outlet concentrations are speculated to result
from the ﬁnite availability of P stored in the Morrow Lake bottom sediments. As this
stored P is removed, subsequent removal becomes more difficult. Between 1999 and
2006, it is estimated that 46,340 kg of P were removed from Morrow Lake during the
growing seasons. Over the same period, the trend in outlet TP concentration declined
by 3.4 pg L'], or 0.000073 pg L'1 kg'1 of P removed. Further P reductions, in
particular DP at the inlet to Morrow Lake from reductions in point source and
catchment inputs, may increase the release of P from the bottom sediments and
accelerate the decline in outlet concentration. For example, increasing mean P
removal by 20% between 2007 and 2012 could result in an additional 0.5 pg L'1
reduction in the outlet concentration by 2012. This example illustrates that reductions
upstream of the Morrow Lake outlet will have a long term effect on the outlet TP

concentration. However, substantial reductions will not be realized short-term.

153

Point source reductions after Morrow Lake

All of the point sources within the KRLAW have exceeded their goal of a
combined 11.5% growing season load reduction as of 2008. Given the other trends
remain the same -and if the point sources after Morrow Lake could produce an
additional 10% reduction over 2001 to a load of 9230 kg— the model predicts PTPKA in
2012 at the mean discharge parameters of 62.8 pg L". This is an additional 2.9 pg L"
reduction.
Catchment input reductions after Morrow Lake

To understand the sensitivity of TPKA to LCAM reductions the model is
evaluated with a reduction in combined catchment and in-stream loading of 20% by
2012. The model predicts at mean discharge parameters a PTPKA concentration of
64.7 ug L'l —an additional reduction of 1.0 pg L".
Watershed-wide reduction implications

The load model provides insight into the contribution reductions in various
watershed inputs may have on the mean growing season TP concentration at the inlet
to Lake Allegan. Discharge parameters inﬂuence the contributions of LpAM and LCAM,
but not LKC to PTPKA. The contributions to PTPKA and the percentage of PTPKA for
the minimum (1934), mean and maximum (1994) discharge parameters for the period
of record are shown in Figure 5.8.

The Morrow Lake outlet concentration and its contribution to the Lake Allegan
inlet concentration (43.4 pg L") are not related to discharge parameters. The point
sources after Morrow Lake are a ﬁxed load and their contribution increases with low

discharge (26.3 pg L" at the minimum) and decreases with high discharge (14.1 pg L"

154

at the maximum). The catchment inputs and in-stream processes are opposite of the
point source inputs. At low discharge they retain P prior to the inlet of Lake Allegan
because of low landscape loading and settling to the stream bed (-32 pg L" at the
minimum). At high discharge they provide the greatest loading because of large
landscape inputs and the transport of resuspended bed load (54.6 pg L" at the
maximum).

120 7

100 7

80 7 . 48.6

60 1 9.7

71.6

24.3 12.6

40

1 15.6 66.0 38.8

20"

 

 

Contribution to PTPKA (ugL‘l)

OT‘

   

Min .

_20 - -87.2

 

-40 ~
KC Discharge Parameters (1933-2006)

I Morrow Lake Outlet I Point Sources after Morrow Catchment & In-stream after Morrow

, Figure 5.8: Predicted 2012 contributions to PTPKA of the modeled P sources at the
minimum, mean and maximum discharge parameters for the period of record at KC.
Percentage contribution to the total listed in bold next to the bars.

TPKc can only be minimally affected by reductions upstream of Morrow Lake

and represents 66% of the concentration at the inlet to Lake Allegan when adjusted to

mean discharge parameters. Stakeholder reduction efforts can only target the

155

remaining 34% of the concentration at the inlet to Lake Allegan. Of that 34%, point

source load reductions will have a greater impact than catchment input reductions.

Discussion

The inlet to Lake Allegan is the site identiﬁed by the MDEQ for assessing
attainment of the KRLAW TMDL P goal. An empirical model was developed to
predict TP concentration to Lake Allegan. Central to this model development is the
identiﬁcation of the control imparted by processes in Morrow Lake on outlet TP
concentrations. The TP control imparted by Morrow Lake disconnects the
downstream Kalamazoo River from the upstream catchment inputs and exhibits recent
trends in mean growing season TP outlet concentrations. In the KRLAW system,
Morrow Lake’s location minimizes the effect of approximately two-thirds of the
watershed. This reduces the model to three terms: 1) the Morrow Lake outlet; 2) point
source inputs aﬁer Morrow Lake; and 3) catchment and in-stream inﬂuences after
Morrow Lake.

A load model was developed identifying statistical trends in recent historical
mean growing season TP loads for these three terms. Future point source loading after
Morrow Lake was estimated. The load model was used to predict the TP
concentration at the inlet to Lake Allegan in 2012, the TMDL goal deadline. The load
model shows the dependency of the predicted TP concentration at the inlet to Lake
Allegan on growing season mean discharge and mean monthly direct, base ﬂow and
total discharge distribution. To account for these discharge dependencies, the

probability of 2012 discharge parameters occurring that satisfy the TMDL goal of less

156

than or equal to 72 pg L" was calculated based on 69 years of discharge data. The
load model for 2012 was also evaluated at mean discharge parameters for the period of
record.

