We are almost two weeks into this year’s hurricane season, and forecasters have been warning this one could be more active than usual.

Hurricanes are by far the costliest natural disasters that affect the United States — they’ve caused well over a trillion dollars in damage over the past 40 years.

But over that period, hurricane forecasts have improved, helping reduce a hurricane’s economic toll.

Soon after Renato Molina moved from California to Florida, he experienced his first hurricane warning.

“I took it seriously, right? So I go to the supermarket, I get a bunch of nonperishable foods, I get batteries, I get water. I get a bottle of wine,” he said.

Molina is an economist at the University of Miami, and he said when forecasters warn of a major storm, people generally respond — by stocking up on wine, sure, but also by protecting their most valuable assets.

“Boarding up your house, getting sandbags so as to protect flooding damage,” he said.

But Molina’s first hurricane warning turned out to be a false alarm. And those can lull people into a false sense of security when forecasters issue the next warning, said Tatyana Deryugina, an environmental economist at the University of Illinois.

“Hurricane storm paths can be so uncertain, you’re not going to try to protect hundreds and hundreds of miles of the coast. And so knowing exactly where it’s going to hit is very valuable,” she said.

Scientists have been getting better and better at that. Thirty years ago, they could predict the point of landfall three days out to within about 250 miles. Now?

“The average error has been cut really by more than half,” said Daniel Brown, a forecaster with the National Hurricane Center.

He said more powerful computing is one reason for the better accuracy. And the improved accuracy is saving money, according to a study published this week by Renato Molina from the University of Miami: In total, about $5 billion in avoided damage over the past 20 years.

“The improvement of the forecast, we estimate has saved about $700,000 per county per hurricane, just due to having better information,” Molina said.

Molina said the next big challenge is better prediction for how quickly hurricanes will intensify as the ocean continues warming.