U.S. Department of the Interior

U.S. Geological Survey

Scientific Investigations Report 2010–5029 

Prepared in cooperation with the U.S. Environmental Protection Agency, 

Great Lakes National Program Office

Concentrations and Estimated Loads of Nutrients, Mercury, 

and Polychlorinated Biphenyls in Selected Tributaries to 

Lake Michigan, 2005–6

Prepared in cooperation with the U.S. Environmental Protection Agency, 

Great Lakes National Program Office

Concentrations and Estimated Loads of Nutrients, Mercury, 

and Polychlorinated Biphenyls in Selected Tributaries to 

Lake Michigan, 2005–6
Cover art: Elements of a study. (Drawing by Benjamin J. Siebers, U.S. Geological Survey, June 2010.) 
Concentrations and Estimated Loads of 

Nutrients, Mercury, and Polychlorinated 

Biphenyls in Selected Tributaries to Lake 

Michigan, 2005–6 

By Stephen M. Westenbroek 

Prepared in cooperation with the U.S. Environmental Protection Agency, 

Great Lakes National Program Office 

Scientific Investigations Report 2010–5029 

U.S. Department of the Interior

U.S. Geological Survey
U.S. Department of the Interior

KEN SALAZAR, Secretary

U.S. Geological Survey

Marcia K. McNutt, Director

U.S. Geological Survey, Reston, Virginia: 2010

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Suggested citation:

Westenbroek, S.M., 2010, Concentrations and estimated loads of nutrients, mercury, and polychlorinated biphenyls 

in selected tributaries to Lake Michigan, 2005–6: U.S. Geological Survey Scientific Investigations Report 2010–5029, 

73 p. 
iii

Acknowledgments 

This project required coordinated and sustained effort from many people. We gratefully 

acknowledge their contributions. Gary Kohlhepp and Christine Aiello (Michigan Department of 

Environmental Quality) rearranged their sampling schedules in order to make coordinated sampling of the Michigan tributaries possible. John Kennedy (Green Bay Metropolitan Sewerage 

District) offered a place to park a mobile laboratory for nearly a year. Judy Beck (U.S. Environmental Protection Agency, Great Lakes National Program Office) found funding opportunities and 

tirelessly promoted the idea of gathering updated tributary monitoring data. 

Thomas Behrendt, Rick Hubbell, Dave Housner, and Nick Hanson (U.S. Geological Survey) put in 

very long days collecting and processing large-volume water samples in all weather conditions. 

Marie Peppler (U.S. Geological Survey) assisted greatly in improving the content and appearance 

of this report. David Hall (formerly of U.S. Geological Survey) located data archives and provided 

insight into data analysis and load computation methods in use during the Lake Michigan Mass 

Balance Project. 
iv

Contents

Acknowledgments........................................................................................................................................iii

Abstract...........................................................................................................................................................1

Introduction.....................................................................................................................................................1

Study Design and Methods..........................................................................................................................2

Tributary Selection................................................................................................................................2

Environmental and Hydrologic Setting..............................................................................................2

Sampling Locations ..............................................................................................................................5

Grand River...................................................................................................................................5

Kalamazoo River ..........................................................................................................................7

St. Joseph River...........................................................................................................................7

Indiana Harbor and Ship Canal .................................................................................................7

Fox River........................................................................................................................................7

Sample Collection and Volume...........................................................................................................7

Environmental Samples ..............................................................................................................7

Quality-Control Samples.............................................................................................................8

Sampling Methods................................................................................................................................9

Analytical Methods...............................................................................................................................9

Nutrients........................................................................................................................................9

Mercury.........................................................................................................................................9

PCB.................................................................................................................................................9

Comparability of Datasets ...................................................................................................................9

Polychlorinated Biphenyl Data Preparation...................................................................................10

Load Estimation Methods..................................................................................................................10

Estimated Loads of Nutrients, Mercury, and Polychlorinated Biphenyls...........................................11

Nutrients......................................................................................................................................11

Mercury.......................................................................................................................................19

Polychlorinated Biphenyl .........................................................................................................22

Summary and Conclusions.........................................................................................................................26

References Cited..........................................................................................................................................26

Appendix 1. Analytical Methods............................................................................................................29

Appendix 2. Quality-Control Data Tables..............................................................................................33

Appendix 3. Data Tables..........................................................................................................................37

Appendix 4. Concentrations of Ammonia Nitrogen and Total Kjeldahl Nitrogen at Five 

Lake Michigan Tributary Monitoring Sites.....................................................................43

Appendix 5. Calculated Loads................................................................................................................47

Appendix 6. Description of Beale Load Calculation and Jackknifing Procedure .........................59

Appendix 7. Regression Model Details.................................................................................................61
v

Figures

1. Map showing location of tributary sampling sites for the Lake Michigan Tributary 

Monitoring Project........................................................................................................................3

2–14. Plots showing:

2. Hydrographs of five Lake Michigan Tributary Monitoring sites, 1994 to 2007...........4

3. Comparison of total mercury analyses between the Wisconsin State 

Laboratory of Hygiene and the U.S. Geological Survey Mercury Research 

Laboratory...........................................................................................................................10

4. Example load calculation and jackknifing result for total polychlorinated 

biphenyl (PCB) at the Fox River, 1994–95 .......................................................................12

5. Total phosphorus concentrations at five Lake Michigan tributary 

monitoring sites, 1994–2006 .............................................................................................13

6. Orthophosphate concentrations at five Lake Michigan tributary 

monitoring sites, 1994–2006 .............................................................................................14

7. Nitrate plus nitrite concentrations at five Lake Michigan tributary 

monitoring sites, 1994–2006 .............................................................................................15

8. Calculated nutrient loads at five Lake Michigan tributary monitoring sites............18

9. Total mercury concentrations at five Lake Michigan tributary monitoring 

sites, 1994–2006..................................................................................................................20

10. Calculated mercury loads at four Lake Michigan tributary monitoring sites..........21

11. Calculated mercury loads at the Fox River tributary monitoring site .......................21

12. Total PCB concentrations at five Lake Michigan tributary monitoring 

sites, 1994–2006..................................................................................................................23

13. Calculated PCB loads at five Lake Michigan tributary monitoring sites..................24

14. Calculated total PCB loads for the Lower Fox River, 1989 to 2006.............................25 

Tables

1. Calculated median discharge for the five Lake Michigan Tributary Monitoring Sites .....5

2. Sampling locations for the Lake Michigan Tributary Monitoring Project, 2004–05...........6

3. Table of sample volumes and requirements for polychlorinated biphenyls (PCB)............8

4. Number of samples at each tributary: Lake Michigan Mass Balance Project 

and this study ................................................................................................................................8

5. Definition of practical significance on the basis of effect size...........................................16

6. Adjusted R-squared values, p-values, and effect size for total phosphorus 

regression models ......................................................................................................................17

7. Adjusted R-squared values, p-values, and effect size for orthophosphate 

regression models ......................................................................................................................17

8. Adjusted R-squared values, p-values, and effect size for nitrate plus nitrite 

regression models ......................................................................................................................17

9. Adjusted R-squared values, p-values, and effect size for total mercury 

regression models ......................................................................................................................19

10. Adjusted R-squared values, p-values, and effect size for PCB regression models........22
vi

Appendix Figures

4–1. Concentrations of ammonia nitrogen at five Lake Michigan tributary monitoring 

sites, 1994–2006...........................................................................................................................44

4–2. Concentrations of total Kjeldahl nitrogen at five Lake Michigan tributary 

monitoring sites, 1994–2006 ......................................................................................................45

Appendix Tables

1–1. Analytical schedule for the Fox River tributary monitoring site .........................................30

1–2. Analytical schedule for the Indiana Harbor and Ship Canal tributary monitoring 

site ................................................................................................................................................31

1–3. Analytical schedule for supplemental sampling at the Grand, Kalamazoo, and 

St. Joseph Rivers ........................................................................................................................31

2–1. Field replicate results for the Grand River at Eastmanville, Michigan ..............................34

2–2. Field replicate results for the Kalamazoo River at 57th Street............................................35

2–3. Field replicate results for the St. Joseph River at St. Joseph, Michigan..........................36

3–1. Concentration data for the Grand River near Riverside Park, Ottawa County, 

Michigan (04119400)...................................................................................................................38

3–2. Concentration data for the Kalamazoo River near New Richmond, 

Michigan (04108660)...................................................................................................................38

3–3. Concentration data for the St. Joseph River near Zollar Drive, Benton Harbor, 

Michigan (STORET 110628) .......................................................................................................39

3–4. Concentration data for the Indiana Harbor and Ship Canal at East Chicago, 

Indiana (04092750) ......................................................................................................................39

3–5. Concentration data for the Lower Fox River at Oil Tank Depot at Green Bay, 

Wisconsin (040851385)...............................................................................................................40

5–1. Estimated annual loads for 1994–2005, site 04120250, Grand River at 

Grand Haven, Michigan.............................................................................................................48

5–2. Estimated annual loads for 1994–2005, site 04108670 Kalamazoo River near 

New Richmond, Michigan.........................................................................................................51

5–3. Estimated annual loads for 1994–2005, site 04102080 St. Joseph River at 

Napier Avenue at St. Joseph, Michigan.................................................................................54

5–4. Estimated annual loads for 1994–2005, site 04092750 Indiana Harbor Canal at 

East Chicago, Indiana ................................................................................................................56

5–5. Estimated annual loads for 1994–2005, site 040851385 Lower Fox River at Oil Tank 

Depot at Green Bay, Wisconsin ...............................................................................................57
vii

Multiply By To obtain

Length

mile (mi) 3.281 kilometer (km)

Area

square mile (mi2

) 2.590 square kilometer (km2)

Volume

liter (L) 0.2642 gallon (gal)

Flow rate

cubic foot per second (ft3

/s) 0.02832 cubic meter per second (m3/s)

cubic meter per second (m3

/s) 35.31 cubic foot per second (ft3/s)

Mass

gram (g) 0.03527 ounce, avoirdupois (oz)

kilogram (kg) 2.205 pound, avoirdupois (lb)

megagram (Mg) 1.102 ton, short (2,000 lb)

Temperature in degrees Celsius (°C) may be converted to degrees Fahrenheit (°F) as follows:

°F=(1.8×°C)+32 

Concentrations are given in milligrams per liter (mg/L), micrograms per liter (μg/L), and 

nanograms per liter (ng/L). A milligram is one-thousandth of a gram, a microgram is onethousandth of a milligram, and a nanogram is one-thousandth of a microgram. 

Conversion Factors, Vertical Datum, and Abbreviations

Abbreviations 

AVM Acoustic velocity meter

BSRE Beale’s stratified ratio estimator

LaMP Lakewide-area management plan

LMMBP Lake Michigan Mass Balance Project

MDEQ Michigan Department of Environmental Quality

MI WSC Michigan Water Science Center

MRL Mercury Research Lab

MWCMP Michigan Water Chemistry Monitoring Program

PCB Polychlorinated biphenyl

RMSE Root mean-squared error

RPD Relative percent difference

SLH Wisconsin State Laboratory of Hygiene

STORET U.S. Environmental Protection Agency data 

STOrage and RETrieval 

USGS U.S. Geological Survey

WI WSC Wisconsin Water Science Center
This page is intentionally blank.
Concentrations and Estimated Loads of Nutrients, 

Mercury, and Polychlorinated Biphenyls in Selected 

Tributaries to Lake Michigan

By Stephen M. Westenbroek 

Abstract

The Lake Michigan Mass Balance Project (LMMBP) 

measured and modeled the concentrations of environmentally 

persistent contaminants in air, river and lake water, sediment, 

and fish and bird tissues in and around Lake Michigan for an 

18-month period spanning 1994–95. Tributary loads were 

calculated as part of the LMMBP. The work described in this 

report was designed to provide updated concentration data and 

load estimates for 5 nutrients, total mercury, and total polychlorinated biphenyl (PCB) at 5 of the original 11 LMMBP 

sampling sites. 

Samples were collected at five Lake Michigan 

tributary monitoring sites during 2005 and 2006. Annual 

loads calculated for the 2005–6 sampling period are as 

much as 50 percent lower relative to the 1994–95 time 

period. Differences between the loads calculated for the 

two time periods are likely related to a combination of 

(1) biases introduced by a reduced level of sampling effort, 

(2) differences in hydrological characteristics, and (3) actual 

environmental change. 

Estimated annual total mercury loads during 2005–6 

ranged from 51 kilograms per year (kg/yr) in the Fox River 

to 2.2 kg/yr in the Indiana Harbor and Ship Canal. Estimated 

annual total PCB loads during 2005–6 ranged from 132 kg/yr 

in the Fox River to 6.2 kg/yr in the Grand River. 

Introduction

Long-term monitoring is critical to detecting change in 

the environment. In 1994 and 1995, baseline conditions for 

several contaminants of concern were established through 

water-column sampling at 11 Lake Michigan Mass Balance 

Project (LMMBP) tributaries. The LMMBP was a multiagency 

effort to measure the loading, transformation, fate, and transport of contaminants into, out of, and within Lake Michigan. 

Designed to provide a framework within which researchers and managers could evaluate the long-term fate of environmentally persistent contaminants, the LMMBP measured 

and modeled the concentrations of environmentally persistent 

contaminants in air, river and lake water, sediment, and fish 

and bird tissues in and around Lake Michigan for an 18-month 

period spanning 1994 and 1995. 

More than 20,000 individual samples were collected 

between 1993 and 1995 from Lake Michigan tributaries and 

Lake Michigan water, sediment, air and biota. The LMMBP 

focused on polychlorinated biphenyl (PCB), trans-nonachlor, 

atrazine, and total mercury; tributary and air deposition samples also were analyzed for additional parameters such as trace 

metals, other chlorinated pesticides, and nutrients. A suite of 

models was developed to simulate the long-term transport and 

fate of persistent contaminants.

As one component of the LMMBP, more than 350 

samples from 11 Lake Michigan tributaries were analyzed 

for PCB and trans-nonachlor (U.S. Environmental Protection 

Agency, 2006). Objectives of the LMMBP included estimating relative loading of contaminants from tributaries to Lake 

Michigan and comparing tributary loads to loads generated 

from other media, such as through air deposition or sediment 

resuspension. Flow measurements also were made to support 

the calculation of load estimates to Lake Michigan from each 

tributary. 

Of the 11 tributaries to Lake Michigan that were sampled 

during the LMMBP, 8 are currently (2009) listed as “Areas of 

Concern” under the Unites States-Canada Great Lakes Water 

Quality Agreement (U.S. Environmental Protection Agency, 

2009a). Areas of Concern are identified as those that have 

conditions likely to cause impairments detrimental to support 

of aquatic life. All of the Lake Michigan Areas of Concern 

are on the list in part because of sediments contaminated with 

mercury, arsenic, or polychlorinated biphenyls. 

The project described in this report was designed to 

revisit 5 of the original 11 LMMBP tributaries, with the goal 

of generating updated concentration data and loading estimates. Specifically, this project was designed to generate current load estimates for five nutrients, total mercury, and total 

PCB at the five selected sampling sites. Concentration data for 

two of the tributaries, the Fox River and Indiana Harbor and 

Ship Canal, were generated as a part of this project. Concentration data for the three Michigan tributaries (the Grand, 
2 Concentrations and Estimated Loads of Nutrients, Mercury, and PCBs in Selected Tributaries to Lake Michigan

Kalamazoo, and St. Joseph Rivers) were not generated as part 

this project but rather as part of the State of Michigan’s Water 

Chemistry Monitoring Program (Michigan Department of 

Environmental Quality, 2008). The general approach for this 

project was developed through discussions between members of the Lake Michigan Monitoring Coordination Council 

(U.S. Geological Survey, 2008).

The LMMBP goal for model accuracy was to be able to 

predict lakewide average concentrations in water, sediment, 

and top predator fish to within a factor of 2; this required 

determination of tributary mass loadings to within ± 25 percent of the actual annual average value (U.S. Environmental 

Protection Agency, 1997a; 1997b). The sampling program 

described here was smaller in scope than that conducted during the LMMBP and could duplicate neither the sampling frequencies nor the confidence intervals associated with the load 

estimates that were part of the original project. Nevertheless, 

knowledge of the changes in calculated loads since completion of LMMBP will be of great value to resource managers, 

modelers, and other Lake Michigan stakeholders in assessing 

progress toward meeting environmental goals.

One important use of the LMMBP data and models is 

in support of the Lakewide Management Plan (LaMP) for 

Lake Michigan. The LaMP documents an approach to reducing loads of persistent contaminants into and concentrations within Lake Michigan (U.S. Environmental Protection 

Agency, 2008). Although models can be extremely useful, 

they cannot substitute for data. The data and load estimates 

generated by this project will allow for further testing and 

refinement of the models in support of the LaMP. 

This report presents the results of sampling in 2005 and 

2006, as well as loading estimates for nutrients, mercury, and 

PCB. Mass load and uncertainty estimates are presented for 

the five sampled Lake Michigan tributaries. Concentration 

and load estimates are compared with the 1994–95 LMMBP 

concentrations and loading estimates. For the Grand, Kalamazoo, and St. Joseph Rivers, additional data generated by 

the Michigan Department of Environmental Quality (MDEQ) 

were used to fill in data gaps for 1999 through 2004 (Michigan 

Department of Environmental Quality, 2008). The MDEQ data 

were included in the analysis because they provide insight into 

the natural year-to-year variability of mass loading estimates.

Study Design and Methods

This project was designed to generate data of comparable 

quality to the data generated during the Lake Michigan Mass 

Balance Project. Accordingly, the study design follows the 

LMMBP Workplan wherever possible (U.S. Environmental 

Protection Agency, 1997b; 1997a). This section summarizes 

the study design and methods used during this project and 

highlights noteworthy departures from the LMMBP Workplan.

Tributary Selection

Sampling sites were chosen to focus on the tributaries 

that had the highest total PCB loads to Lake Michigan during 

the 1994–95 LMMBP sampling period. Previous monitoring 

showed that more than 90 percent of the tributary loading of 

total PCB to Lake Michigan could be captured by sampling 

five tributaries (U.S. Environmental Protection Agency, 2006). 

Due to ongoing work by the Michigan Department of Environmental Quality (MDEQ) and the U.S. Geological Survey 

Michigan Water Science Center (MI WSC), three of the top 

five PCB-contributing tributaries were already scheduled for 

intensive sampling during 2005.

Of the 11 tributaries sampled during the LMMBP, the 

Lower Fox River in Wisconsin (Fox) contributed about 

60 percent of the tributary load of total PCB to Lake Michigan. Following this, the Indiana Harbor and Ship Canal and 

Lower Kalamazoo (Kalamazoo) River each contributed 

approximately 11 percent of the tributary load of total PCB to 

Lake Michigan. The next group of tributaries—the Sheboygan, Milwaukee, Lower Grand (Grand), and Lower St. Joseph 

(St. Joseph) Rivers—each contributed an additional 3 percent. 

The last group of tributaries—the Menominee, Muskegon, 

Manistique, and Pere Marquette Rivers—each contributed 

1 percent or less to the tributary load of total PCB. Combining sampling at the Fox River in Wisconsin and the Indiana 

Harbor and Ship Canal in Indiana with the MDEQ sampling 

at the Grand, Kalamazoo, and St. Joseph Rivers in Michigan 

was expected to capture more than 90 percent of the current 

tributary PCB load to Lake Michigan (fig. 1). 

In addition, LMMBP results for the sampling locations 

shown in figure 1 captured tributary loads to Lake Michigan 

amounting to the following proportions of the total measured 

tributary load:

• total phosphorus: 85 percent

• orthophosphate: 87 percent

• total nitrogen: 84 percent

• total mercury: 88 percent

Thus, focusing monitoring efforts for the current project 

on the Grand, Kalamazoo, St. Joseph, and Fox Rivers and 

the Indiana Harbor and Ship Canal was expected to capture a 

substantial part of the tributary loads for non-PCB constituents 

as well.

Environmental and Hydrologic Setting

The three tributaries in Michigan, although different in 

size, appear to respond in a similar manner to regional weather 

systems (fig. 2). The Fox River in Wisconsin is a highly 

regulated river; discharge is controlled by 14 existing or abandoned dams (Wisconsin Department of Natural Resources, 

2002). The Indiana Harbor and Ship Canal has a highly stable 

flow regime; most of the water in the Indiana Harbor and Ship 

Canal originates as wastewater or cooling water discharge 

(Risch, 2005).
Study Design and Methods 3

Figure 1. Location of tributary sampling sites for the Lake Michigan Tributary Monitoring Project. USGS gaging stations 

are described in table 2. 