Results from the load model indicate a 63% probability that mean growing
season TP concentration —unadjusted for discharge— will meet the 2012 goal assuming
the recent TP trends continue and the point sources aﬁer Morrow Lake maintain their
total loading below 11,282 kg. At mean discharge parameters, the model predicts a
2012 mean growing season TP concentration of 65.7 pg L'1 —6.3 pg L" below the
TMDL goal.

Evaluating the 2012 load model for the period of record discharge parameters
with the lowest and highest result for Lake Allegan inlet concentration yields a range
of 37 to 112 pg L". The probability that either of these discharge extremes will occur
is very low. However, the range reinforces the importance of including discharge
criteria in the speciﬁcation of a TMDL P goal for both the TMDL stakeholder and the
regulatory agency. Discharge conditions could occur by random chance and lead to
success or failure in meeting the TMDL goal when concentration is not adjusted for
discharge.

Results from the model predict progress towards reducing TP concentrations at
the inlet to Lake Allegan. The model provides insight into the impact, interaction and
implications of different P inputs for continued reduction efforts. While catchment
and point source reductions upstream of the Morrow Lake inlet have minimal short-
term effects, these efforts should have long-term effects accelerating the trend in

declining Morrow Lake outlet concentrations. At mean discharge conditions, the

157

catchment and in-stream loads represent less than 10% of the load to Lake Allegan.
Their contribution becomes much greater —as high as 48%— at high discharge and
continued reductions should provide greater protection from P exports during high
discharge conditions. The point sources in general and after Morrow Lake have
exceeded their TMDL load goal, which has contributed to the progress to date.
Further reductions by the point sources after Morrow Lake should have the greatest
short-term impact on Lake Allegan.

In light of these ﬁndings, watershed managers should continue P reduction
efforts throughout the KRLAW, but increase catchment and point source P reduction
efforts after Morrow Lake to maximize the short-term recovery prospects of Lake
Allegan. Morrow Lake impoundment P dynamics should be recognized as a supplier
of P from within the impoundment. Reduction efforts upstream of Morrow Lake
should be evaluated and acknowledged at the inlet to Morrow Lake. Stakeholders
upstream of Morrow Lake should not be discouraged by the lack of short-term
progress reﬂected by the Morrow Lake outlet concentration. Their efforts are required
to accelerate the depletion of P stores in Morrow Lake and will contribute to the long-

term recovery of Lake Allegan.

Conclusions
This study develops an empirical load model for predicting the inlet TP
concentration to Lake Allegan based on statistical trends in limited historical data for
the KRLAW. Insights into DP cycling developed from two years of intensive

sampling reduced the model to three terms that are combined to predict Lake Allegan

158

inlet concentrations from the available historical data. The model predicts TP
concentrations (65.7 pg L") below the TMDL goal (72 pg L" by 2012) at the inlet to
Lake Allegan. A 63% probability is predicted that TP concentrations will be below
the goal without adjustments for discharge. Dependencies between TP concentration
and various discharge parameters are identiﬁed through this model. These
dependencies reinforce the importance of including discharge criteria in evaluating
progress towards the KRLAW P TMDL goal.

Results from this study have implications for point and nonpoint P reduction
strategies in the KRLAW. Reduction efforts upstream of Morrow Lake will have
minimal short-term impact, but will have a long-term effect by accelerating the
declining trend in outlet concentration. Reduction efforts should be focused on point
source and catchment loads after Morrow Lake to maximize the short-term P
reduction to Lake Allegan.

This research has broader implications for P TMDL development and
assessment. The P TMDL development process must include identifying P cycles that
have potential interaction and which compensate for reduction strategies. Accounting
for these processes will lead to improved P goals and reduction timelines. Assessing
progress toward P reduction goals should include monitoring locations before
compensation occurs to acknowledge progress and to maintain motivation for

continued reduction efforts.

159

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phosphorus in natural-waters. Marine Chemistry, 10(2): 109-122.

Wahrer, M.A., Long, D.T. and Lee, R.W., 1996. Selected geochemical characteristics
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of Michigan. US. Geological Survey Water-Resource Investigative Report
944017.

161

Westjohn, DB. and Weaver, T.L., 1997. Hydrogeologic framework of the Michigan
Basin aquifer system. US. Geological Survey Professional Paper 1418. US.
Geological Survey Information Services.

Wetzel, R.G. and Likens, G.B., 2000. Limnological Analyses, third ed. Springer-
Verlag, New York, NY.

Wycheck, J ., 1998. Water quaity and pollution control in Michigan, 1996 Report.

Michigan 305(b) Report. Report No. MI/DEQ/SWQ-98-030, MDEQ, Surface
Water Quality Division.

