In this paper we use a variety of datasets, including observational, reanalysis, and model data. We use a common spatial domain for Europe (30–70∘ N, 10∘ W–50∘ E) and the reference period 1981–2010 unless otherwise stated.

The 2018 summer was an extreme season from a climatological perspective for many regions in Europe. An intense heatwave first affected Scandinavia in mid-July and then extended towards central Europe and later Iberia, spanning a total period of 4 weeks. The maximum heatwave duration was seen in Scandinavian regions, reaching 20 consecutive days (Fig. 1a). Cumulative heat reached peak values in parts of Norway, Sweden, Germany, France, Ireland, and the UK (Fig. 1b). The cUTCI index showed periods of extreme heat stress in Portugal and southwestern Spain; very strong heat stress in northern and central Germany, central-western Poland, large parts of France and Iberia; and strong heat stress in most of eastern Europe, Finland, southern Scandinavia, and parts of the British Isles (Fig. 1c). The high intensities in Turkey and the Caucasian region were not caused by the same weather pattern as the event described in this paper and are thus not discussed here.

In northern and central Europe, the heatwave was preceded and accompanied by intense drought conditions. As an example, the meteorological drought is depicted in terms of the SPEI3 and SPEI6 values for August (Fig. 1d, e) that were particularly low in central and northern Europe. The cumulative effects of low precipitation and high evapotranspiration lead to lower values of the SPEI6 index in many European regions compared to SPEI3. The most extreme values (SPEI6 < -5) are identified for southern Norway and Sweden. The thermopluviogram for Germany depicts temperature and precipitation anomalies for Germany and confirms that the extended warm period of April to October 2018 was the most exceptional in terms of precipitation deficit and heat anomaly compared to the reference period (1981–2010) since 1881 (Fig. 2​​​​​​​). When considering different seasonal periods, such as March to August or June to August only, 2018 remains a very extreme season (see Fig. S1). In summary, while the heatwave was most intense in southern Scandinavia, 2018 stood out as the most intense compound heat and dry event in the observational history for Germany, in agreement with Zscheischler and Fischer (2020).

In order to characterize large-scale circulation features for the summer of 2018, we used a number of different and complementary metrics to describe the multi-faceted characteristics of the event. First, we analyzed the blocking conditions for this season, as the occurrence of heatwaves is directly associated with summer blocking or – for the lower latitudes in Europe – to atmospheric ridges (Woollings et al., 2018; Sousa et al., 2018; Kautz et al., 2022). Using the blocking detection algorithm, we confirm that for the 2018 summer, blocking is detected over Great Britain from late June into the first 10 d of July as well as over Scandinavian and Ural regions for most days of July (Fig. S2). Compared to the climatological occurrence of blocking frequency, the percentage of blocked days in June–July 2018 was 20 %–60 % higher in the mentioned areas (Fig. 3a, b), indicating blocking frequency values above the 90th percentile (Fig. S3). This large-scale setup for the summer time (see e.g., Kautz et al., 2022, their Fig. 2b) leads to the development of a heatwave collocated with the center of the blocking, while unsteady weather conditions may happen on the block edges.

The establishment of a long-lived blocking anticyclone is consistent with the development of a double jet stream state over Eurasia, with two maxima of the zonal mean zonal wind at the 250 hPa level, which started as early as mid-May and persisted until the 25th of July, with only a few days in between not characterized by double jets (Fig. 3c). The period 4–25 July was characterized by a continuous persistent double-jet configuration, according to the SOM-based detection scheme of jet stream states. These 22 consecutive days of double jets make 2018 one of the longest such events in the study period (1979–2020), the longest being that of 2003 (Rousi et al., 2022; their Fig. 4). The initiation of the heatwave in Europe happened a few days after the initiation of this persistent double-jet event (see Fig. 4), highlighting the potential role of the double-jet structure in preconditioning the flow and favoring the onset of a heatwave in the region of weak winds between the two jets, where the blocking anticyclone lies (Rousi et al., 2022). This large-scale setup typically corresponds to the occurrence of the summer NAO+ (sNAO+) regime, as confirmed by the circulation regime approach applied on the 2018 summer. Indeed, most of July 2018 was dominated by a sNAO+ index (Fig. 3d) and a spatial pattern, typically characterized by a more northerly location and a smaller spatial scale than its winter counterpart (Folland et al., 2009). This is in agreement with previous studies (e.g., Drouard et al., 2019) showing a strong positive EOF-based NAO anomaly in this time period that is consistent with large parts of the seasonal anomalies observed during the summer of 2018.