04102533

04101500

04102080

04106000

04108670

04108660

04119400

04119000

04120250

04092750

040851385

L

a k e M i c

h i g

a n

L a k e

S u p e r i o r

L a k e H u r o n

WISCONSIN

MICHIGAN

ILLINOIS INDIANA OHIO

0 25 50 100 Miles

0 50 100 25 Kilometers

EXPLANATION

U.S. Geological Survey (USGS) 

gaging station and identifier

River

Basin boundary

Chicago

Milwaukee

Lansing

Grand River

Kalamazoo River

St. Joseph River

Indiana Harbor and 

Ship Canal

Fox River

Manistique River

Pere Marquette

Muskegon River

Milwaukee

River

Sheboygan

River

Menominee River

87°W 84°W

45°N

42°N
4 Concentrations and Estimated Loads of Nutrients, Mercury, and PCBs in Selected Tributaries to Lake Michigan

DAILY MEAN DISCHARGE, IN CUBIC FEET PER SECOND

5000

3000025000200001500010000

80006000400020005000

1500010000

500

200015001000

5000

200001500010000

1994

1995

1996

1997

1998

1999

2000

2001

2002

2003

2004

2005

2006

2007

Grand RiverKalamazoo RiverSt. Joseph RiverIndiana Harbor and Ship CanalFox River

Figure 2. Hydrographs of five Lake Michigan Tributary Monitoring sites, 1994 to 2007. (Note differences in y-axis scales among the graphs.) 
Study Design and Methods 5

Year-to-year variability in climatic conditions causes 

corresponding variability in median river discharge (table 1). 

Median discharges during the LMMBP are given in the first 

row of table 1. Median discharges during the current round 

of sample collection (2005–6) are in every case less than the 

median discharges during the LMMBP.

Three tributaries—the Kalamazoo, Fox, and Indiana 

Harbor and Ship Canal—have substantial deposits of contaminated sediments within their systems (U.S. Environmental 

Protection Agency, 2009c). In all three of these tributaries, 

PCB and mercury have been identified as contaminants of 

concern (U.S. Environmental Protection Agency, 2009a).

Table 1. Calculated median discharge for the five Lake Michigan Tributary Monitoring Sites.1

Period

Discharge, in cubic feet per second

Grand River Kalamazoo 

River

St. Joseph 

River

Indiana Harbor 

and Ship Canal Fox River

April 1994–September 1995 4,966 1,999 3,681 664 3,545

1999 2,348 1,350 2,892 632 3,480

2000 3,281 1,520 3,357 565 3,355

2001 4,562 2,483 5,057 565 4,070

2002 2,618 1,753 3,439 528 3,840

2003 1,933 1,299 3,159 524 2,910

2004 3,253 1,753 4,134 535 4,005

2005 2,831 1,528 3,006 540 3,470

August 2005–July 2006 3,337 1,616 3,325 553 3,360

1

 Estimated discharge records used for the Grand, Kalamazoo, and St. Joseph Rivers

Sampling Locations

Locations for the 2005–6 sample collection at the Michigan tributaries differed from those visited in the 1994–95 

work. The sampling locations for the Grand River and the 

St. Joseph Rivers in Michigan were moved upstream from 

locations near the river mouths. During the LMMBP, AVMs 

were in operation at both sites; however, they were removed 

toward the end of 1995. In addition, the stream-gaging and 

sample-collection station for the Kalamazoo River was discontinued in 1995. For this study, sites were selected at upstream, 

existing gaging stations that were part of the Michigan Department of Environmental Quality (MDEQ) monitoring network. 

More detail on sampling-site differences is given below and 

summarized in table 2. 

Grand River

During the LMMBP, water samples were collected at 

the Grand River near USGS gaging station 04120250. The 

USGS operated an acoustic velocity meter at this site, which 

was discontinued at the end of the LMMBP. MDEQ has 

been sampling the Grand River (STORET station 700123) as 

one of their Michigan Water Chemistry Monitoring Project 

(MWCMP) “intensive” sites since 1999 (Michigan Department of Environmental Quality, 2008). Water samples for this 

project were obtained at the MDEQ site (STORET station 

700123), which is about 18 river miles upstream from the 

LMMBP sampling location (USGS station 04120250). The 

current sampling location will miss any contributions of 

contaminants from the Grand Haven area and Spring Lake, 

although sediment-core samples collected in 1997 and 1998 

suggest that there are no “hot spots” of PCB or mercury in the 

Grand Haven/Spring Lake area (Rediske and others, 1999).

To allow for comparisons to be made among annual loads 

in 1994–95, 1999, and 2005, a synthetic discharge record was 

created by use of the continuous daily discharge record from 

the Grand River at Grand Rapids, Michigan (04119000). A 

drainage-area ratio approach was used initially in the calculation of a synthetic discharge record (equation 1). Because of 

differences between synthetic and observed hydrographs, the 

initial ratio was decreased to improve agreement between the 

synthetic discharge record and the observed discharge record 

at the Grand Haven gaging station (04120250).

 ratio

DA

DA

square miles

squ DA

Grand Haven

Grand Rapids

= = 5 518

4 900

,

, are miles = 1 126. (1)

Application of the initial drainage-area ratio resulted 

in overestimates of discharges in cases in which the daily 

observed discharge exceeded the median observed discharge. 

Therefore, the sum of squared error between the observed and 

synthetic discharge record was minimized, resulting in a corrected drainage-area ratio of 1.122.
6 Concentrations and Estimated Loads of Nutrients, Mercury, and PCBs in Selected Tributaries to Lake Michigan Table 2. Sampling locations for the Lake Michigan Tributary Monitoring Project, 2004–05. [USGS, U.S. Geological Survey; ID, identification; QW, water quality; LMMBP, Lake Michigan Mass Balance Project; ft3/s, cubic foot per second; ---, undetermined; NA, not applicable] Station type USGS station ID / [STORET number] Drainage area (square miles) Location description Latitude Longitude Period of record2 Mean discharge (ft3/s) Median discharge (ft3/s) Discharge and QW 04092750 Indeterminate Indiana Harbor Canal at East Chicago, Indiana 41°38’57” 87°28’07” 1994–2006 598 574 QW - LMMBP1 04120250 5,518 Grand River at Grand Haven, Michigan 43°03’37” 86°14’25” 1994–1995 6,067 --- Discharge 04119000 4,900 Grand River at Grand Rapids, Michigan 42°57’52” 85°40’35” 1901–2006 3,789 2,600 QW 04119400 / [700123] --- Grand River near Riverside Park, Ottawa County, Michigan 43°01’27” 86°01’35” NA NA NA Discharge and QW - LMMBP1 04108660 / [030077] 1,950 Kalamazoo River at New Richmond, Michigan 42°39’06” 86°06’28” 1994–1995 2,094 --- Discharge 04108670 1,994 Kalamazoo River near New Richmond, Michigan 42°38’41” 86°06’58” 1994–2007 1,969 1,700 Discharge 04106000 1,010 Kalamazoo River at Comstock, Michigan 42°17’08” 85°30’50” 1931–2007 901 758 Discharge and QW 040851385 6,330 Fox River at Oil Tank Depot at Green Bay, Wisconsin 44°31’43” 88°00’36” 1989–2007 4,619 3,770 QW [110628] --- St. Joseph River near Zollar Drive, Benton Harbor 42°03’48” 86°27’56” NA NA NA Discharge 04101500 3,666 St. Joseph River at Niles, Michigan 41°49’45” 86°15’35” 1931–2007 3,443 2,870 Discharge and QW - LMMBP1 04102533 4,670 St. Joseph River at St. Joseph 42°06’48” 86°29’07” 1994–1995 3,639 ---

1 Mean flow is calculated for water year 1994 only. Period of record for these sites was 04-01-1994 to 10-31-1994.2 Period of record refers to the dates of operation of USGS gaging stations. No value is given for sites where only water-quality data are available.
Study Design and Methods 7

Kalamazoo River

During the LMMBP, water samples were collected at 

the Kalamazoo River near USGS gaging station number 

04108660. MDEQ has continued to sample the Kalamazoo 

River at nearly the same location (STORET station 030077) as 

one of their intensive sites since 1999 (Michigan Department 

of Environmental Quality, 2008). Gaging station 04108660 

was discontinued at the end of the LMMBP. A second USGS 

gaging station on the Kalamazoo River near New Richmond 

(04108670) has been in operation intermittently since 1994; 

operation ceased between 1996 and 2002, leaving a gap in 

recorded discharge for the Kalamazoo River. In order to allow 

for comparisons to be made between annual loads in 1994–95, 

1999, and 2005, a synthetic discharge record was created by 

use of the continuous daily discharge record from the Kalamazoo River at Comstock (04106000). 

A drainage-area ratio approach was used initially in 

the calculation of a synthetic discharge record (equation 2). 

Because of significant differences between synthetic and 

observed hydrographs, the initial ratio was increased to 

improve agreement between the synthetic discharge record 

and the observed discharge record at the New Richmond gaging station (04108670). 

 ratio

DA

DA

square miles

squar DA

NewRichmond

Comstock

= = 1 994

1 010

,

, e miles = 1 974. (2)

Ultimately, a correction factor of 2.14 was applied to 

daily discharge at the Comstock gaging station to yield a 

synthetic discharge record for the New Richmond station 

(04108670); the correction factor was determined by minimizing the sum of squared error between the synthetic and 

observed daily discharges at the New Richmond station 

(04108670). The correction factor is about 8 percent larger 

than the drainage-area ratio between the New Richmond and 

Comstock sites.

St. Joseph River

During the LMMBP, samples were collected at the 

St. Joseph River USGS gaging station 04102533. The USGS 

operated an AVM at the site, which was removed at the end 

of the LMMBP. Since 1999, MDEQ has been sampling the 

St. Joseph River at STORET station 110628 as one of their 

integrator sites. Integrator sites are sampled intensively on a 

5-year rotating schedule (Michigan Department of Environmental Quality, 2008). Sampling done as part of this project 

was at the same location as the MDEQ work, about 5.8 mi 

upstream from the sample site used during the LMMBP. The 

current sampling location will miss any contributions of contaminants from downtown St. Joseph/Benton Harbor and from 

the Paw Paw River.

To allow for comparisons to be made between annual 

loads in 1994–95 and 2005, a synthetic discharge record was 

created by use of the continuous daily discharge record from 

the St. Joseph River at Niles (04101500). A correction factor 

of 1.274 was applied to daily discharge at the Niles gaging station to yield a synthetic daily discharge record for site number 

04102533; the correction factor is equal to the drainage-area 

ratio between the two stations (equation 3).

 ratio

DA

DA

square miles

square mile DA

St Joseph

Niles

= = . ,

,

4 670

3 666 s

= 1 274. (3)

Indiana Harbor and Ship Canal

USGS has operated a gaging station at the Indiana Harbor 

and Ship Canal East Chicago site (04092750) since October 

1991. Water samples for this project were collected at the 

same location as those collected during the LMMBP.

Fox River

USGS has operated a gaging station at the Fox River 

Oil Tank Depot site (040851385) continuously since October 

1988. Water samples for this project were collected at the 

same location as those collected during the LMMBP.

Sample Collection and Volume

Twelve environmental samples were collected from each 

tributary. At this level of effort, results of design calculations 

suggested that a 50-percent change in the mean concentration 

could be detected at a 95-percent confidence level, and less 

significant changes in mean concentration were calculated to 

be correspondingly less likely to be detected as statistically 

significant. 

Environmental Samples

Twelve water-column samples were obtained from each 

of the five tributaries included in this study: the Kalamazoo, 

St. Joseph, and Grand Rivers in Michigan, the Indiana Harbor 

and Ship Canal in Indiana, and the Fox River in Wisconsin.

The analytical method used to quantify PCB congeners 

requires large volumes of water to be sampled and run through 

not only a set of filters but also an ion-exchange resin column 

(Wisconsin State Laboratory of Hygiene, 1996). The volume 

of water that must be processed at each site is proportional to 

the expected water-column PCB concentration; a larger sample volume results in lower analytical detection limits. Sample 

volumes processed at each tributary are given in table 3. 
8 Concentrations and Estimated Loads of Nutrients, Mercury, and PCBs in Selected Tributaries to Lake Michigan

The sampling period for the Grand, Kalamazoo, and 

St. Joseph Rivers extended from March 2005 through December 2005. The sampling period for the Fox River and the 

Indiana Harbor and Ship Canal extended from roughly August 

2005 through July 2006. The ratio of samples collected during 

high-flow events relative to base-flow conditions was set at 

3:1 (event: base flow), which is higher than the 2:1 ratio of 

high-flow events to base-flow conditions sampled during the 

LMMBP (U.S. Environmental Protection Agency, 1997a).

Investigators from the USGS Michigan Water Science 

Center (MI WSC) sampled the 3 Michigan tributaries (Kalamazoo, St. Joseph, and Grand), with the goal of collecting 

9 event samples and 3 base flow samples; USGS MI WSC 

investigators obtained 12 scheduled samples, targeting neither 

event nor base flow, from the Indiana Harbor and Ship Canal 

between June 2005 and September 2006. No specific flow conditions were targeted for the Indiana Harbor and Ship Canal 

because of the extremely stable flow at that site. Table 4 lists 

the planned level of sampling effort at each tributary for the 

LMMBP (U.S. Environmental Protection Agency, 1999) and 

for this study.

The Fox River in Wisconsin was sampled by investigators from the USGS WI WSC with the goal of obtaining nine 

event samples and three scheduled base-flow samples.

Quality-Control Samples

Two quality-control samples for water column PCB and 

mercury analyses were obtained for each tributary during the 

project. A field duplicate was obtained to assess the combined 

precision of laboratory and field procedures, and a rinsate 

blank was processed and submitted to the lab to assess the 

efficacy of field-equipment cleaning and decontamination 

procedures. Potential differences in total mercury analysis and 

reporting between the Wisconsin State Laboratory of Hygiene 

(SLH) and the USGS Mercury Research Laboratory (MRL) 

were assessed by sending field duplicates for all Fox River 

sampling events to both laboratories.

A field duplicate sample was also obtained from each 

tributary and analyzed for nutrients. In addition, potential differences between the SLH and the MDEQ Environmental Laboratory were assessed by sending three field duplicate samples 

for each Michigan tributary to both labs for analysis.

Table 3. Table of sample volumes and requirements for 

polychlorinated biphenyl (PCB) sampling. 

[ng/L, nanograms per liter; LOD, limit of detection]

Site

Required 

sample 

volume 

(liters)

Assumed 

minimum 

total PCB 

concentration 

(ng/L)1

Sum of 

congeners 

exceeding 

LOD, 

assuming a 

congener 

distribution 

of 

Aroclor 1242 

(ng/L)

Grand River 160 0.33 0.17

St. Joseph River 160 .33 .17

Kalamazoo River 160 3 2.8

Indiana Harbor 

and Ship Canal

80 24 22.4

Fox River 80

160

11

(March–October)

2.5

(November–February)

10.3

2.3

1

 Assumed minimum concentrations of PCB were estimated from observed 

1994–95 minimum values of PCB.

Table 4. Number of samples at each tributary: Lake Michigan 

Mass Balance Project and this study. 

[---, not applicable] 

Site

Number of planned samples (high 

flow/base flow)

Lake Michigan 

Mass Balance 

Project

This study

Indiana Harbor and 

Ship Canal

16 12

Pere Marquette River* 16 (11/5) ---

Muskegon River* 16 (18/8) ---

Kalamazoo River 26 (18/8) 12 (9/3)

St. Joseph River 26 (18/8) 12 (9/3)

Grand River 36 (24/12) 12 (9/3)

Manistique River* 16 (18/8) ---

Menominee River* 26 (18/8) ---

Fox River 26 (18/8) 12 (9/3)

Milwaukee River* 45 (30/15) ---

Sheboygan River* 45 (30/15) ---

*

Not sampled in this study. 
Study Design and Methods 9

Sampling Methods

Spatially representative samples were collected at each of 

the five sites by compositing samples across the river channel. The compositing method was developed for the original 

LMMBP (U.S. Environmental Protection Agency, 1997b) and 

is similar to the equal discharge interval method (Porterfield, 

1972). The sampling method is designed to yield average constituent concentrations for the river cross section.

At each site, a composite sample was obtained by 

combining subsamples from three locations across the stream 

channel. The three sampling points are designed to capture 

the water moving within subsections of the river having equal 

discharge rates. Subsamples were collected from 0.2 and 0.8 

of the total depth at each of the three sampling points. 

Analytical Methods

A summary of the laboratory analytical methods is 

provided in appendix 1. This section discusses differences 

between analytical methods used in the LMMBP, the Michigan Water Chemistry Monitoring Program (MWCMP), and 

this project.

Nutrients

Nutrient concentrations for the Michigan tributaries were 

determined at the MDEQ Environmental Laboratory. Nutrient 

concentrations for the Indiana Harbor and Ship Canal and the 

Fox River were determined at the SLH. Methods used by the 

two laboratories should be equivalent. Differences between 

the two methods were quantified with duplicate field samples; 

the results of the duplicate field samples are included in 

appendix 2.

Mercury

Total mercury analysis for all tributaries was done by the 

SLH. In addition, field duplicate samples from the Fox River 

were analyzed for total and dissolved mercury and total and 

dissolved methylmercury at the USGS MRL.

During the LMMBP, mercury analyses were done at the 

University of Wisconsin–Madison Water Chemistry Program 

Laboratory. Since that time, the Water Chemistry Laboratory 

has discontinued routine analysis for mercury compounds, and 

the USGS has established a laboratory dedicated to analysis 

of mercury compounds. The USGS MRL uses methodology 

developed originally for the LMMBP at the University of 

Wisconsin–Madison (De Wild and others, 2002). MDEQ has 

been sending surface-water samples to the SLH for routine 

total mercury analysis since 1999. Differences between the 

two methods were quantified with duplicate field samples; the 

results of the duplicate field samples are included in the next 

section.

PCB

Analysis of water-column PCB congeners was done at 

the SLH by method 1293 (Wisconsin State Laboratory of 

Hygiene, 1996). This method analyzes and reports dissolved 

and particulate PCB congeners separately, providing information on the partitioning of congeners between particulate and 

dissolved fractions. For the Michigan tributaries, method 1293 

was used, modified in that dissolved and particulate fractions 

were analyzed and reported together; the modification to 

method 1293 was because information on partitioning between 

dissolved and particulate phases was not needed to accomplish 

the objectives the MWCMP (Michigan Department of Environmental Quality, 2008).

Comparability of Datasets

Split field samples were obtained to confirm that valid 

comparisons can be made between results from the LMMBP, 

the MWCMP, and this project. The use of split field samples 

was limited to constituents for which either the laboratory or 

the analytical method differs substantially from those used 

during the LMMBP. All data collected as part of either the 

MWCMP or this project appears comparable to data generated 

during the LMMBP. Specific results of these comparisons are 

discussed below.

Nutrients. A set of split field samples was obtained to 

assess differences between the analytical methods used to 

quantify phosphorus and nitrogen compounds. A summary 

of these differences is included in appendix 2. The relative 

percent difference (RPD) between the MDEQ and SLH results 

appears to increase as the concentrations decrease toward the 

method reporting limits; at these low concentrations, round-off 

error and result truncation accounts for some of the increase 

in relative percent difference. This is not surprising, because 

analytical variability increases as concentration decreases; 

the observed increase in RPD would occur even if the split 

samples were analyzed by the same method.

Mercury. To determine how results from SLH and the 

USGS MRL compare, split field samples were obtained for 

all sampling events on the Fox River; the split samples were 

sent to both labs for total mercury analysis. Figure 3 shows a 

comparison of quantiles of the field replicate results for total 

mercury. 

A regression of USGS MRL results to SLH results for 

total mercury yields is expressed by the following equation:

CWSC = + CSLH 0 159 0 902. . (4)
10 Concentrations and Estimated Loads of Nutrients, Mercury, and PCBs in Selected Tributaries to Lake Michigan

In other words, the SLH total mercury results (CSLH) are, 

on average, approximately 10 percent greater than the USGS 

MRL (CMRL) total mercury results. The post-LMMBP loads 

are calculated with SLH data, and may thus be expected to 

be as much as 10 percent higher than they would be had the 

calculations been made with USGS MRL data; the latter laboratory’s methods were adapted from those used in the original 

LMMBP and are therefore assumed to be more comparable to 

the original methods.

Polychlorinated Biphenyl Data Preparation

Polychlorinated biphenyls (PCB) are a class of manmade 

chemicals that were widely used for a variety of industrial 

applications during the mid-20th century; most uses of PCBs 

were banned in 1979 (U.S. Environmental Protection Agency, 

2009b). A PCB molecule may take one of 209 possible 

configurations, or congeners (McFarland and Clarke, 1989). 

Because more than 50 individual congeners may be present 

in any given sample, it is common to sum the results for the 

individual congeners and report the sum as total PCB.

Total PCB concentrations included in this report were 

calculated by summing all congener results that are reported 

above the level of detection. Thus, the calculated total PCB 

values include the laboratory-estimated concentrations for 

results reported at concentrations between the level of detection and the level of quantification. 

During the LMMBP, an analytical procedure called 

surrogate-recovery correction was applied to the PCB congener results; the same surrogate-recovery correction methods 

were applied to data generated by this project. Complete 

details regarding the quantification of PCB are given in volume 2, chapter 1 of the Lake Michigan Mass Balance Methods 

Compendium (U.S. Environmental Protection Agency, 1997b). 

A brief description of surrogate spikes and subsequent datacorrection procedures follows.

