European hot and dry summers are projected to become more frequent and expand northwards

Prolonged hot and dry periods substantially impact human health, economies, agriculture, and ecosystems, especially when heatwaves and droughts co-occur as compound events. Temperature and precipitation are interrelated through shared large-scale atmospheric drivers (e.g., persistent anticyclonic conditions) and land–atmosphere feedbacks: soil drying during heatwaves increases sensible heat flux, raising air temperature and evaporative demand, further suppressing precipitation. Summer temperature and precipitation in Europe are strongly correlated, meaning compound hot and dry summers (CHDs) occur more often than expected under independence. With projected summer warming and drying trends, feedbacks are likely to intensify under climate change. Quantifying how the probability of historical CHDs changes with future global warming levels (GWLs) is crucial for risk management and adaptation planning (e.g., water resources, agriculture, energy, transport, urban planning). Evidence of large probability increases strengthens the case for mitigation and adaptation (e.g., alternative cooling for power plants, water conservation, transport alternatives, urban greening). However, CHDs are complex, multivariate, and rare, and observational records are limited for robust probability estimation. Single-Model Initial-Condition Large Ensembles (SMILEs) enable improved quantification by sampling internal variability and providing long datasets. This study identifies the most extreme CHDs over Europe and nine sub-regions for 2001–2022, quantifies their occurrence probability under present climate (~+1.2 °C) and how it changes under +2 °C (GWL2) and +3 °C (GWL3), using ERA5 reanalysis mapped into the space of a high-resolution regional SMILE (CRCM5-LE) and a copula-based multivariate probability framework.

Prior work shows that compound hot–dry events cause disproportionate impacts compared to single hazards and that European summer temperature and precipitation are highly correlated due to shared atmospheric drivers and soil-moisture–temperature feedbacks. Studies highlight increasing summer heat and drying trends that can intensify feedbacks. During CHDs, higher Bowen ratios and lower soil moisture are observed compared to non-compound summers. Large ensembles (SMILEs) have been shown to be useful for investigating compound extremes by separating internal variability from forced responses and providing robust sampling of extremes. Event-based assessments (e.g., 2003, 2010, 2015, 2018 summers) document high impacts and reveal sensitivity to event definitions (e.g., heat accumulation vs. joint temperature–precipitation definitions). Previous estimates often used univariate metrics; multivariate approaches better capture joint rarity relevant to impacts. The study also relates its results to CCLM ensemble findings and to broader climate classification work (e.g., Köppen–Geiger) that indicates northward shifts of warmer/drier climate zones by century’s end.