The analysis of Rossby wave activity permits the evaluation of the development of the blocking, NAO+ phase, and the corresponding double-jet structure for the summer of 2018. Results show an eastward propagation of Rossby wave packets from the Pacific towards the Atlantic Ocean, the British Isles, and finally towards the European continent during the last 10 to 15 d of June and before the initiation of the heatwave over Scandinavia (Fig. 4). On the other hand, this was not the case for August, when the peak over Iberia occurred, which highlights the different mechanisms involved in this heatwave, rather than Rossby wave activity coming from the Pacific. Indeed, heatwaves and precipitation deficits in this location are primarily associated with amplified subtropical atmospheric ridges rather than midlatitude blocking situations (see Woollings et al., 2011; Sousa et al., 2017, 2018).

Further, a backward-trajectory analysis was conducted to determine the origins of the air masses that were present during the different heatwave phases and their evolution. Three grid points were chosen to represent the three affected areas and time segments of the heatwave: one over Scandinavia (Utsjoki, Finland) initialized on 18 July 2018, one over central Europe (Bernburg, Germany) on 31 July, and one over Iberia (Alvega, Portugal) on 4 August 2018 (Fig. 5). The backward trajectories showed the remote origin of the mid-troposphere air masses, especially in the case of Utsjoki (Fig. 5a), where it primarily originated over the central North Atlantic. This is also true for the mid-troposphere air masses in the case of Bernburg (Fig. 5b). However, in the last 48 h, descending air masses were observed, pointing to an adiabatic warming by compression. Trajectories starting in the lowest 200 hPa at Bernburg indicate that air masses stemmed from a region to the south and east close to the starting location, indicating relatively stagnant air masses as already discussed in Spensberger et al. (2020). In the case of Alvega (Fig. 5c), air masses starting between 700 and 1000 hPa experienced several rising and sinking motions on their way from the south and southeast (e.g., the Algerian desert, Atlas Mountains, Mediterranean Sea), towards the Iberian Plateau and coastal regions, thus documenting their local-to-regional origin, in contrast to the remote origin of the air masses seen in central and northern Europe, and largely stagnant conditions (in line with Santos et al., 2015; Sousa et al., 2019).

In order to infer causal hypotheses for the existence of the Scandinavian block, the trajectory approach was extended to obtain the origins of low potential vorticity (PV) air masses that formed the upper-tropospheric part of the Scandinavian anticyclone (see Sect. 2.2.3). For the sake of brevity, only maps of 7 and 3 d trajectory density on 18 July 2018, around the maximum heatwave day in Scandinavia, are shown in Fig. 6, but other days corroborate the inferences below (not shown). Figure 6a shows the density of 7 d backward trajectories, indicating that air masses were steered from the western North Atlantic over the British Isles to Scandinavia. This is in line with the propagation of the corresponding Rossby wave packet discussed above. Moreover, using the method described in Zschenderlein et al. (2020, their Fig. 4), the role of a remote warm conveyor belt is suggested by ascending, diabatically heated trajectories over the western Atlantic (not shown); PV is lowered in the warm conveyor belt and then transported in the upper troposphere into the Scandinavian anticyclone (termed “remote branch” by Zschenderlein et al., 2020). Interestingly, high trajectory densities over central to eastern Europe, which also strongly ascended and were diabatically heated (not shown), point towards an influence of moist convection observed under an upper-level trough in this area by feeding low-PV air towards the Scandinavian anticyclone. Such a “nearby branch” was also mentioned by Zschenderlein et al. (2020) to be important for anticyclone persistence over central Europe. However, in the 2018 case the nearby branch is located to the southeast, not to the southwest as for central Europe; 3 d before the peak of the heatwave, trajectories almost exclusively stem from this nearby branch, now located more to the south of the Scandinavian anticyclone (Fig. 6b). Clearly, determining causal pathways from this analysis is not possible, yet modeling studies with explicit convection could shed more light on the role of the remote branch (warm conveyor belt over the western Atlantic) versus the nearby branch over southeastern Europe for the establishment and maintenance of the Scandinavian anticyclone.

