The National Weather Service has issued three winter weather advisories for Philadelphia so far this winter, with basically nothing to show for them. And it wouldn’t be shocking if the forecast for up to 2 inches Saturday in parts of the region turns out to be a washout.

Should that be the case, the people who predict weather for a living advise it likely won’t be the last time.

Computer modeling has made such advances that rarely are meteorologists ambushed by surprise snows these days. But they readily acknowledge they continue to struggle to answer that fundamental question that the masses care about so deeply: How much snow?

This weekend — with Bucks and parts of Chester and Montgomery Counties under yet another winter weather advisory for up to 3 inches of snow — might provide a clinic on why that answer is so elusive.

Once again, the region will be near the snow-ice-rain boundaries, and might well be treated to a wintry buffet of all three. With temperatures in the 20s, the precipitation started is as snow at mid-morning; that was the easy part. But the key to accumulations will be how quickly everything liquefies.

“The rain/snow line has been a real bugaboo for forecasters,” said Greg Postel, a storm specialist at The Weather Channel. As a Philadelphia native, he is well familiar with the region’s precarious thermal position between the coastal plain and the “fall line” where the land begins its slow rise toward the Appalachians.

“Precipitation types are the killer,” said Jim Eberwine, a meteorologist who used to sweat those forecasting bullets when he worked at the local weather service office, and is now the emergency management chief in his hometown, Absecon. Predicting snow around here, he added, “is not for the faint of heart."

Well, gentlemen, a reader might say, we all have problems. The public is unlikely to care about the likes of chaos theory or vertical-temperature profiles. Just tell us how much.

Said Postel, “It is indeed the case that the expectation has outrun the science.”

The parfait, and the Philadelphia problem

One obvious reason that the region spends so much time on the rain/snow line is that temperatures around here are often near freezing when precipitation starts. In fact, the average daily temperature in Philadelphia is 33 degrees from Jan. 3 through the 31st. It goes up to 34 the first week in February.

That’s at the surface. For precipitation types, the keys are the temperatures in the higher levels of the atmosphere, where the forecasting problems get more complicated.

During storms, Philadelphia frequently is at the bottom of an atmospheric parfait, with layers of air at different temperatures. It might be cold enough to snow where precipitation forms, but if those frozen crystals travel through a warmer layer on the way down they will liquefy. If they fall through an ever-lower layer that’s below freezing, the droplets will refreeze and become balls of sleet.

Being so close to the ocean and Delaware Bay, and east of the mountains, around here storms are prone to import snow-melting warm air at the higher levels even as the cold hangs tough where people live and scrape windshields.

If the snow can remain intact it can accumulate. How efficiently is another matter. It depends on a host of factors, including the quality and size of the flakes. Estimates vary, but on average about 0.5 inches of precipitation yields about 6 inches of snow.

The same amount of precipitation would yield only about 2 inches of sleet, maybe less, and, naturally a half-inch of rain.

Further complicating accumulation forecasts is the fact that the region has quite a complex terrain. Philadelphia, itself, is situated near sea level by the Delaware River and rises to 450 feet-plus in Roxborough and Chestnut Hill.

Temperatures decrease with height, and that can make a huge different in accumulations when readings are near freezing.

What about Saturday?

It might still be in the 20s around noon when the snow is expected to start, but the snow’s not likely to last long, says Alan Reppert, a meteorologist at AccuWeather. The parfait effect will be in force, he says. A warm layer will develop about 6,000 feet up in the early-to-mid-afternoon, and the changeover will begin.

By late afternoon, the cold air at the surface will be scoured away, he said, but the outcome has a degree or two of uncertainty.

If the snow arrives early enough and that warm layer were somehow delayed, the city could see an inch or two. But the more-likely outcome would be an inch or less, and yet another snow shutout for the Philly metro area is definitely in play.

When will we know for sure?

When it’s over, Saturday evening.

To make their calculations, computer models still have to contend with imperfect observations.

Weather balloons launched from surface stations relay vertical temperature profiles of the atmosphere, but the world’s surface is 70 percent water. Satellites fill in some of the gaps, but nothing beats direct measurement.

Meteorologists have made tremendous progress in finding ways to compensate for the gaps, but as you might have noticed, sometimes the forecasts don’t work out so well.

For the foreseeable future, computer models will have to live with an imperfectly observed world.

“Technology has come a long way,” said Reppert, but “we’re still missing a lot of information.”