Using the USGS Landsat Level-1 Data Product

Landsat Collections Level-1 data products consist of quantized and calibrated scaled Digital Numbers (DN) representing the multispectral image data.  Landsat 8 and Landsat 9 data are delivered in 16-bit unsigned integer format. Landsat 1-7 products are delivered in 8-bit unsigned integer format. Landsat Level-1 data can be converted to TOA spectral radiance, reflective band DN’s can be converted to TOA reflectance, and thermal band data can be converted from spectral radiance to TOA  brightness temperature by using the formulas listed below. 
 

Conversion to TOA Radiance

Landsat Level-1 data can be converted to TOA spectral radiance using the radiance rescaling factors in the MTL file:

\(L_\lambda = M_L Q_{cal} + A_L\)

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

Reflective band DN’s can be converted to TOA reflectance using the rescaling coefficients in the MTL file:  

\({\rho _ \lambda} ^ \prime = M_\rho Q_{cal} + A_\rho\)

where:

ρ_λ^'   = 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:

\( \rho _ \lambda = \frac{{\rho _ \lambda} ^ \prime}{\cos \big( \theta _ {SZ} \big)} = \frac{{\rho _ \lambda} ^ \prime}{\sin \big( \theta _ {SE} \big)} \)

where:

ρ_λ=  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. While per-pixel solar zenith angles are not provided with the Landsat Level-1 products, tools are provided which allow users to create angle bands.

Conversion to Top of Atmosphere Brightness Temperature

Thermal band data can be converted from spectral radiance to top of atmosphere brightness temperature using the thermal constants in the MTL file:

\(T = \frac{K_2}{\ln \big( \frac{K_1}{{L _ \lambda} }+ 1 \big)}\)

where: 

T  =  Top of atmosphere brightness temperature (K)where:
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)

The information displayed below is for historical reference only. 

Solar exoatmospheric spectral irradiances (ESUN) for the Landsat 1-7 Pre-Collection Level-1 data 

This information is not relevant to Landsat Collection 1 data so we do not recommend using the ESUN values with Collection 1 Level-1 data products. Landsat 1-7 Collections Level-1 products are cross-calibrated to L8 OLI and provide two sets of scaling factors, one to calculate the TOA reflectance and the other to calculate TOA radiance. The recommended ESUN values Pre-Collection Landsat 1-7 level-1 data are listed below. Although the data are consistently calibrated, calculated TOA reflectance over the same target may differ among the sensors due to the spectral bandpass difference. ESUN values are not required for Landsat 8 and Landsat 9 Level-1 data because the metadata file provides coefficients necessary to convert to radiance and reflectance from the quantized and calibrated DNs of the product. The values can be applied to all MSS sensors, due to cross-calibration of all the MSS sensors to match the Landsat 5 instrument.

ESUN values are derived from the ChKur spectrum, which is the combined Chance-Kurucz Solar Spectrum within MODTRAN 5.