1 Introduction

In the past two decades, Europe experienced several extraordinary heat waves with substantial consequences for ecosystems and society. The 2003 and 2010 ‘mega heat waves’ (Barriopedro et al. 2011) were associated with tens of thousands excess deaths (Robine et al. 2008; Shaposhnikov et al. 2014), decreased plant productivity and crop failures (Bastos et al. 2014), forest fires (Konovalov et al. 2011), record-breaking loss of Alpine glaciers’ mass (De Bono et al. 2004), and other impacts.

Such severe heat waves are one of the main concerns with respect to the ongoing climate change (Kirtman et al. 2013). Beniston (2004) concluded that the summer of 2003 bears a close resemblance to what many climate models simulate for summers in the late twenty-first century. The frequency of heat waves over Central Europe is projected to be roughly doubled in the 2020–2049 period compared to historical climate (1970–1999), and this increment was found under all Representative Concentration Pathways (RCP) scenarios. By contrast, in the late twenty-first century, the increase of the heat wave frequency (by a factor of 2–5) is scenario-dependent (Lhotka et al. 2017). These changes are expected to be primarily driven by a shift of the temperature distribution (Ballester et al. 2010; Lau and Nath 2014), but Fischer and Schär (2010) also identified larger variance of summer temperature distribution in a possible future climate, and Lhotka et al. (2017) pointed out increased temporal autocorrelation of daily maximum temperature, suggesting more persistent heat waves.

Before analysing projections for a possible future climate, model simulations have to be evaluated against historical data. Kotlarski et al. (2014) evaluated regional climate model (RCM) simulations from the EURO-CORDEX project (COordinated Regional climate Downscaling EXperiment, Jacob et al. 2014) that were driven by the ERA-Interim reanalysis (Dee et al. 2011). The majority of RCMs overestimated summertime temperature over Southern and Eastern Europe, while underestimation was found in Scandinavia and the British Isles. The capability of reanalysis-driven EURO-CORDEX RCMs to simulate heat waves over Europe was investigated by Vautard et al. (2013), who concluded that models had too-persistent and too-intense heat waves, even though the influence of the temperature bias was removed. The enhanced severity of heat waves in the ENSEMBLES RCMs (van der Linden and Mitchell 2009) driven by reanalysis was reported by Lhotka and Kyselý (2015b), who found a connection between the magnitude of heat waves and precipitation during and before these events. Inasmuch as most precipitation during heat waves is of convective origin (Stéfanon et al. 2014), this result is in accordance with Vautard et al. (2013), who discussed a possible connection between exaggerated land–atmosphere feedbacks and overestimated heat wave severity in the RCMs.

Soil moisture is an important variable in these land–atmosphere interactions, because it controls the partitioning of available energy between sensible and latent heat fluxes at the surface (Berg et al. 2014). The link between reduced soil moisture and amplified summer temperature in an RCM was shown, for example, by Jaeger and Seneviratne (2011). Using also a reanalysis-driven RCM, Stéfanon et al. (2014) found different relationships between a soil moisture deficit and severity of heat waves over lowlands, mountains, and coastal areas. In lowlands, a reduction of soil moisture led to less evapotranspiration and higher sensible heat flux, which consequently caused a drier atmosphere and therefore less clouds and precipitation. Stéfanon et al. (2014) estimated that this process contributed as much as 20% of the temperature anomaly in Eastern France and Western Germany during heat waves.

Using reanalysis-driven RCMs from the ENSEMBLES project, Stegehuis et al. (2013) demonstrated that most models in their study exhibited overestimated drying during warm seasons, leading to the establishment of a soil moisture-limited regime across Europe in summer. Inasmuch as an analogously large soil moisture deficit was found only over the Iberian Peninsula in observed data from the FLUXNET network (the global network of micrometeorological tower sites, Baldocchi et al. 2001), this RCMs’ deficiency may contribute to overestimation of the frequency and severity of heat waves. The important role of RCMs’ land surface scheme for a proper simulation of temperature and surface fluxes was also shown by Davin et al. (2016), who demonstrated that the COSMO-CLM RCM with more advanced representation of land processes outperforms EURO-CORDEX RCMs in many characteristics.

