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Base of the Landsat TM Histogram Digital Number (DN) Scatter Selection from Chavez (1988)

Atmospheric scatter (path radiance; haze) removal has been based on the dark object subtraction (DOS; Chavez, 1988) method, where the assumption is made that for a satellite image with millions of pixels, there should be some pixels that have no reflectance. The reason there are no pixels with zero reflectance for certain bands, is the result of atmospheric scatter or haze (Chavez, 1988), erroneously increasing surface reflectance to higher values (shifting the entire histogram to the right). This assumption is then combined with "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). Chavez (1988) did not select the lowest value in the image, but the value at the base of the low end of the histogram (where an abrupt increase in frequencies begins) that was still connected with the rest of the histogram, and also had a reasonable high frequency. Keep in mind when viewing the Landsat TM histograms below, that Landsat 8 has much higher radiometric resolution (Landsat TM has an 8-bit range, while Landsat 8 has a 16-bit range when processe to Level-1 data, which result in thousands of more values). Also, Landsat 8 has a much longer statistical tail than Landsat TM. ; this can be seen in the graphics below). Chavez (1996) then calculated the base of the histogram scatter reflectance value to be .01 (as opposed to zero) by deducting .01 from it (this is one-percent dark object reflectance), because of the "fact that very few targets on Earth's surface are absolute black, so an assumed one-percent minimum reflectance is better than zero percent" (Chavez, 1996).

 

Landsat TM band 1 (blue); DN 40 (frequency of 18) is selected as the DN scatter value by Chavez (1988).

Landsat TM Band 1 Histogram DN Base of the Histogram Scatter Selection from Chavez (1988)

 

Landsat TM band 2 (green); DN 13 (frequency of 20) is selected as the DN scatter value by Chavez (1988).

Landsat TM Band 2 Histogram DN Base of the Histogram Scatter Selection from Chavez (1988)

 

Landsat TM band 3 (red); DN 12 (frequency of 69) is selected as the DN scatter value by Chavez (1988). 

Landsat TM Band 3 Histogram DN Base of the Histogram Scatter Selection from Chavez (1988)

 

Landsat TM band 4 (NIR); DN 8 (frequency of 5) is selected as the DN scatter value by Chavez (1988).

Landsat TM Band 4 Histogram DN Base of the Histogram Scatter Selection from Chavez (1988)

 

* Scatter for bandwidths longer than NIR are insignificant enough to ignore. Overall when there is more haze, the scatter amount becomes more proportionally equal between bands but the shorter wavelength band always have more scatter. There should be a power relationship between band center wavelength and scatter.