Three-dimensional analysis reveals diverse heat wave types in Europe

The study addresses the limited understanding of the three-dimensional (3D) structure and drivers of heat waves, which are often analyzed using near-surface temperature alone. Recent unprecedented events (e.g., 2021 Western North America, 2022 Eastern China, and 2022 Western Europe) highlight the need to disentangle contributions from advective, adiabatic, and diabatic processes and to characterize vertical temperature profiles during heat waves. The authors aim to advance understanding by systematically analyzing heat waves as 3D phenomena using ERA5, introducing a classification based on vertical structure in addition to temperature anomaly, duration, and spatial extent across three European regions.

Prior profiling shows major heat waves can involve elevated warming throughout the lower troposphere (e.g., up to at least 4 km in Eastern Europe during 2010). Studies of potential temperature during the 2003 and 2010 European heat waves showed anomalously deep and warm nocturnal residual layers that store heat and merge into the diurnal boundary layer, a behavior also observed in the United States with deeper boundary layers and warmer residual layers during heat waves. Soil desiccation is linked to development of residual layers. Soil moisture availability modulates daily maximum temperatures via latent/sensible heat partitioning, and heat waves are amplified by both local soil drying and advection of sensible heat from upwind dry regions. Soil moisture–temperature coupling is nonlinear, with thresholds below which temperature sensitivity to soil moisture increases markedly, and is further modified by orography and land cover. These findings suggest complex, bidirectional land–atmosphere interactions relevant to 3D heat wave structures.

Data: ERA5 reanalysis at 0.25° resolution, hourly fields aggregated to daily means, for 1979–2022. Variables: 2 m air temperature (T2M), air temperature at 12 pressure levels from 850 to 300 hPa (50 hPa step), and upper-layer volumetric soil water (0–7 cm) over land. Study regions: three PRUDENCE subregions with similar area and mean altitude: British Isles (10°W–2°E, 50–59°N), France (5°W–5°E, 44–50°N), and Middle Europe (2–16°E, 48–55°N). Season: extended summer (June–September). Heat wave detection in 3D: For each region and for summer (June–August), compute the 95th percentile of daily T2M at each grid box. For each day in 1979–2022, compute anomalies above the 95th percentile for T2M and analogously for each of the 12 pressure levels (using daily means; daily maxima were not used due to small diurnal variations aloft). For each level and day, reduce spatial anomaly fields to (i) A: area fraction of the region with positive anomalies above the 95th percentile and (ii) T: mean value (°C) of these positive anomalies. Vertical aggregation: Define three layers for interpretation: near-surface (NS: T2M), lower troposphere (LO: mean over 850–600 hPa), and higher troposphere (HI: mean over 550–300 hPa). For LO and HI, daily A and T are averaged across constituent levels. Heat wave event definition: A heat wave is a sequence of at least 3 consecutive days during which, in any of the layers (NS, LO, or HI), the area A of positive anomalies above the 95th percentile exceeds one-third of the region. Events separated by only 1–2 days are merged into a single event. Extremity metrics: For each layer, compute E_layer = T_layer × A_layer × L, where T_layer and A_layer are averaged over all days of the event and L is event length (days). Overall extremity E_ALL = E_NS + E_LO + E_HI. Type classification: Heat waves are categorized by predominant vertical location based on layer extremities: near-surface (HWG) if E_NS / E_ALL > 0.5; lower-tropospheric (HWL) if E_LO / E_ALL > 0.5; higher-tropospheric (HWH) if E_HI / E_ALL > 0.5; otherwise omnipresent (HWO). Statistical testing: Soil moisture preconditioning assessed using non-parametric Wilcoxon tests. Regionally averaged daily SWVL on (i) first heat wave days and (ii) the 14 days prior to onset were compared to the June–August 1991–2020 climatological mean; significance assessed at 1% level. Outputs include temporal cross-sections of anomalies by level, event statistics (duration, timing within season), extremity rankings, and soil moisture evolution relative to climatology.

