Berlin Is Becoming a Sponge City [video]
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There'd still be flooding, and it would still be bad, but a certain degree of flooding was avoidable.
A city that gives planning permission for a development that is probably going to be destroyed with loss of life in the next hundred years is not serving people well.
I know I didn't really answer your question, but these models were made to represent fields and swamps. So yes, I believe there are lots of studies on large scale effects.
Soil Type & how deep of soil effects how much water the ground can soak up & how fast the water will run. All would be slower runoff than concrete.
Also the slope of the land would make a difference.
These are just the obvious ones. Bottlenecks, whether created on purpose or not would have a huge impact. Where I live we have large snowfall in the winter which creates ice jams & flash flooding in the spring.
I personally like the idea of this.
Think of it like a building being evacuated though a stairwell. Being say 10 vs 11 floors can make a significant difference in average wait time. Except average weight time is equivalent to the height of flood waters.
That said, what would be required to make sure no barrier formed, say from the roots system or something else is really hard to say.
You'd also need some sort of lining that would prevent the moisture from being obsorbed by the building materials themselves.
Sufficiently deep buildings and parking garages might also encounter ground water, so adding soil on top might not even add new problems to the engineering side.
Similarly, the rooftop plants are shown on rooftop designs that would already have to deal with stagnating water
[1] https://upload.wikimedia.org/wikipedia/commons/5/54/Berlin_P...