But the radiative cooling is going to happen with or without the water. It is a different system operating within the same device. Routing air underground to cool it will work regardless of water, at least until things heat up underground, which can be a thing in low-conductivity soils.
These things are extremely well studied by people who know what they're doing. I'll never not be impressed by the ability of a random on an internet forum to 'well akshully'.