The daily maximum surface air temperature (MSAT) and daily precipitation data used in this study are from the European Climate Assessment and Dataset (E-OBS 19.0) with a 0.25° × 0.25° spatial resolution (Cornes et al 2018). The daily geopotential height (Z500) and zonal wind (U500) at 500 hPa, and horizontal wind components (U850, V850) and temperature (T850) at 850 hPa are obtained from the ERA-Interim reanalysis dataset (Dee et al 2011) at a 2.5° × 2.5° spatial resolution. The area (10°W–45°E, 40°N–75°N) is chosen to study European heatwaves, the study period spans from 1979 to 2018, and only boreal summer (June, July and August) is considered. The anomalies for daily variables are calculated by removing the climatological mean for 1979–2018 of each calendar day. We also used one historical simulation (r1i1p1f1) each from a group of 15 Coupled Model Intercomparison Project 6 (CMIP6) models (table S1) from 1980 to 2010, including the daily evolutions of Z500, U500 and surface air temperature (SAT).

The blocking action center over Europe has its greatest frequency in the summer season (Diao et al 2006), indicating that atmospheric blocking plays a key role in modulating the summer weather extremes in Europe. To identify blocking events over Europe, the detection method of Tibaldi and Molteni (1990) (the TM index) is applied. This is a one-dimensional blocking detection method based on the reversal of the Z500 meridional gradient. The method can also identify the longitudinal range and duration of blocks. The specific steps in the TM method are:

(i) One-dimensional blocks: The meridional gradients of Z500 (GHGS and GHGN (referring to geopotential height gradients in the middle and high latitutes respectively)) at a particular longitude are calculated as:

$$\begin{align*} GHGS &= \frac{{Z{\text{50}}{{\text{0}}{{(\varphi _0)}}} - Z{\text{50}}{{\text{0}}{{(\varphi _S)}}}}}{{{\varphi _0} - {\varphi _S}}},\\ GHGN &= \frac{{Z{\text{50}}{{\text{0}}{{(\varphi _N)}}} - Z{\text{50}}{{\text{0}}{{(\varphi _0)}}}}}{{{\varphi _N} - {\varphi _0}}}.\end{align*}$$

where ${\varphi _N} = {80^ \circ }{\text{N}} + \Delta$, ${\varphi _S} = {40^ \circ }{\text{N}} + \Delta$, and ${\varphi _0} = {60^ \circ }{\text{N}} + \Delta$, and Δ = − 5°, 0° or 5°. If GHGS > 0 and GHGN < − 10 gpm (deg. lat.)⁻¹ for any one of the three values of Δ, blocking is defined to have happened at this longitude.

(ii) Blocking event: When more than five contiguous meridian lines (equivalent to 12.5 longitude degrees) are blocked in the region 0°–60°E for a day and this condition persists for at least 3 consecutive days, an EB event is detected.

(iii) Blocking intensity and lifetime: The blocking intensity is defined following Luo et al (2018b) and Li et al (2019, 2020a). The maximum domain-averaged Z500 anomaly for all possible positionings of a 15° lon. × 10° lat. rectangle within the region (10°E–50°E, 50°N–80°N) is defined as the daily blocking intensity. During a blocking event, the day with the maximum blocking intensity is defined as the Lag 0 d. Similar to (Li et al 2019), the lifetime of a blocking is defined by the number of consecutive days with intensities greater than 120 gpm.

The observed NAO index is obtained from the National Oceanic and Atmospheric Administration/Climate Prediction Center (www.cpc.ncep.noaa.gov). It is defined as the leading Rotated Principal Component Analysis (RPCA) mode of the Z500 anomalies. In a similar fashion, the NAO index for each CMIP6 simulation is defined as the leading Rotated Empirical Orthogonal Function (REOF) mode of Z500 anomalies over the North Atlantic region (90°W-40°E, 20°N-80°N) (Wilks 2006). To enable easy comparison, the corresponding principal components of each leading REOF mode are standardized by daily means and standard deviations of the period 1980–2010. An NAO⁺ event is defined as one in which the daily NAO index is equal to or greater than + 1 standard deviation (Std. Dev.) and persists for at least 3 consecutive days (Luo et al 2015a, 2015b; Yao and Luo 2018). An EB event is regarded as related to an NAO⁺ event if the Lag 0 d of the EB event lies within the lifetime of an NAO⁺ event; otherwise, the EB event is NAO⁺-unrelated (Yao and Luo 2018).

