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Here's an idea, use the mirror system to keep it warm and sunny all year round in the midwest, 3 crops a year instead of 1!
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It takes more than just sunshine to grow crops. What happens when the soil is depleted of nutrients? Or if year 'round sun leads to a shortage of water?
Our ecosystem is the end result of literally billions of years of refinement. We are fools to think we can change it for the better overnight.
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There is not exactly a finite amount of water on the earth. More warmth tends to lead to more evaporation/humidity, which means more rain/fresh water. Armed_Scientist is correct. Longer growing seasons are a direct result of a warmer planet.
The only thing working against you would be a higher humidity, creating more clouds, thus reflecting much heat back into space.
The earth is wonderfully self-regulating, but does go through many changes over long periods of time. A few thousand years ago, the Earth was much warmer, and grapes were growing across Canada, and a few thousand years before that, glaciers were melting from across the midwest.
(I am not a big proponent of Global Warming).
Humans have not gotten powerful enough yet to affect the weather in a significant way. One day, we will.
As to the nutrients, they are added through decomposition of animal life, the sun, and rains. Crop rotation provides a method of expanding the useful life of soil, and fertilizing, (natural and artificial) can more than replace what nature does gradually.
I hope I have addressed your concerns, we are launching an orbital mirror tomorrow...