Surrogate spikes were added to each sample prior to 

an extraction step (Wisconsin State Laboratory of Hygiene, 

1996). For PCB analysis, the surrogate spikes are refined, 

radiolabeled isolates of congener numbers 14, 65, and 166, at 

concentrations of 20, 5, and 5 ng/mL, respectively. Surrogate 

spike recovery is the ratio of the quantified mass of each surrogate to the mass of surrogate added at the sample extraction step, in percent. It is a way of quantifying the combined 

performance of the extraction and quantification steps in the 

analysis.

Surrogate-spike-recovery correction is a process by 

which the reported analytical results are adjusted by an 

amount proportional to the surrogate-spike recovery. Congeners are placed into three groups on the basis of their column 

retention times relative to the column retention times of the 

three surrogates. The correction is made by dividing the 

reported analytical result by the appropriate fractional surrogate-spike recovery. PCB concentration data generated for this 

project have been surrogate-corrected and are summarized in 

appendix 3.

Load Estimation Methods

Beale’s stratified ratio estimator (BSRE) was used to 

generate load estimates. The Beale estimator has been consistently used for estimating Lake Michigan tributary loads since 

the 1970s (Sonzogni and others, 1978), and it was used during 

the LMMBP to estimate tributary contaminant loads. Numerical experiments with the BSRE suggest that it generally results 

in the least biased load estimates for total phosphorus, relative 

to other regression and ratio estimation techniques (Young and 

others, 1988); the BSRE has been recommended for application to total phosphorus when concentration data are sparse 

but a daily discharge record is available (Dolan and others, 

1981). 

The concept behind any ratio estimator is that one can use 

more commonly available data, such as discharge, to supplement the more costly data types, such as chemical-concentration data (Cochran, 1977). The key assumption underlying 

ratio methods is that there is a direct correlation between the 

two data types. 

TOTAL MERCURY, IN NANOGRAMS PER LITER, FROM 

WISCONSIN STATE LABORATORY OF HYGIENE

TOTAL MERCURY, IN NANOGRAMS PER LITER, 

FROM U.S. GEOLOGICAL SURVEY 

MERCURY RESEARCH LABORATORY

0 10 20 30 40 50 60

0

10

20

30

40

50

60

Figure 3. Comparison of total mercury analyses between the 

Wisconsin State Laboratory of Hygiene and the U.S. Geological 

Survey Mercury Research Laboratory. Red line is the line of 

perfect agreement. 
Estimated Loads of Nutrients, Mercury, and Polychlorinated Biphenyls 11

The precision of a load estimate may be improved by 

stratifying, or creating subsets of, data within which the ratio 

between discharge and concentration is relatively stable. Strata 

may be formed by assigning samples to groups that share a 

similar range of collection times, discharge values, or both; 

the ratio estimator is applied to each stratum, and results are 

combined to yield a load estimate for the entire calculation 

period (Cochran, 1977). Stratification of the dataset is done 

such that the mean square of error is minimized over all strata 

(Richards, 1999). Load-estimate bias increases and precision 

decreases as the number of samples in the monitoring program 

decreases (Richards and Holloway, 1987). These factors were 

a concern for this study because of the less intensive samplecollection effort compared to that of the LMMBP (table 4).

For this project, loads were calculated by means of the 

Beale Ratio Estimator on time-stratified datasets. The timestratification scheme and load estimate for each dataset was 

developed by means of a modified version of AutoBeale 

(Richards, 1999); the modified version of AutoBeale is 

described further in appendix 6. The automated stratification 

approach taken by AutoBeale generally results in stratification 

schemes that bracket seasonal changes in concentration and 

discharge. 

To better characterize precision in load estimates, a 

jackknife approach (Efron and Tibshirani, 1993) was used to 

estimate tributary loads. The jackknife approach involves calculating loads on successive subsets of the data. During each 

iteration, one concentration observation is deleted, the load is 

calculated, and the result is saved. The deleted observation is 

then restored, and its neighboring observation is deleted, and a 

new mass loading estimate is made. The result is a set of load 

estimates, with the number of estimates equal to the number 

of concentration data points. Figure 4 shows example output 

from the AutoBeale calculation method with and without 

application of the jackknife approach. Additional detail is 

provided in appendix 6.

Estimated Loads of Nutrients, Mercury, 

and Polychlorinated Biphenyls

Concentration data generated from 2005–6 were compared with concentration data from the LMMBP. All data were 

processed by means of the methods discussed previously to 

calculate loads (appendix 6). Load estimates for all sites and 

constituents are given in appendix 5, which includes unstratified, stratified, flow-normalized, and jackknifed load estimates. 

In general, the calculated loads for 2005–6 are less than 

those calculated for the 1994–95, regardless of stratification or 

effects of flow normalization. The reasons for lower calculated 

loads in 2005–6 are likely the result of differences in hydrographs between the two time periods, smaller sample sizes 

relative to the LMMBP effort, and real environmental changes. 

Patterns and trends in calculated loads for nutrients, mercury, 

and PCB are discussed in the following sections.

Nutrients

Concentrations of total phosphorus, orthophosphate, 

and nitrate plus nitrite appear to be increasing at some sites. 

Trends in total phosphorus and orthophosphate concentrations 

appear to be upward for the Fox River and Indiana Harbor 

and Ship Canal (figs. 5 and 6). Trends in nitrate plus nitrite 

concentrations appear to be upward for the Indiana Harbor and 

Ship Canal, Grand River, and possibly the Kalamazoo River 

(fig. 7).

In order to test the significance of apparent trends, 

multiple linear regression models were constructed for the 

concentration data at each tributary. The regressions generally 

included suspended solids, air temperature, discharge, and 

some measure of time as explanatory variables; equation 5 is 

an example of the regression model form and variables: 

 ln( ) ln( )

ln( )

PCB C TSS

C q

C T

C Dec

TSS

discharge

temperature

time

=

+

+

+ Year

 (5)

where

C is a regression coefficient,

TSS is total suspended solids,

q is discharge,

T is air temperature, and

DecYear is the time in decimal years.

For the Fox River and Indiana Harbor and Ship Canal, 

the time coefficient is an indicator (or dummy) variable to 

account for the two different observation periods. For the 

Michigan tributaries, the time coefficient represents the time 

in decimal years because data from more than two observation 

periods are present. Air temperature can act as a surrogate for 

season; nutrients and PCB often exhibit strong seasonality, and 

therefore, some correlation to air temperature. Some constituents, most notably PCB, strongly sorb to suspended solids.

Concentration data and discharge terms were generally 

log-transformed prior to regression analysis to ensure that the 

residuals (observed minus modeled) were normally distributed. The effect size associated with the time coefficient was 

calculated as shown in equation 6 (Cohen, 1962) by setting all 

independent variables in the regressions to mean values and 

altering only the variable associated with the time coefficient.

 f

ed v

fect size predict = alue predicted value

std deviat

2006 − 1994

. ionall data

e (6)
12 Concentrations and Estimated Loads of Nutrients, Mercury, and PCBs in Selected Tributaries to Lake Michigan

DISCHARGE, IN CUBIC FEET PER SECOND 8,000 6,000 4,000

2,000

12,00010,000

Apr−94 Jun−94 Aug−94 Oct−94 Dec−94 Feb−95

150100500

TOTAL PCB, IN NANOGRAMS PER LITER

38.89

97.13

74.71

49.20

40.42

77.72

77.97

90.59

142.64

97.42

82.79

106.75

57.48 65.94

65.99

63.10

57.04 40.40

39.21

16.85

4.66

5.28

5.93

10.19

15.51

24.64

31.0 kg 26.6 kg 19.4 kg 75.7 kg 38.9 kg 12.7 kg

EXPLANATION

DischargePolychlorinated biphenyl (PCB) concentrationStrata boundary

Load: 204.4 kg ± 19.7 kg RMSE: 8.8 kg

Annual load: 204.4 kg ± 19.7 kgAnnual load (jackknife): 192.1 kg ± 90.7 kg

kg Kilogram

RMSE Root mean-squared error

Example load calculation and jackknifing result for total polychlorinated biphenyl (PCB) at the Fox River, 1994–95. Figure 4.
Estimated Loads of Nutrients, Mercury, and Polychlorinated Biphenyls 13

TOTAL PHOSPHORUS, IN MILLIGRAMS PER LITER

Fox River

1994199519961997199819992000200120022003200420052006

0.0

0.1

0.2

0.3

0.4

0.5

(22)

(18)

(4)

(7)

o

x

TOTAL PHOSPHORUS, IN MILLIGRAMS PER LITER

Indiana Harbor and Ship Canal

1994199519961997199819992000200120022003200420052006

0.0

0.1

0.2

0.3

0.4

(4)

(9)

(3)

(8)

o

o

x

TOTAL PHOSPHORUS, IN MILLIGRAMS PER LITER

Grand River

1994199519961997199819992000200120022003200420052006

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

(26)

(21)

(13) (6)

(12)

(12)

(12)

(12)

(12)

o

o

x

x

x

x

x

x

x

TOTAL PHOSPHORUS, IN MILLIGRAMS PER LITER

Kalamazoo River

1994199519961997199819992000200120022003200420052006

0.0

0.1

0.2

0.3

0.4

(21)

(16)

(13)

(6) (12)

(12) (12)

(12)

(12)

o

o

o

x

TOTAL PHOSPHORUS, IN MILLIGRAMS PER LITER

St. Joseph River

1994199519961997199819992000200120022003200420052006

0.0

0.1

0.2

0.3

0.4

(17)

(16)

(12)

(4) (4) (12)

o

o

x

(25) Number of points

o

x

Severe outlier

Moderate outlier

Adjacent value

75thpercentile

Median

25thpercentile

EXPLANATION

Figure 5. Total phosphorus concentrations at five Lake Michigan tributary monitoring sites, 1994–2006. (Note 

differences in y-axis scales among the plots.) 
14 Concentrations and Estimated Loads of Nutrients, Mercury, and PCBs in Selected Tributaries to Lake Michigan ORTHOPHOSPHATE, IN MILLIGRAMS PER LITER

Fox River

1994199519961997199819992000200120022003200420052006

0.00

0.02

0.04

0.06

0.08

0.10 (17)

(16) (4)

(7)

o

x

x

ORTHOPHOSPHATE, IN MILLIGRAMS PER LITER

Indiana Harbor and Ship Canal

1994199519961997199819992000200120022003200420052006

0.00

0.01

0.02

0.03

0.04

0.05

0.06

(4)

(8)

(3)

(8)

ORTHOPHOSPHATE, IN MILLIGRAMS PER LITER

Grand River

1994199519961997199819992000200120022003200420052006

0.00

0.02

0.04

0.06

0.08 (23)

(20)

(13) (5)

(12)

(12)

(12)

(12)

(12)

o

o

x

ORTHOPHOSPHATE, IN MILLIGRAMS PER LITER

Kalamazoo River

1994199519961997199819992000200120022003200420052006

0.00

0.02

0.04

0.06

0.08

0.10

0.12

(19)

(15)

(13)

(6)

(12)

(12) (12) (12)

(12)

o

o

oo

o

o o

x

ORTHOPHOSPHATE, IN MILLIGRAMS PER LITER

St. Joseph River

1994199519961997199819992000200120022003200420052006

0.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

(13) (16)

(12)

(4)

(4) (12)

x

x

(25) Number of points

o

x

Severe outlier

Moderate outlier

Adjacent value

75thpercentile

Median

25thpercentile

EXPLANATION

Figure 6. Orthophosphate concentrations at five Lake Michigan tributary monitoring sites, 1994–2006. (Note 

differences in y-axis scales among the plots.) 
Estimated Loads of Nutrients, Mercury, and Polychlorinated Biphenyls 15

NITRATE PLUS NITRITE, IN MILLIGRAMS PER LITER

Fox River

1994199519961997199819992000200120022003200420052006

0.0

0.5

1.0

1.5

2.0

(21)

(17)

(4)

(7)

o

o

xx

x

x

NITRATE PLUS NITRITE, IN MILLIGRAMS PER LITER

Indiana Harbor and Ship Canal

1994199519961997199819992000200120022003200420052006

0

1

2

3

4

(4)

(9)

(3)

(8)

x

x

NITRATE PLUS NITRITE, IN MILLIGRAMS PER LITER

Grand River

1994199519961997199819992000200120022003200420052006

0

1

2

3

4

5

6

(26)

(21)

(13)

(6)

(12)

(12)

(12)

(12)

(12)

o

o

o

x

xx

x

x

NITRATE PLUS NITRITE, IN MILLIGRAMS PER LITER

Kalamazoo River

1994199519961997199819992000200120022003200420052006

0.0

0.5

1.0

1.5

2.0

2.5

3.0

(21)

(16)

(13)

(6)

(12)

(12)

(12)

(12)

(12)

x

x

x

NITRATE PLUS NITRITE, IN MILLIGRAMS PER LITER

St. Joseph River

1994199519961997199819992000200120022003200420052006

0

1

2

3

4

(17)

(16)

(12)

(4) (4) (12)

(25) Number of points

o

x

Severe outlier

Moderate outlier

Adjacent value

75thpercentile

Median

25thpercentile

EXPLANATION

Figure 7. Nitrate plus nitrite concentrations at five Lake Michigan tributary monitoring sites, 1994–2006. (Note 

differences in y-axis scales among the plots.) 
16 Concentrations and Estimated Loads of Nutrients, Mercury, and PCBs in Selected Tributaries to Lake Michigan

The calculated effect size was used to classify and interpret the practical significance of the multiple linear regression results. For the remainder of this report, effect sizes are 

described as listed in table 5. The classifications in table 5 are 

modeled on those defined by Cohen (1962), and represent a 

subjective but consistent method to interpret regression results. 

Thus, a regression time coefficient might be highly statistically 

significant, but if the effect size as defined in table 5 is negligible, the practical significance of the result would be deemed 

negligible as well.

can influence the value and significance of the other variables 

included in the analysis (Mosteller and Tukey, 1977); the 

addition of other (unknown or unmeasured) variables in this 

case might render the time-related term insignificant. Although 

the increases in concentrations of orthophosphate for the Fox 

River are statistically significant, this result should be viewed 

cautiously because the underlying model explains so little of 

the observed variance.

Small to large increases in nitrate plus nitrite concentrations were identified for the Grand and Kalamazoo Rivers 

and the Indiana Harbor and Ship Canal (table 8). No statistically significant changes in concentrations were found for the 

Fox and St. Joseph Rivers. For the Indiana Harbor and Ship 

Canal, the coefficient with the greatest practical and statistical 

significance is the time-related indicator variable. Inspection 

of figure 7 shows a near-doubling of the median nitrate plus 

nitrite value, suggesting that something has changed in the 

Indiana Harbor and Ship Canal.

The calculated annual nutrient loads show correlation to 

one another both in time and space, reflecting the influence of 

regional climate patterns (fig. 8). The black dots represent the 

load calculated by including all available data, with uncertainty bounds proportional to the mean-squared error over all 

strata. These uncertainty bounds describe the variability of the 

ratio between load and flow over each stratum. By contrast, 

the gray dots on the plot represent the load estimated from 

data subsets by means of a jackknife approach. The intent was 

to illustrate how the structure of the sampling program—and 

indeed, an individual data point—might influence the overall 

load estimate. Lastly, the red dot represents the jackknife estimate of load: the mean of all jackknife load estimates.

Although a confidence interval can be derived from the 

jackknifing calculation (appendix 6), jackknife confidence 

intervals are not reported here; for small sample sizes (n < 20), 

it has been suggested that the jackknife confidence interval 

may be inaccurate (Hinkley, 1977). A statistical resampling 

method, such as bootstrapping, could be used to generate 

uncertainty bounds about the estimated loads. The individual 

AutoBeale load estimates generated during each jackknife 

iteration are presented in figure 8 to serve as visual cues 

regarding the uncertainty of the load estimate.

In most cases, the jackknife estimates are well within the 

AutoBeale uncertainty bounds, and the mean of all jackknife 

load estimates falls in line with the AutoBeale-generated load 

estimate. Exceptions can be seen in the analyses for the Fox 

River (total phosphorus) and Grand River (ammonia-nitrogen, 

nitrate plus nitrite, orthophosphate). The AutoBeale-generated 

load estimate and the jackknife load estimate differ; the 

elimination of one or more samples from the analysis results 

in a substantial change in the estimated load. The combined 

variability in concentration and discharge observed in these 

cases suggests that sampling would need to be more intensive 

in future efforts to reduce variability in the estimated load.

Table 5. Definition of practical significance on the basis of 

effect size. 

[>, greater than]

Effect size Practical significance

0–0.5 Negligible

0.5–1.0 Small

1.0–2.0 Moderate

>2.0 Large

The effect of strong linear relations between predictors 

(collinearity) was quantified by examining the varianceinflation factors for regressions that contained predictors 

known to be correlated. When there are strong relations 

between predictors, the precision of the resulting regression 

coefficients decreases (Fox, 2008). A variance-inflation factor 

of 10 is commonly associated with severe collinearity; when 

the variance-inflation factor exceeds 10, researchers often 

eliminate or combine variables to reduce collinearity (O’Brien, 

2007). None of the variance-inflation factors examined in this 

study were greater than 3, and thus no actions were taken to 

reduce collinearity. As an additional exploration of the data, a 

load/air-temperature/discharge plot was examined for each site 

and each constituent. Examination of the load/air-temperature/

discharge plots provided a visual check and confirmation of 

the regression results. In addition, these plots confirmed that 

the more recent sampling events have covered ranges of air 

temperature and discharge similar to those observed during the 

LMMBP.

Small to moderate increases in total phosphorus concentrations were identified for the Grand River and Indiana 

Harbor and Ship Canal (table 6). Statistically significant concentration increases were identified for the St. Joseph and Fox 

Rivers, but the small effect sizes negate the practical significance of these changes. No statistically significant changes in 

concentrations were found for the Kalamazoo River.

Small to large increases in orthophosphate concentrations 

were identified for the Grand River, Indiana Harbor and Ship 

Canal, and the Fox River (table 7). However, the proportion 

of variance (R-squared) explained by the regression model for 

the Fox River is quite low. It has been demonstrated that the 

choice of variables included in a multiple linear regression 
Estimated Loads of Nutrients, Mercury, and Polychlorinated Biphenyls 17

Table 6. Adjusted R-squared values, p-values, and effect size for total phosphorus regression models. 

[TSS, total suspended solids; ***, either not statistically significant or of no practical significance; ---, variable removed from regression]

Tributary name

Adjusted 

R-squared 

value

Significance of coefficients (p-value) Effect 

size Interpretation

TSS Air 

temperature Discharge Time

Grand River 0.591 1.89E-08 2.44E-02 4.36E-03 8.96E-04 0.52 Small increase

Kalamazoo River .376 2.80E-03 1.09E-02 1.29E-02 8.93E-01 .02 ***

St. Joseph River .574 3.10E-16 --- --- 2.16E-02 .31 ***

Indiana Harbor and 

Ship Canal

.744 1.60E-06 2.10E-01 --- 1.86E-05 1.14 Moderate increase

Fox River .666 1.19E-08 7.66E-02 6.51E-02 8.71E-02 .23 ***

Table 7. Adjusted R-squared values, p-values, and effect size for orthophosphate regression models. 

[TSS, total suspended solids; ---, variable removed from regression; ***, either not statistically significant or of no practical significance]

Tributary name

Adjusted 

R-squared 

value

Significance of coefficients (p-value) Effect 

size Interpretation

TSS Air 

temperature Discharge Time

Grand River 0.381 --- --- 1.51E-13 1.15E-06 1.18 Moderate increase

Kalamazoo River .380 1.66E-01 --- 3.58E-10 1.33E-02 .35 ***

St. Joseph River .097 5.92E-02 1.26E-02 --- 9.25E-03 .43 ***

Indiana Harbor and 

Ship Canal

.627 --- 1.08E-02 --- 1.31E-05 2.48 Large increase

Fox River .080 .230 --- --- .047 .66 Small increase

Table 8. Adjusted R-squared values, p-values, and effect size for nitrate plus nitrite regression models. 

