## DESCRIPTION

i.landsat.toar is used to transform the calibrated digital number of Landsat imagery products to top-of-atmosphere radiance or top-of-atmosphere reflectance and temperature (band 6 of the sensors TM and ETM+). Optionally, it can be used to calculate the at-surface radiance or reflectance with atmospheric correction (DOS method).

Usually, to do so the production date, the acquisition date, and the solar elevation is needed. Moreover, for Landsat-7 ETM+ it is also needed the gain (high or low) of the nine respective bands.

Optionally (recommended), the data can be read from metadata file (.met or MTL.txt) for all Landsat MSS, TM and ETM+. However, if the solar elevation or the product creation date are given the values of the metadata file are overwriten. This is necessary when the data in the .met file is incorrect or not accurate.

Attention: Any null value or smaller than QCALmin in the input raster is set to null in the output raster and it is not included in the equations.

## Uncorrected at-sensor values (method=uncorrected, default)

The standard geometric and radiometric corrections result in a calibrated digital number (QCAL = DN) images. To further standardize the impact of illumination geometry, the QCAL images are first converted first to at-sensor radiance and then to at-sensor reflectance. The thermal band is first converted from QCAL to at-sensor radiance, and then to effective at-sensor temperature in Kelvin degrees.

Radiometric calibration converts QCAL to at-sensor radiance, a radiometric quantity measured in W/(m² * sr * µm) using the equations:

- gain = (Lmax - Lmin) / (QCALmax - QCALmin)
- bias = Lmin - gain * QCALmin
- radiance = gain * QCAL + bias

where, Lmax and Lmin are the calibration constants, and QCALmax and QCALmin are the highest and the lowest points of the range of rescaled radiance in QCAL.

Then, to calculate at-sensor reflectance the equations are:

- sun_radiance = [Esun * sin(e)] / (PI * d^2)
- reflectance = radiance / sun_radiance

where, d is the earth-sun distance in astronomical units, e is the solar elevation angle, and Esun is the mean solar exoatmospheric irradiance in W/(m² * µm).

## Corrected at-sensor values (method=corrected)

At-sensor reflectance values range from zero to one, whereas at-sensor radiance must be greater or equal to zero. However, since Lmin can be a negative number then the at-sensor values can also be negative. To avoid these possible negative values and set the minimum possible values at-sensor to zero, this method corrects the radiance to output a corrected at-sensor values using the equations (not for thermal bands):

- radiance = (uncorrected_radiance - Lmin)
- reflectance = radiance / sun_radiance

Note: Other possibility to avoid negative values is set to zero this values (radiance and/or reflectance), but this option is ease with uncorrected method and r.mapcalc.

## Simplified at-surface values (method=dos[1-4])

Atmospheric correction and reflectance calibration remove the path radiance, i.e. the stray light from the atmosphere, and the spectral effect of solar illumination. To output these simple at-surface radiance and at-surface reflectance, the equations are (not for thermal bands):

- sun_radiance = TAUv * [Esun * sin(e) * TAUz + Esky] / (PI * d^2)
- radiance_path = radiance_dark - percent * sun_radiance
- radiance = (at-sensor_radiance - radiance_path)
- reflectance = radiance / sun_radiance

where, percent is a value between 0.0 and 1.0 (usually 0.01), Esky is the diffuse sky irradiance, TAUz is the atmospheric transmittance along the path from the sun to the ground surface, and TAUv is the atmospheric transmittance along the path from the ground surface to the sensor. radiance_dark is the at-sensor radiance calculated from the darkest object, i.e. DN with a least 'dark_parameter' (usually 1000) pixels for the entire image. The values are,

- DOS1: TAUv = 1.0, TAUz = 1.0 and Esky = 0.0
- DOS2: TAUv = 1.0, Esky = 0.0, and TAUz = sin(e) for all bands with maximum wave length less than 1. (i.e. bands 4-6 MSS, 1-4 TM, and 1-4 ETM+) other bands TAUz = 1.0
- DOS3: TAUv = exp[-t/cos(sat_zenith)], TAUz = exp[-t/sin(e)], Esky = rayleigh
- DOS4: TAUv = exp[-t/cos(sat_zenith)], TAUz = exp[-t/sin(e)], Esky = PI * radiance_dark

Attention: Output radiance remain untouched (i.e. no set to 0. when it is negative) then they are possible negative values. However, output reflectance is set to 0. when is obtained a negative value.

## NOTES

In verbose mode (flag --verbose), the program write basic satellite data and the parameters used in the transformations.

Production date is not an exact value but it is necessary to apply correct calibration constants, which were changed in the dates:

- Landsat-1 MSS: never
- Landsat-2 MSS: July 16, 1975
- Landsat-3 MSS: June 1, 1978
- Landsat-4 MSS: August 26, 1982 and April 1, 1983
- Landsat-4 TM: August 1, 1983 and January 15, 1984
- Landsat-5 MSS: April 6, 1984 and November 9, 1984
- Landsat-5 TM: May 4, 2003 and April, 2 2007
- Landsat-7 ETM+: July 1, 2000

## EXAMPLES

Transform digital numbers of Landsat-7 ETM+ in band rasters 203_30.1, 203_30.2 [...] to uncorrected at-sensor reflectance in output files 203_30.1_toar, 203_30.2_toar [...] and at-sensor temperature in output files 293_39.61_toar and 293_39.62_toar:

    i.landsat.toar input_prefix=203_30. output_prefix=_toar \
      metfile=p203r030_7x20010620.met

or

    i.landsat.toar input_prefix=L5121060_06020060714. \
      output_prefix=L5121060_06020060714_toar \
      metfile=L5121060_06020060714_MTL.txt

or

    i.landsat.toar input_prefix=203_30. output_prefix=_toar \
      sensor=tm7 product_date=2004-06-07 date=2001-06-20 \
      sun_elevation=64.3242970 gain="HHHLHLHHL"

## REFERENCES

- Chander G., B.L. Markham and D.L. Helder, 2009: Remote Sensing of Environment, vol. 113
- Chander G.H. and B. Markham, 2003.: IEEE Transactions On Geoscience And Remote Sensing, vol. 41, no. 11.
- Chavez P.S., jr. 1996. Image-based atmospheric corrections - Revisited and Improved. Photogrammetric Engineering and Remote Sensing 62(9): 1025-1036.
- Huang et al: At-Satellite Reflectance, 2002: A First Order Normalization Of Landsat 7 ETM+ Images.
- R. Irish: Landsat 7. Science Data Users Handbook. February 17, 2007; 15 May 2011.
- Markham B.L. and J.L. Barker, 1986: Landsat MSS and TM Post-Calibration Dynamic Ranges, Exoatmospheric Reflectances and At-Satellite Temperatures. EOSAT Landsat Technical Notes, No. 1.
- Moran M.S., R.D. Jackson, P.N. Slater and P.M. Teillet, 1992: Remote Sensing of Environment, vol. 41.
- Song et al, 2001: Classification and Change Detection Using Landsat TM Data, When and How to Correct Atmospheric Effects? Remote Sensing of Environment, vol. 75.

## SEE ALSO

i.atcorr, r.mapcalc, r.in.gdal

## AUTHOR

E. Jorge Tizado (ej.tizado unileon es), Dept. Biodiversity and Environmental Management, University of León, Spain

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