The flurry of natural disasters has focused attention on the complex work towards establishing a direct link to global warming.
When floods swept through parts of China's Henan province last month, killing at least 302 people, a group of scientists who specialise in analysing the drivers of extreme weather events found themselves unable to help.
Like everyone else, they were horrified by the images of people trapped in water-filled subway stations, as whole blocks of the city of Zhengzhou were flooded by record rainfall.
Their work involves two core questions: did climate change make this disaster more likely? And did it make it worse?
But by the time the storms hit China, the scientists were already fully engaged trying to untangle why the floods in Germany and Belgium earlier in July had been so devastating.
Demand is intensifying for the work of the World Weather Attribution initiative (WWA), a team founded in 2014 which comprises seven core volunteer researchers, all of whom also have day jobs, and which has been unfunded for years.
Two weeks before the German floods, the same questions were being asked about a freak heatwave in North America. This week, fires sparked by record temperatures are blazing across Turkey, Greece and Italy.
"We are already struggling to get the manpower," says Geert Jan van Oldenborgh, co-lead of WWA. As the world warms up, he expects the workload to increase, because "events will get worse".
Is climate change to blame? To the casual observer, the flurry of extreme weather events over the past two months can feel like the obvious consequence of rising average temperatures — and something that many scientists have been warning about for years.
Yet establishing a direct causal link between an individual case of flood, fire or storm and the broader climate is an evolving science — and something that is still desperately hard to do in practice.
A litany of factors can influence a natural disaster, including local weather conditions — which may be changing — the shape of the landscape, human choices and natural variability. Even without climate change, extremes such as heatwaves would occur.
That climate change is making extreme weather more frequent and intense is a connection that has been "well made", says Peter Stott, an expert in climate attribution at the UK's Met Office.
But he adds: "The science gets more difficult when we ask versions of the question to do with a specific [event] . . . and say 'is this due to climate change', or maybe more meaningfully, 'how did climate change contribute to this?'"
If the science of climate attribution becomes more accurate, the implications could be substantial. It could allow more precise predictions about future events and identify areas that are particularly at risk, which would help societies prepare and adapt.
Stronger attribution could also fortify the legal cases that are already being brought against companies and governments seen as partly responsible for climate change.
But the challenge is considerable. "It's quite a tricky question to say 'how much more rain fell in [the European] floods due to climate change'," says Stott. "That is really pushing at the frontiers of science."
Scientists are making some headway. In July, the WWA made the striking pronouncement that the North American heatwave that sent temperatures in the Canadian village of Lytton soaring to 49.6C would have been "virtually impossible without human-caused climate change".
The group reached a similar verdict about a heatwave last year in Siberia, concluding that the 38C recorded in Verkhoyansk would have been "almost impossible without climate change".
"We know that weather varies a lot from day to day," says Flavio Lehner, a climate scientist at Cornell University who works with the WWA. "The question is when [extreme weather events] occur, are they stronger, longer and more severe than they would have been without climate change?"
Yet they are wary about pushing their conclusions too far. "Every time we publish something, I wake up at 4am in the morning to make sure that the numbers are correct," admits van Oldenborgh. "It's essential that we worry . . . [to get] as close to the truth as possible."
Simulating the changing climate
The dramatic series of extreme weather events in recent months has caught the world's attention, and the question about the role of climate has rarely been so present in scientific or political discussion.
Doug Wilson, chief scientist at the UK's Environment Agency, says the question is asked "after virtually every single [extreme weather] event . . . Our response tends to be that this is exactly what we'd expect to see in a changing climate. We're not trying to say that a particular event is a result of climate change."
Other scientists, including from the WWA, spend their time dissecting extreme events in an effort to do just that — or the nearest thing to it, since no event is caused by climate change alone. Findings with the "very strong language" of the North American and Siberian heatwave conclusions are unusual, says Lehner.
And identifying a link is not inevitable: scientists said climate change was not a significant driver of the Brazilian drought of 2014-15, which was caused, in part, by the demands of a growing population.
