I'm stuck in Frankfurt. I missed my connection due to a delay. I was rebooked, but this new flight was also cancelled due to bad weather.
About 30 percent of all flights were cancelled today. However, if the weather is that bad, shouldn't all departures have been cancelled? Why was the weather bad for my flight, but not for other flights that actually departed?
In general, flights get cancelled when arriving flights are delayed or themselves cancelled. Your flight needs three critical things to depart on time, or at all:
Aircraft may not arrive due to weather diversions (couldn't land with fuel on hand, etc). If there's no airplane, your flight obviously can't depart. Same goes for bad weather at your departure airport - if it's too bad, you can't go. If the weather at your destination is bad, the flight may also be delayed because the airport can't handle as many aircraft as normal. That's fairly straightforward. Where it gets most complicated is the crew.
Crew have what are referred to as "duty and rest requirements" (at least in the US; other jurisdictions have similar rules, possibly with a different name). A flight crew is "on duty" when they're first scheduled to fly, whether the flight happens or not, and the number of "duty hours" they can have on a given day are limited. The FAA last revised these rules in 2011, as far as I know, but I'm not an airline pilot. With the 2011 rules, "Flight Duty Period limits under the new rules range from nine to 14 hours". These rules exist to prevent fatigue, a major cause of aviation accidents.
What this means is that if weather delays cause crews to overfly their limits, they may be unable to operate the outbound flight. With your example of Frankfurt, there is weather causing delays to arriving flights.
If a hypothetical crew with a 10 hour duty limit was scheduled to fly, say, three LHR-FRA round trips (call it 3 hours of flight duty time each round trip; this may not be a valid example), but were delayed on their third FRA arrival by 2 hours, they would exceed their duty limits by 1 hour on the return flight (1.5 * 2 + 1.5 * 2 + 1.5 + 2 = 9.5 + 1.5 = 11 > 10). As a result, they would not legally be able to depart.
Normally, airlines plan for this with "reserve" crews that are on call to fill in for missing, sick, overflown, or otherwise unavailable crews so that flights are not seriously delayed. When a huge storm hits, this falls apart as there are not enough reserve crews to operate all the flights, and the situation snowballs out of control.
Our hypothetical crew would be replaced by reserve pilots (and cabin crew) if they were available, and the flight might be delayed by more than the 2-hour flight delay they experienced. If not, the flight would be canceled.
If the bad weather is a hurricane or large thunderstorm cell right over the airport, yes you would expect all flights to be cancelled rather than just some. But if the weather brings low visibility, like parts of Europe have experienced this week, it is a slightly different story. The main reason for cancellations is that the airport cannot operate at full capacity.
Usually, aircraft can takeoff in very low visibility (such as fog), but to land the visibility requirements are higher. So if your aircraft is already on the ground before the bad weather hits, it still might be able to leave, whereas another flight is cancelled because the aircraft operating it can't land.
However big airports with frequent visibility problems usually have a category 3 ILS (Instrument Landing System). This category allows an appropriately certified aircraft and crew to land in virtually zero visibility using Autoland. But this system has limitations. The ground-based transmitters are sensitive and need large protected zones - this means that certain runways and taxiways cannot be used at the same time as an Autoland.
This ties in to Low Visibility Procedures (LVPs). Every airport and airline has their own, but the common theme is that everything slows down. The cumulative effect of both Autoland operations and LVPs is that the amount of movements an airport can safely handle per hour drops dramatically.
You can imagine that if there are 50 scheduled flights per hour, but weather reduces capacity to 30 per hour, 20 flights will spill over into the next one. You'll then have 70 flights fighting to use 30 slots, then 110, and so on as the day progresses. For busy airports, mass cancellations are the only way to get things back on track - but 30 flights per hour can still go ahead. In reality the airlines will be told to cancel a certain number of flights and yours might be one of the unlucky ones picked.
Another thing tor remember is that the bad weather in question might not be at the airport you are at, but rather the destination or en-route. Rather than being stuck in a holding pattern for a few hours waiting for the destination airport to clear, it is preferable to wait on the ground - so even if the weather is sunny at the originating airport, a flight could be delayed or cancelled due to weather at the destination.
As @Ben correctly guessed, Frankfurt airport was (and still currently is) reduced in capacity due to snowfall. I heard about it yesterday and this news article had more details (translation below):
Zwischenzeitlich stand an Deutschlands größtem Luftfahrt-Drehkreuz nur eine Piste für startende und landende Jets zur Verfügung. Eine Sprecherin des Flughafenbetreibers Fraport bezeichnete die Situation als «dramatisch». Selbst auf den geräumten und gestreuten Bahnen seien wegen des anhaltenden Schneefalls nicht die vorgeschriebenen Bremswerte erreicht worden.
Translation:
Temporarily, Germany's largest hub airport only had one runway available for starting and landing jets. A spokeswoman for airport operator Fraport called the situation "dramatic." Even the ploughed and gritted runways did not reach the required deceleration values because of the continuing snowfall.
This might have been a major reason that a major part but not all flights were canceled.
Another requirement for flights is weather minimums at the destination airport. If the destination airport is forecast to have within +/- 1 hour of ETA ceiling and visibility less than 2,000 ft or 3 sm visibility, than a suitable alternate airport with certain weather criteria are needed.
Therefore airplane "A" can not leave because the weather at the destination is too bad or an alternate is not cost effective to divert to if needed. At the same airport, other airplanes are coming and going and airplane "B" will leave because it is headed towards good weather.
This is often the case for long international flights. Say you are planing a 12hr flight from Frankfurt to New York City, USA. If the weather is bad for 500mi around NY, the air carrier may not want to risk being stranded some where else. If the weather is expected to worsen, a lot of bad things can happen during the 12hr flight. But other closer flights, or flights to other areas of the USA my be landing and taking off.
Also two carriers with the same departure and destination airport may have a different risk assessment. One carrier may have attractive alternate flights with good connections later and choose to take the risk. The other carrier may not have good options. Therefore one will be willing to depart and the other will delay "due to weather".
Additionally to all the other answers, there is one factor that could also explain a difference of treatment between two different flights: the capabilities of the aircraft.
Some aircraft are better equipped than others to face bad weather conditions. It depends mainly on their equipment, size and design.
smaller aircraft are more fragile - is that actually true? I mean, aerobatic aircraft are quite small compared to a 777, but they seem quite robust! :)
$\endgroup$
Another reason capacity can go down, one that's given me some close calls: The rules for how far apart aircraft must be is higher when they can't see each other. Take two runways a bit too close together at a busy airport, add fog. Oops, while both runways are usable the airspace can only handle one runway worth of planes. Half the flights get delayed/cancelled due to weather even though the airport is still open. The trip to visit her family used to connect through an airport notorious for this problem.
