U.S. Department of the Interior

U.S. Geological Survey

Scientific Investigations Report 2011–5007

In cooperation with the Michigan Department of Natural Resources and Environment

Predicting Lake Trophic State by Relating Secchi-Disk 

Transparency Measurements to Landsat-Satellite Imagery for 

Michigan Inland Lakes, 2003–05 and 2007–08

Orchard Lake

Sylvan Lake

Elizabeth Lake

Otter Lake

Upper Straits Lake

Lower Long Lake

Island Lake

Upper Long Lake

Crescent Lake

Square Lake

Crystal

Lake

Forest Lake

Green Lake

Hammond

Lake

Turtle Lake

Wabeek

Lake

42

38

47

38

37

44

38

47

49

45

43

49

33

46

44

45 Orchard Lake

37

36

Cass Lake

Pine Lake

Orchard Lake

Sylvan Lake

Elizabeth Lake

Otter Lake

Upper Straits Lake

Lower Long Lake

Island Lake

Upper Long Lake

Crescent Lake

Square Lake

Crystal

Lake

Forest Lake

Green Lake

Hammond

Lake

Turtle Lake

Wabeek

Lake

39

34

42

36

33

38

35

41

51

39

39

49

39

46

37

49 Orchard Lake

35

39

Cass Lake

Pine Lake

Cass Lake

Orchard Lake

Pine Lake

Sylvan Lake

Elizabeth Lake

Otter Lake

Upper Straits Lake

Lower Long Lake

Island Lake

Upper Long Lake

Crescent Lake

Square Lake

Crystal

Lake

Forest Lake

Green Lake

Hammond

Lake

Turtle Lake

Wabeek

Lake

Predicting Lake Trophic State by Relating 

Secchi-Disk Transparency Measurements 

to Landsat-Satellite Imagery for Michigan 

Inland Lakes, 2003–05 and 2007–08 

By L.M. Fuller, R.S. Jodoin, and R.J. Minnerick

In cooperation with the Michigan Department of Natural Resources 

and Environment

Scientific Investigations Report 2011–5007

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: 2011

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reproduce any copyrighted materials contained within this report.

Suggested citation:

Fuller, L.M., Jodoin, R.S., and Minnerick, R.J., 2011, Predicting lake trophic state by relating Secchi-disk transparency 

measurements to Landsat-satellite imagery for Michigan inland lakes, 2003–05 and 2007–08: U.S. Geological Survey 

Scientific Investigations Report 2011–5007, 36 p.
iii

Acknowledgments

Mr. Ralph Bednarz of the Michigan Department of Natural Resources and Environment 

and the volunteers of the Cooperative Lake Monitoring Program (CLMP) were invaluable in 

providing much of the field data used in the project. 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 (USGS) field technicians provided measurements for the Upper 

Peninsula of Michigan to supplement the measurements from volunteers of the CLMP. The 

following USGS 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, D.G. Wydra, and 

J.A. Wilkinson.

v

Contents

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

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

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

Previous Studies Relating Secchi-Disk Transparency to Inland Lakes .......................................2

Purpose and Scope ..............................................................................................................................3

Methods...........................................................................................................................................................4

Landsat-Satellite Imagery Acquisition and Processing .................................................................4

Water-Only Image ........................................................................................................................4

Field Data Collection and Processing ......................................................................................5

Relating Field Data to Landsat-Satellite Imagery ............................................................................7

AOI Method To Select Open-Water Areas ..............................................................................7

Gethist Method To Select Open-Water Areas ........................................................................7

Trophic State Index Calculation for SDT ..................................................................................7

Regression Equations and Tests of Significance ..........................................................................13

Results ...........................................................................................................................................................13

Landsat-Satellite Imagery Data-Processing Improvements .......................................................13

Comparison of the AOI Lake-Average Method and the Gethist Method...................................14

Comparison of Equations 1 and 2 .....................................................................................................15

Summary and Conclusions .........................................................................................................................16

References Cited..........................................................................................................................................17

Appendixes 1 and 2......................................................................................................................................19

1. Results and computations by Landsat-satellite path for Michigan inland lakes, 

2003–05, of measured and predicted Secchi-disk transparency and 

Trophic State Index values for the area of interest, area of interest lakeaverage method, and the Gethist method .............................................................................20

2. Results and computations by Landsat-satellite path for Michigan inland lakes, 

2007–08, of measured and predicted Secchi-disk transparency and 

Trophic State Index values for the area of interest, area of interest lakeaverage method, and the Gethist method .............................................................................28

Figures

 1. Maps showing Landsat coverage for statewide predicted Trophic State Index 

and Secchi-disk transparency for 2003–05 and 2007–08 .......................................................5

 2. Landsat path 20 satellite image for September 22, 2004, in Oakland County, 

Michigan, for A, before satellite-data processing and B, after satellitedata processing ............................................................................................................................6

 3. Photograph of example of Secchi disk used to measure water clarity in lakes. ...............6
vi

4. Scatterplots for A, 2003–05 and B, 2007–08 of A, Michigan measured 

Trophic State Index (TSI) values and Secchi-disk transparency (SDT) values, 

in feet, to predicted TSI and SDT values using equation 1 for both the area of 

interest (AOI) lake-average method and the Gethist method; B, measured TSI 

values and SDT values, in feet, to predicted TSI and SDT values using 

equation 2 for both the AOI lake-average method and the Gethist method; and 

C, predicted TSI and SDT values using equation 1 to predicted TSI and 

SDT values using equation 2.............................................................................................. 11–12

5. Scatterplots for A, 2003–05 and B, 2007–08 of Michigan inland lakes greater 

than 20 acres with available open-water areas for statewide predicted 

Trophic State Index values and Secchi-disk transparency, in feet, using the 

Gethist method for equations 1 and 2......................................................................................13

6. Maps showing Landsat path 20, in Oakland County, Michigan, for 

A, Predicted Trophic State Index values for Michigan inland lakes 2003–05 and 

B, Predicted Trophic State Index values for Michigan inland lakes 2007–08...................14

Tables

1. Lake Trophic State Index and classification ranges using Trophic State Index 

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

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

2. Landsat 5 Thematic Mapper and Landsat 7 Enhanced Thematic Mapper Plus 

bands and corresponding wavelengths ...................................................................................3

3. Landsat-image and calibration-model data for Michigan inland lakes, 2003–05 

and 2007–08 ...................................................................................................................................8

4. Results comparing methods using equations 1 and 2 for 2003–05 and 2007–08 

in percent for measured Secchi-disk transparency values within 2, 5, and 

10 feet of the predicted Secchi-disk transparency; and percent for measured 

Trophic State Index values within 2, 5, and 10 units of the predicted Trophic 

State Index values for Michigan inland lakes........................................................................10

5. Predicted Trophic State Index and Secchi-disk transparency results for 

Fisher’s Transformation Significance Tests for Michigan inland lakes, 2003–05 

and 2007–08 .................................................................................................................................15

6. Comparison of Predicted Trophic State Index and Secchi-disk transparency 

results for equations 1 and 2 using Fisher’s Transformation Significance Tests 

for Michigan inland lakes, 2003–05 and 2007–08...................................................................15

7. Count and percent of measured and statewide predicted Trophic State classes 

for Michigan inland lakes, 2003–05 and 2007–08...................................................................16
vii

Conversion Factors 

Multiply By To obtain

Length

inch (in.) 2.54 centimeter (cm)

foot (ft) 0.3048 meter (m)

meter (m) 3.281 foot (ft) 

Area

acre 4,047 square meter (m2)

square meter (m2) 0.0002471 acre

acre 0.004047 square kilometer (km2)

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).

Abbreviations used in this report

AOI area of interest

Chl-a chlorophyll a

CLMP Cooperative Lakes Monitoring Program

GPS global positioning system

LWQA Lake Water Quality Assessment 

MDNRE Michigan Department of Natural Resources and Environment

R2 coefficient of determination

SDT Secchi-disk transparency

TM Thematic Mapper 

TP total phosphorus

TSI Trophic State Index

USGS U.S. Geological Survey

Predicting Lake Trophic State by Relating Secchi-Disk 

Transparency Measurements to Landsat-Satellite Imagery 

for Michigan Inland Lakes, 2003–05 and 2007–08 

By L.M. Fuller, R.S. Jodoin, and R.J. Minnerick 

Abstract 

Inland lakes are an important economic and environmental resource for Michigan. The U.S. Geological Survey 

and the Michigan Department of Natural Resources and 

Environment have been cooperatively monitoring the quality 

of selected lakes in Michigan through the Lake Water Quality Assessment program. Sampling for this program began 

in 2001; by 2010, 730 of Michigan’s 11,000 inland lakes 

are expected to have been sampled once. Volunteers coordinated by the Michigan Department of Natural Resources and 

Environment began sampling lakes in 1974 and continue to 

sample (in 2010) approximately 250 inland lakes each year 

through the Michigan Cooperative Lakes Monitoring Program. 

Despite these sampling efforts, it still is impossible to physically collect measurements for all Michigan inland lakes; 

however, Landsat-satellite imagery has been used successfully in Minnesota, Wisconsin, Michigan, and elsewhere to 

predict the trophic state of unsampled inland lakes greater than 

20 acres by producing regression equations relating in-place 

Secchi-disk measurements to Landsat bands. This study tested 

three alternatives to methods previously used in Michigan to 

improve results for predicted statewide Trophic State Index 

(TSI) computed from Secchi-disk transparency (TSI (SDT)). 

The alternative methods were used on 14 Landsat-satellite 

scenes with statewide TSI (SDT) for two time periods (2003–

05 and 2007–08). Specifically, the methods were (1) satellitedata processing techniques to remove areas affected by clouds, 

cloud shadows, haze, shoreline, and dense vegetation for 

inland lakes greater than 20 acres in Michigan; (2) comparison 

of the previous method for producing a single open-water predicted TSI (SDT) value (which was based on an area of interest (AOI) and lake-average approach) to an alternative Gethist 

method for identifying open-water areas in inland lakes (which 

follows the initial satellite-data processing and targets the 

darkest pixels, representing the deepest water, before regression equations are created); and (3) checking to see whether 

the predicted TSI (SDT) values compared well between 

two regression equations, one previously used in Michigan 

and an alternative equation from the hydrologic literature. 

The combination of improved satellite-data processing 

techniques and the Gethist method to identify open-water 

areas in inland lakes during 2003–05 and 2007–08 provided a 

stronger relation and statistical significance between predicted 

TSI (SDT) and measured TSI than did the AOI lake-average 

method; differences in results for the two methods were 

significant at the 99-percent confidence level. With regard 

to the comparison of the regression equations, there were no 

statistically significant differences at the 95-percent confidence 

level between results from the two equations. The previously used equation, in combination with the Gethist method, 

yielded coefficient of determination (R2) values of 0.71 and 

0.77 for the periods 2003–05 and 2007–08, respectively. 

The alternative equation, in combination with the Gethist 

method, yielded R2 values of 0.74 and 0.75 for 2003–05 and 

2007–08, respectively. Predicted TSI (SDT) and measured 

TSI (SDT) values for lakes used in the regression equations 

compared well, with R2 values of 0.95 and 0.96 for predicted 

TSI (SDT) for 2003–05 and 2007–08, respectively. The R2

values for statewide predicted TSI (SDT) for all inland lakes 

with available open-water areas for 2003–05 and 2007–08 

were 0.91 and 0.93, respectively. Although the two equations 

predicted similar trophic-state classes, the alternative equation 

is planned to be used for future prediction of TSI (SDT) values 

for Michigan inland lakes, to promote consistency in comparing predicted values between States and for potential use in 

trend analysis. 

Introduction

The State of Michigan has more than 11,000 inland 

lakes; approximately 4,000 of these lakes are greater than 

20 acres in size. The public has access to launches or beaches 

at about 1,300 lakes in Michigan. Recreational, property, and 

ecological values all are closely related to the quality of water 

in these inland lakes (Krysel and others, 2003). Tourism in 

Michigan, much of which involves recreation at inland lakes, 

accounts for nearly $12 billion of economic activity each year 
2 Predicting Lake Trophic State for Michigan Inland Lakes, 2003–05 and 2007–08

(Stynes, 2002). Thus, inland lakes are important economic and 

ecological resources to Michigan.

The U.S. Geological Survey (USGS) and the Michigan 

Department of Natural Resources and Environment (MDNRE) 

have been cooperatively monitoring the quality of inland 

lakes in Michigan through the Lake Water Quality Assessment 

(LWQA) monitoring program funded by the Clean Michigan 

Initiative. Through this program, the USGS has been sampling 

public-access lakes over 25 acres in size in both the spring 

and late summer. Sampling began in 2001; by 2010, 730 such 

lakes are expected to have been sampled. In addition, each 

year the MDNRE plans to provide data from their Cooperative 

Lakes Monitoring Program (CLMP), which is a volunteer network monitoring approximately 250 lakes weekly to monthly. 

Data from those two sampling networks are being used to 

characterize baseline water quality and compute trophic state 

of monitored inland lakes. 

