U.S. Department of the Interior

U.S. Geological Survey

Fact Sheet 2007-3022

August 2007 Printed on recycled paper

Introduction

The State of Michigan has more than 11,000 inland lakes; 

approximately 3,500 of these lakes are greater than 25 acres. The 

USGS, in cooperation with the Michigan Department of Environmental Quality (MDEQ), has been monitoring the quality of 

inland lakes in Michigan through the Lake Water Quality Assessment monitoring program. Approximately 100 inland lakes will 

be sampled per year from 2001 to 2015. Volunteers coordinated 

by MDEQ started sampling lakes in 1974, and continue to sample 

to date approximately 250 inland lakes each year through the 

Cooperative Lakes Monitoring Program (CLMP), Michigan’s volunteer lakes monitoring program. Despite this sampling effort, it 

is still impossible to physically collect the necessary water-quality 

measurements for all 3,500 Michigan inland lakes. Therefore, a 

technique was used by USGS, modeled after Olmanson and others (2001), in cooperation with MDEQ that uses satellite remote 

sensing to predict water quality in unsampled inland lakes greater 

than 25 acres.

Water-quality characteristics that are associated with water 

clarity can be predicted for Michigan inland lakes by relating 

sampled measurements of secchi-disk transparency (SDT) and 

chlorophyll a concentrations (Chl-a), to satellite imagery. The 

trophic state index (TSI) which is an indicator of the biological 

productivity can be calculated based on SDT measurements, Chla concentrations, and total phosphorus (TP) concentrations measured near the lake’s surface. Through this process, unsampled 

inland lakes within the fourteen Landsat satellite scenes encompassing Michigan can be translated into estimated TSI from either 

predicted SDT or Chl-a (fig. 1). 

What is the Trophic State Index?

Carlson (1977) developed a numerical trophic state index 

(TSI) for lakes which can be related to the traditional trophic 

status classification scheme that groups lakes into basic classes 

of oligotrophic (TSI value < 38), mesotrophic (TSI value 38-48), 

eutrophic (TSI value 49-61), and hypereutrophic (TSI value > 

61). Carlson’s TSI was developed for use with lakes that have 

few rooted aquatic plants and only small amounts of inorganic 

suspended matter. Carlson’s TSI can be calculataed from SDT, 

Chl-a, and phosphorus. Water bodies that are oligotrophic have 

high SDT values (high water clarity), and those that are eutrophic 

have low SDT values (low water clarity) (Bukata and others, 

1995). Eutrophic lakes have higher Chl-a concentrations than 

oligotrophic lakes. Of the three measures to compute TSI, SDT 

and Chl-a concentration are quantifiable by means of remote 

sensing techniques; and more specifically, with satellite imagery 

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

others, 2000; Giardino and others, 2001; Kloiber and others, 2002; 

Fuller and others, 2004). Even though table 1 is arranged into 

distinct categories, TSI is a continuum classification scheme with 

boundaries that overlap.

What is Secchi-Disk Transparency?

Water clarity, or transparency, is commonly measured with a 

Secchi disk. The clarity of lake water is reduced by the presence 

of suspended sediment and Marl (CaCO3), bits of organic matter, 

free-floating algae, and zooplankton. Algae are often the dominant influence on transparency of lake water. Therefore, SDT 

is related to the free-floating algae concentration or the primary 

biological productivity of a lake and is used as a trophic state 

indicator. 

 SDT is a low-cost and effective measurement of water 

clarity. A Secchi disk, a 20 centimeter (8 inch) diameter metal 

or weighted plastic disk normally black and white, is attached to 

a measured line and lowered into a lake until it can no longer be 

seen. The depth at which it disappears is known as the SDT. The 

Predicting Water Quality by Relating Secchi-Disk 

Transparency and Chlorophyll a Measurements to Landsat 

Satellite Imagery for Michigan Inland Lakes, 2001–2006

In cooperation with the Michigan Department of Environmental Quality

PATH 25

PATH 24

PATH 23 PATH 22 PATH 21

PATH 20

ROW 29

ROW 30

ROW 31

ROW 28

ROW 27

Lower

Peninsula

Upper

Peninsula

Figure 1. Landsat satellite-scene coverage identified by flight 

path and row number for Michigan.
appearance of Secchi disks in three lakes with differing water 

quality is shown in figure 2.

What is Chlorophyll a?

