Swans, geese, and ducks migrate both by day and by night, so it’s quite likely you were hearing swans. Most songbirds migrate by night as well. Standing outside listening is a wonderful way to appreciate the magnitude of nocturnal migration.
You can also view the magnitude of a night’s migration using NEXRAD weather radar. If you’re interested, Braddock Bay Bird Observatory offers a good example of using radar to see bird migration. Try this site to learn how to identify flight calls of nocturnal migrants. Or just train your spotting scope on the full moon and see how many birds pass by!
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