A flight can circle an airport that looks perfectly usable from the ground and then divert to a city hundreds of miles away. The decision follows published criteria for the specific approach being flown.
What the minimums specify
Each instrument approach at each runway has a published decision height and a required visibility, both determined by the equipment available and the terrain around the airport.
The crew descends along the approach path and must have the required visual reference to the runway environment by the decision point.
If that reference is not established, the approach is discontinued and the aircraft climbs away. The rule is not discretionary and does not depend on how close the aircraft was.
Why the numbers differ between runways
Approaches supported by more precise guidance equipment permit descent to lower heights, because the aircraft's position is known more accurately.
Obstacles near the approach path raise the minimums, since a safe missed approach must be possible from the decision point in every direction the procedure allows.
Approach lighting also matters, because the crew must be able to identify the runway environment visually, and better lighting makes that possible in poorer visibility.
How crew and aircraft qualification enters
Lower minimums require specific equipment on the aircraft, specific ground installations, and crews trained and qualified for that category of operation.
Two aircraft on the same approach in the same conditions can therefore reach different outcomes, with one landing and the other diverting.
The lower the minimums, the more stringent the requirements on all three, which is why the most capable operations are limited to particular airports and fleets.
Why fog is the hardest condition
Fog reduces horizontal visibility while leaving the sky overhead apparently clear, so conditions can look benign from the terminal while being unusable on approach.
It also forms and dissipates unpredictably in shallow layers, and a runway can be usable at one end and obscured at the other.
Because fog often forms overnight under calm clear conditions, it disproportionately affects early morning arrivals, which is when the day's schedule is being established.
What fuel planning forces
Flights carry fuel to reach the destination, then to fly to a designated alternate airport, plus a reserve, and that quantity is fixed before departure.
Holding consumes the margin, so the decision to divert is driven by a fuel deadline rather than by any judgment about improving weather.
Once that point is reached the aircraft leaves for the alternate whether or not conditions improve minutes later, which is why diversions sometimes occur as the fog is lifting.