At the same volume, temp, and pressure, the air with more water vapor is lighter. The density increase from cooling down the air is greater than the decrease from the water vapor added to do it. The "cooled down" moist air will be denser than the surrounding not cooled down and drier air.
But nowhere near what is claimed by Pickett who ignores this issue and hundreds more such.
The tower will work....at no more than 6% of what Pickett claims with his bad science. And that is pretty much considering a perfect tower to get that.
The net continuous output of this beast will be no more than about 20MW. And that can't come close to existing technology in any terms, specially cost. For the $2.2B cost claimed to build this tower, we could build a conventional solar panel farm generating 1.8 GIGA watts.
I have no humble opinions, but I do have opinions and those are what I express in my posts. BUT...I have been wrong before and likely will be wrong again so do your own research and don't blame me if you are too lazy to do so.