[TSS, total suspended solids; ---, variable removed from regression; <, less than; ***, either not statistically significant or of no practical significance]

Tributary name

Adjusted 

R-squared 

value

Significance of coefficients (p-value) Effect 

size Interpretation

TSS Air 

temperature Discharge Time

Grand River 0.568 1.02E-04 --- <2E-16 6.69E-16 2.16 Large increase

Kalamazoo River .344 --- 8.24E-04 2.53E-05 1.04E-02 .63 Small increase

St. Joseph River .561 4.08E-02 2.23E-02 2.96E-06 8.60E-01 -.04 ***

Indiana Harbor and 

Ship Canal

.921 5.06E-01 1.49E-02 1.21E-02 1.24E-09 1.53 Moderate increase

Fox River .374 --- 2.44E-05 6.06E-03 5.51E-01 .09 ***
18 Concentrations and Estimated Loads of Nutrients, Mercury, and PCBs in Selected Tributaries to Lake Michigan LOAD, IN METRIC TONS PER YEAR

1000

2000

3000

4000

5000

6000

0

200

400

600

800

2000

4000

6000

8000

10000

12000

14000

200

400

600

800

0

50

100

150

200

250

300

1994−95

199920002001200220032004

2005−6

1994−95

199920002001200220032004

2005−6

1994−95

200120032004

2005−6

1994−95

2005−6

1994−95

2005−6

Total Kjeldahl nitrogen Ammonia-nitrogen Nitrate plus nitrite Total phosphorus Orthophosphate

Grand River Kalamazoo River St. Joseph River Indiana Harbor and

Ship Canal Lower Fox River

Load calculated with all available data, 

showing 95-percent confidence interval bars

Individual load estimate from the jackknife approach

Mean of all jackknife load estimates

EXPLANATION

Figure 8. Calculated nutrient loads at five Lake Michigan tributary monitoring sites. (Note differences in y-axis 

scales among the plots.) 
Estimated Loads of Nutrients, Mercury, and Polychlorinated Biphenyls 19

Again, an example of the influence of regional weather 

patterns may be seen in the pattern of estimated loads for the 

three Michigan tributaries. Load estimates for 2001 are almost 

uniformly greater than the calculated loads before or since that 

year at the Michigan tributaries. Examination of the hydrographs (fig. 2) shows that although the magnitude of the flows 

differs greatly between the tributaries, there is a high degree of 

similarity in the shape of the hydrographs, particularly for the 

three Michigan tributaries. Mean and annual flows for 2001 

were greater than normal long-term values for the Michigan 

tributaries; the resulting loads are greater than those calculated 

for years before or after 2001. Flow-normalized loads show 

much less year-to-year variability than the stratified AutoBeale 

loads (appendix 5).

There are few obvious trends in annual nutrient loads for 

any of the five tributaries. The generally higher annual load 

estimates for the Michigan tributaries observed in 2001 and 

2004 appear to be a function of (1) higher flows relative to 

other years and (2) higher flows in both late spring (May) and 

late fall (October–December), relative to other years (fig. 2). 

The increased loads at the Indiana Harbor and Ship Canal 

for orthophosphate and nitrate plus nitrite are directly related 

to the significant increases in the concentrations of these 

constituents.

Mercury

Estimated annual total mercury loads ranged from 

51 kg/yr at the Fox River to 2.2 kg/yr at the Indiana Harbor 

and Ship Canal. Total mercury loads and concentrations 

appear to have decreased since the LMMBP for the Michigan 

tributaries. Figure 9 summarizes total mercury concentrations 

at the five tributaries. 

The visual trend and the regression analysis both suggest 

small to moderate decreases in the total mercury concentrations at the Grand, Kalamazoo, and St. Joseph Rivers (table 9). 

No significant regression models could be constructed for 

the Fox River and Indiana Harbor and Ship Canal for total 

mercury; however, the visual patterns of concentration data for 

the Fox River and the Indiana Harbor and Ship Canal suggest 

no change.

The annual load estimates for total mercury are uniformly 

lower relative to the loads estimated during the LMMBP 

(figs. 10 and 11). Some of the decrease in loads may be 

explained by the lower flow volumes in the 2005–6 period relative to the LMMBP period; the fact that downward trends in 

total mercury are also apparent in the flow-normalized annual 

load estimates (clearest for the Kalamazoo and St. Joseph 

Rivers, appendix 5) suggests that part of the decrease in loads 

may be due to environmental change. 

There is reason to believe that mercury loads at all sites 

should be decreasing: wet deposition of mercury appears to 

be decreasing (Butler and others, 2008). In addition, sediment 

cleanup activity has taken place at the Fox and Kalamazoo 

Rivers and at the Indiana Harbor and Ship Canal (U.S. Environmental Protection Agency, 2009c).

Loads for total and dissolved mercury and methylmercury at the Fox River are shown in figure 11. The 2005–6 

AutoBeale loads for total methylmercury generated as part of 

the jackknife iterations are significantly higher than those calculated with all samples retained. The small sample size and 

the strong seasonal pattern in the data result in very different 

stratification schemes when a single point is removed, causing the resulting load estimate to increase relative to the load 

calculated from all available data points. 

Table 9. Adjusted R-squared values, p-values, and effect size for total mercury regression models. 

[TSS, total suspended solids; ---, variable removed from regression; ###, no suitable regression model could be found]

Tributary name

Adjusted 

R-squared 

value

Significance of coefficients (p-value) Effect 

size Interpretation

TSS Air 

temperature Discharge Time

Grand River 0.428 --- --- 2.56E-12 1.70E-03 -0.65 Small decrease

Kalamazoo River .273 --- --- 7.21E-01 2.74E-09 -1.63 Moderate decrease

St. Joseph River .517 --- --- 8.57E-11 9.76E-05 -.743 Small decrease

Indiana Harbor and 

Ship Canal

### ### ### ### ### ### ###

Fox River ### ### ### ### ### ### ###
20 Concentrations and Estimated Loads of Nutrients, Mercury, and PCBs in Selected Tributaries to Lake Michigan TOTAL MERCURY, IN NANOGRAMS PER LITER

Fox River

1994199519961997199819992000200120022003200420052006

0

20

40

60

80

100

120

140

(5)

(17)

(8)

(14)

o

o

x

TOTAL MERCURY, IN NANOGRAMS PER LITER

Indiana Harbor and Ship Canal

1994199519961997199819992000200120022003200420052006

0

5

10

15

20

(1)

(9)

(3)

(7)

TOTAL MERCURY, IN NANOGRAMS PER LITER

Grand River

1994199519961997199819992000200120022003200420052006

0

5

10

15

20

25

30

(5)

(22)

(13)

(6)

(12)

(12)

(12)

(12)

(12)

o

o

o

o

x

x

x

x

x

TOTAL MERCURY, IN NANOGRAMS PER LITER

Kalamazoo River

1994199519961997199819992000200120022003200420052006

0

5

10

15

20

25

(3)

(24)

(13)

(6)

(12)

(12)

(12)

(12)

(12)

x

TOTAL MERCURY, IN NANOGRAMS PER LITER

St. Joseph River

1994199519961997199819992000200120022003200420052006

0

5

10

15

(5)

(19)

(12) (12)

(4) (4)

(12)

o

o

x

(25) Number of points

o

x

Severe outlier

Moderate outlier

Adjacent value

75thpercentile

Median

25thpercentile

EXPLANATION

Figure 9. Total mercury concentrations at five Lake Michigan tributary monitoring sites, 1994–2006. (Note differences in 

y-axis scales among the plots.) 
Estimated Loads of Nutrients, Mercury, and Polychlorinated Biphenyls 21

TOTAL MERCURY LOAD, 

IN KILOGRAMS PER YEAR

20

40

60

80

100

120

1994−95

19992000200120022003

2004

2005−6

1994−95

199920002001200220032004

2005−6

1994−95

1999

2001

20032004

2005−6

1994−95

2005−6

Grand River Kalamazoo River St. Joseph River Indiana Harbor and

Ship Canal

Load calculated with all available data, 

showing 95-percent confidence interval bars

Individual load estimate from the jackknife approach

Mean of all jackknife load estimates

EXPLANATION

Figure 10. Calculated 

mercury loads at four 

Lake Michigan tributary 

monitoring sites. 

1994−95

2005−6

1994−95

2005−6

0.11

0.12

0.13

0.14

0.15

0.16

0.17

Dissolved methylmercury

0.3

0.4

0.5

0.6

Total methylmercury

2

4

6

8

10

Dissolved total mercury

20

40

60

80

100

120

Total mercury

LOAD, IN KILOGRAMS PER YEAR

Load calculated with all available data, 

showing 95-percent confidence interval 

bars

Individual load estimate from the 

jackknife approach

Mean of all jackknife load estimates

EXPLANATION

Figure 11.

Calculated mercury 

loads at the Fox 

River tributary 

monitoring site. 
22 Concentrations and Estimated Loads of Nutrients, Mercury, and PCBs in Selected Tributaries to Lake Michigan

Polychlorinated Biphenyl

Estimated annual total polychlorinated biphenyl (PCB) 

loads ranged from 132 kg/yr at the Fox River to 6.2 kg/yr at 

the Grand River. Total PCB concentrations appear to have 

decreased since the time of the LMMBP at the Michigan tributaries and at the Indiana Harbor and Ship Canal (fig. 12). 

Decreases in PCB concentrations were observed at all 

tributaries except the Fox River. At the Fox River, the highest concentrations of PCB were observed when discharge was 

low (below the median discharge) and air temperatures were 

high (relative to the annual mean air temperature). In addition, 

dredging in Little Lake Butte des Morts on the Fox River was 

started in 2004 (GW Partners, L.L.C., 2009); dredging as a 

sediment cleanup option is known to remobilize small masses 

of contaminants even as large masses of contaminants are 

removed from the system (Steuer, 2000).

Small decreases in PCB concentrations were found 

through regression analysis for the three Michigan tributaries 

(table 10). Moderate decreases in PCB concentrations were 

found for the Indiana Harbor and Ship Canal. The time-related 

coefficient was not significant for the Fox River regression.

All estimated PCB loads for 2005–6 were lower than load 

estimates estimated for the LMMBP (fig. 13). There is good 

reason to believe that PCB loads at all sites should be decreasing: atmospheric deposition of PCB continues to decrease 

(Blanchard and others, 2000), and PCB has been banned from 

use in open systems since 1979 (U.S. Environmental Protection Agency, 2009b). As mentioned previously, some degree 

of sediment cleanup activity has taken place at the Fox and 

Kalamazoo Rivers, and at the Indiana Harbor and Ship Canal 

(U.S. Environmental Protection Agency, 2009c).

One important factor contributing to the lower PCB loads 

is the difference in river discharge for 2005–6 and 1994–95; 

in the 2005–6 period, mean and extreme values of discharge 

generally were lower. However, the apparent downward trend 

in total PCB concentrations, as well as flow-normalized annual 

loads (appendix 5), suggest that part of the decrease in loads is 

due to environmental change.

PCB loads calculated for 2005–6 for the Fox River are 

lower than those calculated during the LMMBP, a fact that 

could be largely explained by decreases in total flow volume 

in 2005–6 relative to the LMMBP. However, examination of 

the historical, current (2005–6) and simulated total PCB loads 

for the Fox River suggests that loadings should be decreasing (fig. 14), and that the current loads could be part of this 

expected downward trend. Simulated PCB loads were calculated from concentration and flow data associated with the noaction scenario generated for the Fox River Remedial Investigation/Feasibility Study (Wisconsin Department of Natural 

Resources and The RETEC Group, 2002). The no-action scenario run begins in 2000 and was run out to 2020. 

Calculated loads for 2005–6 are well within the range 

of values simulated with the no-action scenario for 2005–6. 

A notable pattern apparent in the simulated loads is that even 

as the overall trend in loading goes downward, year-to-year 

variability in loads remains high. Ironically, as environmental 

concentrations decrease over time, greater sampling effort 

(more samples spread over multiple years) will be required 

to fully document changing conditions relative to inherent 

system variability.

Table 10. Adjusted R-squared values, p-values, and effect size for polychlorinated biphenyl (PCB) regression models. 

[TSS, total suspended solids; ---, variable removed from regression; ***, either not statistically significant or of no practical significance]

Tributary name

Adjusted 

R-squared 

value

Significance of coefficients (p-value) Effect 

size Interpretation

TSS Air 

temperature Discharge Time

Grand River 0.552 4.22E-11 --- 2.45E-01 1.54E-03 -0.72 Small decrease

Kalamazoo River .658 3.43E-06 5.15E-01 3.14E-03 6.70E-07 -.99 Small decrease

St. Joseph River .653 5.39E-04 9.32E-05 --- 3.07E-02 -.74 Small decrease

Indiana Harbor and 

Ship Canal

.431 1.42E-02 3.04E-02 --- 4.08E-02 -1.34 Moderate decrease

Fox River .819 1.79E-10 2.85E-07 7.57E-02 5.06E-01 .1 ***
Estimated Loads of Nutrients, Mercury, and Polychlorinated Biphenyls 23

TOTAL PCB, IN NANOGRAMS PER LITER

Fox River

1994199519961997199819992000200120022003200420052006

0

50

100

150 (21)

(18)

(4)

x (7)

TOTAL PCB, IN NANOGRAMS PER LITER

Indiana Harbor and Ship Canal

1994199519961997199819992000200120022003200420052006

0

50

100

150

(4)

(9)

(3)

(8)

x

TOTAL PCB, IN NANOGRAMS PER LITER

Grand River

1994199519961997199819992000200120022003200420052006

0

1

2

3

4

(25)

(21)

(8)

(1) (1)

(1)

(1)

(11)

oo

x

x

x

TOTAL PCB, IN NANOGRAMS PER LITER

Kalamazoo River

1994199519961997199819992000200120022003200420052006

0

10

20

30

40

50 (22)

(16)

(9)

(1) (1)

(1)

(1) (12)

TOTAL PCB, IN NANOGRAMS PER LITER

St. Joseph River

1994199519961997199819992000200120022003200420052006

0

1

2

3

4

5

6

(16)

(16)

(1)

(1)

(1)

(1)

(11)

x (25) Number of points

o

x

Severe outlier

Moderate outlier

Adjacent value

75thpercentile

Median

25thpercentile

EXPLANATION

PCB Polychlorinated biphenyl

Figure 12. Total polychlorinated biphenyl (PCB) concentrations at five Lake Michigan tributary monitoring sites, 

1994–2006. 
24 Concentrations and Estimated Loads of Nutrients, Mercury, and PCBs in Selected Tributaries to Lake Michigan POLYCHLORINATED BIPHENYL (PCB) LOAD, IN KILOGRAMS PER YEAR

5

6

7

8

9

10

11

15

20

25

30

35

40

6

7

8

9

10

20

25

30

100

150

200

1994−95

1999

2005−6

Grand River Kalamazoo River St. Joseph River Indiana Harbor and Ship Canal Lower Fox River

Load calculated with all available data, 

showing 95-percent confidence interval bars

Individual load estimate from the jackknife approach

Mean of all jackknife load estimates

EXPLANATION

Figure 13. Calculated polychlorinated biphenyl (PCB) loads at five Lake Michigan tributary monitoring sites. 
Estimated Loads of Nutrients, Mercury, and Polychlorinated Biphenyls 25

POLYCHLORINATED BIPHENYL (PCB) LOAD, IN KILOGRAMS PER YEAR 100

150

200

1990199520002005201020152020

Load calculated from remedial investigation/feasibility study model, 

no-action scenario (Wisconsin Department of Natural Resources

and the RETEC Group, 2002)

Load calculated from water-column data

EXPLANATION

Figure 14. Calculated total polychlorinated biphenyl (PCB) loads for the Lower Fox River, 1989 to 2006. 
26 Concentrations and Estimated Loads of Nutrients, Mercury, and PCBs in Selected Tributaries to Lake Michigan

Summary and Conclusions

Water samples were collected in 2005 and 2006 to generate concentration data and load estimates for 5 nutrients, total 

mercury, and total PCB at 5 of the original 11 Lake Michigan 

Mass Balance Project sampling sites. New concentration 

datasets were generated as part of the current project for the 

Fox River and for the Indiana Harbor and Ship Canal. Concentration data for the Grand, Kalamazoo, and St. Joseph Rivers 

were obtained through sampling efforts coordinated by the 

Michigan Department of Environmental Quality.

Loads for each of the tributaries were calculated by 

means of Beale’s time-stratified ratio estimator method (Richards, 1998). Uncertainty in load estimates due to the structure 

of the sampling scheme employed was assessed by means of 

a jackknife analysis. Results of the jackknife analysis suggest 

that more intensive sampling may be required in the future, 

particularly on the Fox and Grand Rivers, in order to reduce 

the bias and increase the precision of the estimated load.

Comparison of 2005–6 data to the LMMBP data shows 

the following changes:

• small to moderate increases in total phosphorus and 

orthophosphate concentrations at the Grand River;

• moderate to large increases in total phosphorus and 

orthophosphate concentrations at the Indiana Harbor 

and Ship Canal;

• small to large increases in nitrate plus nitrite concentrations at the Grand and Kalamazoo Rivers, and at 

the Indiana Harbor and Ship Canal;

• small to moderate decreases in concentrations of 

total mercury at the Grand, Kalamazoo, and St. 

Joseph Rivers; and

• small to moderate decreases in concentrations of 

total PCB at the Grand, Kalamazoo, and St. Joseph 

Rivers and at the Indiana Harbor and Ship Canal.

Estimated annual total mercury loads during 2005–6 

ranged from 51 kg/yr at the Fox River to 2.2 kg/yr at the Indiana Harbor and Ship Canal. Estimated total polychlorinated 

biphenyl (PCB) loads during 2005–6 ranged from 132 kg/yr at 

the Fox River to 6.2 kg/yr at the Grand River.

In general, the calculated loads for the 2005–6 are lower 

than those calculated for the LMMBP. Decreases in loads 

are due to a combination of factors, including differences in 

streamflow between the two time periods, smaller sample sizes 

relative to the LMMBP, and actual environmental changes. 

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V.G., 1978, United States Great Lakes tributary loadings—

International Reference Group on Great Lakes pollution 

from land use activities: Washington, D.C., International 

Joint Commission, 187 p.

Steuer, J.J., 2000, A mass-balance approach for assessing 

PCB movement during remediation of a PCB-contaminated 

deposit on the Fox River, Wisconsin: U.S. Geological Survey Water-Resources Investigations Report 2000–4245, 8 p.

U.S. Environmental Protection Agency, 1997, Lake Michigan Mass Budget/Mass Balance Workplan: Great Lakes 

National Program Office, accessed February 2009 at http://

www.epa.gov/greatlakes/lmmb/workplan/index.html

U.S. Environmental Protection Agency, 1997, Lake Michigan Mass Balance Methods Compendium, accessed 

January 2009 at http://www.epa.gov/greatlakes/lmmb/

methods/#Methods

U.S. Environmental Protection Agency, 1999, Quality 

Assurance Plan For Mathematical Modeling: Grosse Ile, 

Mich., Great Lakes National Program Office, Large Lakes 

Research Station, 233 p.

U.S. Environmental Protection Agency, 2006, Results of the 

Lake Michigan Mass Balance Project: Polychlorinated 

Biphenyls Modeling Report: Large Lakes Research Station, 

accessed March 2009 at http://www.epa.gov/med/grosseile_

site/LMMBP/pcb-report.html

U.S. Environmental Protection Agency, 2008, Lake Michigan 

Lakewide Management Plan 2008, accessed March 2009 at

http://epa.gov/greatlakes/lamp/lm_2008/index.html

U.S. Environmental Protection Agency, 2009, Great Lakes 

areas of concern, accessed February 2009 at http://epa.gov/

greatlakes/aoc/index.html

U.S. Environmental Protection Agency, 2009, Basic information—Polychlorinated biphenyls (PCBs), accessed March 

2009 at http://www.epa.gov/epawaste/hazard/tsd/pcbs/pubs/

about.htm

U.S. Environmental Protection Agency, 2009, Great Lakes 

contaminated sediments, accessed May 2009 at http://epa.

gov/greatlakes/sediment/remed/index.html

U.S. Geological Survey, 2008, Lake Michigan Monitoring Coordination Council, accessed June 2009 at http://

wi.water.usgs.gov/lmmcc/index.html

Wisconsin Department of Natural Resources, 2002, White 

Paper No. 4, Dams in Wisconsin and on the Lower Fox 

River—Response to comments by the Fox River Group: 

Madison, Wis., [11] p.

Wisconsin Department of Natural Resources and The RETEC 

Group, 2002, Final Model Documentation Report, RETEC 

Project Number WISCN-14414-262: Madison, Wis., and 

Seattle, Wash., accessed January 2010 at http://dnr.wi.gov/

org/water/wm/foxriver/documents/modeldocs/final_model_

doc.pdf
28 Concentrations and Estimated Loads of Nutrients, Mercury, and PCBs in Selected Tributaries to Lake Michigan

Wisconsin State Laboratory of Hygiene, 1996, PCBs and pesticides in surface water by XAD-2 resin extraction, in Lake 

Michigan Mass Balance Methods Compendium, U.S. Environmental Protection Agency, v. 2, accessed March 2010 at 

http://www.epa.gov/glnpo/lmmb/methods/sec1293.pdf

Young, T.C., DePinto, J.V., and Heidtke, T.M., 1988, Factors 

affecting the efficiency of some estimators of fluvial total 

phosphorus load: Water Resources Research, v. 24, no. 9, 

p. 1535–1540. 
Appendix 1. Analytical Methods 
30 Concentrations and Estimated Loads of Nutrients, Mercury, and PCBs in Selected Tributaries to Lake Michigan Table 1–1. Analytical schedule for the Fox River tributary monitoring site. Analyte Method Number of field samples Number of field duplicates Number of blank samples Total number of samples Wisconsin State Laboratory of Hygiene PCB congeners in surface water - prep O1293P3 12 1 1 14 PCB congeners in 160l surface water - particulate O1293E2 12 1 1 14 PCB congeners in 160l surface water - dissolved O1293E1 12 1 1 14 Ammonia-N (SM 4500-NH3H) I440NLD 12 1 0 13 Nitrate plus nitrite-N I460MLD 12 1 0 13 Total Kjeldahl nitrogen I470BLT 12 1 0 13 Total phosphorus I520PLT 12 1 0 13 Orthophosphate as P, low range I530ALD 12 1 0 13 Total dissolved solids, 180°C, plus total solids I640FLT 12 1 0 13 Suspended solids, 0.7 micron GF/F filter I650HLT 12 1 0 13 Chlorophyll a, fluorescence (Welschmeyer, 1994) I251UNL 12 1 0 13 Total organic carbon O1660 12 1 0 13 Dissolved organic carbon O1662 12 1 0 13 Total mercury I430ZDT 12 1 1 14 U.S. Geological Survey Mercury Research Laboratory Total mercury in water (whole water) WDML SOP001 12 1 1 14 Methyl mercury in water (whole water) WDML SOP004 + SOP005 12 1 1 14 Total mercury in water (filter - i.e. particulate fraction) WDML SOP001 12 1 1 14 Methyl mercury in water (filter - i.e. particulate fraction) WDML SOP004 + SOP005 12 1 1 14
Appendix 1

31

Table 1–2. Analytical schedule for the Indiana Harbor and Ship Canal tributary monitoring site. 