Measured water-quality characteristics of inland lakes are 

critical factors in determining the lakes’ recreational use, habitat and species diversity, and economic return from the tourism 

industry. The USGS and the MDNRE monitor many inland 

lakes, but it is not economically feasible to monitor the quality 

of all 11,000 inland lakes in Michigan 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 protect and manage the quality in 

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), and elsewhere (Baban, 1993; Dekker 

and Peters, 1993; Mayo and others, 1995; Giardino and others, 2001) to estimate Trophic State Index (TSI) Secchi-disk 

transparency (SDT) for unsampled inland lakes. During previous studies in Michigan (Nelson and others, 2003; Wiangwang, 2002), researchers attempted to use existing models 

for relating Landsat-satellite imagery to SDT; however, they 

were unable to obtain as high a coefficient of determination 

(R2; an indicator of the strength of a statistical relation) as 

did researchers in previous studies in Minnesota and Wisconsin. Fuller and others (2004) estimated TSI (SDT) for Lower 

Michigan, using an alternative regression equation to that 

used by Olmanson and others (2001), with slightly higher 

R2 values. Results from a study by Fuller and Minnerick 

(2007) documented a good fit between measured and statewide 

predicted TSI (SDT). Knowledge of improved satellite-data 

processing techniques, an alternative Gethist method to identify the open-water areas in satellite data, and two available 

regression equations used to predict trophic characteristics 

from Landsat-satellite imagery prompted a revisit of methods 

from Fuller and others (2004) to examine which methods 

would produce predictions more reflective of measured values 

for two sets of data from 2003–05 and 2007–08. Refining 

methods would improve and increase the knowledge about 

Michigan’s inland lakes.

Previous Studies Relating Secchi-Disk 

Transparency to Inland Lakes

Carlson (1977) proposed to quantify the trophic state by 

its TSI, which can be classified into basic classes of oligotrophic, mesotrophic, eutrophic, and hypereutrophic. Carlson’s 

TSI model was developed for use with lakes that have few 

rooted aquatic plants and little non-algal turbidity (U.S. Environmental Protection Agency, 2007). The natural progression 

of a lake from oligotrophic to eutrophic can be computed from 

measures of total phosphorus (TP), Secchi-disk transparency 

(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 are

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

TSI = 9.81 ln Chl-a (micrograms per liter (μg/L)) + 30.6

TSI = 14.41 ln TP (μg/L) + 4.15 

SDT is a commonly used, low-cost technique that measures 

water clarity; specifically, a black and white disk is lowered 

into the lake until it no longer can be seen. Water clarity is 

related to the quantity of phytoplankton in the water, although 

non-algal turbidity and tannic acids also can reduce water 

clarity. Chl-a measurements correlate with the concentration 

of phytoplankton within a given volume of lake water and 

are not affected by sediment or acids in the water. Typically, 

computing TSI values for a single lake using all three formulas should yield similar results. Increasing the concentration 

of phosphorus generally results in increased concentration of 

phytoplankton, which results in reduced water clarity. Yet at 

specific times of the year, or on specific lakes, results from 

the three formulas may not be congruous because of phosphorus-nutrient uptake by macrophytes. Therefore, substantial 

Table 1. Lake Trophic State Index and classification ranges 

using Trophic State Index values, Secchi-disk transparency, 

chlorophyll-a, and total phosphorus for Michigan inland lakes, 

2003–05 and 2007–08.

[TSI, Trophic State Index; SDT, Secchi–disk transparency; ft, feet; 

Chl-a; chlorophyll-a; μg/L, micrograms per liter; TP, ttal phosphorus; 

<, less than; >, greater than; data from Warbach (1990) and modified by the 

State of Michigan to account for regional characteristics]

Lake trophic 

condition Carlson TSI SDT(ft)

Chl–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
Introduction 3

amounts of macrophytes in a lake may alter the relation of the 

three TSI values. 

Of the three measures, SDT and concentration of Chl-a

are quantifiable using remote-sensing techniques (Mayo and 

others, 1995; Zilioli and Brivio, 1997; Kloiber and others, 

2000; Giardino and others, 2001; and Kloiber and others, 

2002), though Kutser and others (2006) cautioned that Landsat-satellite imagery does not have adequate narrow spectral 

bands to distinguish the unique spectral signature of Chl-a, 

and regression equations actually may be predicting turbidity 

as it correlates to Chl-a. 

A variety of equations relating SDT to Landsat-satellite 

imagery have been tested in different settings and with different sensors. Olmanson and others (2001) and Kloiber and 

others (2002) used the following equation for Minnesota lakes 

along with data from Landsat 5 Thematic Mapper (TM) and 

Landsat 7 Enhanced Thematic Mapper plus (ETM+) satellites: 

ln(SDT) = a(band1/band3) + b(band1) + c (1)

Fuller and others (2004), who also used Landsat satellite 5 

TM, found an alternative equation for Michigan lakes that 

improved the relation, but the relation was not statistically 

significant at the 95-percent confidence level:

ln(SDT) = a(band1) + b(band2) + c(band3) + d (2) 

The variables a, b, and c are empirically derived coefficients 

from the regression equation. Table 2 shows Landsat (TM) and 

Landsat (ETM+) bands and corresponding wavelength ranges.

In Fuller and others (2004), methods similar to those 

published in Olmanson and others (2001) were followed to 

produce predicted TSI (SDT) for Michigan inland lakes for the 

Lower Peninsula of Michigan. A statewide predicted TSI for 

2003–06 from Fuller and Minnerick (2007) compared well to 

measurements, but the accuracy declined slightly owing to the 

method used to produce a predicted TSI (SDT) value reflective of the open-water area for each lake. Because we do not 

know the deep-basin location for all inland lakes in Michigan, 

the regression equation derived from using an Area of Interest 

(AOI) around the measurements was applied to all areas after 

satellite-data processing within each inland lake. All 30-m 

pixels within the area for each inland lake that remained after 

satellite-data processing were averaged to produce a single 

open-water predicted TSI value for each inland lake.

Minnesota and Wisconsin have used a Gethist program 

to reduce the areas remaining after satellite-data processing 

to identify the darkest pixels, which were then used to both 

produce regression equations and produce a single predicted 

TSI (SDT) value for each inland lake more representative of 

the open-water area. By use of this additional step, Minnesota 

and Wisconsin obtained statewide predicted TSI (SDT) for 

20 and 30 years, respectively, and analyzed potential trends 

(Olmanson and others, 2008 Peckham and Lillesand, 2006). 

With improved methods, Michigan also could follow suit to 

produce predicted TSI (SDT) to monitor potential trends for 

inland lakes. Temporal statewide predictions would be useful 

for lake managers to monitor potential changes in Michigan 

inland lakes. 

Purpose and Scope

This report was written to (1) document alternative 

methods for processing Landsat-satellite imagery that would 

remove areas affected by clouds, cloud shadows, haze, 

shoreline, and dense vegetation for inland lakes greater than 

20 acres in Michigan; (2) compare the previous method of 

producing a single open water predicted TSI (SDT) value 

using an area of interest (AOI) and lake-average method to 

an alternative Gethist method; and (3) ascertain if the predicted TSI (SDT) and SDT values compared well between the 

regression equation in Fuller and others (2004) to the regression equation in Olmanson and others (2001) for statewide 

predictions for two time periods: 2003–05 and 2007–08. The 

methods used to produce the statewide predictions will be 

described, the field data-collection methods will be included 

only by reference.

Table 2. Landsat 5 Thematic Mapper and Landsat 7 Enhanced Thematic Mapper Plus bands and corresponding wavelengths.

[μm, micrometers]

Landsat satellite

Visible spectrum Near-infrared Thermal Mid-infrared Panchromatic

Band 1 Band 2 Band 3 Band 4 Band 5 Band 6 Band 7 Band 8

Landsat 5 Thematic Mapper 0.45–0.52 

μm

0.52–0.60 

μm

0.63–0.69 

μm

0.76–0.90 

μm

1.55–1.75 

μm

10.40–12.50 

μm

2.08–2.35 

μm

Not 

available

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

1.55–1.75 

μm

10.40–12.50 

μm

2.08–2.35 

μm

0.52–0.90 

μm
4 Predicting Lake Trophic State for Michigan Inland Lakes, 2003–05 and 2007–08

Methods

Relating remote-sensing Landsat-satellite imagery to 

Secchi-disk measurements involves several steps, which can 

be grouped into three categories. First, relatively cloud-free 

Landsat-satellite imagery is chosen during the late-summer 

period and processed to remove areas affected by clouds, 

cloud shadows, haze, shoreline, and dense vegetation for 

inland lakes greater than 20 acres in Michigan. Second, 

field data corresponding to the Landsat-satellite imagery are 

obtained. Third, the field data within plus or minus 7 days of 

the Landsat-satellite imagery acquisition date are related to 

produce a regression model specific to each date of Landsatsatellite imagery. The end results are predicted TSI (SDT) 

values for desirable open-water areas for inland lakes greater 

than 20 acres within the Landsat-satellite scenes. 

Landsat-Satellite Imagery Acquisition 

and Processing

Seven paths of Landsat 5 Thematic Mapper (TM) satellite data (14 satellite scenes) were processed for 2003–05 

and 2007–08. The 14 Landsat-satellite scenes encompassing 

Michigan are referenced by both a path number and a row 

number (fig. 1). The Landsat-satellite scenes were selected 

for one date from a 3-month period (July–September) with 

the least amount of cloud cover and haze (preferably less 

than 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, 2000). 

Only one date per Landsat-satellite scene is included 

each year. Although temporal coverage during the season 

would be interesting, Landsat has a 16-day repeat cycle only 

allowing 5 to 6 dates available per scene during the 3-month 

period from mid July to September. Usually only one date per 

scene is available with less than 10 percent cloud cover, the 

percentage necessary to produce reliable predictions. For the 

2003–05 dataset, 3 years of data were used to complete the 

statewide predictions. In 2007, a sampling plan was implemented to produce a statewide predicted TSI (SDT) every 

other year. The sampling plan was to produce paths 20 to 23 

with year 1 Landsat-satellite imagery and paths 24 and 25 with 

year 2 Landsat-satellite imagery; Landsat-satellite imagery for 

2007–08 is shown on figure 1. 

The images arrived in 1P format, which means they were 

systematically corrected (geometric and radiometric corrections) and provided an “end result [that] was a geometrically 

rectified product free from distortions related to the sensor (for 

example, jitter, view angle effects), satellite (for example, attitude deviations from nominal), and Earth (for example, rotation, curvature)” (National Aeronautics Space Administration, 

2003), with ground-control points to improve spatial accuracy. 

The format chosen helped ensure that the image cells would 

correspond to the data-collection points as closely as possible. 

Landsat-imagery processing was completed with ERDAS 

IMAGINE 9.3 and 10.0 software. The Landsat-satellite scenes 

were delivered in the Universal Transverse Mercator projection system by using the World Geodetic System 84 North 

American Datum zone 16 or 17, depending on the scene. 

Each scene was reprojected into Michigan Georef by using an 

Oblique Mercator projection, NAD83 datum, in meters. The 

Michigan Georef projection was used because it ensures one 

zone for all of Michigan, and it is used by most Federal, State, 

and local agencies in Michigan. When each image was compared with the Michigan transportation framework developed 

by the Michigan Center for Geographic Information, it was 

found to be accurate to within 1 to 2 cells or about 30 to 60 m. 

This accuracy was acceptable to place the measurements for 

each inland lake into the deep open-water area.

Landsat satellites record values for each 30- × 30-m 

(900-m2

) area (cell), in wavelength ranges (bands). Bands 1, 2, 

and 3 (visible spectrum of blue, green, and red, respectively) 

are used in this project. All bands have cell sizes of 30 m, so 

900 m2 of Earth are represented in one cell by one value for 

each band. TSI (SDT) predictions are made for lakes greater 

than 20 acres (approximately 81,000 m2) to allow an adequate 

number of cells in the open-water area of the inland lakes to 

produce an accurate predictive model.

Water-Only Image

The water-only images are created to reduce file size 

and target analysis on the open-water area for inland lakes 

greater than 20 acres. Whereas Olmanson and others (2001) 

used an unsupervised classification to obtain open-water areas, 

we used a mask function was used to select pixels from the 

Landsat-satellite imagery that corresponded to a Michigan 

inland lakes polygon shapefile greater than 20 acres (from 

Breck, 2004). When the Landsat-satellite imagery was masked 

to match the inland lakes shapefile, some 30‐m pixels were 

selected as water (inside the lakes-polygon shapefile), including vegetated areas of the shoreline, islands, or shallow water 

with vegetation. 

A Normalized Difference Vegetation Index, which 

responds to the amount of green biomass (Jensen, 2007), was 

applied to remove the vegetated pixels within the inland lakespolygon shapefile that corresponded to shoreline, islands, and 

shallow vegetated water. The resulting pixels had a negative 

value; thus, greenness presence was removed. An unsupervised classification was performed on the remaining pixels 

using 10 classes, 50 iterations, and a 0.99-confidence level. 

If necessary, the unsupervised classification was repeated. 

This step facilitated masking out more areas with clouds, 

shallow areas, or shoreline. 