Chlorophyll a is a photosynthetic pigment that is found in 

all plants, including algae (Wetzel, 2001). Its concentration is 

commonly used to represent the density of the algal population 

in a lake. Free-floating algae (phytoplankton) are the primary 

food producers in the food chain. Moderate concentration of 

algae is necessary for a biologically productive, healthy lake; 

however, excessive concentrations (algal blooms) are undesirable 

and can have profound effects on the water quality. The accelerated production of algae in a lake is generally the result of excess 

nutrients– in particular, phosphorus. The depth at which light can 

penetrate a lake diminishes with more algae in a lake. Thus the 

greater the value of chl-a and phosphorus, the lower the value of 

SDT. This is how water clarity (SDT), algal productivity (estimated from Chl-a), and nutrients (mainly phosphorus) are interrelated in determining water quality and estimating trophic state 

conditions.

are taken every 7 days. For example, path 22 is taken 7 days after 

path 21, and path 20 is taken 7 days before path 21. 

 The fourteen satellite scenes encompassing Michigan are 

referenced by both a path number and a row number (fig. 1). 

Since satellite data is translated into estimated TSI from predicted 

SDT or Chl-a by satellite scene, and all the paths for Michigan are 

not available for the same day, statewide water-quality predictions are available over a 3-month period July through September. 

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). 

Landsat satellites record a value of 0-255 for each 30 x 30 

meter (900 square meters) area, termed a cell, in wavelength 

ranges called bands. Bands 1, 2, 3 (visible spectrum of blue, 

green, and red, respectively), and 7 (middle infrared) are used in 

the project. All four bands have cell sizes of 30 meters, so 900 

square meters of earth are represented in one cell by one value 

for each band. Water-quality predictions can be made only for 

lakes greater than 25 acres (approximately 101,200 square meters) 

because of the cell size, so that the number of cells is adequate to 

produce an accurate predictive model.

Cloud cover is a factor in the quality of Landsat data, and 

satellite scenes are selected for model development only if cloud 

cover is less than 10 percent. Also, because of model requirements, water-quality predictions can not be made for an individual 

inland lake if less than 25 acres is visible because of cloud cover. 

Relating Field Measurements of Water Quality to 

Satellite Imagery

Measurements of SDT or Chl-a from approximately 20 

inland lakes are needed for each of the fourteen satellite scenes 

encompassing Michigan. These measurements are then related 

to a satellite scene to determine a regression equation specific to 

that satellite scene. Each year, the model is recalibrated by satellite scene with corresponding water-quality measurements. The 

regression equation can then be used to predict water-quality characteristics for unsampled inland lakes within each satellite scene. 

Making Field Measurements for Secchi-Disk 

Transparency and Chlorophyll a

Measurements of SDT and Chl-a were used in the project 

that were within a range of 7 days before or after the satellite 

acquisition dates to produce an accurate predictive model, with 

best results obtained from measurements made within a range of 

3 days. Approximately 20 measurements were used per satellite scene, and were made at the deepest point in the lake so that 

reflectance from the bottom of the lake did not affect the measurements. The exact locations of the measurements used were noted 

during sampling, either by using a GPS unit to record latitude and 

longitude coordinates or by clearly marking locations on a map 

during sampling and digitized later to determine their coordinates. 

SDT values were omitted if they were more than two-thirds the 

lake depth (which occurs mostly in shallow lakes), because the 

satellite could also be sensing the lake bottom.

Relating Field Measurements to Satellite Imagery

Areas of interest (AOIs) containing approximately nine 

cells were established around each measurement, and the average 

value (ranging from 0-255) for each band from the satellite scene 

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

found to produce more accurate predicted SDT and Chl-a values 

(Olmanson and others, 2001). Average band values for each meaHow Does Landsat Satellite Imagery Fit In?

Availability of satellite imagery, seasonality, day of month, 

atmospheric conditions, and the size of the inland lakes are all 

factors that are taken into consideration, and effect the ability to 

translate satellite imagery into estimated TSI from either predicted 

SDT or Chl-a. 

Landsat 5 Thematic Mapper (TM) and Landsat 7 Enhanced 

TM plus (data from both satellites were used in the project) record 

data by paths (National Aeronautics and Space Administration, 

2007). Each path has a 16-day repeat cycle, and adjacent paths 

Table 1. Lake trophic states and classification ranges for trophic 

state index, total phosphorus, Secchi-disk transparency, and 

cholorophyll a.

[Based on Michigan Department of Natural Resources (1982) and modified by 

the State of Michigan to account for regional characteristics. TSI, trophic state 

index; SDT, Secchi-disk transparency; Chl-a, chlorophyll a; TP, total phosphorus; ft, feet; mg/L, micrograms per liter]

Lake Trophic State Carlson

TSI

 SDT 

(ft)

Chl-a

(mg/L)

TP

(mg/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

Figure 2. Examples of Secchi disks and their appearance in water 

of decreasing transparency, from left to right, within various lakes 

in Minnesota. Photographs courtesy of Minnesota Pollution Control 

Agency.
surement were used in a statistical analysis program to determine 

the regression equation specific to each satellite scene. Regression equations are what translate the Landsat satellite scenes into 

predicted SDT and Chl-a values.