162

APPENDICES

163

APPENDIX I

KALAMAZOO RIVER/LAKE ALLEGAN WATERSHED STREAM
CHEMISTRY DATASET

164

165

 

 

- :8 2.. 8 2:8 8.8 8.8 8.8 8.2.. 88 88 a8 8.3 2.; 2.8 88.88 cm
- 8.8 8.8 82 8.2 8.8 88 8.8 28 88 :8 8.2 8.8 8.8 8888 um
- 8.:. 8.8 8.2 8.8 8.8 88 8.:. :8 .5 88 2.2 8.2.. 3.8 8888 um
- 8.: 8.8 88 8.8 8.8 88.8 8.8 _8 88 88 8.2 8.9. 8.8 8888 um
- 8.8 5.8 83 3.2 8.8 8.8 8.2. W8 88 8 8.8 8.8 8.8 8888 um
- 8.: :8 2.88 8.8 2.8 E... 8.8 88 a: 88 8.8 :8 8..: 8888 um
- 8.8 :8 a? 8.2 8.8 2.2 8.8 88 8.8 88 8.8 8.8 8.8 8838 um
- 8.: 8.8 $3 8.2 8.8 80.8 8.8 8 a: _8 8.8 8.2. 8.8 8888 um
- 8.8 8.8 8: 8.: 8.8 82.8 8.3. 2... 88 8% 8.8 8.8 8.8 88.28 cm
- 8.8 8.8 8: 8.2 2.8 5.8 8.9. m8 :8 88 8.8 $8 8.8 88:88 um
- 8.8 2.8 3.: 8.2 8.8 2.8 2.8 28 8.“ 88 8.8 8.8 8.8 8888 um
- 8.8 8.8 8: 8.2 8.3. _ 8.8 8.8 88 a: 88 8.2 8.8 8.2. 88.28 cm
- 8.8 5.8 2:: 2.2 8.: 8.8 8.8 ...8 88 8 8.8 8.: 8.8 8888 um
- - - - - - - - - - - 8.8 8; _ 8.8 8888 um
- - - - - - - - - - - 8.8 8.8 8.8 888:. um
- - - - - - - - - - - 8.8 8.8 8.8 8883. um
- - - - - - - - - - - 8.8 8.2 2.8 8883. um
- - - - - - - - - - - m _ .2 8; _ 8.8 88.8. cm

5.83 p-595 2.:an r085 p.85 p.85 9-8.60 p.85 p.85 $3 $585 9.83 p.49: p.88

6 :28 -...oo: 8 .88

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.22 .2888 .832 2888 a 686 86883

I 0 >7 98 HE .0330 .582 8 x85 oﬁmqnom I mm :2 deﬁed—«M 8 8.020 owetom I 0m 52 £95585 8. 82% 0.8me200

I AU— 32 .oonEa—mM doobm 682 2... $2M oo~m§£m¥ I MM HE .8385. 8 83% 885.8me I 0M :2 £080 23mm 8 8320
258mm we 88 52M 8838—30 I mm #2 dame—3. .825 85:30 8 582?. 873 me 8:5 83d oowaESmM I Q :2 £88800
8 8:3 38.82 00 0230 83m conga—av— I 0v— :2 £020 225 8 52M 8585230 I mg :2 883.2 .382 8 ammo—1o.

8:3 8 8:: 83M oomemEM I § :2 .0330 .885 59: 8 83M :30 I m0 ”:2 .5830 ten 8 535. 88..— 2wmm I 0 m ”=2
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166

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167

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28 8.8 8.8 8: 8.8 8.8 888 8.8 m8 8.8 88 8.8 8.8 2.8 8888 mm
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- 2.8 8.8 88.8 8.8 8.8 82 8.8 88 8.8 88 8.8 2.8 8.8 8888 mm
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3 =88 .60: 8 .88
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- 8.8 8.8 :2 8.8 8.8 88.8 8.2 88 8.8 88 2.8 38 8.8 8888 B
- - - - - - - - - - - 8.8 :2 _ 8.8 8888 B
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82 8.8 8.8 88.8 8.2 8.8 22 8.8 m8 8: v8 8.8 2.: 8.2: 8888 mm
882 8.8 8.8 88 3.8 8.8: 288 8.8 88 8.8 28 8.8 8.8 :8 8828 mm
82 8.8 8.8 88.8 8.8 8.8 888 8.8 28 8.8 88 8.2 8.: 8.8 8888 mm
88.8 8.8 8.8 88.8 8.8 8.8 82 8.8 88 8.8 88 8.2 2.8 2.8 8888 mm
88.8 8.8 2.8 38.8 8.8 8.8 888 2.8 88. 8s 88 8.: 8.8 8.8 8888 mm
88.8 8.8 8.8 38.8 8.8 2.8 82 8.8 88 8.8 88 8.8 2.8 8.8 8888 mm
83 8.8 8.8 828 8.8 8.8 888 8.8 88 8: E 8.2 8.8 8.8 8888 mm
88.8 8.8 8.8 88.8 8.8 8.8 82 8.8 88 8.8 88 8.: 8.8 8.8 88:8 mm
28.8 2.8 8.8 88.8 8.8 8.8 _88 8.8 88 8.8 88 8.2 8.8 8.8 8888 mm
22 8.8 8.8 8.8 8.8 :8 888 8.8 :8 8.8 E 8.2 8.8 3.8 888.8 mm
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p.83 p.85 p.85 9.85 5.85 p.85 9.8.5 $8.5 p.85 53 $58.5 p-83 p.83 p.83
a :88 .608 a .88
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169