Before identifying heatwaves, the linear trend of the MSAT anomalies at each grid point is removed. Since the main purpose of this study is to examine the relationship between large-scale atmospheric circulations (blocking highs and NAO⁺ events) and European heatwaves, we define the heatwaves in terms of the land-only and area-weighted average of MSAT anomalies in the European region (MSAT index, referred to as MSATI hereafter). One advantage of this approach is that it reduces or removes the effects of mesoscale or smaller weather systems. A heatwave is defined to occur when the daily MSATI exceeds the 90th percentile of the daily MSATI, calculated on a 31-day window centered on this calendar day for the base period 1981–2010, and persists for at least three consecutive days. The daily MSATI is taken as the daily heatwave intensity (Rocha et al 2020, Sulikowska and Wypych 2020). The daily spatial area of a heatwave is defined as the sum of areas with daily MSAT anomalies larger than the 90th percentile, calculated as the MSATI, at a 0.25° lat/lon grid box (Russo et al 2015, Schaller et al 2018). Heatwaves in the CMIP6 historical simulations are detected in the same way as above but using SAT anomalies.

From the definitions in section 2, 52 heatwaves, 101 NAO⁺ events, and 115 EB events are identified over the 40-year period 1979–2018. Among the EB events, the numbers of NAO⁺-related and the NAO⁺-unrelated cases are 8.25 and 20.5 per decade, respectively. The number of the NAO⁺ events without related EB events is 17.00 per decade. To examine whether the heatwaves are related to the specific circulation modes highlighted here, we have used the following terminology: if the Lag 0 d of a heatwave occurs within the lifetime of an atmospheric circulation event (an EB event or an NAO⁺ event), this heatwave is related to a certain atmospheric circulation. The numbers (frequencies) of heatwaves that are linked to only NAO⁺ events (without related EB events), NAO⁺-unrelated EB events, and NAO⁺-related EB events are 2.25 per decade (13.24%), 4.75 per decade (23.17%) and 3.75 per decade (45.45%), respectively (table 1). The frequency herein refers to the possibility of a heatwave occurring under the condition of an NAO⁺/EB event. This suggests that an NAO⁺ event of itself is not conducive to the formation of a European heatwave, and the lifetime (4.33 d), intensity (3.04 K) and area (1.77 × 10⁶ km²) for related heatwaves are also the lowest. In comparison, for NAO⁺-unrelated EB events, 23.17% of them are linked to heatwaves whose lifetime (5.00 d), intensity (3.38 K) and area (1.95 × 10⁶ km²) are higher. Among the three circulation patterns, an NAO⁺-related EB event is the most favorable for the occurrence of a heatwave, and the related heatwave is longer-lived (6.87 d), more intense (3.64 K), and more widespread (1.97 × 10⁶ km²) than that of the other two types. Notably, there remains nine heatwaves that are not related to either NAO⁺ or EB events. Boschat et al (2016) reminded some caveats when performing composite analyses to form physical hypotheses on climate connections. From what they highlighted (Boschat et al 2016), we propose that European heatwaves are more likely to correspond to a NAO⁺/blocking (necessary condition). However, this does not establish that when you have a NAO⁺/blocking you are more likely to have a European heatwave (sufficient condition). Some other circulation patterns (e.g. the wave trains) as well as the land surface characteristics (e.g. the soil water deficit) also contribute to European heatwaves. Thus, further comparisons concerning these nine heatwaves are not conducted in this study. Then, we evaluate the lifetime, spatial area and intensity of heatwaves simulated by 15 CMIP6 models against the observations. Generally, for the multimodel mean (MMM), NAO⁺-related EB event has the most frequent, longest, strongest and most widespread related heatwaves, which is in good agreement with the observations. However, the MMM slightly overestimates the lifetime and spatial area of the simulated heatwaves, while underestimates the intensity of the simulated heatwaves. In the next subsection, the spatial and temporal variations of daily temperatures and atmospheric circulations associated with NAO⁺-related EB events and NAO⁺-unrelated EB events are further compared in order to understand the different characteristics of their related heatwaves.