- Four distinct 3D heat wave types were identified: near-surface (HWG), lower-tropospheric (HWL), higher-tropospheric (HWH), and omnipresent (HWO), each with characteristic vertical anomaly structures and temporal evolution. - Duration differences are pronounced: HWG exhibits the largest mean and maximum lengths across regions, with maximum lengths 15–17 days; HWH events are shortest, up to 5 days. HWL and HWH dominate among short events, especially in the British Isles (BI) and France (FR). Heat waves longer than one week are more than two-thirds HWG; in BI and Middle Europe (ME), 5 of the 6 longest events were HWG. - Seasonal timing varies by type: In BI and FR, HWG peaks in mid-summer (second half of July) and becomes least frequent by late summer; HWO shows a similar but weaker peak. HWL and HWH occurrences are more evenly distributed with increasing representation into late summer, potentially linked to warmer Mediterranean waters supporting southerly advection aloft. In ME, all types peak around late July to early August, with HWL and HWH most frequent after mid-August. - Frequencies and mean lengths by region and type (1979–2022): BI: N(HWG/HWL/HWH/HWO)=14/23/17/8; mean L=8.1/4.2/3.6/4.5 days. FR: 17/21/20/6; 5.4/4.4/3.2/4.5 days. ME: 14/12/14/13; 6.4/4.2/3.7/4.2 days. - Severe events: The 2003 heat wave ranks as most severe in all three regions by overall extremity (combining duration, intensity, and spatial extent). Other top events include 2016, 2019, and 2022, spanning June–September. June 2019 is HWL; mid-summer 2003, 2019, and 2022 events are HWG or HWO; September 2016 is HWH, highlighted by exceptional higher-tropospheric anomalies not captured by 2D surface metrics. - Mechanistic insights: Long-lasting heat waves require warm advection accompanied by downward propagation of positive temperature anomalies via subsidence and diabatic heating. HWO and other types often show initial higher-tropospheric anomalies that intensify and propagate downward during the event. - Soil moisture links: HWG events predominantly start under dry soils (below the 25th percentile), with significant preconditioning on 14-day timescales at the 1% level across regions. No other type shows consistent significant preconditioning or systematically lower onset soil moisture across all regions; in ME, HWL and HWO show significantly lower soil moisture at onset but less pronounced than HWG. HWL exhibits the most intense soil desiccation during events in all regions, potentially due to stable stratification or lower-tropospheric inversions suppressing convection. - Regional contrasts: The maritime BI climate shows dominance of HWL and HWH and fewer severe HWG events in the 2010s, consistent with a lack of severe/extreme drought, whereas Western and Central Europe experienced frequent droughts (2011–2019), aligning with more severe HWG in FR and ME.

Analyzing heat waves as 3D phenomena reveals that distinct vertical structures correspond to different dominant physical drivers and persistence characteristics. Near-surface dominated events (HWG) are strongly tied to land–atmosphere feedbacks, notably soil desiccation and enhanced diabatic heating, which deepen the boundary layer and sustain multi-week extremes. Lower- and higher-tropospheric types (HWL, HWH) reflect stronger roles for warm advection and atmospheric dynamics aloft; however, higher-tropospheric warming alone does not produce long-lasting events without coupling to the boundary layer through subsidence and diabatic processes. The observed downward propagation of anomalies during HWO and some other events underscores the importance of subsidence and adiabatic warming after initial aloft warming. Regional climate differences modulate type prevalence: maritime climates (BI) favor aloft-dominated types, while continental climates (ME) show larger shares of HWG/HWO, indicating stronger surface flux contributions. These insights help disentangle advective, adiabatic, and diabatic contributions and provide a framework for improving attribution, projection credibility, and climate services related to heat wave risk.

This study presents a first systematic framework to classify and analyze heat waves as three-dimensional structures using ERA5, defining four types by vertical anomaly distribution and quantifying their duration, timing, severity, and soil moisture linkages across three European regions. Key contributions include demonstrating that long-lived heat waves require coupling between aloft advection, subsidence, and surface diabatic heating; identifying HWG as uniquely linked to significant soil moisture preconditioning; and highlighting regional contrasts in type prevalence. Considering 3D structures is essential for disentangling physical drivers and improving the reliability of climate projections and services for heat extremes. Future work will address uncertainties in precipitation–temperature relationships by employing observational datasets (e.g., E-OBS) to better constrain near-surface processes and refine 3D heat wave classifications.

Precipitation is not assimilated in ERA5 but generated by model parameterizations, introducing uncertainties in the precipitation–temperature relationship that may affect near-surface temperatures and the derived 3D heat wave types. These uncertainties are slated for further investigation using observational precipitation datasets (e.g., E-OBS).