A series of "once-in-a-millennium" rainstorms have lashed the United States in recent weeks, flooding areas baked dry by long-term droughts, as human-caused climate change brings weather whiplash.

And scientists warn that global warming means once-rare events are already much more likely, upending the models they have long used to predict possible disasters -- with worse to come.

At least 40 people have been killed in the last month by storms in Kentucky, Illinois, Texas and Missouri, inundating areas that in some cases had seen little to no rain for months.

Up to 12 inches (30 centimeters) fell in one of these storms -- the kind of downpour that statistical models say should only happen once in a thousand years.

"This is 'weather whiplash'," tweeted Peter Gleick, co-founder of the Pacific Institute, a non-governmental organization that works on water issues around the world.

It is "caused by an intensification of the global hydrological cycle & how it distributes water around the planet, influenced by human-caused climate change."

The warnings scientists have been sounding for decades about the effects of unchecked fossil fuel use are suddenly coming into focus for millions of people.

A warming planet is not a benign place in a far-off future where it is always a bit sunnier; it's a place of wild swings, where the wets are wetter and the dries are drier. And it's now.

"The commonality between these and other extreme rainfall events is you need just the right set of ingredients to come together," said David Novak, director of the Weather Prediction Center at the National Weather Service.

"You need moisture, you need instability in the atmosphere. And you need some sort of... feature to kind of ignite the storms."

While a rainstorm in Texas or Kentucky or Illinois is not unheard of at this time of year, these events were supercharged by an oversupply of atmospheric moisture -- a direct consequence of the planet being hotter.

"There's scientific consensus absolutely on the fact that warmer air can hold more moisture," Novak told AFP.

"There is more moisture available... for these fronts to tap, and so you can get these really intense rainfall events."

The science is uncontroversial -- if a little complicated for those not familiar with linear equations and difficult-to-pronounce chemistry.

The Clausius-Clapeyron equation shows that for every one degree celsius (1.8 F) the air warms, it can hold seven percent more moisture.

That's what makes hot, equatorial places noticeably more humid than cooler climes, says Novak.

And it's also what's messing with the statistics and making the one-in-1,000-year storms -- like the five that hit the US in the last month -- a lot more common.

Storms like these had a 0.1 percent chance of occurring in any given year in pre-industrial conditions, meaning that on average they would happen once every 1,000 years.

But their percentage chance of happening in a warmer environment that holds more moisture rises dramatically.

In other words, the recurrence interval -- the periods expected between these once relatively rare events -- is shrinking.

"Something that really wasn't very likely at all, just a little bit more moisture can make that quite a bit more likely," said Novak.

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