Update: The National Weather Service on Friday updated the snow total at Philadelphia International Airport to 2 inches. This story has been revised to reflect that change.

It was a balmy 66 degrees in Philadelphia when the archdiocese announced Wednesday afternoon that it was declaring a snow day for Thursday. Other schools in the region followed its lead. The city declared a preemptive state of emergency.

The science of meteorology evidently still instills faith: The National Weather Service had posted a winter-storm warning for the next morning, calling for perhaps eight inches of snow.

It did indeed snow, and traveling Thursday morning was dicey, but the official total in Philadelphia wasn't eight inches but 2. Heavy snow had been expected through the morning, but by 10 a.m. the sun was out.

What happened? Several factors ambushed a forecast that became yet another case study in the marvels and limits of computer models.

Perhaps ironically, the storm represented a scientific triumph. As early as Sunday, models had sniffed out that a nor'easter would tap cold air to the north and rout the invasion of April in the Northeast, where parts of New York, especially Long Island, and southern New England did get creamed Thursday.

In terms of the forecasts, "it's been a good day," said Louis I. Uccellini, director of the National Weather Service and one of the nation's premier winter-storm experts. "To me, this was a remarkable advance."

He also is aware that the typical Philadelphian might not share his assessment.

"We say all forecasts are local," he said.

Locally, the forecast was hardly a complete bust. Some places not far outside the city did receive three to five inches of snow, but "there was a sharp cutoff," said Mitchell Gaines, a meteorologist at the weather service office in Mount Holly.

Snow Totals in the Region

Reported totals as of 1 p.m. Thursday.

SOURCE: National Weather Service
Staff Graphic

In the immediate Philadelphia area, a delay in the changeover from rain to snow seriously dampened the totals. Snowfall amounts of one to two inches an hour were forecast, and one doesn't need to know advanced calculus to figure that a two-hour delay would thus subtract two to four inches.

The changeover was held up by a stubborn warm layer of air a few thousand feet up, Gaines said. In elevated areas nearby, such as along the Main Line, the change to snow came more quickly; temperatures decrease with height, and even 300 or 400 feet of elevation can make a huge difference in accumulation.

Perhaps the biggest element holding down snow totals was the obvious one. Snowstorms on days after the temperature reaches 66 are rare for a reason. The ground was quite warm, and snow had a hard time sticking.

Snow-accumulation forecasts remain one of the more vexing problems in meteorology.

The estimates are based on how much precipitation will fall, and then how much of that will fall as snow – the snow-to-liquid ratio.

On average, the ratio is about 12:1, or a foot for every inch of precipitation, but that varies with temperatures and flake size.

In a storm such as this, where temperatures are falling through different layers of the atmosphere, that ratio becomes a moving target, said Bill Deger, a meteorologist with AccuWeather Inc. Computer models aren't capable of nailing such micro-details.

The models have one overwhelming weakness: The atmosphere is imprecisely observed.

Forecasts rely on capturing "the initial condition" of the atmosphere, analyzing how it has changed in recent hours, and how it will change going forward in time.

Earth's 10-mile-deep atmosphere, a chaotic, three-dimensional gas that behaves like a fluid, still has observation gaps, and missing pieces skew computer solutions. Different computer models use various methods to compensate for the gaps, but none is perfect.

"The computer models gradually improve," said Gaines, "but we have to learn to see how much they have improved."

Computers still are only machines, and the meteorologists only human.