8.8 8.8 88.8 8.8 8.8 88.8 8.2 28 8.8 _8 2.8: 8.: 2:2 8828 20
8.8 8.2 83 8.8 8.8 82 8.2 88 8.8 88 2.8 8.2 8.8 8888 80
8.8 8.8 821 8.8 8.8 8: 8.: 88 8.8 88 2.8 8.8 8.8 8888 80
8.8 8.8 8: 8: 8.: 88.2 8.2 88 8E 88 8.8 2.8 8.8 8888 80
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p.82 p.225 p-425 p.425 p.425 p.425 525 9.225 £25 22 285851782 p.83 p.83
3 :88 .60: 2 .88
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APPENDIX II

KALAMAZOO RIVER/LAKE ALLEGAN WATERSHED STREAM TRACE
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5 _z 8 on :2 5 > :. am 2 m 33 25

196

 

 

 

 

 

 

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22 D “a am am 8 5 é um 3 cm can 25

198

 

 

 

 

 

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£3 £3 $3 £13 £13 £13 $3 33 ﬁg 31.: £3

32 3 ha 5 am 8 _m 5: om ...... aN 25 25

199

APPENDIX III

HISTORICAL MEAN GROWING SEASON DATA

200

Historical mean growing season data by year for total phosphorus (TPsmg), discharge

('Dsn‘g) and P load (LSOURCJE)
Year TPKM TPKC TPKA DKM DKC

(uglJ') (ugL"> mgr”) (m3s") (m’s")
2008
2007
2006 62.4 70.4 78.1 22.8 23.8
2005 47.9 70.3 79.5 19.3 20.1
2004 63.0 69.0 91.0 26.9 28.0
2003 58.0 117.0 115.0 19.2 20.0
2002 49.0 72.0 104.0 26.1 27.2
2001 61.0 61.0 91.0 30.5 31.8

2000 86.0 73.0 - 23.8 24.8
1999 65.0 72.0 - 20.7 21.5
1998 - 66.0 100.0 26.6 27.7
1997 - - - - 26.7
1996 - - - - 21.3
1995 - - - - 24.3
1994 - 68.5 - - 27.6
1993 - 79.2 - - 35.7
1992 - 85.4 - - 25.8
1991 - 72.0 - - 27.2
1990 - 72.7 - - 28.6
1989 - 72.2 - - 32.8
1988 - 88.4 - - 21.1
1987 - 78.0 - - 19.3
1986 - 67.1 - — 29.9
1985 - 77.9 - - 30.0
1984 - 76.5 - - -

1983 - 87.1 - - -

1982 - 76.5 - - -

1981 - 78.5 — - -

1980 - 98.3 — - -

1979 - 126.0 - - 24.8
1978 - 135.3 - - 27.2
1977 - 137.1 - - 18.3
1976 - 93.9 - - 29.9
1975 - 106.3 - - 34.9
1974 - - - - 34.1
1973 - - - - 36.1

201

 

Year TPKM TPKC
(ungr‘) (ugU') mgr‘) (m3s"> (m3s">

1972
1971
1970
1969
1968
1967
1966
1965
1964
1963
1962
1961
1960
1959
1958
1957
1956
1955
1954
1953
1952
1951
1950
1949
1948
1947
1946
1945
1944
1943
1942
1941
1940
1939
1938
1937
1936
1935
1934
1933

11637
1601)

TPKA

Dm

DKC

2537
1637
2737
321)
2513
2232
1813
1632
1L0
1213
YI4
Hi3
28J
F19
K16
1837
2633
“55
2035
F12
2733
2637
3932
21.1
2715
44L8
hi7
25J
24A
4233
2735
16x1
211)
H18
2235
2813
13.1
1615
1431
2211

 

202

 

Year

2008
2007
2006
2005
2004
2003
2002
2001
2000
1999
1998
1997
1996
1995
1994
1993
1992
1991
1990
1989
1988
1987
1986
1985
1984
1983
1982
1981
1980
1979
1978
1977
1976
1975
1974
1973

203

 

Year

1972
1971
1970
1969
1968
1967
1966
1965
1964
1963
1962
1961
1960
1959
1958
1957
1956
1955
1954
1953
1952
1951
1950
1949
1948
1947
1946
1945
1944
1943
1942
1941
1940
1939
1938
1937
1936
1935
1934
1933

DKA

(m3s">

LPBM

(kg)

LPAM
(kg)

LCBM
(kg)

LCAM
(kg)

 

204

APPENDIX IV

HISTORICAL MEAN MONTHLY DISCHARGE DATASET

205

Historical data by year for monthly mean total discharge (MDmonm), direct discharge
(MDDmomh) and base ﬂow discharge (MBDmonm) for USGS gaging station number
04106000, the Kalamazoo River at Comstock, MI.

