USGS

In cooperation with the Michigan Department of Environmental Quality

Scientific Investigations Report 2004–5086

Predicting Water Quality by Relating Secchi-Disk Transparency and Chlorophyll a Measurements to Satellite Imagery for Michigan Inland Lakes, August 2002

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

The PDF for the report is 17,590 MB


Table of Contents

Abstract

Introduction

Methods

Results

Summary and Conclusions

Acknowledgments

References Cited

Appendix A

Figures

Figure 1. Secchi-disk transparency and chlorophyll a sample locations, Mich...

Figure 2. Radiometric-correction (top of atmosphere) reflectance values com...

Figure 3. Predicted and actual secchi-disk transparency for (A) path 21, ro...

Figure 4. Computed trophic state index from predicted secchi-disk transpare...

Figure 5. Predicted and actual chlorophyll a for path 21, row 29.

Figure 6. Computed trophic state index from predicted chlorophyll a for Lan...

Tables

Table 1. Lake trophic states and classification ranges for trophic state...

Table 2. MODTRAN4 atmospheric-correction parameters and input.

Table 3. R2 values and Fisher's Transformation significance tests used to...

Table 4. Stepwise regression trials and R2 values to predict trophic state...


Conversion Factors and Abbreviations

Multiply By To obtain
Length
foot (ft) 0.3048 meter (m)
mile (mi) 1.609 kilometer (km)
kilometer (km) 0.6214 mile (mi)
Area
acre 0.001562 square mile (mi2)
acre 0.4047 hectare (ha)
micrometer (µm) 0.001 millimeter (mm)
Concentration
micrograms per liter (µg/L) 0.001 milligrams per liter (mg/L)

Abbreviated water-quality units used in this report: Chemical concentrations for Chlorophyll a and phosphorus are given in micrograms per liter (µg/L). Micrograms per liter is a unit expressing the concentration of chemical constituents in solution as a weight (micrograms) of solute per unit volume (liter) of water.

Miscellaneous Abbreviations

USGS
U.S. Geological Survey
MDEQ
Michigan Department of Environmental Quality
LWQA
Lake Water Quality Assessment program
CLMP
Cooperative Lakes Monitoring Program
SDT
Secchi-disk transparency
Chl-a
Chlorophyll a
AOI
Area of Interest

Abstract

Inland lakes are an important economic and environmental resource for Michigan. The U.S. Geological Survey and the Michigan Department of Environmental Quality have been cooperatively monitoring the quality of selected lakes in Michigan through the Lake Water Quality Assessment program. Through this program, approximately 730 of Michigan's 11,000 inland lakes will be monitored once during this 15-year study. Targeted lakes will be sampled during spring turnover and again in late summer to characterize water quality. Because more extensive and more frequent sampling is not economically feasible in the Lake Water Quality Assessment program, the U.S. Geological Survey and Michigan Department of Environmental Quality investigate the use of satellite imagery as a means of estimating water quality in unsampled lakes. Satellite imagery has been successfully used in Minnesota, Wisconsin, and elsewhere to compute the trophic state of inland lakes from predicted secchi-disk measurements. Previous attempts of this kind in Michigan resulted in a poorer fit between observed and predicted data than was found for Minnesota or Wisconsin. This study tested whether estimates could be improved by using atmospherically corrected satellite imagery, whether a more appropriate regression model could be obtained for Michigan, and whether chlorophyll a concentrations could be reliably predicted from satellite imagery in order to compute trophic state of inland lakes. Although the atmospheric-correction did not significantly improve estimates of lake-water quality, a new regression equation was identified that consistently yielded better results than an equation obtained from the literature. A stepwise regression was used to determine an equation that accurately predicts chlorophyll a concentrations in northern Lower Michigan.

Introduction

The State of Michigan has more than 11,000 inland lakes; approximately 3,500 of these lakes are greater than 25 acres in size. Nearly all of these lakes greater than 25 acres have developed communities with permanent residences or vacation homes. The general public has access to launches or beaches at about 1,300 lakes in Michigan. Recreational value, property values, and ecological value are all 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 $15 billion of economic activity each year (Stynes, 2002). Thus, inland lakes are important economic and ecological resources to Michigan.

The U.S. Geological Survey (USGS) and the Michigan Department of Environmental Quality (MDEQ) 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 will sample approximately 730 lakes over 25 acres in size with public access during a 15-year period. The 730 lakes are grouped into 45 major watershed management units. In a given year, a set of 7 to 10 of the 45 major watershed management units is chosen for sampling and lakes to be sampled are randomly selected from this set. After 5 years, at least some lakes in each of the 45 major watershed management units will have been sampled. This 5-year rotation will continue until year 2015, when all targeted 730 lakes have been sampled once. In addition, each year the MDEQ will provide data from their Cooperative Lakes Monitoring Program (CLMP), which is a volunteer network monitoring more than 200 lakes. Data from those two sampling networks are 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 their recreational use, habitat and species diversity, and the economic return from the tourism industry. The USGS and the MDEQ 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 help protect and manage the quality in all of Michigan's inland lakes.

Satellite imagery has been successfully used in Minnesota (Olmanson and others, 2001), Wisconsin (Batzli, 2003), and elsewhere (Baban, 1993; Dekker and Peters, 1993; Mayo and others 1995; Giardino and others, 2001) to estimate water quality for unsampled inland lakes. In previous studies in Michigan (Nelson and others, 2002; Wianwang, 2002) researchers attempted to use existing models for relating satellite imagery to specific water-quality variables; however, they were unable to obtain as high a coefficient of determination (R2), which indicates the strength of a statistical relation, as previous studies in Minnesota and Wisconsin. A better method to predict trophic characteristics from satellite imagery would increase the knowledge every year about more of Michigan's inland lakes.

Purpose and Scope

The purpose of this report is to describe the methods and techniques used to develop estimates of Michigan lake-water quality on the basis of satellite images. Specifically, this report presents a brief overview of the conceptual basis for predicting trophic state on the basis of satellite images, describes methods used to develop a new alternative regression model for predicting secchi-disk transparency, and offers a new regression equation for predicting chlorophyll a concentrations in northern Lower Michigan. These two measures can further be used to estimate the trophic state of Michigan inland lakes.

Background

Naumann (1919) proposed a classification of lake-water quality ranging from oligotrophic (low phytoplankton populations and low primary productivity) to eutrophic (high phytoplankton populations and high primary productivity). Carlson (1977) proposed to quantify the trophic state by using a Trophic State Index (TSI), which can be used to group lakes into basic classes of oligotrophic, mesotrophic, eutrophic, and hypereutrophic. 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).

TP is measured directly by sampling and chemical analysis. 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 can no longer 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. The formulas for computing TSI values are (Carlson, 1977):


Equations 1,2, and 3


The range of TSI values and how each measure is classified into oligotrophic, mesotrophic, eutrophic, and hypereutrophic is listed in table 1.

Table 1. Lake trophic states and classification ranges for trophic state index, total phosphorus, secchi-disk transparency, and chlorophyll a.

[Based on Michigan Department of Environmental Quality report (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; µg/L, micrograms per liter]

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

Typically, computing TSI values for a single lake using all three formulas should yield similar results. Increasing the phosphorus concentration generally results in increased phytoplankton concentration, which results in reduced water clarity. Yet at specific times of the year, results from the three formulas may not be congruous because of phosphorus nutrient uptake by macrophytes. Therefore, substantial amounts of macrophytes in a lake may alter the relation of the three TSI values. Of the three measures, SDT and Chl-a concentration have been quantified by use of satellite imagery techniques (Mayo and others, 1995; Zilioli and Brivio, 1997; Cox and others, 1998; Kloiber and others, 2000; Giardino and others, 2001; Kloiber and others, 2002).

Satellites have been used to predict water characteristics since the 1970s. For example, the National Aeronautics Space Administration (NASA) Earth Resources Technology Satellite (ERTS-1) was used to determine an algal bloom in Lake Erie in 1972 (Strong, 1974). NASA's Landsat satellite series improved the spatial, spectral, and radiometrical resolutions allowing more water-quality parameters to be studied. The idea to relate SDT to satellite imagery started in the late 1970s and studies involving Chl-a, turbidity, and other water-quality characteristics soon followed (Scarpace and others, 1979; Lillesand and others, 1983; Verdin, 1985; Lathrop and Lillesand, 1986; Dekker and Peters, 1993; Mayo and others, 1995; Zilioli and Brivio, 1997). Landsat bands 1 through 4 signifying the visible and near infrared portions of the electromagnetic spectrum, were found to correlate well with water-quality characteristics (Lathrop and Lillesand, 1986). However, Lathrop (1992) found it difficult to use the same regression equation to characterize the water quality of different lakes. Recent studies found that, with improved methods, it was possible to predict water quality for unsampled lakes by use of regression equations relating existing measurements to remotely sensed data (Pulliainen and others, 2001; Kloiber and others, 2002; Thiemann and Kaufmann, 2002). These most recent studies form the basis for this project.