An important factor conducive to heat waves is atmospheric circulation. Severe European heat waves are triggered by a combination of radiative heating due to clear-sky conditions and southerly to easterly advection of warm air masses (e.g. Della-Marta et al. 2007; Kyselý 2008). This favourable setting is especially prolonged during atmospheric blocking episodes (e.g. Schubert et al. 2014). Plavcová and Kyselý (2016) demonstrated that RCMs driven by reanalysis simulate atmospheric circulation during heat waves reasonably well, which is related to the fact that the large-scale flow in RCMs is primarily given by lateral boundary conditions (Plavcová and Kyselý 2012). RCMs seem to be capable, however, of modifying atmospheric circulation through processes inside their domains. For example, Haarsma et al. (2009) showed that an inaccurate simulation of soil moisture regime over Southern Europe may lead to the development of thermal low and consequent easterly advection to Central Europe, with implication for heat waves’ severity.

Due to these model deficiencies, it is important to understand whether heat waves in models occur for the same reasons that they do in nature (Fischer 2014). In this study, we analysed the severity of past heat waves in the 1950–2016 period and identified three ‘major heat waves’ in 1994, 2006, and 2015 that were used as analogues for RCM simulations. Anomalies in atmospheric circulation, precipitation, and surface fluxes are assessed for the observed major heat waves and compared with those simulated by RCMs from the EURO-CORDEX project in the 1970–2016 period. The study is performed over Central Europe, which was recently affected by pronounced heat and drought in summer 2015 (Hoy et al. 2016) and heat waves during this summer were exceptional also at the continental scale (Russo et al. 2015). In contrast to previous studies, the RCMs are driven by global climate models (GCMs) in order to evaluate RCM × GCM combinations that can be used for future projections and to analyse the sources of biases in simulating severe temperature events.

2 Data and methods

2.1 Regional climate model simulations

14 regional climate model (RCM) simulations driven by global climate models (GCMs) were taken from the EURO-CORDEX project (Jacob et al. 2014) and are listed in Table 1. All RCMs use the 0.11° rotated grid but were recalculated to the 0.22° grid through averaging four respective grid points in order to allow a direct comparison with the E-OBS data set. An analogous procedure was applied by Kotlarski et al. (2014) when comparing the performance of EURO-CORDEX and ENSEMBLES models driven by reanalyses. We employed all available RCM × GCM combinations from the Earth System Grid Federation (ESGF) data node that use the 0.11° rotated grid. Most simulations start in 1950 or 1951 (except for simulations from SMHI, which start in 1970), and they all use historical forcing until 2005. The RCP 4.5 scenario runs (Thomson et al. 2011) were selected for the most recent 2006–2016 period (note that differences between individual scenarios are small in this early period).

Table 1 Regional climate models (RCMs) driven by global climate models (GCMs) from the EURO-CORDEX project used in this study
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2.2 Meteorological variables

Observed heat waves were analysed using daily maximum temperature (Tmax) from the E-OBS 14.0 gridded data set (Haylock et al. 2008). This data set is available from 1950 to the present and has the 0.22° rotated grid, which is the same as the recalculated grid in the EURO-CORDEX RCMs. Besides Tmax, daily precipitation was also taken from this data set. Sea level pressure (SLP), 500 hPa geopotential height (Z500, both at 12 UTC), and surface radiation and energy fluxes (daily means from hourly values) were taken from the ERA-Interim reanalysis (0.25° grid), which is available from 1979 and is regularly updated (Dee et al. 2011). Analogous variables were taken from the RCM simulations, which are analysed for the overlapping 1970–2016 period on a daily basis (Online Resource 1).

2.3 Area of interest

Relationships between major heat waves and the meteorological factors were analysed over Central Europe (Fig. 1a). This region exhibits relatively homogeneous climate and contains 40 × 26 grid points in the 0.22° rotated grid. The area of interest was slightly different when analysing surface radiation and energy fluxes due to a different geographical projection in the ERA-Interim data set.

Fig. 1
figure 1

a Definition of Central Europe (black dashed polygon), with colour shading representing the 90% quantile of summer daily maximum temperature (calculated for the 1981–2010 period); b points used for calculation of circulation indices (black numbered dots) and summer daily maximum temperature standard deviation (colour shading, 1981–2010)

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2.4 Definition of heat waves

The definition of heat waves was analogous to that used in Lhotka and Kyselý (2015a) and was based on positive deviations from the 90% quantile of the summer (June–August, JJA) Tmax distribution, which was calculated for the 1981–2010 reference period. For each day between May 1 and September 30, differences between actual Tmax and the 90% quantile were calculated for every grid point (1,040). The Tmax deviations were then averaged over the grid points and if a resulting number was positive, the given day was considered a hot day. Subsequently, a heat wave occurs if at least three consecutive hot days occur. The extended May–September period was chosen because the warming climate provides a larger potential for early or late heat waves (e.g. the September 2015 heat wave, Hoy et al. 2016). Note that the 90% quantile is still calculated for the summer (JJA) period only.

This definition of heat waves was also applied for RCMs, where the 90% quantiles were calculated separately for each simulation in order to remove the influence of the Tmax bias. This approach is suitable when focusing on the behaviour of the right tail of the Tmax distribution and the spatial and temporal structure of daily temperatures (which are essential for heat waves) rather than on the Tmax bias itself. The overall magnitude of heat waves is assessed through the extremity index (Lhotka and Kyselý 2015a), calculated as the sum of positive Tmax anomalies from the 90% quantile during all days when a heat wave persists (scaled by the number of grid points in Central Europe, i.e. 1,040). This index captures joint effects of the temperature anomaly, length, and spatial extent of heat waves, and ‘major heat waves’ are defined based on its value of at least 25 °C (see Sect. 3).

2.5 Calculation of circulation indices

Circulation indices were derived from daily gridded SLP data at the 16 grid points shown in Fig. 1b (Jenkinson and Collison 1977; Blenkinsop et al. 2009; Plavcová and Kyselý 2012). In RCMs, SLP values were obtained using an inverse distance-weighted mean of four grid points adjacent to given coordinates, because RCMs do not use a latitude-longitude grid. The western flow component (w) is defined as a pressure gradient between 45°N and 55°N and it is calculated using the formula

$${\text{w}}\;=\;0.5 \times ({\text{p}}4+{\text{p}}5) - 0.5 \times ({\text{p}}12+{\text{p}}13)$$

where p(X) is a SLP in a given grid point (Fig. 1b). The southern flow component (s) is the gradient between 10°E and 20°E, given by the formula

$${\text{s}}\;=\;\frac{1}{{\cos \left( {\varphi \times \frac{\pi }{{180}}} \right)}} \times [0.25 \times ({\text{p}}13+2 \times {\text{p}}9+{\text{p}}5) - 0.25 \times ({\text{p}}12+2 \times {\text{p}}8+{\text{p}}4)]$$

where φ represents the latitude of the centre (50°N) in degrees and p(X) is a SLP in a given grid point, analogously to the western flow component. The total vorticity (vort) is the sum of its zonal (zw) and meridional (zs) components and reflects the rotation of an air mass. It is calculated using the formulas

$${\text{zw}}\;=\;\frac{{\sin \left( {\varphi \times \frac{\pi }{{180}}} \right)}}{{\sin \left[ {(\varphi - 5)} \right] \times \frac{\pi }{{180}}}} \times [0.5 \times ({\text{p}}1+{\text{p}}2) - 0.5 \times ({\text{p}}8+{\text{p}}9)] - \frac{{\sin \left( {\varphi \times \frac{\pi }{{180}}} \right)}}{{\sin \left[ {(\varphi - 5)} \right] \times \frac{\pi }{{180}}}} \times [0.5 \times ({\text{p}}8+{\text{p}}9 - 0.5 \times ({\text{p}}8+{\text{p}}9)]$$
$${\text{zs}}\;=\;\frac{1}{{2 \times {{\left( {\cos \left( {\frac{\pi }{{180}}} \right)} \right)}^2}}} \times [0.5 \times ({\text{p}}14+{\text{p}}2 \times {\text{p}}10+{\text{p}}6)] - 0.25 \times ({\text{p}}12+2 \times {\text{p}}5+p4)+0.25 \times ({\text{p}}11+2 \times {\text{p}}7+{\text{p}}3)]$$
$${\text{vort\, =\, zw+zs}}$$

where φ represents the latitude of the centre (50°N) in degrees and p(X) is a SLP in a given grid point. Positive (negative) values indicate cyclonic (anticyclonic) conditions.

2.6 Links between major heat waves and meteorological factors

At first, precipitation, net solar radiation, and evaporative fraction from both observed and modelled data were averaged over Central Europe (Fig. 1a) in order to obtain regionally-averaged daily values. Precipitation deficits were calculated for the period during and prior to the major heat waves. The last day of a major heat wave was omitted, because these events are usually terminated by the passage of a cold front, which often brings a large amount of rainfall. Preceding precipitation deficits were assessed for 30-day periods prior to major heat waves. The sum of precipitation during a given period was compared to the 1981–2010 daily-based climatology (calculated for JJA) and expressed as a percentage.

For periods during major heat waves, the daily average of net solar radiation (difference between incoming shortwave radiation at the surface and reflected shortwave radiation) was calculated and expressed in watts per square meter. The amount of soil moisture during major heat waves was assessed indirectly through evaporative fraction, which is the ratio between latent heat flux and the sum of latent and sensible heat fluxes. Note that soil moisture cannot be compared directly between RCMs and the ERA-Interim reanalysis due to different thickness of soil layers (Dee et al. 2011; Kotlarski et al. 2014). Analogously to precipitation, net solar radiation and evaporative fraction during heat waves were compared to the 1981–2010 daily-based climatology and expressed as a percentage.