Year MD4 MD5 MD6 M1)7 MD8 MD9
(m3s-1) (m3s-1) (m3S-1) ("138-1) (mBS-l) (m3s-1)
2008 - - - - - -
2007 - - - - - -
2006 30.0 34.3 23.4 19.0 16.0 20.0
2005 29.6 23.7 20.4 20.1 14.3 12.6
2004 22.3 47.7 38.1 22.3 19.9 17.5
2003 32.5 30.9 17.9 13.3 12.5 13.0
2002 40.2 41.9 25.3 18.4 21.4 15.8
2001 36.0 49.2 38.6 21.1 21.6 24.1
2000 25.0 35.6 30.3 20.1 18.9 18.6
1999 41.7 25.8 17.8 20.6 12.7 10.7
1998 50.0 35.8 22.8 23.5 18.6 15.4
1997 37.7 32.0 29.3 18.8 17.1 25.3
1996 27.8 30.7 29.6 14.9 12.8 12.1
1995 33.8 32.5 21.4 19.8 22.7 15.7
1994 33.1 26.1 25.1 28.3 34.5 18.6
1993 58.3 34.4 38.2 29.4 21.7 32.0
1992 37.7 27.3 20.5 20.9 23.7 24.7
1991 52.1 34.5 22.7 18.4 19.4 16.2
1990 41.4 41.5 24.5 24.1 20.3 19.8
1989 38.9 27.2 58.4 24.1 21.0 27.3
1988 42.5 23.1 13.8 12.0 13.3 21.7
1987 27.9 19.8 15.3 14.6 17.2 20.9
1986 34.9 31.4 36.4 30.6 19.9 26.4
1985 65.1 31.0 24.5 21.0 18.3 20.0
1984 - - - - - -
1983 - - - - - -
1982 - - - - - -
1981 - - - - - -
1980 - - - - - -
1979 43.1 32.5 20.1 20.2 19.9 12.8
1978 44.6 27.7 28.1 28.7 14.5 19.7
1977 36.1 19.5 13.9 11.8 12.4 16.2
1976 44.6 50.0 28.5 26.0 15.7 14.3
1975 57.7 42.7 34.2 18.5 23.0 33.1
1974 59.1 51.8 35.9 20.5 18.9 18.2
1973 49.2 44.9 44.9 31.4 27.5 18.5

 

 

206

 

Year

 

1972
1971
1970
1969
1968
1967
1966
1965
1964
1963
1962
1961
1960
1959
1958
1957
1956
1955
1954
1953
1952
1951
1950
1949
1948
1947
1946
1945
1944
1943
1942
1941
1940
1939
1938
1937
1936
1935
1934
1933

M134 M135 MI)6 MD-, MD8 MD9
(“138-1) ("138-1) ("138-1) ("138-1) (m3S-1) (m3s-1)
38.4 30.9 22.7 18.6 19.6 23.8
26.5 18.5 14.8 14.1 11.8 14.3
47.0 36.3 21.8 25.4 20.5 16.6
49.1 41.8 38.5 27.9 19.5 15.1
30.5 21.2 26.4 36.5 21.8 18.5
43.8 25.0 22.3 17.1 12.4 12.5
26.9 34.6 17.0 12.1 12.3 9.8
35.9 15.4 14.0 9.3 10.4 12.2
17.5 14.5 9.6 8.0 7.3 8.9
19.4 19.5 11.0 9.6 9.2 7.9
28.1 24.4 14.2 13.4 13.2 10.9
32.0 25.7 16.6 11.9 13.3 16.5
48.4 29.0 36.5 24.8 15.8 13.9
35.6 22.1 15.1 12.8 11.9 10.0
19.2 13.0 13.1 14.4 11.4 10.2
28.3 29.8 16.6 15.3 10.3 11.7
32.3 58.4 20.5 19.0 15.6 12.0
26.2 17.0 18.2 15.8 11.3 10.2
35.4 19.9 28.1 16.5 12.1 11.3
25.3 22.0 19.7 14.3 12.7 9.5
48.8 38.0 26.6 19.8 15.4 14.9
37.3 33.9 26.3 24.6 20.9 17.0
85.5 41.1 34.5 27.3 18.3 28.2
40.8 23.1 21.6 13.9 13.2 14.3
43.5 53.2 21.9 19.0 14.0 13.6
83.8 50.4 45.9 24.3 19.3 26.9
18.5 19.2 18.7 11.7 9.8 10.1
25.9 44.8 33.6 17.0 13.2 16.0
48.6 32.4 23.2 13.4 13.1 14.0
30.3 70.3 57.9 41.0 22.6 31.5
33.9 25.8 33.0 23.4 29.7 18.9
30.5 17.9 18.4 13.9 8.8 8.8
27.7 19.5 23.3 14.7 16.7 24.1
40.9 21.8 17.3 14.3 14.4 10.2
30.0 25.0 30.9 16.3 17.5 15.4
39.6 26.8 41.0 30.7 20.4 14.0
22.4 17.7 10.0 7.8 7.8 13.2
18.0 23.1 21.0 10.2 16.8 10.6
38.5 14.6 8.6 7.6 6.6 10.6
37.5 35.9 16.4 21.9 12.0 10.9

