Prepared in cooperation with the Michigan Department of Environmental Quality

Estimation of a Trophic State Index for Selected Inland Lakes 

in Michigan, 1999–2013

Michigan

Scientific Investigations Report 2016–5023

U.S. Department of the Interior

U.S. Geological Survey

Estimation of a Trophic State Index for 

Selected Inland Lakes in Michigan, 

1999–2013

By Lori M. Fuller and Richard S. Jodoin

Prepared in cooperation with the Michigan 

Department of Environmental Quality

Scientific Investigations Report 2016–5023

U.S. Department of the Interior

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

SALLY JEWELL, Secretary

U.S. Geological Survey

Suzette M. Kimball, Director

U.S. Geological Survey, Reston, Virginia: 2016

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U.S. Government.

Although this information product, for the most part, is in the public domain, it also may contain copyrighted materials 

as noted in the text. Permission to reproduce copyrighted items must be secured from the copyright owner.

Suggested citation:

Fuller, L.M., and Jodoin, R.S., 2016, Estimation of a Trophic State Index for selected inland lakes in Michigan, 

1999–2013: U.S. Geological Survey Scientific Investigations Report 2016–5023, 16 p., http://dx.doi.org/10.3133/

sir20165023.

ISSN 2328-0328 (online)
iii

Acknowledgments

The Michigan Department of Environmental Quality and the volunteers of the Cooperative Lake 

Monitoring Program were invaluable in providing much of the field data used in this project. The 

Wisconsin Department of Natural Resources Surface Water Integrated Monitoring System Database was key to additional field data for the western half of the Upper Peninsula of Michigan. 

Leif Olmanson of the Remote Sensing and Geospatial Analysis Laboratory, Department of Forest 

Resources, University of Minnesota provided the GetHist program for use in analyzing Michigan 

inland lakes.

U.S. Geological Survey field technicians provided measurements for the Upper Peninsula of 

Michigan to supplement the measurements from volunteers of the Cooperative Lake Monitoring 

Program. The following U.S. Geological Survey, Michigan Water Science Center employees were 

involved in the collection of data for this study: D. Burdett, J.M. Ellis, S.B. Horton, J. Knudsen, C. 

Taricska, D.G. Wydra, and J.A. Wilkinson.

v

Contents

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

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

Purpose and Scope ..............................................................................................................................2

Methods...........................................................................................................................................................2

Results .............................................................................................................................................................4

Summary........................................................................................................................................................15

References Cited..........................................................................................................................................15

Figures

1. Map showing landsat satellite scenes covering Michigan ..................................................3

2. Graphs showing landsat estimated Trophic State Index (eTSI) vs field-measured 

TSI, Michigan inland lakes, 1999–2013......................................................................................8

3. Graphs showing distribution of lakes by trophic class for the 1999–2013 

datasets .......................................................................................................................................10

4. Map showing Environmental Protection Agency Level III Ecoregions for 

Michigan ......................................................................................................................................11

5. Graphs showing estimated Trophic State Index (eTSI ) by TSI class and 

Environmental Protection Agency Level III Ecoregions for the 1999–2013 

datasets........................................................................................................................................12

6. Graph showing comparison of program results based on Secchi-disk 

transparency to determine Trophic State Indexes (TSIs) for 2007.....................................14
vi

Tables

1. Lake Trophic State Index (TSI) and classification ranges using Trophic State Index 

values, Secchi-disk transparency (SDT), chlorophyll-a, and total phosphorus for 

Michigan inland lakes, 2003–05 and 2007–08...........................................................................2

2. Landsat 5–8 bands used in regression equations with corresponding 

wavelengths ..................................................................................................................................4

3. Landsat-image and calibration-model data for estimated Trophic State Index 

(eTSI), Michigan inland lakes, 1999–2013.................................................................................5

4. Results for datasets of measured Secchi-disk transparency values compared to 

estimated Secchi-disk transparency within 2, 5, and 10 feet; Trophic State Index 

values within 2, 5, and 10 units; and estimated to measured Trophic State Index 

class for Michigan inland lakes .................................................................................................7

5. Statistical summary of statewide estimated Trophic State Index (eTSI) and 

estimated Secchi-disk transparency (eSDT) for Michigan inland lakes by dataset.........9

6. Analysis of variance for estimated Trophic State Index (eTSI) and Secchi-disk 

transparency (SDT) for Michigan inland lakes from 7 datasets from 1999–2013...............9

7. Tukey’s test for estimated Trophic State Index (eTSI) and Secchi-disk 

transparency (SDT) for Michigan inland lakes from 7 datasets from 1999–2013.............10

8. Mean estimated Trophic State Index (eTSI) and Secchi-disk transparency (SDT) 

by U.S. Environmental Protection Agency Level III Ecoregions for Michigan inland 

lakes by dataset..........................................................................................................................11
vii

Conversion Factors

International System of Units to Inch/Pound

Multiply By To obtain

Length

meter (m) 3.281 foot (ft)

Area

square meter (m2) 0.0002471 acre

hectare (ha) 2.471 acre

Concentration

micrograms per liter (μg/L) 0.001 milligrams per liter (mg/L)

Vertical coordinate information is referenced to the North American Datum of 1983 (NAD 83).

Concentrations of chemical constituents in water are given either in milligrams per liter (mg/L) 

or micrograms per liter (μg/L). 

Abbreviations

ANOVA Analysis of Variance

CLMP Cooperative Lakes Monitoring Program

MDEQ Michigan Department of Environmental Quality

NLA National Lakes Assessment

R2 coefficient of determination

SDT Secchi-disk transparency

eSDT estimated Secchi-disk transparency

TSI Trophic State Index

eTSI estimated Trophic State Index

EPA Environmental Protection Agency

USGS U.S. Geological Survey

Estimation of a Trophic State Index for Selected Inland 

Lakes in Michigan, 1999–2013

By Lori M. Fuller and Richard S. Jodoin

Abstract

A 15-year estimated Trophic State Index (eTSI) for 

Michigan inland lakes is available, and it spans seven datasets, 

each representing 1 to 3 years of data from 1999 to 2013. On 

average, 3,000 inland lake eTSI values are represented in each 

of the datasets by a process that relates field-measured Secchidisk transparency (SDT) to Landsat satellite imagery to provide eTSI values for unsampled inland lakes. The correlation 

between eTSI values and field-measured Trophic State Index 

(TSI) values from SDT was strong as shown by R2 values 

from 0.71 to 0.83. Mean eTSI values ranged from 42.7 to 46.8 

units, which when converted to estimated SDT (eSDT) ranged 

from 8.9 to 12.5 feet for the datasets. Most eTSI values for 

Michigan inland lakes are in the mesotrophic TSI class. The 

Environmental Protection Agency (EPA) Level III Ecoregions 

were used to illustrate and compare the spatial distribution of 

eTSI classes for Michigan inland lakes. Lakes in the Northern Lakes and Forests, North Central Hardwood Forests, and 

Southern Michigan/Northern Indiana Drift Plains ecoregions 

are predominantly in the mesotrophic TSI class. The Huron/

Erie Lake Plains and Eastern Corn Belt Plains ecoregions, 

had predominantly eutrophic class lakes and also the highest 

percent of hypereutrophic lakes than other ecoregions in the 

State. Data from multiple sampling programs—including data 

collected by volunteers with the Cooperative Lakes Monitoring Program (CLMP) through the Michigan Department of 

Environmental Quality (MDEQ), and the 2007 National Lakes 

Assessment (NLA)—were compiled to compare the distribution of lake TSI classes between each program. The seven 

eTSI datasets are available for viewing and download with 

eSDT from the Michigan Lake Water Clarity Interactive Map 

Viewer at http://mi.water.usgs.gov/projects/RemoteSensing/

index.html.

