"Stop lying to make @realDonaldTrump look bad," the president's son admonished Cooper, triggering a harsh response from the CNN journalist, who was part of his network's team covering Florence's landfall in North Carolina.
"I didn't see him down in North Carolina in the last few days helping out, lending a hand, but I'm sure he was busy doing something important besides just tweeting lies," Cooper said on his show Monday.
Ever since President George W. Bush's administration was crippled by its response to Hurricane Katrina, politicians and news organizations have been acutely aware of the stakes raised by big storms. Some Republicans never forgave former New Jersey Gov. Chris Christie for being photographed with President Barack Obama after Sandy struck just before the 2012 election.
"A storm and responding to it the right way can make or break a political career," said Gary Lackmann, a professor of atmospheric science at North Carolina State University.
Florence formed in the Atlantic just as President Donald Trump's response to Hurricane Maria in Puerto Rico returned to the news with a revised estimate that nearly 3,000 people died in that storm and its aftermath. Since Trump vigorously disputed the report, calling his administration's response "an incredible, unsung success," it led some media figures to question whether he would be responsive to Florence.
Three days before Florence struck, the Washington Post editorialized that Trump was complicit in damage caused by extreme weather. "He plays down humans' role in increasing the risks, and he continues to dismantle efforts to address those risks," the newspaper said.
That drew a predictably fierce response from the president's defenders.
"The left will not skip any single moment to condemn this president," said Pete Hegseth on the Fox Business Network. "In this case, it's a hurricane."
When a news organization infuses hurricane coverage with political infighting, it sends a message to people in the path of a dangerous storm that its reporters don't necessarily care about them, said Gabriel Williams, a professor of atmospheric physics at the College of Charleston in South Carolina.
"It's unnecessary," Williams said. "It defeats the purpose. It distracts from what you actually want to happen, which is to get people prepared for the storm."
With a hurricane bearing down, "politicos think 'this is going to be the dominant story this week. How can we get our spin into this?'" said Tim Graham, director of media analysis for the Media Research Center.
A natural disaster "should be a time when we should all be Americans," and put such differences aside, he said.
Still, the conservative media watchdog that Graham works for was not above getting its own licks in, criticizing Sunday morning network hosts, who it said "harangued" federal disaster relief officials with questions about Trump's response to Hurricane Maria. It also attacked MSNBC's Katy Tur for introducing the issue of climate change to Florence coverage.
And it reposted an infamous decade-old video of an NBC News reporter covering a hurricane from a rowboat, as a wider view captured men nearby sloshing through water that barely topped their ankles.
The Weather Channel's Mike Seidel similarly became a meme victim during Florence for video that depicted him struggling to stay vertical in the storm's winds, while men walked behind him seemingly unbothered; his network said Seidel had a hard time keeping his footing because he was on wet grass.
For the people who spread the videos, the idea is to undermine reporters covering the story, to depict them as people more interested in seeking attention than in keeping viewers informed about what's going on.
That was the thinking behind Trump Jr.'s tweet of the Cooper photo. It showed him in water much deeper than his own camera technician, who stood a few feet away in water that didn't reach his knees.
On Monday, Cooper said the picture wasn't even from his Florence coverage, but rather from the aftermath of Hurricane Ike in Texas in 2008. He said he was trying to stay off a road where the water was shallower to not get in people's way, and to convey that there was still a lot of deep water creating dangerous situations.
Climate change and its impact on hurricanes is a third-rail topic for media covering the storms. Many conservatives get mad when it's brought up at all, while liberals believe it is not discussed enough.
In the days before Florence struck, four scientists posted a study they said illustrated how forecasts of the storm's intensity were worse than what a similarly situated hurricane would have been in the days before climate change.
It got some media attention, but apparently none among the cable news networks that spent several days in near-constant coverage of Florence's approach, said Kevin Reed, a professor at Stony Brook University in New York and one of the authors. He said it's important to discuss the impact of climate change during extreme weather events because that's when the public is focused on it.
But North Carolina State's Lackmann said that releasing such information before the storm makes landfall is "pushing it."
It's better to wait until after the storm when data could be closely studied, particularly since Florence's wind intensity dropped off from what was predicted, said Lackmann, noting that early indications show that hurricanes may be less frequent in a time of climate change but the strong storms are even stronger.
While the storm is bearing down, climate change is "not the most important thing people should be thinking about," Williams said.
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