Arthur J. Richardson, "Relating Landsat digital count values to ground reflectance for optically thin atmospheric conditions," Appl. Opt. 21, 1457-1464 (1982)
The data from seven separate investigations that relate corrected Landsat digital count (DCc) values to ground-measured bidirectional reflectance R were summarized and examined as a single data set. As shown in the results these seven different sources of data were in significant agreement in estimating R from DCc. Thus a simplified linear formulation was derived for estimating R (0–100%) from Landsat DCc for conditions that approximate optically thin atmospheres. The relations are R4 = −5.9 + 0.476DCc4, R5 = −1.94 + 0.373DCc5, R6 = −1.40 + 0.412DCc6, and R7 = −0.49 + 1.220DCc7. The original Landsat digital count (DCo) data were corrected to a sun zenith angle of 39° and for the 1/22/75–7/15/75 Landsat-2 calibration period to determine DCc.
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Constants for Converting All Landsat-1, -2, and -3 Digital Counts to the Landsat-2 Calibration Period 22 Jan.–15 July 1975; Conversion Constants are Based on Landsat Calibration Coefficients Given in Richardson et al.5
Landsat MSS sensor
Landsat conversion constants
Calibration time period
MSS 4
MSS 5
MSS 6
MSS 7
1
K0
−6.369
−5.983
−6.667
−2.198
8/25/72–1/10/78
K1
1.242
1.342
1.314
1.146
2
K0
0
0
0
0
1/22/75–7/15/75
K1
1
1
1
1
2
K0
−1.274
−0.855
−0.952
−0.471
7/16/75–present
K1
1.280
1.145
1.095
0.947
3
K0
−3.822
−3.419
−3.809
−1.727
3/05/78–5/31/78
K1
1.083
1.154
1.067
0.965
3
K0
−3.822
−3.419
−3.809
−1.727
6/01/78–present
K1
1.280
1.188
1.095
0.947
Table II
Atmospheric Radiative Transfer Constants for the Four Landsat MSS Bandsa
Radiative transfer constants
Landsat MSS bands
MSS 4
MSS 5
MSS 6
MSS 7
1. A0
0.10
0.07
0.07
0.14
2. A1
0.0157
0.0117
0.0105
0.0637
3. B
0.061
0.035
0.025
0.013
4. Wg
0.027
0.021
0.029
0.050
5. E0
17.7
15.15
12.37
24.91
Explanations for each line of constants are as follows: 1 and 2. Landsat-2 calibration coefficients for the time period from 1/22/75 to 7/15/75 taken from Richardson et al.5. 3. Backscattering optical thickness of the atmosphere from Otterman et al.7. 4. Gas absorption coefficients assuming 10 mm of precipitable water in a vertical column from Otterman et al.7. 5. Solar constant (mW/cm2) from Otterman and Fraser.3
Table III
Listing of Original Digital Count (DCo), Corrected Digital Count (DCc), and Ground Reflectance R Taken From Five Published Sources; DCo Were Corrected By the Solar Zenith Angle and Calibration Coefficients for Each Landsat to Obtain the DCc
Date
Solar zenith angle
Landsat series
Original digital counts
Corrected digital counts
Ground reflectance
DCo4
DCo5
DCo6
DCo7
DCc4
DCc5
DCc6
DCc7
R4
R5
R6
R7
Ballew, dark pumice sand