Introduction

The State of Michigan has over 11,000 inland lakes that 

are valuable ecological, aesthetic, and recreational resources. 

Approximately 4,000 of these lakes are larger than 20 acres 

in size, and about 1,300 of those lakes have public access to 

boat launches or beaches. Recreational, property, and ecological values are closely related to the quality of water in these 

inland lakes (Krysel and others, 2003). In 2014, tourism in 

Michigan accounted for $22.8 billion in economic activity, 

much of which was related to recreational activities at Michigan’s lakes (Wichtner-Zoia and Nicholls, 2015). Thus, inland 

lakes are an important economic and ecological resource to 

Michigan.

The water-quality characteristics of inland lakes are 

critical factors in determining a lakes’ recreational use and 

diversity of habitat and species. The U.S. Geological Survey 

(USGS) and the Michigan Department of Environmental 

Quality (MDEQ) monitor many of Michigan’s lakes, but 

it is not economically feasible to monitor the quality of all 

11,000 inland lakes by use of conventional sampling techniques. Knowledge of the biological productivity of unsampled inland lakes is needed to assist resource managers in their 

efforts to collect data for inland lakes, helping to protect and 

manage the quality of all of Michigan’s inland lakes.

Landsat satellite imagery has been used successfully in 

Minnesota (Olmanson and others, 2001; Kloiber and others, 2002), Wisconsin (Chipman and others, 2004; Peckham 

and Lillesand, 2006), Michigan (Fuller and others, 2011) and 

elsewhere (Baban, 1993; Dekker and Peters, 1993; Mayo and 

others, 1995; Giardino and others, 2001) to estimate a Trophic State Index (eTSI) from Secchi disk transparency (SDT) 

measurements for inland lakes. Carlson (1977) proposed to 
2 Estimation of a Trophic State Index for Selected Inland Lakes in Michigan, 1999–2013

quantify the trophic state of a waterbody by its Trophic State 

Index (TSI) value, which can be classified into four basic 

classes: oligotrophic, mesotrophic, eutrophic, and hypereutrophic. Carlson’s TSI model was developed for use with lakes 

that have few rooted aquatic plants and little nonalgal turbidity 

(Environmental Protection Agency, 2007). The progression of 

a lake from oligotrophic to eutrophic can be computed from 

measures of total phosphorus (TP), SDT, and chlorophyll a

(Chl-a). Table 1 shows the range of TSI values and how each 

measure is classified into oligotrophic, mesotrophic, eutrophic, 

and hypereutrophic.

The formulas for calculating TSI values from TP, SDT 

and Chl-a are.

TSI = 14.41 ln TP (micrograms per liter, (μg/L)) + 4.15 (1)

TSI = 60 – 14.41 ln (SDT feet * 0.3048) (2)

TSI = 9.81 ln Chl-a (μg/L) + 30.6 (3)

Previous studies to produce eTSI values from fieldmeasurements of SDT in Michigan include Fuller and others 

(2004, 2011). To date, there are 15 years of eTSI values for 

Michigan’s inland lakes larger than 20 acres, within 7 datasets 

grouped as either single or multiple years—due to cloud cover 

preventing full statewide coverage for a single year—including 1999–2000, 2002, 2003–05, 2007–08, 2009–10, 2011, and 

2013. Landsat satellite imagery with 30-meter cells is cost 

effective and available throughout the late summer season, 

allowing for eTSI values for lakes larger than 20 acres. eTSI 

values for Michigan inland lakes provide additional information for lake managers by extending existing sampling 

programs. These datasets are available online for viewing and 

download from the (http://mi.water.usgs.gov/projects/RemoteSensing/index.html).

Table 1. Lake Trophic State Index (TSI) and classification ranges using Trophic State Index values, Secchi-disk transparency (SDT), 

chlorophyll-a, and total phosphorus for Michigan inland lakes, 2003–05 and 2007–08.

[TSI, Trophic Status Index; SDT, Secchi-disk transparency; ft, feet; Chy-a; chlorophyll-a; μg/L, micrograms per liter; TP, total phosphorus; <, less than; >, 

greater than; data from Warbach (1990) and modified by the State of Michigan to account for regional characteristics]

Lake trophic condition TSI value SDT 

(ft)

Chy-a

(μg/l)

 TP 

(μg/L)

Oligotrophic < 38 > 15 < 2.2 < 10

Mesotrophic 38–48 7.5–15 2.2–6 10–20

Eutrophic 49–61 3–7.4 6.1–22 20.1–50

Hypereutrophic > 61 < 3 > 22 > 50

Warbach, J.D., 1990, Protecting inland lakes: a watershed management guidebook, Lansing, MI, Planning & Zoning Center, Inc.,

Purpose and Scope

The purpose of this report is to provide an overview of 

the process used to provide eTSI values for unsampled inland 

lakes in Michigan by correlation of Landsat satellite imagery 

to SDT measurements obtained in the field. Information about 

the eTSI datasets is summarized, and those available for viewing and downloading are described. Technical details on the 

process to produce the eTSI values can be found in the previous reports by Fuller and others (2004, 2011).

Methods

The process to produce eTSI values for inland lakes is 

described in Fuller and others (2011) and summarized here. 

First, Landsat satellite imagery with minimal cloud cover is 

selected from late-summer (July–September) and processed to 

mask out nonwater areas and isolate inland lakes larger than 

20 acres by use of inland lake polygons (Breck, 2004). Second, field-measurements of SDT corresponding to the Landsat 

satellite imagery are obtained. Third, field-measurements of 

SDT, within plus or minus 10 days of the Landsat satellite 

imagery acquisition date, are correlated to the satellite imagery 

to produce a regression model specific to each date of Landsat 

satellite imagery. The end results are eTSI values for openwater areas of inland lakes larger than 20 acres within the 

Landsat satellite imagery.

