The Fraction of Attributable Risk: How Scientists Quantify the Human Influence on Extreme Weather Events

In December 2004, the journal Nature published a paper analyzing the European heatwave that had killed tens of thousands of people the previous summer. The researchers, Peter Stott, D.A. Stone, and Myles Allen, did not just observe that the heat was unusual; they introduced a mathematical framework to quantify exactly how much human activity was to blame. They calculated that anthropogenic climate change had very likely more than doubled the risk of such a heatwave occurring.[6]

That calculation relied on a metric called the Fraction of Attributable Risk (FAR). Today, FAR is the structural engine of extreme event attribution, the statistical method that allows scientists to state that a specific flood, drought, or storm was made five, ten, or fifty times more likely by global warming.[1][2]

The mechanism of FAR relies on comparing two distinct realities. The first is the factual world—our current climate system, which contains the elevated concentrations of greenhouse gases emitted since the Industrial Revolution. The second is the counterfactual world—a simulated baseline climate that removes human emissions, representing the Earth as it would exist without anthropogenic interference.[1][5]

"Extreme event attribution is not about asking if climate change 'caused' an event, because all weather is now occurring in an altered environment," notes the National Oceanic and Atmospheric Administration (NOAA). Instead, the discipline asks whether climate change altered the probability or the magnitude of the specific event in question.[5]

The mathematics of FAR are straightforward in principle. The formula is expressed as FAR = 1 - (P0 / P1), where P1 is the probability of the event occurring in the factual world, and P0 is the probability of it occurring in the counterfactual world.[2][4]

If a severe heatwave has a 1-in-10 chance of happening today (P1 = 0.1) but only a 1-in-100 chance in the pre-industrial simulation (P0 = 0.01), the FAR is 0.9. This result indicates that 90% of the risk of that heatwave occurring is directly attributable to anthropogenic climate change.[2][4]

Since the foundational 2004 study, the volume and speed of these calculations have transformed the field. A 2024 mapping project by Carbon Brief analyzed over 500 extreme weather events globally, finding that 71% of them were made more likely or more severe by human-caused climate change.[6][8]

The Bulletin of the American Meteorological Society (BAMS) publishes an annual report explaining extreme events from a climate perspective. In their review of 2020 events, researchers documented specific extreme heat anomalies in Asia that would have been virtually impossible without anthropogenic warming—yielding a FAR approaching 1.0.[7]

The most significant shift in attribution science is operational latency. The 2003 European heatwave analysis took 16 months to publish. Today, initiatives like World Weather Attribution use peer-reviewed methodologies to calculate FAR while a disaster is still unfolding, often releasing findings within days.[4][6]

However, the science has structural limits. A July 2026 report from the National Academies of Sciences, Engineering, and Medicine evaluated the state of the field, noting that while the discipline has matured, significant hurdles persist.

"The science of extreme event attribution has advanced significantly, but challenges remain in communicating the uncertainties," the National Academies report stated.

The report emphasized that while attribution for extreme heat and cold is highly reliable, quantifying the FAR for complex, multi-variable events like severe thunderstorms, tornadoes, and prolonged droughts remains difficult due to observational limitations and the resolution limits of climate models.[1]

Despite these modeling constraints, researchers are pushing the framework beyond meteorology. Environmental Research Letters recently published frameworks for impact attribution, which extends the FAR calculation past the weather variable itself to quantify the resulting on-the-ground damages, such as crop losses, infrastructure failures, and human mortality.[3]

This translation from atmospheric physics to concrete damages is where FAR enters the legal and financial sectors. If a municipality determines that the FAR of a catastrophic flood is 0.8, it establishes a statistical argument that 80% of the recovery costs are tied to the altered climate baseline.[2][3]

Consequently, the insurance industry and legal scholars are increasingly utilizing FAR in climate litigation. When plaintiffs sue fossil fuel companies or governments for damages, FAR provides the mathematical chain of causation required by courts to link global emissions to local harm.[2]

The Fraction of Attributable Risk does not prevent the next storm, but it strips away the ambiguity of its origin. As the latency of these calculations approaches zero, the gap between a disaster occurring and the quantification of its human fingerprint effectively vanishes.[4][9]