The final check was to input the remaining areas after the 

satellite-data processing into ArcMap 9.3 and display with a 

band 1,6,6 combination (mapping the blue band onto band 1, 

and bands 6 onto the green and red bands, respectively) to 

identify if any lakes were affected by haze or cloud shadows 

(a technique suggested by Olmanson and others, 2008). Lakes 
Methods 5

were removed from the calculation if they were affected by 

haze, and affected areas were removed from large lakes that 

still had good representation in the open-water areas. See 

figure 2 for before-and-after Landsat-imagery processing to 

obtain open-water areas for use in regression equations for a 

portion of Oakland County, Michigan, inland lakes. 

Field Data Collection and Processing

A Secchi disk is a common tool used to measure the 

overall clarity of water. The Secchi disk is an 8-in.-diameter 

circular disk painted black and white in alternating quadrants 

(fig. 3). The disk is lowered into the water, and the depth 

at which the disk is no longer visible is known as the SDT. 

Measurements of SDT were obtained from volunteers in the 

MDNRE CLMP who routinely measure SDT for various lakes 

in Michigan. SDT measurements done by volunteers have 

been studied and proven to be comparable with measurements 

done by professionals (Canfield and others, 2002; Obrecht 

and others, 1998). USGS field technicians collected samples 

in the Northern Lower Peninsula and the Upper Peninsula 

of Michigan immediately after Landsat-satellite scenes with 

low cloud cover to supplement measurements made by 

CLMP volunteers. 

Figure 1. Landsat coverage for statewide predicted Trophic State Index and Secchi-disk transparency for 2003–05 and 2007–08.

Shapefiles were created with measurements in the 

Michigan Georef projection that corresponded to a window 

of 7 days before or after satellite-acquisition dates, and this 

approach produced accurate predictive models. This window 

produced the best results in predictive SDT models (Kloiber 

and others, 2002). The number of measurements per path varied but a minimum of 20 measurements per Landsat-satellite 

scene in a path was desirable. Measurements were made at the 

deepest point in the lake so that reflectance from the bottom 

of the lake did not affect the measurements. The locations of 

the measurements used were noted during sampling, either by 

using a global positioning system (GPS) unit to record latitude 

and longitude coordinates or by clearly marking locations 

on a map during sampling and digitizing later to determine 

their coordinates. 

All SDT measurements were reviewed; some were 

omitted owing to clouds, cloud shadows, or haze covering 

the open-water areas of the inland lake. Clouds and cloud 

shadows along with haze are limiting factors in producing 

accurate regression equations to predict water clarity and are 

why imagery should be chosen on clear satellite-overpass 

days (Olmanson and others, 2008). Measurements were omitted if information was available to determine that measured 

SDTs were more than two-thirds the lake depth (which occurs 
6 Predicting Lake Trophic State for Michigan Inland Lakes, 2003–05 and 2007–08

Figure 2. Landsat path 20 satellite image for September 22, 2004, in Oakland County, Michigan, for A, before satellite-data processing 

and B, after satellite-data processing.

Figure 3. Example of Secchi disk used to measure water clarity in lakes.
Methods 7

mostly in shallow lakes), because of possible interference 

from the lake bottom. 

Occasionally, latitude and longitude locations of measurements plotted outside the lake. In these circumstances, the 

coordinates were changed to correspond to the deepest location if a bathymetric map was available. If a bathymetric map 

could not be located, the measurement was omitted. Some 

lakes did not have latitude and longitude for measurements, 

nor could accurate bathymetric maps be located; these measurements were omitted. Table 3 summarizes measurements 

per Landsat-satellite scene.

Relating Field Data to Landsat-Satellite Imagery

The field SDT measurements were related to the Landsatsatellite imagery by using the AOI method documented in 

Fuller and others (2004) and an alternative Gethist method 

that selects a portion of the open-water areas remaining after 

satellite-data processing (as documented in Olmanson and others, 2001). Mean values for each band in the Landsat-satellite 

imagery then were used in two equations (differing in the 

bands used) to produce statewide TSI (SDT) predictions for 

2003–05 and 2007–08. 

AOI Method To Select Open-Water Areas

AOIs containing approximately nine cells were established around each measurement, and the average band values 

were recorded. Taking an average for each band in its AOI was 

found to smooth the radiometric noise and to produce more 

accurate predicted SDT values (Olmanson and others, 2001). 

Average band values for each measurement were used in a statistical analysis program to determine the regression equation 

specific to each path or scene of Landsat-satellite data. 

Gethist Method To Select Open-Water Areas

The open-water areas remaining after satellite-data 

processing for lakes greater than 20 acres were used in the 

Gethist program documented in Olmanson and others (2001). 

The Gethist program further reduced the remaining areas in 

each lake to identify the darkest pixels that should represent 

deeper open water. Specifications were set to ignore zeros, 

use 50 percent of the histogram, and use the bottom N percent 

pixels to represent the darkest pixels. The Gethist program 

returned mean values for each band of the Landsat-satellite 

imagery for each inland lake. The output was used in a statistical analysis program to produce regression equations specific 

to each path of satellite data. 

Trophic State Index Calculation for SDT

Tibco Spotfire S+ 8.1 software was used for multiple 

regression calculations for each path. The equation documented in Fuller and others (2004) was applied to each path of 

satellite data for both the AOI and the Gethist method: 

ln(SDT) = a(band1) + b(band2) + c(band3) + d (1)

The resulting equation used the natural log of SDT for the 

dependent variable, and the independent variables were bands 

1, 2, and 3. 

The equation used in Olmanson and others (2001) and 

Kloiber and others (2002) was applied to each path of satellite 

data for both the AOI and the Gethist method: 

ln(SDT) = a(band1/band3) + b(band1) + c (2)

The natural log of SDT was the dependent variable, and 

the independent variables were a ratio of band 1 and 3, and 

band 1. The variables a, b, and c were derived coefficients 

from the regression equation. 

TSI values then could be computed on the natural log of 

the SDT images derived previously using the equation from 

Carlson (1977).

The measured TSI (SDT) and SDT values were compared 

to the predicted TSI (SDT) and SDT values from equations 

1 and 2. Results for both 2003–05 and 2007–08, by path, 

are listed in table 3. For the 2003–05 years, path 21, row 28 

did not have an adequate number of measurements available 

during the Landsat-satellite imagery-acquisition date, so the 

regression equation from path 21, rows 29 to 31 was applied 

to that Landsat-satellite scene. A comparison (as percentages) 

for both sets of years of data using both methods and equations to measured TSI (SDT) and SDT is presented in table 4. 

Scatterplots with R2 values are shown on figures 4A and 4B for 

2003–05 and 2007–08, respectively, for all measured values 

of TSI (SDT) and SDT for the AOI lake-average method and 

the Gethist method generated by use of equations 1 and 2. 

Scatterplots comparing the predicted TSI (SDT) for all lakes 

with desirable pixels from 2003–05 and 2007–08 are shown 

for equations 1 and 2 on figure 5. The predicted paths were 

merged together to produce statewide 2003–05 and 2007–08 

predictions on figures 6A and 6B, respectively. Appendixes 1 

and 2 list the measurements used for the regression equations.
Table 3. Landsat-image and calibration-model data for Michigan inland lakes, 2003–05 and 2007–08.—Continued [SDT, Secchi–disk transparency; AOI, area of interest; R2, coefficient of determination; SEE, Standard Error of Estimate; TM, Thematic Mapper; <, less than] Image date Path Rows Number of images Satellite Percent cloud cover Days prior Days past Number of measure- ments SDT range (m) SDT range (ft) R2 SEE Number of lakes assessed Equation 1 R2 S

2003–05 SDT AOI 9/22/2004 20 30–31 2 Landsat TM 5 < 10 6 4 20 1.5–7.3 5.0–24.0 0.72 0.227 573 x = B1(0.0190) + B2(0.1355) + B3(–0.5709) + 4.6406 0.67 0

9/13/2004 21 *28–31 4 Landsat TM 5 < 10 8 6 72 0.8–8.5 2.5–28.0 0.70 0.244 1597 x = B1(0.0976) + B2(–0.0690) + B3(–0.2452) + 0.7801 0.66 09/20/2004 22 28–31 4 Landsat TM 5 < 10 7 6 49 0.9–5.9 3.0–19.0 0.72 0.194 1368 x = B1(0.0210) + B2(0.0482) + B3(–0.3498) + 3.0269 0.69 09/21/2005 24 27 1 Landsat TM 5 < 10 0 5 10 2.0–5.3 6.5–17.5 0.67 0.227 72 x = B1(0.2464) + B2(–0.1678) + B3(–0.2477) + –4.7251 0.66 07/19/2005 24 28 1 Landsat TM 5 < 10 0 6 15 2.1–6.7 7.0–22.0 0.72 0.188 463 x = B1(0.0343) + B2(–0.1110) + B3(–0.3256) + 5.3142 0.66 08/22/2003 25 28 1 Landsat TM 5 < 10 10 6 12 6.0–20.5 1.8–6.3 0.55 0.310 172 x = B1(0.0491) + B2(0.2245) + B3(–0.3501) + –0.5287 0.45 0

2003–05 SDT Gethist 9/22/2004 20 30–31 2 Landsat TM 5 < 10 6 4 22 1.5–7.3 5.0–24.0 0.78 0.220 573 x = B1(0.0198) + B2(0.2138) + B3(–0.7569) + 5.2799 0.73 0

9/13/2004 21 *28–31 4 Landsat TM 5 < 10 8 6 75 0.8–8.5 2.5–28 0.72 0.233 1597 x = B1(0.1112) + B2(–0.0496) + 

B3(–0.3008) + 0.4164

0.69 0

9/20/2004 22 28–31 4 Landsat TM 5 < 10 7 6 50 0.9–5.9 3–19.0 0.74 0.187 1368 x = B1(0.0159) + B2(0.0898) + 

B3(–0.4580) + 3.5664

0.72 0

1/11/1900 24 27 1 Landsat TM 5 < 10 0 5 10 2.0–5.3 6.5–17.5 0.73 0.207 72 x = B1(0.2417) + B2(–0.0502) + 

B3(–0.4146) + –4.4840

0.73 0

7/19/2005 24 28 1 Landsat TM 5 < 10 0 6 15 2.1–6.7 7.0–22.0 0.77 0.205 463 x = B1(0.0883) + B2(0.2556) + 

B3(–0.5212) + –1.4099

0.73 0

8/22/2003 25 28 1 Landsat TM 5 < 10 10 6 12 6.0–20.5 1.8–6.3 0.68 0.262 172 x = B1(0.1840) + B2(0.0937) + 

B3(–0.4114) + –4.0418

0.65 0
Table 3. Landsat-image and calibration-model data for Michigan inland lakes, 2003–05 and 2007–08.—Continued[SDT, Secchi–disk transparency; AOI, area of interest; R2, coefficient of determination; SEE, Standard Error of Estimate; TM, Thematic Mapper; <, less than]

Image 

date Path Rows

Number 

of 

images

Satellite

Percent 

cloud 

cover

Days 

prior

Days 

past

Number of 

measurements

SDT 

range 

(m)

SDT 

range 

(ft)

R2 SEE

Number of lakes 

assessed

Equation 1 R2 S

2007–08 SDT AOI

8/30/2007 20 30–31 2 Landsat TM 5 < 10 6 3 18 1.8–4.9 6.0–16.0 0.75 0.155 506 x = B1(0.1320) + B2(–0.0021) + 

B3(–0.4418) + 0.2371

0.74 0

9/22/2007 21 28–31 3 Landsat TM 5 < 10 7 0 68 0.8–6.7 2.5–22.0 0.69 0.205 1603 x = B1(0.0379) + B2(0.0366) + 

B3(–0.4568) + 4.0436

0.66 0

6/25/2007 22 28 1 Landsat TM 5 < 10 0 3 15 2.4–6.4 8.0–21.0 0.70 0.182 349 x = B1(0.0810) + B2(0.0499) + 

B3(–0.2736) + –0.2435

0.74 0

9/13/2007 22 29–31 3 Landsat TM 5 < 10 5 7 56 2.5–23.0 0.8–7.0 0.73 0.205 892 x = B1(0.0844) + B2(–0.1191) + 

B3(–0.1500) + 1.0328

0.63 0

8/3/2007 23 28 1 Landsat TM 5 < 10 0 5 15 2.9–6.1 9.5–20.0 0.74 0.121 464 x = B1(0.1313) + B2(–0.0065) + 

B3(–0.1344) + –3.5666

0.71 0

7/27/2008 24 27–28 2 Landsat TM 5 < 10 0 4 17 2.1–5.0 6.8–16.4 0.67 0.154 432 x = B1(0.0694) + B2(0.0070) + 

B3(–0.0852) + –1.7354

0.73 0

8/3/2008 25 28 1 Landsat TM 5 < 10 0 3 14 1.7–7.3 5.5–24.0 0.79 0.233 168 x = B1(–0.0992) + B2(–0.2703) + 

B3(0.1156) + 10.7408

0.65 0

2007–08 SDT Gethist

8/30/2007 20 30–31 2 Landsat TM 5 < 10 6 3 18 1.8–4.9 6.0–16.0 0.72 0.165 506 x = B1(0.1810) + B2(0.0617) + 

