Perhaps because chaos theory has been a part of meteorological thinking for nearly four decades, professional weather forecasters have become comfortable treating uncertainty the way a stock trader or poker player might. When weather.gov says that there’s a 20 percent chance of rain in Central Park, it’s because the National Weather Service recognizes that our capacity to measure and predict the weather is accurate only up to a point. “The forecasters look at lots of different models: Euro, Canadian, our model — there’s models all over the place, and they don’t tell the same story,” Ben Kyger, a director of operations for the National Oceanic and Atmospheric Administration, told me. “Which means they’re all basically wrong.” The National Weather Service forecasters who adjusted temperature gradients with their light pens were merely interpreting what was coming out of those models and making adjustments themselves. “I’ve learned to live with it, and I know how to correct for it,” Kyger said. “My whole career might be based on how to interpret what it’s telling me.”

Despite their astounding ability to crunch numbers in nanoseconds, there are still things that computers can’t do, contends Hoke at the National Weather Service. They are especially bad at seeing the big picture when it comes to weather. They are also too literal, unable to recognize the pattern once it’s subjected to even the slightest degree of manipulation. Supercomputers, for instance, aren’t good at forecasting atmospheric details in the center of storms. One particular model, Hoke said, tends to forecast precipitation too far south by around 100 miles under certain weather conditions in the Eastern United States. So whenever forecasters see that situation, they know to forecast the precipitation farther north.

But there are literally countless other areas in which weather models fail in more subtle ways and rely on human correction. Perhaps the computer tends to be too conservative on forecasting nighttime rainfalls in Seattle when there’s a low-pressure system in Puget Sound. Perhaps it doesn’t know that the fog in Acadia National Park in Maine will clear up by sunrise if the wind is blowing in one direction but can linger until midmorning if it’s coming from another. These are the sorts of distinctions that forecasters glean over time as they learn to work around potential flaws in the computer’s forecasting model, in the way that a skilled pool player can adjust to the dead spots on the table at his local bar.

Among the National Weather Service’s detailed records is a thorough comparison of how well the computers are doing by themselves alongside the value that humans are contributing. According to the agency’s statistics, humans improve the accuracy of precipitation forecasts by about 25 percent over the computer guidance alone. They improve the temperature forecasts by about 10 percent. Humans are good enough, in fact, that when the organization’s Cray supercomputer burned down, in 1999, their high-temperature forecasts remained remarkably accurate. “You almost can’t have a meeting without someone mentioning the glory days of the Cray fire,” Kyger said, pointing to a mangled, half-burnt piece of the computer that was proudly displayed in the office where I met him. “If you weren’t here for that, you really weren’t part of the brotherhood.”

Still, most people take their forecasts for granted. Like a baseball umpire, a weather forecaster rarely gets credit for getting the call right. Last summer, meteorologists at the National Hurricane Center were tipped off to something serious when nearly all their computer models indicated that a fierce storm was going to be climbing the Northeast Corridor. The eerily similar results between models helped the center amplify its warning for Hurricane Irene well before it touched down on the Atlantic shore, prompting thousands to evacuate their homes. To many, particularly in New York, Irene was viewed as a media-manufactured nonevent, but that was largely because the Hurricane Center nailed its forecast. Six years earlier, the National Weather Service also made a nearly perfect forecast of Hurricane Katrina, anticipating its exact landfall almost 60 hours in advance. If public officials hadn’t bungled the evacuation of New Orleans, the death toll might have been remarkably low.

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. A long-term study of political forecasts conducted by Philip Tetlock, a professor at the University of Pennsylvania, found that when political experts described an event as being absolutely certain, it failed to transpire an astonishing 25 percent of the time.

The Weather Service has struggled over the years with how much to let the public in on what it doesn’t exactly know. In April 1997, Grand Forks, N.D., was threatened by the flooding Red River, which bisects the city. Snowfall had been especially heavy in the Great Plains that winter, and the service, anticipating runoff as the snow melted, predicted that the Red would crest to 49 feet, close to the record. Because the levees in Grand Forks were built to handle a flood of 52 feet, a small miss in the forecast could prove catastrophic. The margin of error on the Weather Service’s forecast — based on how well its flood forecasts had done in the past — implied about a 35 percent chance of the levees’ being topped.