I always seem to show up on topics a day late and a dollar short, but here we go...
The total latent heat released by this much water falling as rain would be 1.15x10^24 J. The problem is that this heat has to go somewhere. The energy is partially released as wind, which is what drives hurricanes so there should be mega-hurricanes all over the earth, but eventually nearly all of the heat will be absorbed by the air. The mass of the atmosphere is about 5x10^21 g and the heat capacity of atmosphere gases is only about 1 j/g so just one meter of global rain releases enough heat to heat the atmosphere by about 200 C. Of course that won't happen. As the air temperature rises the vapor pressure of water will increase and the rain will stop falling.
I'm also wondering, as all of this is going on, what the effects would be upon the weather of having nearly the entire troposphere displaced upwards by the torential rains and rising flood waters into the area now occupied by the stratosphere. (I understand that the highest parts of Mount Everest may actually be in the stratosphere at times depending upon the weather.) It seems to me that this would cause already unimaginably freakish weather to become even more freakish. How freakish??
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