Six paths of Landsat satellite data cover the State of 

Michigan; each path (except for path 23) is separated into 

multiple scenes that are referenced by path and row numbers 

(fig. 1). Each path of Landsat satellite data is acquired on the 

same date; thus multiple scenes from the same path can be 

grouped if all scenes are free of cloud cover and haze. The 

Landsat satellite scenes for each path were selected from 

1 day over a 3-month period (July through September) with 

the least amount of cloud cover and haze (preferably less than 
Methods 3

Row 27

Row 28

Row 29

Row 30

Row 31

Path 25 Path 24 Path 23 Path 22 Path 21 Path 20

EXPLANATION

0 50 100 MILES

0 50 100 KILOMETERS

Landsat satellite scenes

County boundary

Landsat row or path line

Michigan

Figure 1. Landsat satellite scenes covering Michigan.
4 Estimation of a Trophic State Index for Selected Inland Lakes in Michigan, 1999–2013

10 percent cloud cover). These months have been shown to 

produce the most accurate predictive models because the lakes 

are at their maximum biological productivity (Kloiber and 

others, 2002). The satellite imagery was processed to remove 

areas affected by clouds, cloud shadows, haze, shoreline, and 

dense vegetation (Fuller and others, 2011). For some years, 

enough satellite imagery was available with minimal cloud 

coverage to provide eTSI values for a single year, such as 

2002. Other years were combined, such as 1999–2000, when 

cloud cover prevented eTSI values for a single year.

SDT measurements are obtained using a Secchi disk, 

which is an 8-inch-diameter circular disk, painted black and 

white in alternating quadrants to measure water clarity. The 

Secchi disk is lowered into the lake, usually from a boat, 

and the depth at which the disk becomes no longer visible is 

known as the SDT. Field-measured SDT were obtained from 

the MDEQ Cooperative Lakes Monitoring Program (CLMP), 

which is a volunteer network monitoring approximately 

250 lakes weekly during the months of April to October 

(http://www.mcgi.state.mi.us/miswims/). Other sources of data 

included the USGS and the Wisconsin Department of Natural Resources Surface Water Integrated Monitoring System 

Database; those data sources were used to supplement information in the western Upper Peninsula of Michigan where 

CLMP measurements were sparse (http://dnr.wi.gov/topic/

surfacewater/swims/). Starting in 2002, the USGS, in cooperation with the MDEQ, provided a newsletter to the CLMP 

volunteers to educate them on the remote sensing initiative. 

The newsletter provided satellite overpass dates for each year, 

allowing CLMP volunteers to plan, when possible, to take 

their SDT measurements within plus or minus 3 days of the 

satellite imagery acquisition date. The 6-day window would 

allow for more useable measurements surrounding the satellite 

imagery date, although up to 10 days were found acceptable 

from Olmanson (2002). Since the newsletter was initiated in 

2002, there was an increase in the number of SDT measurements more closely surrounding the satellite acquisition dates.

Field-measurements of SDT were correlated to the Landsat satellite imagery by using the GetHist program, which uses 

a portion of the open-water areas remaining after satellite data 

processing (as documented in Olmanson and others, 2001) 

to obtain mean reflectance values for each inland lake. The 

output values from the GetHist program were used to produce 

regression equations specific to each path of satellite data. In 

table 2, the bands with corresponding wavelengths are noted. 

The regression equation used to produce eTSI values for 

Landsat 5 and 7 was (Kloiber and others, 2002):

ln(SDT) = a(band1/band3) + b(band1) + c (4)

The regression equation used to produce eTSI values for 

Landsat 8, due to a different collection interval of bands, was

ln(SDT) = a(band2/band4) + b(band2) + c (5)

Table 2. Landsat 5–8 bands used in regression equations with 

corresponding wavelengths.

[μm, micrometers, ]

Landsat satellite Band 1 Band 2 Band 3 Band 4

Landsat 5 Thematic Mapper0.45–0.52 

μm

0.52–0.60 

μm

0.63–0.69 

μm

0.76–0.90 

μm

Landsat 7 

Enhanced Thematic Mapper 

plus

0.45–0.52 

μm

0.52–0.60 

μm

0.63–0.69 

μm

0.77–0.90 

μm

Landsat 8 Operational Land 

Imager 

0.43–0.45 

μm

0.45–0.51 

μm

0.53–0.59 

μm

0.64–0.67 

μm

Shaded bands used in regression equations

In both equations, the variables a, b, and c were derived 

coefficients from the regression equation.

The regression equation was then applied to the processed Landsat imagery for all unsampled lakes larger than 

20 acres in the Landsat path for that date. Not all lakes had an 

eTSI value for every dataset, depending if field-measured SDT 

were available (path 23 in the Upper Peninsula had sparse coverage in some years), or if cloud cover, cloud shadows, or haze 

prevented an estimation.

The resulting eTSI and eSDT values for each path were 

combined for each dataset using highest to lowest R2 values. 

An analysis of variance test (ANOVA) was used to determine 

if there was a statistically significant difference at the 95-percent confidence interval between the eTSI and eSDT means 

of the datasets. ANOVA determines if there was a difference 

between the means of the datasets, but not which datasets were 

different from each other. The ANOVA test was chosen due to 

the large number of lakes (approximately 3,000 per dataset), 

and because the TSI values reflect a normal distribution. To 

determine which datasets were statistically significant from 

each other, Tukey’s honest significant difference (HSD) test 

was used (Coolidge, 2000).

Results

Seven datasets of eTSI values are available for Michigan 

inland lakes, spanning a 15-year period from 1999 to 2013. A 

total of 45 Landsat paths of satellite data were processed, and 

5–8 paths with unique dates merged together to create eTSI 

values for each dataset. A summary of the image dates, with 

information on the field-measurements of SDT used and the 

regression equation information specific to each image date, is 

provided in table 3. The equations used to produce eTSI values 

are unique to each image date of Landsat data. The R2 value 
Results 

5

Table 3. Landsat-image and calibration-model data for estimated Trophic State Index (eTSI), Michigan inland lakes, 1999–2013.—Continued[SDT, Secchi-disk transparency; m, meter; ft, feet, R2, coefficient of determination; SEE, Standard Error of Estimate; TM, Thematic Mapper; x, eTSI; B, Landsat satellite band number]

Image 

date Path Rows

Number 

of images 

used in 

path

Satellite Days prior Days past Number of mea- surements SDT range (m) SDT range (ft) R2 SEE Equation:

1999–2000 Estimated TSI

7/17/2000 20 30–31 2 Landsat TM 5 4 6 22 1.7–6.4 5.5–21.0 0.75 0.098 x = B1/B3(2.4709) + B1(-0.0111) + -3.06077/30/1999 21 28–31 4 Landsat TM 5 7 7 54 0.9–10.0 3.0–33.0 0.69 0.2344 x = B1/B3(1.0250) + B1(-0.0040) + -2.61278/24/2000 22 28–31 4 Landsat TM 5 7 7 46 0.8–8.5 2.5–28.0 0.78 0.231 x = B1/B3(1.0489) + B1(-0.0314) + -1.16728/22/2000 24 27–28 2 Landsat TM 5 7 7 41 0.9–8.0 3.0–26.0 0.82 0.229 x = B1/B3(3.5069) + B1(0.1356) + -19.91728/29/2000 25 28 1 Landsat TM 5 7 7 90 0.6–6.9 2.0–22.5 0.81 0.239 x = B1/B3(1.6309) + B1(0.0468) + -7.6868

