Quantitative relationships of near-surface spectra to Landsat radiometric data

REMOTE SENSING OF ENVIRONMENT

10:241-261(1980)

241

Quantitative Relationships of Near-Surface Spectra to Landsat Radiometric Data

STUART E. MARSH* and RONALD J. P. LYON Department of Applied Earth Sciences, Stanford University, Stanford, California 94305 The aim of our research has been to determine the quantitative relationship between the surface spectral character of a variety of geologic terrains and that sensed by the Landsat multispectr~ scanner. A spectral sampling and measurement program was conducted to accurately characterize the surface spectral reflectance of the Landsat resolution element and, for the first time, to establish statistically the degree of sampling required for a variety of natural terrains. Results from the study showed that for typical homogeneous and moderately heterogeneous terrains, the number of samples required to estimate the mean reflectance of a pixel is small. Only 9 - 2 0 samples are required to be within 2% reflectance at the 95% probability level. Coincident field measurements and satellite observations were used to test the equivalency and correlation of the reflectance data. Before the Landsat data could be compared with the surface measurements the satellite brightness values must be converted to absolute radiometric units, and corrected for atmospheric attenuation and scattering. A conversion method using a standard/target comparison, which indirectly compensated for atmospheric attenuation and scattering, produced a Landsat equivalent retleetanee that exhibited a reot-mean-square error of +-4% reflectance, when compared with the surface measured value at 12 test sites. Although the equivalence of the surface and satellite data cannot be shown to be better than 4% reflectance, statistical study indicates that the surface and satellite data are highly correlated within defined contrast constraints. However, this correlation is present only after the satellite brightness values are corrected for betweenband gain differences and compensation is made for atmospheric attenuation and scattering.

1.

Introduction

Many studies have been conducted which demonstrate the application of Landsat spectral measurements to geology and agriculture. However, the exact relationship between the surface spectral condition and the same condition as recorded by the satellite system has never been established. Understanding this relationship was considered to be essential

*Now with Gulf Science and Technology Company, P.O. Drawer 2038, Pittsburgh, PA 15230.

©Elsevier North Holland Inc., 1980 52 Vanderhilt Ave., New York, NY 10017

if the scientific credibility of Landsat multispectral data was to be ensured. Therefore, the aim of this study was to determine the quantitative relationships between the surface spectral character of a variety of geologic terrains and the spectra sensed by the Landsat multispectral scanner. No previous experiments have been reported to determine the degree of ground spectral sampling necessary to accurately represent the integrated Landsat resolution element, nor to assess whether these values can even be equated. The research thus encompassed two reciprocal

0034-4257/80/080241 + 21501.75

242

S. E. MARSH A N D R. J. P. LYON

objectives: to determine the type and degree of ground spectral sampling necessary to portray the Landsat pixel; and to determine if the spectral data from the satellite system, within acceptable precision limits, match that of the surface spectra. 2.

Field Spectral Sampling 2.1 Test Sites

Twelve test sites were chosen to determine the type and amount of ground spectral sampling necessary to accurately express the mean spectral character of an area corresponding to the Landsat resolution element, and to determine if the spectral data from the satellite system are equivalent to the surface spectra. The general locations of these test sites,

the Hawthorne and Yerington districts, Nevada, (Fig. 1) were selected on the basis of their having ultimate geologic or mineral exploration applications. The exact locations and reference numbers of the sites are listed in Table 1, the surface characteristics of each site are given in Table 2. The first sites chosen were in the Hawthorne area at Garfield Flat, about 35 km southeast of Hawthorne, Nevada. The sites "Garfield Flat" (1) and "Garfield Sage" (2) were the first selected for study. These sites represent cases of nearly homogeneous bare playa, and vegetation-covered playa with a high degree of surface heterogeneity, respectively. Each of the initial test sites at Yerington was selected for its relative homogeneity, and also to represent a variety of

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RELATIONSHIPS OF NEAR-SURFACE SPECTRA TO LANDSAT DATA

243

TABLE 1 Test Site Locations TOPOGEAPmC TEST S I T E

1. Garfield Flat 2. Garfield Sage 3. Artesia 4. Bluestone Mine 5. South Dump 6. Standard Slag 7. Mason Pass 8. Wabnska Knob 9. Mason Butte 10. Gallagher Pass 11. Fourmile Flat 12. Smith Creek

QUADRANGLE Moho Mountain Moho Mountain Wellington Yerington Yerington Como Wabnska Wabuska Wabuska Como Fourmile Flat Iron Mountain

terrain types. "Artesia" (3), "Bluestone Mine" (4), "South Dump" (5), and "Standard Slag" (6), are essentially unvegetated, sand, clay-silt surfaces. The next series of test sites for the measurement and mapping program were selected to represent more typical terrain and they have a greater heterogeneity than the other sites. "Mason Pass" (7), "Wabuska Knob" (8), "Mason Butte" (9), and "Gallagher Pass" (10), are vegetated

LOCATION

SOc. 22, T.6N., R.33E. Sec. 22, T.6N., R.33E. Sec. 25, T.13N., R.23E. Sec. 29, T.13N., R.25E. See. 21, T.13N., R.25E. T.14N., R.24E. Sec. 31, T.14N., R.24.E. Sec. 24, T.15N., R.24E. Sec. 15, T.14N., R.25E. T.14., R.24E. SOc. 12, T.16N., R.31E. T.17N., B.40E.

surfaces of outcrop, sedimentary soil, alluvium, and talus in the Yerington area. The final sites, "Fourmile Flat" (11) and "Smith Creek" (12), are outside of the Hawthorne-Yerington area and were investigated for their homogeneity. The Fourmile Flat site is a saline playa 35 km southeast of Fallon, Nevada. Smith Creek is a bare clay-silt playa about 40 km southeast of Austin, Nevada. All sites selected for this study exhibit

TABLE 2 Description of Test Site Sudaces SITE

1. Garfield Flat 2. Garfield Sage 3. Artesia 4. Bluestone Mine 5. South Dump

6. StandardS~g 7. Mason Pass

8. Wabuska Knob

9. Mason Butte

10. Gallagher Pass

11. Fourmile Flat 12, Smith Creek

MATERIAL

Bare clay-silt playa Bare playa and vegetation covered windblown sand Bare alluvium Windblown sand, bare soft, eroded clay-silt railings Crushed granodiorite and quartz monzonite waste rock Silt-clay leach pond railings Alluvial fan soil derived from a tertiary ignimbrite Strongly welded, red-brown, ash-flow tuff outcrop and pebbly talus Granediorite outcrop, pebble size talus, and sedimentary soft Greyish-wldte air-fall rhyolitic tuff and float of red-brown ash-flow tuff Saline (NaCI) playa Bare clay-silt playa

