Why we should observe an increment on the mean intensity in rainfalls and an increment on mean dry days with global warming?
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This site by climate scientist Frank Wentz discusses the rainfall possibilities of increased temperatures. Although warmer atmosphere contains more water thereby increasing rainfall, changes in circulation could minimize rainfall.
It's also possible that currently wet areas will get wetter and currently dry areas will get drier.
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Because the statement isn't true while it is more convenient for the popular idea that there is some climate change to worry about.
In reality, irregularities and extremes in precipitation, temperatures etc. are driven primarily by temperature gradients. Because the cold poles are predicted to warm faster than the warm equatorial areas because of various feedbacks, the pole-equator temperature difference is predicted to drop. If true, this will reduce temperature gradients and make many location-dependent quantities more spatially uniform. A higher temporal uniformity is expected as well.
So if there were (significant) global warming, precipition and other processes would probably get more uniform and less extreme. The frequency of rains that are stronger than a given threshold would drop. However, the relative difference in the intensity of rain etc. would be very small because one or few Celsius degrees is a tiny change of the absolute temperature while the natural noise and fluctuations in quantities describing precipitation are of order 100 percent.
This is a textbook material. I was taught those things mainly by Richard Lindzen but e.g. his textbook on atmospheric physics is recommended: