Calibrated Landsat Digital Number (DN) to
Top of Atmosphere (TOA) Reflectance
Conversion
Richard Irish - SSAI/GSFC
[email protected]
Remote Sensing Basics | August, 19 2008
Spectral Radiance
The landsat TM and ETM+ instruments are not household digital cameras
placed in space.
Rather they are highly calibrated imaging radiometers that produce
scientifically useful observations in units of spectral radiance.
The term radiance is used to characterize the entire solar spectrum while
spectral radiance is used to characterize the light at a single wavelength
or band interval
Spectral radiance is a precise scientific term used to describe the power
density of radiation; it has units of W-m-2-sr-1- µm-1 (i.e. watts per unit
source area, per unit solid angle, and per unit wavelength
Remote Sensing Basics | August, 19 2008
Spherical Integrating Source
ETM+ SIS is calibrated by SBRS to National Institute of Standards and Technology
(NIIST) traceable standards of spectral radiance.
Remote Sensing Basics | August, 19 2008
Calibration Function
The SIS100 is equipped with 18 200-watt lamps; 6 45-watt lamps, and 10 8-watt
lamps. It provided radiance levels covering the full dynamic range of the instrument
in all bands, and at least 10 usable radiance levels for each band for both gain states
The quantized detector(d) by detector responses, Q(d,b,s) were regressed against the
integrating sphere radiance levels Lλ(b,s) per the calibration equation:
Q(d,b,s) = G(d,b) Lλ(b,s) + B(d,b)
where the slopes of these regression lines are the responsivities or gains, G(d,b),
and the intercepts are the biases, B(d,b)
After launch, raw DNs are converted to radiances per the equation:
Lλ(b,s) = (Q(d,b,s) - B(d,b)) / G(d,b)
Remote Sensing Basics | August, 19 2008
Band Specific Post-calibration Lower and Upper
Dynamic Range Limits
Band
Number
1
2
3
4
5
6
7
8
Table 1. ETM+ Spectral Radiance Range
watts/(meter squared * ster * µm)
Before July 1, 2000
After July 1, 2000
Low Gain
High Gain
Low Gain
High Gain
LMIN
LMAX
LMIN
LMAX
LMIN
LMAX
LMIN
LMAX
-6.2
297.5
-6.2
194.3
-6.2
293.7
-6.2
191.6
-6.0
303.4
-6.0
202.4
-6.4
300.9
-6.4
196.5
-4.5
235.5
-4.5
158.6
-5.0
234.4
-5.0
152.9
-4.5
235.0
-4.5
157.5
-5.1
241.1
-5.1
157.4
-1.0
47.70
-1.0
31.76
-1.0
47.57
-1.0
31.06
0.0
17.04
3.2
12.65
0.0
17.04
3.2
12.65
-0.35
16.60
-0.35
10.932
-0.35
16.54
-0.35
10.80
-5.0
244.00
-5.0
158.40
-4.7
243.1
-4.7
158.3
Quantized ETM+ Output
Q(DN)
255
5% margin
HIGH GAIN
LOW GAIN
Bias 5
Lλ
Spectral Radiance, L
Remote Sensing Basics | August, 19 2008
Lλ
Calibrated DN to Spectral Radiance Conversion
Lλ = ((LMAXλ - LMINλ )/(QCALMAX-QCALMIN)) * (QCAL-QCALMIN) + LMINλ
where:
Lλ
QCAL
= spectral radiance at the sensor’s aperture
= the quantized calibrated pixel value in DN
LMINλ = the spectral radiance scaled to QCALMIN in watts/(meter squared * ster * µm)
LMAXλ = the spectral radiance scaled to QCALMAX in watts/(meter squared * ster * µm)
QCALMIN = the minimum quantized calibrated pixel value (corresponding to LMIN ) in DN
λ
1 for LPGS products, 0 for NLAPS products
QCALMAX = the maximum quantized calibrated pixel value
(corresponding to LMAXλ) in DN = 255
Remote Sensing Basics | August, 19 2008
Gain State Determination
Curiously, unlike the Landsat Archive products the metadata accompanying
the GLS products does not contain gain state information.
Using Glovis go to Collections ->> Landsat Archive ->> SLC-off (2003 -> present)
Under the Fill pull-down select Download Visible Browse and metadata.
Open the metadata file and scroll down to view the following entries:
gain_band_1 = H
gain_band_2 = H
gain_band_3 = H
gain_band_4 = L
gain_band_5 = H
gain_band_6_vcid_1 = L
gain_band_6_vcid_2 = H
gain_band_7 = H
gain_band_8 = L
Remote Sensing Basics | August, 19 2008
Spectral Radiance to TOA Reflectance Conversion
ρP = π * Lλ * d 2/ ESUNλ * cos(ϑ)
S
where:
ρ P = unitless TOA or planetary reflectance
Lλ = spectral radiance at the sensor’s aperture
d
ESUNλ
= Earth-Sun distance in astronomical units from
nautical handbook or interpolated values
= mean solar exoatmospheric spectral irradiance
cos(ϑ)S = solar zenith angle in degrees
Remote Sensing Basics | August, 19 2008
Seasonal Sun Angle Variations
Remote Sensing Basics | August, 19 2008
Solar Zenith Angle
From the metadata file that accompanies the GLS, GeoCover and Landsat Archive Products: SUN_ELEVATION = 51.6035637
Remote Sensing Basics | August, 19 2008
ESUNλ
Table 2. ETM+ Solar Spectral Irradiances
watts/(meter squared * µm)
Band
1
1969.000
2
1840.000
3
1551.000
4
1044.000
5
225.700
7
82.07
8
1368.000
d
Julian
Day
1
15
32
46
60
Distance
.9832
.9836
.9853
.9878
.9909
Table 3. Earth-Sun Distance in Astronomical Units
Julian
Julian
Julian
Distance
Distance
Distance
Day
Day
Day
74
.9945
152
1.0140
227
1.0128
91
.9993
166
1.0158
242
1.0092
106
1.0033
182
1.0167
258
1.0057
121
1.0076
196
1.0165
274
1.0011
135
1.0109
213
1.0149
288
.9972
Julian
Day
305
319
335
349
365
One astronomical unit equals 150,000,000 kilometers
Remote Sensing Basics | August, 19 2008
Distance
.9925
.9892
.9860
.9843
.9833
Summary
In most cases it’s preferable to convert satellite image data to physical quantities
before using the data to intrepret the landscape.
Important physical quantities include spectral radiance (surface or TOA) and
spectral reflectance.
It is the surface or TOA reflectance that is characteristic of a particular surface type.
Temporal analyses are enhanced when variability between scenes is normalized
(I.e. subtraction of illumination differences).
Global change and long-term monitoring of the Earth programs and models require
extraction of remotely sensed science information from multiple sensors. Accurate,
consistent, and “sensor-independent” scientific observations defined by a
common denominator (I.e. spectral reflectance) are essential to success.
Remote Sensing Basics | August, 19 2008