2002 Estimated TSI

9/1/2002 20 30–31 2 Landsat TM 5 7 5 27 1.8–5.0 6.0–16.5 0.71 0.146 x = B1/B3(0.7484) + B1(-0.0264) + -0.32079/8/2002 21 28–31 4 Landsat TM 5 6 7 75 0.8–8.0 2.5–26.5 0.80 0.189 x = B1/B3(1.6781) + B1(0.0301) + -6.76727/13/2002 22 28–31 4 Landsat TM 5 6 7 59 0.9–8.2 3.0–27.0 0.80 0.202 x = B1/B3(1.2221) + B1(0.0236) + -4.89958/30/2002 22 29–31 4 Landsat TM 5 4 6 57 0.9–9.9 3.0–32.5 0.82 0.203 x = B1/B3(1.5958) + B1(0.0535) + -7.85187/11/2002 24 27–28 2 Landsat TM 5 7 7 69 1.1–2.0 3.5–25.0 0.85 0.173 x = B1/B3(1.5083) + B1(0.0492) + -7.73919/4/2002 25 28 1 Landsat TM 5 7 7 83 0.9–7.3 3.0–24.0 0.86 0.184 x = B1/B3(1.4881) + B1(-0.0335) + -3.5791

2003–05 Estimated TSI

9/22/2004 20 30–31 2 Landsat TM 5 6 4 22 1.5–7.3 5.0–24.0 0.73 0.238 x = B1/B3(1.6413) + B1(-0.0196) + -4.86129/13/2004 21 28–31 4 Landsat TM 5 8 6 75 0.8–8.5 2.5–28 0.69 0.243 x = B1/B3(1.3398) + B1(0.0104) + -4.48219/20/2004 22 28–31 4 Landsat TM 5 7 6 50 0.9–5.9 3.0–19.0 0.72 0.192 x = B1/B3(0.8592) + B1(-0.0380) + -1.06629/21/2005 24 27 1 Landsat TM 5 0 5 10 2.0–5.3 6.5–17.5 0.73 0.194 x = B1/B3(1.1798) + B1(0.1401) + -10.05807/19/2005 24 28 1 Landsat TM 5 0 6 15 2.1–6.7 7.0–22.0 0.73 0.214 x = B1/B3(0.7688) + B1(0.1562) + -9.6935 8/22/2003 25 28 1 Landsat TM 5 10 6 12 6.0–20.5 1.8–6.3 0.65 0.256 x = B1/B3(1.1529) + B1(0.0945) + -7.8513

2007–08 Estimated TSI

8/30/2007 20 30–31 2 Landsat TM 5 6 3 18 1.8–4.9 6.0–16.0 0.72 0.159 x = B1/B3(2.1944) + B1(0.0401) + -9.64379/22/2007 21 28–31 3 Landsat TM 5 7 0 72 0.8–7.0 2.5–23.0 0.75 0.183 x = B1/B3(1.3083) + B1(-0.0631) + -1.29376/25/2007 22 28 1 Landsat TM 5 0 3 15 2.4–6.4 8.0–21.0 0.74 0.161 x = B1/B3(1.0580) + B1(0.0103) + -3.33949/13/2007 22 29–31 3 Landsat TM 5 5 7 56 2.5–23.0 0.8–7.0 0.67 0.223 x = B1/B3(0.9800) + B1(-0.0046) + -2.52538/3/2007 23 28 1 Landsat TM 5 0 5 15 2.9–6.1 9.5–20.0 0.67 0.130 x = B1/B3(0.3153) + B1(0.1069) + -5.28947/27/2008 24 27–28 2 Landsat TM 5 0 4 18 2.1–5.6 6.8–18.3 0.68 0.166 x = B1/B3(0.4080) + B1(0.0512) + -3.38108/3/2008 25 28 1 Landsat TM 5 0 3 14 1.7–7.3 5.5–24.0 0.73 0.256 x = B1/B3(1.6371) + B1(-0.0239) + -3.3531
6 Estimation of a Trophic State Index for Selected Inland Lakes in Michigan, 1999–2013 Table 3. Landsat-image and calibration-model data for estimated Trophic State Index (eTSI), Michigan inland lakes, 1999–2013.—Continued [SDT, Secchi-disk transparency; m, meter; ft, feet, R2, coefficient of determination; SEE, Standard Error of Estimate; TM, Thematic Mapper; x, eTSI; B, Landsat satellite band number] Image date Path Rows Number of images used in path Satellite Days prior Days past Number of mea- surements SDT range (m) SDT range (ft)

R2 SEE Equation:

2009–10 Estimated TSI

9/4/2009 20 30–31 2 Landsat TM 5 5 4 12 0.8–6.4 2.5–21 0.76 0.304 x = B1/B3(2.5645) + B1(0.0870) + -13.1486 7/9/2009 21 28 1 Landsat TM 5 0 5 14 1.4–6.1 4.5–20 0.78 0.233 x = B1/B3(1.8087) + B1(-0.0106) + -5.89779/11/2009 21 29–31 3 Landsat TM 5 3 3 52 0.8–7 2.5–23 0.76 0.208 x = B1/B3(1.6664) + B1(0.0667) + -8.7592 9/2/2009 22 28 1 Landsat TM 5 8 2 21 1.5–5.3 5.0–17.5 0.73 0.210 x = B1/B3(2.1777) + B1(-0.1237) + -1.48339/2/2009 22 29–31 3 Landsat TM 5 3 4 69 0.8–8.2 2.5–27 0.78 0.211 x = B1/B3(1.0289) + B1(-0.0662) + 0.4062 8/31/2009 24 27–28 2 Landsat TM 5 7 7 88 0.8–10 2.8–33 0.73 0.297 x = B1/B3(1.8777) + B1(-0.0198) + -5.1770 7/8/2010 25 28 1 Landsat TM 5 3 8 36 1.2–7.3 4.0–24 0.81 0.191 x = B1/B3(1.5708) + B1(0.0421) + -6.9965 