Imagery used in this study was collected by the Landsat 7 Enhanced Thematic Mapper Plus (ETM+) satellite launched in 1999 by NASA. The satellite orbits at an altitude of approximately 705 km with a sun-synchronous 98-degree inclination and a descending equatorial crossing time of 10:00 a.m. (Williams, 2003). Every 16 days, the satellite will repeat coverage for each scene coinciding with the Landsat Worldwide Reference System (WRS), which records satellite scenes into a grid reference system made up of 233 paths and 248 rows. The Landsat 7 ETM+ sensor collects information in nine bands, distinct portions of the electromagnetic spectrum. Bands 1, 2, 3, 4, and 8 are sensed within a spectral range between 0.4 and 1 µm. Bands 1, 2, and 3 correspond to the visible spectrum of blue, green, and red, and band 4 is infrared; together, these bands span the spectral range of 0.45 to 0.90 µm. Bands 5 and 7 are short-wavelength infrared bands sensed within a spectral range between 1 and 3 µm. Bands 6a and 6b are thermal long wavelengths sensed within a spectral range between 8 and 12 µm. Band 8 is the panchromatic band that combines bands 2, 3, and 4 with a spectral range of 0.52 to 0.90 µm (Williams, 2003). Data are reported in digital numbers as 8-bit integers, ranging from 1 to 256.

Several distortion factors affect satellite imagery. These factors include geometric distortions that are the result of small imprecisions in maneuvering the sensor; radiometric distortions that arise from small differences in the calibration of the sensor and geometry of the earth, sun, and satellite; and atmospheric distortions that arise from scattering of light by moisture and particulates in the atmosphere. However, procedures have been developed to help correct for these factors. Geometric and radiometric corrections can be made with little or no field data. However, most studies of this scope suggest that the imagery should be geometrically, radiometrically, and atmospherically corrected (Brivio and others, 2001; Zilioli and Brivio, 1997; Kloiber and others, 2002).

A variety of equations relating satellite imagery to STD have been tested in different settings and with different sensors. Researchers that use imagery from the Landsat 7 ETM+ satellite (Kloiber and others, 2002) have generally used the following equation:


Equation 4

The variables a, b, and c are empirically derived coefficients from the regression equation.

Nelson and others (2002) used raw digital numbers from the images and the regression equation identified in Kloiber and others (2002) to estimate SDT for lakes in Lower Michigan. Kloiber and others (2002) reported predictions with R2 values between 0.72 and 0.93. Nelson and others (2002) achieved an R2 of only 0.43 for Landsat ETM+ scenes in path 21, rows 29, 30, and 31. Wiangwang (2002) used the same imagery and field data as Nelson and others (2002) but radiometrically corrected the images before determining regression equations. This type of correction is termed "Top of Atmosphere" (TOA) reflectance because, although it accounts for differences in illumination angle and sensor performance, it does not adjust for haze or diffusion within the atmosphere. The R2 value using SDT and Landsat 7 ETM+ TOA corrected imagery for path 21, rows 29, 30, and 31 was 0.558 (Wiangwong, 2002). This result suggests that a full atmospheric-correction of the imagery could in theory further improve the R2 values. The combination of all of these techniques in the same case study should improve the regression equations, and thus lead to better methodology to estimate water quality from satellite imagery.

Study Area

The study area was determined by the location of LWQA sampling planned for the 2002 water year (the 2002 water year was a portion of the inland lakes chosen to be sampled from 10 out of the 45 basins in Michigan). Most measurements fell within five Landsat 7 ETM+ satellite scenes covering the majority of Lower Michigan. The locations of the satellite scenes and the lakes with collected SDT measurements within a window of plus or minus 7 days of the imagery acquisition, are shown in figure 1.


Secchi-disk transparency and chlorophyll-a sample locations

Figure 1. Secchi-disk transparency and chlorophyll a sample locations, Michigan, August 2002.


Methods

The general process to predict SDT and Chl-a measurements from satellite imagery involves several steps. First, field data must be obtained and digitized. Second, cloud-free satellite imagery from approximately the same date as the field data collection must be obtained. Third, the imagery must be corrected to compensate for geometric, radiometric, and atmospheric distortions in the imagery. Fourth, the field data must be compared to the imagery through the creation of Areas of Interest (AOI) within the satellite image. Fifth, a regression model must be developed for each scene to relate the field data to the spectral data collected in each AOI. Finally, the regression equation must be applied to all lakes over 25 acres in the satellite scene, to predict the water-quality characteristics at unmeasured locations.

Field Data Collection and Preprocessing

USGS scientists and community volunteers from the CLMP routinely measure SDT in various lakes in Michigan. A secchi disk is a common tool for measuring the overall clarity of water. The Secchi disk is an 8-in. diameter circular disk painted black and white in alternating quadrants. The disk is lowered into the water, and the depth at which the disk is no longer visible is called the secchi depth. Chl-a, TP, several forms of nitrogen, and major ions are also measured at USGS sample sites. Samples from both the CLMP and USGS were used from the months of August and September 2002. This late-summer index period, when a lake is at the maximum biological productivity, was found to be the best period for relating SDT and Chl-a samples to satellite imagery (Kloiber and others, 2000).

USGS measurements were referenced by coordinates obtained from the Global Positioning System (GPS) and were used to create a shapefile. A shapefile is the file format ArcGIS software uses to store the location, shape, and attribute information. The SDT measurements from CLMP were recorded on paper and did not include precise coordinates for the measurements; however, a bathymetric map for each lake marked in the approximate location for each measurement. With this information, another shapefile was made by manually digitizing the correct location for all data within the lakes.

Volunteer SDT measurements have been studied and proven to be comparable with those made by professionals (Canfield and others, 2002; Obrecht and others, 1998). However, careful consideration was involved in choosing which CLMP SDT measurements were used in this study. Only measurements that were clearly marked on attached bathymetric maps were digitized. Some volunteer data were excluded where multiple measurements were made in a single lake (only one measurement per lake was chosen within the deepest basin) and when the location of measurements could not be determined from the published bathymetric maps.

Only measurements collected within 7 days of an image acquisition date were used. This restriction was shown to produce the best results in predictive SDT models (Kloiber and others, 2002). The final exclusions for all measurements were dependent upon the satellite imagery. Measurements when clouds or cloud shadows covered the lake or measurement location were excluded. Clouds and shadows are limiting factors and are the reason imagery should be chosen on clear satellite overpass days. (For a summary of sample numbers per scene refer to table 4.)

Satellite Imagery Acquisition and Preprocessing

Five Landsat 7 ETM+ scenes were purchased from the Tropical Rain Forest Information Center, a member of NASA Federation of Earth Science Information Partners at the Center for Global Change and Earth Observations, Michigan State University. The scenes from path 20, rows 30 and 31, and path 21, rows 29, 30, and 31 were chosen because they had minimal cloud cover and were acquired closest to the dates when the measurements were collected. For reference, see figure 1, which depicts satellite scene locations with the placement of SDT and Chl-a measurements.

The data arrived with a geometric systematic correction, which helped ensure that the image cells would correspond to the data-collection points as closely as possible. The systematic correction refers to the type of geometric correction. "The end result is a geometrically rectified product free from distortions related to the sensor (e.g. jitter, view angle effects), satellite (e.g. attitude deviations from nominal), and earth (e.g. rotation, curvature)" (National Aeronautics Space Administration, 2003). However, the geometric correction did not use ground-control points to ensure complete geodetic accuracy, and NASA only claimed residual error to 250 m in flat terrain at sea level. When each image was compared with the Michigan transportation framework developed by the Michigan Center for Geographic Information, however, it was found to be accurate to within 2 cells, or about 60 m.