Study design and datasets: - Periods and warming levels: Three 20-year periods from CRCM5-LE were used to represent global warming levels relative to 1850–1900: PRES (+1.2 °C; 2001–2020), GWL2 (+2 °C; 2021–2040), GWL3 (+3 °C; 2042–2061). Each period comprises 50 members × 20 years = 1000 summers. ERA5 (1959–2022) provides observed summers mapped into model space. A secondary ensemble, CESM-CCLM (21 members, 0.44°), serves for comparison (PRES: 2001–2020, GWL2: 2033–2052, GWL3: 2052–2071). - Variables and season: Seasonal means of temperature and precipitation for June–July–August (JJA) define CHDs. - Detrending and mapping: Temperatures were linearly detrended within each period. ERA5 was quantile-mapped into the CRCM5-LE (and CCLM) worlds to ensure comparable marginal and joint structures; Kolmogorov–Smirnov tests for marginals and TwoCop tests for copula structure confirmed adequate representation at α = 0.05. Regions: - CHD probability maps (per grid cell, per year) from CRCM5-LE PRES were used to cluster simultaneous CHD occurrences via agglomerative hierarchical clustering with cosine-similarity distance, considering only P_sk < 0.1 and events covering ≥500 grid cells (~1% land area). The elbow method and majority-cluster filtering yielded nine sub-regions: SWE (South-West Europe), CMD (Central Mediterranean), BP (Balkan Peninsula), AC (Atlantic Coast), CE (Central Europe), EE (Eastern Europe), NBS (North and Baltic Sea), NEE (North-East Europe), NSC (North Scandinavia). Probability framework: - Multivariate dependency was modeled with copulas. Marginal distributions: precipitation via empirical distribution with Weibull plotting positions; temperature via empirical distribution below 95th percentile and Generalized Pareto above 95th percentile. - Fifteen copula families were fitted; Bayesian Information Criterion (BIC) selected the best per grid cell/region; goodness-of-fit via Kendall’s process at α = 0.05. - Survival Kendall probability (P_sk) quantified joint exceedance rarity, estimating the probability of having an event at least as rare as the observed in the bivariate survival space. Return periods correspond to 1/P_sk (annual scale). - Regional probabilities were computed by averaging JJA temperature and precipitation over each sub-region, then applying the copula-based P_sk calculation. Event selection and analysis: - The most extreme CHDs (lowest P_sk) were identified over Europe and per sub-region for 2001–2022 based on ERA5 mapped into model space. Continental-scale extremeness was evaluated by averaging P_sk over land and by the fraction of area with P_sk below 10%, 5%, and 1%. - For each selected historical CHD, probabilities were estimated under PRES, GWL2, and GWL3 using CRCM5-LE, and cross-checked distributionally with CESM-CCLM. Future CHD climatology matching: - For each grid cell, distributions of CHDs (P_sk < 5%) were extracted for PRES and GWL3. Representative points for each cluster were identified by minimizing the sum of symmetric Kullback–Leibler divergences (D = 0.5 KL(p||q) + 0.5 KL(q||p)) within the cluster. - Climatology analogues were found by matching GWL3 CHD distributions to the most similar PRES regional representative distributions, revealing spatial shifts in hot–dry CHD regimes. Software and data access: - Copulas via VineCopula (R); statistical tests per cited methods; KL divergence estimation via KD-tree nearest-neighbour approach (Python implementation). CRCM5-LE (ClimEx), ERA5 (CDS), and CESM-CCLM (upon request) data sources are provided in the paper.

- Continental and regional extremeness: The summer of 2003 is confirmed as the most extreme CHD at the European scale (very low P_sk across a large fraction of land). Regionally, the most extreme CHDs (2001–2022) are: 2002 (NSC), 2003 (SWE, CMD, AC, CE), 2006 (NEE), 2012 (BP), 2015 (EE), 2018 (NBS). - Present-climate rarity: Under PRES, estimated annual CHD probabilities are extremely low, corresponding to return periods from ~45 years to >10,000 years. Examples: BP-2012 ~0.002%; NEE-2006 and NBS-2018 up to ~2.2%. - Large probability increases with warming: Many historical CHDs become much more frequent under warming. CHDs from 2002, 2003, and 2018 exceed 5% probability already under GWL2; some rise to as high as ~46% under GWL3 (e.g., 2003 CMD), implying occurrence in roughly every second summer. For specific summers, occurrence probability increases by approximately 5–6× from GWL2 to GWL3. - Divergent drivers: A twofold pattern emerges. Events dominated by extreme precipitation deficits (e.g., 2006 NEE, 2012 BP, 2015 EE; univariate precipitation probabilities below ~0.6% under PRES) show smaller drying shifts and thus remain relatively rare even under GWL2/GWL3 (P_sk ≤ 5% to ~10%). Temperature-dominated events (e.g., 2003 in SWE, CMD, AC; 2002; 2018) exhibit strong warming shifts and, where accompanied by drying, become frequent (>5% to ~46%). For 2003 in CE, both warming and drying contribute to increased probability. - Distributional shifts: Under GWL2 and especially GWL3, the PRES distributions of temperature and precipitation shift such that previously extreme hot–dry conditions (e.g., 2003) fall within or even below the 95th percentile range—2003-like temperatures would be considered relatively cool under GWL3 at the continental scale; drying also becomes less exceptional. - Northward expansion of hot–dry CHD climatologies: Matching analyses show marked northward shifts under GWL3. The present BP-type hot–dry climate expands across much of Southern Europe and extends northward into parts of the Iberian Peninsula, southern France, Italy, and Eastern Europe. EE-type CHD climate expands into Central Europe and along the Baltic coast, including southern Sweden and Finland. The relatively cool–moist NSC-type climate contracts (e.g., in Alpine regions). Overall, all hot–dry climate zones shift northward under GWL3. - Cross-ensemble comparison: CESM-CCLM supports the main conclusions (warming and, to a degree, drying). CRCM5 shows stronger warming and drying at GWL3 at the European scale; CCLM often exhibits narrower precipitation distributions. Regional differences in the magnitude of shifts exist, but qualitative patterns are consistent.