Analyte Method Number of field samples Number of field duplicates Number of blank samples Total number of samples

Wisconsin State Laboratory of Hygiene

PCB congeners in surface water - prep O1293P3 12 1 1 14PCB congeners in 160l surface water - particulate O1293E2 12 1 1 14PCB congeners in 160l surface water - dissolved O1293E1 12 1 1 14Ammonia-N (SM 4500-NH3H) I440NLD 12 1 0 13Nitrate plus nitrite-N I460MLD 12 1 0 13Total Kjeldahl nitrogen I470BLT 12 1 0 13Total phosphorus I520PLT 12 1 0 13Orthophosphate as P, low range I530ALD 12 1 0 13Total dissolved solids, 180°C, plus total solids I640FLT 12 1 0 13Suspended solids, 0.7 micron GF/F filter I650HLT 12 1 0 13Total organic carbon O1660 12 1 0 13Dissolved organic carbon O1662 12 1 0 13Total mercury I430ZDT 12 1 1 14

Table 1–3. Analytical schedule for supplemental sampling at the Grand, Kalamazoo, and St. Joseph Rivers. 

Analyte Method Number of field samples Number of field duplicates Number of blank samples Total number of samples

Wisconsin State Laboratory of Hygiene

Ammonia-N (SM 4500-NH3H) I440NLD 12 0 0 12Nitrate plus nitrite-N I460MLD 12 0 0 12Total Kjeldahl nitrogen I470BLT 12 0 0 12Total phosphorus I520PLT 12 0 0 12Orthophosphate as P, low range I530ALD 12 0 0 12Total dissolved solids, 180°C, plus total solids I640FLT 12 0 0 12Suspended solids, 0.7 micron GF/F filter I650HLT 12 0 0 12Total organic carbon O1660 12 0 0 12Dissolved organic carbon O1662 12 0 0 12
This page is intentionally blank.
Appendix 2. Quality-Control Data Tables 
34 Concentrations and Estimated Loads of Nutrients, Mercury, and PCBs in Selected Tributaries to Lake Michigan

Table 2–1. Field replicate results for the Grand River at Eastmanville, Michigan. 

[Laboratory results in milligrams per liter; <, less than; ---, not determined]

Sample date Michigan Department 

of Environmental Quality

Wisconsin State 

Laboratory of Hygiene

Relative percent 

difference

Phosphorus

10/04/2005 0.086 0.103 18.0

10/26/2005 .082 .085 3.6

11/21/2005 .060 .118 65.2

Phosphorus, orthophosphate as Phosphorus

10/04/2005 0.003 0.003 0.0

10/26/2005 .002 .006 100.0

11/21/2005 .025 .020 22.2

Nitrogen, ammonia (NH3

) as Nitrogen

10/04/2005 0.015 <0.015 ---

10/26/2005 .270 .247 8.9

11/21/2005 .133 .120 10.3

Nitrogen, Kjeldahl, as Nitrogen

10/04/2005 0.96 1.03 7.0

10/26/2005 .90 .85 5.7

11/21/2005 .65 .61 6.3

Nitrate plus nitrite, as Nitrogen

10/04/2005 1.06 1.33 22.6

10/26/2005 1.35 1.40 3.6

11/21/2005 1.59 1.62 16.8
Appendix 2 35

Table 2–2. Field replicate results for the Kalamazoo River at 57th Street. 

[Laboratory results in milligrams per liter; *, result is approximate because of interferences; 

---, not determined; ND, not detected]

Sample date Michigan Department 

of Environmental Quality

Wisconsin State 

Laboratory of Hygiene

Relative percent 

difference

Phosphorus

09/27/2005 0.069 0.069 0.0

10/18/2005 .056 .053 5.5

11/02/2005 .039 *.047 ---

11/22/2005 .040 .091 77.9

Phosphorus, orthophosphate as Phosphorus

09/27/2005 0.005 0.004 22.2

10/18/2005 .002 .003 40.0

11/02/2005 .001 *.002 ---

11/22/2005 .012 .010 18.2

Nitrogen, ammonia (NH3

) as Nitrogen

09/27/2005 0.029 ND ---

10/18/2005 .004 ND ---

11/02/2005 .026 .024 8.0

11/22/2005 .078 .063 21.3

Nitrogen, Kjeldahl, as Nitrogen

09/27/2005 0.770 0.610 23.2

10/18/2005 .580 .700 18.8

11/02/2005 .500 .500 .0

11/22/2005 .480 .400 18.2

Nitrate plus nitrite, as Nitrogen

09/27/2005 0.840 0.866 3.0

10/18/2005 1.040 1.090 4.7

11/02/2005 1.200 1.230 2.5

11/22/2005 1.280 1.300 1.6
36 Concentrations and Estimated Loads of Nutrients, Mercury, and PCBs in Selected Tributaries to Lake Michigan

Table 2–3. Field replicate results for the St. Joseph River at St. Joseph, Michigan. 

[Laboratory results in milligrams per liter; *, result is approximate because of interferences; 

---, not determined; ND, not detected]

Sample date Michigan Department 

of Environmental Quality

Wisconsin State 

Laboratory of Hygiene

Relative percent 

difference

Phosphorus

09/29/2005 0.065 0.072 10.2

10/19/2005 .042 .047 11.2

11/03/2005 .054 *.063 ---

11/16/2005 .042 *.116 ---

Phosphorus, orthophosphate as Phosphorus

09/29/2005 0.024 0.020 18.2

10/19/2005 .017 .021 21.1

11/03/2005 .026 *.031 ---

11/16/2005 .013 .014 7.4

Nitrogen, ammonia (NH3

) as Nitrogen

09/29/2005 0.046 0.035 27.2

10/19/2005 .021 .025 17.4

11/03/2005 .005 ND ---

11/16/2005 .018 ND ---

Nitrogen, Kjeldahl, as Nitrogen

09/29/2005 0.44 0.55 22.2

10/19/2005 .32 .27 16.9

11/03/2005 .31 .40 25.4

11/16/2005 .37 .45 19.5

Nitrate plus nitrite, as Nitrogen

09/29/2005 1.36 1.37 0.7

10/19/2005 1.44 1.49 3.4

11/03/2005 1.63 1.68 3.3

11/16/2005 1.62 1.69 4.2
Appendix 3. Data Tables 
38 Concentrations and Estimated Loads of Nutrients, Mercury, and PCBs in Selected Tributaries to Lake Michigan

Table 3–1. Concentration data for the Grand River near Riverside Park, Ottawa County, Michigan (04119400). 

[m3/s, cubic meters per second; mg/L, milligrams per liter; ng/L, nanograms per liter; <, less than; ---, not determined]

Date of 

sample

Flow 

(m3

/s)1

Ammonia 

(mg/L)

Orthophosphate 

(mg/L)

NO2 + NO3 

(mg/L)

Polychlorinated 

biphenyl 

(ng/L)

Total 

Kjeldahl 

nitrogen 

(mg/L)

Total 

mercury 

(ng/L)

Total 

phosphorus 

(mg/L)

03/22/2005 187.2 0.430 0.030 2.10 1.47 1.22 2.24 0.072

04/11/2005 154.0 .220 .005 2.20 2.88 1.16 4.95 .097

05/11/2005 95.7 .200 .008 2.13 1.40 1.45 2.63 .110

06/08/2005 73.3 .015 .004 1.17 --- 1.50 5.08 .131

06/27/2005 60.9 .014 .014 2.60 2.55 1.38 1.14 .098

07/19/2005 47.8 .020 .016 .56 2.26 1.59 5.13 .143

08/02/2005 56.4 .015 .017 .79 1.69 1.34 3.63 .099

08/23/2005 34.1 .013 .017 1.09 1.27 1.26 1.27 .100

09/20/2005 34.4 .046 .009 2.02 1.27 .96 1.88 .106

10/04/2005 47.8 .015 .003 2.57 1.37 .90 1.85 .086

10/26/2005 38.0 .270 <.002 2.62 1.00 .90 .92 .082

11/21/2005 67.0 .133 .025 3.16 1.13 .65 1.18 .060

1

Flow estimated from the Grand River at Grand Rapids, Michigan, streamgaging station (04119000). 

Table 3–2. Concentration data for the Kalamazoo River near New Richmond, Michigan (04108660). 

[m3/s, cubic meters per second; mg/L, milligrams per liter; ng/L, nanograms per liter]

Date of 

sample

Flow 

(m3

/s)1

Ammonia 

(mg/L)

Orthophosphate 

(mg/L)

NO2 + NO3 

(mg/L)

Polychlorinated 

biphenyl 

(ng/L)

Total 

Kjeldahl 

nitrogen 

(mg/L)

Total 

mercury 

(ng/L)

Total 

phosphorus 

(mg/L)

03/21/2005 95.8 0.051 0.009 1.68 5.65 0.55 3.48 0.038

05/04/2005 54.5 .010 .003 .62 13.39 .98 3.04 .085

06/01/2005 41.0 .012 .007 .70 17.71 1.07 7.09 .101

06/28/2005 35.3 .101 .012 .32 15.65 1.22 7.30 .118

07/20/2005 44.0 .193 .003 .44 18.25 1.36 9.16 .132

08/03/2005 40.5 .062 .006 .50 14.08 .93 6.50 .085

08/24/2005 29.8 .045 .005 .60 12.88 .77 5.84 .123

09/14/2005 25.4 .048 .002 .68 7.45 .71 3.88 .062

09/27/2005 29.4 .029 .005 .84 12.09 .77 4.17 .069

10/18/2005 29.4 .004 .002 1.04 9.12 .58 3.06 .056

11/02/2005 36.4 .026 .001 1.20 6.88 .50 2.24 .039

11/22/2005 28.8 .078 .012 1.28 6.00 .48 2.01 .040

1

Flow estimated from the Kalamazoo River at Comstock, Michigan, streamgaging station (04106000). 
Appendix 3 39

Table 3–3. Concentration data for the St. Joseph River near Zollar Drive, Benton Harbor, Michigan (STORET 110628). 

[m3/s, cubic meters per second; mg/L, milligrams per liter; ng/L, nanograms per liter; ---, not determined]

Date of 

sample

Flow 

(m3

/s)1

Ammonia 

(mg/L)

Orthophosphate 

(mg/L)

NO2 + NO3 

(mg/L)

Polychlorinated 

biphenyl 

(ng/L)

Total 

Kjeldahl 

nitrogen 

(mg/L)

Total 

mercury 

(ng/L)

Total 

phosphorus 

(mg/L)

03/28/2005 203.1 0.011 0.004 2.21 1.32 0.46 1.75 0.034

05/05/2005 111.1 .006 .004 1.74 2.16 .50 1.99 .036

06/02/2005 91.3 .007 .006 1.20 2.22 .78 3.18 .062

06/29/2005 61.7 .008 .009 .96 1.98 .68 1.67 .058

07/21/2005 85.1 .011 .002 .98 --- .69 2.92 .085

08/04/2005 68.5 .011 .002 .78 2.52 .77 2.25 .062

08/25/2005 51.9 .005 .006 1.08 1.82 .59 1.57 .056

09/15/2005 33.7 .015 .002 .94 2.22 .60 1.71 .054

09/29/2005 65.7 .046 .024 1.36 2.21 .44 3.04 .065

10/19/2005 45.8 .021 .017 1.44 1.12 .32 1.26 .042

11/03/2005 57.7 .006 .026 1.63 1.34 .31 .96 .054

11/16/2005 51.6 .018 .013 1.62 1.40 .37 1.85 .042

1

Flow estimated from the St. Joseph River at Niles, Michigan, streamgaging station (04101500). 

Table 3–4. Concentration data for the Indiana Harbor and Ship Canal at East Chicago, Indiana (04092750). 

[m3/s, cubic meters per second; mg/L, milligrams per liter; ng/L, nanograms per liter]

Date of 

sample

Flow 

(m3

/s)

Ammonia 

(mg/L)

Orthophosphate 

(mg/L)

NO2 + NO3 

(mg/L)

Polychlorinated 

biphenyl 

(ng/L)

Polychlorinated 

biphenyl, 

surrogatecorrected 

(ng/L)

Total 

Kjeldahl 

nitrogen 

(mg/L)

Total 

mercury 

(ng/L)

Total 

phosphorus 

(mg/L)

09/28/2005 11.5 0.255 0.058 3.93 58.85 67.97 0.73 6.71 0.106

10/27/2005 10.2 .347 .050 4.04 32.16 38.03 .70 4.42 .089

12/07/2005 9.9 1.150 .037 4.20 12.09 14.01 1.38 5.13 .081

01/10/2006 10.0 .470 .042 3.48 48.76 56.21 1.27 114.50 .365

02/07/2006 10.9 .494 .046 3.73 26.22 30.79 1.16 6.36 .093

03/07/2006 10.7 .542 .034 3.53 34.28 41.85 1.07 4.47 .073

03/07/2006 10.7 .543 .034 3.56 32.08 39.17 1.02 4.45 .072

04/04/2006 11.2 .541 .032 3.68 63.41 80.94 .79 9.07 .082

04/24/2006 12.2 .331 .023 3.07 42.57 50.11 .68 6.13 .080

05/23/2006 14.2 .328 .040 3.60 67.59 84.22 .77 5.48 .083

06/12/2006 15.6 .269 .054 2.64 68.57 81.38 .72 9.05 .091

07/10/2006 11.5 .116 .050 3.32 37.13 42.82 .61 5.41 .090
40 Concentrations and Estimated Loads of Nutrients, Mercury, and PCBs in Selected Tributaries to Lake Michigan

Table 3–5. Concentration data for the Lower Fox River at Oil Tank Depot at Green Bay, Wisconsin (040851385). 

[m3/s, cubic meters per second; mg/L, milligrams per liter; ng/L, nanograms per liter; <, less than; MRL, U.S. Geological Survey Mercury 

Research Laboratory; SLH, Wisconsin State Laboratory of Hygiene; μg/L, micrograms per liter; ---, not determined]

Date of 

sample

Flow 

(m3

/s)

Ammonia 

(mg/L)

Orthophosphate 

(mg/L)

NO2 + NO3 

(mg/L)

Polychlorinated 

biphenyl 

(ng/L)

Polychlorinated 

biphenyl, 

surrogatecorrected 

(ng/L)

Total 

Kjeldahl 

nitrogen 

(mg/L)

Total 

phosphorus 

(mg/L)

08/03/2005 56.9 <0.015 0.078 <0.019 82.66 88.09 1.80 0.261

09/15/2005 59.5 .017 .090 <.019 151.95 155.55 1.91 .331

09/15/2005 59.5 <.015 .088 <.019 148.59 155.33 --- .325

10/19/2005 74.8 .159 .079 .42 124.01 133.45 1.71 .252

11/08/2005 85.5 .199 .064 .34 51.95 56.71 1.00 .280

01/10/2006 160.3 .165 .049 .57 4.52 5.33 .85 .087

03/22/2006 130.3 .048 .011 .54 16.37 20.18 .85 .063

04/25/2006 120.1 .186 .020 .91 75.80 94.70 .98 .120

05/17/2006 325.6 .120 .042 1.46 40.64 44.43 1.25 .118

06/21/2006 32.0 .144 .038 .48 44.61 60.17 1.23 .147

07/06/2006 39.4 .072 .041 .02 66.85 76.87 1.57 .188

07/26/2006 51.0 .099 .030 .12 88.45 88.38 1.92 .192

08/09/2006 28.6 <.015 .053 <.019 91.66 90.15 1.62 .209
Appendix 3 41

Table 3–5. Concentration data for the Lower Fox River at Oil Tank Depot at Green Bay, Wisconsin (040851385). —Continued

[m3/s, cubic meters per second; mg/L, milligrams per liter; ng/L, nanograms per liter; <, less than; MRL, U.S. Geological Survey Mercury Research Laboratory; SLH, Wisconsin State Laboratory of Hygiene; μg/L, micrograms per liter; ---, not determined]

Date of 

sample

Flow 

(m3

/s)

Total 

mercury, 

MRL, 

(ng/L)

Total 

mercury, 

SLH, 

(ng/L)

Dissolved 

methylmercury 

(ng/L)

Total 

methylmercury 

(ng/L)

Total 

suspended 

solids 

(mg/L)

Total 

organic 

carbon 

(mg/L)

Dissolved 

organic 

carbon 

(mg/L)

Chlorophyll-a

(μg/L)

08/03/2005 56.9 30.06 37.30 0.04 0.328 56 11.0 7.3 92.5

09/15/2005 59.5 48.08 52.82 .04 .338 85 11.0 7.9 105

09/15/2005 59.5 48.59 51.97 .04 .379 --- 10.0 8.2 106

10/19/2005 74.8 54.02 58.56 .04 .333 55 8.4 7.9 *46.1

11/08/2005 85.5 18.44 19.26 .04 .109 28 7.4 7.7 11.9

01/10/2006 160.3 4.47 5.57 .04 .014 6 8.4 7.8 2

03/22/2006 130.3 2.60 3.92 .04 .028 9 8.3 7.6 12

04/25/2006 120.1 28.10 30.85 .06 .230 43 8.5 6.8 *20.9

05/17/2006 325.6 19.52 21.80 .07 .164 36 7.4 7.0 10.8

06/21/2006 32.0 13.34 12.21 .05 .140 25 9.0 7.8 38

07/06/2006 39.4 22.92 24.85 .04 .228 39 7.9 7.9 67.1

07/26/2006 51.0 18.00 21.64 .07 .213 33 9.5 9.5 79.4

08/09/2006 28.6 19.38 18.65 .06 .203 43 9.9 10.0 109

*

Laboratory interference.
This page is intentionally blank.
Appendix 4. Concentrations of Ammonia 

Nitrogen and Total Kjeldahl Nitrogen at Five 

Lake Michigan Tributary Monitoring Sites
44 Concentrations and Estimated Loads of Nutrients, Mercury, and PCBs in Selected Tributaries to Lake Michigan AMMONIA NITROGEN, IN MILLIGRAMS PER LITER

Fox River

1994199519961997199819992000200120022003200420052006

0.0

0.1

0.2

0.3

0.4

(21)

(17)

(4) (7)

AMMONIA NITROGEN, IN MILLIGRAMS PER LITER

Indiana Harbor and Ship Canal

1994199519961997199819992000200120022003200420052006

0.0

0.2

0.4

0.6

0.8

1.0

1.2

(4) (9)

(3)

(8)

AMMONIA NITROGEN, IN MILLIGRAMS PER LITER

Grand River

1994199519961997199819992000200120022003200420052006

0.0

0.2

0.4

0.6

0.8

(26)

(21)

(13) (6)

(12) (12)

(12)

(12) (12)

AMMONIA NITROGEN, IN MILLIGRAMS PER LITER

Kalamazoo River

1994199519961997199819992000200120022003200420052006

0.00

0.05

0.10

0.15

0.20

0.25

0.30

(20)

(16) (13)

(6)

(12)

(12)

(12)

(12)

(12)

x

x

AMMONIA NITROGEN, IN MILLIGRAMS PER LITER

St. Joseph River

1994199519961997199819992000200120022003200420052006

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

(17)

(16)

(12)

(3)

(4) (12)

o

x

x (25) Number of points

o

x

Severe outlier

Moderate outlier

Adjacent value

75thpercentile

Median

25thpercentile

EXPLANATION

Figure 4–1. Concentrations of ammonia nitrogen at five Lake Michigan tributary monitoring sites, 1994–2006.
Appendix 4 45

TOTAL KJELDAHL NITROGEN, 

IN MILLIGRAMS PER LITER

Fox River

1994199519961997199819992000200120022003200420052006

0.0

0.5

1.0

1.5

2.0 (21)

(17)

(4) (7)

TOTAL KJELDAHL NITROGEN, 

IN MILLIGRAMS PER LITER

Indiana Harbor and Ship Canal

1994199519961997199819992000200120022003200420052006

0.0

0.5

1.0

1.5

(4)

(9)

(3)

(8)

