People love to hate weather forecasts, though it’s getting a lot harder to find fault. Forecasts gave plenty of advance warning that Chicago would see a bitter high of around minus 24.5 on Wednesday, and lows Wednesday night comparable to a bad day in Antarctica. Public officials closed schools and issued warnings, and police saved lives by combing the streets for homeless people before the worst hit.

Today, a five-day forecast is just as accurate as a one-day forecast was in 1980, giving us more time to prepare — or overreact and panic.

Weather watchers in the Northeast United States saw this cold snap coming for days. Storms are now forecast within a range of around 80 km and timed to within a couple of hours. An icy storm that hit the Northeast on Jan. 20 was in the forecast before it even existed anywhere, said Richard Alley, a geosciences professor at Penn State University and co-author of a new paper in Science magazine on weather prediction.

There’s even more room to improve, he said. Better forecasts save money — on plows and road salt, on crops, and on making sun and wind energy more predictable. Sometimes forecasts can have even bigger consequences.

Historians say D-Day might have gone very differently if weather had followed the German forecast for storms rather than the Allies’ more accurate forecast of fair skies and calm seas. Bad weather thwarted Napoleon and later Hitler in attempts to defeat Russia. Lost explorers over the ages might have planned differently. Ernest Shackleton might have avoided getting his ship locked into the Antarctic ice.

A century later, I take advantage of forecasts those early explorers couldn’t have dreamed of. I plan many of my weekends around sailboat races, and in Rhode Island, there are at least four venues where people race all winter. Even a week ahead of time I can get a reasonable estimate of temperature, precipitation, wind speed and direction. We don’t go out if the forecast shows anything life-threatening.

It makes sense that weather is inherently more predictable than, say, the economy. Ultimately, weather does reduce down to basic laws of physics — Newton’s laws, the Coriolis effect and the like, said Alley. The limiting factor is the complexity of the system: To build a good model you have to take into consideration where there’s ocean, where all the mountains are, and even where corn fields grow in the Midwest.

And even then, there’s a problem, which was laid out in James Gleick’s 1987 book “Chaos.” Mathematician and meteorologist Edward Lorenz discovered that while the physical world is in principle deterministic, in reality minuscule changes in initial conditions can lead to big differences in weather. Consider Lorenz’s famously titled 1972 talk: “Does the flap of a butterfly’s wings in Brazil set off a tornado in Texas?”

Alley said that indeed there’s a limit on the accuracy and range of weather forecasting, but since the 1970s it went from mediocre to amazing. He chalks up the improvements to additional satellites and other data collecting devices, more powerful computers to crunch the data and improved models.

He uses the game show “Wheel of Fortune” to show how forecasts work in the face of the butterfly effect. The wheel is divided unevenly into segments, so right off you can calculate how often over many spins it will hit, say, the skinny million-dollar-jackpot segment. That’s why long-term climate patterns are easier to forecast than the weather on any given day.

A single spin, or a single day, is hard to predict, but as the wheel starts to slow down, you can start to guesstimate where it will land — just as the weather forecasts for a particular race day are more accurate as the day comes closer. The models are so good, he said, that once you figure in all the topography, the atmospheric density and Earth’s rotation, you don’t have to add in the Gulf Stream. The laws of physics predict there will be a Gulf Stream. They also predict there will be a semi-periodic current pattern called El Nino, as well as long-term global warming.

In his book “The Signal and the Noise,” Nate Silver discusses the same idea using a coin toss, which is essentially a deterministic physical phenomenon. If a machine flips a coin exactly the same way it will get a dependable outcome. But when we humans toss a coin it behaves randomly because the outcome depends on tiny variations in its trajectory. His weather chapter was excerpted in a New York Times Magazine story called “The Weatherman Is Not a Moron.”

That was back in 2012, but already there were huge improvements. Silver attributed this to better computers and more data as well as better estimates of uncertainty. Sometimes the weather people are sure, sometimes not so sure. But saying so, he laments, has its cost.

In a time when forecasters of all types make overconfident proclamations about political, economic or natural events, uncertainty is a tough sell. It’s much easier to hawk overconfidence, no matter if it’s any good.

That’s a long-standing problem for many kinds of scientists. People might wrongly equate honesty about uncertainty with being wishy-washy. But there are objective tests of predictions. So-called “superforecasters” (who win forecasting tournaments) say that understanding their own uncertainty is critical.

People probably won’t stop complaining about the weather forecasts, said Alley, because even missing the mark by a degree or so can mean the difference between snow and rain. It’s also improved so slowly that it’s been hard to see. What’s all this worth in dollars and cents? Alley cited several papers, listing the benefits of weather forecasting and estimating that spending on weather forecasting technology can deliver a much greater return on investment. But to get specific there, you’ve got to factor in humans and the economy, which are not nearly so predictable.

Science writer Faye Flam is a Bloomberg Opinion columnist.