The equivalence of three separate investigations that related LANDSAT digital count (DC) to ground measured reflectance (R) was demonstrated. One investigator related DC data to the cosZ, where Z is the solar zenith angle, for surfaces of constant R. The second investigator corrected the DC data to the solar zenith angle of 39 degrees before relating to surface R. Both of these investigators used LANDSAT 1 and 2 data from overpass dates 1972 through 1977. A third investigator calculated the relation between DC and R based on atmospheric radiative transfer theory. The equation coefficients obtained from these three investigators for all four LANDSAT MSS bands were shown to be equivalent although differences in ground reflectance measurement procedures have created coefficient variations among the three investigations. These relations should be useful for testing atmospheric radiative transfer theory

Richardson, A. J.

English

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TM EMWALeea OF
 TM EE TEKHNiQUB FOR ESTIMATING
GROUND RBUCTANCE FRom LANDSAT DIGITAL COUNT DATA
ARTHUR J. RICHARDSON
USDA-ARS
RS RU
WESLACO, TEXAS 78596
(E83- 10378) THL tQUI ® ALEMCE OF THREE	 083-32131
TECHNIVUES FOR E57INA21MG GROUND RM"ikrLE
FROB LANDSAT DIGITAL COUNT DATA
(Agriculturai Research Service) 11 p 	 Unclas
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1.	 Na. 2. CNWOrnwarit Acemion No. 3 Rfti	 -$ Ceti" fYee.
EW-U3-04407
d. TWO and SAO* S. MW Deft
The Equivalence of Three Techniques for Estimating Ground April 1983
Reflectance From Landsat Digital Count Data 8,
7. Aut1	 sI 8. Piufo" t wmalit on RapaR No.
Arthur J. Richardson
10. Week Unk No.
>i. ^
	