When addressing possible precursors for European heatwaves, SST anomalies over the North Atlantic (Dunstone et al., 2019; Ossó et al., 2020; Beobide-Arsuaga et al., 2023) and soil moisture anomalies over continental Europe (Quesada et al., 2012) are among the primary candidates, as outlined in the Introduction. A tripolar SST pattern with negative anomalies over the subpolar gyre (SPG) was evident in spring (MAM, northern box of Fig. 7a, b). At the same time, a pronounced precipitation deficit over Scandinavia in the spring of 2018 was present (Fig. 7c). The SST tripolar pattern persisted over time, with the cold SPG anomaly intensifying in summer (JJA, Fig. 7b), and the same is true for the precipitation deficit, which increased particularly in Germany and central Europe (Fig. 7d), as also discussed in Toreti et al. (2019). The soil moisture anomaly for the 2018 spring and summer (Fig. 7e, f) shows a pattern consistent with the precipitation anomaly.

Having established that the large-scale soil moisture anomaly is consistent with the SST and precipitation anomalies, we investigated the temporal development of the soil moisture pattern over Germany. Reduced soil moisture often facilitates the occurrence of summer drought and heatwaves (Teuling, 2018), as the soil moisture determinant for evapotranspiration (or lack thereof) directly links to the surface temperature and relative humidity at the land surface (Stéfanon et al., 2014; Miralles et al., 2018). Thus, soil moisture and latent heat flux were used to identify periods of moisture limitation (denoted by positive correlation coefficients between the two) and wet conditions (negative correlation coefficients), under which the latent heat flux is primarily controlled by the atmosphere. The derived time series for the soil-moisture-latent heat flux correlations are based on daily data centered on 92 d running periods for Germany (Fig. 8). Additionally, centered 92 d running mean soil moisture is shown. The time series were spatially averaged over all land points for northern (Fig. 8a, c) and southern Germany (Fig. 8b, d). Germany is usually not in the moisture-limited regime, but extraordinary hydrologic conditions can lead to a shift from an energy-limited evaporative regime to moisture-limited conditions (Lo et al., 2021), increasing the surface temperature and enhancing the sensible heat flux. The soil moisture anomaly in March 2018 was low all over Germany (Fig. 8a, b) and thus did not yet limit evapotranspiration and latent heat flux. Warm conditions in spring caused a high latent heat flux all over Germany, indicating a strong energy limitation (Fig. 8c, d). High latent heat fluxes, in turn, lead to a severe depletion of the soil moisture up to a depth of 1 m, starting at the end of March and continuing until July in northern Germany and mid-August in southern Germany. The precipitation deficit (Fig. 7c, d) further exacerbated the drying of the soils and shifted the evaporative regime from energy-limited to moisture-limited conditions. The latter prevailed between June and August 2018, indicating that the anomalously dry soils during the 2018 summer further augmented the hot surface temperatures (Dirmeyer et al., 2021; Orth, 2021).

In summary, the observed and modeled spring and early summer SST anomalies over the North Atlantic and European soil moisture anomaly patterns for 2018 are in line with those identified for other recent hot summers. Moreover, the dried-out soils and vegetation may have enhanced the maximum temperatures by leading to anomalous latent heat fluxes not only locally, but also downwind via advected sensible heat that can lead to abrupt increases in air temperatures, further enhancing local land–atmosphere feedbacks (Schumacher et al., 2022).

This section evaluates how anthropogenic climate change has affected the likelihood of similar heatwaves under present climate conditions and how it will affect their likelihood at global warming levels of +1.5 and +2 ∘C compared to pre-industrial times.

As defined by the cumulative heat metric, the 2018 summer was the second warmest summer over Europe following 2010, surpassed again in 2019 and 2021 (not shown), ranking it the fourth warmest by now. In the period of 1979–2021, ERA5 data exhibit a 7 % likelihood of 2018 cumulative heat levels (black PDF in Fig. 9). MPI-GE, which is shown to adequately represent the variability and forced anthropogenic changes in observed temperatures (Suarez-Gutierrez et al., 2018, 2021), is also able to capture cumulative heat well (gray PDF in Fig. 9), as compared to ERA5. Under recent climate (1979–2021) conditions, the 100 members of MPI-GE simulate a 9 % likelihood of exceeding 2018 levels, making this roughly a 1-in-10-year event. This is in line with an earlier attribution study by the World Weather Attribution (WWA) team who found return periods of about 1 in 10 years for Scandinavia and slightly less in the Netherlands (WWA, 2018). Vogel et al. (2019) also showed that events of this type, exhibiting concurrent hot temperature extremes over large parts of the Northern Hemisphere, were unprecedented before 2010, and it is virtually certain that the 2018 events would not have occurred without human-induced climate change. Under increased global warming, this likelihood reaches 69 % in a +1.5 ∘C world and 96 % in a +2 ∘C world (orange and red PDFs in Fig. 9). Thus, conditions as extreme as the summer of 2018 are projected to occur two out of every three summers in a 1.5 ∘C warmer world, while in a 2 ∘C warmer world they occur virtually every single summer. The extreme summer of 2018 represents a fairly average summer in a 1.5 ∘C warmer world. In a 2 ∘C warmer world, the cumulative heat during the average summer is twice as large as the 2018 levels, while the most extreme 2 ∘C warmer world summers could exhibit more than 4 times more excess heat compared to recent climate conditions.