Figures 2(a)–(c) show the composite MSAT anomalies on the Lag 0 d of NAO⁺-related EB events and NAO⁺-unrelated EB events, together with their differences. Positive MSAT anomalies of NAO⁺-related EB events stretch from northern Europe to western Europe, while the east part of southern Europe exhibits negative MSAT anomalies (figure 2(a)). The largest positive MSAT anomalies are located in the northern parts of Norway, Sweden and Finland. By contrast, positive MSAT anomalies are weaker and mainly concentrated over the northern part of Europe for NAO⁺-unrelated EB events (figure 2(b)). Figure 3(b) verifies that NAO⁺-related EB events are associated with much warmer regions over the northern and western Europe and cooler regions over southeastern Europe when compared with NAO⁺-unrelated EB events. The spatial distribution of SAT anomalies in the MMM is in good agreement with the observations (figures 2(d)–(f)). For each of the 15 CMIP6 models, the SAT anomalies simulated by BCC-ESM1, CESM2 and MPI-ESM1-2-HR are closer to the observations (figure S1 (available online at https://stacks.iop.org/ERL/15/114003/mmedia)). BCC-CSM2-MR, MPI-ESM1-2-LR and NorESM2-MM models show a large underestimation of positive differences in SAT anomalies in northern Europe, while ACCESS-CM2, CESM2-WACCM, EC-Earth3 and MIROC6 models underestimate the positive differences in SAT anomalies in southwestern Europe (figure S1(c)). The remaining models exhibit small differences in SAT anomalies in both regions (figure S1(c)). The time series of intensity and spatial area of MSAT anomalies related to EB events are also analyzed following the relevant definitions of heatwaves in section 2 (figures 2(g) and (h)). The lifetime of the high temperature is defined as the number of days with MSATI above the 90th percentile. Five thousand subsets, each containing 33 (82) random days in the summers of 1979–2018, are produced. The 90th percentile is calculated by the averaged MSATI of the 5000 Monte Carlo subsets. Figure 2 shows that the differences for composite MSATI of the two types are statistically significant at 90% from Lag −1 to Lag 10 (95% from Lag −1 to Lag 3 and from Lag 5 to Lag 10). The high temperature lasts 13 d for NAO⁺-related EB events, which is 3 d longer than that of the NAO⁺-unrelated EB events. In addition, the high temperatures of NAO⁺-related EB events occupy a larger spatial area, which also last for a longer time. Figures 2(i) and (j) suggest that the intensity and spatial area of high temperatures simulated by CMIP6 models are consistent with the observations. High temperatures of NAO⁺-related EB events also last longer in the MMM. Only EC-Earth3, GFDL-CM4 and NorESM2-MM simulate weaker and less widespread high temperatures for NAO⁺-related EB events (figure S2).

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As known from previous studies, heatwaves are usually related to an atmospheric blocking system. The observational and model analyses above further suggest that EB events related to the NAO⁺ pattern can cause heatwaves with larger scope, stronger intensity, and longer lifetime. Notably, the 2018 heatwave discussed in section 3 has a similar spatial distribution of MSAT anomaly as that in the composite NAO⁺-related EB events, and this heatwave is closely associated with three NAO⁺ events. This further implies the important role of collaborative impacts of EB events and the NAO⁺ pattern in European heatwaves.