5/26/73
29
1
27.6
24.0
17.7
4.6
24.7
23.3
14.7
2.7
8.1
8.8
8.8
8.3
10/22/73
54
1
20.3
16.3
12.3
3.1
24.9
21.0
12.5
1.7
7.1
7.8
7.9
7.6
Ballew, light pumice sand
5/26/73
29
1
59.0
60.0
50.2
19.0
59.4
66.2
52.6
17.3
21.4
21.9
24.3
21.8
10/22/73
54
1
40.0
39.7
33.2
12.2
57.2
62.5
48:8
15.5
22.4
25.7
24.1
26.8
Otterman, arid and semiarid regions
1/2/73
62
1
38.0
51.0
53.0
24.0
67.5
103.0
104.2
41.8
28.1
36.7
39.4
55.6
1/2/73
39
1
42.0
41.0
46.0
23.0
45.7
49.0
53.7
24.1
16.5
15.9
19.9
30.7
10/22/72
39
1
76.0
105.0
97.0
38.0
88.0
134.9
120.7
41.3
34.7
45.5
43.6
51.1
8/9/72
31
1
91.0
115.0
103.0
41.0
96.6
134.4
116.6
40.6
37.2
45.3
41.7
49.4
Richardson, Silverleaf sunflower plant
6/2/77
34
3
26.0
26.0
68.0
33.0
30.0
27.1
68.9
28.8
10.7
7.8
28.4
31.5
Ahern, oligotrophic lake
5/27/76
39
3
13.0
10.0
9.0
1.0
15.3
10.5
8.9
0.4
0.5
0.4
0.2
0.1
9/12/76
39
3
12.0
12.0
14.0
4.0
14.0
12.8
14.3
3.3
0.4
0.3
0.2
0.1
Lyon, concrete runway
7/ /73
28
1
75.9
79.4
67.9
26.4
77.3
88.5
72.6
24.6
27.9
31.0
30.0
32.1
8/26/73
38
1
71.7
73.8
63.7
25.6
81.5
91.7
75.9
26.7
27.9
31.0
30.0
32.1
12/30/72
67
1
36.2
35.3
30.6
11.8
76.7
82.6
66.7
22.5
27.9
31.0
30.0
32.1
Lyon, carbon black dump
6/10/74
29
1
23.5
13.9
13.5
2.6
20.2
11.2
9.8
0.6
0.5
0.5
0.5
0.5
8/25/73
38
1
21.1
12.6
10.5
2.3
19.5
10.7
7.0
0.4
0.5
0.5
0.5
0.5
12/30/73
67
1
14.2
8.2
5.8
1.2
22.4
9.9
1.8
0.0
0.5
0.5
0.5
0.5
Lyon, rangeland
6/10/74
29
1
38.0
46.0
64.0
31.0
36.2
49.5
68.7
29.6
9.0
14.0
18.0
25.0
8/26/73
38
1
34.0
43.0
45.0
25.0
35.3
51.0
51.7
26.0
16.0
20.0
25.0
32.0
11/24/73
63
1
18.0
14.0
23.0
13.0
27.3
21.9
40.3
21.7
7.0
9.0
16.0
22.0
Table IV
The B0, B1, and B2 Coefficients That Relate Landsat Digital Count Data (DCc) to Ground-Measured Reflectance R for Optically Thin Atmospheric Conditions are Listed; the Estimated Digital Count Data From These Relations are for a Sun Zenith Angle of 39° for the Landsat-2 Calibration Period from 1/22/75 to 7/15/75
Landsat MSS bands
MSS 4
MSS 5
MSS 6
MSS 7
Malila
B0
16.0
8.0
11.0
3.0
regression
B1
2.09
2.63
2.25
0.84
n = 135
r2
0.71
0.71
0.71
0.80
Otterman
B0
6.8
2.7
−1.0
−1.2
theoretical
B1
2.085
2.689
2.463
0.793
B2
0.0034
0.00224
0.00146
0.00025
Combined Data
B0
14.4
4.8
0.2
−0.5
regression
B1
2.11
2.73
2.58
0.82
n = 82
r2
0.944
0.964
0.913
0.950
DCc = B0 + B1(R) + B2(R2). Reflectance values R range from 0 to 100%.
Table V
The B0 and B1 Coefficients that Relate Landsat Digital Count (DCc) to Ground Reflectance R as Derived from Results for Five Sites on Two Dates Reported by Dana8; the Coefficients Yield Estimates of Digital Count for a Sun Zenith Angle of 39° for the Landsat-2 Calibration Period 1/22/75– 7/15/75; the Equation is DCc = B0 + B1(R), Where R Ranges from 0 to 100%
Site
MSS 4
MSS 5
MSS 6
MSS 7
B0
B1
B0
B1
B0
B1
B0
B1
20 Apr. 1976
Monday Pt.
