I'm certainly no expert, but as they pointed out this is basically a trompe, which...
>Compressed air from a trompe is at the temperature of the water, and its partial pressure of water vapor is that of the dewpoint of the water's temperature. If the water is cool, the compressed air can be made very dry by passing it through pipes that are warmer than the water. Often, ordinary outside air can warm the pipes enough to produce dry, cool compressed air.
>Compressed air from a trompe is at the temperature of the water, and its partial pressure of water vapor is that of the dewpoint of the water's temperature. If the water is cool, the compressed air can be made very dry by passing it through pipes that are warmer than the water. Often, ordinary outside air can warm the pipes enough to produce dry, cool compressed air.
[https://en.wikipedia.org/wiki/Trompe]
So use a better heat exchanger to cool the water, and then heat up the air until it's dry enough, I guess?