Such meteorological detective work relies in large part on complex computerised models. In simple terms, attribution scientists run simulations of Earth's climate system — which might represent thousands of theoretical days — to see how often an event of a certain magnitude occurs in different scenarios.
Scenarios might include the Earth as it was 200 years ago, before man-made warming set in, present day conditions and a future scenario in which the planet has warmed more than the 1.2C already observed. Researchers then compare how many times the event occurred in each scenario, and make a judgment about whether climate change made it more likely.
These models, however, are not perfect. They work by dividing the globe up into a grid that might be as small as 1km by 1km, or as large as 100km by 100km. A wider grid might be used to cover a larger area, but can mean "the picture is very pixelated, providing us with good estimates globally, but lacking detail when it comes to local weather events," says Professor Christian Jakob, from the School of Earth Atmosphere and Environment at Australia's Monash University.
Wildfires, for example, can be difficult to analyse without a very detailed model, since they can occur over relatively small areas of land and be influenced by local weather conditions, including those created by the blaze itself.
In light of the fast-growing number of record-breaking weather events, many researchers are now stressing the need to use models that are more precise.
"We can't attribute [the recent extreme weather] events to climate change, because the models can't simulate them," says Tim Palmer, Royal Society research professor of climate physics at Oxford university. "The tools we have are not adequate."
At the same time, he adds, it is a "wrong conclusion" to assume that these events are therefore not driven or exacerbated by climate change.
However, running the sort of high-resolution models that might answer these questions better requires huge processing power — supercomputers that are enormously expensive to build and use.
"We need significantly more funding for climate science," says Lehner. "Our ability to understand and predict climate change, and extremes like we have just seen, is not limited by our knowledge. It is limited by computing time, ie resources."
In a briefing for policymakers this year, the Royal Society, the UK's independent scientific academy, called for the creation of an international climate modelling centre where resources would be pooled.
The world "needs more detailed and precise information to enable robust decision-making in the face of rapidly amplifying climate change," the briefing said. The inability of models to simulate certain events in fine detail "accounts for the most significant uncertainties in future climate, especially at regional and local levels."
As the world struggles to comprehend the devastation wrought by disasters from Henan province to Cologne, interest in climate modelling from beyond the scientific community is growing.
Tom Delworth, a senior scientist at the US National Oceanic and Atmospheric Administration, describes "explosively growing demand" from policymakers for information about how things might change.
"One of the groups that has expressed the most intense desire to understand that is our intelligence services and the military," which are interested in predicting how the consequences of climate change — such as water shortages — might spark conflicts and create new risks, he adds.
However, not everyone agrees that there is value in striving for certainty on the causation question.
Giza Gaspar Martins, chair of the least developed countries group at the UN climate negotiations in 2015, argues that debating whether individual events were made worse by climate change is a distraction.
"I am beyond attribution science," he says, adding that "we waste time" on this work when the priority should be cutting greenhouse gas emissions and adapting to a changing reality.
Angola, for example, is already experiencing more severe drought and flood cycles, he adds about his home country. "We are sufficiently convinced [these] are linked to climate change. And that's all we need."
But Mamadou Honadia, a former lead negotiator for Burkina Faso at the UN negotiations, says being able to attribute individual events to warming helps developing nations argue for climate funding — one of the key issues on the table at November's climate conference, known as COP26.
"It really is very difficult to convince the international community that floods, which happen in developing countries, are due to climate change, without any science-based information," he adds.
Some scientists have even proposed that establishing causal links could help with the rising number of legal cases being brought against companies and governments for their roles in driving climate change.
Plaintiffs could make "better use of climate science — particularly in the field of attribution," wrote a group of Oxford university researchers, including the WWA's other co-leader, Friederike Otto, this year.
"It does not seem far-fetched any more to suggest that — supported by the right scientific evidence — future cases will compel companies to pay compensation to communities impacted by climate change."