We first compare the daily variations of atmospheric circulations associated with NAO⁺-related EB events and NAO⁺-unrelated EB events from reanalysis and model simulations. We then set out to explain the MSAT anomalies based on these atmospheric circulations, in section 4.4. Daily Z500 and Z500 anomaly fields in reanalysis of these two types are composited from Lag −8 to Lag 8 (figure 3). In figure 3(a), an NAO⁺ pattern over the North Atlantic is clearly apparent at Lag −8, with a strong cyclone over the Greenland and a wide anticyclone situated from the Gulf Stream extension to Europe. A weak Z500 ridge is situated over Europe and the related surface warming is dispersive. From Lag −6 to Lag 0, the weak Z500 ridge evolves to be a strong blocking system with meridional Z500 reversals. The Z500 ridge as well as the blocking anticyclone tend to have a northeast-southwest direction, especially after Lag −2, and a trough is accompanied to their southeast, where cold anomalies tend to occur. Correspondingly, significant MSAT anomalies control northern Europe and western Europe, while the east part of southern Europe has significant negative MSAT anomalies. At Lag 0, the composite blocking high reaches its maximum intensity, together with the more intense warming in Europe, whereas the NAO⁺ pattern is getting weaker. After Lag 0, the blocking high begins to decay and move westward.

For EB events unrelated to NAO⁺, no NAO⁺ signals can be identified from Lag −8 to Lag 8 over the North Atlantic region (figure 3(b)). A weak anticyclone forms at Lag −6, which is situated to the east of northern Europe, and high temperatures form at very small regions. From Lag −4 to Lag 0, the anticyclone develops to be a blocking system, which shows a west-east symmetric ‘Ω’ structure at Lag 0. Corresponds with the shape of the blocking high, the blocking anticyclone mainly controls the north part of Europe, where significant positive MSAT anomalies occur. At the same time, a trough forms to the southwest of the ridge of blocking at Lag −2, and it gradually moves to the south of the ridge at Lag 0, which corresponds to the negative MSAT anomalies in southern Europe. Starting from Lag 2, the blocking anticyclone quickly moves towards the west and eventually controls the Greenland at Lag 6. Compared with figure 3(a), this blocking anticyclone moves more quickly and follows a more northerly path.

The main differences in the daily variations of atmospheric circulations for NAO⁺-related EB events and NAO⁺-unrelated EB events are well reproduced by model simulations (figure 4). The NAO⁺ pattern occurs prior to the formation of EB related to NAO⁺, indicating that NAO⁺-related EB events are mainly formed by the energy dispersion from the upstream NAO⁺, while the upstream circulations for NAO⁺-unrelated EB events are too weak to discern. In addition, EB events of these two types have different shapes; the blocking ridge of NAO⁺-related (NAO⁺-unrelated) EB events show a northeast–southwest (north–south) distribution with a more southeastward (southward) trough. Also, NAO⁺-unrelated EB events seem to be more mobile and have a more rapid westward movement during the dissipating stage.

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We now relate the different characteristics of high temperatures with atmospheric circulations for NAO⁺-related EB events and NAO⁺-unrelated EB events. The time–longitude evolution of composite Z500 anomalies averaged over 55°–65°N (52.5°–62.5°N) for NAO⁺-related (NAO⁺-unrelated) EB events is shown in figure5(a) (figure 5(b)). The Z500 anomaly has its largest value of 128.33 gpm for NAO⁺-related EB events, which is stronger than that (85.64 gpm) of NAO⁺-unrelated EB events. Additionally, the composite Z500 anomaly larger than 50 gpm persists for 7 d for NAO⁺-related EB events, which is 2 d longer than in the NAO⁺-unrelated case. We also calculate the slopes of arrows that denote the travelling speeds of composite EB events. The composite NAO⁺-related EB events move at a speed of 6.85 (3.00) longitude degrees per day at their forming (decaying) stage, which is nearly a half (a quarter) of the travelling speed (12.50 longitude degrees per day) of the NAO⁺-unrelated EB events. These analyses suggest that the composite NAO⁺-related EB events are stronger and more stable (quasi-stationarity) over Europe. These strong and persistent blocking events could favor stronger and longer-lived heatwaves through accumulating more heat brought by increased solar radiation, warm advection, adiabatic subsidence, etc. Notably, the NAO⁺-related EB events are even more stable during dissipation, which favors the continuous high temperatures after Lag 0 d of EB events (figures 2(g) and (h)). The simulated time–longitude evolution of composite Z500 anomalies for NAO⁺-related EB events and NAO⁺-unrelated EB events resembles that in reanalysis (figures 5(c) and (d)). One difference in the MMM from the reanalysis is that the movement of NAO⁺-unrelated EB events can also be divided into two stages. The blocking anticyclone in the dissipating stage has a slower speed (5.89 longitude degrees per day) than that (3.63 longitude degrees per day) of the forming stage for NAO⁺-related EB events, while the blocking anticyclone is more movable in the dissipating stage (17.50 longitude degrees per day) than in the forming stage (8.33 longitude degrees per day) for NAO⁺-unrelated EB events.