VEGETATION

None Greasewood and sage (~40% cover) None Sage ( < 1% cover) None None Desert grass Greasewood and shadescale ( ~ 16% cover)

Greasewood and shadescale ( ~ 10% cover) Greasewood and sage (~8% cover) None None

244

S.E. MARSH AND R. J. P. LYON

tivity" (or reflectance R) of the surface. Reflectance is the dimensionless ratio of the reflected radiant flux to the incident radiant energy flux. Previous field studies of terrain reflectance have generally characterized the bidirectional reflectance (Rb) of the surface, (Longshaw, 1974; Raines and Lee, 1974; Lyon, 1975). The bidirectional reflectance is the reflected radiant flux divided by the radiant flux from a standard reflector, generally MgO or Fiberfrax, which has a nearly cosine response at high solar incidence angles (Fig. 2). The reflectance equipment employed for this investigation consisted of two 2.2 Field spectral measurements Exotech model 100 radiometers. The inThe unit of measure employed for field strument employs four spectral filters, spectral sampling is generally the "reflec- designed to match the Landsat system's

very minor topographic relief. This criterion for selection was necessary to avoid ambiguous spectral measurements arising from shadowing or slope angle effects. Based on field observations, the Garfield Flat, Artesia, South Dump, Standard Slag, and Mason Pass sites are considered homogeneous because they represent essentially pure areas of clay, silt, sand or grass. The Bluestone Mine, Wabuska Knob, Mason Butte, Gallagher Pass, and Garfield Sage sites are considered heterogeneous because they represent some mixture of clay, soil, rock outcrop, and/or vegetation.

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Comparison of the geometries of apertured and bidirectional surface measured reflectance.

RELATIONSHIPS O F NEAR-SURFACE SPECTRA T O LANDSAT DATA

spectral bands, and provides four channels of calibrated radiometric data with parallel voltage output. The incident radiation is measured by use of an opaline diffusing disk pointing skyward to record the 2¢r global irradiance (E). The reflected radiation is measured by use of a glass window and aperture stop providing a 15 ° circular field of view of the surface. The aper~red receptor measures reflected radiance (L) in a small solid angle. Laboratory calibration of the cosine and apertured receptors by the manufacturer (Exotech, 1973) permits the conversion of output voltages from engineering units (V), recorded on a digital voltmeter, to a radiation measure in W / c m 2. This calibration procedure thus converts the target radiance to an equivalent radiant flux density or exitance (M). Because of the availability of two Exotech units, the measurement program could employ one radiometer viewing the target and one simultaneously viewing irradiance. The ratio obtained by dividing these quantities is here termed the apertured reflectance (Ra). This term is analagous to Bauer and Dutton's (1962) beam albedo. Concern over the degradation of any white reflectance standard under field conditions while measuring bidirectional reflectance, and the desirability to directly measure and monitor global irradiance prompted the use of the apertured reflectance (R a) for this investigation. 2.3 Sampling procedures A square-grid sampling scheme was employed during the field measurement program with sample points equally spaced within each pixel. The size and orientation of the Landsat resolution ele-

245

ment is a function of the instantaneous field of view (IFOV), the dimensions of the fiber optics at the focal plan, and the orbital elevation of the satellite. The instantaneous field of view of the Landsat system is 0.086 mrad, square fiber optics are employed; thus for nominal orbit parameters the resolution element is a 79 m 2 (260 ft 9) (NASA, 1971). The orientation of the resolution elements are determined by the satellite orbital track and site latitude. The pixels are rectangular and skewed to the northeast by the satellite motion relative to that of the Earth. Before the measurement program was begun the exact "along track" (north-south) and "across track" (east-west) orientation were established for each site. The sampling procedures began by establishing the location of a known map point on the ground. This was accomplished by either triangulation or measuring ground distances from an obvious feature on the 1:24,000 orthophoto quadrangle or topographic map of the area. Once established, the dimensions and sample distances for the number of samples to be taken were measured out on the ground using a rolling wheel measuring device from the known map point along the proper pixel orientation. At a sample site, the tripod-mounted Exotech radiometers were placed over the established sample locations. The ground viewing radiometer was kept on the tripod at a constant elevation of 75 cm. This height yields a circular resolution cell 20 cm in diameter. After recording the four pairs of radiant exitance and irradiance values, a color photograph of the site was taken for future reference. Field sampling was begun in May and continued through November 1977. The

246

S. E. MARSH AND R. J. P. LYON TABLE 3 Timing of Test Site Spectral Sampling and Landsat-2 Overpass Dates TEST SITE 1. Garfield Flat 2. Garfield S a g e 3. Artesia 4. Bluestone M i n e 5. South Dump 6. Standard S l a g 7. Mason P a s s 8. Wabuska K n o b 9. Mason Butte 10. Gallagher Pass 11. Fourmile Flat 12. Smith Creek

FIELDSAMPLING 5/27/77-5/30/77 6/1/77-6/4/77 6/19/77

6/21/77-6124/77 7/3/77 7/4/77-7/5/77 7/6/77-7/7/77 11/10/77-11/12/77 11/13/77 11/12/77 10/5/77 10/7/77

initial test sites studied were the Garfield Flat and Garfield Sage sites. Measurements at all test sites were conducted nearly coincident (within 1 - 2 days) with a Landsat-2 overpass in order to prevent inaccuracies due to changes in surface state, when correlating ground and satellite data. Table 3 lists the sampling dates at each site with the coincident satellite

LAND~AT-2 OVERPASS 6/1/77 6/1/77 6/19/77 6/19/77 7/7/77 7/7/77 7/7/77 11/10/77 11/10/77 11/i0/77 10/5/77 10/5/77

overlapped pixel edges, and an ultimate sample size of nine samples per pixel was selected for each of the six pixels studied. The South Dump and Standard Slag sites contained only one pixel and a greater sampling density (20 spectra South Dump, 40 spectra Standard Slag) was more easily obtained. At the Mason Pass site, it was unclear how heterogeneous the site would appear and an interoverpass. The number of field spectra sampled mediate value of 16 samples per pixel per pixel varied between test sites. The was employed. number of samples measured generally The four-pixel area at the Wabuska depended on the degree of heterogeneity Knob site was studied with nine samples the site exhibited, and the size of the test per pixel. The Mason Butte and Galsite in number of pixels. lagher Pass sites are significantly more The Garfield Flat and Garfield Sage heterogeneous, and therefore 25 samples sites exhibit the maximum degree of per pixel area were measured. homogeneity and heterogeneity of all The two-pixel area at Fourmile Flat sites. Nine samples per pixel were mea- and the four-pixel area at the Smith Creek sured for the 3 × 3 pixel matrix at Gar- playa were characterized by 16 samples field Flat, and 9 and 25 spectral samples per pixel. The Exotech radiometer was were recorded at the Garfield Sage site. here equipped with a 1 ° field of view. The Artesia test site is a homogeneous Although it has a distinctly smaller samtarget of bare soil, therefore, the mini- piing area (approximately 1 cm diameter), mum of nine samples were recorded for this should not alter the significance of the two test site pixels. A greater hetero- the mean. The standard deviations are geneity was apparent in the Bluestone unexpectedly large, as these are essenMine test site area and a total of 101 tially homogeneous sites. The small samspectral samples was measured. Ap- piing area of the 1 ° lens appears to be proximately half of these measurements affecting the results by reflecting the

RELATIONSHIPS OF NEAR-SURFACE SPECTRA TO LANDSAT DATA

greater degree of small-scale heterogeneity (shadowing, etc.). 2.4 Sampling results The test sites selected for investigation exhibit a variety of geologic terrains which yield a characteristic spectral response. Spectral sampling of the test sites [employing a range (9-40) of measurements per pixel], has shown the squaregrid sampling scheme to be a simple means of characterizing the spectral character of the Landsat resolution element (Marsh, 1978). Nevertheless, a quantitative assessment of the number of samples necessary to depict the Landsat pixel has yet to be established. This number dearly depends on the homogeneity of the pixel. A method was implemented which employed the statistical confidence interval to assess the sampling level required to accurately describe a pixel. The confidence interval is related to the sample size and standard deviation, and is the interval around the sample mean in which the theoretical population mean will fall for a predefined probability. The probability term is derived from the t distribution, a distribution similar to the standard normal distribution but involving a sample standard deviation in place of an unknown population standard deviation. The formula for determining the minim u m number of samples needed to estimate the average reflectance of a pixel has the form t2s 2 nmal =

e2

,

(1)

where nmin = the minimum number of sampies t = t distribution term for a speci-

247

lied probability and sample size s = the sample standard deviation e = the maximum allowable error in reflectance, i.e. the half-width of the confidence interval. The t distribution term used in this calculation was based upon a 95% probability; that is, there is a 95% probability the "true" reflectance falls within the established maximum allowable error. The value of t is also dependent on the number of samples and the value initially employed to determine t was the number of samples measured in the field. However, the number of samples calculated with formula (1) may exceed or fall below the original sample size and therefore an incorrect t value has been employed. To compensate for this error, the calculation must be redone with the correct t term. Results for a maximum allowable error in R~ of plus or minus 0.5, 1.0, and 2.0% reflectance are given in Table 4 for the four Exotech/Landsat bandpass intervals. Depending upon the type of investigation, the maximum allowable error will vary with the spectral similarity of the terrains which are to be distinguished. Thus for field studies of spectrally similar terrains (homogeneous) within Landsat resolution elements, the results from Table 4 indicate a relatively small number of field spectra will be required to maintain a 95% probability on the mean reflectance. However, for spectrally dissimilar terrains (heterogeneous) to maintain a maximum allowable error of + 2% reflectance a large number of samples would be required. The test sites employed in this study show considerable range in mean reflectance and degree of heterogeneity.

248

S.E. MARSH AND R. J. P. LYON TABLE 4 Minimum Number of Samples Required to be Within the Specified Error of the Mean Reflectance Based upon a Two-tailed t test and 95% Probability for the Surface Aportured Reflectance BAND

4

ErmoE %RF~I~CTANCE 0.5 SITE Garfield Flat Garfield Sage Artesia Bluestone Mine South Dump Standard Slag Mason Pass Wabuska Knob Mason Butte Gallagher Pass Fourmile Flat Smith Creek

30 600 87 90 77 58 52 107 169 372 156 178

5

6

7

1.O

2.0

0.5

1.0

2.0

0.5

1.0

2.0

0.5

1.0

2.0

10 152 24 32 22 17 16 29 45 96 89 44

7 40 8 9 9 8 8 10 14 26 24 14

36 740 93 194 84 65 81 252 189 449 416 219

11 187 27 56 24 19 23 65 50 115 106 57

7 50 9 14 8 8 1O 19 16 35 29 17

56 970 121 268 106 67 88 255 450 502 355 208

16 244 33 69 29 19 25 56 114 126 91 55

7 63 11 19 10 8 10 19 32 34 25 16

53 778 118 405 129 72 110 390 483 1034 471 192

16 195 31 163 35 21 30 98 121 259 134 51

7 51 1O 28 12 9 11 27 33 68 32 15

Hence, a maximum allowable error of _ 2% reflectance was considered suitable due to the inherent errors already present in the calibration of the satellite data. The number of samples required is obviously strongly dependent on the standard deviation of the sample. Employing the 2% reflectance maximum error, the range in the number of samples required for the test sites previously grouped as homogeneous, moderately heterogeneous, and heterogeneous was determined (Table 5). These results indicate that the field sampling was, in general, sufficient in degree to maintain the 95% probability. The heterogeneous sites do not always meet the 95% probability criterion and recalculation indicated that for the worst case, Garfield Sage, the sample mean

should be considered to fall within 2% reflectance of the population mean only at the 50% probability level. The significance of these results is not the demonstration that homogeneous sites require far less sampling than do heterogeneous sites. The significance of this sampling study is that, for the first time, the number of field spectral samples required to characterize the Landsat resolution element for a variety of geologic terrains has been quantitatively established. 3. Correction of Landsat Data for Atmospheric Effects Any attempt to quantify brightness values from the Landsat multispectral scanner necessitates converting the origi-

TABLE 5 Minimum Number of Samples Required to be Within 2% Reflectance of the Mean Based Upon a Two-tailed t test and 95% Probability HOMOGENEOUS

Band 4 Band 5 Band 6 Band 7

6-9 6-12 6-14 6-16

~[ODERATI~Y H.ETEBOGENEOUS

6-26 5-45 6-34 6-70

HETEROGENEOUS

40 50 63 51

RELATIONSHIPS OF NEAR-SURFACE SPECTRA TO LANDSAT DATA

nal digital data to absolute radiometric units which account for the effects of atmospheric attenuation and scattering and instrument factors. Spectral data recorded by the satellite represent less than the absolute radiance leaving the surface due to atmospheric, molecular, and aerosol absorption and scattering on the way to the sensor. Correction methods which involve standard atmosphere parameters to remove these effects from Landsat data (Struve and others, 1977) are only as good as the model employed. However, two methods are available to eliminate atmospheric effect which extrapolate point measurements of the atmosphere to an area of interest within the Landsat scene. One method, developed by Rogers and Peacock (1973) and subsequently modified by Ahern and others (1977), uses direct measurements of atmospheric transmittance and path radiance. Their method requires that a measurement program be carried out coincident with the exact time of imaging, relies on the prelaunch calibration factors for digital number to radiance conversion, and is applicable to the day of imaging only. The second method developed by Honey and others (1974), Ballew (1975), and Lyon and others (1975), employs ground calibration sites of known reflectance. This method employs the field reflectance measurements of "light" and "dark" targets of essentially fixed reflectivity, and also assumes a linear relationship exists between ground reflectance and satellite digital number. This method does not require the measurement program be coincident with satellite imaging, nor does it rely on conversion of satellite digital number to radiance. The measurements can be employed for any number of satellite overpasses, as long as the targets remain unchanged.

249

Previous comparison of these two methods by Marsh (1978) employed in situ reflectance and atmosphere parameter measurements over a homogeneous area of approximately 40,000 m 2 (9 pixels). Results indicated that the stand a r d / t a r g e t reflectance conversion method produced Landsat reflectance values (Rs) in far better agreement to the surface reflectance (R a) than did the method based on measurements of atmosphere transmittance and path radiance. To employ the standard/target reflectance conversion method to indirectly compensate for atmospheric attenuation and scattering, appropriate field standards had to be selected. The standard sites must be (1) homogeneous, (2) of relatively large areal extent, and (3) able to recover quickly from soft moisture variations. Unvegetated natural surface as well as artificial surfaces may be used as standard sites, (Lyon and others, 1975). These targets are measured throughout a range of solar elevation angles, preferably on a single day. The Garfield Flat test site was chosen as the light standard. The nine pixels measured at the site are homogeneous and no significant rainfall occurred prior to satellite overpass during the six-month period of this investigation, thus eliminating any concern over near-surface moisture affecting the surface reflectance. The prior measurement of the surface reflectance (R a) of a water body (Felt Lake Reservoir, Stanford, California), considered to be similar to Walker l a k e (Fig. 1), permitted the use of this lake as the dark standard. For each scene that was studied, about 6,000 pixels for the central region of Walker Lake were extracted, and the four mean digital numbers employed as the dark standard. The standard deviations of the extracted values were less than 1.0 DN. The mean

250 TABLE 6

S.E. MARSH AND R. J. P. LYON Standard Target Digital Numbers and Associated Surface Apertured Reflectance (Ra) DN 6/1/77

6/19/77

80.2 119.2 120.8 90.2

69.9 102.0 102.6 75,8

13.1 7.9 2.5 0.0

14.2 9.6 4,5 0,4

7/7/7

/~ 10/5/77

11/10/77

I~FLE~rANcE

74.7 109.4 113.2 83.6

52.0 75.2 75.0 54.7

37.7 57. l 56.7 42.7

29.4 34.5 39.2 40.9

12.3 7.6 2.9 0.0

9.5 6.1 1.7 0.0

6.5 4.0 0.4 0.0

1.0 0.9 0.4 0.3

Garfield Flat Band 4 Band 5 Band 6 Band 7 Walker Lake Band4 Band5 Band6 Band7

digital numbers and their associated mean surface apertured reflectance values for these two sites for the Landsat scenes used in this study are given in Table 6. The mean digital number (DN) for the dark and light standards are then plotted against the mean surface-measured reflectance (ffa) and a linear regression equation is then used to convert digital number to reflectance. To insure the assumption of linearity for the relationship between digital number and surface reflectance, a linear regression analysis was run for the 7 July and 10 November scenes, including three of the measured test sites in addition to the Garfield Flat and Walker Lake targets. The test sites included were those measured nearly coincident with that overpass to avoid any possible discrepancies due to seasonal changes in the reflectance of these targets. Results for both the 7 July and 10 November scenes, employing five test sites, yield correlation coefficients (r) greater than 0.98, for all four bands. The slope of the regression line for five test sites is within 2% of the slope of the line employing only the dark (Walker Lake) and light (Garfield Flat) standards, thus supporting the assumption of linearity. The standard/target method was thus

adopted for the correction of Landsat data for atmospheric effects and their subsequent conversion to reflectance. Satellite values reported as "reflectance" in the ensuing text are the satellite equivalent apertured reflectance based upon the Garfield Flat light standard and Walker Lake dark standard (Rs) (Table 6). These standards were used for all test sites except Garfield Flat, because it was serving as a standard. The Garfield Flat 1 June 1977, satellite equivalent reflectance values, reported, are based upon standards previously employed by Ballew (1975), of light pumice sand and black basalt lapilli near Mono Lake, California. 4. Correspondence of Surface and Landsat Spectra 4.1 Landsat data extraction

Extraction and analysis of the Landsat digital data contained on the computer compatible tapes was carried out through the Stanford Remote Sensing Lab's STANSOaT interactive computer program (Honey and others, 1974; Lyon, 1975). The STANSORTsystem enables the digital data to be evaluated by enhancement of images, interband ratioing, clustering, and pattern recognition techniques, as well as the removal of atmospheric effects by the

RELATIONSHIPS O F NEAR-SURFACE SPECTRA T O LANDSAT DATA

standard/target reflectance conversion method. The interactive nature of the program allows for easy operation of the system by anyone with limited computer experience, and provides for great flexibility in operation. STANSORT was developed on a PDP-10 computer at Stanford University, but is now operating on a P D P - 1 1 / 3 4 minicomputer. The STANSORT system is designed for detailed analysis of small areas of Landsat scenes by displaying the enhanced images either onto a color TV display, or as shaded prints from a matrix lineprinter which have near photographic fidelity. The difficulty of locating individual pixels on large-scale maps was overcome by Ballew and Lyon (1977) with the development of a technique to produce lineprinter images, called dotprints, at fixed nominal scales of 1:24,000, 1:50,000, and 1:62,500. The true scale of the dotprints is within 1% of the nominal map scale, and this has allowed the location of even individual pixels at the test sites, especially when the dotprints are used in conjunction with maps or orthophotos. Dotprints were generated for each of the test sites at 1:24,000 scale to match the U.S. Geological Survey orthophoto series. An area of 60 × 68 pixels can be displayed on one 8.5× 11 inch sheet of output at this scale. Fourteen gray levels are available in the display of 1:24,000 dotprints. The digital data used for the creation of the individual dotprints were linearly stretched to permit maximum use of the 14 gray levels available to create the sharpest contrast between known boundaries. The 1:24,000 scale dotprints were then overlain onto 1:24,000 scale orthophoto quadrangles of that area. The exact pixel locations for those data had been out-

251

lined on the orthophotos with the appropriate orientation for that latitude. Photo-dotprint tie points were accurately located over a light table. These were one or two pixels in size and included such features as small water bodies, roads, small areas of bare ground or alteration, dark shadows, or other distinct borders between terrain features. Once the tie points were established and the dotprint correctly located, the pixel-row and -column coordinates corresponding to the areas measured at each test site were determined. The raw digital number and reflectance values at each test site were then extracted from the CCTs using the STANSORT computer program. The accuracy of the site locations, at a scale of 1:24,000 and using orthophotos, is considered to be within half a pixel. The location of single, diagnostic pixels on many of the dotprints helped to produce this accuracy. However, at all test sites except Bluestone Mine and Standard Slag, the terrain surrounding the test site is essentially the same as the pixels studied. This fact should help to compensate for any inaccuracies in pixel locations. 4.2 Equivalency of surface and satellite data

The initial quantitative comparison of the surface and satellite data involved the compilation of the observed differences in reflectance (Table 7). To accomplish this evaluation the root-meansquare error (RMSE) for each test site was calculated (Table 7): RMSE = ( ( N - 1 ) - 1 •

(Ra-R~)2f/2. (2)

To summarize the results and to avoid inaccuracies caused by calculating a mean

252

S. E. MARSH AND R. J. P. LYON TABLE 7 Observed Difference Between Surface ( R a) and Satellite (R s) Reflectance SiTE

BAND 4

BAND5

BAND 6

BAND 7

1.2 2.2 1.4 2.6 0.5 2.7 1.8 1.46 1.35 1.98

5.5 2.4 4.6 6.5 4.4 6.0 2.1 5.3 5.3 4.68 1.52 4.92

6.9 2.9 4.2 5.0 4.9 4.6 3.6 6.7 4.7 4.83 1.30 5.01

3.7 -1.1 1.30 3.39 3.63

4.7 -1.1 1.80 4.10 4.48

5.5 -2.5 1.50 5.66 5.85

4.8 -0.1 2.35 3.46 4.19

-6.6 -5.4 -6.00 0.85 6.06

-5.2 -5.8 -5.50 0.42 5.52

-5.6 -6.1 -5.85 0.35 5.86

-5.8 -5.0 -5.40 0.57 5.43

-3.7 -8.5 -4.2 10.8 10.8 -8.7 -7.78 3.13 8.39

1.3 -2.5 2.3 -8.3 -9.1 -7.9 -4.03 5.09 6.50

-1.6 -4.2 3.9

-8.9 -5.90 6.52 8.80

4.3 -0.7 5.4 -9.1 14.1 7.8 -3.68 7.90 8.72

Garfield Flat 1.8 0.0 - 1.0 0.6 0.2 0.8 0.8 0.9 0.5 0.51 0.76 0.92

Pixel 1 Pixd 2 Pixel 3 Pixel 4 Pixel 5 Pixel 6 Pixel 7 Pixel 8 Pixel 9 Mean SD RMSE

2.3 -

1 . 6

Garfield Sage Pixel 1 Pixel 2 Mean SD RMSE Artesia Pixel 1 Pixel 2 Mean SD RMSE Bluestone Mine Pixel 1 Pixel 2 Pixel 3 Pixel 4 Pixel 5 Pixel 6 Mean SD RMSE

-

-

-

1 0 . 9

-

1 3 . 7

-

-

South Dump

0.80

1.70

1.60

2.60

Standard Slag

0.10

0.90

1.50

1.60

1.2 1.6 -0.4 0.9 1.0 -0.8 0.28 1.11 1.14

2.9 3.2 1.2 0.7 2.2 1.7 1.98 0.97 2.21

2.2 1.8 0.9 1.6 1.3 0.7 0.88 1.34 1.60

2.8 2.8 0.2 0.3 1.3 0.7 1.35 1.19 1.80

Mason Pass Pixel 1 Pixel 2 Pixel 3 Pixel 4 Pixel 5 Pixel 6 Mean SD RMSE

-

-

Walmska Knob Pixel 1 Pixei 2 Pixel 3

-2.0 1.0

-

-

1 . 7

1.2 -2.4 -0.7 -

-2.6 -4.7 1.8 -

-5.5 -5.6 -3.1

RELATIONSHIPS OF NEAR-SURFACE SPECTRA TO LANDSAT DATA

TABLE 7

253

cont/nued

SITE

BAND 4

Bsa~rv 5

BAND 6

BANV 7

Pixel 4 Mean SD RMSE

- 2.4 - 1.78 0.59 1.87

- 1.3 - 1.40 0.72 1.57

- 4.6 - 3.43 1.45 3.72

- 4.6 - 4.70 1.16 4.84

Mason Butte

-2.50

- 1.60

-3.90

-3.80

G a l l a g h e r Pass

1.20

1.30

- 2.80

1.80

1.7 2.4 2.05 0.49 2.11

- 2.4 -0.3 - 1.35 1.48 2.01

- 3.4 -2.1 - 2.75 0.92 2.90

- 6.2 -6.9 - 6.55 0.49 6.57

6~ 8.7 5.3 7.5 6.~ 1.49 7.~

4.6 5.5 5.1 4.1 4.~ 0.61 4.80

Fourmile Flat Pixel 1 Pixel 2 Mean SD RMSE S m i t h Creek Pixel 1 Pixel 2 Pixel 3 Pixel 4 Mean SD RMSE

of the root-mean-square errors, the discrepancies between the test site means (Ra, Re, in each band) were calculated and the overall RMSE calculated. The overall RMSE for the 12 test sites (Table 8) indicate that we can expect the satellite reflectance (Re) to be within ___4% reflectance of the surface reflectance

(no). The RMSE was also calculated for the five satellite scenes employed to determine ff any significant temporal differences were apparent (Table 8). The 19 June and 5 October data appear to have a significantly greater error than the other dates. Two key points should be noted before an explanation is offered. The observed differences for the two sites measured on 19 June are negative (surface > satellite), while in general the remaining sites exhibit predominantly positive differences (satellite> surface). The second factor is that on the afternoon of 19 June it rained in the Yerington area.

1.9 4.6 -0.2 2.0 2.~ 1.~ 2.~

4.5 3.0 1.8 3.6 3.~ 1.13 3.~

(Though radiosonde data from Winnemucca, Nevada, were available and exhibited a greater atmospheric moisture content on 19 June, the 250-km distance between the areas prohibits any conclusive statements). The greater error in the reflectance conversion technique on 19 June appears to be the result of a moister (less transmissive) atmosphere. The fact that the satellite values are consistently less than the surface measured reflectance may indicate that the conversion method has not fully compensated for the greater attenuation expected from a moister atmosphere. The 5 October data are for the Fourmile Flat and Smith Creek sites which are at a considerably greater distance from the standard targets. The larger error in these sites is considered the result of the atmosphere over the standards not being representative of the atmosphere over these targets. A comparison was also made of the

254

S.E. MARSH AND R. l' P" LYON TABLE 8

Root-Mean-Square Error (RMSE) Results

TEST SIT]EGROUPING Total sites, N = 12 1 June 1977 19 June 1977 7 July 1977 10 November 1977 5 October 1977 Unvegetated sites Garfield, Artesia, Bluestone, South Dump, Standard Slag Vegetated sites Mason Pass grass, Wabuska Knob, Mason Butte, Gallagher Pass Bright (R a > 20%) sites Garfield, Bluestone, Garfield Sage, South Dump, Gallagher Pass Dark ( R a < 20%) sites Standard Slag, Mason Pass grass, Wabuska Knob, Mason Butte, Artesia

BAND 4

BAND 5

BAND 6

BAND 7

3.68 1.06 6.49 0.54 2.22 5.72 4.42

2.86 1.78 4.87 1.59 1.72 4.70 3.57

3.59 3.84 5.75 1.39 3.41 3.48 4.81

4.09 3.97 5.19 1.96 4.17 7.14 4.56

1.87

1.81

3.17

3.63

3.77

2.54

4.17

3.52

2.97

3.68

3.77

4.26

root-mean-square error for sites with and surface and satellite response. This correwithout vegetation cover, and for rela- lation was determined between Landsat tively bright (Ra>20%) and dark sites bands, between individual pixels at a test (R a<20% ) (Table 8). The dark and site, and between test sites. The first test of this correlation vegetated sites appear to have slightly lower RMSE; however, these differences analyzed the correspondence of their cannot be considered statistically signifi- spectral response. Because the four-band data cannot be assumed to have a normal cant. distribution the Spearman rank correlation coefficient (rs) was employed, rather 4.3 Correlation of than the usual Pearson linear method. By surface and satellite data ranking each band in terms of the mean Because of the indeterminate nature of reflectance of that band (for the satellite atmospheric parameters within this study, and surface data) and by then determinany absolute quantitative comparison of ing the correlation of these rankings, a near-surface and satellite spectral mea- quantitative measure of the similarity of surements will be testing the atmospheric the character of the four-band spectra is correction method along with the equiva- achieved (Fig. 3). If the mean surface lence of the data. However, an analysis (R-a) and satellite (/~s) reflectance for a of the statistical correlation between the test site in each band are ranked and surface and satellite data is a means of these rankings are denoted X i a n d Y~, determining the equivalency of the respectively, the rank correlation coeffi-

RELATIONSHIPS OF NEAR-SURFACE SPECTRA TO LANDSAT DATA DETERMINATION OF TEST SITE BETWEEN PIXEL RANK CORRELATION COEFFICIENT

DETERMINATION OF RANK CORRELATION COEFFICIENT FOR THE FOUR BAND SPECTRAL RESPONSE

BAND 4

5

6

TEST SITEPgCELS 6 4

7

Ra ~

255

4

25

21

26

24

22

23

3

2

I

23

22

21

17

20

19

Ra BAND 4 rs= i

~

Rsl

Rs2

~

rS = 0.4

4

Rs BAND 4

BAND

ORDER PIXEL

4

Ra

RsI

Rs2

I

I

3

5

3

3

2

6

2

2

I

7

4

4

4

1.0

0.4

rS =

r =l-

6y.(x,-Y,)

n(n

'

(3)

where X t = surface reflectance rank in band i, Yt = satellite reflectance rank in band i, n = number of pairs of observations = 4. This same rank correlation was calculated for reflectance comparing (1) the digital number and (2) the satellite digital number corrected for path radiance by a scene "dark-value" subtraction (DNLp). This dark-value method was attempted to correct Landsat digital values for

ORDER

I

3

2

2 3 4 5 6

2 4 6 1 5

3 1 4 5 6

FIGURE 3. Example of determination of the rank between-band and between-pixel data.

cient is

r S = 0.09

correlationcoefficientusing

atmospheric scattering by subtracting the digital value from a target assumed to have a near-zero reflectance within the scene. However, the electronic gain factors differ between the four spectral bands and these differences are inherent within the digital number values. To compensate for these gain differences, the digital numbers were also converted, using the NASA correction factors to radiance (Ls), and to radiance corrected for path radiance (LsLp). The rank correlation coefficient results comparing the four-band spectral response of R a with R,, digital number, path radiance corrected digital number, radiance, and path radiance corrected radiance, are given in Table 9.

256

S. E. MARSH AND R. J. P. LYON TABLE 9 Rank Correlation Coefficients Comparing the Four-Band Spectral Response of the Surface Measured Reflectance (Ra) with the Satellite Response TEST SITE 1. Garfield Flat 2. Garfield Sage 3. Artesia 4. Bluestone Mine 5. South Dump 6. Standard Slag 7. Mason Pass 8. Wabuska Knob 9. Mason Butte 10. Gallagher Pass 11. Fourmile Flat 12. Smith Creek

Bs

DN

DNLp

Ls

LsL p

1 1 1 1 1 1 1 1 1 1 1 1

0.40 0.40 0.40 0.40 0.50 0.10 0.40 0.40 0.20 0.40 0 - 0.10

0.40 0.40 0.40 0.40 0.40 0.20 0.40 0.40 0.40 0.40 0 0.40

0.20 0.20 0.20 0.40 0.20 0.20 0.20 0.20 0.20 0.20 -0.40 0.20

0.80 0.80 1 0.80 0.80 0.80 1 1 0.80 0.80 0.20 0.20

It should be apparent from these re- ings were analyzed in each band (Table sults that the conversion to reflectance 10). Results show generally poor correlacreates a very high correlation with tion for the pattern within test site pixels surface spectra (rs --- 1). The lack of corre- between R a and R,. The test sites which lation with satellite digital number, dig- exhibit relatively good correlation, Garital number corrected for path radiance, field Sage, Artesia, Fourmfle Flat, and and radiance, together with the vastly Smith Creek, are in general two-pixel improved correlation with radiance cor- sites which exhibit in the surface mearected for atmospheric path radiance, in- surements the greatest variation between dicated that the satellite spectra only p a d s , hence a ranking is easy to observe. correspond to the surface-measured specThese correlation results appear to tra, when the satellite spectra are cor- demonstrate an expected phenomenon, rected for variations in between-band that of a greater variability in the surface system gain differences and atmospheric data. The ground measurements are attenuation and scattering. showing variations between pixels that The rank correlation calculation was the satellite cannot resolve. Though this then applied to the spectral variation phenomenon was anticipated, the meawithin multiple-pixel test sites (Fig. 3). surements permit this effect to be quantiThe pixels within each site were ranked fied. It must also be true that the apby reflectance and the R a and R, rank- parent variation b e t w e e n surfaceTABLE 10 Between-Pixe| Rank Correlation Coefficients at a Test Site for the Surface (Ro) Compared with the Satellite Reflectance (R,) SITE Garfield Flat Garfield Sage Artesia Bluestone Mine Mason Pass grass Wabuska Knob Fourmile Flat Smith Creek

N

B~a~ 4

BAND5

BAND6

BAND 7

9 2 2 6 6 4 2 4

0.20 1 0.50 -0.61 -0.60 0.50 1 0.80

-0.11 1 1 0.01 0.04 0.95 1 0.80

-0.78 1 1 -0.09 -0.11 0.35 0.50 0.15

-0.20 1 0.50 -0.10 -0.51 0.40 I 0.95

RELATIONSHIPS OF NEAR-SURFACE SPECTRA TO LANDSAT DATA TABLE II h t i o of the Coefficient of Variation (COV Surface and Satellite Reflectance Between Pixels SITE Garfield Flat Garfield Sage Artesia Bluestone Mine Mason Pass grass Wabuska Knob Fourmile Flat Smith Creek

257

Ra/COV Rs) Betweenthe

N

BAND4

BArrY 5

B~rv 6

BAND7

9 2 2 6 6 5 2 4

0.9 5.0 0.9 2.0 1.3 1.3 2.8

2.3 4.5 0.4 2.2 2.7 0.5 2.4 1.3

1.0 7.7 0.8 1.8 0.8 0.4 2.3

1.8 2.6 0.7 2.2 1.4 0.9 0.7 0.8

measured pixels, need not be an effect of ability between similar pixels employing greater sensitivity, but may be simply surface measurements compared to the due to variations in the sampling process. satellite values. Thus the spectral variTable 11 gives the ratio of the variabil- ability between similar pixels at the ity of the test sites between the surface surface must display at least three times and satellite data. This value is de- greater variability to be seen in the termined by dividing the coefficient of Landsat data. The final correlation was run comparvariation (COV) of the surface measurements by the satellite COV (COV=the ing the overall linear relationship bestandard deviation divided by the mean). tween the surface and satellite data. With the exception of the Wabuska Knob This analysis determined the Pearson and Artesia test sites (which show un- (product-moment) correlation between usual homogeneity between pixel means), the mean surface measured reflectance the range of surface variation detected is (/~a) at each test site with the satellite from one to seven times greater than the reflectance (Rs), the satellite digital variation detected by the satellite system. number (DN), and the path radiance corThe mean values are: band 4, 2.6; band rected digital number (DNLp), for each Landsat spectral band (Table 12). 5, 3.2; band 6, 2.0; and band 7, 2.7. The application of these results should The analysis includes data from all five have particular significance to dis- Landsat coverages employed in the study crimination of terrains. The four cases in and therefore is a measure of the global which the pixel ranks were correlated correlation of the ground and satellite have a ratio of the variability within the data. The results, summarized in Table test sites of 2.9 over the four bands. We 12, indicate that the surface (na) and are observing about three times the vari- satellite (/~s) reflectance are very highly TABLE 12 Comparison of the Correlation Coefficient for the Surfaee Measured Beflectance (/~o) and the Satellite Besponse BAND4

BAND5

Bs.m~ 6

BS2qD 7

Ra vs. R,

0.96

/~a vs. DN

0.82

0.97

0.97

0.95

0.78

0.71

Ra vs. DNLp

0.64

0.86

0.80

0.72

/ ~ vs. R~

0.64

0.96

0.96

0.96

0.94

258

correlated, while this same degree of correlation is not present for the satellite digital number or path radiance corrected digital number. The lack of correlation of R a with DN results from the data being uncorrected for seasonal variations in solar illumination. To compensate for this effect DNLp was converted to a radiance using the NASA correction factors. This value was then converted to an illumination-corrected reflectance (R,) by multiplying by ~r and dividing by the global irradiance (E), recorded on the ground at the time of satellite overpass, These results (Table 12), corrected for variations in illumination, now display good correlation between the surface and satellite data. Though the standard/target reflectance conversion produced a significant RMSE (-+4% reflectance) when compared with the ground the strong correlation coefficients in each band indicate the response of the satellite system is accurately representing the surface spectral habit.

5. Summary--Capabilities and Limitations Several conclusions have been presented concerning the equality of surface and satellite spectral measurements, which together present a strong case for the acceptance of the system's performance as accurately representing the surface state. The standard/target conversion produces a satellite equivalent reflectance-that has a root-mean-square error of ---4% when compared with that of the surface measurements. This error can be considered acceptable for many applications where target spectral separability is high.

S.E. MARSH AND R. J. P. LYON

The source of this error is considered to be mainly the inability of the method to fnlly compensate for atmospheric attenuation and scattering. However, other possible sources must be defined: 1. System errors within the satellite scanner yield an accuracy of no better than +2% reflectance (NASA, 1971); 2. Discrepancies between the bandpass filter response of the Exotech and Landsat scanner may affect the magnitude of the spectral response; 3. Inaccuracies in pixel locations (approximately _+0.5 pixel) may sometimes be a source of error, probably subordinate; and 4. Surface measurements have inherent sampling variability (+__2% reflectance). Though the absolute equivalency of the surface and satellite data cannot be shown to be better than +_4% reflectance, analysis of the statistical correlation of the data indicates the surface and satellite values are highly correlated. This analysis also indicated that the character (shape) of the four-band spectra are also highly correlated, and thus the spectral response can be considered equivalent. These correlations were only present after the satellite digital number is corrected for both gain differences between bands, and for atmospheric attenuation and scattering by converting the DN to an equivalent reflectance. Though the between-band and between-test site correlations comparing surface and satellite reflectance values are very good, the correlation between pixels within an individual test site is poor. The sensitivity of the system is incapable of accurately portraying the variations between pixels within similar

RELATIONSHIPS O F NEAR-SURFACE SPECTRA T O LANDSAT DATA

259

%

BAND 5

71•

SMITH CREEK

40-

35-

GARFIELD FLAT

BLUESTONE x 4 I .f

u~

GARFIELD SAGE

ARTESIA MASON PASS

KNOB

15

20

25

30

35

40

45

50

%

SATELLITE R s

FIGURE 4.

