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The panel on the right depicts the detector field of view for the 3.9 and 10.7 micron channels. Within this field of view, there is a cold cloud at temperature T(t) which is covering a fraction, N. The background at temperature T(b) covers the remainder of the field of view, 1-N.
The total energy, R, consists of energy from the cloud and surrounding background. Radiance in the 3.9 micron channel increases more rapidly with temperature than the radiance in the 10.7 micron channel.
The effect of this difference in temperature is shown in the graph on the left. The x-axis represents the fractional coverage by the target. The y-axis represents the brightness temperature of the scene. Neglecting emissivity differences, for clear or completely cloudy fields of view, the two channels yield the same brightness temperature.
The lines represent the scene temperatures measured by the 3.9 and 10.7 micron channels as the coverage by the subpixel target changes from 0 to 100%.
When the fractional coverage is between 0 and 1, the brightness temperature from the 3.9 micron channel will always be warmer than from the 10.7 micron channel because the 3.9 micron channel is less sensitive to subpixel clouds than the 10.7 micron channel.
During daytime, a reflected solar contribution to the total energy must be added to the expression for the 3.9 micron channel. The effect of this contribution is to increase the temperature at 3.9 microns for all N as seen by the blue curve on the graph.