TOTAL KJELDAHL NITROGEN, 

IN MILLIGRAMS PER LITER

Grand River

1994199519961997199819992000200120022003200420052006

0.0

0.5

1.0

1.5

2.0

2.5

3.0

(26)

(21)

(13)

(6)

(12)

(12)

(12)

(12)

(12)

o

o

x

x

x

x

TOTAL KJELDAHL NITROGEN, 

IN MILLIGRAMS PER LITER

Kalamazoo River

1994199519961997199819992000200120022003200420052006

0.0

0.5

1.0

1.5

(21)

(16)

(13)

(6)

(12) (12)

(12) (12)

(12)

o

o

x

x

x

x

x

x

TOTAL KJELDAHL NITROGEN, 

IN MILLIGRAMS PER LITER

St. Joseph River

1994199519961997199819992000200120022003200420052006

0.0

0.5

1.0

1.5

(17)

(16)

(12)

(4)

(4)

(12)

(25) Number of points

o

x

Severe outlier

Moderate outlier

Adjacent value

75thpercentile

Median

25thpercentile

EXPLANATION

Figure 4–2. Concentrations of total Kjeldahl nitrogen at five Lake Michigan tributary monitoring sites, 1994–2006. 
This page is intentionally blank.
Appendix 5. Calculated Loads 
48 Concentrations and Estimated Loads of Nutrients, Mercury, and PCBs in Selected Tributaries to Lake Michigan Table 5–1. Estimated annual loads for 1994–2005, site 04120250, Grand River at Grand Haven, Michigan. —Continued [Discharge estimated from station 04119000, unless otherwise noted. Loads calculated from datasets with six or less samples have relatively large confidence intervals and are colored red] Constituent Start date End date UNSTRATIFIED STRATIFIED STRATI- FIED, JACKKNIFE Footnote Combined degrees of freedom Annual load1 95-percent confidence interval Optimum number of time strata Combined degrees of freedom Annual load1 95-percent confidence interval Flow- normalized annual load3 Annual load1 Nutrients Ammonia-Nitrogen 4/1/1994 10/31/1995 46.0 726 109 9 21.1 665 73 665 702 2 Ammonia-Nitrogen 4/1/1994 10/31/1995 46.0 734 111 4 37.6 764 82 764 720 Ammonia-Nitrogen 1/1/1999 12/31/1999 12.0 252 71 2 9.7 234 50 384 226 Ammonia-Nitrogen 1/1/2000 12/31/2000 5.0 310 235 2 2.7 158 62 213 152 Ammonia-Nitrogen 1/1/2001 12/31/2001 11.0 1,144.0 373 5 3.4 774 113 782 842 Ammonia-Nitrogen 1/1/2002 12/31/2002 11.0 478 151 5 2.2 446 80 628 427 Ammonia-Nitrogen 1/1/2003 12/31/2003 11.0 773 561 4 4.3 732 128 1,493 730 Ammonia-Nitrogen 1/1/2004 12/31/2004 11.0 554 222 3 7.6 548 93 602 546 Ammonia-Nitrogen 1/1/2005 12/31/2005 11.0 473 249 3 7.6 538 65 769 568 Nitrate plus Nitrite 4/1/1994 10/31/1995 46.0 7,772 2,158 5 24.7 6,487 831 6,487 6,514 2 Nitrate plus Nitrite 4/1/1994 10/31/1995 46.0 7,865 2,222 9 15.8 5,821 348 5,821 6,438 Nitrate plus Nitrite 1/1/1999 12/31/1999 12.0 7,126 2,358 4 5.4 5,429 680 8,900 5,572 Nitrate plus Nitrite 1/1/2000 12/31/2000 5.0 7,007 2,698 1 5.0 7,007 2,698 9,469 6,594 Nitrate plus Nitrite 1/1/2001 12/31/2001 11.0 12,993 3,739 5 5.3 10,020 1,590 10,121 10,227 Nitrate plus Nitrite 1/1/2002 12/31/2002 11.0 8,129 2,518 2 7.2 8,055 1,688 11,345 7,799 Nitrate plus Nitrite 1/1/2003 12/31/2003 11.0 5,608 1,921 3 5.3 4,579 1,040 9,346 4,775 Nitrate plus Nitrite 1/1/2004 12/31/2004 11.0 15,053 4,886 4 4.1 12,541 1,055 13,781 13,263 Nitrate plus Nitrite 1/1/2005 12/31/2005 11.0 6,913 1,399 5 3.2 7,257 614 10,367 7,294 Total Kjeldahl Nitrogen 4/1/1994 10/31/1995 46.0 5,488 269 12 19.4 5,318 174 5,318 5,262 2 Total Kjeldahl Nitrogen 4/1/1994 10/31/1995 46.0 5,503 274 9 17.9 5,235 151 5,235 5,265 Total Kjeldahl Nitrogen 1/1/1999 12/31/1999 12.0 3,784 313 3 9.2 3608 167 5,914 3,661 Total Kjeldahl Nitrogen 1/1/2000 12/31/2000 5.0 3,852 989 2 3.0 3,875 675 5,237 3,786 Total Kjeldahl Nitrogen 1/1/2001 12/31/2001 11.0 5805 294 1 11.0 5,805 294 5,863 5,775 Total Kjeldahl Nitrogen 1/1/2002 12/31/2002 11.0 2,938 520 1 11.0 2,938 520 4,138 2,965

Total Kjeldahl Nitrogen 1/1/2003 12/31/2003 11.0 3,624 1,213 4 2.1 3,449 573 7,038 3,386
Appendix 5

49

Table 5–1. Estimated annual loads for 1994–2005, site 04120250, Grand River at Grand Haven, Michigan. —Continued[Discharge estimated from station 04119000, unless otherwise noted. Loads calculated from datasets with six or less samples have relatively large confidence intervals and are colored red]

Constituent Start date End date

UNSTRATIFIED STRATIFIED

STRATIFIED, 

JACKKNIFE

Footnote Combined 

degrees of 

freedom

Annual 

load1

95-percent 

confidence 

interval

Optimum 

number 

of time 

strata

Combined 

degrees 

of 

freedom

Annual 

load1

95-percent 

confidence 

interval

Flownormalized 

annual 

load3

Annual 

load1

Nutrients—continued

Total Kjeldahl Nitrogen 1/1/2004 12/31/2004 11.0 5,263 515 3 6.9 4,949 369 5,439 4,911

Total Kjeldahl Nitrogen 1/1/2005 12/31/2005 11.0 3,721 975 1 11.0 3,721 975 5,316 3,730

Orthophosphate 4/1/1994 10/31/1995 42.0 129 38 8 15.7 120 21 120 108 2

Orthophosphate 4/1/1994 10/31/1995 42.0 130 37 6 21.6 100 16 100 107

Orthophosphate 1/1/1999 12/31/1999 12.0 111 70 4 5.8 49 12 80 51

Orthophosphate 1/1/2000 12/31/2000 4.0 188 151 1 4.0 188 151 254 185

Orthophosphate 1/1/2001 12/31/2001 11.0 276 83 5 3.5 193 38 195 210

Orthophosphate 1/1/2002 12/31/2002 11.0 105 48 2 4.5 94 32 132 93

Orthophosphate 1/1/2003 12/31/2003 11.0 90 39 2 9.4 80 29 163 78

Orthophosphate 1/1/2004 12/31/2004 11.0 207 54 5 5.8 168 34 185 182

Orthophosphate 1/1/2005 12/31/2005 11.0 39 17 1 11.0 39 17 56 38

Total Phosphorus 4/1/1994 10/31/1995 46.0 552 77 11 14.7 471 27 471 485 2

Total Phosphorus 4/1/1994 10/31/1995 46.0 552 76 10 20.0 471 27 471 485

Total Phosphorus 1/1/1999 12/31/1999 12.0 489 145 4 7.6 387 63 634 386

Total Phosphorus 1/1/2000 12/31/2000 5.0 619 436 2 2.9 530 253 716 559

Total Phosphorus 1/1/2001 12/31/2001 11.0 822 217 4 5.5 666 76 673 668

Total Phosphorus 1/1/2002 12/31/2002 11.0 340 53 3 5.4 333 34 469 331

Total Phosphorus 1/1/2003 12/31/2003 11.0 375 143 1 11.0 375 143 766 362

Total Phosphorus 1/1/2004 12/31/2004 11.0 709 124 4 5.1 624 89 685 620

Total Phosphorus 1/1/2005 12/31/2005 11.0 325 57 1 11.0 325 57 465 325

Mercury

Total Mercury 4/1/1994 10/31/1995 26.0 32.8 15.7 5 10.5 23.2 4.0 23.2 23.7 2

Total Mercury 4/1/1994 10/31/1995 26.0 32.4 15.6 5 7.6 23.0 4.9 23.0 23.7

Total Mercury 1/1/1999 12/31/1999 12.0 32.3 14.8 6 2.5 23.9 10.4 39.2 25.1

Total Mercury 1/1/2000 12/31/2000 5.0 17.8 13.6 2 3.8 15.3 10.2 20.7 15.6
50 Concentrations and Estimated Loads of Nutrients, Mercury, and PCBs in Selected Tributaries to Lake Michigan Table 5–1. Estimated annual loads for 1994–2005, site 04120250, Grand River at Grand Haven, Michigan. —Continued [Discharge estimated from station 04119000, unless otherwise noted. Loads calculated from datasets with six or less samples have relatively large confidence intervals and are colored red] Constituent Start date End date UNSTRATIFIED STRATIFIED STRATI- FIED, JACKKNIFE Footnote Combined degrees of freedom Annual load1 95-percent confidence interval Optimum number of time strata Combined degrees of freedom Annual load1 95-percent confidence interval Flow- normalized annual load3 Annual load1 Mercury—continued Total Mercury 1/1/2001 12/31/2001 11.0 25.6 14.3 4 5.4 16.4 3.8 16.5 17.0 Total Mercury 1/1/2002 12/31/2002 11.0 15.6 6.0 2 3.1 13.6 4.7 19.2 14.0 Total Mercury 1/1/2003 12/31/2003 11.0 15.2 6.8 1 11.0 15.2 6.8 31.0 14.9 Total Mercury 1/1/2004 12/31/2004 11.0 32.4 10.8 3 5.6 24.6 6.6 27.0 24.7 Total Mercury 1/1/2005 12/31/2005 11.0 10.2 3.9 2 9.0 10.0 3.7 14.3 10.1 Polychlorinated biphenyls (PCBs) Total PCB 4/1/1994 10/31/1995 45.0 10.9 1.1 9 22.2 10.6 0.5 10.6 10.3 2 Total PCB 4/1/1994 10/31/1995 45.0 10.8 1.1 6 15.0 10.4 .6 10.4 10.3 Total PCB 1/1/1999 12/31/1999 7.0 10.4 2.5 2 3.9 10.0 1.9 16.4 10.0 Total PCB 1/1/2005 12/31/2005 10.0 6.2 2.0 2 8.0 6.2 2.0 8.8 6.2

1Annual loads are presented in metric tons per year for nutrients and kilograms per year for mercury and PCBs.2Discharge from acoustic velocity meter at station 04120250.3Loads in this column are multiplied by a factor equal to the annual flow volume for the sampling period divided by the annual flow volume during the Lake Michigan Mass Balance Project. 
Appendix 5

51

Table 5–2. Estimated annual loads for 1994–2005, site 04108670 Kalamazoo River near New Richmond, Michigan. —Continued[Loads calculated from datasets with six or less samples have relatively large confidence intervals and are colored red]

Constituent Start date End date

UNSTRATIFIED STRATIFIED STRATIFIED, JACKKNIFE

Combined 

degrees of 

freedom

Annual 

load1

95-percent 

confidence 

interval

Optimum 

number 

of time 

strata

Combined 

degrees 

of 

freedom

Annual 

load1

95-percent 

confidence 

interval

Flownormalized 

annual 

load2

Annual load1

Nutrients

Ammonia-Nitrogen 4/1/1994 10/31/1995 35.0 88 20 6 26.9 95 12 95 92

Ammonia-Nitrogen 1/1/1999 12/31/1999 12.0 60 25 3 8.9 66 22 84 62

Ammonia-Nitrogen 1/1/2000 12/31/2000 5.0 78 49 1 5.0 78 49 95 76

Ammonia-Nitrogen 1/1/2001 12/31/2001 11.0 273 163 4 4.5 165 63 124 178

Ammonia-Nitrogen 1/1/2002 12/31/2002 11.0 95 41 1 11.0 95 41 95 94

Ammonia-Nitrogen 1/1/2003 12/31/2003 11.0 92 48 2 6.0 92 35 124 94

Ammonia-Nitrogen 1/1/2004 12/31/2004 11.0 106 47 5 4.9 92 30 93 97

Ammonia-Nitrogen 1/1/2005 12/31/2005 11.0 96 60 1 11.0 96 60 103 83

Nitrate plus Nitrite 4/1/1994 10/31/1995 36.0 1,798 191 8 15.6 1,689 90 1,688.8 1,708

Nitrate plus Nitrite 1/1/1999 12/31/1999 12.0 1,616 389 2 7.3 1,321 205 1,693.4 1,305

Nitrate plus Nitrite 1/1/2000 12/31/2000 5.0 1,992 704 1 5.0 1,992 704 2,428.8 1,953

Nitrate plus Nitrite 1/1/2001 12/31/2001 11.0 3,949 870 5 5.3 3,304 252 2,484.6 3,666

Nitrate plus Nitrite 1/1/2002 12/31/2002 11.0 2,547 543 4 5.1 2,522 139 2,522.2 2,525

Nitrate plus Nitrite 1/1/2003 12/31/2003 11.0 2,493 717 2 8.2 2,441 577 3,299.1 2,453

Nitrate plus Nitrite 1/1/2004 12/31/2004 11.0 2,594 669 5 5.0 2,541 188 2,567.1 2,545

Nitrate plus Nitrite 1/1/2005 12/31/2005 11.0 1,607 706 1 11.0 1,607 706 1,727.8 1,595

Total Kjeldahl Nitrogen 4/1/1994 10/31/1995 36.0 1,577 90 6 21.7 1,613 65 1,613 1,608

Total Kjeldahl Nitrogen 1/1/1999 12/31/1999 12.0 1,386 80 3 9.2 1,399 65 1,794 1,406

Total Kjeldahl Nitrogen 1/1/2000 12/31/2000 5.0 1,303 266 1 5.0 1,303 266 1,589 1,327

Total Kjeldahl Nitrogen 1/1/2001 12/31/2001 11.0 2,104 236 1 11.0 2,104 236 1,582 2,128

Total Kjeldahl Nitrogen 1/1/2002 12/31/2002 11.0 1,329 206 3 4.5 1,369 158 1,369 1,352

Total Kjeldahl Nitrogen 1/1/2003 12/31/2003 11.0 1,313 124 1 11.0 1,313 124 1,774 1,312

Total Kjeldahl Nitrogen 1/1/2004 12/31/2004 11.0 1,583 196 3 6.0 1,476 113 1,490 1,505

Total Kjeldahl Nitrogen 1/1/2005 12/31/2005 11.0 1,420 362 1 11.0 1,420 362 1,527 1,427
52 Concentrations and Estimated Loads of Nutrients, Mercury, and PCBs in Selected Tributaries to Lake Michigan Table 5–2. Estimated annual loads for 1994–2005, site 04108670 Kalamazoo River near New Richmond, Michigan. —Continued [Loads calculated from datasets with six or less samples have relatively large confidence intervals and are colored red] Constituent Start date End date UNSTRATIFIED STRATIFIED STRATIFIED, JACKKNIFE Combined degrees of freedom Annual load1 95-percent confidence interval Optimum number of time strata Combined degrees of freedom Annual load1 95-percent confidence interval Flow- normalized annual load2 Annual load1 Nutrients—continued Orthophosphate 4/1/1994 10/31/1995 33.0 22.5 8.8 8 12.6 18.1 3.4 18.1 18.9 Orthophosphate 1/1/1999 12/31/1999 12.0 38.3 26.5 5 2.4 20.9 10.4 26.8 21.5 Orthophosphate 1/1/2000 12/31/2000 5.0 55.1 45.8 2 4.0 46.6 18.3 56.8 46.1 Orthophosphate 1/1/2001 12/31/2001 11.0 89.5 57.6 2 5.7 61.5 32.1 46.2 62.7 Orthophosphate 1/1/2002 12/31/2002 11.0 36.0 26.7 1 11.0 36.0 26.7 36.0 35.9 Orthophosphate 1/1/2003 12/31/2003 11.0 32.6 14.9 2 8.2 33.7 14.1 45.6 32.9 Orthophosphate 1/1/2004 12/31/2004 11.0 50.3 24.9 4 4.4 42.8 18.0 43.2 41.9 Orthophosphate 1/1/2005 12/31/2005 11.0 10.4 4.2 1 11.0 10.4 4.2 11.2 10.6 Total Phosphorus 4/1/1994 10/31/1995 36.0 165 27 7 15.3 154 16 154 156 Total Phosphorus 1/1/1999 12/31/1999 12.0 138 27 2 9.2 134 22 172 135 Total Phosphorus 1/1/2000 12/31/2000 5.0 158 70 2 3.0 157 55 191 158 Total Phosphorus 1/1/2001 12/31/2001 11.0 257 70 3 6.7 258 52 194 249 Total Phosphorus 1/1/2002 12/31/2002 11.0 145 49 1 11.0 145 49 145 144 Total Phosphorus 1/1/2003 12/31/2003 11.0 140 31 2 9.2 144 27 194 141 Total Phosphorus 1/1/2004 12/31/2004 11.0 166 30 3 8.4 153 22 155 151 Total Phosphorus 1/1/2005 12/31/2005 11.0 131 44 1 11.0 131 44 141 131 Mercury Total Mercury 9/1/1994 10/31/1995 26.0 19.1 3.1 4 18.2 18.39 2.03 18.39 18.23 Total Mercury 1/1/1999 12/31/1999 12.0 14.1 2.3 2 10.9 13.34 1.66 17.10 13.23 Total Mercury 1/1/2000 12/31/2000 5.0 9.6 3.9 2 3.8 10.99 1.73 13.40 10.13 Total Mercury 1/1/2001 12/31/2001 11.0 12.9 5.0 3 7.4 11.56 1.63 8.69 12.17 Total Mercury 1/1/2002 12/31/2002 11.0 7.4 1.5 2 7.2 7.6 .83 7.60 7.59 Total Mercury 1/1/2003 12/31/2003 11.0 8.9 1.8 3 5.4 8.49 1.55 11.47 8.8 Total Mercury 1/1/2004 12/31/2004 11.0 10.6 2.2 3 8.5 9.31 1.18 9.40 9.59

Total Mercury 1/1/2005 12/31/2005 11.0 8.2 2.6 3 3.5 6.9 .99 7.42 7.25
Appendix 5

53

Table 5–2. Estimated annual loads for 1994–2005, site 04108670 Kalamazoo River near New Richmond, Michigan. —Continued[Loads calculated from datasets with six or less samples have relatively large confidence intervals and are colored red]

Constituent Start date End date

UNSTRATIFIED STRATIFIED STRATIFIED, JACKKNIFE

Combined 

degrees of 

freedom

Annual 

load1

95-percent 

confidence 

interval

Optimum 

number 

of time 

strata

Combined 

degrees 

of 

freedom

Annual 

load1

95-percent 

confidence 

interval

Flownormalized 

annual 

load2

Annual load1

Polychlorinated biphenyls (PCBs)

