Landsat 4, 5, and 8 are different satellite sensors but they share formulas to calculate Radiance, Reflectance, and converting the thermal data to temperature. The formulas (listed below) require multipliers and additive constants (found in the metadata, usually an ancillary file with a name such as <image>.met, or <image>_MTL.txt) that are unique for each satellite platform and frequently unique for each image.
Landsat 7 has different formulas to calculate Radiance and Reflectance and has different metadata fields. However a dialog is already provided in ERDAS IMAGINE on the Raster tab / Resolution group / Radiometric pulldown to calculate Landsat 7 Reflectance values.
This model implements the formulas published by the USGS for converting the quantized and calibrated scaled Digital Numbers (DN) representing multispectral image data acquired by Landsat 4 and 5 and the Landsat 8 Operational Land Imager (OLI) and Thermal Infrared Sensor (TIRS) to Radiance and Temperature. All Landsat spectral and thermal data can be converted to radiance, but only the spectral data (Landsat 4-5 bands 1-5 and 7 and Landsat 8 bands 1-9) can be converted to reflectance (see separate article on Reflectance conversion). Thermal data (Landsat 4-5 band 6 and Landsat 8 bands 10-11) can be converted to temperature but not reflectance and this is the conversion covered by this model.
The conversion formulas require values stored in the metadata for each satellite platform.
The published formulas are:
Ll = MlQcal + Al
Ll = Top of Atmosphere (TOA) radiance in (Watts/m2*srad*um))
Ml = Band-specific multiplicative rescaling factor from the metadata (RADIANCE_MULT_BAND_x, where x is the band number)
Qcal = Quantized and calibrated standard product pixel values (DN)
Al = Band-specific additive rescaling factor from the metadata (RADIANCE_ADD_BAND_x, where x is the band number)
This formula is relevant to all data bands.
At-Satellite Temperature of Landsat 4-5 thermal and Landsat 8 TIRS Bands:
T = K2 / ln (K1/Ll +1)
T = at-satellite brightness temperature in degrees Kelvin
K2 = Band-specific thermal conversion constant from the metadata (K2_CONSTANT_BAND_x where x is band number 10 or 11)
K1 = Band-specific thermal conversion constant from the metadata (K1_CONSTANT_BAND_x where x is band number 10 or 11)
Ll = product of the Radiance formula
The model also provides an output units choice. The basic formula converts the radiance values to degrees Kelvin (K). However, most of us do not know what our Kelvin temperature (310.15) is, but we do know our body temperature is supposed to be near 98.6 degrees Fahrenheit or 37 degrees Celsius. So the model gives the user the choice of specifying the output units by typing in 1 for Kelvin, 2 for Celsius, or 3 for Fahrenheit.
Since the USGS reports that the Band 11 thermal information from Landsat 8 should no longer be used for quantitative analysis this model has been designed to process only a single band from the input image (usually Landsat 8 Band 10). However, the formula is the same for both Landsat 8 Thermal bands, so if you wish to input an image with Band 11, simply use the *_BAND_11 values mentioned below. Similarly, the Thermal band of Landsat 4 and 5 can be corrected using the appropriate correction parameters.
RADIANCE_MULT_BAND_n, RADIANCE_ADD_BAND_n, K1_CONSTANT_BAND_n, and K2_CONSTANT_BAND_n (where n is usually 10) are variables which can be found in the original image's metadata (<image>_MTL.txt) file.
The processes a single band only and so only a single band (not a range) should be specified in the Thermal Band Number field. The model will accept multiple band images (and input Thermal Band Number ranges), such as a Landsat 8 two-band TIR composite, but only a single set of correction values can be entered and so they would be applied to all bands (whereas they would only be valid for one). The model can be easily modified to process multiple bands with multiple sets of correction values if desired.
The user will need to manually review the image's metadata file (usually an ancillary file with a name such as <image>.met, or <image>_MTL.txt) to determine several of the necessary correction parameters. A separate Spatial Recipe article will provide a model for use with ERDAS IMAGINE 2016 or later that will automatically parse the metadata file to acquire these values.
Landsat 8 Thermal Band 10: Input an image which contains the Thermal IR wavelength of Landsat 8 (or 4 / 5) data.
Temperature Output: Name of the output single-band, floating-point image with values measured in the units specified in the next field.
Specify 1 = Kelvin; 2 = Celsius; or 3 = Fahrenheit: Enter the number 1, 2 or 3 to specify the desired temperature units.
Landsat 8 Band 10 K1 Constant: Enter the value of the image-specific K1 Constant value. This value can usually be found by reviewing the image's metadata file (<image>_MTL.txt) for the K1_CONSTANT_BAND_10 keyword.
Landsat 8 Band 10 K2 Constant: Enter the value of the image-specific K2 Constant value. This value can usually be found by reviewing the image's metadata file (<image>_MTL.txt) for the K2_CONSTANT_BAND_10 keyword.
RADIANCE_MULT_BAND_10: Enter the value of the image-specific Band 10 radiance multiplier. This value can usually be found by reviewing the image's metadata file (<image>_MTL.txt) for the RADIANCE_MULT_BAND_10 keyword.
RADIANCE_ADD_BAND_10: Enter the value of the image-specific Band 10 radiance multiplier. This value can usually be found by reviewing the image's metadata file (<image>_MTL.txt) for the RADIANCE_ADD_BAND_10 keyword.
Thermal Band Number: Enter the band number in the input file which represents the Thermal band to be processed. For example, band 1 in a Landsat 8 TIR composite file is usually the Thermal Band 10, whereas in a 7-band Landsat 5 image, band 6 might be the Thermal information. Note: If you have a Landsat 8 MSI/TIR (9 band) composite, the 8th band of the file represents Thermal Band 10 of the sensor (because the Pan [Band 8] and Cirrus [Band 9] wavelengths are not included in the composite)! You do not need to enter a range (e.g. 1:1), a single value is acceptable (e.g. 1).