The rapid succession this year of extreme events has prompted anxious questions about whether the realities of climate change are outstripping what models had predicted.
In its assessment of the North American heatwave, the WWA said temperatures were so extreme and unusual that they could be the result of "non-linear" climate change, where extreme events do not occur smoothly in line with temperature rises, but more suddenly or intensely.
The Climate Crisis Advisory Group, which is led by the UK government's former chief scientific adviser Sir David King, said the severity of the heatwave in North America and the flooding in Europe were "difficult to explain" as solely the result of 1.2C of warming from pre-industrial levels.
"Climate change is happening faster than anticipated," the group said. Rapid warming and melting Arctic ice may have "triggered additional changes in how our weather works."
Not all scientists share the concerns that current models are not up to the job.
"These are extreme events, but we saw them being produced by climate models . . . I'm really less surprised than some of my vocal colleagues," says Lehner. The sequence of recent catastrophes "might just be by chance. We might not see similar things for a long time in any of these specific places," he added.
The shocked reactions to this year's extreme weather events may also reflect a more general misunderstanding about the realities of living with climate change.
"I think it's fair to say that the communication has been a bit abstract and gives the impression that climate change is far away," says Ted Shepherd, Grantham chair in climate science at the UK's University of Reading.
As the world continues to warm up, extreme events are set to continue. In July, a study published in the journal Nature Climate Change found that "record-shattering extremes" that would be "nearly impossible in the absence of warming" were likely to occur in the coming decades.
Further investigation into the likelihood of such events was "vital", since communities tended to plan for worst-case scenarios based on what had been observed in the past, rather than what is possible in future, it added.
An autopsy of a storm, fire or flood — and the destruction they cause — is likely to find numerous and interrelated drivers, but that can be an unpalatable answer.
"Some people feel that somehow [looking at multiple causes] takes the spotlight off climate change too much," says Shepherd.
But he says it still makes sense to study the causes because the preventive actions that people can choose to take, such as installing flood defences or warning systems, or the reactions of policymakers to a disaster once it hits, will also impact how damaging an extreme event is. "You shouldn't let local governments off the hook for bad management," says Shepherd.
The political debate around climate is changing, even if the science can still seem imprecise. As people watch their homes burn, or disintegrate under floodwater, the support for climate scepticism is waning, says MP Francis Scarpaleggia, who chairs the Canadian House of Commons' standing committee on environment and sustainable development.
The public is increasingly convinced of the link between extreme weather and climate change, "regardless of whether the academic work precisely links the two", says Scarpaleggia. "It's one thing to read about the science, but you need to see the tangible impacts for that science to sink in."
Yet the fear that any uncertainty might fuel climate denial is powerful.
Bjorn Stevens, a professor at Hamburg's Max Planck Institute for Meteorology, says "some people get really nervous when we say there are some things that we don't understand" because they worry that climate unknowns may "undermine the case for reducing carbon".
But he adds:: "I tend to think people are more sophisticated than that. Just because you don't know everything, doesn't mean you don't know anything."
Significant climate events in June
• Africa - Warmest June on record
• Antarctica - Largest June sea ice coverage since 2015, 0.8 per cent above average
• Arctic - Sixth smallest June sea ice coverage on record, 9 per cent below 1981-2010 average
• Asia - Second hottest June on record, tied with 2010
• Atlantic - Most named storms so far in the Atlantic hurricane basin season, tying with three other years since 2012
• Europe - Second warmest June on record
• North America - Hottest June on record. Unprecedented heatwave across northwestern mainland USA and western Canada. June tied with other years for the most named storms so far in the northeastern Pacific basin season, including Hurricane Enrique in Mexico
• Oceania - Warmest June in New Zealand on record
• South America - Warmer than average June temperatures in the north of the continent, near average in the south
Source: National Oceanic and Atmospheric Administration
Written by: Camilla Hodgson and Alexandra Heal
© Financial Times