21.4
1.85
16.1
2.23
9.0
2.20
1.2
0.69
Dameron Marsh
18.0
2.74
14.3
3.07
12.0
3.30
2.5
0.70
Windmill Pt.
20.0
1.77
14.3
2.23
11.0
1.99
1.5
0.64
Millers Tavern
21.4
1.63
17.9
2.06
11.0
2.06
1.0
0.67
Lake Caroline
21.4
1.63
18.8
1.81
11.0
2.17
1.5
0.73
19 Apr. 1976
Monday Pt.
21.4
1.91
14.3
2.40
7.0
2.39
0.4
0.75
Dameron Marsh
14.7
3.48
12.5
3.62
18.0
2.21
6.3
0.62
Windmill Pt.
18.7
2.30
12.5
2.67
9.0
2.31
0.8
0.71
Combined results
12.4
2.10
5.2
2.68
3.4
2.43
0.4
0.82
Tables (5)
Table I
Constants for Converting All Landsat-1, -2, and -3 Digital Counts to the Landsat-2 Calibration Period 22 Jan.–15 July 1975; Conversion Constants are Based on Landsat Calibration Coefficients Given in Richardson et al.5
Landsat MSS sensor
Landsat conversion constants
Calibration time period
MSS 4
MSS 5
MSS 6
MSS 7
1
K0
−6.369
−5.983
−6.667
−2.198
8/25/72–1/10/78
K1
1.242
1.342
1.314
1.146
2
K0
0
0
0
0
1/22/75–7/15/75
K1
1
1
1
1
2
K0
−1.274
−0.855
−0.952
−0.471
7/16/75–present
K1
1.280
1.145
1.095
0.947
3
K0
−3.822
−3.419
−3.809
−1.727
3/05/78–5/31/78
K1
1.083
1.154
1.067
0.965
3
K0
−3.822
−3.419
−3.809
−1.727
6/01/78–present
K1
1.280
1.188
1.095
0.947
Table II
Atmospheric Radiative Transfer Constants for the Four Landsat MSS Bandsa
Radiative transfer constants
Landsat MSS bands
MSS 4
MSS 5
MSS 6
MSS 7
1. A0
0.10
0.07
0.07
0.14
2. A1
0.0157
0.0117
0.0105
0.0637
3. B
0.061
0.035
0.025
0.013
4. Wg
0.027
0.021
0.029
0.050
5. E0
17.7
15.15
12.37
24.91
Explanations for each line of constants are as follows: 1 and 2. Landsat-2 calibration coefficients for the time period from 1/22/75 to 7/15/75 taken from Richardson et al.5. 3. Backscattering optical thickness of the atmosphere from Otterman et al.7. 4. Gas absorption coefficients assuming 10 mm of precipitable water in a vertical column from Otterman et al.7. 5. Solar constant (mW/cm2) from Otterman and Fraser.3
Table III
Listing of Original Digital Count (DCo), Corrected Digital Count (DCc), and Ground Reflectance R Taken From Five Published Sources; DCo Were Corrected By the Solar Zenith Angle and Calibration Coefficients for Each Landsat to Obtain the DCc
Date
Solar zenith angle
Landsat series
Original digital counts
Corrected digital counts
Ground reflectance
DCo4
DCo5
DCo6
DCo7
DCc4
DCc5
DCc6
DCc7
R4
R5
R6
R7
Ballew, dark pumice sand
5/26/73
29
1
27.6
24.0
17.7
4.6
24.7
23.3
14.7
2.7
8.1
8.8
8.8
8.3
10/22/73
54
1
20.3
16.3
12.3
3.1
24.9
21.0
12.5
1.7
7.1
7.8
7.9
7.6
Ballew, light pumice sand
5/26/73
29
1
59.0
60.0
50.2
19.0
59.4