The satellite imagery was also radiometrically corrected by use of a radiative transfer model. Radiometric corrections are needed because the brightness of each pixel in a satellite image is "affected by sun angle, atmospheric interference, changes in detector response, and numerous other factors" (Kloiber and others, 2002). The atmospheric-correction method used was MODTRAN4, released by the Air Force Research Lab, Space Vehicles Directorate, in March 1999. This model is an atmospheric radiative transfer code and algorithm (Hoke, 1999).

Atmospheric-Correction

To test whether atmospherically correcting the imagery would achieve better fit regression equations, path 21, rows 29, 30, and 31 were atmospherically corrected. The atmospheric correction model MODTRAN4 (Hoke, 1999) was used. Each satellite scene was run seven times through the model, keeping all parameters constant for each scene except the surface percent reflectance, which started at 0.1 and increased to 0.7. The different surface percent reflectances were used to construct regression equations that accounted for atmospheric scattering of both incoming solar radiation and outgoing reflected radiation. The results were equations describing the relation between reflected radiation and radiation measured at the sensor. These equations were then applied to their corresponding bands to atmospherically correct the imagery. The inputs are listed in table 2. The output slope and intercept coefficients for each band were used in an Erdas IMAGINE model (Erdas Inc, 2001) to build the equations to compute atmospherically corrected images. The equations take into account that shorter wavelengths, such as band 1, scatter more than longer wavelengths, such as band 5. The values for all bands generally increase with this correction, but band 1 shows the most increase and band 5, the least. Typical change between the TOA reflectance values and the resulting atmospheric-correction values for Lake Lansing in Ingham County are shown in figure 2.

Table 2. MODTRAN4 atmospheric-correction parameters and input.

[km, kilometers]

Parameter Input
Surface percent reflectance 0.1 to 0.7
Atmospheric model Midlatitude summer
Aerosol model Rural extinction (default visibility = 23 km)
Season Spring-summer
Visibility 23 km
Day of year Dependent upon satellite scene
Latitude and longitude Varied depending on center of satellite scene
Greenwich mean time of image acquisition 1430

reflectance values compared to atmospheric-correction values

Figure 2. Radiometric-correction (top of atmosphere) reflectance values compared to atmospheric-correction values, Lake Lansing, Ingham County, Mich.


Relating Field Data to Satellite Imagery

Area of Interest Creation

The six shapefiles that were created corresponding to the SDT and Chl-a measurements for each scene were opened on top of the appropriate satellite scene in Erdas IMAGINE. Areas of Interest (AOIs) were digitized around the SDT measurements for five scenes, and Chl-a measurements for one scene. An area was drawn around each measurement to include pixels surrounding the measurements to help smooth radiometric noise. The AOI sizes depended on the size of the lake but were between the minimum of 8 pixels and the maximum of 1,000 pixels set by Olmanson and others (2001). The smallest AOI was 8 pixels, the mean was 12 pixels, and the maximum was 33 pixels.

Once all the AOIs were drawn around measurements within a satellite scene, each one was added to the signature file and the minimum, maximum, standard deviation, and mean value for each band within the AOI was computed. These results were then exported into a datafile format for further calculation. Results for the measurement values within the corresponding AOIs can be found in Appendix A.

Water-Only Imagery

A few steps were performed in Erdas IMAGINE to extract pixels in each image that would correspond to an inland lake greater than 25 acres. First, an unsupervised classification identified the water pixels (30-m cells). Next, the pixels were grouped into contiguous bodies of water to identify the inland lakes that were greater than 25 acres or 125 pixels. Finally, the pixels that corresponded to an inland lake greater than 25 acres were coded to a value of 1, with all other pixels coded to a no-data value to complete the water-only images.

Regression Equations and Tests of Significance for Secchi-Disk Transparency

In preparation for regression analysis, the band1/band3 ratio, the natural log of SDT (in meters) were computed. The data were then transferred into S-Plus 2000 (Data Analysis Products Division, 1999) for multiple regression calculations based on scene and type of measurement. (The combinations used in the regression equations are listed in table 3).

Table 3. R2 values and Fisher's Transformation significance tests used to compute trophic state index for Michigan's inland lakes from predicted secchi-disk transparency.

[ln, natural log; ETM+, Enhanced Thematic Mapper Plus; TOA, Radiometric-correction values of Top of Atmosphere Reflectance; ATM, Atmospheric-Correction; R2, R Squared; Eq, equation; ☐, Not tested]

Equation 1        Independent variable: ln (secchi depth in meters)
Secchi-disk transparency        Dependent variables: band 1/band 3, and band 1
Landsat 7 ETM+ scenes        Samples TOA R2 ATM R2
path 20, row 30        15 0.5075
path 20, row 31        13 .3003
path 21, row 29        28 .6640 0.6737
path 21, row 30        29 .7995 .7995
path 21, row 31        25 .6014 .6072
Equation 2        Independent variable: ln (secchi depth in meters)
Secchi-disk transparency        Dependent variables: band 1, band 2, band 3
Landsat 7 ETM+ scenes        Samples TOA R2 ATM R2
path 20, row 30        15 0.7190
path 20, row 31        13 .6659
path 21, row 29        28 .7824 0.7875
path 21, row 30        29 .7964 .7964
path 21, row 31        25 .6058 .6101
Fisher's Transformation: R2 Equation 1 and Equation 2, R2 TOA and ATM ( >1.96 = significant)
Secchi-disk transparency        Samples Eq1 & Eq2 TOA Eq1 & Eq2 ATM Eq 1 TOA & ATM Eq 2 TOA & ATM
Landsat 7 ETM+ scenes       
path 20, row 30        15 1.199
path 20, row 31        13 1.637
path 21, row 29        28 1.233 1.212 0.065 0.086
path 21, row 30        29 .043 .043 .000 .000
path 21, row 31        25 .032 .022 .032 .043

The equation developed by Kloiber and others (2000):


Equation 5


was applied to each TOA and atmospherically corrected scene. The variables a, b, and c were derived coefficients from the regression equation. In an effort to improve the goodness of fit for the model, various combinations of bands were tested. For the Kloiber (2000) equation, TOA and atmospherically corrected R2 values were compared. A new, alternative equation also was developed during the project. For the new alternative equation,


Equation 6


TOA and atmospherically corrected R2 values were compared.

To test whether there was a statistically significant difference between the R2 values, Fisher's Transformation was used:


Equation 7


In the equation, r1 and r2 represent the two R2 values that were being tested, ln refers to base e and n refers to the number of samples. The results of Fisher's Transformation had to surpass 1.96 for a 95-percent confidence interval. This test was also used to determine whether there was any difference between the two equations to compute TSI from the predicted natural log of SDT and to test whether there was any difference between using the TOA or atmospherically corrected scenes from path 21.

Stepwise Regression Equations for chlorophyll a

To identify the best-fit regression equation for predicting Chl-a, a stepwise regression was used. In this process the natural log of measured Chl-a and various combinations of bands were used in four separate trials to determine the bands or combinations of bands with the best coefficients. For a list of the variables tested, refer to table 4.

Table 4. Stepwise regression trials and R2 values to predict trophic state index from chlorophyll a.

[TM, Landsat ETM + band; R2, R-squared; *, Landsat ETM+ satellite bands used for regression in each trial; --, Landsat ETM+ satellite bands not used]

Stepwise regression trials
Trial 1 Best coefficients Trial 2 Best coefficients
TM 1 -- TM 4 / TM 3 --
TM 2 * TM 2 / TM 3 --
TM 3 * TM 2 - TM 3 --
TM 4 -- TM 1 / TM 2 --
TM 5 -- TM 3 / TM 1 *
TM 7 * R2 value 0.6341
R2 value 0.8101              
                           
Trial 3 Best coefficients Trial 4 Best coefficients
(TM 2 + TM 3) / TM 2 -- TM 2 --
TM 22 -- TM 3 *
TM 32 * TM 7 *
(TM 1 + TM 2) / 2 -- TM 3 / TM 1 --
(TM 1 + TM 3) / 2 * TM 32 --
TM 3 / TM 4 -- (TM 1 + TM 3) / 2 *
R2 value 0.6592 R2 value 0.8045

Results

Comparison of Top of Atmosphere Reflection and Atmospheric-Correction Using Secchi-Disk Transparency

An initial expectation for this project was that use of atmospherically corrected images would produce higher R2 values than use of the radiometrically corrected images. However, the R2 results were not significantly different. In some cases, the atmospheric-correction produced slightly higher R2 values than the radiometric-correction and in others produced slightly lower R2 values (these differences in the R2 values were only in the hundredths).

When Fisher's Transformation was used to test for the difference between R2 values for the atmospherically corrected imagery and R2 values for the radiometrically corrected imagery (tested on the R2 values resulting from both regression equations), the values for each scene ranged between 0.000 and 0.086. Therefore, imagery atmospherically corrected by use of MODTRAN4 did not produce a better-fit equation or statistically higher R2 values than did the radiometrically corrected imagery. The result from this test was that atmospherically corrected imagery was not necessary, and that radiometrically corrected imagery would be used to compute TSI values in this report. The R2 values from atmospherically corrected imagery or radiometrically corrected imagery for either regression equation are listed in table 3.

Prediction of Secchi-Disk Transparency by Use of Two Different Regression Equations

In comparison of results for the equation of Kloiber and others (2002),


Equation 8


and the alternative regression equation that was derived and tested during the project,


Equation 9


the alternative regression equation produced a better-fit equation and returned higher R2 values for four of the five scenes with very little difference in values for the fifth scene. Figure 3 shows the predicted and actual SDT for path 21, row 30, (which returned the highest R2 value), and for path 21, row 31, (which produced the lowest R2 value).

When Fisher's Transformation was used to test for differences between R2 values for the alternative regression equation and R2 values from the first equation (tested on the R2 values resulting from the atmospherically corrected imagery, and the radiometrically corrected imagery), the values for each scene were between 0.022 and 1.637. For each scene, the alternative regression equation had a higher R2 value, but the difference was not statistically significant (table 4). Because the alternative regression equation improved the R2 values for most scenes, it was substantially used to predict SDT for computing TSI values for lakes within the imagery. The computed TSI values for all lakes within the satellite imagery are shown on figure 4.


Predicted and actual secchi-disk transparency

Figure 3. Predicted and actual secchi-disk transparency for (A) path 21, row 30, and (B) path 21, row 31.


Computed trophic state index

Figure 4. Computed trophic state index from predicted secchi-disk transparency, August 2002.


Trophic State Index Computation from Predicted chlorophyll a Measurements

In the stepwise regression used to identify an equation for relating the natural log of Chl-a to satellite imagery, the combination of band 2 (Green), band 3 (Red), and band 7 (short wave infrared) produced the highest R2 values:


Equation 10


The resulting R2 value for predicting Chl-a measurements for path 21, row 29 was 0.81. Figure 5 shows predicted values and actual Chl-a values, figure 6 shows the computed TSI results from predicted Chl-a, and table 3 lists details of the stepwise regression variables and results.


Predicted and actual chlorophyll-a

Figure 5. Predicted and actual chlorophyll a for path 21, row 29.


Computed trophic state index

Figure 6. Computed trophic state index from predicted chlorophyll a for Landsat 7 ETM+ path 21, row 29, August 2002.


Summary and Conclusions

The USGS and MDEQ 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. The LWQA and MDEQ Cooperative Lakes Monitoring Program monitor water quality for selected inland lakes each year. Since Michigan has many inland lakes, it is impossible to physically collect the necessary data to compute TSI values for all inland lakes. Remote sensing is an effective and economical tool to enhance the value of conventional sampling data by producing regression equations to predict SDT and Chl-a measurements from satellite imagery. From these predictions of SDT and Chl-a, TSI values can be computed for most of Michigan's inland lakes.

This study focused on 5 Landsat 7 ETM+ satellite scenes within Michigan, 87 SDT measurements, and 12 Chl-a measurements to find the best methods of predicting TSI values for inland lakes. As part of the study, atmospherically corrected images were tested against radiometrically corrected images to determine whether the atmospheric corrections would significantly improve the prediction of SDT. Differences between the R2 values, for the two sets of images were small and not statistically significant.

A second part of the study was to test was whether an alternative regression equation would fit the SDT data better and produce higher R2 values than a previously published equation from Kloiber and others (2000).


Equation 8


This equation produced R2 values ranging from 0.30 to 0.80. An alternative equation was found to produce a better correlation and higher R2 values ranging from 0.61 to 0.80.


Equation 9


The improvement in R2 values was not statistically significant but it was adopted for subsequent prediction of SDT on account of the higher R2 values.

Finally, a stepwise regression was used to determine the best-fit equation between existing Chl-a measurements and various bands within the satellite imagery. This equation was developed for path 21, row 29 because that was the only scene with Chl-a measurements within plus or minus 7 days of the acquiring the imagery. The result of the stepwise regression was a regression equation that produced an R2 value of 0.81.


Equation 10


In addition to providing TSI estimates in unsampled lakes, remote-sensing techniques provide a cost-effective means of measuring both change through time and variability of water quality within a lake. Although TSI derived from satellite imagery is only an estimate of what the actual field sampled value might be, the cost per lake is dramatically lower compared to sampling. By using the high-quality measurements from the LWQA and CLMP programs, estimates can be made for entire Landsat scenes for approximately 10 percent the cost of field sampling. Operating both the field program and the remote sensing program will provide spatially continuous estimates of TSI for all lakes 25 acres or larger in size across Michigan, not just those selected for monitoring, and will increase temporal coverage because satellite-based estimates can be made for the same lakes on an annual or semiannual basis.

Acknowledgments

Mr. Ralph Bednarz of the Michigan Department of Environmental Quality and the volunteers of the Cooperative Lake Monitoring Program were invaluable in providing much of the field data used in the project. Dr. Jiagou Qi of the Michigan State University Department of Geography provided technical assistance with the atmospheric-correction process. Finally, Dr. Stacy Nelson, now at North Carolina State University, and Mrs. Naruman Wianwang of Michigan State University graciously provided assistance with this project.

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APPENDIX A

Results and computations from the Areas of Interest created from the Landsat 7 Enhanced Thematic Mapper Plus satellite scenes in Lower Michigan by use of radiometrically corrected imagery and atmospherically corrected imagery

[Abbreviations: AOI, Area of Interest; ft, feet; m, meters; ln, natural log; SDT, secchi-disk transparency; TOA, radiometrically corrected top of atmosphere reflectance values; MDEQ, Michigan Department of Environmental Quality; CLMP, Cooperative Lakes Monitoring Program; ATM, atmospherically corrected values; Chl-a, chlorophyll-a; USGS, U.S. Geological Survey; µg/L, micrograms per liter; band values recorded in digital numbers (0–255)]

Satellite scene/ Lake name AOI pixels band 1 band 2 band 3 band 4 band 5 band 1/ band 3 SDT (ft) SDT (m) ln (SDT m)
path 20, row 30 TOA MDEQ CLMP
Lake Nepessing 77 73.9870 48.8961 36.5325 17.4935 12.3507 2.0252 10.00 3.05 1.114
Baseline 57 65.5263 42.3509 31.0702 14.0526 11.3158 2.1090 11.50 3.51 1.254
Bass 37 69.3243 48.1351 33.0540 14.2432 11.6216 2.0973 9.83 3.00 1.097
East Crooked 50 67.0200 43.3600 31.7600 14.3400 11.9400 2.1102 10.00 3.05 1.114
West Crooked 26 66.0385 42.6154 31.7692 14.4231 11.8846 2.0787 6.50 1.98 .684
                                                                            
Ore 48 76.2500 58.8542 38.1250 14.5625 11.9167 2.0000 6.00 1.83 .604
Strawberry 33 68.7273 48.3636 34.9091 14.8182 11.7576 1.9688 6.17 1.88 .632
Zukey 24 75.0417 55.3750 37.2083 14.4583 11.8750 2.0168 8.34 2.54 .933
Green 26 71.8846 47.0000 32.9615 15.8462 12.3077 2.1809 14.00 4.27 1.451
Lakeville 37 73.1892 50.1892 36.8108 17.3243 12.2973 1.9883 12.00 3.66 1.297
                                                                            
