But even in an administration known for defying forecasts, the wayward prediction of an unpredictable president has dominated the national conversation, despite how little would seem to be at stake politically.

It started on Sunday when the president warned on Twitter that Alabama, among other states, could be hit by the storm “(much) harder than anticipated.”

In an attempt to head off panic, the Birmingham forecasters quickly sent out their own tweet, assuring residents that they were not, in fact, in harm’s way. “Alabama will NOT see any impacts from #Dorian,” the local office wrote. “We repeat, no impacts from Hurricane #Dorian will be felt across Alabama.”

Angry at the mockery that followed, particularly on cable television and social media, Mr. Trump has ever since sought to justify his contentions to the point that he even called on his homeland security secretary to display a map in the Oval Office that appeared to have been altered by a black Sharpie pen to suggest Alabama was in the potential path of the storm.

As so often happens in Washington, a serious dispute eventually devolved into fund-raising. Mr. Trump’s campaign sought to capitalize on the attention by offering to sell pens with the president’s signature on them; a set of five went for $15.

“Buy the official Trump marker, which is different than every other marker on the market, because this one has the special ability to drive @CNN and the rest of the fake news crazy!” Brad Parscale, the president’s campaign manager, tweeted, adding the hashtag: “#KeepMarkersGreat.”

Mr. Trump’s wrath at his critics, however, left the Birmingham forecasters caught in the path of a presidential storm. For five days, NOAA had no public objection to their conclusion. Only after Mr. Trump insisted on sticking by his disputed claim did NOAA finally weigh in — and no spokesperson attached a name to the statement.