# Is there a way to recalculate radar detection range given the old and new probability of detection and false alarm?

I'm reading through some radar books and I'm trying to find out if there's an easy method or equation to recalculate radar detection range given only the original radar detection range, original probability of detection (pd) and probability of false alarm (pfa), and a new pd and pfa. Is this possible or do I need to consider more input variables?

Unfortunately, the signal power will depend on distance depending on the environment. In vacuum it's $1/r^4$, because of the two way path. But if there's any kind of multipath effect from the ground it could be worse. If not ground to ground radar you can assume you can ignore the multipath, otherwise not.