Stanford AI Study Ties Post Paris Emissions to a Third of a Degree of Extra Heat in Europe

Europe has endured a run of punishing summers, and the heat has been arriving with a ferocity that scientists have struggled to attribute cleanly to any single cause. The continent is warming at more than twice the global average rate, and the June and July of 2025 broke records across the region, with surface air temperatures climbing above 40 degrees Celsius (104 degrees Fahrenheit) in several countries and reaching up to 46 degrees Celsius (114.8 degrees Fahrenheit) in Spain and Portugal.

Those extremes came with a human cost. The scorching temperatures killed several thousand people across Europe in 2025, producing the hottest June ever observed in the region, at least until heat waves broke that record again in 2026. This summer's back to back heat waves broke heat records and contributed to at least 35,000 excess deaths.

The backdrop is the 2015 Paris Agreement, a legally binding international treaty on climate change adopted by nearly 200 countries in December 2015 with the aim of limiting global warming to 1.5 degrees Celsius above preindustrial temperatures. Almost one fifth of all carbon dioxide emissions from burning fossil fuels have been emitted in the decade since that agreement was adopted, most of it from burning oil, natural gas and coal.

Now a Stanford University team says it can measure what that specific slice of emissions has done to Europe's worst heat. A study published on September 22, 2026 in Geophysical Research Letters uses a generative AI diffusion model trained on 10 global climate models to show it is more than 99 percent likely that emissions released since the Paris Agreement intensified Europe's June 2025 heat wave, raising average daily temperatures in some regions by roughly 0.33 degrees Celsius, or just over half a degree Fahrenheit.

Key Facts

Time reported on September 22, 2026 that the heat waves Europe has seen in recent years were made measurably more intense because of the greenhouse gases emitted since the 2015 Paris Climate Agreement. Lead author Jared Trok, a PhD student in Earth system science at the Stanford Doerr School of Sustainability, said the team found that the emissions released since the signing of the Paris Agreement in 2015 have substantially and significantly increased the intensity of Europe's recent individual heat waves.

Phys.org reported on September 22, 2026 that the study indicates there is more than a 99 percent chance that emissions during this decade intensified Europe's deadly June 2025 heat wave, and that researchers estimated those emissions increased average daily temperatures in some regions by roughly a third of a degree Celsius, or just over half a degree Fahrenheit. Trok said that if Europe's heat wave in the summer of 2025 had occurred without the emissions since 2015, it very likely would have been cooler, and that the result is not unique to the 2025 heat wave but also true for Europe's hottest week in every individual year since at least 2021.

Scienmag reported on September 22, 2026 that the odds are more than 99 in 100 that emissions accumulated since the Paris Agreement intensified the June 2025 heat wave, which contributed to several thousand deaths across the continent and produced the hottest June ever observed there until 2026 broke the record again. Trok described the challenge as a signal to noise issue, explaining that 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.

The peer reviewed study, which Geophysical Research Letters reported on September 22, 2026, analyzed each climate model's simulated data for the years 1850 to 2100 so the diffusion model could learn how surface temperatures over Europe vary with different emission levels and with weather conditions such as atmospheric pressure patterns and soil moisture levels. The team then gave the model the observed weather conditions that caused Europe's most intense annual heat waves from 2016 to 2025, which typically coincided with a persistent high pressure system known as a heat dome, and had it predict daily temperatures under emission levels at the time of each extreme heat event and under the lower emissions levels of 2015. The work carries DOI 10.1029/2026GL125079.

Analysis

The methodological move is the story as much as the temperature number. Classical attribution studies typically ask how a heat wave would have looked in a world without any human influence at all. This work instead carves out one subset of emissions, the decade's worth released since December 2015, and asks what that slice alone contributed. It also builds on a 2024 attribution framework by the same Stanford group, extending a technique that the authors argue can systematically and objectively interrogate pieces of the historical emissions record, including individual heat waves.

What this really means is that the accounting for recent European warming is no longer all or nothing. The Stanford team reports that emissions from the last decade increased the intensity of 2025 heat waves by roughly a third of a degree Celsius, and that this holds for Europe's hottest week in every individual year since at least 2021. Trok acknowledged that a third of a degree might seem very small, perhaps imperceptible to someone walking around, but pointed to a large body of scientific literature showing that even small increments of temperature on a hot day can have disproportionate impacts on the damages caused by heat waves.

The framing puts pressure on a familiar shorthand in public debate, which treats the 1.5 degree Celsius target as a switch that either protects Europe or does not. Co-author Noah Diffenbaugh, the William Wrigley Professor and Kimmelman Family Senior Fellow in the Stanford Doerr School of Sustainability, said the research shows the team can systematically and objectively ask questions about subsets of historical emissions, including individual heat waves, and warned that even in the context of the most optimistic, ambitious future for reducing emissions, there is still more intensification of extremes that is essentially committed.

He added that 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, and that the study highlights that the kinds of extreme heat waves Europe has been experiencing recently can be expected to intensify even more in the coming years. Read together, the results turn a general statement about global warming into a dated claim about a specific treaty period and a specific set of named weather events.

Why It Matters

The numbers attached to this research are not abstract. Summer 2026 heat waves contributed to at least 35,000 excess deaths, and the 2025 season killed several thousand people across Europe. Heat that pushes surface air temperatures above 40 degrees Celsius (104 degrees Fahrenheit) in several countries and up to 46 degrees Celsius (114.8 degrees Fahrenheit) in Spain and Portugal strains emergency services, power grids and hospitals, and the study ties a measurable share of that extra intensity to emissions released only since December 2015.

Attribution findings of this kind also feed directly into the legal arena. The paper appears amid several thousand lawsuits seeking to hold fossil fuel producers accountable for loss and damage from extreme weather, and a peer reviewed result that segments emissions by period gives plaintiffs and regulators a finer grained tool than the older, all or nothing framing. Because the Paris Agreement was adopted as a legally binding treaty by nearly 200 countries, the decade it covers is a defined and defensible accounting window.

For Europe specifically, the finding compounds an already difficult trajectory. The continent is heating at more than twice the global average rate, the hottest June on record in 2025 was followed by a 2026 season that broke records again, and almost one fifth of all fossil fuel carbon dioxide ever emitted entered the atmosphere during the decade in which the world was supposed to be cutting back.

Next Up

The Stanford group's next move is implied by its own framing: extending the diffusion model approach to more regions, more types of events and finer subsets of emissions, since the method already handles heat waves from 2016 through 2025 and simulated data stretching from 1850 to 2100. The authors argue the technique can be aimed at other historical windows and other extreme weather, using the 2024 framework as the template, while the paper itself lands amid the growing wave of loss and damage litigation.

That sets the terms for the next round of research and policy argument alike. With almost one fifth of all fossil fuel carbon dioxide ever emitted already released in the decade since the Paris Agreement, and with additional emissions effectively locked in even under the most optimistic reduction timelines, the open question is not whether Europe's heat waves will keep setting records, but how much of the added intensity scientists will be able to trace back to the years in which the world was supposed to be cutting back.