You’ve probably seen the latest alarming headlines: Rising sea levels from climate change could flood 187 million people out of their homes. Don’t believe it. That figure is unrealistic—and it isn’t even new. It appears in a new scholarly paper, whose authors plucked it from a paper published in 2011. What the earlier paper actually found was that 187 million could be forced to move in the unlikely event that, in the next 80 years, no one does anything to adapt to dramatic rises in sea level.

In real life, the 2011 paper explained, humans “adapt proactively,” and “such adaptation can greatly reduce the possible impacts.” That means “the problem of environmental refugees almost disappears.” Realistic assumptions reduce the number to between 41,000 and 305,000—at most, less than 1/600th of the figure in those headlines.

Sober findings get less attention than alarming and far-fetched speculation. The United Nations’ climate-panel scenarios all show that the world will be far richer and more resilient by the end of the century. That means we’ll be better able to tackle challenges like flooding—as much poorer societies have done for centuries. We have more know-how and technology than ever to build dikes, surge barriers and dams, expand beaches and construct dunes, make ecosystem-based barriers like mangrove buffers, improve building codes and construction techniques, and use land planning and hazard mapping to minimize flooding.

Journalists looking for alarming headlines get help from climate scientists who gloss over adaptation and from public-relations teams that know their audience. A 2018 paper looked at two scenarios. In the first, sea levels rise almost 3 feet during the next 81 years, yet no one thinks to change the height of a single dike anywhere in the world. That would cost $14 trillion globally a year.

The authors acknowledge this wouldn’t happen: “It is clear that all coastal nations have, and will continue to adapt by varying degrees to sea level rise.” In the second scenario, they try to account for adaptation, though they assume that as soon as any nation gets as rich as Romania is today, it will freeze its efforts. Even with this odd assumption, estimated flooding costs still fall 88%. The press release announcing the study skipped the second scenario and trumpeted the $14 trillion figure. So did every news story.