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Landsat 8 ESUN (for Atmospheric Correction), Radiance, and TOA Reflectance

Related pages: Landsat 8 Relative Scatter Selection  Dark Objects for Landsat 8 Scatter Values

ESUN values have been calculated by GIS Ag Maps and are listed below but are not necessary to convert Landsat 8 to DOS surface reflectance (the correct image-based atmospheric correction model for Landsat 8) as they were for previous Landsat satellites. The Landsat 8 DOS Method can be applied, which avoids many steps previously necessary to retrieve surface reflectance.

Important: Read the following two paragraphs about the easier DOS atmospheric correction surface reflectance method that should be used for Landsat 8.

ESUN values needed to be established for Landsat 8 in order to determine if the COST or DOS method should be used to calculate surface reflectance (TOA is not surface reflectance). Correct ESUN values were calculated by GIS Ag Maps and are listed and described in the Landsat 8 ESUN Values section. It has been determined by GIS Ag Maps, based on information shown in this website, that the DOS method is best for Landsat 8 surface reflectance; this makes atmospheric correction for Landsat 8 easier as is explained in the next paragraph. Data that show DOS should be used can be viewed on the following pages of this website: Landsat 8 DOS vs. COST NIR Reflectance  Landsat 8 vs. Landsat 7 LEDAPS Soybean Reflectance    Landsat 8 vs. Landsat 7 LEDAPS Reflectance.  

The fact that DOS is best for Landsat 8 reduces the steps necessary in the atmospheric correction process; simply apply the steps for the method that follows in this paragraph (the following Landsat 8 DOS Method was published by GIS Ag Maps at www.gisagmaps.com on 9/5/2013 and is based on the DOS method from Chavez [1988]): 1) Convert the digital number (DN) values to TOA reflectance with the USGS Landsat 8 Conversion to TOA Reflectance Equation (USGS, 2013b; included near bottom of page), making sure to apply the sun angle correction factor. As of now, the following equation applies to all bands: ([DN * .00002) - .1] / [cosine of the solar zenith]). This will compute TOA reflectance for all bands. 2) Establish one-percent haze reflectance.  First, establish the haze DN as shown in the Calculating Lhaze section of the Landsat 8 Atmospheric Correction page and in the Haze Selection Methods section of the Atmospheric Correction Guide (this step involves the most time). Apply the Conversion to TOA Reflectance Equation (same reflectance equation as above) to calculate haze reflectance from the DN(making sure to apply the sun angle correction factor). Subtract .01 from the haze amount to calculate one-percent haze reflectance. Subtracting .01 reflectance units will result in the established dark object subtraction pixel having one-percent reflectance and should be applied because of " the fact that very few targets on the Earth's surface are absolute black, so an assumed one-percent minimum reflectance is better than zero percent" (Chavez, 1996). 3) Subtract the one-percent haze amount (haze reflectance - .01) from all TOA reflectance values to calculate surface reflectance. Because DOS should be applied for Landsat 8 image-based atmospheric correction instead of COST, this much simpler method can be used to retrieve surface reflectance as opposed to using all the DOS steps shown in the Landsat 8 Atmospheric Correction page.

 

Landsat 8 ESUN Values

There are currently no Landsat 8 exoatmospheric irradiance ESUN values posted by NASA for the public; however, ESUN values are not necessary to convert Landsat 8 to DOS surface reflectance (the correct image-based model for Landsat 8) as they were for previous Landsat satellites (as is explained at the top of the page).

Correct ESUN values to use are listed below as ESUN TOA * and are explained below. The values can be used for COST or DOS atmospheric correction but can be proven to be correct by applying them to TOA reflectance. Landsat 8 TOA reflectance will be the same whether calculated based on the standard TOA equation using the ESUN values or with the Landsat 8 Conversion TOA Reflectance equation (shown near bottom of page which does not include ESUN values but has them embedded in the equation).  

