For those interested the Spectral radiance scaling method used to convert the Digital Number value from the imagery is as follows for the Landsat 5 & 7 output.  

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radiance =((LMAX-LMIN)/(QCALmax-qcalmin))*(Qcal-Qcalmin)+Lmin

• Lmax = max radiance value of the image

• Lmin = minimum radiance value of the image

• QCalmax = maximum calibrated DN value for the image

• QCalmin = minimum calibrated DN for the image

• QCal = the specific DN of a pixel

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For the Landsat 8 output the math is slightly different:

Radiance: 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)

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Luckily enough for all of us this can be done by ArcGIS inside the program software, this is extremely valuable as there could be millions of pixels in one image, let's work smarter and have the system do the math.

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Once you have the radiance calculated for each pixel then you need to have the radiance converted to Kelvin.  In this example the calculation was done without undertaking an atmospheric correction and so the formula is as follows:

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Temp in Kelvin= k2/(ln(k1/RADIANCE+1))

k2 and k1 are calibration constants that are generated for each sensor (these are available in the imagery metadata)

for Landsat 5 k1=607.76 & k2=1260.56

for Landsat 7 k1=666.09 & k2=1282.71

for Landsat 8 k1=774.8853 & k2=1321.0789

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This is also done by ArcGIS and calculates a temperature in Kelvin for every pixel in the image.  The quick and simple last step is to have ArcGIS subtract 273.15 from each of those temperatures to convert the value to a temperature in Celsius.  With the new temperature values you can then create a map like you see in the gallery of Potential Results.

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