I do too, it's a great idea, from the notion that an umbrella left outside will collect dew, even in a desert. I also love the notion of two layers of roofs; in a hot climate it's very good biomimicry (building in the shade, as it were).
However, I wonder if there might be a logic error in scaling up a 4' diameter umbrella to a 80' one...dew is tiny in scale, and has to battle considerable friction while rolling down to the collection well - by the time it travels 40', how much of it has evaporated away?
I would suggest to the designers, to investigate the Johnson Wax Building as a form-maker (not that I am a tremendous Wright fan, I'm not).
Obviously the umbrellas would be shaped differently, and you'd make their edges fit closely together, and they'd be not-concrete, but this sort of repetition and spacing would probably be more efficient in water collection, and more easily withstand wind storms, with multiple support/tie down points throughout.