The study set out to quantify how the probabilities of historically observed European CHDs change with global warming and to determine whether the climatology of such events migrates spatially. Using a copula-based multivariate probability framework with large ensembles, the results show that many past extreme summers will become much more common as warming progresses, particularly those where temperature is the dominant driver and where drying compounds the effect. This directly answers the research question by providing probability estimates under GWL2 and GWL3 and demonstrating that events once considered exceptional (e.g., 2003) may occur in a substantial fraction of summers under GWL3, emphasizing the risk escalation with additional warming beyond +2 °C. The identification of two driver regimes clarifies regional risk differences: precipitation-dominated extremes (e.g., 2012 BP, 2015 EE, 2006 NEE) remain rare even at higher warming levels due to weaker precipitation shifts, whereas temperature-dominated extremes (e.g., 2002, 2003, 2018) become frequent. These insights are salient for sectoral planning (e.g., agriculture, water resources, energy cooling requirements) and underscore that mitigation limiting warming to +2 °C can substantially reduce the frequency of the most disruptive CHDs. Spatial analogue analyses reveal that the climatology of CHDs shifts northward under GWL3, bringing BP- and EE-like hot–dry conditions into regions currently experiencing cooler, wetter summers (e.g., Central Europe, Baltic coasts, southern Scandinavia). This has direct implications for preparedness, infrastructure design, and ecosystem management in regions with historically lower exposure to CHDs. Cross-ensemble checks with CESM-CCLM corroborate the qualitative findings, enhancing confidence despite model-specific quantitative differences.

This work provides three main contributions: (1) It demonstrates the utility of a high-resolution regional SMILE (CRCM5-LE) for robustly relating to observed compound extremes and resolving spatial heterogeneity relevant to shifts in CHD climatologies. (2) It presents a methodology to quantify probabilities of historical CHDs using a copula-based Survival Kendall probability framework applied to large ensembles. (3) It reveals a pronounced northward shift of hot–dry CHD climatologies under +3 °C warming, with BP- and EE-like conditions expanding into Central and Northern Europe. Key implications include a strong increase in occurrence probabilities for many historical CHDs—up to ~46% under GWL3 for some regions—and a substantial risk reduction if warming is limited to +2 °C. The findings can inform adaptation and risk management for water, agriculture, energy, transport, and urban planning. Future research directions include: extending analyses to monthly timescales and absolute-threshold impact metrics (e.g., health, energy demand); examining physical drivers of future compound extremes; applying the methodology to other multivariate extremes; and assessing CHD climatology shifts across additional high-resolution ensembles, especially those driven by CMIP6 models.

- Seasonal definition: Using JJA seasonal means may omit events starting earlier or ending later than summer and may include seasons with high intra-seasonal variability (e.g., one wet/cool month and two hot/dry months). - Relative vs absolute thresholds: CHDs are defined relative to local climatology, suitable for ecological impacts but not necessarily for impacts tied to absolute thresholds (e.g., human mortality). A CHD in NSC likely has different absolute impacts than in SWE. - Model biases and ensemble dependence: CanESM2–CRCM5 tends toward warmer and drier summer changes than many EURO-CORDEX models; while scaling by GWLs mitigates sensitivity to forcing scenario, CRCM5 exhibits stronger regional warming at GWL3 than CCLM. CHD projections and spatial patterns depend on the driving GCM; CMIP5 models have documented issues and inter-model uncertainty for hot–dry season likelihoods. - Variable selection: Focusing on temperature and precipitation excludes other potentially relevant variables (e.g., wind), which could influence joint probabilities. - Definition dependence: Probability estimates depend on the chosen extreme definition and statistical framework; alternative metrics (e.g., heat accumulation, different spatial/event definitions) yield different probabilities. - Coupling and scenario assumptions: No two-way coupling between RCM and GCM (downscaling does not feed back). The GWL approach assumes relative independence from the emissions scenario, which warrants further validation. - Ensemble coverage: Results would benefit from additional high-resolution SMILEs, particularly those driven by CMIP6, to better sample model structural uncertainty.