Correlation results related to the spectral sensitivity of the Landsat system.

terrain. Figure 4 demonstrates that the individual pixels at a test site are a nebulous cluster of points with no correlation; however, when the mean reflectance of all of the 12 sites are compared ( R a versus lqs), a high degree of correlation is present. The results for the between-pixel correlation, for the 12 test sites, indicates that this sensitivity to variations between spectrally similar terrain is on an order of three times lower than that detected by surface spectral measurements. The reason for this loss of contrast within the satellite data may be attributed to either (1) the sampling (___2%) and inherent satellite system (___2%) error, or to (2) atmospheric attenuation and scattering. If this loss of contrast is a result of the standard/target correction methods inability to fully compensate for the atmo-

spheric conditions, then the sensitivity of the satellite data to variations in the surface spectra should change with imaging conditions. The data support this concept, that the loss of contrast is a function of the atmospheric condition. The relationship between the surface (R a) and satellite (Rs) data for the five imaging dates at the Bluestone Mine site is given in Fig. 5. The variability in the surface spectra is represented by the spread of the data points along the ordinate, and the variability in the satellite spectra is represented by the spread of data along the abscissa. Assigning the surface variability a value of 1, the variability within the satellite data is some fraction of the surface value. For the 19 June data the satellite value is approximately one-third that of the surface; however, for the remaining image dates

260

S . E . MARSH AND R. J. P. LYON

JUNE

JULY 7

I

35

35

0,8

0.9 Ra

BAND5

25

15

Ra 25

JUNE 19

35 15

15

~0.3--

35

25

[ ** I

I 25

15

,,, ~

Lq L 35

Rs

OCT 5

a25

NOV

I0

35

35 0,8

0,9 15

25

35

Rs

2s!

25

15

R o

I

15

I

25

35 R$

15

15

1

•

1

I

25

35 Rs

FIGURE 5. Relationship of the variability between surface ( R , ) and satellite (R,) data for varying imaging dates.

(1 June, 7 July, 5 October, 10 November), the variability in the satellite data is nearly 0.8-0.9 that exhibited by the surface spectra. As already noted, the atmospheric conditions on 19 June exhibited far worse conditions (attenuation) than on the remaining imaging dates, and it is on this date the loss of contrast is most severe. The between-pixel rank correlation between the surface and satellite data (Fig. 5) remains poor, even when the variability in the satellite data is nearly that exhibited by the surface spectra. This is a result of the inherent satellite system (digitizing) error and the associated sampiing error. Integrating the sampling and correlation results establishes the quantitative accuracy of the Landsat multispectral data for a wide variety of natural terrain.

Within defined contrast constraints, and after compensation is made for atmospheric attenuation and scattering, the system can accurately portray the spectral character of the Earth's surface. These results should not only allow the geologist to accept Landsat radiometric data as an accurate representation of the spectral character of the surface environm e n t , b u t these conclusion have hopefully clearly defined the quantitative constraints upon the data for it to be used intelligently.

The U.S. Geological Survey's EROS Program supported all field work for this study. Funds for computing at the Stanford Institute for Mathematical Studies in the Social Sciences were provided to the Stanford Remote Sensing Lab by the National Aeronautics and Space Administra-

RELATIONSHIPS OF NEAR-SURFACE SPECTRA TO LANDSAT DATA

261

tion, the U.S. Geological Survey's EROS Lyon, R. J. P. (1975), Evaluation of ERTS multispectral signatures in relation to Program, and the U.S. Bureau of Mines. ground control signatures using a nested The authors wish to thank Dr. Richard S. sampling approach, Stanford Remote SensWilliams, USGS, for his assistance ing Laboratory, Final Report NAS 5-21884, throughout this project, and Dr. Paul 600p. Switzer, Stanford, and Michael Abrams, IPL, for their constructive criticism of the Lyon, R. J. P., Honey, F. R., and G. I. Ballew (1975), A comparison of observed and manuscript. References

model predicted atmospheric pertuberations on target radiance measured by ERTS, Proceedings, IEEE (Control System

Ahem, F. J., Goodenough, D. G., Jain, S. C., and V. R. Rao (1977), Use of clear lakes as standard reflectors for atmospheric measurements, Proceedings of the Eleventh In-

Society) Conference on Decision and Control, Applications of Remote Sensing Imagery to Mineral and Petroleum Exploration (75CH1016-5CS), Houston, TX, pp. 244-

249. ternational Symposium on Remote Sensing of Environment, Vol. 1, ERIM, Ann Arbor, Marsh, S. E. (1978), Quantitative relation-

ships of surface geology and spectral habit to satellite radiometric data, Stanford University Ph.D. Dissertation, Stanford, CA 94305, 225 p. National Aeronautics and Space Administration (1971), Data Users Handbook (for Earth Resources Technology Satellite), NASA, Goddard Space Flight Center, Doc. 71SD4249, variously paged. Raines, G. L. and K. Lee (1974), Spectral reflectance measurements, Photogram. Eng. Remote Sens. 40:547-550. Rogers, R. H., and K. Peacock (1973), A technique for correcting ERTS data for solar and atmospheric effects, Symposium on Significant Results Obtained from the Earth Resources Technology Satellite, NASA SP-327, 1 (b), pp. 1115-1122. Strnve, H., Grabau, W. E., and H. W. West (1977), Acquisition of terrain information using Landsat multispectral data, Report 1: Correction of Landsat multispectral data International Symposium on Remote Sensfor extrinsic effects, U.S. Army Engineering of Environment, ERIM, Ann Arbor, ing Waterways Experimental Station MI, pp. 857-905. Technical Report M-77-2, 50 p. Longshaw, T. G. (1974), Field spectroscopy for multispectral remote sensing: An anaReceit~l 6 August 1979; revised 14 1uly 1980. lytical approach, Appl. Opt. 6:1487-1493.

MI, pp. 731-755. Ballew, G. I. (1975), A method for converting LANDSAT-1 MSS data to reflectance by means of ground calibration sites, Stanford Remote Sensing Lab Technical Report 75-7, pp. 285-379. Ballew, G. I., and R. J. P. Lyon (1977), The display of LANDSAT data at large scales by matrix printer, Photograrn. Eng. Remote Sens. 43:1147-1150. Bauer, K. G., and Dutton, J. A. (1962), A1bedo variations measured from an airplane over several types of surfaces, J. Geophys. Res., 67:2367-2376. Exotech (1973), ERTS Model 100 Radiometer Instruction Manual, Exotech Inc., Gaithersburg, MD, 19 p. Honey, R. F., Prelat, A., and R. J. P. Lyon (1974), Stansort: Stanford Remote Sensing Laboratory pattern recognition and classification system, Proceedings of the Ninth