2011 Estimated TSI

7/8/2011 20 30–31 2 Landsat TM 5 6 7 32 0.6–5.8 2.0–19.0 0.80 0.228 x = B1/B3(1.5391) + B1(0.0022) + -4.48717/15/2011 21 28 1 Landsat TM 5 0 4 12 1.4–4.3 4.5–14.0 0.70 0.210 x = B1/B3(1.1372) + B1(0.0948) + -8.63988/16/2011 21 29–31 3 Landsat TM 5 5 6 98 0.6–10.7 2.0–35.0 0.83 0.201 x = B1/B3(1.6740) + B1(-0.0161) + -4.66318/23/2011 22 28 1 Landsat TM 5 0 3 12 1.5–5.6 5.0–18.5 0.76 0.229 x = B1/B3(1.9254) + B1(0.0160) + -6.98187/6/2011 22 29–31 3 Landsat TM 5 4 7 41 1.7–7.2 5.5–23.5 0.70 0.160 x = B1/B3(0.5054) + B1(-0.0145) + 0.51878/14/2011 23 28 1 Landsat TM 5 2 3 12 2.6–5.2 8.5–17.0 0.69 0.125 x = B1/B3(-1.3926) + B1(0.0261) + 5.65558/6/2011 24 27–28 2 Landsat TM 5 7 7 47 1.5–5.5 4.8–18.0 0.80 0.124 x = B1/B3(0.9107) + B1(-0.0661) + 0.82367/11/2011 25 28 1 Landsat TM 5 7 6 113 0.9–8.2 3.0–27.0 0.81 0.213 x = B1/B3(1.4013) + B1(0.0571) + -7.1141 

2013 Estimated TSI

7/13/2013 20 30–31 2 Landsat 8 6 8 18 2.1–5.5 7.0–18.0 0.71 0.157 x = B2/B4(11.4066) + B2(-0.0005) + -9.63047/20/2013 21 28–29 2 Landsat 8 6 4 16 2.4–8.2 8.0–27.0 0.74 0.214 x = B2/B4(18.4695) + B2(-0.0002) + -21.68178/21/2013 21 29–31 3 Landsat 8 6 10 30 1.2–5.0 4.0–16.5 0.71 0.216 x = B2/B4(13.5427) + B2(-0.0005) + -12.14577/11/2013 22 28–31 4 Landsat 8 4 10 28 1.2–7.6 4.0–25.0 0.77 0.187 x = B2/B4(10.4659) + B2(-0.0004) + -8.75289/11/2013 24 27–28 2 Landsat 8 7 7 47 0.9–7.1 3.0–23.5 0.7414 0.224 x = B2/B4(17.0272) + B2(-0.0005) + -17.02269/26/2013 25 28 1 Landsat 7 7 8 37 1.2–5.9 4.0–19.5 0.81 0.201 x = B1/B3(3.0070) + B1(-0.0197) + -4.5451
Results 7

for each image date of eTSI ranged from 0.65 to 0.86, with a 

mean of 0.75, and an average standard of error of 0.20. These 

relationships between Landsat satellite-derived eTSI values 

and field-measured SDT converted to TSI values were strong, 

as shown in figure 2. The R2 values ranged from 0.71 to 0.83.

eSDT and eTSI for Michigan inland lakes were compared to the field-measured SDT and TSI from SDT (table 4). 

The eSDT dataset values ranged from 67 to 70 percent within 

2 SDT feet, 94 to 98 percent within 5 SDT feet, and all except 

Table 4. Results for datasets of measured Secchi-disk transparency values compared to estimated Secchi-disk transparency 

within 2, 5, and 10 feet; Trophic State Index values within 2, 5, and 10 units; and estimated to measured Trophic State Index class for 

Michigan inland lakes.

[SDT, Secchi-disk transparency; TSI, Trophic State Index]

Dateset

Percentage 

within 2 SDT 

feet

Percentage 

within 5 SDT 

feet

Percentage 

within 10 SDT 

feet

Percentage 

within 2 TSI 

units

Percentage 

within 5 TSI 

units

Percentage 

within 10 TSI 

units

Percentage 

within correct 

TSI class 

1999–2000 68 94 100 49 84 100 77

2002 76 98 100 60 98 100 80

2003–05 68 96 100 48 95 100 78

2007–08 75 97 100 75 98 100 86

2009–10 67 94 99 51 91 100 79

2011 76 98 100 61 98 100 80

2013 70 96 100 52 93 100 74

one eSDT dataset had 100 percent within 10 SDT feet. For the 

eTSI, 48 to75 percent were within 2 TSI units, 84 to 98 percent within 5 TSI units, and all eTSI datasets were 100 percent 

within 10 TSI units. For all of the datasets, 74 to 86 percent of 

eTSI values were estimated to the correct TSI class.

On average, about 3,000 eTSI values are available for 

each of the 7 datasets. Summary statistics for eTSI units and 

eSDT (in feet) are shown in table 5. Mean eTSI ranged from 

42.7 to 46.8 units and the mean eSDT ranged from 8.9 to 

12.5 feet. When comparing the 1999–2000 and 2013 datasets, 

the eSDT mean increased from 8.9 to 12.5 feet and the median 

from 8.8 to 11.6 feet,, and the eTSI mean decreased from 

46.8 to 42.7 TSI values and the median from 45.8 to 41.8 TSI 

values. If the 1999–2000 and 2013 datasets are removed, the 

eTSI and eSDT mean and median values remain relatively 

consistent among the middle year datasets (table 5). When 

comparing datasets, it is important to note that not all lakes 

have adequate representation in each dataset due to cloud 

cover, cloud shadow, haze, and dense vegetation. Additional 

factors affecting lakes not represented in each dataset could 

be due to the date and climate for that dataset, along with the 

Landsat platform used. Without eTSI and eSDT for missing 

lakes, it is difficult to determine how their inclusion might 

change the statistics.

To determine if there was a statistically significant difference at the 95-percent confidence interval, the ANOVA test 

was used to determine the significance between both the eTSI 

and the eSDT values for each dataset. The ANOVA F distribution for eTSI was 115.7, and for the eSDT was 171.1, both of 

which were larger than the F critical value of 2.1, which indicates that there was a statistical difference among the datasets 

(table 6). To determine which datasets were statistically 

significant, a Tukey’s test value of 0.36 was used. Tukey’s 

test values were greater for the eTSI between the 1999–2000 

and 2013 datasets, and most of the 2011 dataset; values were 

greater for the eSDT between the 1999–2000, 2011 and 2013 

datasets (table 7). In summary, eTSI values decreased, and 

eSDT values increased with time.

Most of Michigan’s inland lakes are in the mesotrophic 

TSI class. Figure 3 shows the distribution of lakes by trophic 

class for each of the 1999–2013 datasets.

Five EPA level III ecoregions are in Michigan (fig. 4), 

and they differ by vegetation, soils, geology, climate, hydrology, and land use (Environmental Protection Agency, 2011). 