Walled 48 70.5208 45.3750 32.9167 14.6250 11.9375 2.1424 17.75 5.41 1.688
White Lake 22 68.6818 43.2727 31.0454 15.0455 11.8182 2.2123 20.00 6.10 1.808
Byram 18 70.2778 48.8333 34.5556 16.0000 12.4444 2.0338 7.00 2.13 .758
Ponemah 29 69.1724 45.7241 34.2759 15.4483 11.9310 2.0181 8.17 2.49 .912
Lansing 88 78.8182 52.6818 40.4545 20.0909 13.6477 1.9483 10.00 3.05 1.114
path 20, row 30 ATM MDEQ CLMP
Lake Nepessing 77 120.5974 79.5065 56.0779 26.9740 17.4026 2.1505 10.00 3.05 1.114
Baseline 57 106.5439 68.7895 47.8421 21.1404 16.1754 2.2270 11.50 3.51 1.254
Bass 37 112.7838 78.2162 50.8649 21.5405 16.5405 2.2173 9.83 3.00 1.097
East Crooked 50 109.0600 70.3000 48.9200 21.6800 16.9600 2.2294 10.00 3.05 1.114
West Crooked 26 107.4231 69.1539 48.8462 21.8846 16.8462 2.1992 6.50 1.98 .684
                                                                            
Ore 48 124.1875 95.5833 58.4583 22.1250 16.9375 2.1244 6.00 1.83 .604
Strawberry 33 111.9697 78.6364 53.5758 22.6364 16.7273 2.0899 6.17 1.88 .632
Zukey 24 122.3333 89.8750 57.0000 21.9167 16.7917 2.1462 8.34 2.54 .933
Green 26 117.1154 76.2692 50.6923 24.6923 17.3846 2.3103 14.00 4.27 1.451
Lakeville 37 119.3243 81.4865 56.4865 26.6757 17.3243 2.1124 12.00 3.66 1.297
                                                                            
Walled 48 114.8125 73.6250 50.5833 22.2500 16.9167 2.2698 17.75 5.41 1.688
White Lake 22 111.7727 70.0909 47.9545 23.0909 16.7727 2.3308 20.00 6.10 1.808
Byram 18 114.5000 79.5000 53.1111 25.0000 17.5000 2.1559 7.00 2.13 .758
Ponemah 29 112.5517 74.2414 52.5517 23.8966 16.9310 2.1417 8.17 2.49 .912
Lansing 88 128.4204 85.4773 62.0909 31.0114 19.2046 2.0683 10.00 3.05 1.114
path 20, row 31 TOA MDEQ CLMP
Baseline 57 65.9649 42.7193 31.3684 14.1228 11.4561 2.1029 11.50 3.51 1.254
Bass 37 69.3784 48.2162 33.1351 14.2162 11.7297 2.0938 9.83 3.00 1.097
Coon 15 65.3333 41.5333 31.4667 15.2000 12.5333 2.0763 5.50 1.68 .517
East Crooked 50 67.0000 43.5200 31.8000 14.4400 11.9800 2.1069 10.00 3.05 1.114
West Crooked 26 66.3461 42.7692 31.7692 14.3077 11.8846 2.0884 6.50 1.98 .684
                                                                            
Ore 48 76.3125 58.7917 38.0417 14.5625 11.8542 2.0060 6.00 1.83 .604
Strawberry 33 69.0000 48.4545 35.2121 14.8788 11.7273 1.9595 6.17 1.88 .632
Zukey 24 75.0417 55.2917 36.9167 14.4583 11.8333 2.0327 8.34 2.54 .933
Walled 48 70.4375 45.6042 33.3542 14.7917 11.9167 2.1118 17.75 5.41 1.688
Portage 82 65.7927 42.8902 30.5732 13.5488 11.2317 2.1520 13.40 4.08 1.407
Clear 59 67.7966 44.7458 31.2034 15.6441 12.1525 2.1727 9.00 2.74 1.009
Pleasant 24 66.6250 43.8750 32.3333 15.0000 12.0417 2.0606 7.08 2.16 .769
Vineyard 20 77.8000 52.6000 38.4000 18.7500 13.1000 2.0260 10.50 3.20 1.163
path 20, row 31 ATM MDEQ CLMP
Baseline 57 109.6316 70.2807 48.3509 21.2807 16.3333 2.2674 11.50 3.51 1.254
Bass 37 114.8378 79.1081 50.9730 21.4595 16.6487 2.2529 9.83 3.00 1.097
Coon 15 108.6000 68.2667 48.4000 23.4000 17.6000 2.2438 5.50 1.68 .517
East Crooked 50 111.2400 71.5200 49.0400 21.8800 17.0200 2.2683 10.00 3.05 1.114
West Crooked 26 110.1539 70.3077 48.8846 21.6538 16.8462 2.2533 6.50 1.98 .684
                                                                            
Ore 48 126.4375 96.5000 58.3333 22.1250 16.8542 2.1675 6.00 1.83 .604
Strawberry 33 114.4242 79.4242 54.0303 22.7576 16.6667 2.1178 6.17 1.88 .632
Zukey 24 124.4583 90.7500 56.5833 21.9167 16.7500 2.1996 8.34 2.54 .933
Walled 48 116.7083 74.6458 51.2708 22.6250 16.8958 2.2763 17.75 5.41 1.688
Portage 82 109.2073 70.5122 47.0854 20.5122 16.0976 2.3194 13.40 4.08 1.407
                                                                            
Clear 59 112.4407 73.3729 48.0508 24.2034 17.1525 2.3400 9.00 2.74 1.009
Pleasant 24 110.7083 72.1667 49.8333 23.0000 17.0417 2.2216 7.08 2.16 .769
Vineyard 20 128.9500 86.2500 58.9500 28.7500 18.4000 2.1875 10.50 3.20 1.163
path 24, row 28 TOA USGS LWQA
Arfelin 18 56.1667 33.5556 23.6111 12.1667 11.2778 2.3788 22.00 6.71 1.903
Witch 19 55.2105 33.1053 24.4737 12.1579 11.6316 2.2559 15.00 4.57 1.520
Horseshoe 16 54.3125 34.2500 24.3750 12.0000 11.0625 2.2282 8.00 2.44 .891
Keewaydin 17 54.1765 32.4706 23.6471 13.4706 11.4706 2.2910 9.00 2.74 1.009
Silver 10 54.4000 32.6000 24.7000 13.0000 11.7000 2.2024 10.00 3.05 1.114
                                                                            
Buck 18 54.9444 34.3889 24.2222 12.0000 11.1111 2.2683 8.00 2.44 .891
Indian 14 56.7857 35.7143 24.2143 11.8571 10.8571 2.3451 15.00 4.57 1.520
Emily 16 55.6250 34.5625 25.9375 12.0625 10.8750 2.1446 8.00 2.44 .891
Ottawa 21 56.9524 34.8571 23.8571 11.4762 10.4286 2.3872 19.00 5.79 1.756
path 24, row 28 ATM USGS LWQA
Arfelin 18 91.3333 54.6111 36.2222 18.3333 16.1111 2.5215 22.00 6.71 1.903
Witch 19 89.6316 54.0000 37.4211 18.5263 16.5263 2.3952 15.00 4.57 1.520
Horseshoe 16 88.1875 55.6250 37.3125 18.3125 15.7500 2.3635 8.00 2.44 .891
Keewaydin 17 88.0000 52.8824 36.2941 20.5294 16.3529 2.4246 9.00 2.74 1.009
Silver 10 88.4000 52.9000 37.8000 19.8000 16.7000 2.3386 10.00 3.05 1.114
                                                                            
Buck 18 89.2778 55.8889 37.1667 18.1111 16.0000 2.4021 8.00 2.44 .891
Indian 14 92.1429 57.7857 37.0714 17.9286 15.6429 2.4855 15.00 4.57 1.520
Emily 16 90.3125 56.0000 39.5625 18.3125 15.6875 2.2828 8.00 2.44 .891
Ottawa 21 92.5714 56.5238 36.4286 17.4286 14.8571 2.5412 19.00 5.79 1.756
path 21, row 29 TOA USGS LWQA
Brownlee 15 63.4667 41.6000 29.6000 13.4000 12.6000 2.1441 6.00 1.83 .604
Alcona Dam Pond 15 59.6000 37.4667 27.5333 13.5333 12.2667 2.1646 15.00 4.57 1.520
Jewell 11 64.7273 43.4545 31.2727 16.0909 13.5455 2.0698 11.00 3.35 1.210
Van Etten 14 64.2857 46.7143 34.9286 13.9286 11.9286 1.8405 4.00 1.22 0.198
Foote Dam Pond 14 60.8571 36.5000 27.3571 12.7143 12.0714 2.2245 21.00 6.40 1.856
Shupac 19 63.1053 39.3158 27.0526 14.3158 11.9474 2.3327 26.00 7.92 2.070
West Twin 18 62.4444 40.3333 27.3333 12.8889 10.7778 2.2846 10.00 3.05 1.114
Dixon 12 64.6667 42.2500 28.1667 15.8333 12.7500 2.2959 16.00 4.88 1.584
                                                                            