Neaw and Addn.
R5 _RSRU
P.O. Box 267
11. Contract or Grant No.
Weslaco, Texas	 78595
13. Type of Report and Period Cmered
Technical ReportIt. Sponsoring Aker Name and AAdress
USDA+ARS id.	
ApmV CodeEarly Warnina/Croo Condition Assessment Project
. 1050 Bay Area Blvd., Houston, Texas 	 77058
18. Suppien+MKary Notes
ta. AbWM
The equivalence of three separate investigations that related Landsat diqital count (DC)
to ground measured reflectance (R) was demonstrated. 	 One investigator related DC data
to the cosZ, where Z is the solar Zenith angle, for surfaces of constant R. 	 The second
investigator corrected the DC data to the solar zenith angle of 39 degrees before relat-
ing to surface R.	 Both of these investigators used Landsat 1 and 2 data from overpass
dates 1972 through 1977.	 A third investigator calculated the relation between DC and R
based on atmospheric radiative transfer theory.
	 The equation coefficients obtained from
these three investigators for all four Landsat MSS bands were shown to be equivalent
although differences in ground reflectance measurement procedures have created coefficient
variations among the three investigations.
	 These relations should be useful for testing
atmospheric radiative transfer theory.
17. Key Words (suggested by Authors)) 18. Distribution Statement
Landsat
Atmos pheric radiative transfer
transfer theory
reflectance measurements
18. Security Galsif. (of this report) 20. Security Ciaseif. (of this pegs) 21. No. of Pages 22. Price'
Unclassified Unclassified 8
'Feu We by the Nat*W TechMnl Information Service, Spri A&M. VirgMis 22161
EW413-04401
THE EQUIVALENCE OF THREE TECHNIQUES
FOR ESTIMATING GROUND REFLECTANCE
FROM LANDSAT DIGITAL COUNT DATA
PRINCIPAL INVESTIGATORS
Arthur J. Richardson
APPROVED BY
s 
s	 	 '!i
Glenn Ts 6. BoAwright, .onager
Early Warning/Crop Condition Assessment Project
AgRISTARS Program
Houston, Texas
April 1983
TIE EQUIVALENCE OF TBRRE TSCRNIQURS POR EBTINATING GROUND
REFLECTANCE FROM LANDSAT DIGITAL COUNT DATA
Arthur J. Richardson
Author is a Research Physicist with the
USDA, ARS, RSRU, P. O. Box 267, Weslaco, Texas 78596
ABSTRACT
4
The equivalence of three separate investigations that related Landsat
digital count (DC) data to ground measured reflectance (R) was demonstrated.
One investigator related DC data to the cost, where 2 is the solar senith
angle, for surfaces of constant R. The second investigator corrected the DC
data to the solar zenith angle of 39 degrees before relating to surface R.
Both of these investigators used Landsat 1 and 2 data from overpass dates 1972
through 1977. A third investigator calculated the relation between DC and R
based on atmospheric radiative transfer theory . The equation coefficients
obtained from these three investigators for all four Landsat MSS bands were
shown to be equivalent although differences in ground reflectance measurement
procedures have created coefficient variations among the three investigations.
These relations should be useful for testing atmospheric radiative transfer
theory.
INTRODUCTION
Three recent studies have demonstrated the repetitive radiometric accuracy
of the Landsat multispecteral scanners (MSS) as applied to the fundamental
problem of estimating ground reflectance (Rowalik et al., 1982; Richardson,
1982; and Jackson et al., 1982). The first two studies evolved simple linear
equations that related gound reflectances (R), measured with hand-held
radiometers, with Landsat digital count (DC) data. These data were obtained
.	 from and locations, to minimize atmospheric and solar zenithy angle (Z)
effects, for all four Landsat MSS bands in the 0.5 to 1.1 um range. Jackson's
et al. (1982) approach was based on atmospheric radiative transfer theory. The
objective for this paper was to demonstrate that these three different
procedures produced equivalent relations between DC and R data.
EXPERIMENTAL PROCEDURE
Rovalik et al. (1982) related DC data to the cosZ for surfaces of constant
reflectance over several Landsat sample dates. He obtained DC data from 10
computer compatible tapes (CCT) containing Landsat data for 12 small sites of
constant ground reflectance in the Walker Lake area of Western Nevada. He used
two Exotech Model 100 ERTS Radiometers to measure the corresponding ground
reflectance for Landsat 1 and 2 overpass dates in 1972, 1973, and 1977.
Richardson (1982) corrected all DC data to a reference solar zenith angle
o` 39 degrees and to the LANDSAT 22 January 1975 to 15 July 1975 calibration
period and then related the corrected DC data to surface R. Richardson
obtained DC and ground reflectance data from seven published sources from
Landsat 1 and 2 overpass dates in 1972, 1973, 1975, 1976, and 1977; providing
82 observations altoget.her.
3Jackson et al. (1982) obtained relations between radiance at the top of
the atmosphere and ground reflectance using atmospheric radiative theory
developed by Herman and Browning (1975).
The equation coefficients obtained from these published sources comprised
the basic data for this study. Equivalency was demaistrated by algebraically
rearranging Kowalik's and Jackson's original equations obtained for each of the
four Landsat bands to compare with Richardson's original equations by using the
ratios of the slopes of each of the four equations fro® all approaches.
RESULTS AND DISCUSSION
The albebraic results obtained from rearranging Kowalik's original
equations is shown for Landsat MSS band 7(0.8 to 1.1 um range). Kowalik's
original relation is:
R7 - 2.41 + 0.315*2*DC1/cost; (1)
notice that Kowalik doubled the DC values in band 7. Richardson obtained
corrected DCc values as follows:
DCc - DC*cos39/cosZ,	 (2)
so that
DC a DCc*cosZ/cos39. 	 (3)
Thus, multiplying the slope in (1) by 2 and substituting (3) into (1) yields
R7 - 2.41 + 0.630 *DCc7/cos39. (4)
Equation (4) is further simpl:.fied since cos39 equals to 0.777 so that
Kowalik's et al. (1982) original equation (1) reduces to
R7 - 2.41 + 0.811*DCc7	 (5)
_rI
4
