# Landsat8 DN to TOA Reflectance (minus values)

I'm learning how to perform atmospheric correction manually, hence not using the automated methods available in ENVI

metadata (band 1) for my Landsat 8 scene is as follows;

REFLECTANCE_MULT_BAND_1 = 2.0000E-05

SUN_ELEVATION = 48.12237303

So when I use band math to calculate TOA Radiance I type in this:

(0.012344*B1)-61.72016

And it yields a spectral statistics that look kind-of right

When I use any of the following band math formulae;

TOA Reflectance (excluding sun elevation adjustment)

(B1*0.00002)-0.1

TOA Reflectance (including sun elevation adjustment)

((B1*0.00002)-0.1)/0.74457226676389733207607359928648

Or calculate straight from the raw DN to TOA Reflectance (including sun elevation adjustment)

((((0.012344*B1)-61.72016)*0.00002)-0.1)/0.74457226676389733207607359928648

I end up with something like this:

which looks incorrect.

I've googled and either my search terms are rubbish or no one uses manual band math to do this.

[EDIT]

Mikkel's answer below with the revised band math calculation (omitting the intermediate steps) yielded the following statistics:

which look somewhat more realistic.

Wondering if i should add 13.4305 to each band, or ignore the negative minimum?

[END EDIT]

[EDIT #2]

Mikkel was spot on again, in suggesting that the -13.4305 values were isolated to the "no data" areas around the image;

as you can see, isolated only to the northern edge of the scene.

[END EDIT #2]

One flaw in your approach. You don't need to go through DN to radiance.
You can go straight to the DN to reflectance.
Just stick to ((B1*0.00002)-0.1)/0.74457226676389733207607359928648.

• this worked pretty well! i suppose either it was never explained that TOA radiance / TOA reflectance excl. sun elevation weren't necessary steps in the correction sequence. Oct 12, 2015 at 8:09
• per the edited post above, is it necessary to add 13.4305 to each band to bring them up to min = 0, or is that unnecessary?? Oct 12, 2015 at 8:16
• @kyuss , try checking where those -0.134305 are located. I suspect that it is the no-data areas around the edge of the image. Oct 12, 2015 at 8:19
• brilliant, i didn't even check anything but the southern borders where there werent negative values. thanks for all of your help. Oct 12, 2015 at 8:24
• @kyuss now the next step in your process is "simply" to do the atmospheric correction. Oct 12, 2015 at 8:34

Here's a good read on the physics of atmospheric correction, and might help with the issue... I'm a button pushing guy, I feel your pain, at least you can just click that beautiful QUAC or FLAASH button once you're outside of academia.

http://modis.gsfc.nasa.gov/data/atbd/atbd_mod08.pdf

• thanks Steven. i have - as you've inferred - learned much during my study but that modis document may well help fill out my understanding gaps re: radiative transfer. Oct 12, 2015 at 8:18