These ecoregions were used to determine and compare the 

spatial distribution of eTSI values for Michigan’s inland lakes 

(fig. 4). The North Central Hardwood Forests ecoregion generally has more oligotrophic and mesotrophic, and fewer eutrophic classified lakes, and the mean eTSI values are generally 

lower and eSDT values are generally higher than in the other 

ecoregions of the State (table 8). The Northern Lakes and Forest ecoregion has the highest number of lakes with eTSI values 

in four out of the seven datasets (fig. 5), and is comparable 
8 Estimation of a Trophic State Index for Selected Inland Lakes in Michigan, 1999–2013

R2 = 0.7818

20

30

40

50

60

70

R2 = 0.8335

20

30

40

50

60

70

R2 = 0.7104

20

30

40

50

60

70

R2 = 0.746

20

30

40

50

60

70

R2 = 0.7073

20

30

40

50

60

70

R2 = 0.8119

20

30

40

50

60

70

20 30 40 50 60 70

R2 = 0.7608

20

30

40

50

60

70

20 30 40 50 60 70

1999–2000 2002

2003–05 2007–08

2009–10 2011

2013

Estimated Trophic State Index

Field-measured Trophic State Index from Secchi-disk transparency

Field-measured Trophic State Index from Secchi-disk transparency

Figure 2. Landsat estimated Trophic State Index (eTSI) vs field-measured TSI, Michigan inland lakes, 1999–2013.
Results 9

Table 5. Statistical summary of statewide estimated Trophic State Index (eTSI) and estimated Secchi-disk transparency (eSDT) for 

Michigan inland lakes by dataset.

Statewide estimated Trophic State Index (eSTI) 

1999–2000 2002 2003–05 2007–08 2009–10 2011 2013

count 3,265 3,278 2,955 2,876 2,465 3,071 3,171

minimum 20.4 10.7 19.5 28.9 25.6 5.2 18.2

25th percentile 42.7 41.2 40.7 41.1 40.4 40.1 37.9

median 45.8 44.4 44.2 44.1 44.1 43.7 41.8

mean 46.8 45.3 45.3 44.9 45.1 44.7 42.7

75th percentile 50.6 48.8 48.9 47.3 48.1 47.4 45.9

maximum 82.6 80.3 79.2 83.2 84.1 87.8 99.3

standard deviation 6.2 6.6 6.9 6.3 6.9 7.3 8.3

Statewide estimated Secchi-disk transparency (eSDT) (in feet)

1999–2000 2002 2003–05 2007–08 2009–10 2011 2013

count 3,265 3,278 2,955 2,876 2,465 3,071 3,171

minimum 0.7 0.8 0.9 0.7 0.6 0.5 0.2

25th percentile 6.3 7.2 7.1 7.9 7.5 7.9 8.7

median 8.8 9.7 9.9 9.9 9.9 10.2 11.6

mean 8.9 10.1 10.1 10.1 10.1 10.6 12.5

75th percentile 10.9 12.1 12.5 12.2 12.8 13.0 15.2

maximum 51.3 100.2 54.5 28.4 35.8 146.8 59.7

standard deviation 3.8 5.0 4.4 3.7 4.0 5.3 6.1

Table 6. Analysis of variance for estimated Trophic State Index (eTSI) and Secchi-disk transparency (SDT) for Michigan inland lakes 

from 7 datasets from 1999–2013.

ANOVA - estimated Trophic State Index (eTSI)

Source of variation Sum of square Degrees of 

freedom Mean squares F distribution P-value F critical value

Between Groups 32,599 6 5,433 116 0.0 2.1

Within Groups 988,524 21,055 47

Total 1,021,123 21,061

ANOVA - Secchi-disk transparency (SDT)

Source of variation Sum of square Degrees of 

freedom Mean squares F distribution P-value F critical value

Between Groups 22,809 6 3,802 171 0.0 2.1

Within Groups 467,796 21,055 22

Total 490,605 21,061
10 Estimation of a Trophic State Index for Selected Inland Lakes in Michigan, 1999–2013

Table 7. Tukey’s test for estimated Trophic State Index (eTSI) and Secchi-disk transparency (SDT) for Michigan inland lakes from 

7 datasets from 1999–2013.

Tukey’s - Difference of means for estimated Trophic State Index (eTSI)

1999–2000 2002 2003–05 2007–08 2009–10 2011 2013

1999–2000 0

2002 * 1.53 0

2003–05 * 1.53 0.00 0

2007–08 * 1.93 * 0.40 * 0.39 0

2009–10 * 1.66 0.13 0.13 0.27 0

2011 * 2.07 * 0.54 * 0.53 0.14 * 0.41 0

2013 * 4.40 * 2.87 * 2.87 * 2.48 * 2.74 * 2.34 0

Tukey’s - Difference of means for Secchi-disk transparency (SDT)

1999–2000 2002 2003–05 2007–08 2009–10 2011 2013

1999–2000 0

2002 * 1.13 0

2003–05 * 1.15 0.02 0

2007–08 * 1.20 0.07 0.05 0

2009–10 * 1.19 0.05 0.04 0.01 0

2011 * 1.63 * 0.50 * 0.48 * 0.43 * 0.44 0

2013 * 3.63 * 2.49 * 2.48 * 2.43 * 2.44 * 2.00 0

*

Tukey’s HSD test values greater than 0.36 are statistically significant at the 95-percent confidence interval.

0

10

20

30

40

50

60

70

80

1999−2000 2002 2003−05 2007−08 2009−10 2011 2013

(3,265) (3,278) (2,955) (2,876) (2,465) (3,071) (3,171)

Percentage of lakes with an estimated

Trophic State Index value by Trophic class

Dataset years

Trophic class

Oligotrophic

Mesotrophic

Eutrophic

Hypereutrophic

Number of lakes in dataset

EXPLANATION

(3,265)

1999−2000 2002 2003−05 2007−08 2009−10 2011 2013

Number of lakes with an estimated

Trophic State Index value by Trophic class

(3,265) (3,278) (2,955) (2,876) (2,465) (3,071) (3,171)

2,500

0

500

1,000

1,500

2,000

Dataset years

Figure 3. Distribution of lakes by trophic class for the 1999–2013 datasets.
Results 11

0 50 100 MILES

0 50 100 KILOMETERS

U.S. Environmental Protection Agency Level III 

Ecoregions (U.S. Environmental Protection Agency, 2011)

EXPLANATION

50 Northern Lakes and Forests

51 North Central Hardwood Forests

55 Eastern Corn Belt Plains

56 Southern Michigan/Northern Indiana Drift Plains

57 Huron/Erie Lake Plains

Michigan

Figure 4. Environmental Protection Agency Level III Ecoregions for Michigan.

Table 8. Mean estimated Trophic State Index (eTSI) and Secchi-disk transparency (SDT) by U.S. Environmental Protection Agency 

Level III Ecoregions for Michigan inland lakes by dataset.