An Example of an AOI around a Secchi-disk measurement 

for Lake Lansing in Ingham County, Mich. (path 21 row 30), is 

shown in figure 3, and table 2 is the corresponding AOI information that would be used to produce the regression equation for 

that satellite scene. Approximately 20 measurements are used to 

produce the regression equation per satellite scene. The following 

equations were used to predict SDT and Chl-a: 

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

ln(Chl-a) = a(band2) + b(band3) + c(band7) + d (2)

In the equations, the natural log (ln) of SDT was calculated 

in units of meters, the ln of Chl-a was calculated in units of milligrams per liter, and band values ranged from 0 through 255. The 

letters a–d are parameters that are specific to the equations for 

each satellite scene.

areas within a lake that might need further examination. Predicted 

TSI values available by satellite scene from 2001 through 2006 

are shown in figure 6. Future plans are to have complete coverage for Michigan of predicted TSI values, available on a 2-year 

rotation. The TSI predictions are viewable on an Internet Map 

Server site (IMS) at: http://mi.water.usgs.gov/splan1/sp00301/

remotesensing.php under “IMS sites”. 

Predicting Trophic State Index for Unsampled Lakes 

From Field Measurements

Figure 4 is a graphical depiction of equation (1) where 

approximately 20 SDT measurements from 2003 are related to a 

2003 Landsat satellite scene path 21 row 29 located in the northern Lower Peninsula of Michigan (fig. 1). Figure 4 is showing the 

relation or best fit between 2003 SDT values and the corresponding satellite scene for that year. 

Predicted TSI values computed from predicted SDT or Chl-a

are available from 2001 through 2006. All predicted TSI values 

were based on SDT measurements except for 2004, when Chl-a

measurements were used for the TSI predictions in the Lower 

Peninsula (fig. 1). TSI predictions are available in a grid format 

that shows intra-lake variability (variability of 30-meter grid cell 

values within a lake) and by an average predicted TSI value by 

lake (fig. 5). Intralake variability can be useful for identifying 

Measured and Predicted Values of TSI Compare Well

Comparisons of data show that the predicted TSI values 

correlate well to the measured TSI values. An average from 2001 

through 2006 shows that 71 percent of the predicted TSI values 

were in the correct measured TSI classes of oligotrophic, mesotrophic, eutrophic, and hypereutrophic (as defined in table 1). 

Another examination of the results shows that 42 percent of the 

predicted TSI values were within 2 TSI units of the measured TSI, 

80 percent were within 5 TSI units, and 98 percent were within 10 

TSI units of the field measurements. The majority of the data is 

predicting to the correct class, and is also predicting close to the 

measured TSI value.

0.6 0.8 1.0 1.2 1.4 1.6 1.8

0.5 1.0 1.5 2.0

Fitted: Landsat 5 Thematic Mapper Bands 1, 2, and 3

natural log of (secchi-disk transparency in meters)

x = Band 1(0.1402) + Band 2(-0.0588) + Band 3(-0.3061) + -0.8009

0 0.25 0.5 MILES

0 0.25 0.5 KILOMETERS

Explanation

Trophic state index values

(Secchi-disk values in feet)

< 38 ( > 15)

38 - 48 (7.5 - 15)

49 - 61 (3 - 7.4)

> 61 ( < 3)

Figure 5. Predicted trophic state index and corresponding Secchidisk values for Lake Lansing in Ingham County, Mich. (lakewide 

average on the left, and intralake variability on the right).

Figure 4. Graph of the relation between 2003 Secchi-disk 

measurements and a 2003 Landsat 5 TM satellite scene path 21, row 

29; northern Lower Peninsula of Michigan.

Table 2. Area-of -interest (AOI) information averaged from nine cells 

surrounding a 2002 Secchi-disk transparency (SDT) measurement 

from a 2002 Landsat 5 TM satellite image of Lake Lansing, Mich.

Figure 3. Landsat 5 TM 

satellite scene of Lake 

Lansing, Ingham County, Mich. 

(path 21 row 30). Yellow dot 

indicates location of a 2003 

Secchi-disk transparency 

(SDT) measurement, and ring 

of black dots surrounding area 

of interest (AOI) consisting of 

nine cells.

Lake Name Band 1 Band 2 Band 3 SDT m ln(SDTm)

Lansing 64.77 41.38 30.46 3.05 1.11

[SDT, Secchi-disk transparency; m, meters; ln, natural log]
Predictions are Reliable and Economical

Michigan has more than 11,000 inland lakes with approximately 3,500 over 25 acres. It is economically and logistically 

impossible to physically collect the necessary water-quality 

measurements for all 3,500 inland lakes greater than 25 acres 

through volunteers with the CLMP or through the USGS. Remote 

sensing is an effective and economical tool to enhance the value 

of conventional sampling data by producing regression equations 

that translate satellite imagery into predicted TSI values from SDT 

or Chl-a for Michigan inland lakes greater than 25 acres (approximately 101,200 square meters) in size. 

