SILVER SPRING, Md. — On Friday morning in the suburbs of Washington, D.C., government scientists in khakis and sensible shoes bustled to work — beneath a towering bronze sculpture of a hand releasing seabirds — heading for a small scientific agency caught up in a political mess triggered by President Trump’s tweet about Hurricane Dorian.

One of the arriving employees was Neil Jacobs, the head of the agency, the National Oceanic and Atmospheric Administration. “We’re under investigation,” a weary looking Dr. Jacobs said, a large messenger bag slung over his shoulder. “I can’t talk.”

The investigations are examining an attack on the independence of an agency that, despite its enormous importance to the United States economy, typically flies well below the radar. That changed in recent weeks when meteorologists working for NOAA corrected Mr. Trump on Twitter after he inaccurately described Hurricane Dorian’s path. The president then ordered the agency to support his version of events, triggering a political clash .

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The National Oceanic and Atmospheric Administration is hardly a household name, yet it plays a significant role in modern life.