Mean estimated Trophic State Index (eTSI) value

Level III Ecoregion 1999–2000 2002 2003–05 2007–08 2009–10 2011 2013

Northern Lakes and Forests 46.4 45.2 44.4 43.7 45.6 44.0 43.3

North Central Hardwood Forests 43.8 40.5 45.6 44.9 43.0 41.2 38.1

Eastern Corn Belt Plains 55.2 54.6 57.7 59.5 47.2 62.5 47.5

Southern Michigan/Northern Indiana Drift Plains 47.2 45.6 45.8 45.7 44.7 45.6 41.5

Huron/Erie Lake Plains 50.8 51.1 54.9 60.3 56.1 53.1 48.0

Mean estimated Secchi-disk transparency (eSDT) (in feet)

Level III Ecoregion 1999–2000 2002 2003–05 2007–08 2009–10 2011 2013

Northern Lakes and Forests 9.4 10.3 10.9 10.9 10.0 11.2 12.2

North Central Hardwood Forests 11.5 15.9 9.7 9.8 11.6 14.0 17.1

Eastern Corn Belt Plains 5.2 5.2 4.7 5.0 9.8 4.1 9.8

Southern Michigan/Northern Indiana Drift Plains 8.4 9.5 9.5 9.5 10.1 9.7 12.7

Huron/Erie Lake Plains 7.3 7.6 6.5 4.3 5.0 7.8 9.7
12 Estimation of a Trophic State Index for Selected Inland Lakes in Michigan, 1999–2013

Northern Lakes and Forests

North Central Hardwood Forests

Eastern Corn Belt Plains

1999−2000 2002 2003−05 2007−08 2009−10 2011 2013

(1,413) (1,600) (1,318) (1,321) (1,247) (1,488) (1,609) (1,413) (1,600) (1,318) (1,321) (1,247) (1,488) (1,609)

(126) (122) (116) (109) (122) (124) (93) (126) (122) (116) (109) (122) (124) (93)

(7) (15) (12) (10) (6) (12) (9) (7) (15) (12) (10) (6) (12) (9)

Number of lakes with an estimated

Trophic State Index value by Trophic class

Percentage of lakes with an estimated

Trophic State Index value by Trophic class

0

200

400

600

800

1,000

1,200

0

10

20

30

40

50

60

70

80

0

10

20

30

40

50

60

70

80

90

0

10

20

30

40

50

60

70

80

0

2

4

6

8

10

12

14

0

10

20

30

40

50

60

70

80

1999−2000 2002 2003−05 2007−08 2009−10 2011 2013

1999−2000 2002 2003−05 2007−08 2009−10 2011 2013

Number of lakes with an estimated

Trophic State Index value by Trophic class

Percentage of lakes with an estimated

Trophic State Index value by Trophic class

1999−2000 2002 2003−05 2007−08 2009−10 2011 2013

1999−2000 2002 2003−05 2007−08 2009−10 2011 2013

Number of lakes with an estimated

Trophic State Index value by Trophic class

Dataset years

Percentage of lakes with an estimated

Trophic State Index value by Trophic class

1999−2000 2002 2003−05 2007−08 2009−10 2011 2013

Dataset years

100

Trophic class

Oligotrophic

Mesotrophic

Eutrophic

Hypereutrophic

Number of lakes in dataset

EXPLANATION

(1,234)

Figure 5. Estimated Trophic State Index (eTSI ) by TSI class and Environmental Protection Agency Level III Ecoregions for the 

1999–2013 datasets.
Results 13

Southern Michigan/Northern Indiana Drift Plains

Huron/Erie Lake Plains

1999−2000 2002 2003−05 2007−08 2009−10 2011 2013

Number of lakes with an estimated

Trophic State Index value by Trophic class

Percentage of lakes with an estimated

Trophic State Index value by Trophic class

0

200

400

600

800

1,000

1,200

0

10

20

30

40

50

60

70

80

0

5

10

15

20

0

10

20

30

40

50

60

70

80

1999−2000 2002 2003−05 2007−08 2009−10 2011 2013

1999−2000 2002 2003−05 2007−08 2009−10 2011 2013

Number of lakes with an estimated

Trophic State Index value by Trophic class

Dataset years

Percentage of lakes with an estimated

Trophic State Index value by Trophic class

1999−2000 2002 2003−05 2007−08 2009−10 2011 2013

Dataset years

25

(1,679) (1,490) (1,072) (1,522) (1,421) (1,431) (1,430) (1,679) (1,490) (1,522) (1,421) (1,072) (1,431) (1,430)

(40) (19) (19) (15) (18) (16) (30) (40) (19) (19) (15) (18) (16) (30)

Trophic class

Oligotrophic

Mesotrophic

Eutrophic

Hypereutrophic

Number of lakes in dataset

EXPLANATION

(1,234)

1999–2013 datasets.—Continued

Figure 5. Estimated Trophic State Index (eTSI ) by TSI class and Environmental Protection Agency Level III Ecoregions for the 

in TSI class distribution to the North Central Hardwood 

Forests ecoregion. The Southern Michigan/Northern Indiana 

Drift Plains ecoregion had the largest number of lakes with 

eTSI values in three out of the seven datasets, though had the 

highest number of lakes with eTSI values when all datasets 

were combined. It also had comparable representation to the 

Northern Lakes and Forest ecoregion, though there are fewer 

oligotrophic and more eutrophic lakes. The smallest ecoregions, located in the southern Lower Peninsula of Michigan, 

had mostly eutrophic lakes and more hypereutrophic lakes 

than the other ecoregions.

Although most eTSI datasets vary somewhat in the 

distribution of lakes in the TSI classes, it is noticeable that 

the 2013 dataset has the highest mean eSDT and lowest mean 

eTSI values among the ecoregions (table 8). Although this 

dataset has one of the highest numbers of lakes, and possibly 

more oligotrophic lakes were included in the output, 2013 is 

the only year Landsat 8 satellite imagery was used. Factors 

that could contribute to the shift for an increase in eSDT and 

a decrease in eTSI values include the TSI class, types of cloud 

and haze free lakes in the dataset, the date of the imagery, 

climate conditions for that year, and the different Landsat 8 

satellite data used.

Comparison of the programs that provide TSI for 

Michigan inland lakes shows interesting results. Volunteers 

with the CLMP measure approximately 250 inland lakes each 
14 Estimation of a Trophic State Index for Selected Inland Lakes in Michigan, 1999–2013

year. These measurements, plus supplemental measurements, 

are used to produce eTSI by use of remotely sensed Landsat 

satellite imagery. The National Lakes Assessment (NLA) randomly selected—based on chemical, physical, and biological 

data—and measured lakes nationwide during 2007 to provide 

a statistically valid, probability-designed estimate of the condition of lakes on a national and regional scale (Environmental 

Protection Agency, 2009). When the TSI determined from the 

SDT was compared for the CLMP from 2007 to the eTSI for 

the 2007–08 dataset, similar percentages for trophic-status 

categories emerged; on average, however, the CLMP percentage of lakes for the oligotrophic class was slightly higher, and 

for the hypereutrophic class was slightly lower (fig. 6). This 

may be due to more volunteers living on or having access to 

clearer lakes than those with access to impaired lakes. The 

percentages for NLA TSI from SDT, when comparing the 

National 2007 data and the Michigan-specific 2007 TSI from 

SDT, showed a difference for the mesotrophic, eutrophic, and 

hypereutrophic classes. The percentage for the mesotrophic 

class is much lower than the other datasets and higher for the 

eutrophic and hypereutrophic classes. Also, data in the NLA 

set were not available, mainly because an SDT value was not 

recorded if the Secchi-disk hit lake bottom, and this could 

contribute to the difference between classes.

