Remote Sensing Basics | August, 19 2008

Calibrated Landsat Digital Number (DN) to Top of Atmosphere (TOA) Reflectance

Conversion

Richard Irish - SSAI/GSFCrichard.r.irish@nasa.gov

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.