IN 1979 it was Claudette; in 2001 it was Allison; now it is Harvey: in 50 years, the city of Houston has been hit by three separate “500-year floods”. A 500-year flood does not have to happen only twice a millennium. But a run of three in one place does make it feel as if the past climate were no longer a reliable guide to the present—as if the climate itself were changing.

So, of course, it is. The world’s average temperature is between 0.6 and 0.7°C (1.1- 1.3°F) higher than it was in 1979. Scientists have understood since the 1850s that hotter air holds more water vapour; a law known as the Clausius-Clapeyron equation states that for every degree Celsius of warming, the atmosphere will hold 7% more moisture. In 1989 two Japanese researchers used computers to model this phenomenon and concluded that this wetter air would lead to more of the heaviest rains rather than, say, near-perpetual drizzle. It is thus no surprise that insurers see an increase in water-related disasters (see chart 1).

Other lines of evidence bear out the insurers’ loss data. In 2015 researchers from the Potsdam Institute for Climate Impact Research in Germany compared computer models of the atmosphere as it now is and as it used to be to see how much of an impact these effects might be having. They found that the planet Earth experienced 12% more record-breaking downpours between 1980 and 2010 than might have been expected had the climate not been changing (see chart 2). The same year Reto Knutti and Erich Fischer at ETH Zurich, a Swiss university, found that the warming recorded since pre-industrial times made new one-day records for rainfall over land 18% more likely. For 2°C of warming, the target below which countries vowed to keep global warming under the Paris agreement of 2015, the figure would rise to 40%.

Despite these general relationships, climate scientists have for the most part been cautious about blaming particular events on the climate change driven by the emission of greenhouse gases. Heavy storms, for example, result from a complex confluence of factors. What made Hurricane Harvey so unusual—and unusually destructive—is that it intensified very quickly in the 24 hours before it hit Texas, thanks to a particularly warm eddy of water in the Gulf, and it then stopped dead in its tracks, held between two high-pressure systems as though in a vice. But the fact that severe storms, like Tolstoy’s unhappy families, all differ in their details does not mean that there are no generalisations to be made about the chances that something will make a family unhappy, or a storm severe. By running climate models again and again under different conditions it is possible to get a sense of how much more likely a given event is under today’s conditions versus yesterday’s. “If climate change doubles the probability of an event, there is a sense in which half the blame is attributable to humans,” argues Myles Allen of Oxford University. Since 2012 the American Meteorological Society has published an annual bulletin entitled “Explaining Extreme Events from a Climate Perspective”. Sometimes no link is found between specific meteorological anomalies and man-made climate change: that was the case with Britain’s winter storms at the start of 2014 and the water shortages in south-east Brazil later that year. In other cases—droughts in Kenya in 2012, a Japanese heatwave in 2013, torrential downpours in south-west China two years later—signs of human exacerbation can be discerned.

Coming for some time

All this matters because the models engineers rely on to build resilience into roads, buildings, bridges, dams and levees have tended to presuppose that the climate of the recent past represents the climate of the foreseeable future. This opens them up to two sorts of surprise: that tomorrow’s climate may be different; and that the day-before-yesterday’s climate may have been more variable than their records suggest. The likelihood of calamities that fall beyond the range seen in the recorded data is determined by extrapolating what the “tails” of the sample distribution might look like. Those extrapolations, it now appears, have sometimes been conservative.

Victor Baker, a palaeohydrologist at the University of Arizona, studies floods far away in time and space (he is particularly renowned for his work on catastrophic torrents in the distant past of Mars). The scars left by the biggest past events provide benchmarks for what might happen again: as Mr Baker puts it, “What has happened, can happen.” In 2013 he and his colleagues analysed 44 ancient inundations of the Upper Colorado River, estimating the floods’ intensity from the volume of sediment and establishing their age using a technique which reveals when quartz in those sediments was last exposed to daylight. Their analysis showed that the river’s “500-year floods” were twice as severe as estimates based on modern records alone implied: what had been considered a once-a-millennium flood turns out to occur more than once a century.

Chinese hydrologists, prevented from setting up modern rain-gauge infrastructure in the 20th century by invasion, civil war and the Cultural Revolution, have long relied on ancient records, both geological and human, to inform the design of dams and canals. Although in the 1990s America’s Bureau of Reclamation developed similar techniques to study the potential risks to large dams from very rare, extreme flooding, most Western hydrologists have tended to regard such things with scepticism, highlighting the difficulty of reliably interpreting the geological record. But interest in the field has grown. In September Mr Baker will give the keynote address at a big geologists’ shindig in London and, a month later, another to the annual meeting of the Geological Society of America.

A greater respect for the past will help people modelling hazards. So will better statistics. Advances in so-called “extreme-value analysis” have helped statisticians improve their projections of the under-sampled tails in their data. And modellers can augment the real world with thousands of computer-simulated scenarios.

Besides supplementing real-world data for statistical purposes, generating virtual weather this way is handy for risk assessment. As Mr Allen remarks, “We are, almost by definition, harmed by events that haven’t happened before.” Lea Müller, a natural-hazards expert at Swiss Re, a reinsurance company, recalls how one north-Atlantic storm simulation had charted the curious path that Hurricane Sandy subsequently took when it buffeted New York in 2012. It was just one of many generated scenarios and came too late for the city to impose stricter building standards, say. But it shows that scrutiny of possible worlds may alert people to potential perils in much the same way Mr Baker’s excavations can.

In 2015 the Federal Highway Administration asked the National Oceanic and Atmospheric Administration (NOAA) to assess how much the assumption of an unchanging climate affects “Atlas 14”, NOAA’s repository of flood-risk estimates. Sanja Perica, who led the project, says the idea was to see how greater weight could be given to more recent data, which are more indicative of what a hotter future may look like. “The project ended with more questions than answers,” he admits. But his team soldiers on (though some fear that the flow of federal cash for such projects may dry up under President Donald Trump, whose budget has cut funding for various climate-change initiatives).

Understanding the risk of flooding in the future will demand pursuing many courses: statistics, simulations and sediment studies all have a role to play, says Peter Thorne of Maynooth University in Ireland, who contributed to the latest report of the Intergovernmental Panel on Climate Change and the current US Climate Assessment. The good news is that scientists are on the case. Sadly, engineers and their political taskmasters have been reluctant to embrace the advances they feel they can offer. They cling to “old data, poor data or no data at all,” gripes Mr Thorne.

Perhaps, Mr Knutti ventures, they prefer what they know and understand. Swiss building standards have not been updated in 40 years. Updating NOAA’s Atlas 14 may require a political decision, and given the lamentable stance of the administration support is far from assured, Harvey notwithstanding. What looks certain is that Houston, Mumbai and a host of other cities can expect more “hundred-year” floods before the century ends.