WASHINGTON — The nations’ top intelligence official is declassifying three secret U.S. court opinions showing how the National Security Agency scooped up as many as 56,000 e-mails annually over three years and other communications by Americans with no connection to terrorism, how it revealed the error to the court and changed how it gathered Internet communications.

Director of National Intelligence James Clapper authorized the release Wednesday.

The opinions show that when the NSA reported to the court in 2011 that it was inadvertently collecting as many as 56,000 Internet communications by Americans with no connection to terrorism, the court ordered the NSA to find ways to limit what it collects and how long it keeps it.