The study, published in the journal Weather and Climate Dynamics, was led by Belinda Hotz, together with Heini Wernli, Matthias Röthlisberger, and Robin Noyelle, all atmospheric scientists at ETH Zürich. The team drew on ERA5, the flagship reanalysis dataset of the European Centre for Medium-Range Weather Forecasts, which blends observations with a numerical weather model to produce a physically consistent picture of the atmosphere across seven decades. From this dataset they extracted the vertical temperature anomaly profiles, the deviation of temperature from its climatological mean at every level from the ground up to about 30 hectopascals, during the single hottest three-hourly moment of each year at every land grid point, an event type known in climate statistics as TXx.

The methodological challenge was considerable. Temperature anomalies naturally vary in magnitude from place to place, and simply comparing raw profiles would conflate the intensity of an event with its shape. To isolate the shape, the researchers first normalised each temperature anomaly by the local standard deviation at that altitude, expressing anomalies in units of sigma. They then scaled each vertical profile by its surface value, producing a dimensionless description of how anomalous each layer is relative to the ground. This scaling step proved essential: it allowed a two-sigma heat event in Siberia to be compared, shape for shape, with a four-sigma event in the American Midwest, independent of local climate and event strength.

With the profiles prepared, the team applied a principal component analysis to compress the high-dimensional data, retaining eight components that explain more than 95 percent of the variance, and then ran an area-weighted k-means clustering algorithm. The silhouette score, a standard measure of clustering quality, peaked decisively at three clusters. The resulting global map was striking: the clusters traced the meridional climate zones with remarkable fidelity, grouping the tropics together, the mid-latitudes together, and the polar regions together. This suggests that the dominant distinction in how heat extremes are structured vertically is not regional idiosyncrasy but climate zone itself, a finding that had never been demonstrated at global scale before.

Each cluster tells a different physical story. In the tropical cluster, positive temperature anomalies are confined almost entirely to the boundary layer, the often very deep layer of air stirred by the hot surface, with the strongest anomalies near 900 hectopascals and essentially no anomaly in the free troposphere. This vertical confinement reflects a fundamental property of the tropical atmosphere: weak horizontal temperature gradients and efficient adjustment by gravity waves keep the free troposphere close to a moist adiabatic profile, so surface heat extremes there arise when moist convection is suppressed, often by dry soils or the entrainment of dry air aloft, allowing heat to accumulate locally in a deepening boundary layer.

The mid-latitude cluster looks strikingly different. Here the temperature anomalies are bottom-heavy but extend through the entire troposphere, revealing a strong vertical coupling between the surface and the upper levels. This structure is consistent with the well-documented role of upper-level anticyclones and atmospheric blocking in mid-latitude heatwaves: subsidence beneath the anticyclone warms the column adiabatically, while warm advection and latent heating in upstream weather systems can raise temperatures aloft, as occurred spectacularly during the record-shattering Pacific Northwest heatwave of 2021. Remarkably, despite the documented diversity of regional mechanisms, from soil-moisture feedbacks in Europe to heat advection from arid upwind regions, all mid-latitude profiles converge into a single cluster, underscoring their shared vertical architecture.

The polar cluster adds a third signature. Like the mid-latitudes, polar heat extremes feature anomalies throughout the troposphere, likely driven by the poleward transport of warm, moist air and subsidence within upper-level anticyclones. But the layer of strongest anomalies near the surface is much thinner, and the researchers interpret this as the erosion of the near-surface temperature inversion, the stable layer that normally decouples the cold polar surface from the flow above. When warm, moist air intrudes over ice-covered surfaces, increased downward long-wave radiation can erode the inversion, mixing warmer air down to the ground in a shallow but intense layer. This mechanism mirrors observations from the extraordinary East Antarctic heatwave of March 2022.

The temporal evolution of the profiles adds further insight into how each type of heat extreme is born and dies. In all three clusters, anomalies build from a near-climatological state over roughly five days before the event. In the tropics, the warming is gradual and uniform within the boundary layer, pointing to progressive local heat accumulation. In the mid-latitudes, the entire troposphere warms together, with the upper levels nearly reaching their final anomaly a day before the surface, after which the lower troposphere and boundary layer intensify rapidly, consistent with land-atmosphere feedbacks and enhanced subsidence. In polar regions, deep tropospheric warming precedes a dramatic jump in the lowest 50 hectopascals just before the event, the fingerprint of inversion erosion. After the events, the surface anomalies fade first while upper-level anomalies linger, reflecting the longer lifetimes of anticyclones.

Perhaps the most consequential finding concerns the most extreme events. When the researchers compared the ten hottest TXx events at each grid point with more moderate ones, they found that the most intense events deviate less, in relative terms, from the cluster median profiles. In other words, the more extreme a heat event becomes, the more typical its vertical structure. This convergence aligns with predictions from large deviation theory, a mathematical framework holding that highly improbable events occur through the most probable dynamical pathway. Previous evidence for this so-called typicality came from long climate model simulations, including studies of the 2021 Western North America heatwave; this study provides observational support from reanalysis data, suggesting that record-shattering heatwaves are not freak occurrences but follow increasingly constrained dynamical routes.

The implications reach beyond academic classification. Because the most extreme heat events adhere closely to predictable vertical profiles, the framework could improve how scientists anticipate the structure, and potentially the intensity, of future record-breaking heatwaves. It also offers a physically grounded way to evaluate climate models: if a model reproduces the three-cluster structure and its climate-zone geography, confidence in its heat extreme projections grows. As the planet continues to warm and heat records fall with unsettling regularity, knowing that every extreme heat event carries one of three characteristic vertical fingerprints, and that the rarest events follow the most typical paths of all, turns the chaotic spectacle of heatwaves into something closer to a legible atmospheric signature.

Subject of Research: Vertical temperature anomaly structure of land heat extremes in the ERA5 reanalysis

Article Title: Global characterisation of the vertical temperature anomaly structure of heat extremes over land in ERA5

Article References: Hotz, B., Wernli, H., Röthlisberger, M., & Noyelle, R. (2026). Global characterisation of the vertical temperature anomaly structure of heat extremes over land in ERA5. Weather and Climate Dynamics, 7(3), 1875-1897. https://doi.org/10.5194/wcd-7-1875-2026

Image Credits: AI Generated

DOI: 10.5194/wcd-7-1875-2026

Keywords: heat extremes, heatwaves, ERA5 reanalysis, vertical temperature profiles, k-means clustering, climate zones, atmospheric blocking, planetary boundary layer, temperature inversions, large deviation theory, TXx events, Weather and Climate Dynamics