Opal 9 63.8889 40.3333 27.0000 14.6667 12.0000 2.3663 12.00 3.66 1.297
K.P. 13 62.0000 38.8462 27.4615 14.3077 12.0000 2.2577 9.00 2.74 1.009
Emerald 12 59.5000 37.4167 26.3333 15.0000 12.3333 2.2595 11.00 3.35 1.210
Heart 12 63.3333 39.9167 27.4167 16.1667 12.7500 2.3100 22.00 6.71 1.903
path 21, row 29 ATM USGS LWQA
Brownlee 15 101.2667 66.2000 44.7333 20.4000 17.5333 2.2638 6.00 1.83 .604
Alcona Dam Pond 15 95.0667 59.4000 41.6667 20.5333 17.2667 2.2816 15.00 4.57 1.520
Jewell 11 103.1818 69.0000 47.2727 24.3636 19.0909 2.1827 11.00 3.35 1.210
Van Etten 14 102.6429 74.2857 52.5714 21.0714 16.7143 1.9524 4.00 1.22 .198
Foote Dam Pond 14 97.1429 57.9286 41.3571 19.2143 16.7143 2.3489 21.00 6.40 1.856
                                                                            
Shupac 19 100.7368 62.5789 40.7895 21.6842 16.6842 2.4697 26.00 7.92 2.070
West Twin 18 99.7778 64.1667 41.3333 19.5556 14.9444 2.4140 10.00 3.05 1.114
Dixon 12 103.3333 67.0833 42.4167 23.9167 17.9167 2.4361 16.00 4.88 1.584
Opal 9 102.0000 64.3333 40.7778 22.2222 16.8889 2.5014 12.00 3.66 1.297
K.P. 13 99.0769 61.7692 41.5385 21.6154 16.7692 2.3852 9.00 2.74 1.009
                                                                            
Emerald 12 95.0000 59.3333 39.7500 22.8333 17.2500 2.3899 11.00 3.35 1.210
Heart 12 101.1667 63.5833 41.3333 24.5000 18.0000 2.4476 22.00 6.71 1.903
path 21, row 29 TOA MDEQ CLMP
Vaughn 27 58.1852 35.2593 25.3704 14.9259 12.2593 2.2934 11.00 3.35 1.210
Jewell 22 64.6818 42.6818 30.7727 15.3636 13.5000 2.1019 9.00 2.74 1.009
Arnold 42 62.0476 38.5714 27.2619 14.7143 12.2143 2.2760 15.00 4.57 1.520
Lake Margrethe 91 64.5824 40.4725 27.6923 12.6154 11.0000 2.3321 12.00 3.66 1.297
Sage 42 58.7857 36.3333 25.9762 12.6190 11.1667 2.2631 12.50 3.81 1.338
                                                                            
North 21 59.7619 37.4286 26.7619 14.4286 12.4762 2.2331 14.00 4.27 1.451
Lake George 17 62.1765 39.2941 28.1765 16.0588 12.4706 2.2067 10.00 3.05 1.114
Shingle 15 62.4667 39.2000 28.8000 16.2667 13.2000 2.1690 11.00 3.35 1.210
Chain 12 58.3333 36.7500 25.9167 13.8333 12.3333 2.2508 12.00 3.66 1.297
Cub 21 65.2857 41.2381 27.8095 15.1905 12.2381 2.3476 19.00 5.79 1.756
                                                                            
Starvation 25 65.6800 40.4400 28.4000 15.7200 11.9600 2.3127 26.17 7.98 2.077
Avalon 109 67.6606 41.4495 26.7064 13.0917 10.9908 2.5335 25.00 7.62 2.031
East Twin 83 64.2892 42.5904 29.3012 13.1205 10.8554 2.1941 10.00 3.05 1.114
West Twin 38 62.4474 40.7105 27.3421 12.5789 10.8421 2.2839 11.00 3.35 1.210
Austin 16 63.6250 39.4375 28.5625 15.5000 12.5000 2.2276 10.00 3.05 1.114
                                                                            
Center 22 66.2273 41.0909 30.2727 18.2727 13.5909 2.1877 18.50 5.64 1.730
Wells 14 63.7857 39.7857 28.2857 15.6429 12.7143 2.2551 17.50 5.33 1.674
Stone Ledge 22 65.5455 42.2273 30.9545 16.0455 12.8182 2.1175 8.00 2.44 .891
Beaver 57 65.2807 43.0000 29.1228 13.4912 11.3158 2.2416 10.00 3.05 1.114
Crooked 16 59.0000 37.0625 25.6875 13.7500 11.9375 2.2968 16.50 5.03 1.615
Hubbard 769 61.1534 38.5176 26.1222 11.0988 10.2263 2.3410 17.00 5.18 1.645
Cedar - Schmidt's Point 44 67.8182 51.6364 35.3864 11.8182 10.7045 1.9165 3.42 1.04 .042
Mullett - Red Pine Point 243 66.6872 43.0000 28.9959 12.0000 10.6049 2.2999 15.42 4.70 1.548
                                                                            
Wildwood 16 62.5625 39.1875 28.9375 14.1875 11.8750 2.1620 9.80 2.99 1.094
Lily 20 62.4500 38.3000 28.2000 14.7000 11.8000 2.2145 11.25 3.43 1.232
Bear 42 67.4762 40.8571 27.4048 14.0952 11.4286 2.4622 32.50 9.91 2.293
Indian 17 64.0000 39.8235 27.5294 16.1765 12.5882 2.3248 19.00 5.79 1.756
Big Bradford 28 62.8929 39.5714 26.7500 14.1786 11.9286 2.3511 16.00 4.88 1.584
path 21, row 29 ATM MDEQ CLMP
Vaughn 27 93.0741 56.1111 38.3704 22.5926 17.0741 2.4257 11.00 3.35 1.210
Jewell 22 103.2273 67.8182 46.4091 23.3636 19.0455 2.2243 9.00 2.74 1.009
Arnold 42 99.1190 61.2857 41.1905 22.4048 17.0714 2.4064 15.00 4.57 1.520
Lake Margrethe 91 103.1319 64.4725 41.8462 19.1978 15.2857 2.4645 12.00 3.66 1.297
Sage 42 93.9762 57.8571 39.3095 19.1905 15.5000 2.3907 12.50 3.81 1.338
                                                                            
North 21 95.3333 59.4286 40.3333 22.0000 17.5714 2.3636 14.00 4.27 1.451
Lake George 17 99.2353 62.4706 42.5294 24.1176 17.4706 2.3333 10.00 3.05 1.114
Shingle 15 99.8000 62.2667 43.4000 24.5333 18.6000 2.2995 11.00 3.35 1.210
Chain 12 93.0833 58.4167 39.2500 21.0000 17.2500 2.3715 12.00 3.66 1.297
Cub 21 104.2381 65.6667 41.9048 23.0476 17.1905 2.4875 19.00 5.79 1.756
                                                                            
Starvation 25 104.7200 64.4800 42.8800 23.7600 16.7600 2.4422 26.17 7.98 2.077
Avalon 109 107.8624 65.9633 40.2385 20.0092 15.2294 2.6806 25.00 7.62 2.031
East Twin 83 102.6265 67.6024 44.1928 20.0723 15.0723 2.3222 10.00 3.05 1.114
West Twin 38 99.7105 64.8158 41.2368 19.1053 15.0000 2.4180 11.00 3.35 1.210
Austin 16 101.6250 62.8125 43.1875 23.5000 17.4375 2.3531 10.00 3.05 1.114
                                                                            
Center 22 105.5000 65.4545 45.7273 27.5909 19.1818 2.3072 18.50 5.64 1.730
Wells 14 101.9286 63.3571 42.7143 23.5714 17.6429 2.3863 17.50 5.33 1.674
Stone Ledge 22 104.6364 67.0455 46.7273 24.2273 17.9091 2.2393 8.00 2.44 .891
Beaver 57 104.1930 68.2632 43.9474 20.4211 15.6842 2.3709 10.00 3.05 1.114
Crooked 16 94.3125 58.8750 38.8125 20.8125 16.6875 2.4300 16.50 5.03 1.615
                                                                            