(3,265)

16 62 21

1

0 20 40 60 80 100

CLMP

2007 (207)

Percentage of lakes by Trophic class

eTSI 

2007-08 (3,024) 7 74 17

2

NLA 2007

National (1,091)

NLA 2007 for

Michigan (50)

6 24 30

7 35 32

31

12

9

14

Michigan Cooperative Lakes Monitoring Program (CLMP) Trophic State Index

Michigan Estimated Trophic State Index (eTSI)

National Lakes Assessment (NLA) 2007 Trophic State Index

National Lakes Assessment (NLA) 2007 Trophic State Index for Michigan lakes

EXPLANATION

Oligotrophic

Mesotrophic

Eutrophic

Hypereutrophic

No data (Secchi-disk hit lake 

bottom, or data not collected)

Number of lakes in dataset

Figure 6. Comparison of program results based on Secchi-disk transparency to determine Trophic State Indexes (TSIs) for 2007.
References Cited 15

Summary

Long-term data are required to effectively manage the 

more than 11,000 Michigan inland lakes, 4,000 of which are 

larger than 20 acres. Lake sampling programs provide data to 

determine lake condition; that information can be extended 

by use of Landsat satellite data to produce estimated Trophic 

State Index (eTSI) for lakes larger than 20 acres. Seven datasets of eTSI from 1999 to 2013 are available for an average of 

about 3,000 lakes of that size and clear of cloud interference, 

cloud shadows, haze, and dense vegetation. These datasets 

provide long-term regional and spatial eTSI to monitor lakes.

The method used to produce eTSI for inland lakes 

involves choosing Landsat satellite imagery with minimal 

cloud cover from the late-summer period and then process that 

imagery to mask out nonwater areas for the inland lakes larger 

than 20 acres in size. Field measurements of Secchi-disk transparency (SDT) corresponding to the Landsat satellite imagery obtained within 10 days of the Landsat satellite imagery 

acquisition date are then correlated to the satellite imagery to 

produce a regression equation specific to each date of Landsat 

satellite imagery. The result is an eTSI for open-water areas of 

inland lakes larger than 20 acres.

Each of the seven datasets from 1999 to 2013 showed 

strong relationships between Landsat satellite derived eTSI 

and field-measured Trophic State Index (TSI) by use of SDT 

measurements with R2 values that ranged from 0.65 to 0.86. 

Mean eTSI ranged from 42.7 to 46.8 units, and mean estimated Secchi-disk transparency (eSDT) ranged from 8.9 to 

12.5 feet. eTSI units decreased and eSDT increased when the 

1999–2000 estimated mean and median values were compared to the 2013 values. However, if the 1999–2000 and 

2013 datasets are removed, the mean and median values are 

relatively consistent between the 2002, 2003–05, 2007–08, 

2009–10, and 2011 datasets. An ANOVA test determined that 

there was a statistically significant difference at the 95-percent confidence interval among the datasets, and Tukey’s test 

results showed a significant difference at the 95-percent confidence interval between the 1999–2000, 2013, and between 

most datasets and the 2011 dataset for eTSI, and between the 

1999–2000, 2011 and 2013 datasets for eSDT. In summary, 

eTSI values decreased, and eSDT increased.

Many factors could affect the eTSI among datasets, such 

as the lakes included or not available for estimated values in 

a dataset, the date and climate for a particular dataset, or a 

difference among Landsat satellite platforms. Not all lakes 

have representation in each dataset due to cloud cover, cloud 

shadow, haze, and dense vegetation preventing an estimated 

value, and without the estimated values for missing lakes, it 

is difficult to determine how their inclusion might change the 

statistics.

The Environmental Protection Agency (EPA) Level III 

Ecoregions in Michigan were used to determine and compare 

the spatial distribution of eTSI for inland lakes. The Northern 

Lakes and Forests and North Central Hardwood Forests ecoregion lakes were predominantly in the mesotrophic TSI class. 

The Southern Michigan/Northern Indiana Drift Plains ecoregion also had predominantly mesotrophic class lakes, but had 

a higher percentage of eutrophic lakes and fewer oligotrophic 

lakes than the Northern Lakes and Forests and North Central 

Hardwood Forests ecoregions. The Huron/Erie Lake Plains 

and Eastern Corn Belt Plains ecoregions, were the smallest 

ecoregions and had the fewest number of lakes having eTSI 

values; those regions had lakes that were predominantly in the 

eutrophic class, and had the highest percentage of hypereutrophic lakes relative to the other ecoregions.

Two sampling programs—the Cooperative Lakes Monitoring Program (CLMP) and the National Lakes Assessment 

(NLA)—were compared to the eTSI dataset for comparable 

years. The CLMP data collected by volunteers through the 

Michigan Department of Environmental Quality (MDEQ) 

for 2007 are similar to the NLA data, though the percent of 

oligotrophic lakes was greater in the CLMP data, which could 

result from more volunteers living and having access on the 

oligotrophic lakes. The NLA data specifically from Michigan 

for 2007 show a difference for the mesotrophic, eutrophic, 

and hypereutrophic classes. The percentage of lakes in the 

mesotrophic class is much lower than in the other datasets and 

higher for the eutrophic and hypereutrophic classes. These 

sampling programs can provide different pictures for Michigan inland lakes.

A long-term regional and spatial picture for lake managers can be created using different monitoring programs for 

Michigan inland lakes. Although in-situ data are a valuable 

resource, it is not physically and economically feasible to 

measure all 11,000 Michigan inland lakes. Extending measurements from existing lake monitoring programs has helped to 

provide additional lake eTSI values. The 15 years with seven 

datasets are available for viewing and download at (http://

mi.water.usgs.gov/projects/RemoteSensing/index.html).

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Publishing support provided by the 

U.S. Geological Survey Science Publishing Network,

Madison Publishing Service Center 

West Trenton Publishing Service Center

For more information concerning the research in this report, contact:

Director, Michigan Water Science Center

U.S. Geological Survey

6520 Mercantile Way, Suite 5

Lansing, MI 48911-5991

http://mi.water.usgs.gov/
Fuller and Jodoin— Estimation of a Trophic State Index for Selected Inland Lakes in Michigan, 1999–2013—Scientific Investigations Report 2016–5023

ISSN 2328-0328 (online)

http://dx.doi.org/10.3133/sir20165023