B3(–0.6804) + –0.5065

0.72 0

9/22/2007 21 28–31 3 Landsat TM 5 < 10 7 0 72 0.8–7.0 2.5–23.0 0.76 0.182 1603 x = B1(0.0117) + B2(0.1001) + 

B3(–0.5401) + 5.0105

0.75 0

6/25/2007 22 28 1 Landsat TM 5 < 10 0 3 15 2.4–6.4 8.0–21.0 0.73 0.174 349 x = B1(0.0569) + B2(0.0919) + 

B3(–0.2803) + 0.4328

0.74 0

9/13/2007 22 29–31 3 Landsat TM 5 < 10 5 7 56 2.5–23.0 0.8–7.0 0.72 0.207 892 x = B1(0.0811) + B2(–0.0860) + 

B3(–0.1948) + 1.1367

0.67 0

8/3/2007 23 28 1 Landsat TM 5 < 10 0 5 15 2.9–6.1 9.5–20.0 0.67 0.135 464 x = B1(0.1308) + B2(0.0088) + 

B3(–0.1204) + –3.8703

0.67 0

7/27/2008 24 27–28 2 Landsat TM 5 < 10 0 4 18 2.1–5.6 6.8–18.3 0.68 0.173 432 x = B1(0.0289) + B2(0.1545) + 

B3(–0.1423) + –1.3854 

0.68 0

8/3/2008 25 28 1 Landsat TM 5 < 10 0 3 14 1.7–7.3 5.5–24.0 0.81 0.224 168 x = B1(0.1929) + B2(–0.3452) + 

B3(–0.2916) + 1.9305

0.73 0

* No in–situ measurements available in Path 22 Row 28.
10 Predicting Lake Trophic State for Michigan Inland Lakes, 2003–05 and 2007–08

Table 4. Results comparing methods using equations 1 and 2 for 2003–05 and 2007–08 in percent for measured Secchi-disk 

transparency values within 2, 5, and 10 feet of the predicted Secchi-disk transparency; and percent for measured Trophic State Index 

values within 2, 5, and 10 units of the predicted Trophic State Index values for Michigan inland lakes.

[SDT, Secchi-disk transparency; TSI, Trophic State Index; AOI, area of interest; Eq, equation; LakeAve, Lake average; all data are in percent]

2003–05

2 SDT feet 5 SDT feet 10 SDT feet 2 TSI units 5 TSI units 10 TSI units Correct TSI Class

AOIEq1 63 93 100 50 94 100 77

LakeAveAOIEq1 51 81 97 39 72 96 64

GethistEq1 68 97 100 54 98 100 79

AOIEq2 69 95 100 45 89 100 76

LakeAveAOIEq2 56 85 99 37 73 97 68

GethistEq2 68 96 100 48 95 100 78

2007–08

2 SDT feet 5 SDT feet 10 SDT feet 2 TSI units 5 TSI units 10 TSI units Correct TSI Class

AOIEq1 77 97 100 61 100 100 81

LakeAveAOIEq1 55 88 99 43 79 97 73

GethistEq1 76 97 100 65 97 100 85

AOIEq2 74 97 100 59 94 100 79

LakeAveAOIEq2 67 90 100 51 83 99 77

GethistEq2 75 97 100 75 98 100 86
Methods 11

25

Figure 4A. Scatterplots for 2003–05 of A, Michigan measured Trophic State Index (TSI) values and Secchi-disk transparency (SDT) 

values, in feet, to predicted TSI and SDT values using equation 1 for both the area of interest (AOI) lake-average method and the 

Gethist method; B, measured TSI values and SDT values, in feet, to predicted TSI and SDT values using equation 2 for both the AOI lakeaverage method and the Gethist method; and C, predicted TSI and SDT values using equation 1 to predicted TSI and SDT values using 

equation 2.
12 Predicting Lake Trophic State for Michigan Inland Lakes, 2003–05 and 2007–08

25

30

35

40

45

50

55

60

65

PREDICTED TROPHIC STATE INDEX VALUES, EQUATION 2,AOI LAKE AVERAGE METHOD

Figure 4B. Scatterplots for 2007–08 of A, Michigan measured Trophic State Index (TSI) values and Secchi-disk transparency (SDT) 

values, in feet, to predicted TSI and SDT values using equation 1 for both the area of interest (AOI) lake-average method and the 

Gethist method; B, measured TSI values and SDT values, in feet, to predicted TSI and SDT values using equation 2 for both the AOI lakeaverage method and the Gethist method; and C, predicted TSI and SDT values using equation 1 to predicted TSI and SDT values using 

equation 2.
Results 13

Figure 5. Scatterplots of A, 2003–05 and B, 2007–08 for Michigan inland lakes greater than 

20 acres with available open-water areas for statewide predicted Trophic State Index values 

and Secchi-disk transparency, in feet, using the Gethist method for equations 1 and 2.

Regression Equations and Tests of Significance

Fisher’s Transformation (Yamane, 1973) was used to 

test the difference of two correlation coefficients to determine 

whether there was a statistically significant difference between 

the AOI lake-average method and the Gethist method, and also 

between equations 1 and 2. The square root of the R2 values 

was used for Fisher’s Transformation of R. Results of Fisher’s 

Transformation (tables 5 and 6) higher than 2.579 mean that 

differences were statistically significant at the 99-percent confidence level, whereas those lower than 1.96 mean that differences were not statistically significant even at the 95-percent 

confidence level. 

Results

Fourteen Landsat 5 satellite scenes were processed to 

produce two statewide predicted TSI (SDT) and SDT layers for Michigan inland lakes. One scene—path 23, row 28 

in the 2003–05 period—did not have an adequate number of 

field measurements remaining after removing lakes effected 

by clouds, cloud shadows, and haze to produce a regression 

equation. Although approximately 20 field measurements 

within each Landsat-satellite scene are desirable, fewer measurements were available for a few scenes, especially in the 

Upper Peninsula. Even so, the R2 values from the resulting 

regression equations were still comparable to those for other 

satellite paths. All 14 Landsat-satellite scenes had coverage for 

2007–08. Whereas Landsat-satellite scenes are selected on the 

basis of their low cloud cover, predictions could not be made 

for all lakes greater than 20 acres for every statewide time 

period because some lakes lacked a large enough remaining 

open-water area after the satellite-data processing.

Landsat-Satellite Imagery Data-Processing 

Improvements

Improvements to the satellite-data processing included 

how lakes are selected and how selected areas are determined. 

First, lakes were selected by masking known lake-polygon 

locations, as per the approach of Breck (2004); this ensured 

that all lakes greater than 20 acres had representation. Previous methods in Fuller and others (2004) did not ensure that 

all lakes would be selected. Second, a Normalized Difference 

Vegetation Index was used to remove vegetated areas, which 

assisted in the removal of shoreline, islands, and shallow 

vegetated areas within the lake-polygon locations. Third, an 

unsupervised classification was run to further remove shallow, 

vegetated, and cloud areas. Finally, the image was viewed in 

a band 1, 6, 6 (mapping the blue band onto band 1, and bands 

6 onto the green and red bands, respectively) combination to 

identify haze and remove affected lakes or portions of lakes. 
14 Predicting Lake Trophic State for Michigan Inland Lakes, 2003–05 and 2007–08

Comparison of the AOI Lake-Average Method 

and the Gethist Method

The measured and predicted TSI (SDT) and SDT compared well between the AOI lake average and Gethist methods; however, the R2

 values and also the percent of lakes predicting close to the measured values were lower for the AOI 

lake-average method. To allow application of the regression 

equation, a method from Fuller and others (2004) averaged 

all areas remaining in each lake after satellite-data processing, because all deep-basin locations or open-water areas are 

not known for all inland lakes greater than 20 acres. The AOI 

lake-average method lowered the percentage of lakes within 

2 and 5 TSI (SDT) units or 2 and 5 SDT, in feet (table 4). 

This difference also can be seen in figures 4A and 4B with 

scatterplots and R2

 values showing the strength of the relation between the AOI lake-average and Gethist methods. For 

2003–05, the measured to predicted TSI (SDT) AOI lake-average method returned R2

 values of 0.39 and 0.40 using equations 1 and 2, respectively (0.50 and 0.51 R2

 for 2007–08), 

and the Gethist method returned R2 values of 0.71 and 0.74 

using equations 1 and 2, respectively (0.77 and 0.75 R2 for 

2007–08). Similar comparisons were found for the measured 

and predicted SDT.

Fisher’s Transformation was used to determine whether 

there was a statistically significant difference between the 

AOI lake-average and Gethist methods. Table 5 illustrates that 

for both 2003–05 and 2007–08, using either equation 1 or 2, 

there was a statistically significant difference at the 99‐percent 

confidence level. 

Orchard Lake Orchard Lake

39

Figure 6. Landsat path 20, in Oakland County, Michigan, for A, Predicted Trophic State Index values for Michigan inland lakes 2003–05 

and B, Predicted Trophic State Index values for Michigan inland lakes 2007–08
Results 15

Comparison of Equations 1 and 2

The R2 values for the regression equations to predict 

TSI (SDT) and SDT for 2003–05 and 2007–08 using the 

Gethist method were similar for equations 1 and 2. Fisher’s 

Transformation was used to determine whether there was a 

statistically significant differences between equations 1 and 2 

using the Gethist method. Table 6 illustrates that there was no 

statistically significant difference at the 95-percent confidence 

level between equations 1 and 2 using the Gethist method.

When the predicted TSI (SDT) and SDT values for the 

subset of lakes with measurements were plotted in a scatterplot 

for equations 1 and 2, the R2 value for 2003–05 was 0.95 and 

for 2007–08 was 0.96. When the regression predictions were 

extended to all lakes greater than 20 acres with open-water 

areas, the R2 values decreased slightly to 0.91 for 2003–05 

and 0.93 for 2007–08. Although the relation is still strong, 

the scatterplots in figure 5 show that equation 1 can predict 

higher TSI values. This discrepancy between the two predicted 

datasets starts around a TSI of 60, which corresponds to the 

hypereutrophic category. Although the majority of lakes do 

not change trophic-state categories between the equations, 

the TSI values are different. Similarly, when comparing the 

predicted SDT between equations 1 and 2, equation 2 predicts 

higher SDT (lower TSI), starting around 20 ft and greater, than 

equation 1. Whereas inland lakes with an SDT greater than 

15 ft all would be classified in the oligotrophic category, the 

actual TSI values from the two equations can differ. 

Unfortunately, there are only 10 out of 184 measurements 

for 2003–05 and 12 out of 208 measurements for 2007–08 

with SDT values greater than 20 ft (TSI < 34) and greater than 

60 TSI units (SDT < 3.5 ft) for 2003–05. Measurements that 

do fall within these ranges show no pattern for overpredicting 

in either range of values. The difference between the equations 

is beyond the range of lakes with available data. 

The relation between equations 1 and 2 is strong for 

measured and predicted TSI (SDT) and SDT; however, for 

ease of comparison for predicted TSI (SDT) or SDT values 

between Minnesota and Wisconsin, and also for future trend 

analysis that might focus solely on the predicted TSI (SDT) or 

SDT values, equation 2 will be used for 2003–05, 2007–08, 

and future statewide predictions. The count and percentage for 

measured and predicted TSI (SDT) for equations 1 and 2 by 

Trophic State class can be found in table 7. 

Table 5. Predicted Trophic State Index and Secchi-disk 

transparency results for Fisher’s Transformation Significance 

Tests for Michigan inland lakes, 2003–05 and 2007–08.

[TSI, Trophic State index; AOI, areas of interest; R2, coefficient of determination; SDT, Secchi-disk transparency]

TSI

AOI lake 

average R2

Gethist

R2

Fisher’s 

Transformation*

2003–05, Equation 1 0.39 0.71 4.70

2003–05, Equation 2 0.40 0.74 5.18

2007–08, Equation 1 0.50 0.77 4.56

2007–08, Equation 2 0.51 0.75 3.97

SDT

AOI lake 

average R2

Gethist

R2

Fisher’s 

Transformation*

2003–05, Equation 1 0.36 0.70 4.87

2003–05, Equation 2 0.41 0.67 3.71

2007–08, Equation 1 0.45 0.73 4.34

2007–08, Equation 2 0.47 0.72 3.88

*

 Fisher’s Transformation values greater than 2.576 are statistically significant at the 99-percent confidence interval.

Table 6. Comparison of Predicted Trophic State Index and 

Secchi-disk transparency results for equations 1 and 2 using 

Fisher’s Transformation Significance Tests for Michigan inland 

lakes, 2003–05 and 2007–08.

