The FAA says that, specifically the 7110.65 which governs ATC rules and procedures. In a radar environment it allows for departures when the arriving aircraft is 2+ miles from the runway, and there will be at least 3 miles of separation within 1 min of takeoff. A separate rule requires that the departing aircraft is at least 6000ft down the runway and airborne before the arrival crosses the runway threshold.
If there is a departing plane rolling up to the hold short line and confirmed ready for immediate takeoff, there is possibly time to get them out and maintain separation. If it's low visibility, the departing plane is rolling slowly and not confirmed ready, then it's a bad bad idea.
Juan Brown [1] made an interesting point also. For a Cat II or III approach, and this one was definitely Cat III, there is an ILS critical area that Southwest would have impinged on as it was taking off.
The controller very clearly made a huge mistake.
Just to keep stating this: I'm not at all defending the AUS controller here. A squeeze play like this in low visibility is needlessly reckless.
[1] https://www.faa.gov/air_traffic/publications/atpubs/atc_html...
(And they do have GPS, They also have ADSB, and ground based position detection, and, and, and..)
They don't know if Southwest was moving?
This is nothing one can solve by throwing even more sensors and technology in, and have that run by ChatGPT or something. Highly trained people with the right amount and kind of technology are the solution.
Edit: Sensors and stuff tell you were aircraft is, not what the human pilots are going to do when within the aloted period of time they have to do whatever they are cleared to do. Hence, you do the logical thing and ask them.
Poor visibility should not ever be a factor when we can have sensors that show exactly where the plane is on the ground. And yes we are definitely at a point where machine learning can predict the likely actions based on the human communication and warn if the predicted path could lead to a collision. The point is to have multiple safty systems (inclduing the human operators) so that one mistake doesn't kill hundreds of people because there are secondary systems to catch it.
The controller had at least one screen displaying their positionx probably several. It may fuse multiple data sources. They may also have been able to see the Southwest aircraft, although maybe not clearly or only as lights.
Despite this it can be difficult to judge the speed of an object at long distances under less than ideal circumstances and at night without a long observation period.
So yeah they knew where they were but not the acceleration.
It's also worth pointing out that the controller may have been in sudden stress due to realising the aircraft were too close, and so may have made a call that they already knew the answer to.