Facing days to come under the volcano's unpredictable, ashy plume, Europeans are looking at temporary airport layoffs and getting creative with flight patterns to try to weather this extraordinary event.
Modern Europe has never seen such a travel disruption. Air space across a swath from Britain to Ukraine was closed and set to stay that way until Monday in some countries, affecting airports from New Zealand to San Francisco. Millions of passengers have had plans foiled or delayed.
Activity in the volcano at the heart of this increased early Saturday, and showed no sign of abating.
"There doesn't seem to be an end in sight," Icelandic geologist Magnus Tumi Gudmundsson said. "The activity has been quite vigorous overnight, causing the eruption column to grow."
Scientists say that because the volcano is situated below a glacial ice cap, the magma is being cooled quickly, causing explosions and plumes of grit that can be catastrophic to plane engines, depending on prevailing winds.
In Iceland, winds dragged the ashes over new farmland, to the southwest of the glacier, causing farmers to scramble to secure their cattle and board up windows.
With the sky blackened out and the wind driving a fine, sticky dust, dairy farmer Berglind Hilmarsdottir teamed up with neighbors to round her animals and get them to shelter. The ash is toxic - the fluoride causes long-term bone damage that makes teeth fall out and bones break.
"This is bad. There are no words for it," said Hilmarsdottir, whose pastures near the town of Skogar were already covered in a gray paste of ash.
Forecasters say light prevailing winds in Europe - and large amounts of unmelted glacial ice above the volcano - mean that the situation is unlikely to change quickly.
"Currently the U.K. and much of Europe is under the influence of high pressure, which means winds are relatively light and the dispersal of the cloud is slow," said Graeme Leitch, a meteorologist at Britain's National Weather Service. "We don't expect a great deal of change over the next few days."
A Dutch geologist who is in Iceland observing the volcano, Edwin Zanen, described it to Dutch state broadcaster NOS:
"We're at 25 kilometers distance from the crater now. We're looking at a sun-soaked ice shelf, and above it is looming a cloud of ashes of, oh, 4 to 5 kilometers high. There are lightning flashes in it. It's a real inferno we're looking at.
"There's absolutely no sign that the thing is calming down. On the contrary, we can see that at this moment it's extraordinarily active," he said.
With the prospect of days under the cloud of ash, pilots and aviation officials sought to dodge the dangerous grit by adjusting altitude levels.
Germany's airspace ban allows for low-level flights to go ahead under so-called visual flight rules, in which pilots don't rely on their instruments.
Lufthansa took advantage of that to fly 10 empty planes to Frankfurt from Munich on Saturday to have them in the right place when the restrictions are lifted, airline spokesman Wolfgang Weber said.
The planes flew at about 9,800 feet - well below their usual altitude - in close coordination with air traffic control.
KLM is carrying out a test flight from Schiphol to Dusseldorf at the same level or lower, hoping for approval to carry out more low-altitude flights in Europe if the ash problem continues.
The Swiss looked the other direction - above the ash cloud. The Swiss Federal Office of Civil Aviation began allowing flights Saturday above Swiss air space as long as the aircraft were at least at 36,000 feet. It also allowed flights at lower altitudes under visual flight rules, aimed at small, private aircraft.
All air space in Poland - which is hosting a huge state funeral for late President Lech Kaczynski - remained closed Saturday to flights above the cloud level of 20,000 feet because of the ash cloud.
Some low-level flights are being allowed in the south, however, which is how the Polish Air Force will be able to ferry the coffins of Kaczynski and his wife from Warsaw to Krakow aboard a prop-powered military cargo plane early Sunday morning.
Several world leaders, including President Barack Obama, had to abandon plans to attend the funeral because of ash-related disruptions.
European businesses are testing their flexibility to cope with this new crisis.
The aviation industry, already reeling from a punishing period, is facing at least $200 million in losses every day, according to the International Air Transport Association.
Scandinavian airline operator SAS AB said it has given notice of a temporary layoff of up to 2,500 ground service staff in Norway as a result of the flight disruptions. Airline spokeswoman Elisabeth Manzi said it is a precautionary move, and that said eventual temporary layoffs may not affect all 2,500 notified.
Budget airline Norwegian ASA, losing $1.5 million to $1.7 million a day because of the ash-driven closures, is conducting meetings with unions Monday to discuss potential temporary layoffs, spokeswoman Asta Braathen said.
"If we are looking at the future, we cannot maintain the cost of all this forever," said Geert Sciot, communications manager of Brussels Airlines, citing such costs as providing buses to passengers meant to fly from Athens or Lisbon to Brussels.
German mail and logistics company Deutsche Post DHL AG rerouted packages that were supposed to be flown via the company's Leipzig, Germany, hub via Italy and other points south, while those already in the areas affected were diverted to trucks and trains, spokesman Stefan Hess said.
"The longer it lasts, the more difficult it gets in principle - but a cloud like this isn't static," he said.
Producers of Italy's milky white, prized buffalo mozzarella, which is highly perishable, pondered their options.
"In the next couple of days we have to decide," said Vito Amendolara, head of the farmers lobby Coldiretti's office in Campania, the region around Naples famed for the cheese. "We cannot sell buffalo milk as it is, because it is too fatty and is meant solely for production of mozzarella. We will either have to throw away the milk or find alternative markets" by heavily promoting it locally.
Around the world, anxious passengers have told stories of missed weddings, business deals and holidays because of the ominous plume. Stranded passengers reported the delays were causing financial hardships. Some had to check out of hotels and sleep in airports.
"It's like a refugee camp," said Rhiannon Thomas, of Birmingham, England, describing the scene at New York's Kennedy Airport.
Her family spent the night at the airport Friday, and may be there for days before they can get a flight home. "At least we got beds," said Thomas' mother, Pat, referring to the hundreds of narrow blue cots brought in to JFK's Terminal 4. "Some people slept on cardboard."
German Chancellor Angela Merkel was heading homeward in an armored car along an Italian highway Saturday - continuing a long and circuitous return from the United States.
Merkel was diverted to Lisbon, spent the night in the Portuguese capital, then flew to Rome on Saturday. From there, she and her delegation set off by road toward northern Italy's South Tyrol region for another overnight stay.
Pope Benedict XVI's flight to Malta for a weekend pilgrimage was one of the few to depart Saturday from Rome. Greeting journalists aboard the plane, the pontiff told them he hoped they would have "nice trip without this dark cloud that has arrived on the rest of Europe."
Southern Iceland's Eyjafjallajokull volcano began erupting for the second time in a month Wednesday, sending ash several miles into the air.
In Iceland, torrents of water have carried away chunks of ice the size of small houses. More floods from melting waters are expected as long as the volcano keeps erupting - and in 1821, the same volcano managed to erupt for more than a year.