[TSI, Trophic State index; R2, coefficient of determination; SDT, Secchidisk transparency]

Equation 1 

R2

Equation 2 

R2

Fisher’s

Transformation*

2003–05 Gethist TSI 0.71 0.74 0.60

2003–05 Gethist SDT 0.77 0.75 0.45

Equation 1 

R2

Equation 2 

R2

Fisher’s 

Transformation*

2007–08 Gethist TSI 0.70 0.67 0.53

2007–08 Gethist SDT 0.73 0.72 0.20

*

 Fisher’s Transformation values greater than 1.96 are statistically significant at the 95-percent confidence interval.
16 Predicting Lake Trophic State for Michigan Inland Lakes, 2003–05 and 2007–08

Summary and Conclusions

Michigan has more than 11,000 inland lakes, and their 

sheer number poses a physical and economical problem for 

collection of data needed to compute a statewide Trophic 

State Index (TSI). Volunteers with the Michigan Department 

of Natural Resources and Environment (MDNRE) Cooperative Lake Monitoring Program (CLMP) and field technicians 

of the U.S. Geological Survey (USGS) monitor selected 

lakes each year. An economical and feasible tool to expand 

the use of the sampling data is to relate Secchi-disk transparency (SDT) measurements to Landsat-satellite imagery with 

regression equations. These regression equations then can 

be applied to Landsat-satellite imagery to produce predicted 

statewide TSI (SDT) values for unmeasured open-water areas 

of inland lakes.

The purpose of this publication is to describe a refinement of methods originally published in Fuller and others 

(2004); the goal of the refinement was to produce a statewide 

predicted TSI for Michigan inland lakes that is more representative of the open-water area than was possible previously. 

The methods used in the refinement are (1) techniques used 

for processing Landsat-satellite imagery to identify open-water 

areas in lakes, (2) comparison of two methods— the area of 

Table 7. Count and percent of measured and statewide predicted Trophic State classes for Michigan inland 

lakes, 2003–05 and 2007–08.

[TSI, Trophic State Index]

interest (AOI) lake-average method and the Gethist method 

(Olmanson and others, 2001)—to return a single predicted TSI 

representing the open-water area of lakes, and (3) comparison 

of two equations from Fuller and others (2004) to equations 

from Olmanson and others (2001) and Kloiber and others 

(2002) to ascertain which equation produces predictions most 

reflective of measured values. 

The satellite-data processing technique used to select 

inland lakes ensures that all inland lakes greater than 20 acres 

from the Michigan lake polygons shapefile (Breck, 2004) will 

be included unless intentionally removed during further data 

evaluation and processing. Running a Normalized Difference 

Vegetated Index on the pixels within the inland lake shapefile 

aided in the removal of vegetated pixels associated with shoreline, islands, or shallow water. An unsupervised classification 

then was run to further remove clouds and shallow water. 

Together, these satellite-data processing techniques did a better 

job than previous techniques to remove lake areas that would 

confound regression analysis and to better confine the dataset 

to unobscured open-water areas suitable for analysis.

Incorporating the Gethist image-processing method 

provided R2 values more comparable to the R2 values from 

the AOI areas used to produce the regression equations from 

Fuller and others (2004). Even though the Gethist areas were, 

2003–05

Oligotrophic Mesotrophic Eutrophic Hypereutrophic

Measured TSI count 36 122 25 1

Statewide predicted equation 1 count 184 1,979 759 199

Statewide predicted equation 2 count 245 2,014 757 105

Measured TSI percent 19.6 66.3 13.6 0.5

Statewide predicted equation 1 percent 5.9 63.4 24.3 6.4

Statewide predicted equation 2 percent 7.9 64.5 24.3 3.4

2007–08

Oligotrophic Mesotrophic Eutrophic Hypereutrophic

Measured TSI count 30 155 21 2

Statewide predicted equation 1 count 208 2,247 474 95

Statewide predicted equation 2 count 213 2,242 499 70

Measured TSI percent 14.4 74.5 10.1 1.0

Statewide predicted equation 1 percent 6.9 74.3 15.7 3.1

Statewide predicted equation 2 percent 7.0 74.1 16.5 2.3
References Cited 17

on average, larger than the AOI areas used previously to 

produce the regression equations, the Gethist method provided 

higher R2 values than the AOI lake-average method, which 

was used to apply the regression equations previously created 

using the AOI areas from Fuller and others (2004). The larger 

benefit is that the Gethist method can be applied to all lakes 

and does not require knowledge of the deep open-water areas, 

thus providing a predicted TSI (SDT) result more reflective of the deep open-water areas for unsampled inland lakes 

in Michigan.

Another benefit of the Gethist method is that it does not 

require the analyst to know the lake-measurement location. 

Unlike with the AOI method, measurements do not need to be 

removed from the analytical dataset if they do not have a corresponding latitude and longitude or if a bathymetric map is 

unavailable to estimate the measurement location. The Gethist 

method outputs the average band values for each lake in the 

Landsat-satellite imagery. The average band values reflect a 

reduced area representing the darkest values from the areas 

identified after satellite-data processing. The resulting average band values from the Gethist method then are related to 

available SDT measurements in the Landsat-satellite scenes. 

Predicted TSI (SDT) for inland lakes with field measurements 

using the Gethist method and equation 1 from Fuller and others (2004) compared well with equation 2 found in Olmanson 

and others (2001) and Kloiber and others (2002). There was no 

statistically significant difference at the 95-percent confidence 

level between results from the two equations for either dataset.

Comparison of predicted TSI (SDTs) for the subset 

of lakes with field measurements in 2003–05 and 2007–08 

resulted in R2 values of 0.95 and 0.96, respectively. When 

the statewide predicted TSI (SDTs) were applied to all lakes 

greater than 20 acres without interference from clouds, cloud 

shadows, haze, or dense vegetation using equations 1 and 2, 

the R2 values were 0.91 for 2003–05 and 0.93 for 2007–08. 

Although this is still a strong relation indicating minimal 

differences in results, equation 1 nevertheless predicts higher 

than equation 2 for TSI values greater than 60 (SDT < 3.5 ft) 

and lower for SDT values greater than 20 ft (TSI < 34). The 

few measurements available in these high and low ranges did 

not reflect the pattern for overpredicting and underpredicting, and measurements were not available at the far extremes 

on either side to provide insight. Although the lakes still 

predicted to the correct trophic state category, the predicted 

TSI (SDT) and SDT values were different at the extreme ends 

of the TSI scale. For ease of comparison between Minnesota 

and Wisconsin statewide predictions, and also for future trend 

analysis that might focus solely on the predicted TSI (SDT) or 

SDT values, equation 2 is planned to be used for 2003–05 and 

2007–08 and future statewide predictions. 

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the Thematic Mapper for the analysis of eutrophic 

lakes—A case study in the Netherlands: International Journal of Remote Sensing, v. 4, no. 5, p. 799–821.

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inland lakes, 2001–06: U.S. Geological Survey Fact Sheet 

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fs/2007/3022/.

Fuller, L.M., and Minnerick, R.J., 2008, State and regional 

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(also available at http://pubs.water.usgs.gov/sir20085188/).
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and Zilioli, Eugenio, 2001, Detecting chlorophyll, Secchi 

disk depth and surface temperature in a sub-alpine lake 

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Bauer, M.E., and Brown, D.A., 2000, Trophic state assessment of lakes in the Twin Cities (Minnesota, USA) region 

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and Skole, D.L., 2003, Regional assessment of lake water 

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Ready, Diana; and Jones, J.R., 1998, Evaluation of data 

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no. 11, p. 4,086–4,097.

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Brezonik, P.L., 2001, Image processing protocol for 

regional assessments of lake water quality: St. Paul, Minn., 

University of Minnesota, Water Resources Center and 

Remote Sensing Laboratory, p. 1–13.

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and temporal trends in Wisconsin lake water clarity using 

Landsat-derived estimates of Secchi depth: Lake and Reservoir Management, v. 22, no. 4, p. 331–341.

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economic impact estimates 1998–2000: Accessed November 2003 at http://web4.canr.msu.edu/mgm2/econ/miteim/

MichiganSatExec.pdf. 

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(3d ed): New York, Harper & Row, p. 493–498.

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water quality: Science of the Total Environment, v. 196, 

p. 229–245.
Appendixes 1 and 2 19

Appendixes 1 and 2

Appendix 1. Results and computations by Landsat–satellite path for Michigan inland lakes, 

2003–05, of measured and predicted Secchi-disk transparency and Trophic State 

Index values for the area of interest, area of interest lake-average method, and the 

Gethist method.................................................................................................................... p. 20–27

Appendix 2. Results and computations by Landsat–satellite path for Michigan inland lakes, 

2007–08, of measured and predicted Secchi-disk transparency and Trophic State 

Index values for the area of interest, area of interest lake-average method, and the 

Gethist method.................................................................................................................... p. 28–36
Appendix 1. Results and computations by Landsat-satellite path for Michigan inland lakes, 2003–05, of measured and predicted Secchi-disk transpaIndex values for the area of interest, area of interest lake-average method, and the Gethist method.—Continued [SDT, Secchi-disk transparency; AOI, area of interest; TSI, Trophic State Index; Eq, equation; *, measurement not used owing to issue with placement] Landsat satellite Measured SDT AOI TSI AOI lake av

TSI 

Path Row Lake Name County Acres Sampled SDT ft SDT m TSI Eq1 Eq2 Eq1 

20 30–31 Round Lake Clinton 87 2004–09–25 5.5 1.7 53 51 48 53 20 30–31 Byram Lake Genesee 134 2004–09–19 12.0 3.7 41 42 44 48 20 30–31 Fenton Lake Genesee 866 2004–09–19 15.5 4.7 38 34 32 44 20 30–31 Ponemah Lake Genesee 410 2004–09–25 12.5 3.8 41 41 41 45 20 30–31 Silver Lake Genesee 339 2004–09–26 15.0 4.6 38 40 40 43 20 30–31 Clear Lake Jackson 129 2004–09–21 11.5 3.5 42 44 44 48 20 30–31 Gilletts Lake Jackson 334 2004–09–16 7.5 2.3 48 43 43 61 20 30–31 Grass Lake Jackson 353 2004–09–18 5.0 1.5 54 * * * 20 30–31 Vineyard Lake Jackson 541 2004–09–21 14.0 4.3 39 37 38 46 20 30–31 Nepessing Lake Lapeer 427 2004–09–23 17.0 5.2 36 38 38 43 20 30–31 Evans Lake Lenawee 215 2004–09–22 24.0 7.3 31 37 36 39 20 30–31 East Crooked Lake Livingston 248 2004–09–20 19.0 5.8 35 41 42 46 20 30–31 Gut Lake Livingston 32 2004–09–20 13.0 4.0 40 40 40 38 20 30–31 Hamburg Lake Livingston 99 2004–09–21 17.0 5.2 36 36 37 41 20 30–31 Oneida Lake Livingston 46 2004–09–19 10.0 3.0 44 43 43 49 20 30–31 Strawberry Lake Livingston 261 2004–09–24 9.0 2.7 45 44 43 46 20 30–31 West Crooked Lake Livingston 191 2004–09–19 8.5 2.6 46 41 43 47 20 30–31 Buckhorn Lake Oakland 43 2004–09–25 13.0 4.0 40 44 42 50 20 30–31 Taylor Lake Oakland 39 2004–09–25 20.0 6.1 34 * * * 20 30–31 Leisure Lake Shiawassee 45 2004–09–22 5.0 1.5 54 55 54 55 20 30–31 Pleasant Lake Washtenaw 193 2004–09–22 10.0 3.0 44 43 45 47 20 30–31 Portage Lake Washtenaw 641 2004–09–19 10.0 3.0 44 41 42 52 21 28–31 Hubbard Lake Alcona 8768 2004–09–13 14.0 4.3 39 37 36 40 
Appendix 1. Results and computations by Landsat-satellite path for Michigan inland lakes, 2003–05, of measured and predicted Secchi-disk transpaIndex values for the area of interest, area of interest lake-average method, and the Gethist method.—Continued[SDT, Secchi-disk transparency; AOI, area of interest; TSI, Trophic State Index; Eq, equation; *, measurement not used owing to issue with placement]