Total PCB 4/1/1994 10/31/1995 37.0 38.0 6.0 9 22.2 38.8 2.4 38.8 38.8

Total PCB 1/1/1999 12/31/1999 8.0 17.3 6.0 4 3.3 20.1 2.0 25.8 19.9

Total PCB 1/1/2005 12/31/2005 11.0 19.4 6.2 1 11.0 19.4 6.2 20.9 19.6

1Annual loads are presented in metric tons per year for nutrients and kilograms per year for mercury and PCBs.2Loads in this column are multiplied by a factor equal to the annual flow volume for the sampling period divided by the annual flow volume during the Lake Michigan Mass Balance Project. 
54 Concentrations and Estimated Loads of Nutrients, Mercury, and PCBs in Selected Tributaries to Lake Michigan Table 5–3. Estimated annual loads for 1994–2005, site 04102080 St. Joseph River at Napier Avenue at St. Joseph, Michigan. —Continued [Loads calculated from datasets with six or less samples have relatively large confidence intervals and are colored red] Constituent Start date End date UNSTRATIFIED STRATIFIED STRATIFIED, JACKKNIFE Combined degrees of freedom Annual load1 95-percent confidence interval Optimum number of time strata Combined degrees of freedom Annual load1 95-percent confidence interval Flow- normalized annual load2 Annual load1 Nutrients Ammonia-Nitrogen 4/1/1994 10/31/1995 32.0 190 48 3 18.6 175 32 175 174 Ammonia-Nitrogen 1/1/2001 12/31/2001 11.0 640 417 3 3.2 361 128 262 362 Ammonia-Nitrogen 1/1/2003 12/31/2003 2.0 49 38 1 2.0 49 38 56 49 Ammonia-Nitrogen 1/1/2004 12/31/2004 3.0 107 112 1 3.0 107 112 92 106 Ammonia-Nitrogen 1/1/2005 12/31/2005 11.0 47 24 3 6.4 38 10 36 38 Nitrate plus Nitrite 4/1/1994 10/31/1995 32.0 6,008 598 9 10.2 5,677 360 5,677 5,780 Nitrate plus Nitrite 1/1/2001 12/31/2001 11.0 13,185 3,876 2 9.8 11,314 2,203 8,198 11,315 Nitrate plus Nitrite 1/1/2003 12/31/2003 3.0 5,872 2,297 1 3.0 5,872 2,297 6,672 5,839 Nitrate plus Nitrite 1/1/2004 12/31/2004 3.0 7,127 3,363 1 3.0 7,127 3,363 6,144 7,118 Nitrate plus Nitrite 1/1/2005 12/31/2005 11.0 5,622 1,645 1 11.0 5,622 1,645 5,304 5,617 Total Kjeldahl Nitrogen 4/1/1994 10/31/1995 32.0 2,874 275 8 19.0 2,780 105 2,780 2,736 Total Kjeldahl Nitrogen 1/1/2001 12/31/2001 11.0 5,098 1,485 4 5.0 4,308 933 3,122 4,246 Total Kjeldahl Nitrogen 1/1/2003 12/31/2003 3.0 2,342 274 1 3.0 2,342 274 2,662 2,338 Total Kjeldahl Nitrogen 1/1/2004 12/31/2004 3.0 2,130 744 1 3.0 2,130 744 1,836 2,134 Total Kjeldahl Nitrogen 1/1/2005 12/31/2005 11.0 1,927 470 1 11.0 1,927 470 1,818 1,927 Orthophosphate 4/1/1994 10/31/1995 28.0 42 16 7 12.2 39 8 39 39 Orthophosphate 1/1/2001 12/31/2001 11.0 281 162 3 4.3 192 80 139 192 Orthophosphate 1/1/2003 12/31/2003 3.0 43 42 1 3.0 43 42 49 42 Orthophosphate 1/1/2004 12/31/2004 3.0 76 80 1 3.0 76 80 66 76 Orthophosphate 1/1/2005 12/31/2005 11.0 30 19 3 4.9 23 4 22 23 Total Phosphorus 4/1/1994 10/31/1995 32.0 269 45 8 12.7 253 17 253 251 Total Phosphorus 1/1/2001 12/31/2001 11.0 934 491 2 4.7 687 260 498 690 Total Phosphorus 1/1/2003 12/31/2003 3.0 235 29 1 3.0 235 28 267 235 Total Phosphorus 1/1/2004 12/31/2004 3.0 237 179 1 3.0 237 179 205 238

Total Phosphorus 1/1/2005 12/31/2005 11.0 183 56 1 11.0 183 56 173 183
Appendix 5

55

Table 5–3. Estimated annual loads for 1994–2005, site 04102080 St. Joseph River at Napier Avenue at St. Joseph, Michigan. —Continued[Loads calculated from datasets with six or less samples have relatively large confidence intervals and are colored red]

Constituent Start date End date

UNSTRATIFIED STRATIFIED STRATIFIED, JACKKNIFE

Combined 

degrees of 

freedom

Annual 

load1

95-percent 

confidence 

interval

Optimum 

number 

of time 

strata

Combined 

degrees 

of 

freedom

Annual 

load1

95-percent 

confidence 

interval

Flownormalized 

annual 

load2

Annual load1

Mercury

Total Mercury 1/1/1994 10/31/1995 23.0 19.6 3.4 2 21.9 19.3 3.3 19.3 19.2

Total Mercury 1/1/1999 12/31/1999 11.0 28.3 15.0 4 5.8 21.4 4.9 19.8 19.7

Total Mercury 1/1/2001 12/31/2001 11.0 40.7 15.7 2 9.8 32.4 9.5 23.4 32.6

Total Mercury 1/1/2003 12/31/2003 3.0 15.1 7.4 1 3.0 15.1 7.4 17.2 15.0

Total Mercury 1/1/2004 12/31/2004 3.0 13.0 11.4 1 3.0 13.0 11.4 11.2 13.1

Total Mercury 1/1/2005 12/31/2005 11.0 7.7 1.7 2 3.6 7.2 1.3 6.8 7.3

Polychlorinated biphenyls (PCBs)

Total PCB 4/1/1994 10/31/1995 31.0 10.2 1.5 9 16.9 9.5 0.7 9.5 9.6

Total PCB 1/1/2005 12/31/2005 10.0 6.7 1.4 1 10.0 6.7 1.4 6.3 6.7

1Annual loads are presented in metric tons per year for nutrients and kilograms per year for mercury and PCBs.2Loads in this column are multiplied by a factor equal to the annual flow volume for the sampling period divided by the annual flow volume during the Lake Michigan Mass Balance Project. 
56 Concentrations and Estimated Loads of Nutrients, Mercury, and PCBs in Selected Tributaries to Lake Michigan Table 5–4. Estimated annual loads for 1994–2005, site 04092750 Indiana Harbor Canal at East Chicago, Indiana. Constituent Start date End date UNSTRATIFIED STRATIFIED STRATIFIED, JACKKNIFE Combined degrees of freedom Annual load1 95-percent confidence interval Optimum number of time strata Combined degrees of freedom Annual load1 95-percent confidence interval Flow- normalized annual load2 Annual load1 Nutrients Ammonia-Nitrogen 10/1/1994 10/31/1995 12.0 230 57 5 4.8 209 19 209 218 Ammonia-Nitrogen 8/1/2005 7/31/2006 10.0 154 61 3 6.5 141 38 168 146 Nitrate plus Nitrite 10/1/1994 10/31/1995 12.0 668 62 4 8.2 676 39 676 673 Nitrate plus Nitrite 8/1/2005 7/31/2006 10.0 1,290 122 2 8.5 1,331 79 1,585 1,324 Total Kjeldahl Nitrogen 10/1/1994 10/31/1995 12.0 452 82 3 9.0 423 32 423 439 Total Kjeldahl Nitrogen 8/1/2005 7/31/2006 10.0 321 61 5 5.5 308 15 366 311 Orthophosphate 10/1/1994 10/31/1995 11.0 5.7 2.0 5 4.0 5.7 1.9 5.7 5.6 Orthophosphate 8/1/2005 7/31/2006 10.0 15.6 2.7 4 5.1 16.5 1.5 19.7 16 Total Phosphorus 10/1/1994 10/31/1995 12.0 30 6 3 8.0 29 5 29 29 Total Phosphorus 8/1/2005 7/31/2006 10.0 40 18 2 7.4 38 15 46 38 Mercury Total Mercury 10/1/1994 10/31/1995 9.0 4.1 1.3 2 7.7 4.0 1.2 4.0 4.1 Total Mercury 8/1/2005 7/31/2006 10.0 5.4 7.0 2 7.0 4.6 5.9 5.5 4.7 Total Mercury 8/1/2005 7/31/2006 9.0 2.3 .5 2 8.0 2.2 .4 2.6 32.2 Polychlorinated biphenyls (PCBs) Total PCB 10/1/1994 10/31/1995 12.0 33 6 5 4.6 31 4 31 31 Total PCB 8/1/2005 7/31/2006 10.0 21 6 2 9.0 20 5 24 20

1Annual loads are presented in metric tons per year for nutrients and kilograms per year for mercury and PCBs.2Loads in this column are multiplied by a factor equal to the annual flow volume for the sampling period divided by the annual flow volume during the Lake Michigan Mass Balance Project. 3Outlier removed.
Appendix 5

57

Table 5–5. Estimated annual loads for 1994–2005, site 040851385 Lower Fox River at Oil Tank Depot at Green Bay, Wisconsin. [MRL, Mercury Research Lab]

Constituent Start date End date

UNSTRATIFIED STRATIFIED STRATIFIED, JACKKNIFE

Combined 

degrees of 

freedom

Annual 

load1

95-percent 

confidence 

interval

Optimum 

number 

of time 

strata

Combined 

degrees 

of 

freedom

Annual 

load1

95-percent 

confidence 

interval

Flownormalized 

annual 

load2

Annual load1

Nutrients

Ammonia-Nitrogen 4/1/1994 10/31/1995 37.0 482 137 9 13.1 418 74 418 431

Ammonia-Nitrogen 8/1/2005 7/31/2006 10.0 364 118 4 3.5 371 94 464 382

Nitrate plus Nitrite 4/1/1994 10/31/1995 37.0 1,485 503 6 12.1 1,244 239 1,244 1,306

Nitrate plus Nitrite 8/1/2005 7/31/2006 10.0 2,342 1,666 4 4.5 1,515 278 1,893 1,497

Total Kjeldahl Nitrogen 4/1/1994 10/31/1995 37.0 4,863 388 6 8.9 4,889 250 4,889 4,876

Total Kjeldahl Nitrogen 8/1/2005 7/31/2006 10.0 3,676 727 4 5.3 3,271 260 4,089 3,378

Orthophosphate 4/1/1994 10/31/1995 32.0 139 44 4 15.3 130 33 130 129

Orthophosphate 8/1/2005 7/31/2006 10.0 133 45 3 5.3 121 30 152 130

Total Phosphorus 4/1/1994 10/31/1995 39.0 570 127 6 5.4 532 68 532 537

Total Phosphorus 8/1/2005 7/31/2006 10.0 449 174 2 9.0 510 67 637 479

Mercury

Total Mercury 4/1/1994 10/31/1995 21.0 111 37 5 5.2 101 20 101 103

Total Mercury 8/1/2005 7/31/2006 10.0 67.6 33 5 3.8 46 13 57 52

Total Mercury (MRL) 3 8/1/2005 7/31/2006 10.0 60 30 3 4.8 40 13 50 46

Total Methylmercury 1/1/1995 8/31/1995 14.0 .67 .18 4 9.0 .58 .10 .58 .59

Total Methylmercury 8/1/2005 7/31/2006 10.0 .48 .24 3 5.4 .30 .09 .38 .41

Dissolved Total Mercury 6/1/1994 10/31/1995 23.0 13.40 10.60 5 8.4 8.10 3.16 8.10 8.40

Dissolved Total Mercury 8/1/2005 7/31/2006 10.0 2.20 .39 3 5.2 2.11 .29 2.64 2.15

Dissolved Methylmercury 1/1/1995 8/31/1995 16.0 .13 .04 5 8.89 .14 .02 .14 .14

Dissolved Methylmercury 8/1/2005 7/31/2006 10.0 .16 .04 2 4.0 .14 .01 .18 .14

Polychlorinated biphenyls (PCBs)

Total PCB 5/1/1989 12/1/1989 74 152.5 10.4 9 24.29 151.7 7.2 185 149

Total PCB 4/1/1994 10/31/1995 38.0 212 32 6 20.8 199 22 199 204

Total PCB 8/1/2005 7/31/2006 10.0 174 94 3 5.2 114 55 142 141

1Annual loads are presented in metric tons per year for nutrients and kilograms per year for mercury and PCBs.2Loads in this column are multiplied by a factor equal to the annual flow volume for the sampling period divided by the annual flow volume during the Lake Michigan Mass Balance Project (LMMBP).3The methods used at the U.S. Geological Survey MRL are most similar to those used during the LMMBP. 
This page is intentionally blank.
Appendix 6 59

Appendix 6. Description of Beale Load Calculation and Jackknifing Procedure 

Many techniques have been used to calculate loads on 

the basis of observed discharge and concentration. These 

techniques include direct numerical integration, workedrecord interpretation, regression analysis, and ratio estimation 

(Richards, 1998).

For this work, the AutoBeale source code (Richards, 

1999) was modified in two ways in order to allow jackknifing 

estimates to be made. First, the code was modified to allow a 

genetic algorithm routine to optimize the number and arrangement of stratification boundaries. The genetic algorithm 

replaced a complicated rules-based stratification selection 

routine. Second, a jackknifing control module was added to 

the code to generate the jackknife estimate of load.

The genetic algorithm code PIKAIA was incorporated 

into AutoBeale; PIKAIA is a public-domain code developed at 

the National Center for Atmospheric Research’s High Altitude Observatory (Charbonneau and Knapp, 1995; Charbonneau, 2002). PIKAIA belongs to a class of methods aimed 

at numerical optimization known as genetic algorithm-based 

optimizers. 

A function was written to provide PIKAIA with a “fitness function”; this function in turn was related to the sum of 

mean-squared error calculated by AutoBeale. PIKAIA seeks to 

maximize the fitness function, whereas for this work the intent 

was to minimize the sum of mean-squared error. Therefore, 

the fitness function was defined as 1 over the calculated sum 

of mean-squared error times a scaling factor. As the root 

mean-squared error decreased, the fitness function increased, 

providing a measure of the optimization progress to PIKAIA. 

PIKAIA finds optimum strata boundaries by performing 

the following steps:

1. Generate an initial “population” of solutions; each 

member of the population is defined by a “genome,” 

an integer value that can be converted to a series of 

real values between 0 and 1.

2. Generate strata boundaries. The real values (between 

0 and 1) correspond to the boundary location relative 

to the starting and ending Julian day.

3. Evaluate the fitness of each member of the population by running AutoBeale with the current set of 

strata boundaries.

4. Eliminate one or more of the members of the population with the lowest fitness scores.

5. Replace the eliminated population members with 

new, randomly generated members via reproduction 

between the population members with the highest 

fitness scores. Each parent’s genome is split, and two 

fragments are pasted together to form a new genome, 

which is inserted into the population. Random mutations in the genome are allowed to occur in a small 

fraction of new genomes.

6. Repeat steps 2 through 5 above for all members of 

the population over hundreds of generations.

At the end of the optimization process, a single individual 

with the best fitness score is selected, and the strata boundaries 

are evaluated and reported.

Various combinations of genetic algorithm parameters 

were tested with AutoBeale. The results reported here were 

obtained by running the combined PIKAIA/AutoBeale code 

with a population of 150, for a maximum of 700 generations. 

For the datasets described in this report, the mean square of 

residual error generally increased for strata numbers exceeding 

about 8; therefore, the combined PIKAIA/AutoBeale code was 

limited to examining stratification schemes with 15 or fewer 

strata in them.

The AutoBeale program provides an estimate of uncertainty (95-percent confidence interval) for load estimates on 

the basis of the sum of the mean-squared error over all strata; 

generally, the stronger the relation between flow and load 

within a given strata, the lower the mean-squared error and 

the associated confidence interval. However, this method for 

estimating the confidence interval is dependent on the specifics of the timing and number of samples collected. In order to 

include possible effects involving the structure of the sampling 

program, a jackknifing module was added to the AutoBeale 

program.

The jackknife “plug-in” estimate of the load is calculated 

as follows (Efron and Tibshirani, 1993):

ˆ ˆ

(.) ( ) q q = ∑

n =1 i i

n

(1) 1

where

q

ˆ

i

 is the load as calculated when the i

th

concentration data point has been 

excluded, and 

n is the number of concentration data points; ˆ

(.) q is effectively the mean of the loads calculated 

in this manner.

The estimate of standard error associated with the load 

estimate may be made as follows (Efron and Tibshirani, 1993):

se

n

n jack = i

− ∑( ) − 1 2

ˆ ˆ

( ) (.) q q (2)
60 Concentrations and Estimated Loads of Nutrients, Mercury, and PCBs in Selected Tributaries to Lake Michigan

An estimate of the confidence interval associated with the 

load estimate may be made by means of the t-distribution:

CI t se = ± n jack −

ˆ ( ) − θ α

1

1 (3)

where

α = 0.05 if one is interested in estimating a 

95-percent confidence interval.

As noted by Efron and Tibshirani (1993), the use of the 

t-distribution in the calculation of the confidence intervals 

does not take into account any skewness in the underlying 

population, nor does it account for any other errors that can 

occur when q is not the sample mean. 
Appendix 7 61

Appendix 7. Regression Model Details

This section contains details regarding linear regression model construction. In addition, this section provides a summary of 

key model diagnostics, including the effect size as defined in the text and the variance inflation factors. 

Polychlorinated Biphenyl

Grand River

Call:

lm(formula = log(PCB) ~ log(TSS) + log(q) + DecYear, data = subset(grand, 

 !is.na(grand$PCB)))

Residuals:

 Min 1Q Median 3Q Max 

-0.50320 -0.15189 -0.03107 0.12054 0.57086 

Coefficients:

 Estimate Std. Error t value Pr(>|t|) 

(Intercept) 56.971433 17.518006 3.252 0.00182 ** 

log(TSS) 0.431029 0.054493 7.910 4.22e-11 ***

log(q) -0.058696 0.050002 -1.174 0.24473 

DecYear -0.028593 0.008648 -3.306 0.00154 ** 

---

Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 

Residual standard error: 0.2405 on 65 degrees of freedom

Multiple R-squared: 0.5722, Adjusted R-squared: 0.5524 

F-statistic: 28.98 on 3 and 65 DF, p-value: 5.161e-12 

Effect size: -0.7175

Variance inflation factors:

log(TSS) log(q) DecYear 

1.102815 1.571789 1.489625

Kalamazoo River

> summary(lm.pcb.kzoo1)

Call:

lm(formula = log(PCB) ~ log(TSS) + log(q) + HOL.temp + DecYear, 

 data = subset(kzoo, !is.na(kzoo$PCB)))

Residuals:

 Min 1Q Median 3Q Max 

-1.20162 -0.09872 0.03502 0.18460 0.60616 

Coefficients:

 Estimate Std. Error t value Pr(>|t|) 

(Intercept) 141.696769 24.702523 5.736 5.61e-07 ***

log(TSS) 0.643513 0.123207 5.223 3.43e-06 ***

log(q) -0.379450 0.122258 -3.104 0.00314 ** 

HOL.temp 0.003206 0.004889 0.656 0.51499 

DecYear -0.069159 0.012163 -5.686 6.70e-07 ***

---

Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 
62 Concentrations and Estimated Loads of Nutrients, Mercury, and PCBs in Selected Tributaries to Lake Michigan

Residual standard error: 0.326 on 50 degrees of freedom

 (8 observations deleted due to missingness)

Multiple R-squared: 0.6833, Adjusted R-squared: 0.658 

F-statistic: 26.97 on 4 and 50 DF, p-value: 5.918e-12

Effect size: -0.9880

Variance inflation factors:

log(TSS) log(q) HOL.temp DecYear 

1.931384 1.436364 2.189684 1.445048

St. Joseph River

Call:

lm(formula = log(PCB) ~ log(TSS) + SH.temp + DecYear, data = stjo)

Residuals:

 Min 1Q Median 3Q Max 

-0.50319 -0.14526 -0.03719 0.10285 0.74913 

Coefficients:

 Estimate Std. Error t value Pr(>|t|) 

(Intercept) 53.085091 24.263972 2.188 0.034741 * 

log(TSS) 0.382731 0.101482 3.771 0.000539 ***

SH.temp 0.015037 0.003452 4.356 9.32e-05 ***

DecYear -0.027093 0.012085 -2.242 0.030733 * 

---

Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 

Residual standard error: 0.2552 on 39 degrees of freedom

 (68 observations deleted due to missingness)

Multiple R-squared: 0.6782, Adjusted R-squared: 0.6534 

F-statistic: 27.39 on 3 and 39 DF, p-value: 1.060e-09 

Effect size: -0.7339

Variance inflation factors:

log(TSS) SH.temp DecYear 

1.992054 1.268239 2.130678

Indiana Harbor and Ship Canal

Call:

lm(formula = log(PCB) ~ log(TSS) + IND.temp + Year.grp, data = gcal)

Residuals:

 Min 1Q Median 3Q Max 

-0.91258 -0.18013 -0.02856 0.24030 0.48657 

Coefficients:

 Estimate Std. Error t value Pr(>|t|) 

(Intercept) 2.703749 0.551187 4.905 9.83e-05 ***

log(TSS) 0.464582 0.172135 2.699 0.0142 * 

IND.temp 0.012624 0.005396 2.340 0.0304 * 

Year.grp2005-2006 -0.355586 0.162014 -2.195 0.0408 * 

---

Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 

Residual standard error: 0.3726 on 19 degrees of freedom

 (4360 observations deleted due to missingness)

Multiple R-squared: 0.4946, Adjusted R-squared: 0.4148 

F-statistic: 6.199 on 3 and 19 DF, p-value: 0.004065

Effect size: -1.3419
Appendix 7 63

Variance inflation factors:

log(TSS) IND.temp Year.grp 

1.269597 1.183216 1.084841

Fox River

Call:

lm(formula = log(PCB) ~ log(TSS) + log(q) + GB.temp + Year.grp, 

 data = subset(fox, !is.na(fox$PCB)))

Residuals:

 Min 1Q Median 3Q Max 

-1.06353 -0.19403 0.03782 0.16287 0.57711 

Coefficients:

 Estimate Std. Error t value Pr(>|t|) 

(Intercept) 1.401490 0.764056 1.834 0.0732 . 

log(TSS) 0.708804 0.086489 8.195 1.79e-10 ***

log(q) -0.164219 0.090333 -1.818 0.0757 . 