Hubbard 769 97.6112 61.1664 39.4421 16.9025 14.2471 2.4748 17.00 5.18 1.645
Cedar - Schmidt's Point 44 108.1136 82.2045 53.2955 17.9091 14.8182 2.0286 3.42 1.04 .042
Mullett - Red Pine Point 243 106.2798 68.2798 43.7407 18.2099 14.6914 2.4298 15.42 4.70 1.548
Wildwood 16 99.9375 62.2500 43.7500 21.4375 16.5625 2.2843 9.80 2.99 1.094
Lily 20 99.7000 60.7500 42.5500 22.4000 16.4000 2.3431 11.25 3.43 1.232
                                                                            
Bear 42 107.5952 65.0238 41.3810 21.2381 15.8571 2.6001 32.50 9.91 2.293
Indian 17 102.2941 63.4706 41.5882 24.4118 17.7059 2.4597 19.00 5.79 1.756
Big Bradford 28 100.4643 63.0000 40.3929 21.5000 16.7143 2.4872 16.00 4.88 1.584
path 21, row 30 TOA MDEQ CLMP
Lansing 50 65.1600 41.9600 30.3200 13.6200 11.7400 2.1491 10.00 3.05 1.114
Clear 29 64.5862 42.3448 30.3103 14.5172 12.9655 2.1308 9.00 2.74 1.009
Sanford 39 64.8974 40.5897 30.2821 14.8974 11.7692 2.1431 9.50 2.90 1.063
Lake George 16 62.1250 39.6250 27.7500 16.1875 12.3125 2.2387 10.00 3.05 1.114
Shingle 12 62.5833 39.0833 28.7500 16.0000 13.2500 2.1768 11.00 3.35 1.210
                                                                            
Bostwick 54 65.6852 43.8333 29.5741 13.2407 11.2593 2.2210 8.00 2.44 .891
Freska 12 61.9167 39.0000 27.5000 15.6667 12.5000 2.2515 9.00 2.74 1.009
Murray 30 65.1000 42.2667 29.4000 15.2000 12.1667 2.2143 7.50 2.29 .827
Reeds 43 68.0465 48.8605 33.4651 13.5814 11.2791 2.0334 4.10 1.25 .223
Derby 43 64.0698 39.9302 27.1860 14.0465 11.6977 2.3567 18.00 5.49 1.702
                                                                            
Brooks 31 66.8710 48.3871 34.0968 14.5161 11.5484 1.9612 3.50 1.07 .065
Hess 150 68.7667 54.0600 39.0333 13.4133 10.7133 1.7617 3.00 .91 -.089
Robinson 22 62.6818 38.3182 27.5000 14.0000 11.6818 2.2793 11.00 3.35 1.210
Austin 13 63.3077 39.5385 28.5385 15.5385 12.5385 2.2183 10.00 3.05 1.114
Big 43 65.5349 41.7907 30.0465 15.0698 11.7907 2.1811 9.83 3.00 1.097
                                                                            
Wells 13 63.7692 40.1538 28.3846 15.8462 12.5385 2.2466 17.50 5.33 1.674
Hutchins 38 64.8421 41.8947 28.8947 13.3947 11.6053 2.2441 9.00 2.74 1.009
Barlow 16 66.1250 43.0625 27.6875 13.9375 11.6250 2.3883 9.00 2.74 1.009
Jordan 38 65.6842 48.7895 33.1053 13.6579 11.2895 1.9841 5.50 1.68 .517
Lily 31 62.3226 38.4194 27.9032 14.6452 12.0000 2.2335 11.25 3.43 1.232
                                                                            
Camp 31 63.7419 39.4516 27.9032 13.9677 11.6452 2.2844 14.00 4.27 1.451
Blue 23 64.0435 42.0000 29.5217 13.6957 11.3913 2.1694 10.00 3.05 1.114
Round 23 63.9130 40.3043 29.0435 14.4348 12.1304 2.2006 9.00 2.74 1.009
Baldwin 9 63.4444 40.5556 27.8889 14.1111 11.7778 2.2749 8.00 2.44 .891
Clifford 18 62.6667 39.6111 28.6111 14.0000 11.7778 2.1903 15.00 4.57 1.520
                                                                            
Indian Lake 40 63.0250 39.6250 28.7250 14.0250 11.3750 2.1941 9.00 2.74 1.009
Bills 29 67.3793 44.4483 28.7241 13.5517 11.4138 2.3457 8.00 2.44 .891
Crystal 63 64.1429 39.1905 27.3016 13.9206 11.7302 2.3494 15.00 4.57 1.520
Indian 21 64.0000 39.9524 27.5238 16.4286 12.6190 2.3253 19.00 5.79 1.756
path 21, row 30 ATM MDEQ CLMP
Lansing 50 102.5400 65.7800 45.1800 20.2800 16.3600 2.2696 10.00 3.05 1.114
Clear 29 101.6897 66.3103 45.2414 21.5172 17.9655 2.2477 9.00 2.74 1.009
Sanford 39 102.1795 63.6667 45.2051 22.0513 16.4359 2.2604 9.50 2.90 1.063
Lake George 16 97.8750 62.0000 41.3750 24.1875 17.2500 2.3656 10.00 3.05 1.114
Shingle 12 98.5833 61.3333 42.9167 23.9167 18.2500 2.2971 11.00 3.35 1.210
                                                                            
Bostwick 54 103.3148 68.7593 44.1667 19.5741 15.5741 2.3392 8.00 2.44 .891
Freska 12 97.5833 61.2500 40.9167 23.2500 17.3333 2.3849 9.00 2.74 1.009
Murray 30 102.4000 66.1000 43.9000 22.4333 17.0000 2.3326 7.50 2.29 .827
Reeds 43 107.1860 76.6047 50.0000 20.1628 15.6279 2.1437 4.10 1.25 .223
Derby 43 100.8837 62.6512 40.5581 20.9767 16.3256 2.4874 18.00 5.49 1.702
                                                                            
Brooks 31 105.0968 75.8387 50.8710 21.5161 16.0323 2.0659 3.50 1.07 0.065
Hess 150 108.2933 84.8267 58.3133 19.8600 14.8000 1.8571 3.00 .91 -.089
Robinson 22 98.7273 60.0909 40.9545 20.8182 16.2273 2.4107 11.00 3.35 1.210
Austin 13 99.6923 62.0000 42.5385 23.0769 17.4615 2.3436 10.00 3.05 1.114
Big 43 103.0233 65.4419 44.8140 22.2791 16.4651 2.2989 9.83 3.00 1.097
                                                                            
Wells 13 100.3846 63.0000 42.1538 23.6154 17.3846 2.3814 17.50 5.33 1.674
Hutchins 38 102.0526 65.5526 43.1053 19.9211 16.2368 2.3675 9.00 2.74 1.009
Barlow 16 103.8750 67.3750 41.1875 20.8750 16.2500 2.5220 9.00 2.74 1.009
Jordan 38 103.3421 76.4474 49.3947 20.2368 15.6842 2.0922 5.50 1.68 .517
Lily 31 98.1613 60.3871 41.5806 21.6452 16.7097 2.3607 11.25 3.43 1.232
                                                                            
Camp 31 100.3871 61.9677 41.6452 20.7097 16.1613 2.4105 14.00 4.27 1.451
Blue 23 100.7391 65.7391 44.0435 20.4348 15.7826 2.2873 10.00 3.05 1.114
Round 23 100.5652 63.1739 43.2174 21.4348 16.9565 2.3270 9.00 2.74 1.009
Baldwin 9 99.8889 63.5556 41.6667 20.7778 16.4444 2.3973 8.00 2.44 .891
Clifford 18 98.6111 62.2222 42.6667 20.7778 16.3333 2.3112 15.00 4.57 1.520
                                                                            
Indian Lake 40 99.2750 62.1500 42.9000 20.7500 15.8500 2.3141 9.00 2.74 1.009
Bills 29 105.9655 69.7586 42.8276 20.0690 15.8276 2.4742 8.00 2.44 .891
Crystal 63 100.9683 61.5556 40.6508 20.6984 16.3651 2.4838 15.00 4.57 1.520
Indian 21 100.7143 62.7143 41.0000 24.4286 17.5714 2.4564 19.00 5.79 1.756
path 21, row 31 TOA MDEQ CLMP
Randall 55 62.5636 42.0545 30.3091 13.8909 11.6000 2.0642 4.50 1.37 .316
Coldwater 124 63.9597 44.6210 30.1048 13.1774 12.2500 2.1246 6.00 1.83 .604
Birch 68 70.0441 45.0147 28.3824 14.3529 11.7353 2.4679 14.00 4.27 1.451
Diamond 95 66.9263 43.2737 28.2211 13.4842 11.2000 2.3715 10.00 3.05 1.114
Clear 56 64.5357 42.4464 30.1250 14.5000 12.9286 2.1423 9.00 2.74 1.009
                                                                            