AOI lake av

Landsat satellite Measured SDT AOI TSI 

TSI

Path Row Lake Name County Acres Sampled SDT ft SDT m TSI Eq1 Eq2 Eq1 

21 28–31 Jewell Lake Alcona 184 2004–09–12 8.5 2.6 46 43 43 53 21 28–31 Bellaire Lake Antrim 1789 2004–09–14 16.0 4.9 37 34 34 40 21 28–31 Clam Lake Antrim 438 2004–09–15 21.0 6.4 33 33 32 40 21 28–31 Barlow Lake Barry 181 2004–09–15 7.5 2.3 48 42 42 46 21 28–31 Randall N Cemetary L Branch 511 2004–09–16 7.5 2.3 48 47 47 48 21 28–31 Birch Lake Cass 282 2004–09–13 12.0 3.7 41 45 44 46 21 28–31 Christiana Cass 560 2004–09–14 6.5 2.0 50 47 47 48 21 28–31 Diamond Lake Cass 1041 2004–09–14 12.0 3.7 41 43 43 47 21 28–31 Juno Cass 560 2004–09–14 6.5 2.0 50 48 48 48 21 28–31 Magician Lake Cass 522 2004–09–15 7.0 2.1 49 45 45 50 21 28–31 Painter Cass 560 2004–09–14 5.5 1.7 53 48 48 48 21 28–31 Shavehead Lake Cass 299 2004–09–19 8.0 2.4 47 45 43 48 21 28–31 Twin Lake (north) Cass 61 2004–09–11 12.5 3.8 41 46 46 49 21 28–31 Twin Lake (south) Cass 43 2004–09–12 7.0 2.1 49 45 45 51 21 28–31 Shingle Lake Clare 30 2004–09–14 11.0 3.4 43 40 40 40 21 28–31 Windover Lake Clare 68 2004–09–13 21.0 6.4 33 35 34 43 21 28–31 Round Lake Clinton 87 2004–09–12 6.0 1.8 51 46 47 48 21 28–31 Byram Lake Genesee 134 2004–09–19 12.0 3.7 41 46 46 46 21 28–31 Fenton Lake Genesee 866 2004–09–11 16.0 4.9 37 37 37 43 21 28–31 Ponemah Lake Genesee 410 2004–09–10 11.5 3.5 42 42 42 42 21 28–31 Silver Lake Genesee 339 2004–09–12 12.5 3.8 41 42 41 44 21 28–31 Lake Twenty Gladwin 124 2004–09–08 9.5 2.9 45 38 37 43 21 28–31 Crystal Lake Hillsdale 130 2004–09–15 14.0 4.3 39 44 45 44 
Appendix 1. Results and computations by Landsat-satellite path for Michigan inland lakes, 2003–05, of measured and predicted Secchi-disk transpaIndex values for the area of interest, area of interest lake-average method, and the Gethist method.—Continued [SDT, Secchi-disk transparency; AOI, area of interest; TSI, Trophic State Index; Eq, equation; *, measurement not used owing to issue with placement] AOI lake av

Landsat satellite Measured SDT AOI TSI 

TSI Path Row Lake Name County Acres Sampled SDT ft SDT m TSI Eq1 Eq2 Eq1 

21 28–31 Perch Lake Hillsdale 46 2004–09–16 8.0 2.4 47 46 46 45 21 28–31 Cedar Lake Iosco 142 2004–09–13 8.5 2.6 46 * * * 21 28–31 Van Etten Lake Iosco 1409 2004–09–10 7.5 2.3 48 48 48 45 21 28–31 Gilletts Lake Jackson 334 2004–09–16 7.5 2.3 48 * * * 21 28–31 Grass Lake Jackson 353 2004–09–18 5.0 1.5 54 49 50 49 21 28–31 Portage Lake Jackson 398 2004–09–18 11.0 3.4 43 45 45 51 21 28–31 Vineyard Lake Jackson 541 2004–09–09 10.0 3.0 44 46 46 53 21 28–31 Indian Lake Kalamazoo 788 2004–09–13 6.0 1.8 51 51 49 53 21 28–31 Bear Lake Kalkaska 313 2004–09–16 28.0 8.5 29 32 29 37 21 28–31 Cub Lake Kalkaska 57 2004–09–10 24.0 7.3 31 36 35 40 21 28–31 Bostwick Lake Kent 213 2004–09–17 6.5 2.0 50 43 44 46 21 28–31 Freska Lake Kent 59 2004–09–16 8.0 2.4 47 * * * 21 28–31 Murray Lake Kent 312 2004–09–16 11.0 3.4 43 44 44 45 21 28–31 East Crooked Lake Livingston 248 2004–09–13 16.0 4.9 37 40 40 45 21 28–31 Gut Lake Livingston 32 2004–09–11 13.0 4.0 40 40 41 42 21 28–31 Oneida Lake Livingston 46 2004–09–12 10.5 3.2 43 42 43 44 21 28–31 Strawberry Lake Livingston 261 2004–09–11 8.0 2.4 47 45 46 45 21 28–31 West Crooked Lake Livingston 191 2004–09–12 7.5 2.3 48 46 47 47 21 28–31 Horsehead Lake Mecosta 443 2004–09–15 12.0 3.7 41 43 44 46 21 28–31 Mecosta Lake Mecosta 312 2004–09–07 9.0 2.7 45 43 43 46 21 28–31 Pretty Lake Mecosta 116 2004–09–19 11.0 3.4 43 40 40 41 21 28–31 Round Lake Mecosta 157 2004–09–18 14.0 4.3 39 43 45 42 21 28–31 West Canadian Lake Mescoda 133 2004–09–10 12.0 3.7 41 39 40 43 
Appendix 1. Results and computations by Landsat-satellite path for Michigan inland lakes, 2003–05, of measured and predicted Secchi-disk transpaIndex values for the area of interest, area of interest lake-average method, and the Gethist method.—Continued[SDT, Secchi-disk transparency; AOI, area of interest; TSI, Trophic State Index; Eq, equation; *, measurement not used owing to issue with placement]

AOI lake av

Landsat satellite Measured SDT AOI TSI 

TSI

Path Row Lake Name County Acres Sampled SDT ft SDT m TSI Eq1 Eq2 Eq1 

21 28–31 Sanford Lake Midland 1402 2004–09–11 9.0 2.7 45 39 39 42 21 28–31 Baldwin Lake Montcalm 62 2004–09–18 9.5 2.9 45 41 42 43 21 28–31 Clifford Lake Montcalm 195 2004–09–15 11.0 3.4 43 44 45 44 21 28–31 Derby Lake Montcalm 114 2004–09–15 19.0 5.8 35 40 41 43 21 28–31 Muskellunge Lake Montcalm 137 2004–09–10 11.0 3.4 43 42 43 44 21 28–31 Picnic Lake Montcalm 23 2004–09–07 2.5 0.8 64 60 55 61 21 28–31 Avalon Lake Montmorency 386 2004–09–15 27.0 8.2 30 31 29 33 21 28–31 Bills Lake Newaygo 200 2004–09–16 10.0 3.0 44 41 42 44 21 28–31 Sylvan Lake Newaygo 102 2004–09–16 10.0 3.0 44 40 42 43 21 28–31 Island Lake Ogemaw 60 2004–09–13 15.0 4.6 38 43 44 45 21 28–31 Center Lake Osceola 41 2004–09–12 17.0 5.2 36 37 38 37 21 28–31 Hicks Lake Osceola 160 2004–09–09 3.5 1.1 59 59 55 56 21 28–31 Wells Lake Osceola 48 2004–09–15 18.0 5.5 35 39 40 41 21 28–31 Big Bradford Lake Otsego 256 2004–09–06 17.0 5.2 36 39 38 39 21 28–31 Big Lake Otsego 124 2004–09–10 19.0 5.8 35 36 36 38 21 28–31 Viking Lake Otsego 36 2004–09–12 6.0 1.8 51 53 51 52 21 28–31 Corey Lake St. Joseph 599 2004–09–16 8.0 2.4 47 43 44 48 21 28–31 Fishers Lake St. Joseph 330 2004–09–11 10.0 3.0 44 48 47 49 21 28–31 Fishers Lake St. Joseph 330 2004–09–11 10.0 3.0 44 47 47 49 21 28–31 Klinger Lake St. Joseph 835 2004–09–15 11.0 3.4 43 46 45 47 21 28–31 Pleasant Lake St. Joseph 256 2004–09–15 13.0 4.0 40 44 45 49 21 28–31 Cedar Lake Van Buren 275 2004–09–10 13.5 4.1 40 43 44 47 21 28–31 Crooked Lake Van Buren 117 2004–09–05 12.0 3.7 41 46 47 46 
Appendix 1. Results and computations by Landsat-satellite path for Michigan inland lakes, 2003–05, of measured and predicted Secchi-disk transpaIndex values for the area of interest, area of interest lake-average method, and the Gethist method.—Continued [SDT, Secchi-disk transparency; AOI, area of interest; TSI, Trophic State Index; Eq, equation; *, measurement not used owing to issue with placement] AOI lake av

Landsat satellite Measured SDT AOI TSI 

TSI Path Row Lake Name County Acres Sampled SDT ft SDT m TSI Eq1 Eq2 Eq1 

21 28–31 Crooked Lake Little Van Buren 114 2004–09–14 14.0 4.3 39 45 46 45 21 28–31 Silver Lake Van Buren 50 2004–09–13 12.5 3.8 41 41 43 43 21 28–31 Pleasant Lake Washtenaw 193 2004–09–16 10.5 3.2 43 48 48 47 21 28–31 Portage Lake Washtenaw 641 2004–09–12 9.5 2.9 45 48 48 50 21 28–31 Stone Ledge Lake Wexford 83 2004–09–18 13.0 4.0 40 38 37 39 22 28–31 Goshorn Lake Allegan 28 2004–09–18 6.5 2.0 50 48 47 48 22 28–31 Hutchins Lake Allegan 379 2004–09–17 8.0 2.4 47 42 43 50 22 28–31 Torch Lake Antrim 18722 2004–09–23 16.5 5.0 37 38 38 39 22 28–31 Ann Lake Benzie 501 2004–09–17 13.0 4.0 40 42 43 47 22 28–31 Crystal Lake Benzie 9869 2004–09–26 18.0 5.5 35 36 33 37 22 28–31 Christiana Cass 560 2004–09–22 7.5 2.3 48 48 47 48 22 28–31 Diamond Lake Cass 1041 2004–09–23 12.0 3.7 41 40 41 49 22 28–31 Juno Cass 560 2004–09–22 7.0 2.1 49 44 44 47 22 28–31 Painter Cass 560 2004–09–22 6.5 2.0 50 47 47 47 22 28–31 Shavehead Lake Cass 299 2004–09–19 8.0 2.4 47 49 50 51 22 28–31 Twin Lake (north) Cass 61 2004–09–19 18.0 5.5 35 41 41 46 22 28–31 Twin Lake (south) Cass 43 2004–09–23 10.0 3.0 44 41 41 54 22 28–31 Lily Lake Clare 190 2004–09–24 9.5 2.9 45 42 42 42 22 28–31 Shingle Lake Clare 30 2004–09–22 13.0 4.0 40 40 40 42 22 28–31 Arbutus Lake Grand Trave 378 2004–09–15 14.0 4.3 39 42 42 45 22 28–31 Long Lake Grand Trave 2911 2004–09–18 19.0 5.8 35 40 39 43 22 28–31 Indian Lake Kalamazoo 788 2004–09–25 7.0 2.1 49 53 52 55 22 28–31 Freska Lake Kent 59 2004–09–23 9.5 2.9 45 42 42 42 
Appendix 1. Results and computations by Landsat-satellite path for Michigan inland lakes, 2003–05, of measured and predicted Secchi-disk transpaIndex values for the area of interest, area of interest lake-average method, and the Gethist method.—Continued[SDT, Secchi-disk transparency; AOI, area of interest; TSI, Trophic State Index; Eq, equation; *, measurement not used owing to issue with placement]

AOI lake av

Landsat satellite Measured SDT AOI TSI 

TSI

Path Row Lake Name County Acres Sampled SDT ft SDT m TSI Eq1 Eq2 Eq1 

22 28–31 Murray Lake Kent 312 2004–09–16 11.0 3.4 43 46 46 45 22 28–31 Big Star Lake Lake 890 2004–09–18 11.5 3.5 42 38 38 42 22 28–31 Glen Lake Little Leelanau 1415 2004–09–22 7.0 2.1 49 47 47 46 22 28–31 Hamlin Lake Mason 4622 2004–09–19 13.5 4.1 40 42 41 42 22 28–31 Hamlin Lake Mason 4622 2004–09–23 9.5 2.9 45 41 40 43 22 28–31 Horsehead Lake Mecosta 443 2004–09–20 15.5 4.7 38 41 41 46 22 28–31 Mecosta Lake Mecosta 312 2004–09–18 15.0 4.6 38 41 41 45 22 28–31 Pretty Lake Mecosta 116 2004–09–19 11.0 3.4 43 41 42 42 22 28–31 Round Lake Mecosta 157 2004–09–18 14.0 4.3 39 39 38 41 22 28–31 West Canadian Lake Mescoda 133 2004–09–17 11.5 3.5 42 40 40 43 22 28–31 Sapphire Lake Missaukee 246 2004–09–13 7.5 2.3 48 47 47 48 22 28–31 Baldwin Lake Montcalm 62 2004–09–18 9.5 2.9 45 43 44 44 22 28–31 Clifford Lake Montcalm 195 2004–09–23 12.0 3.7 41 43 43 44 22 28–31 Bills Lake Newaygo 200 2004–09–18 12.0 3.7 41 40 41 46 22 28–31 Kimball Lake Newaygo 147 2004–09–19 6.0 1.8 51 52 52 52 22 28–31 Pickerel Lake Newaygo 308 2004–09–19 12.0 3.7 41 39 39 45 22 28–31 Sylvan Lake Newaygo 102 2004–09–16 10.0 3.0 44 42 43 44 22 28–31 Crystal Lake Oceana 121 2004–09–20 8.0 2.4 47 44 45 44 22 28–31 Robinson Lake Oceana 134 2004–09–14 10.0 3.0 44 41 40 41 22 28–31 Stony Lake Oceana 287 2004–09–15 12.0 3.7 41 41 41 42 22 28–31 Center Lake Osceola 41 2004–09–19 18.0 5.5 35 40 40 40 22 28–31 Hicks Lake Osceola 160 2004–09–25 3.0 0.9 61 60 57 60 22 28–31 Corey Lake St. Joseph 599 2004–09–24 8.5 2.6 46 47 48 49 
Appendix 1. Results and computations by Landsat-satellite path for Michigan inland lakes, 2003–05, of measured and predicted Secchi-disk transpaIndex values for the area of interest, area of interest lake-average method, and the Gethist method.—Continued [SDT, Secchi-disk transparency; AOI, area of interest; TSI, Trophic State Index; Eq, equation; *, measurement not used owing to issue with placement] AOI lake av

