## 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 are 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, ETM+ and OLI/TIRS. However, if the solar elevation is given the value of the metadata file is overwritten. This is necessary when the data in the .met file is incorrect or not accurate. Also, if acquisition or production dates are not found in the metadata file then the command line values are used.

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).

## 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 0.0 when it is negative) then they are possible negative values. However, output reflectance is set to 0.0 when is obtained a negative value.

## NOTES

The output raster cell values can be rescaled with the scale parameter (e.g., with 100 in case of using reflectance output in i.gensigset).

### On Landsat-8 metadata file

NASA reports a structure of the L1G Metadata file (LDCM-DFCB-004.pdf) for Landsat Data Continuity Mission (i.e. Landsat-8).

NASA retains in MIN_MAX_RADIANCE group the necessary information to transform Digital Numbers (DN) in radiance values. Then, i.landsat.toar replaces the possible standard values with the metadata values. The results match with the values reported by the metada file in RADIOMETRIC_RESCALING group.

Also, NASA reports the same values of reflectance for all bands in max-min values and in gain-bias values. This is strange that all bands have the same range of reflectance. Also, they wrote in the web page as to calculate reflectance directly from DN, first with RADIOMETRIC_RESCALING values and second divided by sin(sun_elevation).

This is a simple rescaling

- reflectance = radiance / sun_radiance = (DN * RADIANCE_MULT + RADIANCE_ADD) / sun_radiance
- now reflectance = DN * REFLECTANCE_MULT + REFLECTANCE_ADD
- then REFLECTANCE_MULT = RADIANCE_MULT / sun_radiance
- and REFLECTANCE_ADD = RADIANCE_ADD / sun_radiance

The problem arises when we need ESUN values (not provided) to compute sun_radiance and DOS. We assume that REFLECTANCE_MAXIMUM corresponds to the RADIANCE_MAXIMUM, then

- REFLECTANCE_MAXIMUM / sin(e) = RADIANCE_MAXIMUM / sun_radiance
- Esun = (PI * d^2) * RADIANCE_MAXIMUM / REFLECTANCE_MAXIMUM

where d is the earth-sun distance provided by metadata file or computed inside the program.

The i.landsat.toar reverts back the NASA rescaling to continue using Lmax, Lmin, and Esun values to compute the constant to convert DN to radiance and radiance to reflectance with the "traditional" equations and simple atmospheric corrections. Attention: When MAXIMUM values are not provided, i.landsat.toar tries to calculate Lmax, Lmin, and Esun from RADIOMETRIC_RESCALING (in tests the results were the same).

### Calibration constants

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
- Landsat-8 OLI/TIRS: launched in 2013

## EXAMPLES

### Metadata file 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=203_30. output=_toar \
      metfile=p203r030_7x20010620.met

or

    i.landsat.toar input=L5121060_06020060714. \
      output=L5121060_06020060714_toar \
      metfile=L5121060_06020060714_MTL.txt

or

    i.landsat.toar input=LC80160352013134LGN03_B output=toar \
      metfile=LC80160352013134LGN03_MTL.txt sensor=oli8 date=2013-05-14

### DOS1 example

DN to reflectance using DOS1:

    # rename channels or make a copy to match i.landsat.toar's input scheme:
    g.copy raster=lsat7_2002_10,lsat7_2002.1
    g.copy raster=lsat7_2002_20,lsat7_2002.2
    g.copy raster=lsat7_2002_30,lsat7_2002.3
    g.copy raster=lsat7_2002_40,lsat7_2002.4
    g.copy raster=lsat7_2002_50,lsat7_2002.5
    g.copy raster=lsat7_2002_61,lsat7_2002.61
    g.copy raster=lsat7_2002_62,lsat7_2002.62
    g.copy raster=lsat7_2002_70,lsat7_2002.7
    g.copy raster=lsat7_2002_80,lsat7_2002.8

Calculation of reflectance values from DN using DOS1 (metadata obtained from p016r035_7x20020524.met.gz):

    i.landsat.toar input=lsat7_2002. output=lsat7_2002_toar. sensor=tm7 \
      method=dos1 date=2002-05-24 sun_elevation=64.7730999 \
      product_date=2004-02-12 gain=HHHLHLHHL

The resulting Landsat channels are named `lsat7_2002_toar.1 .. lsat7_2002_toar.8`.

## 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, i.colors.enhance, r.mapcalc, r.in.gdal

Landsat Data Dictionary by USGS

## AUTHOR

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