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II. Quantitative Analys<strong>is</strong> <strong>of</strong> Landsat Thermal Imagery<br />

I. Conversion <strong>of</strong> DN values to Absolute Radiance<br />

ETM+ images are acquired in either a low or high gain state (Figure 1). The science goal in<br />

switching gain states <strong>is</strong> to maximize the instrument's 8-bit radiometric resolution without saturating<br />

the detectors. <strong>Th<strong>is</strong></strong> requires matching the gain state for a given scene to the expected brightness<br />

conditions. For all bands, the low gain dynamic range <strong>is</strong> approximately 1.5 times the high gain<br />

dynamic range. It makes sense, therefore, to image in low gain mode when surface brightness <strong>is</strong> high<br />

and in high gain mode when surface brightness <strong>is</strong> lower.<br />

Figure 1 Design ETM+ Reflective Band High and Low gain Dynamic Ranges<br />

http://landsathandbook.gsfc.nasa.gov/handbook/handbook_htmls/chapter6/chapter6.html<br />

The per-band sensitivity <strong>of</strong> the instrument <strong>is</strong> set by adjusting the gain to conditions expected for that<br />

time <strong>of</strong> year. Bands 1, 2 and 3 are set to high or low gain as a group. Gain settings for bands 5 and 7<br />

are set similarly. Band 6 acquired in both high and low gain mode, while bands 4 and 8 are set<br />

individually according to land surface brightness conditions. Band gains are set on a month by<br />

month bas<strong>is</strong>. The DN values <strong>of</strong> each Landsat image band were scaled from the absolute radiance<br />

measure to byte values prior to media output using the gain and bias (<strong>of</strong>fset) values given for each<br />

band. The DN values can be converted back to the radiance units using the following equation:<br />

Which can also be expressed as:<br />

Radiance = gain*DN + <strong>of</strong>fset (1)<br />

Radiance = ((L MAX-L MIN)/(Q CALMAX-Q CALMIN))*(Q CAL-Q CALMIN) + L MIN (2)<br />

Where: Q CALMIN=0, Q CALMAX=255 and Q CAL=Digital Number<br />

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