Landsat satellite Measured SDT AOI TSI 

TSI Path Row Lake Name County Acres Sampled SDT ft SDT m TSI Eq1 Eq2 Eq1 

22 28–31 Fishers Lake St. Joseph 330 2004–09–25 13.5 4.1 40 43 43 48 22 28–31 Fishers Lake St. Joseph 330 2004–09–18 14.0 4.3 39 42 43 53 22 28–31 Pleasant Lake St. Joseph 256 2004–09–22 15.0 4.6 38 41 41 46 22 28–31 Wahbememe St. Joseph 22 2004–09–19 16.0 4.9 37 * * * 22 28–31 Cedar Lake Van Buren 275 2004–09–18 13.0 4.0 40 42 42 45 22 28–31 Crooked Lake Van Buren 117 2004–09–19 11.0 3.4 43 39 38 44 22 28–31 Crooked Lake Little Van Buren 114 2004–09–14 14.0 4.3 39 41 41 43 22 28–31 Silver Lake Van Buren 50 2004–09–19 13.5 4.1 40 40 39 41 22 28–31 Stone Ledge Lake Wexford 83 2004–09–18 13.0 4.0 40 43 43 43 24 27 Clear Lake Houghton 23 2005–09–26 17.5 5.3 36 38 37 37 24 27 Gerald Lake Houghton 356 2005–09–24 13.5 4.1 40 36 37 41 24 27 Pike Lake Houghton 83 2005–09–26 8.5 2.6 46 42 42 42 24 27 Portage Lake Houghton 10808 2005–09–24 8.5 2.6 46 43 41 47 24 27 Roland Lake Houghton 258 2005–09–24 16.0 4.9 37 39 39 41 24 27 Torch Lake Houghton 2400 2005–09–24 13.5 4.1 40 33 33 38 24 27 Fanny Hooe Lake Keweenaw 230 2005–09–23 14.5 4.4 39 38 38 39 24 27 Manganese Lake Keweenaw 56 2005–09–23 12.0 3.7 41 41 42 41 24 27 Medora Lake Keweenaw 690 2005–09–23 9.0 2.7 45 42 43 41 24 27 Lake Independence Marquette 2041 2005–09–26 6.5 2.0 50 51 48 50 24 28 Bass Lake Dickinson 60 2005–07–21 22.0 6.7 33 33 33 38 24 28 Carney Lake Dickinson 115 2005–07–25 17.0 5.2 36 39 39 42 24 28 Hanbury Lake Dickinson 78 2005–07–25 19.5 5.9 34 38 37 42 24 28 Mary Lake Dickinson 85 2005–07–25 15.0 4.6 38 34 35 53 
Appendix 1. Results and computations by Landsat-satellite path for Michigan inland lakes, 2003–05, of measured and predicted Secchi-disk transpaIndex values for the area of interest, area of interest lake-average method, and the Gethist method.—Continued[SDT, Secchi-disk transparency; AOI, area of interest; TSI, Trophic State Index; Eq, equation; *, measurement not used owing to issue with placement]

AOI lake av

Landsat satellite Measured SDT AOI TSI 

TSI

Path Row Lake Name County Acres Sampled SDT ft SDT m TSI Eq1 Eq2 Eq1 

24 28 Pickerel Lake Dickinson 68 2005–07–25 15.5 4.7 38 36 36 48 24 28 Bass Lake Marquette 76 2005–07–25 16.5 5.0 37 37 37 39 24 28 Bass Lake Marquette 273 2005–07–21 8.5 2.6 46 43 43 51 24 28 Deer Lake Marquette 906 2005–07–22 7.0 2.1 49 46 45 47 24 28 Engman Lake Marquette 48 2005–07–21 11.5 3.5 42 44 45 45 24 28 Fish Lake Marquette 151 2005–07–22 8.5 2.6 46 36 38 34 24 28 Greenwood Reservoir Marquette 1073 2005–07–22 8.5 2.6 46 36 38 34 24 28 Horseshoe Lake Marquette 126 2005–07–22 9.0 2.7 45 40 40 46 24 28 Johnson Lake Marquette 78 2005–07–21 18.0 5.5 35 36 35 42 24 28 Little Lake Marquette 460 2005–07–21 17.0 5.2 36 39 38 55 24 28 Squaw Lake Marquette 247 2005–07–22 18.5 5.6 35 35 36 39 25 28 Allen Lake Gogebic 78 2003–08–28 8.5 2.6 46 45 43 44 25 28 Bass Lake Gogebic 200 2003–08–25 8.5 2.6 46 43 43 41 25 28 Beatons Lake Gogebic 324 2003–08–27 18.5 5.6 35 38 38 41 25 28 Clark Lake Gogebic 836 2003–08–26 20.5 6.2 34 39 41 38 25 28 Dinner Lake Gogebic 108 2003–08–12 10.5 3.2 43 40 43 43 25 28 Duck Lake Gogebic 612 2003–08–12 9.5 2.9 45 42 44 50 25 28 Lac Vieux Desert Gogebic 4370 2003–08–12 6.5 2.0 50 49 48 45 25 28 Oxbow Lake Gogebic 98 2003–08–13 8.0 2.4 47 42 40 43 25 28 Pomeroy Lake Gogebic 314 2003–08–13 6.0 1.8 51 53 53 49 25 28 Thousand Island Lake Gogebic 1009 2003–08–27 12.5 3.8 41 43 44 42 25 28 Bond Falls Flowage Ontonagon 2127 2003–08–26 9.0 2.7 45 42 42 41 25 28 County Line Lake Ontonagon 67 2003–08–27 16.0 4.9 37 45 43 45 
Appendix 2. Results and computations by Landsat-satellite path for Michigan inland lakes, 2007–08, of measured and predicted Secchi-disk transpaIndex values for the area of interest, area of interest lake-average method, and the Gethist method.—Continued [SDT, Secchi-disk transparency; AOI, area of interest; TSI, Trophic State Index; Eq, equation; *, measurement not used owing to issue with placement] Landsat satellite Measured SDT AOI TSI AOI lak

Path Row Lake Name County Acres Sampled SDT ft SDT m TSI Eq1 Eq2 Eq1 

20 3031 Byram Lake Genesee 134 2007–09–02 15.0 4.6 38 39 39 50 20 3031 Clear Lake Jackson 129 2007–08–31 12.0 3.7 41 39 39 53 20 3031 Vineyard Lake Jackson 541 2007–08–31 12.0 3.7 41 43 44 49 20 3031 Base Line Lake Livingston 244 2007–08–24 11.5 3.5 42 40 40 38 20 3031 Chemung Lake Livingston 313 2007–08–27 15.0 4.6 38 38 38 49 20 3031 Earl Lake Livingston 53 2007–08–29 6.0 1.8 51 48 48 43 20 3031 Gallagher Lake Livingston 189 2007–09–02 10.5 3.2 43 42 42 41 20 3031 Green Oak Lake Livingston 152 2007–08–24 13.5 4.1 40 41 41 46 20 3031 Gut Lake Livingston 32 2007–08–30 13.0 4.0 40 41 41 48 20 3031 Hamburg Lake Livingston 99 2007–08–29 16.0 4.9 37 41 41 48 20 3031 Oneida Lake Livingston 46 2007–08–25 7.0 2.1 49 48 48 49 20 3031 Ore Lake Livingston 231 2007–09–01 11.0 3.4 43 42 42 41 20 3031 Round Lake Livingston 74 2007–08–25 7.5 2.3 48 47 47 42 20 3031 Strawberry Lake Livingston 261 2007–09–01 8.0 2.4 47 45 46 46 20 3031 Buckhorn Lake Oakland 43 2007–09–02 13.0 4.0 40 42 42 48 20 3031 Long Lake Oakland 104 2007–08–30 13.0 4.0 40 43 43 45 20 3031 Middle Straits Lake Oakland 178 2007–08–26 14.0 4.3 39 37 37 46 20 3031 Portage Lake Washtenaw 641 2007–08–31 10.0 3.0 44 47 47 46 21 2831 Cedar Lake Alcona 912 2007–09–20 8.0 2.4 47 48 49 57 21 2831 Hubbard Lake Alcona 8768 2007–09–16 12.0 3.7 41 41 42 44 21 2831 Vaughn Lake Alcona 112 2007–09–20 15.0 4.6 38 37 37 41 21 2831 Osterhout Lake Allegan 172 2007–09–18 10.0 3.0 44 45 45 48 21 2831 Bellaire Lake Antrim 1789 2007–09–20 16.0 4.9 37 * * * 21 2831 Barlow Lake Barry 181 2007–09–17 10.0 3.0 44 45 43 47 
Appendix 2. Results and computations by Landsat-satellite path for Michigan inland lakes, 2007–08, of measured and predicted Secchi-disk transpaIndex values for the area of interest, area of interest lake-average method, and the Gethist method.—Continued[SDT, Secchi-disk transparency; AOI, area of interest; TSI, Trophic State Index; Eq, equation; *, measurement not used owing to issue with placement]

Landsat satellite Measured SDT AOI TSI AOI lak

Path Row Lake Name County Acres Sampled SDT ft SDT m TSI Eq1 Eq2 Eq1 

212121212121212121212121212121212121212121212121

283128312831283128312831283128312831283128312831283128312831283128312831283128312831283128312831

Cobb LakePayne LakeStuart LakeUpper Brace LakeBirch LakeDiamond LakeEagle LakeMagician LakePuterbaugh LakeTwin Lake (north)Twin Lake (south)Arnold LakeGeorge LakeLily LakeShingle LakeRound LakeMargrethe LakePonemah LakeLake TwentySmallwood LakeLake DianeRebeck LakeLansing LakeChain Lakes (west)

BarryBarryCalhounCalhounCassCassCassCassCassCassCassClareClareClareClareClintonCrawfordGeneseeGladwinGladwinHillsdaleHillsdaleInghamIosco

92

113115

71

282

1041

400522

446143

121129190

3087

1922

410124371266

50

456

84

2007–09–212007–09–222007–09–212007–09–212007–09–202007–09–192007–09–192007–09–152007–09–202007–09–192007–09–192007–09–192007–09–182007–09–222007–09–182007–09–162007–09–162007–09–212007–09–202007–09–182007–09–222007–09–152007–09–202007–09–22

13.0

11.0

13.012.020.013.010.510.0

9.5

10.0

11.5

17.0

11.511.0

14.0

7.5

12.014.012.0

9.02.56.56.0

12.0

4.03.44.03.76.14.03.23.02.93.03.55.23.53.44.32.33.74.33.72.70.82.01.83.7

404340413440434445444236424339484139414564505141

424145413841

*

4447

*

4436413941443740434360464641

414145413842

*

4447

*

4436413941443740434358454642

454949464142

*

4750

*

4441434143504542455168485055
Appendix 2. Results and computations by Landsat-satellite path for Michigan inland lakes, 2007–08, of measured and predicted Secchi-disk transpaIndex values for the area of interest, area of interest lake-average method, and the Gethist method.—Continued [SDT, Secchi-disk transparency; AOI, area of interest; TSI, Trophic State Index; Eq, equation; *, measurement not used owing to issue with placement] Landsat satellite Measured SDT AOI TSI AOI lak

Path Row Lake Name County Acres Sampled SDT ft SDT m TSI Eq1 Eq2 Eq1 

212121212121212121212121212121212121212121212121

283128312831283128312831283128312831283128312831283128312831283128312831283128312831283128312831

Clark LakeClear LakeVineyard LakeWamplers LakeSherman LakeCub LakeEagle LakeNorth Blue LakeStarvation LakeTwin LakeEvans LakeRound LakeChemung LakeEarl LakeBlue LakeCanadian LakesHorsehead LakeMecosta LakePretty LakeRound LakeWest Canadian LakeBaldwin LakeClifford LakeEast Twin Lake

JacksonJacksonJacksonJacksonKalamazooKalkaskaKalkaskaKalkaskaKalkaskaKalkaskaLenaweeLenaweeLivingstonLivingstonMecostaMecostaMecostaMecostaMecostaMecostaMescodaMontcalmMontcalmMontmorency

576129541797148

57255699

209215512313

53

229321443312

116

157133

62

195820

2007–09–202007–09–182007–09–212007–09–192007–09–162007–09–202007–09–162007–09–222007–09–202007–09–222007–09–192007–09–162007–09–172007–09–202007–09–182007–09–202007–09–202007–09–222007–09–222007–09–222007–09–202007–09–182007–09–222007–09–22