(band 8 [not shown] is panchromatic; bands 10 and 11 [also not shown] are both thermal)

(Landsat 8 low and high band designation are derived from data from USGS [2013b] which can be accessed at:  http://landsat.usgs.gov/band_designations_landsat_satellites.php; opens in new tab)

           
      
     Landsat 8                          
  ESUN   
        Band                Low           High          Center  Linear     TOA*       
      2 (blue)            0.45         0.51      0.480  1991 * *    2067     
      3 (green)            0.53         0.59      0.560  1812 * * *    1893    
      4 (red)            0.64         0.67      0.655  1549    1603     
      5 (NIR)            0.85         0.88      0.865  962.6    972.6     
      6 (SWIR)            1.57         1.65      1.610  251.7    245.0     
      7 (SWIR)            2.11         2.29      2.200  86.30    79.72     
      9 (SWIR)            1.36         1.38      1.370  385.4    399.7     

 

Band 1 is indigo and is used for coastal applications; Band 8 is panchromatic; bands 10 and 11 are thermal and can be converted to at-satellite brightness temperature as shown at the bottom of this page.

ESUN TOA calculation method. The ESUN value is derived by solving for it in the standard TOA equation (for a single scene); where, TOA reflectance = (at sensor radiance x pi x earth-sun distance²] / [cosine of solar azimuth x ESUN]). Landsat 8 TOA reflectance can be computed with the Landsat 8 Conversion to TOA Reflectance equations (USGS, 2013) shown at the bottom of the page (the sun angle factor needs to be applied). ESUN values are calculated by solving for them in the standard TOA equation. To derive the ESUN values, TOA reflectance was first calculated with the Landsat 8 Conversion to TOA Reflectance equation, then the TOA reflectance values (for each band) were used to solve for the ESUN values in the standard TOA equation (once TOA reflectance is known, all values in the standard TOA equation except ESUN are known, so ESUN can be solved for). When the ESUN TOA values above are input into the standard TOA reflectance equation, the calculated reflectance is the same as the value calculated by the USGS Landsat 8 TOA Reflectance equation (to the 10,000 place or virtually the 10,000 place where .01 is one-percent).

ESUN Linear above is the linear estimation of Landsat 8 ESUN values based on band wavelength centers and associated published ESUN values of Landsat 5, 7, and EO-1 satellites.  

* *  Landsat 8 band 2 (.480 center wavelength) ESUN value is estimated based on linear interpolation of center wavelengths from of EO-1 band 1p (.440) and EO-1 band 1 (.4825).  Landsat 8 band 2 and EO-1 band 1 have virtually the same center bandwidth (.480 versus .4825 for Landsat and EO-1, respectively); therefore, the estimated Landat 8 band 2 ESUN value (1991) is nearly the same as the published EO-1 band 1 value (1996) (well within one percent of each other). Additionally, Landsat 8 band 2 has nearly the same center wavelength as Landsat 7 band 1 (.480 versus .483 for Landsat, respectively); as a result, the estimated Landsat 8 band 2 ESUN value is nearly the same as the published Landsat 7 band 1 ESUN value (1991 versus 1997 for Landsat 8 and 7, respectively).

* * *  Landsat 8 band 3 and Landsat 7 band 2 have the same center wavelength; the ESUN value for Landsat 7 band 2 is 1812 so this value can be used to estimate Landsat 8 band 3.

ESUN Linear above is the linear estimation of Landsat 8 ESUN values based on band wavelength centers and associated published ESUN values of Landsat 5, 7, and EO-1 satellites. All remaining Landat 8 estimated ESUN values (those not previously discussed  associate with above asterisks) were linearly interpolated from band wavelength centers immediately larger and smaller from the list below of Landsat and EO-1 values; all are based on at least one Landsat value. 

 

Correlation between band center wavelength (x-axis) from blue to short wave infrared regions and published ESUN values (pdf) (y-axis) for Landsat 5, Landsat 7, and EO-1 satellites. Relationship of trendline is exponential; data for plot is listed below. Although there is a strong overall exponential relationship, the curve does not pass through many values so linear interpolation from point to point is applied to estimate Landsat 8 ESUN values. Although solving for ESUN in the TOA reflectance equation (as described above) is the preferred method to estimate Landsat 8 ESUN values; if preferred, an approximation can be made based on past values at band center wavelengths as plotted below. The plot below applies to Landsat band 2 and larger (Landsat band 1 is indigo which decreases in ESUN value from blue). 