that compares to Richardson's (1982) original equation,
R7 a
 -0.49 + 1.22*DCc7.	 (6)
This same procedure was used to transform Kowalik's original equations for
Landsat MSS bands 4, 5, and 6, as shown in Table 1, for comparison to
Richardson's equations. The ratio of Richardson's to Kowalik's slope values
(RJK) are shown in Table 1. These ratios show that Richardson's and KoVatik's
slope coefficients differ by 21%, 11%, and 132 in Landsat MSS bands 4, 5, and
6, respectively. There is a 502 difference in band 7. Thus, Richardson's
slope coefficients are greater in all four bands than Kowalik's.
The reasons for these differences in equation slopes are not clear. Both
studies have used reflectance data from light and dark pumice sand located at
Mono Lake, California. Richardson's reflectance data for this area was
obtained by Bellew (1975) concurrently with the Landsat overpass time and are
higher in all fair bands than those reported by Kowalik (Table 2). This could
mean that Kowalik's method of obtaining ground reflectance consistently yielded
lower values than those reported by Bellew (1975). Kowalik used two
radiometers; one viewed vertically upward to record the hemispherical
irradiance and the other viewed downward to measure the surface radiance with a
15 degree FOV. The surface radiance was divided by the hemispherical
irradiance to yield apertured reflectance. Bellew obtained bidirectional
reflectance by referencing surface measured radiance to the measured radiance
of Rastman white paint on aluminum. It may be that apertured reflectance will
always be lower than bidirectional reflectance explaining Kowalik's lower slope
values.
5An example of the algebraic results obtained by rearranging Jickson's
original equations is shown here for Landsat MSS band 7 (0.8 to 1.1 us range).
Jackson's at al. (1982) original equation is:
F7 a 0.0015 + 0.2202*R7 + 0.00467*R7**2,	 (7)
where F7 is the ratio of radiance to irradiance at the top of a clear
atmosphere detected by LANDSAT in MSS band 7 for a solar zenith angle of 45
degrees. (Units of 1/sr)
in general, the radiance (Li), at the top of the atmosphere, is related to
DCi (Richardson et al., 1980) by using calibration coefficients (Ai and Bi) and
solar constant values (Ei) for each Landsat MSS band as follows:
DCi • (Li - BOW,	 (8)
where Li - FiEi and i a 4, 5, 6, and 7, for each Landsat MSS band. Thus,
substituting equation (8) into equation (7), for i = 7, and neglecting the
squared term in equation (7), yields:
DO - -1.61 + 0.868*R7. 	 (9)
Equation (9) was multiplied by cos39/cos45-1.0991 to convert from a solar
zenith angle of 45 degrees to 39 degrees and the resulting equation solved for
R7:
R7 = 1.86 + 1.05 DC7,	 (10)
that compares to Richardson's equation (6).
a
6This same process was used to transform Jackson's original equations for
Landsat MSS bands 4, 5, and 6, as shown in Table 1, for comparison to
Richardson's equation. The ratio of Richardson's to Jackson's slope values
(R/J) are also shown in Table 1. These ratios show that Richardson's and
Jackson's slope values differ by 14%, 12%, 20%, and 16% for Landsat MSS bands
4, 5, 6, and 7, respectively. Thus, it appears that Richardson's slope values
are higher than both Jackson's and Kowalik's. Jackson's and Kowalik's slope
values (JJK) are in good agreement for bands 4, 5, and 6. There is a wide
range of slope values for band 7 among all three investigators; possibly due to
variation in atmospheric moisture that affects MSS band 7 more than the other
MSS bands.
CONCLUSIONS
In conclusion, even though there were differences in equation slope values
obtained for Kowalik's and Jackson's equations, as compared to Richardson's
equation, it appears that the three approaches are probably equivalent. If
ground reflectance measurements were comparable, in an absolute sense, then
algebraically we should expect identical results from each approach. The
radiometric accuracy of the Landsat MSS sensors are probably more repetitive
than the various sources of ground reflectance measurements obtained from the
three studies. Thus, it appears that the basic relations obtained by these
studies are good approximations of the actual atmospheric transformations
needed to convert Landsat DC to ground R for clear atmospheres. These
relations, in their various algebraic forms, should be useful for testing
atmospheric radiative transfer theory.
7REFERENCES
Ballow, C. I. 1975. A method for converting Landsat MSS data to reflectance
by means of calibration sites. Stanford Remote Sensing Laboratory
Report 75-5. 91 p.
Herman, S. M., and Drowning, S. R. 1975. The effect of aerosols an the
earth-atmosphere albedo. J. Atmos. Sci. 32:1430-1443.
Jackson, R. D., P. N. Slater, and Pinter, Jr., P. J. 1982. Discrimination
of growth and water stress in wheat by various vegetation indices
through a clear and a turbid atmosphere. AgRISTARS EW U2-04298
JSC-18241. 40 p.
Eowalik, W. S., Marsh, S. E., and Lyon, R. J. P. 1982. A relation between
Landsst Digital Numbers, Surface Reflectance, and the Cosine of the
solar zenith angle. Remote Sensing of Environment. 12(1):39-55.
Richardson, A. J. 1982. Relating Landsat digital count values to ground
reflectance for optically thin atmospheric conditions. Applied Optics.
21(8) :1457-1464 .
Richardson, A. J., Escobar, D. E., Gausman, H. W., and Everitt, J. H. 1960.
Comparison of Landsat-2 and field spectrometer reflectance signatures of
south Texas rangeland plant communities. Pro. Sixth Symp. Machine Proc.
of Remotely Sensed Data. LARS, Purdue Uuiv., West Lafayette, IN.
pp. 88-97.
8Table 1 Comparison of Landsat equation s0 and al coefficients between Kowalik
at a1. ( 1982) and Richardson ( 1982). Slope ratios are cued by
dividing Richardson al values by Kowalik al values WO O Richardson
by Jackson (RJJ), and Jackson by Kowalik (J/K).
- -- ------------------------------------:r----:--------r^-----r--s_r-_-__.^sa-s_s
	Kowalik ' s	 Jackson ' s	 Richardson's
Landsat	 Coefficients	 Coefficients	 Coefficients
	 Slope Ratios
	