 

207

 

Year MDD4

MDDS

MDD6

(mss-I) (m3s'l) (m3s'l) (m3s'l) (m3s'l) ("1315-1)

M131)7

MDD8

MDD9

 

2008
2007
2006
2005
2004
2003
2002
2001
2000
1999
1998
1997
1996
1995
1994
1993
1992
1991
1990
1989
1988
1987
1986
1985
1984
1983
1982
1981
1980
1979
1978
1977
1976
1975
1974
1973

I18
237
211
'14
7J
'16
83
H13
512
5J
81)
'12
417
1L8
'19
12J
'13
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H13

1811
11.8
911

10J
4J
2013
835
933
h19
1L3

H18
H18

114
4J
511
215
233
I12
6J
I16
‘15
(18
'12
I14
93
1L0
I19
25
213
H14
L8
211
832
3J

H18
213
118
515
I16
8J

I14
511
5J
I12
337
I18
25
119
117
I22
L5
116
43
I19
53
33
56
237
211
28
'13
41)

208

I15
21)
£16
219
4L6
511
117
237
337
113
211
611
H17
£13
532
411
412
I13
3J
5J
333
I12

418
337
31)
337
2J
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£16
233
25
'16
31)
211
23
S17
65
4A~
55
(17
81)
SJ
911
4J

L9
58
‘17
I14
813
I17
116

 

Year

 

1972
1971
1970
1969
1968
1967
1966
1965
1964
1963
1962
1961
1960
1959
1958
1957
1956
1955
1954
1953
1952
1951
1950
1949
1948
1947
1946
1945
1944
1943
1942
1941
1940
1939
1938
1937
1936
1935
1934
1933

MDD4 MDDS M131)6 MDD7 M131)8 MDD9
(m3s’l) (m3S-1) (m3s") (m3s'l) (m3s-1) (m3S-1)
8.5 5.2 4.0 3.4 5.3 6.5
2.5 2.7 1.9 3.1 2.0 4.3
14.5 7.7 3.1 7.1 3.0 3.6
13.1 6.7 9.1 7.8 2.1 2.7
5.5 4.5 9.1 10.2 3.0 5.1
8.0 1.6 5.4 2.4 2.2 2.5
6.7 8.0 2.0 1.9 3.0 1.6
9.8 1.1 3.0 1.5 3.1 2.7
4.2 2.6 1.7 1.4 1.3 2.3
1.6 4.3 1.8 2.2 1.8 1.3
2.0 6.1 3.0 3.2 2.2 2.3
10.5 2.3 2.3 2.0 3.3 4.1
14.8 5.9 12.6 5.5 2.5 2.7
6.1 3.9 3.4 2.9 1.9 1.4
3.6 3.2 3.8 3.3 1.9 1.9
9.1 8.4 3.4 3.8 2.1 2.5
9.3 18.5 4.6 3.8 2.5 2.1
4.1 2.2 4.5 3.4 2.0 1.6
5.2 1.1 9.8 2.7 3.1 2.5
4.3 2.9 5.4 2.5 2.5 1.6
10.6 11.0 2.3 3.9 2.1 3.0
9.0 6.2 5.7 6.2 3.1 3.0
25.8 4.0 6.9 6.8 2.1 8.7
11.3 4.2 5.7 1.5 2.4 3.3
4.8 16.4 5.6 2.5 2.4 3.0
28.4 13.4 8.0 3.6 4.4 6.6
1.5 4.8 3.7 1.2 1.7 2.3
6.2 16.7 4.6 2.6 2.0 4.7
10.3 9.4 4.1 1.7 3.3 2.5
3.7 27.4 10.0 8.9 2.4 8.2
2.6 5.3 8.2 4.4 6.6 2.2
7.4 1.0 4.4 2.1 1.2 2.2
5.1 3.2 7.1 2.3 6.7 6.0
13.1 3.3 3.3 2.0 4.4 2.0
5.5 9.7 7.4 3.3 4.4 3.6
14.8 3.7 20.4 5.3 6.0 3.8
4.4 3.8 2.1 1.4 1.8 4.5
1.3 7.2 5.8 2.2 4.8 1.7
12.4 1.0 1.4 1.4 1.3 3.3
8.6 8.3 1.6 5.5 1.5 3.4

 