14.0

11.0

13.0

7.0

20.516.016.017.016.023.015.012.014.0

5.0

12.0

11.0

10.012.012.014.012.010.013.0

8.5

4.33.44.02.16.24.94.95.24.97.04.63.74.31.53.73.43.03.73.74.33.73.04.02.6

394340493437373637323841395441434441413941444046

444442453941413541464146405437414337384244404044

454442453841403441464147405237424437384244414045

454752504045423841394648445643464747454444454546
Appendix 2. Results and computations by Landsat-satellite path for Michigan inland lakes, 2007–08, of measured and predicted Secchi-disk transpaIndex values for the area of interest, area of interest lake-average method, and the Gethist method.—Continued[SDT, Secchi-disk transparency; AOI, area of interest; TSI, Trophic State Index; Eq, equation; *, measurement not used owing to issue with placement]

Landsat satellite Measured SDT AOI TSI AOI lak

Path Row Lake Name County Acres Sampled SDT ft SDT m TSI Eq1 Eq2 Eq1 

212121212121212121212121212121212121222222222222

283128312831283128312831283128312831283128312831283128312831283128312831

282828282828

West Twin LakeBills LakePickerel LakeCenter LakeHicks LakeBig Bradford LakeBig LakeCrockery LakeCorey LakeFishers LakeKlinger LakePerrin LakeCedar LakeCrooked LakeCrooked Lake LittleGravel LakeMaple LakeStone Ledge LakeFrenchman LakeTrout LakeWegwaas LakeBass LakeBodi LakeCulhane Lake

MontmorencyNewaygoNewaygoOsceolaOsceolaOtsegoOtsegoOttawaSt. JosephSt. JosephSt. JosephSt. JosephVan BurenVan BurenVan BurenVan BurenVan BurenWexfordChippewaChippewaChippewaLuceLuceLuce

1306

200308

41

160256124104599330835109275

117114

297193

83

185568148144275100

2007–09–202007–09–222007–09–152007–09–162007–09–172007–09–212007–09–172007–09–172007–09–182007–09–222007–09–202007–09–212007–09–172007–09–212007–09–212007–09–202007–09–182007–09–182007–06–262007–06–262007–06–262007–06–282007–06–272007–06–27

8.5

12.012.020.0

5.5

22.019.0

7.0

14.512.0

11.0

10.013.010.5

11.5

9.57.08.5

12.0

11.5

10.021.010.0

11.0

2.63.73.76.11.76.75.82.14.43.73.43.04.03.23.52.92.12.63.73.53.06.43.03.4

464141345333354939414344404342454946414244334443

483641395235394840424542404041

*

4546434143364845

483641395135394840434542403939

*

4547434143354845

504243425342415043454651444343

*

5048454644374944
Appendix 2. Results and computations by Landsat-satellite path for Michigan inland lakes, 2007–08, of measured and predicted Secchi-disk transpaIndex values for the area of interest, area of interest lake-average method, and the Gethist method.—Continued [SDT, Secchi-disk transparency; AOI, area of interest; TSI, Trophic State Index; Eq, equation; *, measurement not used owing to issue with placement] Landsat satellite Measured SDT AOI TSI AOI lak

Path Row Lake Name County Acres Sampled SDT ft SDT m TSI Eq1 Eq2 Eq1 

222222222222222222222222222222222222222222222222

282828282828282828

293129312931293129312931293129312931293129312931293129312931

East LakeKaks LakeMuskallonge LakePerch LakePike LakeBrevoort LakeEast LakeMillecoquins LakeDutch Fred LakeOsterhout LakeWetmore LakeTorch LakeWoods Lake of theBarlow LakeCobb LakeCrooked LakePayne LakeAnn LakeCrystal LakePlatte LakeSanford LakeDiamond LakeEagle LakeMagician Lake

LuceLuceLuceLuceLuceMackinacMackinacMackinacSchoolcraftAlleganAlleganAntrimAntrimBarryBarryBarryBarryBenzieBenzieBenzieBenzieCassCassCass

125

59

762

91

286

4315

927

1123

34

172

46

18722

172181

92

644

113

501

98692532

53

1041

400522

2007–06–282007–06–282007–06–272007–06–272007–06–272007–06–262007–06–262007–06–262007–06–282007–09–142007–09–202007–09–082007–09–132007–09–152007–09–132007–09–092007–09–082007–09–082007–09–082007–09–092007–09–102007–09–112007–09–192007–09–15

10.0

9.59.0

19.0

9.5

13.010.5

8.0

19.0

7.07.5

21.0

5.0

10.515.0

7.57.5

14.523.0

11.011.0

10.010.510.0

3.02.92.75.82.94.03.22.45.82.12.36.41.53.24.62.32.34.47.03.43.43.03.23.0

444545354540434735494833544338484839324343444344

394342364341444536464329544142484742364642434644

404343364342444536454531514242484743384543394443

404343374244465037474532554342494944374744474948
Appendix 2. Results and computations by Landsat-satellite path for Michigan inland lakes, 2007–08, of measured and predicted Secchi-disk transpaIndex values for the area of interest, area of interest lake-average method, and the Gethist method.—Continued[SDT, Secchi-disk transparency; AOI, area of interest; TSI, Trophic State Index; Eq, equation; *, measurement not used owing to issue with placement]

Landsat satellite Measured SDT AOI TSI AOI lak

Path Row Lake Name County Acres Sampled SDT ft SDT m TSI Eq1 Eq2 Eq1 

222222222222222222222222222222222222222222222222

293129312931293129312931293129312931293129312931293129312931293129312931293129312931293129312931

Puterbaugh LakeTwin Lake (north)Twin Lake (south)George LakeWindover LakeMargrethe LakeBostwick LakeFreska LakeReeds LakeBig Star LakeGlen LakeHamlin LakeBlue LakeCanadian LakesHorsehead LakeMecosta LakeWest Canadian LakeSapphire LakeBaldwin LakeClifford LakeBills LakeEmerald LakeFremont LakeHess Lake

CassCassCassClareClareCrawfordKentKentKentLakeLeelanauMasonMecostaMecostaMecostaMecostaMescodaMissaukeeMontcalmMontcalmNewaygoNewaygoNewaygoNewaygo

446143

129

68

1922

213

59

270890

48714622

229321443312133246

62

195200

77

825765

2007–09–122007–09–142007–09–082007–09–092007–09–082007–09–162007–09–132007–09–112007–09–192007–09–112007–09–122007–09–142007–09–152007–09–202007–09–132007–09–132007–09–202007–09–102007–09–132007–09–152007–09–142007–09–132007–09–122007–09–11

7.09.5

10.5

11.0

12.012.0

5.5

10.0

4.0

11.0

14.513.0

11.011.0

9.5

10.012.0

7.59.09.0

10.5

11.5

8.02.5

2.12.93.23.43.73.71.73.01.23.44.44.03.43.42.93.03.72.32.72.73.23.52.40.8

494543434141534457433940434345444148454543424764

504144464746484354443443424346464546444543445162

474041474647494453463446434548474747454642445057

504549455049484455433644464549494648454646455162
Appendix 2. Results and computations by Landsat-satellite path for Michigan inland lakes, 2007–08, of measured and predicted Secchi-disk transpaIndex values for the area of interest, area of interest lake-average method, and the Gethist method.—Continued [SDT, Secchi-disk transparency; AOI, area of interest; TSI, Trophic State Index; Eq, equation; *, measurement not used owing to issue with placement] Landsat satellite Measured SDT AOI TSI AOI lak

Path Row Lake Name County Acres Sampled SDT ft SDT m TSI Eq1 Eq2 Eq1 

222222222222222222222222222222222223232323232323

29312931293129312931293129312931293129312931293129312931293129312931

28282828282828

Kimball LakePickerel LakeSylvan LakeRobinson LakeStony LakeHicks LakeViking LakeCrockery LakeCorey LakeCedar LakeCrooked LakeCrooked Lake LittleGravel LakeSchool Section LakeSilver LakePleasant LakeStone Ledge LakeDeer LakeFish LakeDana LakeDeep LakeRound LakeBass LakeEngman Lake

NewaygoNewaygoNewaygoOceanaOceanaOsceolaOtsegoOttawaSt. JosephVan BurenVan BurenVan BurenVan BurenVan BurenVan BurenWexfordWexfordAlgerAlgerDeltaDeltaDeltaMarquetteMarquette

147308102134287160

36

104599275

117114

297

7950

130

83

266134

8539

482

7648

2007–09–152007–09–152007–09–132007–09–162007–09–142007–09–092007–09–202007–09–112007–09–112007–09–152007–09–092007–09–122007–09–132007–09–132007–09–132007–09–132007–09–142007–08–072007–08–072007–08–072007–08–072007–08–072007–08–062007–08–06

6.5

12.0

11.0

9.58.05.54.07.0

14.516.5

11.0

13.0

9.09.0

10.0

8.59.0

11.0

14.5

9.5

14.515.520.010.0

2.03.73.42.92.41.71.22.14.45.03.44.02.72.73.02.62.73.44.42.94.44.76.13.0

504143454753574939374340454544464543394539383444

484443454250514643404137434841464544384540393741

484542474351494542404037434741484544374540393741

474645464350514845444543444842464841414341423642
Appendix 2. Results and computations by Landsat-satellite path for Michigan inland lakes, 2007–08, of measured and predicted Secchi-disk transpaIndex values for the area of interest, area of interest lake-average method, and the Gethist method.—Continued[SDT, Secchi-disk transparency; AOI, area of interest; TSI, Trophic State Index; Eq, equation; *, measurement not used owing to issue with placement]

Landsat satellite Measured SDT AOI TSI AOI lak

Path Row Lake Name County Acres Sampled SDT ft SDT m TSI Eq1 Eq2 Eq1 

232323232323232324242424242424242424242424242424

2828282828282828

2728272827282728272827282728272827282728272827282728272827282728

Johnson LakeLittle Shag LakePike LakeShag LakeSporley LakeGrassy LakeMcKeever LakePetes LakeBass LakeCarney LakeHanbury LakeMary LakeGerald LakeOtter LakePike LakeRoland LakeSandy LakeTorch LakeLa Belle LacManganese LakeMedora LakeEngman LakeFish LakeGreenwood Reservoir

MarquetteMarquetteMarquetteMarquetteMarquetteSchoolcraftSchoolcraftSchoolcraftDickinsonDickinsonDickinsonDickinsonHoughtonHoughtonHoughtonHoughtonHoughtonHoughtonKeweenawKeweenawKeweenawMarquetteMarquetteMarquette

78

107

90

195

77

188147194

60

115

7885

356863

83

258101

24001205

56

690

48

151

1073

2007–08–062007–08–062007–08–062007–08–062007–08–062007–08–082007–08–082007–08–082008–07–312008–07–312008–07–312008–07–312008–07–292008–07–302008–07–292008–07–292008–07–292008–07–302008–07–302008–07–302008–07–302008–07–302008–07–282008–07–28

18.014.014.013.514.0

11.0

13.017.016.4

11.1

18.314.8

11.811.5

7.9

11.3

7.0

10.0

8.09.59.0

10.0

7.96.8

5.54.34.34.14.33.44.05.25.03.45.64.53.63.52.43.42.13.02.42.92.73.02.42.1

353939403943403637423538424247424944474545444749

36373939384140373839

*

40454448444743464445454746

36374039384239373839

*

39444548444743464345454746

38384141394342363839

*

40464546454645464645454746
Appendix 2. Results and computations by Landsat-satellite path for Michigan inland lakes, 2007–08, of measured and predicted Secchi-disk transpaIndex values for the area of interest, area of interest lake-average method, and the Gethist method.—Continued [SDT, Secchi-disk transparency; AOI, area of interest; TSI, Trophic State Index; Eq, equation; *, measurement not used owing to issue with placement] Landsat satellite Measured SDT AOI TSI AOI lak

Path Row Lake Name County Acres Sampled SDT ft SDT m TSI Eq1 Eq2 Eq1 

24242525252525252525252525252525

27282728

2828282828282828282828282828

Lake IndependenceLake MichigammeAllen LakeBeatons LakeCisco LakeDuck LakeImp LakeLac Vieux DesertLittle Duck LakeMarion LakeThousand Island LakeGolden LakeHagerman LakeOttawa LakeSmoky LakeLake Gogebic

MarquetteMarquetteGogebicGogebicGogebicGogebicGogebicGogebicGogebicGogebicGogebicIronIronIronIronOntonagon

20414292

78

324567612

91

4370

44

297

1009

274565532596

13127

2008–07–282008–07–292008–08–062008–08–052008–08–052008–08–062008–08–062008–08–062008–08–062008–08–062008–08–062008–08–042008–08–042008–08–042008–08–042008–08–05

10.5

8.8

14.522.0

5.5

11.5

24.0

7.5

19.012.012.522.017.020.514.5

8.0

3.22.74.46.71.73.57.32.35.83.73.86.75.26.24.42.4

43463933534231483541413336343947

44463533494428473941393338394143

44463934474628424039403340403746

45463332443833423532383842414150

Fuller and others— Predicting Lake Trophic State for Michigan Inland Lakes, 2003–05 and 2007–08—Scientific Investigations Report 2011–5007