To estimate how much more likely the heat event of 2018 has become in Germany in recent decades due to anthropogenic climate change, its probability ratio was calculated based on historical and hist-nat (pre-industrial-type) simulations from the CMIP6 archive. In the first step, we defined the extreme event for which the tailored attribution analysis for Germany was conducted. We analyzed the maximum daily temperature (Tmax⁡) averaged for a box over Germany (47.5–55∘ N, 6–15∘ E), and to account for the prolonged heat of 2018, we used the Tmax⁡ as a spatial average over 17 d (Tmax⁡17). This length was defined based on the longest period of consecutive days with Tmax⁡ above 30 ∘C in German weather stations on record. Using this length resulted in the longest return period. Thus, annual block maxima of this variable (Tmax⁡17) were constructed within the GEV fit, and the return periods were calculated. The return period of the 2018 summer Tmax⁡17 (approximately 31 ∘C in E-OBS) was estimated as 108 years, making it a heatwave that is expected less than once in a lifetime and which can therefore have considerable impacts. It should be acknowledged that such a return period estimate contains uncertainties, as the time series used to calculate it are shorter (about 70 years). Following the analysis of observation-based data, the following models were analyzed: CanESM5, CNRM-CM6-1, ACCESS-ESM1-5, IPSL-CM6A-LR, HadGEM3-GC31-LL, and MRI-ESM2-0 (see Table S1 for further details on the models used).

The probability ratio of the 2018 summer heatwave occurrence in Germany is shown for all analyzed models in Fig. 10. For all models the probability ratio estimated on the original simulation data is larger than 1, meaning that the probability of such a heatwave has increased due to anthropogenic climate change. The red bars provide uncertainty ranges bases on the 1000 bootstraps. The best estimate in all analyzed CMIP6 models (black squares) is > 2, again in line with the WWA findings despite a rather different event definition (WWA, 2018). For readability of the results, the x axis in Fig. 10 is only extended to a value of 100, with larger values omitted due to the large uncertainties. In fact, the upper range of the probability ratios for some models is invalid, as the event had a zero probability of occurrence in the hist-nat scenario, indicating that such an extended heatwave would have been very improbable under pre-industrial conditions.

In summary, the analysis of the impact of anthropogenic climate change on the heatwave in the summer of 2018 shows that such heat events have already become more frequent, i.e., their probability has increased compared to pre-industrial conditions. Furthermore, it is expected that such heat events will become even more likely in a warmer world.

Drought attribution is notoriously difficult due to the fact that global models only crudely reproduce convective precipitation, which is the main mode of rainfall in summer. While evapotranspiration is increasing with warming, the question of whether or not this can be compensated by stronger downpours to avoid hydrological (or agricultural) drought cannot be answered with any degree of certainty at the moment. Drought episodes are expected to increase (IPCC, 2021) across the world, but the frequency of occurrence and the actual change in risk cannot be quantified yet. Nevertheless, it is likely that the prolonged 2018 drought, followed by two more below-average rainfall years in 2019 and 2020 in Germany, is partially attributable to human-induced climate change. Given that attributable global warming is approximately 1.1 ∘C (2011–2020), corresponding to 100 % of the observed warming, and warming over land is much more rapid, Europe has already warmed disproportionately by ∼ 2 ∘C compared to pre-industrial times, with summer warming being particularly amplified due to soil moisture feedbacks under increased sensible heat fluxes. Together with the potential dynamic feedback discussed above, the average summer Tmax⁡ in Europe may well exceed 3 ∘C above pre-industrial conditions already. This is corroborated by a recent WWA study, which analyzed the UK heat record during the exceptional 2022 heatwave (18–19 July 2022) and found that climate change added 4 ∘C to the observed record Tmax⁡. What used to be a 36 ∘C day is now a 40 ∘C day (WWA, 2022).