209

 

 

Year MBD4 M131)5 MBD6 MBD7 MBD8 MBD9
(m3S-1) (m3s'l) (m3s'l) (m3s'l) (m3s'1) (m3s'l)
2008 - - - - - -
2007 - - - - - -
2006 26.2 24.2 19.0 15.6 12.5 15.2
2005 26.9 19.6 16.3 14.6 12.3 8.8
2004 19.9 26.9 32.8 17.2 15.3 14.5
2003 25.1 22.4 15.3 10.1 9.6 9.3
2002 33.1 32.6 23.0 14.7 16.8 13.6
2001 28.4 34.3 35.4 17.3 16.1 18.1
2000 16.7 24.3 24.2 17.6 14.3 14.0
1999 25.4 23.7 14.2 15.7 10.0 8.4
1998 40.7 30.2 18.3 18.8 14.9 12.9
1997 32.7 25.5 22.5 16.6 12.8 17.6
1996 19.8 24.9 22.4 13.4 10.4 9.1
1995 26.7 26.1 18.0 15.1 16.2 13.3
1994 28.4 22.6 15.8 24.0 23.8 16.3
1993 46.5 31.8 27.2 25.5 17.4 22.3
1992 29.9 24.9 16.6 15.1 18.5 18.3
1991 40.1 32.1 20.2 15.1 15.0 11.9
1990 34.1 31.7 22.0 18.4 16.1 14.3
1989 33.7 22.1 40.0 21.4 17.7 20.6
1988 32.2 21.1 12.0 9.6 10.3 13.7
1987 22.7 16.9 12.9 11.7 12.1 15.8
1986 31.5 24.8 28.1 23.4 16.6 17.0
1985 50.3 26.7 21.4 17.0 15.2 15.9
1984 - - — - - -
1983 - - - - - -
1982 - - - - - -
1981 - - - - - -
1980 - - - - - -
1979 33.6 27.5 16.6 15.9 14.7 11.0
1978 36.9 21.5 17.4 24.2 12.4 13.8
1977 28.5 17.9 11.1 9.8 9.2 11.4
1976 35.3 41.4 23.7 20.2 13.7 11.0
1975 39.3 38.5 28.7 16.3 13.9 24.5
1974 47.3 39.0 32.3 18.4 15.3 14.5
1973 39.8 34.0 36.8 25.8 22.0 13.9

210

 

 

Year MDD9 MBD4 MBDS MBD6 MBD7 MBDS MBD9

(m3s-1) (m3s'l) (m3s'l) (m3s'l) (m3s-1) (m3s'l) (m3s'l)
1972 6.5 29.9 25.7 18.7 15.3 14.3 17.3
1971 4.3 24.1 15.8 12.9 11.0 9.8 10.1
1970 3.6 32.5 28.6 18.8 18.3 17.5 13.0
1969 2.7 36.1 35.2 29.4 20.2 17.4 12.4
1968 5.1 25.0 16.8 17.4 26.3 18.8 13.3
1967 2.5 35.8 23.4 16.9 14.6 10.3 10.1
1966 1.6 20.2 26.6 15.0 10.2 9.3 8.2
1965 2.7 26.1 14.3 11.0 7.8 7.3 9.5
1964 2.3 13.3 11.9 7.9 6.6 5.9 6.5
1963 1.3 17.8 15.2 9.2 7.4 7.4 6.6
1962 2.3 26.0 18.2 11.2 10.3 11.0 8.6
1961 4.1 21.5 23.4 14.2 9.9 10.0 12.4
1960 2.7 33.6 23.1 23.9 19.3 13.3 11.2
1959 1.4 29.5 18.2 11.7 9.9 10.0 8.5
1958 1.9 15.5 9.8 9.3 11.1 9.5 8.3
1957 2.5 19.2 21.4 13.2 11.5 8.2 9.2
1956 2.1 23.0 39.9 15.9 15.2 13.1 10.0
1955 1.6 22.1 14.8 13.8 12.4 9.3 8.6
1954 2.5 30.2 18.8 18.3 13.8 9.0 8.8
1953 1.6 21.0 19.1 14.3 11.8 10.2 7.8
1952 3.0 38.2 27.1 24.3 15.9 13.3 12.0
1951 3.0 28.3 27.7 20.6 18.4 17.8 14.0
1950 8.7 59.6 37.1 27.6 20.5 16.3 19.6
1949 3.3 29.5 18.9 15.9 12.5 10.8 10.9
1948 3.0 38.7 36.8 16.4 16.6 11.7 10.7
1947 6.6 55.3 37.1 37.9 20.7 14.9 20.3
1946 2.3 17.0 14.3 15.0 10.5 8.2 7.8
1945 4.7 19.7 28.2 29.1 14.4 11.2 11.3
1944 2.5 38.3 23.1 19.1 11.7 9.8 11.5
1943 8.2 26.7 42.9 47.9 32.0 20.2 23.3
1942 2.2 31.3 20.5 24.8 18.9 23.1 16.7
1941 2.2 23.1 16.9 14.0 11.8 7.6 6.6
1940 6.0 22.6 16.3 16.2 12.4 10.0 18.1
1939 2.0 27.8 18.5 14.0 12.3 10.0 8.2
1938 3.6 24.5 15.3 23.5 13.0 13.1 11.8
1937 3.8 24.9 23.1 20.7 25.4 14.4 10.2
1936 4.5 18.0 13.9 7.8 6.5 6.0 8.8
1935 1.7 16.7 15.9 15.2 8.0 12.0 9.0
1934 3.3 26.1 13.5 7.2 6.2 5.4 7.4
1933 3.4 28.9 27.7 14.8 16.4 10.6 7.6