By L.M. Fuller and R.J. Minnerick

References Cited

Bukata, R.P., Jerome, J.H., Kondratyev, K.Y., and Pozdnyakov, 

D.V., 1995, Optical properties and remote sensing of inland and 

coastal waters: Boca Raton, Fla., CRC Press, p. 214–216.

Carlson, R.E., 1977, A trophic state index for lakes: Limnology 

and Oceanography: v. 22, no. 2, p. 361–369.

Fuller, L.M., Aichele, S.S., and Minnerick, R.J., 2004, Predicting 

water quality by relating Secchi-disk transparency and chlorophyll a measurements to satellite imagery for Michigan inland 

lakes, August 2002: U.S. Geological Survery Scientific Investigations Report 2004–5086, 25 p.

Giardino, Claudia; Pepe, Monica; Brivio, P.A.; Ghezzi, Paolo; and 

Zilioli, Eugenio, 2001, Detecting chlorophyll, Secchi disk depth 

and surface temperature in a sub-alpine lake using Landsat imagery: Science of the Total Environment: v. 268, p. 19–29.

Kloiber, S.M., Anderle, T.H., Brezonik, P.L., Olmanson, L., Bauer, 

M.E. and Brown, D.A., 2000, Trophic state assessment of lakes 

in the Twin Cities (Minnesota, USA) region by satellite imagery: 

Archiv für Hydrobiologie, Special Issues, Advances in Limnology, v. 55, p. 137–151.

Kloiber, S.M., Brezonik, P.L., Olmanson, L.G., and Bauer, M.E., 

2002, A procedure for regional lake water clarity assessment 

using Landsat multispectral data: Remote Sensing of Environment: v. 82, p. 38–47.

Mayo, M., Gitelson A., Yacobi Y.Z., and Ben-Avraham Z., 1995, 

Chlorophyll distribution in Lake Kinneret determined from 

Landsat Thematic Mapper data: International Journal of Remote 

Sensing: v. 16, no. 1, p. 175–182. 

Michigan Department of Natural Resources, 1982, Michigan Inland 

Lake Project: Identification, Survey and Classification: U.S. 

Environmental Protection Agency Clean Lakes Agreement No. S 

005511-01 Final Project Report, September 1982.

National Aeronautics and Space Administration, 2007, The Landsat 

program: Accessed January 30, 2007, at http://landsat.gsfc.nasa.

gov/

Olmanson, L.G., Kloiber, S.M., Bauer, M.E., and Brezonik, P.L., 

2001, Image processing protocol for regional assessments of lake 

water quality: University of Minnesota,Water Resources Center 

and Remote Sensing Laboratory, Public Report Series no. 14, 

19 p.

Wetzel, R.G., 2001, Limnology—Lake and river ecosystems (3rd 

ed.): San Diego, Calif., Academic Press, 1,006 p.

Zilioli, E., and Brivio, P.A., 1997, The satellite derived optical 

information for the comparative assessment of lacustrine water 

quality: Science of the Total Environment, v. 196, p. 229–245.

For More Information

For more information on the remote sensing project, a report 

describing the process used for 2002 data is listed at http://pubs.

usgs.gov/sir/2004/5086/ and the Web site for the project, with a 

link to a website with the viewable Secchi-disk transparency and 

Chl-a predictions, can be found at http://mi.water.usgs.gov/splan1/

sp00301/remotesensing.php

Minnesota and Wisconsin have similar websites with viewable 

predictions accessible at: http://resac.gis.umn.edu/water/regional_

water_clarity/regional_water_clarity.htm

Additional information on the MDEQ and USGS inland lake 

water-quality sampling program can be found at http://pubs.usgs.

gov/fs/2004/3048/

Additional information on the Cooperative Lakes Monitoring Program can be found at http://www.michigan.gov/

deq/0,1607,7-135-3313_3686_3731---,00.html

Figure 6. Availability of predicted trophic state index values 

for Michigan, 2001–2006, based on relations of Secchi-disk 

transparency or chlorophyll a values to satellite data. Boxed 

boundaries are approximations of Landsat satellite scene locations 

by which trophic state index predictions were made.

0 50 100 KILOMETERS

0 50 100 MILES

2003

2004

Explanation

Predicted trophic state index values

from Secchi-disk measurements

Predicted trophic state index values

from chlorophyll a measurements

2005 2006

2001 2002