66.2
52.6
17.3
21.4
21.9
24.3
21.8
10/22/73
54
1
40.0
39.7
33.2
12.2
57.2
62.5
48:8
15.5
22.4
25.7
24.1
26.8
Otterman, arid and semiarid regions
1/2/73
62
1
38.0
51.0
53.0
24.0
67.5
103.0
104.2
41.8
28.1
36.7
39.4
55.6
1/2/73
39
1
42.0
41.0
46.0
23.0
45.7
49.0
53.7
24.1
16.5
15.9
19.9
30.7
10/22/72
39
1
76.0
105.0
97.0
38.0
88.0
134.9
120.7
41.3
34.7
45.5
43.6
51.1
8/9/72
31
1
91.0
115.0
103.0
41.0
96.6
134.4
116.6
40.6
37.2
45.3
41.7
49.4
Richardson, Silverleaf sunflower plant
6/2/77
34
3
26.0
26.0
68.0
33.0
30.0
27.1
68.9
28.8
10.7
7.8
28.4
31.5
Ahern, oligotrophic lake
5/27/76
39
3
13.0
10.0
9.0
1.0
15.3
10.5
8.9
0.4
0.5
0.4
0.2
0.1
9/12/76
39
3
12.0
12.0
14.0
4.0
14.0
12.8
14.3
3.3
0.4
0.3
0.2
0.1
Lyon, concrete runway
7/ /73
28
1
75.9
79.4
67.9
26.4
77.3
88.5
72.6
24.6
27.9
31.0
30.0
32.1
8/26/73
38
1
71.7
73.8
63.7
25.6
81.5
91.7
75.9
26.7
27.9
31.0
30.0
32.1
12/30/72
67
1
36.2
35.3
30.6
11.8
76.7
82.6
66.7
22.5
27.9
31.0
30.0
32.1
Lyon, carbon black dump
6/10/74
29
1
23.5
13.9
13.5
2.6
20.2
11.2
9.8
0.6
0.5
0.5
0.5
0.5
8/25/73
38
1
21.1
12.6
10.5
2.3
19.5
10.7
7.0
0.4
0.5
0.5
0.5
0.5
12/30/73
67
1
14.2
8.2
5.8
1.2
22.4
9.9
1.8
0.0
0.5
0.5
0.5
0.5
Lyon, rangeland
6/10/74
29
1
38.0
46.0
64.0
31.0
36.2
49.5
68.7
29.6
9.0
14.0
18.0
25.0
8/26/73
38
1
34.0
43.0
45.0
25.0
35.3
51.0
51.7
26.0
16.0
20.0
25.0
32.0
11/24/73
63
1
18.0
14.0
23.0
13.0
27.3
21.9
40.3
21.7
7.0
9.0
16.0
22.0
Table IV
The B0, B1, and B2 Coefficients That Relate Landsat Digital Count Data (DCc) to Ground-Measured Reflectance R for Optically Thin Atmospheric Conditions are Listed; the Estimated Digital Count Data From These Relations are for a Sun Zenith Angle of 39° for the Landsat-2 Calibration Period from 1/22/75 to 7/15/75
Landsat MSS bands
MSS 4
MSS 5
MSS 6
MSS 7
Malila
B0
16.0
8.0
11.0
3.0
regression
B1
2.09
2.63
2.25
0.84
n = 135
r2
0.71
0.71
0.71
0.80
Otterman
B0
6.8
2.7
−1.0
−1.2
theoretical
B1
2.085
2.689
2.463
0.793
B2
0.0034
0.00224
0.00146
0.00025
Combined Data
B0
14.4
4.8
0.2
−0.5
regression
B1
2.11
2.73
2.58
0.82
n = 82
r2
0.944
0.964
0.913
0.950
DCc = B0 + B1(R) + B2(R2). Reflectance values R range from 0 to 100%.
Table V
The B0 and B1 Coefficients that Relate Landsat Digital Count (DCc) to Ground Reflectance R as Derived from Results for Five Sites on Two Dates Reported by Dana8; the Coefficients Yield Estimates of Digital Count for a Sun Zenith Angle of 39° for the Landsat-2 Calibration Period 1/22/75– 7/15/75; the Equation is DCc = B0 + B1(R), Where R Ranges from 0 to 100%