Dr. Jeff Masters gives it a name -- "weather whiplash" -- and explains how it happens:
I'm often asked about the seemingly contradictory predictions from climate models that the world will see both worse floods and worse droughts due to global warming. Well, we have seen a classic example in the Midwest U.S. over the past two years of just how this kind of weather whiplash is possible. A warmer atmosphere is capable of bringing heavier downpours, since warmer air can hold more water vapor. We saw an example of this on Thursday morning, when an upper air balloon sounding over Lincoln, Illinois revealed near-record amounts of moisture for this time of year. The precipitable water--how much rain could fall if one condensed all the water vapor in a column above the ground into rain--was 1.62", just barely short of the Illinois April record for precipitable water of 1.64" set on April 20, 2000 (upper air records go back to 1948.) Thursday's powerful low pressure system was able to lift that copious moisture, cool it, and condense it into record rains. So how can you have worse droughts with more moisture in the air? Well, you still need a low pressure system to come along and wring that moisture out of the air to get rain. When natural fluctuations in jet stream patterns take storms away from a region, creating a drought, the extra water vapor in the air won't do you any good. There will be no mechanism to lift the moisture, condense it, and generate drought-busting rains. The drought that ensues will be more intense, since temperatures will be hotter and the soil will dry out more.
The new normal in the coming decades is going to be more and more extreme flood-drought-flood cycles like we are seeing now in the Midwest, and this sort of weather whiplash is going to be an increasingly severe pain in the neck for society. We'd better prepare for it, by building a more flood-resistant infrastructure and developing more drought-resistant grains, for example. And if we continue to allow heat-trapping gases like carbon dioxide continue to build up in the atmosphere at the current near-record pace, no amount of adaptation can prevent increasingly more violent cases of weather whiplash from being a serious threat to the global economy and the well-being of billions of people.
It's hard to comprehend the scale of the threat, as is so often the case with climate change. Here's a NASA image, from the Precipitation Measurement Mission, to try to help: