Sub-pixel Response
Another reason why the band around 3.9 μm is more capable of detecting fires is because of a process called "Sub-pixel response".
Imagine a fire occupying the whole pixel on a clear dry night (no clouds and no solar radiation). In this case, the temperature across the pixel would be approximately uniform and we should expect the same radiance temperature at the 3.9 μm and 10.8 μm bands! In this case, it would not be possible to identify a fire pixel by comparing the two bands.
Luckily, the fire front does not occupy the entire pixel. First, this is good because a large forest area is not being burned all at once! Second, this is the way to detect a fire through satellite remote sensing!
Basically, the concept of sub-pixel response states that if there is variability within a field-of-view (FOV), then the radiance measured by the satellite for that FOV is the average of the individual radiances in the sub-pixels and not of their temperatures.
In this example over Portugal we have one MSG SEVIRI pixel which is divided into four sub-pixels. Among these sub-pixels we find a "hot spot" of 500 K. Using Rayleigh-Jeans law (5.1.3) we can then calculate the following brightness temperatures (BT) for the MSG SEVIRI pixel for the IR10.8 and IR3.9 channels.
You see that in a pixel partly covered by a fire, the radiance at 3.9 μm is larger than at 10.8 μm due to the stronger response at 3.9 μm to the warmer portion (fire) inside the pixel. In fact, EUMETSAT´s algorithm shown at the beginning of this chapter uses the temperature difference IR3.9-IR10.8 (different temperature ranges for day and night) as a proxy for fire probability - the larger the difference, the higher the probability!
The EUMETSAT algorithm also includes thresholds for pixel radiances at 3.9 μm and for the standard deviation of radiances over 3x3 pixel boxes at 3.9 μm and 10.8 μm. The standard deviation at 3.9 μm is used to split small fires from large hot fires and the standard deviation at 10.8 μm is used to discard inhomogeneous land or clouds previously undetected in a cloud mask.