GB.temp 0.025747 0.004272 6.027 2.85e-07 ***

Year.grp2005-2006 0.090313 0.134641 0.671 0.5058 

---

Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 

Residual standard error: 0.3616 on 45 degrees of freedom

Multiple R-squared: 0.834, Adjusted R-squared: 0.8193 

F-statistic: 56.53 on 4 and 45 DF, p-value: < 2.2e-16

Effect size: 0.0991

Variance inflation factors:

log(TSS) log(q) GB.temp Year.grp 

1.449605 1.194269 1.448892 1.189630
64 Concentrations and Estimated Loads of Nutrients, Mercury, and PCBs in Selected Tributaries to Lake Michigan

Total Mercury

Grand River

Call:

lm(formula = log(TotHg) ~ log(q) + DecYear, data = subset(grand, 

 !is.na(grand$TotHg)))

Residuals:

 Min 1Q Median 3Q Max 

-1.12776 -0.41128 -0.03742 0.33670 1.51398 

Coefficients:

 Estimate Std. Error t value Pr(>|t|) 

(Intercept) 94.80774 30.60938 3.097 0.00249 ** 

log(q) 0.56478 0.07144 7.906 2.56e-12 ***

DecYear -0.04909 0.01525 -3.220 0.00170 ** 

---

Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 

Residual standard error: 0.5848 on 107 degrees of freedom

Multiple R-squared: 0.4389, Adjusted R-squared: 0.4284 

F-statistic: 41.85 on 2 and 107 DF, p-value: 3.752e-14 

Effect size: -0.6457

Kalamazoo River

Call:

lm(formula = log(TotHg) ~ log(q) + DecYear, data = subset(kzoo, 

 !is.na(kzoo$TotHg)))

Residuals:

 Min 1Q Median 3Q Max 

-1.56182 -0.28483 0.02265 0.37270 0.97855 

Coefficients:

 Estimate Std. Error t value Pr(>|t|) 

(Intercept) 174.62547 26.55765 6.575 1.88e-09 ***

log(q) -0.03166 0.08851 -0.358 0.721 

DecYear -0.08625 0.01328 -6.496 2.74e-09 ***

---

Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 

Residual standard error: 0.508 on 106 degrees of freedom

Multiple R-squared: 0.2859, Adjusted R-squared: 0.2725 

F-statistic: 21.22 on 2 and 106 DF, p-value: 1.771e-08

Effect size: -1.6313

St. Joseph River

Call:

lm(formula = log(TotHg) ~ log(q) + DecYear, data = subset(stjo, 

 !is.na(stjo$TotHg)))

Residuals:

 Min 1Q Median 3Q Max 

-1.26595 -0.21420 0.01999 0.33185 1.18307 
Appendix 7 65

Coefficients:

 Estimate Std. Error t value Pr(>|t|) 

(Intercept) 99.74935 25.40154 3.927 0.000186 ***

log(q) 0.65949 0.08772 7.518 8.57e-11 ***

DecYear -0.05194 0.01263 -4.111 9.76e-05 ***

---

Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 

Residual standard error: 0.4275 on 77 degrees of freedom

Multiple R-squared: 0.5294, Adjusted R-squared: 0.5172 

F-statistic: 43.31 on 2 and 77 DF, p-value: 2.493e-13

Effect size: -0.7431

Indiana Harbor and Ship Canal

Call:

lm(formula = log(TotHg) ~ IND.temp + Year.grp, data = subset(gcal, 

 !is.na(gcal$TotHg) & gcal$TotHg < 100))

Residuals:

 Min 1Q Median 3Q Max 

-0.47451 -0.24045 -0.05943 0.21005 0.68346 

Coefficients:

 Estimate Std. Error t value Pr(>|t|) 

(Intercept) 2.080294 0.242970 8.562 6.03e-08 ***

IND.temp 0.001972 0.003661 0.539 0.5964 

Year.grp2005-2006 -0.383636 0.143758 -2.669 0.0152 * 

---

Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 

Residual standard error: 0.3254 on 19 degrees of freedom

Multiple R-squared: 0.3128, Adjusted R-squared: 0.2404 

F-statistic: 4.324 on 2 and 19 DF, p-value: 0.02834 

Effect size: -0.1292

Fox River

Call:

lm(formula = TotHg ~ GB.temp + TSS + Year.grp, data = subset(fox, 

 !is.na(fox$TotHg)))

Residuals:

 Min 1Q Median 3Q Max 

-28.347 -5.193 -2.192 7.110 66.338 

Coefficients:

 Estimate Std. Error t value Pr(>|t|) 

(Intercept) 45.8626 18.6825 2.455 0.0289 *

GB.temp -0.5499 0.5263 -1.045 0.3152 

TSS 0.9601 0.3768 2.548 0.0243 *

Year.grp2005-2006 -26.8974 14.8596 -1.810 0.0934 .

---

Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 

Residual standard error: 23.17 on 13 degrees of freedom

 (20 observations deleted due to missingness)

Multiple R-squared: 0.4448, Adjusted R-squared: 0.3166 

F-statistic: 3.471 on 3 and 13 DF, p-value: 0.0477 

Effect size: -0.0472

Variance inflation factors:

 GB.temp TSS Year.grp 

2.441819 1.930609 1.451307
66 Concentrations and Estimated Loads of Nutrients, Mercury, and PCBs in Selected Tributaries to Lake Michigan

Total Phosphorus

Grand River

Call:

lm(formula = log(TotalP) ~ HOL.temp + log(TSS) + log(q) + DecYear, 

 data = subset(grand, !is.na(grand$TotalP)))

Residuals:

 Min 1Q Median 3Q Max 

-1.350098 -0.127960 -0.008224 0.151922 0.441226 

Coefficients:

 Estimate Std. Error t value Pr(>|t|) 

(Intercept) -48.513426 12.848660 -3.776 0.000287 ***

HOL.temp 0.006136 0.002681 2.289 0.024443 * 

log(TSS) 0.330498 0.053483 6.179 1.89e-08 ***

log(q) 0.142910 0.048843 2.926 0.004358 ** 

DecYear 0.021817 0.006347 3.437 0.000896 ***

---

Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 

Residual standard error: 0.2383 on 89 degrees of freedom

 (31 observations deleted due to missingness)

Multiple R-squared: 0.6084, Adjusted R-squared: 0.5908 

F-statistic: 34.57 on 4 and 89 DF, p-value: < 2.2e-16 

Effect size: 0.5192

Variance inflation factors:

HOL.temp log(TSS) log(q) DecYear 

1.951206 1.950271 2.484232 1.287642

Kalamazoo River

Call:

lm(formula = log(TotalP) ~ HOL.temp + log(TSS) + log(q) + DecYear, 

 data = subset(kzoo, !is.na(kzoo$TotalP)))

Residuals:

 Min 1Q Median 3Q Max 

-1.80432 -0.07277 0.02870 0.11478 1.42776 

Coefficients:

 Estimate Std. Error t value Pr(>|t|) 

(Intercept) -8.699384 21.393590 -0.407 0.68538 

HOL.temp 0.011896 0.004559 2.609 0.01085 * 

log(TSS) 0.317870 0.103033 3.085 0.00280 **

log(q) 0.222487 0.087473 2.543 0.01293 * 

DecYear 0.001434 0.010605 0.135 0.89277 

---

Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 

Residual standard error: 0.3699 on 79 degrees of freedom

 (32 observations deleted due to missingness)

Multiple R-squared: 0.4059, Adjusted R-squared: 0.3758 

F-statistic: 13.49 on 4 and 79 DF, p-value: 1.994e-08 

Effect size: 0.0220
Appendix 7 67

St. Joseph River

Call:

lm(formula = log(TotalP) ~ log(TSS) + DecYear, data = subset(stjo, 

 !is.na(stjo$TotalP)))

Residuals:

 Min 1Q Median 3Q Max 

-1.411168 -0.126776 0.002127 0.147847 0.732862 

Coefficients:

 Estimate Std. Error t value Pr(>|t|) 

(Intercept) -48.001292 18.605503 -2.580 0.0118 * 

log(TSS) 0.657543 0.063727 10.318 3.1e-16 ***

DecYear 0.021731 0.009268 2.345 0.0216 * 

---

Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 

Residual standard error: 0.3098 on 78 degrees of freedom

 (2 observations deleted due to missingness)

Multiple R-squared: 0.5844, Adjusted R-squared: 0.5738 

F-statistic: 54.84 on 2 and 78 DF, p-value: 1.342e-15

Effect size: 0.3068

Indiana Harbor and Ship Canal

Call:

lm(formula = log(TotalP) ~ IND.temp + log(TSS) + Year.grp, data = subset(gcal, 

 !is.na(gcal$TotalP)))

Residuals:

 Min 1Q Median 3Q Max 

-0.328861 -0.135679 -0.000894 0.137678 0.443854 

Coefficients:

 Estimate Std. Error t value Pr(>|t|) 

(Intercept) -4.302637 0.304345 -14.137 1.55e-11 ***

IND.temp 0.003864 0.002979 1.297 0.21 

log(TSS) 0.669149 0.095047 7.040 1.06e-06 ***

Year.grp2005-2006 0.506433 0.089458 5.661 1.86e-05 ***

---

Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 

Residual standard error: 0.2058 on 19 degrees of freedom

 (1 observation deleted due to missingness)

Multiple R-squared: 0.7787, Adjusted R-squared: 0.7437 

F-statistic: 22.28 on 3 and 19 DF, p-value: 1.937e-06

Effect size: 1.1434

Variance inflation factors:

IND.temp log(TSS) Year.grp 

1.183216 1.269597 1.084841
68 Concentrations and Estimated Loads of Nutrients, Mercury, and PCBs in Selected Tributaries to Lake Michigan

Fox River

Call:

lm(formula = log(TotalP) ~ GB.temp + log(TSS) + log(q) + Year.grp, 

 data = subset(fox, !is.na(fox$TotalP)))

Residuals:

 Min 1Q Median 3Q Max 

-0.40417 -0.17394 -0.06649 0.21142 0.66529 

Coefficients:

 Estimate Std. Error t value Pr(>|t|) 

(Intercept) -2.767350 0.541413 -5.111 6.04e-06 ***

GB.temp 0.005428 0.002997 1.811 0.0766 . 

log(TSS) 0.425447 0.061451 6.923 1.19e-08 ***

log(q) -0.120899 0.063969 -1.890 0.0651 . 

Year.grp2005-2006 0.164916 0.094324 1.748 0.0871 . 

---

Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 

Residual standard error: 0.2577 on 46 degrees of freedom

Multiple R-squared: 0.6928, Adjusted R-squared: 0.6661 

F-statistic: 25.93 on 4 and 46 DF, p-value: 2.752e-11

Effect size: 0.2287

Variance inflation factors:

GB.temp log(TSS) log(q) Year.grp 

1.485857 1.465013 1.212904 1.228945
Appendix 7 69

Orthophosphate

Grand River

Call:

lm(formula = log(OrthoP) ~ log(q) + DecYear, data = subset(grand, 

 !is.na(grand$OrthoP)))

Residuals:

 Min 1Q Median 3Q Max 

-2.7430 -0.4777 0.1231 0.5411 1.4745 

Coefficients:

 Estimate Std. Error t value Pr(>|t|) 

(Intercept) -220.26282 40.99755 -5.373 4.01e-07 ***

log(q) 0.85790 0.10264 8.359 1.51e-13 ***

DecYear 0.10440 0.02034 5.132 1.15e-06 ***

---

Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 

Residual standard error: 0.8417 on 117 degrees of freedom

Multiple R-squared: 0.3913, Adjusted R-squared: 0.3809 

F-statistic: 37.6 on 2 and 117 DF, p-value: 2.450e-13 

Effect size: 1.1842

Kalamazoo River

Call:

lm(formula = log(OrthoP) ~ log(TSS) + log(q) + DecYear, data = subset(kzoo, 

 !is.na(kzoo$OrthoP)))

Residuals:

 Min 1Q Median 3Q Max 

-2.34316 -0.44964 0.01780 0.49665 2.51359 

Coefficients:

 Estimate Std. Error t value Pr(>|t|) 

(Intercept) -115.57693 41.57398 -2.780 0.00644 ** 

log(TSS) -0.20931 0.15012 -1.394 0.16617 

log(q) 1.02449 0.14792 6.926 3.58e-10 ***

DecYear 0.05188 0.02059 2.519 0.01327 * 

---

Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 

Residual standard error: 0.8103 on 105 degrees of freedom

 (4 observations deleted due to missingness)

Multiple R-squared: 0.3659, Adjusted R-squared: 0.3478 

F-statistic: 20.2 on 3 and 105 DF, p-value: 2.077e-10 

Effect size: 0.3469

St. Joseph River

Call:

lm(formula = log(OrthoP) ~ SH.temp + log(TSS) + DecYear, data = subset(stjo, 

 !is.na(stjo$OrthoP)))

Residuals:

 Min 1Q Median 3Q Max 

-1.7354 -0.7384 0.0088 0.8290 1.8913 
70 Concentrations and Estimated Loads of Nutrients, Mercury, and PCBs in Selected Tributaries to Lake Michigan

Coefficients:

 Estimate Std. Error t value Pr(>|t|) 

(Intercept) -212.22643 77.27659 -2.746 0.00801 **

SH.temp -0.02965 0.01151 -2.575 0.01259 * 

log(TSS) 0.54461 0.28296 1.925 0.05918 . 

DecYear 0.10382 0.03856 2.693 0.00925 **

---

Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 

Residual standard error: 1.01 on 58 degrees of freedom

 (17 observations deleted due to missingness)

Multiple R-squared: 0.1415, Adjusted R-squared: 0.09709 

F-statistic: 3.187 on 3 and 58 DF, p-value: 0.03032

Effect size: 0.4306

Variance inflation factors:

SH.temp log(TSS) DecYear 

1.295028 1.554839 1.701087

Indiana Harbor and Ship Canal

Call:

lm(formula = log(OrthoP) ~ IND.temp + Year.grp, data = subset(gcal, 

 !is.na(gcal$OrthoP)))

Residuals:

 Min 1Q Median 3Q Max 

-1.8891 -0.1421 0.1549 0.3318 0.5100 

Coefficients:

 Estimate Std. Error t value Pr(>|t|) 

(Intercept) -5.629023 0.435783 -12.917 3.66e-11 ***

IND.temp 0.022143 0.007879 2.811 0.0108 * 

Year.grp2005-2006 1.334024 0.232717 5.732 1.31e-05 ***

---

Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 

Residual standard error: 0.5566 on 20 degrees of freedom

Multiple R-squared: 0.6613, Adjusted R-squared: 0.6274 

F-statistic: 19.52 on 2 and 20 DF, p-value: 1.988e-05 

Effect size: 2.4825

Fox River

Call:

lm(formula = log(OrthoP) ~ log(TSS) + Year.grp, data = subset(fox, 

 !is.na(fox$OrthoP)))

Residuals:

 Min 1Q Median 3Q Max 

-3.2016 -0.3380 0.1714 0.5307 1.2197 

Coefficients:

 Estimate Std. Error t value Pr(>|t|) 

(Intercept) -4.4848 0.6293 -7.126 1.09e-08 ***

log(TSS) 0.2179 0.1786 1.220 0.2295 

Year.grp2005-2006 0.5846 0.2858 2.045 0.0473 * 

---

Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 

Residual standard error: 0.8443 on 41 degrees of freedom

Multiple R-squared: 0.1225, Adjusted R-squared: 0.07971 

F-statistic: 2.862 on 2 and 41 DF, p-value: 0.06862 

Effect size: 0.6580
Appendix 7 71

Nitrate Plus Nitrite

Grand River

Call:

lm(formula = log(NO2NO3) ~ log(TSS) + log(q) + DecYear, data = subset(grand, 

 !is.na(grand$NO2NO3)))

Residuals:

 Min 1Q Median 3Q Max 

-1.16247 -0.17300 -0.02276 0.26517 1.29805 

Coefficients:

 Estimate Std. Error t value Pr(>|t|) 

(Intercept) -1.851e+02 1.953e+01 -9.478 3.23e-16 ***

log(TSS) -2.538e-01 6.311e-02 -4.021 0.000102 ***

log(q) 6.084e-01 5.321e-02 11.434 < 2e-16 ***

DecYear 9.058e-02 9.693e-03 9.344 6.69e-16 ***

---

Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 

Residual standard error: 0.4075 on 119 degrees of freedom

 (2 observations deleted due to missingness)

Multiple R-squared: 0.5788, Adjusted R-squared: 0.5682 

F-statistic: 54.51 on 3 and 119 DF, p-value: < 2.2e-16

Effect size: 2.1598

Kalamazoo River

Call:

lm(formula = log(NO2NO3) ~ HOL.temp + log(q) + DecYear, data = subset(kzoo, 

 !is.na(kzoo$NO2NO3)))

Residuals:

 Min 1Q Median 3Q Max 

-3.94300 -0.10999 0.06285 0.19600 0.84750 

Coefficients:

 Estimate Std. Error t value Pr(>|t|) 

(Intercept) -71.064803 26.078788 -2.725 0.007840 ** 

HOL.temp -0.015304 0.004408 -3.472 0.000824 ***

log(q) 0.526249 0.117934 4.462 2.53e-05 ***

DecYear 0.033911 0.012932 2.622 0.010389 * 

---

Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 

Residual standard error: 0.5062 on 83 degrees of freedom

 (29 observations deleted due to missingness)

Multiple R-squared: 0.3669, Adjusted R-squared: 0.344 

F-statistic: 16.03 on 3 and 83 DF, p-value: 2.619e-08

Effect size: 0.6316
72 Concentrations and Estimated Loads of Nutrients, Mercury, and PCBs in Selected Tributaries to Lake Michigan

St. Joseph River

Call:

lm(formula = log(NO2NO3) ~ SH.temp + log(TSS) + log(q) + DecYear, 

 data = subset(stjo, !is.na(stjo$NO2NO3)))

Residuals:

 Min 1Q Median 3Q Max 

-0.38526 -0.11747 -0.02865 0.09390 0.56377 

Coefficients:

 Estimate Std. Error t value Pr(>|t|) 

(Intercept) 0.944938 14.671585 0.064 0.9489 

SH.temp -0.006757 0.002882 -2.344 0.0223 * 

log(TSS) -0.139186 0.066595 -2.090 0.0408 * 

log(q) 0.346676 0.067326 5.149 2.96e-06 ***

DecYear -0.001301 0.007367 -0.177 0.8604 

---

Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 

Residual standard error: 0.1984 on 61 degrees of freedom

 (17 observations deleted due to missingness)

Multiple R-squared: 0.5878, Adjusted R-squared: 0.5608 

F-statistic: 21.75 on 4 and 61 DF, p-value: 3.449e-11 

Effect size: -0.0372

Indiana Harbor and Ship Canal

Call:

lm(formula = log(NO2NO3) ~ IND.temp + log(TSS) + log(q) + Year.grp, 

 data = subset(gcal, !is.na(gcal$NO2NO3)))

Residuals:

 Min 1Q Median 3Q Max 

-0.20888 -0.07794 -0.01245 0.07376 

Coefficients:

 Estimate Std. Error t value Pr(>|t|) 

(Intercept) 4.224621 1.275096 3.313 0.00387 ** 

IND.temp -0.004733 0.001758 -2.693 0.01488 * 

log(TSS) 0.039837 0.058680 0.679 0.50585 

log(q) -0.557705 0.200030 -2.788 0.01214 * 

Year.grp2005-2006 0.696422 0.061384 11.345 1.24e-09 ***

---

Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 

Residual standard error: 0.1202 on 18 degrees of freedom

 (1 observation deleted due to missingness)

Multiple R-squared: 0.9355, Adjusted R-squared: 0.9211 

F-statistic: 65.22 on 4 and 18 DF, p-value: 1.832e-10

Effect size: 1.5269

Variance inflation factors:

IND.temp log(TSS) log(q) Year.grp 

1.206304 1.417746 1.757600 1.496444
Appendix 7 73

Fox River

Call:

lm(formula = log(NO2NO3) ~ GB.temp + log(q) + Year.grp, data = subset(fox, 

 !is.na(fox$NO2NO3)))

Residuals:

 Min 1Q Median 3Q Max 

-3.1040559 -0.5426493 0.0008888 0.6582535 2.3119109 

Coefficients:

 Estimate Std. Error t value Pr(>|t|) 

(Intercept) -5.51127 2.40506 -2.292 0.02667 * 

GB.temp -0.04972 0.01057 -4.705 2.44e-05 ***

log(q) 0.79640 0.27647 2.881 0.00606 ** 

Year.grp2005-2006 0.23567 0.39179 0.602 0.55051 

---

Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 

Residual standard error: 1.048 on 45 degrees of freedom

Multiple R-squared: 0.4135, Adjusted R-squared: 0.3744 

F-statistic: 10.57 on 3 and 45 DF, p-value: 2.203e-05 

Effect size: 0.0919 
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S.M. Westenbroek—Concentrations and Estimated Loads of Nutrients, Mercury, and PCBs in Tributaries to Lake Michigan—Scientific Investigations Report 2010–5029