remote sensing basics | august, 19 2008 calibrated landsat digital number (dn) to top of atmosphere...
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Remote Sensing Basics | August, 19 2008
Calibrated Landsat Digital Number (DN) to Top of Atmosphere (TOA) Reflectance
Conversion
Richard Irish - SSAI/[email protected]
Remote Sensing Basics | August, 19 2008
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- m-1 (i.e. watts per unit source area, per unit solid angle, and per unit wavelength
Spectral Radiance
Remote Sensing Basics | August, 19 2008
ETM+ SIS is calibrated by SBRS to National Institute of Standards and Technology
(NIIST) traceable standards of spectral radiance.
Spherical Integrating Source
Remote Sensing Basics | August, 19 2008
The SIS100 is equipped with 18 200-watt lamps; 6 45-watt lamps, and 10 8-wattlamps. 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 theintegrating sphere radiance levels L(b,s) per the calibration equation:
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: L(b,s) = (Q(d,b,s) - B(d,b)) / G(d,b)
Calibration Function
Q(d,b,s) = G(d,b) L(b,s) + B(d,b)
Remote Sensing Basics | August, 19 2008
Table 1. ETM+ Spectral Radiance Rangewatts/(meter squared * ster * m)
Before J ul y1, 2000 Af ter July 1, 2000Low Gain H ighGain Low Gain H ighGainBand
Number LMIN LMAX LMIN LMAX LMIN LMAX LMIN LMAX1 -6.2 297.5 -6.2 194.3 -6.2 293.7 -6.2 191.62 -6.0 303.4 -6.0 202.4 -6.4 300.9 -6.4 196.53 -4.5 235.5 -4.5 158.6 -5.0 234.4 -5.0 152.94 -4.5 235.0 -4.5 157.5 -5.1 241.1 -5.1 157.45 -1.0 47.70 -1.0 31.76 -1.0 47.57 -1.0 31.066 0.0 17.04 3.2 12.65 0.0 17.04 3.2 12.657 -0.35 16.60 -0.35 10.932 -0.35 16.54 -0.35 10.808 -5.0 244.00 -5.0 158.40 -4.7 243.1 -4.7 158.3
Band Specific Post-calibration Lower and UpperDynamic Range Limits
Bias 5
255 5% margin
Qu a
nti z
ed E
TM+
Ou t
put
Q( D
N)
Spectral Radiance, L
HIGH GAIN
LOW GAIN
L L
Remote Sensing Basics | August, 19 2008
L = ((LMAX - LMIN )/(QCALMAX-QCALMIN)) * (QCAL-QCALMIN) + LMIN
Calibrated DN to Spectral Radiance Conversion
where:
= spectral radiance at the sensor’s aperture
= the quantized calibrated pixel value in DN
= the spectral radiance scaled to QCALMIN in watts/(meter squared * ster * m)
= the spectral radiance scaled to QCALMAX in watts/(meter squared * ster * m)
= the minimum quantized calibrated pixel value (corresponding to LMINλ) in DN
= the maximum quantized calibrated pixel value
L
1 for LPGS products, 0 for NLAPS products
QCAL
LMIN
LMAX
QCALMIN
QCALMAX
(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 = Hgain_band_2 = Hgain_band_3 = Hgain_band_4 = Lgain_band_5 = Hgain_band_6_vcid_1 = Lgain_band_6_vcid_2 = Hgain_band_7 = Hgain_band_8 = L
Remote Sensing Basics | August, 19 2008
Spectral Radiance to TOA Reflectance Conversion
= L d / ESUN cos()P 2
S
P
where:
= unitless TOA or planetary reflectance
= spectral radiance at the sensor’s aperture
= Earth-Sun distance in astronomical units from
L
d
ESUN
cos()S
nautical handbook or interpolated values
= mean solar exoatmospheric spectral irradiance
= solar zenith angle in degrees
Remote Sensing Basics | August, 19 2008
Seasonal Sun Angle Variations
Remote Sensing Basics | August, 19 2008
From the metadata file that accompanies the GLS, GeoCover and Landsat Archive Products: SUN_ELEVATION = 51.6035637
Solar Zenith Angle
Remote Sensing Basics | August, 19 2008
Table 3. Earth-Sun Distance in Astronomical UnitsJulianDay Distance Julian
Day Distance JulianDay Distance Julian
Day Distance JulianDay Distance
1 .9832 74 .9945 152 1.0140 227 1.0128 305 .992515 .9836 91 .9993 166 1.0158 242 1.0092 319 .989232 .9853 106 1.0033 182 1.0167 258 1.0057 335 .986046 .9878 121 1.0076 196 1.0165 274 1.0011 349 .984360 .9909 135 1.0109 213 1.0149 288 .9972 365 .9833
Table 2. ETM+ Solar Spectral IrradiancesBand watts/(meter squared * m)1 1969.0002 1840.0003 1551.0004 1044.0005 225.7007 82.078 1368.000
One astronomical unit equals 150,000,000 kilometers
ESUN
d
Remote Sensing Basics | August, 19 2008
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.