(Exponent in above equation is -1.857x)

The data for the plot above is shown below in order of low to high center wavelength of bands. The Landsat and EO-1 bands included were those that most closely matched the spectral range of Landsat 8 bands 2 - 7 and 9 (Landsat 8 band 1 is for coastal/aerosol purpose and has virtually the same bandwidth as EO-1 band 1p which has an ESUN value of 1857, both bands are centered in indigo region of spectrum where ESUN values decrease from the blue region; band 8 is panchromatic; bands 10 and 11 are thermal and can be converted to at-satellite brightness temperature as shown at the bottom of this page):

      Satellite Band  Low  High Center ESUN
        EO-1    1 0.450 0.515 0.4825 1996
        L7    1 0.452 0.514 0.4830 1997
        L5    1 0.452 0.518 0.4850 1983
        L7    2 0.519 0.601 0.5600 1812
        EO-1    2 0.525 0.605 0.5650 1807
        L5    2 0.528 0.609 0.5685 1796
        L5    3 0.626 0.693 0.6595 1536
        L7    3 0.631 0.692 0.6615 1533
        EO-1    3 0.633 0.690 0.6615 1536
        EO-1    4 0.775 0.805 0.7900 1145
        L7    4 0.772 0.898 0.8350 1039
        L5    4 0.776 0.904 0.8400 1031
        EO-1    4p 0.845 0.890 0.8675 955.8
        EO-1    5p 1.200 1.300 1.2500 452.3
        L7    5 1.547 1.748 1.6475 230.8
        EO-1    5 1.550 1.750 1.6500 235.1
        L5    5 1.567 1.784 1.6755 220.0
        L7    7 2.065 2.346 2.2055 84.90
        EO-1    7 2.080 2.350 2.2150 82.38
        L5    7 2.097 2.349 2.2230 83.44

 

For Landsat 8, TOA radiance can be calculated from data in the corresponding .MTL file as shown on this USGS Landsat 8 webpage (USGSb, 2013) (outside page; opens in new tab) (the information from this USGS Landsat 8 page is also included below). TOA radiance is calculated the same as Lsatrad in the COST model described on the main Atmospheric Correction pageso this radiance value can be used as the radiance for models. Earth-sun distance is included in Landsat 8 files which is new for Landsat metadata files. For atmospheric correction, Landsat 8-related values are input into a reflectance model similarly to other Landsats (an satellites in general); a main benefit of Landsat 8, however, is that there is no need to apply the total atmospheric precipitable water correction factor for NIR bands.

 

The following is from USGSb (2013): Using the USGS Landsat 8 Product (cited at: http://landsat7.usgs.gov/Landsat8_Using_Product.php)

Background
The standard Landsat 8 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. Further details can be found in the LDCM Cal/Val Algorithm Description Document and the Landsat 8 Science Users’ Handbook available from the Landsat website (location coming soon).    

 

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:

Lλ = MLQcal + AL 

where:              

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

 

Conversion to TOA Reflectance (need to apply the sun angle correction as shown below)

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' = MρQcal + Aρ 

where:              

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

 

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

where:              

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

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:

where:              

T           = At-satellite brightness temperature (K)
Lλ          = TOA spectral radiance (Watts/( m2 * srad * μm))
K1          = Band-specific thermal conversion constant from the metadata (K1_CONSTANT_BAND_x, where x is the band number, 10 or 11)
K2          = Band-specific thermal conversion constant from the metadata (K2_CONSTANT_BAND_x, where x is the band number, 10 or 11)

 

References

Chavez, P.S., Jr. 1996. Image-based atmospheric corrections–revisited and improved. Photogrammetric Engineering and Remote Sensing 62(9): pp.1025-1036.

Chavez, P.S., Jr. 1988. An improved dark-object subtraction technique for atmospheric scattering correction of multispectral data. Remote Sensing of Environment 24: pp.459-479.

USGS. 2013b.  Using the USGS Landsat 8 Product. Cited at: http://landsat7.usgs.gov/Landsat8_Using_Product.php

USGS. 2013b. Landsat Missions: Frequently Asked Questions About the Landsat Missions. USGS. Last modified: 5/30/123. Cited at: http://landsat.usgs.gov/band_designations_landsat_satellites.php