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One possible explanation for the differences in the intensity and movement of EB events for the two types, as described above, is in the nature of the upstream NAO pattern. The daily variations of composite NAO indices and upstream domain-averaged (80°W–0°, 40°–60°N) U500 anomalies are presented in figures5(e) and (f). The NAO index of NAO⁺-related EB events is significantly larger than that of the NAO⁺-unrelated EB events during the whole study period (from Lag −10 to Lag 10). Specifically, the NAO index is above the 90th percentile for NAO⁺-related EB events from Lag −10 to Lag 4, whereas NAO⁺-unrelated EB events have negative NAO index values less than the 10% percentile from Lag 1 to Lag 9. Corresponding to the NAO indices, large discrepancies can also be seen in the composite U500 anomalies, where significant differences can be seen from Lag −10 to Lag −2. The increased upstream zonal wind, together with the NAO⁺ pattern at the formation stage of the NAO⁺-related EB events, could favor the reinforcement and persistence of EB events through strengthening the energy dispersion (Yao et al 2017, Luo et al 2018a). The simulated NAO indices and upstream U500 anomalies for NAO⁺-related EB events also have significantly increased values prior to EB events. The peak of NAO index (upstream U500 anomaly) leads the Lag 0 d of NAO⁺-related EB events by 1 d (4 d) in MMM, while the leading time is 4 d (5 d) in reanalysis.

In addition to their intensity and persistence, EB events also have different shapes for the NAO⁺-related case and the NAO⁺-unrelated case. NAO⁺-related EB events with a northeast–southwest orientation contribute to strong and widespread southerly wind vectors to their west, and hence strong warm air advection (figure 6(a)). The southern cyclonic circulation of the blocking is situated more to the east, which brings anomalous cold air to southeastern Europe. Associated with the northeast–southwest orientated blocking, most of Europe has negative precipitation anomalies, except that the southeastern Europe has significantly increased precipitation (figure 6(a)). It is suggested that the strong warm air currents and a lack of precipitation could explain the distribution of high temperatures associated with NAO⁺-related EB events. Compared with the large range of high temperatures for NAO⁺-related EB events, positive MSAT anomalies are mainly concentrated in the northern part of Europe for NAO⁺-unrelated EB events. This could be attributable to the symmetric ‘Ω’ shape of the NAO⁺-unrelated EB ridge. The anticyclonic circulation and warm airflow only control the north part of Europe, while the cyclonic circulation which could increase precipitation situated over the south part of Europe (figure 6(b)). Thus, MSAT anomalies in the south part of Europe are reduced, and positive MSAT anomalies are only confined to the northern Europe. Compared with NAO⁺-related EB events, the warm wind vectors are less strong and less widespread for the NAO⁺-unrelated case, which also explains their weaker and smaller-area high temperature. These findings suggest that the shape of the blocking events could further impact the intensity and scope of high temperatures through changing the warm airflow and precipitation.

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