Mother nature is a freak but a smart freak. I do wonder what the "yang" would be to this "ying". Dinkering with nature, on a global level, could result in some unwanted side effects. What those might be one can not say. BUT you have to start somewhere and this idea has merit on that fact alone. To improve you must first try. If nothing else this idea makes good fodder for a science fiction story. I like the concept.

This concept has been suggested by people in the past as a way to terraform Venus or Mars. I think the terraforming schemes are ludicrous, but your scheme is at least more reasonable than those. Still, the amount of heat you would need to supply in order to change the weather is extremely high. Might it not be more feasible to find a way to generate heat on the ground? It seems rather needless to go up into space to heat the Earth when we're already on the Earth to start with. I also have serious doubts about the viability of making those giant mirrors. Thin film isn't going to last long in space. The micro-meteors will erode it very quickly. Subtle variations in the pressure from the solar wind would play havoc with the attitude control. The shear size of the mirrors would pose a daunting challenge. It is easy to say that we could build a one square kilometer mirror, but you should keep in mind that nobody has ever built an object that large even on the ground much less in space.

Worst of all, even with thousands of these mirrors, it is doubtful that we could affect the weather enough to actually produce a desired effect. The problem that all space mirror advocates fail to appreciate is the scale. Even flying over in low Earth orbit, a 1 km mirror would look very small. How small? At an altitude of 300 km, which is lower than the International Space Station, A 1 km mirror will look the same size as a 1 inch square would look from 300 inches, which is 25 feet. Try looking at a 1 inch square from 25 feet away. It looks mighty small! Realistically, they would probably need to be in a much higher orbit, which would make them look tiny. This isn't going to provide enough shade to do diddly. It isn't going to be able to reflect enough light Earthward to do much either. Even a few thousand won't do much because the Earth is a really big place. At any given moment, only a few would be over a given spot on the planet. It's doubtful that they could change the temperature on the ground enough to even be detectable by meteorological instuments. Bear in mind, you are try to use the solar energy falling on a few thousand square km of mirrors to try to change the weather on a planet with a suface area of more than 510,000,000 square km! That means there is approx. 25,000 times more light hitting the Earth than there would be hitting 10,000 sq km of space mirror. When you look at the numbers, you can see that this isn't feasible at all.

Dwane Anderson:
The area to be heated is only the sunny side and away from the poles.

In my estimation, the intent is to nudge temp/press relationships to change critical values.

One mirror would illuminate 10 times it's own area to limit the increased lumin intensity. The people in Canada would not want the luminous intensity of Florida.

Space-based systems allow for rapid redirection of resources over a very large area.

The piezo-electric structure allows for active optics.

It is as important to provide the conditions to cool a land mass as it is to heat the same land mass. Things are already warm enough if global warming is a reality.

Ground-based systems often use chemicals to cause weather changes, this may be environmentally more problematic. Directing heat in significant quantities from one place to another is quite difficult for land-based systems.

All problems have solutions; we just need people with the intellect to make those solutions a reality, and visionaries with deep pockets to support them.

Did you look at the numbers above? Did you digest their significance? This is not feasible at all.

"Directing heat in significant quantities from one place to another is quite difficult for land-based systems." True, but do you think building and maintaining colossal space mirrors would be easier? A giant heat-pump/AC system on the ground would be easier to build than giant mirrors in space. Plus, I know it will definitely produce a noticable temperature change on the ground. I have to admit, I am not a good enough physicist to calculate the heat that a mirror could produce on the ground. If you know someone who is, I would love to see the numbers.

Mirrors in orbit will have to keep moving by unless they're in geosynchronous orbit, around 18,600 miles away. From G.O. the light will lose a lot of intensity due to divergence. A mirror is also not 100% efficient. Some of the energy will be absorbed and if the film is thin, some light will probably pass though.

If the mirror is only used during the day, then the mirror and the sun will be on the same side of the Earth. This means that the mirror will have to sit at an angle to reflect the light Earthward. If the sun and mirror are on opposite horizons, one east the other west, the angle can be reduced, but greatest light intensity is achieved when the source is directly over head. The optimal energy deliver to the ground (during the day)would probably be in the early morning or late evening with the mirror more or less over the target zone sitting at about a 45 degree angle to the surface. Absolute maximum possible would be in the middle of the night, as the mirror would be facing almost straight on. It can't be perfectly straight on because it would be eclipsed by the Earth.

I wonder what such a mirror would look like from the ground? I would think that it would look like an extraordinarily bright star. It would be visible in broad daylight, even more so in the morning or evening when the sky is not only darker but the mirror is actually brighter. It would only be visible in the target zone.