The moon is not actually larger when it is on the horizon, but seems larger because of an optical illusion.
When the moon is on the horizon, it is seen next to buildings or trees, terrestrial items you are familiar with, and the juxtaposition of the two images changes depth cues.
You know the building is right in front of you, and the brain compensates by assuming the moon disk is larger than it is when it is high in the sky, away from objects for comparison.
At sea, where there are no buildings or trees, this illusion is absent because there are no cues to suggest it.
Another test is to look at the moon between your legs upside down.
All depth cues are completely thrown off, so the effect is lessened. When the moon is seen beside an upside-down tree, the tree is perceived as just a shape, not a tree.
A way to convince yourself that you have been fooled by an optical illusion is by measuring the size of the moon’s disk in the sky.
The best way is to use a piece of paper carefully positioned on a window, tracing the moon once when it is near the horizon and again when it is at the top of the sky.
The head must be lined up so it is exactly the same distance from the paper for both sightings.
The atmosphere does not have a significant magnifying effect on the moon.
If it does anything, it makes the full moon appear slightly shallower from top to bottom, or slightly oval.