This is one example of an impact probability map. It was posted in this question and is from Aerospace Corporation. But My question is about the process, not this particular map, although it is a good working example to pose this question.
With a given spacecraft, its most recent TLE or the last few, and an arbitrary time window defined by $t_1$ and $t_2$, one can use SGP4 to propagate the orbit between those two times to make a ground-track plot, which would be a series of wavy, thin lines.
That's roughly the process outlined in this comment, but it is not enough. Probably $t_1$ and $t_2$ should be chosen to safely bracket any reasonable guess as to the time of impact. So at $t_1$ it's almost for sure still in orbit, and at $t_2$ it's almost for sure on the ground (or vaporized, or some of both). Ground tracks at those points should contribute minimally to the final 2D areal probability histogram.
A corollary to that might address what happens to the histogram below the ground track at the most likely time of impact. Image below: is from the ESA RocketScience blog post Tiangong-1 Reentry Updates. Click for full size.
Looking closer at the 2D probability histogram (see below), a few things stand out.
- The inner borders between the wide, inner, green region (lower prob) and narrow yellow (higher prob) bands near the extremes of latitude are jagged! Since the atmosphere itself does not have this structure, this must be some kind of residual effect due to the finite number of orbits considered. They are no longer thin lines, but their effect is still seen.
- Outside of the narrow high probability bands near the extremes are a second pair of even more narrow bands between high probability and zero probability. This is not what one would get by looking at the probability of ground track dwell time alone.
So there seems to be a lot more than just "what you need is the time it spends over a given unit area of surface over the course of many orbits" going on here.
Question: How are impact probability maps rigorously calculated?
above: Cropped from a larger version of the map, found here.