Band	 --------------	 --------------	 -------------- ---_---,.------
	
um	 Rmao+al*DCc
	 Rnao+al*DCc
	
R-ao+al*DCc
	 R/K RIJ JfK
--------------------------------------------- --------------------- m ------
	80	 al	 40	 al	 a0	 al
0.5-0.6	 -2.94 0.394	 -1.91 0.416
	 -5." 0.476	 1.21 1.14 1.05
0.6-0.7	 -2.93 0.337	 -0.11 0.334
	 -1.94 0.373	 1.11 1.12 0.99
0.7-0.8	 -0.76 0.363	 1.61 0.334	 -1.40 0.412	 1.13 1.20 0.95
0.8-1.1	 2.61 0.811	 1.86 1.05
	
-0.49 1.220
	 1.30 1.16 1.29
------------------------------------------------------------------------------
Table 2 Comparison of mean ground reflectance values obtained of dark and
light pumice sand areas located at Mono Lake, California, as measured
by Ballow on clear summer days of July 26, and August 6, of 1976 and
by Kowalik in 1977. Kowalik measured apertured reflectance while
Ballow measured bidirectional reflectance.
------------------------------------------------------------------------------
Mono Lake, California Pumice Sand Reflectance (2)
Source	 ------------------------------------------------------------
	
MSS4	 MSSS	 MSS6	 M887 (X)
Kowalik (Dark)	 5.3	 5.8	 6.5
	
6.3
	
(Light)	 18.1	 19.0	 22.3	 21.6
Ballow ( Dark)	 7.6	 8.3	 8.4	 8.0
	
(Light)	 21.9	 23.8	 24.2	 24.3
------------------------------------------------------------------------------


The equivalence of three techniques for estimating ground reflectance from LANDSAT digital count data

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