Corey 93 67.2258 44.2258 28.3118 13.2043 11.1075 2.3745 9.50 2.90 1.063
Long 16 59.5625 38.5000 28.6250 14.6250 12.6250 2.0808 5.00 1.52 .421
Farwell 22 77.0909 54.6818 30.8636 14.8182 12.8636 2.4978 9.00 2.74 1.009
Vineyard 35 63.6286 43.8571 29.6286 13.4286 11.9143 2.1475 10.50 3.20 1.163
Indian 53 69.4151 50.4340 31.0943 13.2830 11.1509 2.2324 8.00 2.44 .891
                                                                            
Evans 32 59.2813 37.2188 26.0938 13.1250 11.9375 2.2719 18.00 5.49 1.702
Clear.0 46 63.0870 38.8913 27.3478 13.5000 11.7609 2.3068 11.50 3.51 1.254
Cedar 51 63.6667 38.8824 26.8039 13.0980 11.6667 2.3753 17.50 5.33 1.674
Fish 10 62.6000 39.8000 28.1000 14.9000 12.1000 2.2278 10.00 3.05 1.114
Lake of the Woods 39 63.0769 38.4872 27.3846 13.8974 11.6923 2.3034 12.00 3.66 1.297
                                                                            
Eagle 43 63.2326 38.7674 26.5349 13.4186 11.6047 2.3830 15.50 4.72 1.553
Hutchins 53 65.2830 41.6792 28.8868 13.4151 11.5094 2.2600 9.00 2.74 1.009
Osterhout 30 63.8333 39.8000 27.9333 14.4333 11.9000 2.2852 10.00 3.05 1.114
Christiana 53 64.5094 41.1698 29.3019 14.0189 11.4906 2.2015 5.50 1.68 .517
Juno 90 64.1778 40.2778 29.1111 14.2444 11.4000 2.2046 5.50 1.68 .517
                                                                            
Painter 32 64.2813 39.8438 29.4063 14.8750 12.0313 2.1860 6.00 1.83 0.604
Gourdneck 40 63.1500 38.9750 28.0750 13.4000 11.2500 2.2493 12.00 3.66 1.297
Keeler 45 66.5778 43.2000 30.4444 14.6889 12.7111 2.1869 9.50 2.90 1.063
Reynolds (lower) 16 63.5625 40.3750 28.8125 15.5000 13.1250 2.2061 14.00 4.27 1.451
Reynolds (upper) 27 63.7407 39.5926 27.4444 13.5556 11.4815 2.3225 22.00 6.71 1.903
path 21, row 31 ATM MDEQ CLMP
Randall 55 95.5455 64.3273 44.0909 19.9818 15.6727 2.1670 4.50 1.37 .316
Coldwater 124 97.6774 68.1532 43.7419 18.9677 16.6210 2.2330 6.00 1.83 .604
Birch 68 107.2941 68.7353 41.3382 20.7353 15.8382 2.5955 14.00 4.27 1.451
Diamond 95 102.2421 66.1368 41.0421 19.4526 15.0211 2.4912 10.00 3.05 1.114
Clear 56 98.6250 64.9464 43.8750 20.9821 17.5893 2.2479 9.00 2.74 1.009
                                                                            
Corey 93 102.7204 67.5806 41.2258 19.2043 14.9032 2.4917 9.50 2.90 1.063
Long 16 91.0625 58.8750 41.6250 21.1250 17.1875 2.1877 5.00 1.52 .421
Farwell 22 117.8182 83.8182 44.7273 21.5000 17.5000 2.6341 9.00 2.74 1.009
Vineyard 35 97.2286 67.0286 43.1429 19.4286 16.0857 2.2536 10.50 3.20 1.163
Indian 53 106.3019 77.0377 45.1321 19.2264 15.0189 2.3554 8.00 2.44 .891
                                                                            
Evans 32 90.6875 57.0938 37.9063 18.9688 16.0938 2.3924 18.00 5.49 1.702
Clear.0 46 96.4130 59.5652 39.7609 19.5217 15.8913 2.4248 11.50 3.51 1.254
Cedar 51 97.2157 59.5294 38.9020 18.8824 15.8039 2.4990 17.50 5.33 1.674
Fish 10 95.5000 60.9000 40.9000 21.7000 16.5000 2.3350 10.00 3.05 1.114
Lake of the Woods 39 96.4359 59.0513 39.8205 19.9231 15.6667 2.4218 12.00 3.66 1.297
                                                                            
Eagle 43 96.6047 59.4186 38.5581 19.4186 15.5814 2.5054 15.50 4.72 1.553
Hutchins 53 99.7358 63.8679 42.0566 19.4151 15.5094 2.3715 9.00 2.74 1.009
Osterhout 30 97.5333 60.9667 40.6333 20.8667 16.0333 2.4003 10.00 3.05 1.114
Christiana 53 98.4906 63.0189 42.6604 20.1509 15.4528 2.3087 5.50 1.68 .517
Juno 90 98.0667 61.6556 42.3889 20.5444 15.3778 2.3135 5.50 1.68 .517
                                                                            
Painter 32 98.1875 60.9375 42.7500 21.6563 16.2813 2.2968 6.00 1.83 .604
Gourdneck 40 96.4250 59.7250 40.8500 19.4000 15.0750 2.3605 12.00 3.66 1.297
Keeler 45 101.6889 66.0444 44.3333 21.3333 17.2889 2.2937 9.50 2.90 1.063
Reynolds (lower) 16 97.0000 61.7500 42.0000 22.5625 17.9375 2.3095 14.00 4.27 1.451
Reynolds (upper) 27 97.3333 60.6296 39.9259 19.5926 15.4444 2.4378 22.00 6.71 1.903

[Abbreviations: AOI, Area of Interest; ft, feet; m, meters; ln, natural log; SDT, secchi-disk transparency; TOA, radiometrically corrected top of atmosphere reflectance values; MDEQ, Michigan Department of Environmental Quality; CLMP, Cooperative Lakes Monitoring Program; ATM, atmospherically corrected values; Chl-a, chlorophyll-a; USGS, U.S. Geological Survey; µg/L, micrograms per liter; band values recorded in digital numbers (0–255)]

Satellite scene/ Lake name AOI Pixels band 1 band 2 band 3 band 4 band 5 band 7 Chl-a (µg/L) ln (Chl-a)       
path 21, row 29 USGS Chl-a
Brownlee 13 62.92308 41.69231 29.69231 13.30769 12.69231 11.30769 3 1.10       
Alcona Dam Pond 9 59.88889 37.66667 27.11111 13.77778 12.22222 11.11111 1 .00       
Jewell 12 64.83333 43.41667 31.16667 16.08333 13.41667 11.66667 2 .69       
Van Etten 10 64.30000 47.30000 35.20000 15.60000 12.30000 10.30000 21 3.04       
Foote Dam Pond 13 61.30769 37.38462 26.92308 12.76923 12.38462 10.76923 2 .69       
                                                                            
East Twin 18 65.16667 42.72222 28.77778 12.88889 11.00000 10.22222 4 1.39       
Shupac 12 63.75000 39.50000 26.58333 14.50000 12.08333 11.00000 1 .00       
West Twin 13 62.84615 41.69231 28.30769 12.84615 11.07692 9.76923 3 1.10       
Dixion 14 65.71429 43.92857 29.21429 15.57143 12.85714 11.07143 1 .00       
Opal 11 64.90909 42.00000 27.18182 14.63636 12.18182 10.36364 1 .00       
                                                                            
Emerald 8 59.50000 37.37500 26.37500 14.87500 12.50000 10.87500 4 1.39       
Heart 9 63.44444 40.22222 27.55556 16.11111 12.88889 10.55556 2 .69       


For more information concerning the research in this report, contact:
Jim Nicholas, District Chief
U.S. Geological Survey
6520 Mercantile Way, Suite 5
Lansing, MI 48911-5991


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