Lead author Jared Trok, a PhD student in Earth system science at the Stanford Doerr School of Sustainability, and his colleagues focused their analysis on Europe’s most intense annual heat waves from 2016 through 2025. Their conclusion was striking in its statistical strength: the odds are more than 99 in 100 that emissions accumulated since the Paris Agreement intensified Europe’s deadly June 2025 heat wave, which contributed to several thousand deaths across the continent and produced the hottest June ever observed in the region, at least until heat waves broke that record again in 2026. The researchers estimated that post-2015 emissions increased average daily temperatures in some affected regions by roughly a third of a degree Celsius, or just over half a degree Fahrenheit, during the event.

That fractional rise may sound trivial against the backdrop of a scorching summer, but the study’s authors are emphatic that it is anything but. “That third of a degree temperature change may seem small,” Trok said, “but a large body of literature shows that small changes in temperature can have meaningful impacts on the damages caused by those extreme weather events.” The evidence supporting that claim is substantial. Previous work by Trok, Diffenbaugh, and collaborators found that a modest climb in temperature can disproportionately increase the risk of heat-related deaths in Europe, where aging populations, urban heat islands, and infrastructure designed for milder climates leave millions vulnerable. Other research has shown that shifts in daily temperature have outsized effects on electricity demand, mortality rates, agricultural yields, and labor productivity across the United States, meaning that incremental warming translates into cascading consequences for health systems, power grids, and economies.

The scale of the emissions involved underscores why the finding matters. Almost one-fifth of all carbon dioxide ever released from burning fossil fuels has entered the atmosphere in the decade since the Paris Agreement was adopted, with most of that output coming from the combustion of oil, natural gas, and coal. Nearly 200 countries signed the landmark accord, pledging to hold global warming well below 2 degrees Celsius above pre-industrial levels while pursuing efforts to limit it to 1.5 degrees Celsius, or 2.7 degrees Fahrenheit. Yet global temperatures are already approaching that more ambitious threshold, and stabilizing the climate will require driving emissions to net zero, the point at which greenhouse gases released by human activity are balanced by natural removal mechanisms or advanced carbon-capture technologies.

“Even in the most optimistic timelines for reducing emissions, there will still be more emissions in the future than there have been in the last decade since the Paris Agreement,” said co-author Noah Diffenbaugh, the William Wrigley Professor and Kimmelman Family Senior Fellow at the Stanford Doerr School of Sustainability. “This study highlights that we can expect the kinds of extreme heat waves we’ve been experiencing recently to intensify even more in the coming years.” In other words, even a successful decarbonization effort does not spare the world from worsening heat in the near term; the emissions already locked in during the past ten years, and those still to come before net zero is achieved, guarantee further intensification of the kind of extremes that have recently killed thousands and strained national infrastructures.

The scientific challenge the Stanford team set out to overcome is one of signal and noise. Climate scientists have spent two decades developing attribution methods to determine how historical emissions have shaped heat waves, hurricanes, droughts, and wildfires, but detecting the influence of a small subset of total human emissions on a single weather event is far harder than measuring the effect of a century and a half of industrial-era warming. “It’s a signal-to-noise issue,” Trok explained. “The role of random, natural variability on specific weather events is large, which makes it difficult to detect the influence from a small amount of human emissions.” Natural fluctuations in atmospheric circulation, soil moisture, and sea surface temperatures can swing regional temperatures by degrees, potentially drowning out the modest warming contribution of a decade’s worth of greenhouse gases.

To cut through that noise, the researchers built on a framework they first developed in 2024, training a type of generative AI known as a diffusion model on simulated weather data from ten global climate models. Diffusion models, which have gained fame for generating realistic images, work by learning the underlying structure of data and then producing new examples that respect that structure. In this case, by analyzing each climate model’s simulated output for the years 1850 to 2100, the diffusion model learned how surface temperatures over Europe vary with different emission levels and weather conditions, such as atmospheric pressure patterns and soil moisture deficits. Because generative AI models have randomness built into their predictions, they naturally produce a spread of possible outcomes rather than a single deterministic answer, which gave the team a powerful way to quantify uncertainty in the temperature difference between two emission scenarios.

Validating such a novel tool was a critical step. The team compared the model’s range of temperature predictions against decades of real European weather data that had been excluded from training, and confirmed that the model accurately reproduces the continent’s long-term temperature trends. Only after establishing that the framework could reliably predict temperature behavior across different levels of global emissions did the researchers deploy it for attribution. They fed the model the observed meteorological conditions that drove Europe’s most intense annual heat waves from 2016 to 2025, conditions that typically involved a persistent high-pressure system colloquially known as a heat dome, which traps hot air over a region for days or weeks. The model then predicted daily temperatures under the actual emission levels at the time of each event and under the lower emission levels of 2015, allowing a direct, probabilistic comparison.

The results were consistent and unambiguous. For Europe’s most intense annual heat waves since 2021, the predicted temperature ranges were systematically lower when the model assumed 2015 emission levels, and the minimal overlap between the two distributions provided what the researchers describe as strong evidence that post-2015 emissions intensified each event. Encouraged by that clarity, the team pushed further, testing whether even smaller fractions of total emissions could be detected in the June 2025 heat wave. They found high confidence for emissions totals equivalent to as little as one-eighth of all human-caused emissions since the 1800s, a sensitivity that surprised even the study’s senior authors.

“Based on my experience using traditional methods like global climate models, I would have told you that the noise of natural variability makes detecting the influence of that level of emissions on a specific weather event highly uncertain,” Diffenbaugh said. “That a diffusion model which is trained on those same climate models and then given real meteorological data as inputs is able to distinguish the signal from the noise is a big step forward.” The advance arrives at a moment of growing legal and political relevance: several thousand lawsuits are currently underway worldwide seeking to hold oil companies and other fossil fuel producers accountable for loss and damage linked to extreme weather, and attribution science of this precision could increasingly inform those proceedings. The study’s co-authors include researchers from Boston University, Colorado State University, and the University of Auckland, with computing resources provided by the Stanford Doerr School of Sustainability Center for Computation. As Europe braces for summers that may grow hotter still, the message from the research is clear: the emissions of the last ten years are already written into the record heat, and the choices of the next decade will determine how much worse it becomes.

Subject of Research: Attribution of recent European heat wave intensification to greenhouse gas emissions since the 2015 Paris Climate Agreement using generative AI climate modeling.

Article Title: Emissions from the past decade have made Europe’s recent heat waves worse

Article References: Emissions from the past decade have made Europe’s recent heat waves worse. (n.d.). Original publication

Image Credits: AI Generated

DOI: Not provided

Keywords: Europe heat waves, climate change attribution, Paris Agreement, greenhouse gas emissions, generative AI, diffusion model, Stanford University, Geophysical Research Letters, extreme weather, global warming, heat dome, climate models