 

211

APPENDIX V

MIXED LINEAR MODEL THEORY

212

Mixed Linear Model Theory

An overview of a likelihood-based approach to the mixed linear models
(MLM) used for this research is presented here. This approach simpliﬁes and uniﬁes
many common statistical analyses, including those involving repeated measures,
random effects and random coefﬁcients. The basic assumption is that the data are
linearly related to unobserved multivariate normal random variables. Only the model
options used for this analysis are included in this discussion. Many options are
available for the construction of MLMS and additional theory with examples is
provided in Littell et a1. (2006). This information has been consolidated from
numerous references (Littel et al., 2006; Milliken and Johnson, 1984; SAS, 1999;

Searle, 1971; Taskinen etal., 2008; University of Oregon, 2007).

Formulation of the mixed model
The classical general linear model can be written as

y = Xﬂ + a (1)
where y is a vector of observations, X is a known matrix of explanatory variables, [3 is
an unknown ﬁxed effects parameter vector and a is an unobserved vector of residuals.
The residuals are often assumed to be independent and identically distributed. In
many cases this is unrealistic. Correlations and heterogeneities between the terms of 8
can be taken into account in a MLM, written as

y = X13 + Z“! + 8 (2)
with the addition of a known design matrix Z and a vector y of unknown random

terms added to the classical linear model. Equation 2 is called a mixed model because

213

it contains both deterministic, I3, and random, 7, components. A key assumption is

that y and e are zero-mean, normally distributed with

E1z1=121wa1z1=1m

V denotes the variance of y and is determined by the matrix Z and by the covariance
matrices, G and R through the formula V = ZGZ' + R.
Parameter estimation for the mixed model

The general linear model requires only an estimate of [3, where in the MLM 7,
G and R are unknown and must be estimated along with [3. Instead of the least
squares method (LS) the generalized least squares (GLS) method is more appropriate.
The GLS minimizes

(y - XB)'V'1(Y - X13) (4)

Since G and R and therefore V are unknown, the GLS solution can be estimated in
which some reasonable estimate for V is inserted into the minimization problem. To
ﬁnd a reasonable estimate of G and R, the method of maximum likelihood (ML) was
implemented in the PROC MIXED procedure of SAS 9.1.3 (SAS, 2007). Based on
the assumption that 7 and e are normally distributed, the solution minimizes the

following for G and R:
I(G,R) = — glogIVI — ér'V'W — glogan) (5)

where r = y — X(X'V'X)' X'V"Xy and ’ denotes a generalized inverse (Searle, 1971).

214

PROC MIXED actual minimizes -2 times the function in equation 5 using a ridge-
stabilized Newton-Raphson algorithm.
The G and R estimates are denoted f; and ii, respectively. To obtain

estimates of [3 and y, the standard method is to solve the mixed model equations

(Henderson, 1984):

x'ii-lx x'ii-lxz B = [X'R'ly] (6)
z'ii-lx z'ii.-1z+(;-l 7

The solution can also be expressed as
is = (x'V-Ix)‘ X'V"y (7)

= GZ'V'l (y—XB) (8)

<1

If G and R are known, B is the best linear unbiased estimator (BLUE) of [3 and
I? is the best linear unbiased predictor (BLUP) of y, where “best” means minimum
mean square error. In this study, G and R are unknown and estimated using the ML
method. BLUE and BLUP are no longer appropriate and the word empirical is added
to indicate the approximation, leading to the acronyms EBLUE and EBLUP.

Statistical inferences and test statistics

For inferences concerning the ﬁxed and random effects parameters in the

MLM, estimable linear combinations of the form

L["] (9)
Y
are considered. Statistical inferences are made by testing the hypothesis

215

or by constructing point and interval estimates.
When the rank of L (number of ﬁxed effects) is greater than one, a general F -

statistic can be constructed as follows:

E y p“ -1 [B]
F = [7]L (L CL) L y (10)
rank(L)

where E is the left hand side matrix of equation 6. The F -statistic enables making
inferences about the ﬁxed effects which account for the selected variance-covariance

model.

216

APPENDIX VI

KALMAZOO RIVER/LAKE ALLEGAN SUBWATERSHED LAND USE AND
LAND USE EFFECT DATA

217

 

218

 

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222

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