Convert Satellite Image to TOA Reflectance and At-Satellite Brightness Temperature

Background

Standard Landsat 8 data products provided by the USGS EROS Center consist of quantized and calibrated scaled Digital Numbers (DN) representing multispectral image data acquired by both the Operational Land Imager (OLI) and Thermal Infrared Sensor (TIRS). The products are delivered in 16-bit unsigned integer format and can be rescaled to the Top Of Atmosphere (TOA) reflectance and/or radiance using radiometric rescaling coefficients provided in the product metadata file (MTL file), as briefly described below.  The MTL file also contains the thermal constants needed to convert TIRS data to the at-satellite brightness temperature.

While the TIRS bands were designed to allow the use of split-window surface temperature retrieval algorithms, (such as the use of split window techniques for atmospheric correction and retrieval of surface temperature values), it is recommended that users refrain from relying on band 11 data in quantitative analysis of the TIRS data due to the larger calibration uncertainty associated with this band.

Since the launch of Landsat 8 in 2013, thermal energy from outside the normal field of view (stray light) has affected the data collected in TIRS Bands 10 and 11. This varies throughout each scene and depends upon radiance outside the instrument field of view, which users cannot correct in the Landsat Level-1 data product. Band 11 is significantly more contaminated by stray light than Band 10. It is recommended that users refrain from using Band 11 data in quantitative analysis including use of Band 11 in split-wind surface temperature retrieval algorithms. Details about Landsat 8 TIRS stray light can be found in Appendix A of the Landsat 8 Data User Handbook.

Conversion to TOA Radiance

OLI and TIRS band data can be converted to TOA spectral radiance using the radiance rescaling factors provided in the metadata file:
 

L_λ = M_LQ_cal + A_L 

where:              

L_λ          = TOA spectral radiance (Watts/( m2 * srad * μm))
M_L         = Band-specific multiplicative rescaling factor from the metadata (RADIANCE_MULT_BAND_x, where x is the band number)
A_L          = Band-specific additive rescaling factor from the metadata (RADIANCE_ADD_BAND_x, where x is the band number)
Q_cal        = Quantized and calibrated standard product pixel values (DN)         

Conversion to TOA Reflectance

OLI band data can also be converted to TOA planetary reflectance using reflectance rescaling coefficients provided in the product metadata file (MTL file).  The following equation is used to convert DN values to TOA reflectance for OLI data as follows:
 

ρλ^' = M_ρQ_cal + A_ρ 

where:              

ρλ^'          = TOA planetary reflectance, without correction for solar angle.  Note that ρλ' does not contain a correction for the sun angle.
M_ρ         = Band-specific multiplicative rescaling factor from the metadata (REFLECTANCE_MULT_BAND_x, where x is the band number)
A_ρ          = Band-specific additive rescaling factor from the metadata (REFLECTANCE_ADD_BAND_x, where x is the band number)
Q_cal        = Quantized and calibrated standard product pixel values (DN)

TOA reflectance with a correction for the sun angle is then:
 

ρλ =	ρλ'	=	ρλ'
	cos(θSZ)		sin(θSE)

where:              

ρλ          = TOA planetary reflectance
θ_SE         = Local sun elevation angle. The scene center sun elevation angle in degrees is provided in the metadata (SUN_ELEVATION).
θ_SZ         = Local solar zenith angle;  θ_SZ = 90° - θ_SE

For more accurate reflectance calculations, per pixel solar angles could be used instead of the scene center solar angle, but per pixel solar zenith angles are not currently provided with the Landsat 8 products.

Conversion to At-Satellite Brightness Temperature

TIRS band data can be converted from spectral radiance to brightness temperature using the thermal constants provided in the metadata file:
 

T =
	K2
	ln(	K1	+1)
		Lλ

where:              

T           = At-satellite brightness temperature (K)
L_λ          = TOA spectral radiance (Watts/( m2 * srad * μm))
K₁          = Band-specific thermal conversion constant from the metadata (K1_CONSTANT_BAND_x, where x is the thermal band number)
K₂          = Band-specific thermal conversion constant from the metadata (K2_CONSTANT_BAND_x, where x is the thermal band number)

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