Changes in atmospheric circulation during major heat waves were assessed through composite maps of SLP and 500 hPa geopotential height and by analysing differences in western and southern flow components and vorticity against their 1981–2010 daily-based climatology. All these characteristics were calculated for individual major heat waves (both observed and simulated) and averaged thereafter.

3 Observed major heat waves and related meteorological factors

In Central Europe, the summer of 2015 was the most distinctive over the 1950–2016 period, according to the seasonal number of hot days and the sum of the heat wave extremity index (Fig. 2). Since 2010, each summer was marked by at least one heat wave and two of the three most extreme summers (according to the seasonal sums of the extremity index) occurred during this 7-year long period.

Fig. 2
figure 2

Time series of the seasonal number of hot days (dots) over Central Europe and the sum of the heat wave extremity index (bars) in the E-OBS data set for the 1950–2016 period. Solid lines represent the locally weighted scatter plot smoothing (LOESS) filter curves

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In 1950–2016, 41 individual heat waves were found (Online Resource 2). Their length ranged from 3 days (by definition) to 16 days and their extremity index varied from 2.7 to 41.5 °C. The selection of ‘major heat waves’ was based on the distribution of extremity index, which represents joint effects of temperature, length and spatial extent of heat waves (cf. Section 2.4). A large majority of heat waves have an extremity index lower than 20 °C (Fig. 3), and the three most severe heat waves (in 1994, 2015, and 2006) according to the extremity index are also the longest ones (16, 11, and 13 days, respectively). Therefore, a major heat wave is defined as an event with extremity index ≥25 °C, in order to capture the natural break in the distribution of this characteristic (Fig. 3). Different values were also tested but usage of higher thresholds led to a very small sample size (several RCMs had no major heat wave), while lower thresholds resulted in a presence of relatively short events with very high temperature anomalies that do not share much similarity with persistent heat waves (1994, 2006, and 2015). A sensitivity analysis shows, however, that the main conclusions are little affected by the particular setting of the threshold used to delimit major heat waves.

Fig. 3
figure 3

Dot plots of extremity indices for individual heat waves in E-OBS in the 1950–2016 period

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The 1994 major heat wave (Fig. 4, left column) persisted for 16 days between Jul 22 – Aug 6 and the largest sums of temperature anomalies were observed in the northeastern part of Central Europe, Poland and Baltic countries. Positive SLP anomalies were located mainly over Fennoscandia and the Baltic region during this event (Fig. 4, middle row). This anticyclone was associated with an elevated Z500 (roughly by up to 150 m), which was a part of a mid-troposphere pattern resembling a so-called ‘Rossby wave train’ (Fig. 4, bottom row). An Ω blocking pattern is related to this sequence of negative and positive Z500 anomalies that led to reduced zonal flow and advection of warm air masses to Central Europe.

Fig. 4
figure 4

Sum of positive temperature deviations from the 90% quantile of summer Tmax distribution (upper row), mean sea level pressure (middle row), and 500 hPa geopotential height (lower row) averaged during the 1994 (left column), 2006 (middle column), and 2015 (right column) major heat waves. Anomalies from the summer (JJA) climatology are shown by contour lines

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The 2006 major heat wave (Fig. 4, middle column) occurred during the Jul 18 – Jul 28 period and it was the shortest (11 days) of the three events. Compared to the 1994 major heat wave, positive temperature anomalies were located more towards the west, affecting also Western European countries. This shift is linked to positive SLP and Z500 anomalies situated between the British Isles and Scandinavia.

The most recent 2015 major heat wave (Fig. 4, right column) took place during Aug 3–Aug 15 (13 days), and affected mostly Central and Eastern Europe. Although it was shorter than the 1994 heat wave, extremity indices of both events were comparable, suggesting higher daily temperature anomalies in 2015. The largest positive SLP anomalies were located north-east of Central Europe, allowing a relatively intense south-easterly advection of tropical air masses.

In addition to the analysis of atmospheric circulation fields, links of the observed major heat waves to precipitation, shortwave radiation, evaporative fraction, and the western and southern flow components and vorticity over Central Europe were analysed (Table 2). All major heat waves were associated with the precipitation deficits during the events and 30 days before their onset. Only roughly one-fifth of precipitation was observed during the major heat waves compared to the 1981–2010 daily based climatology. In the 30-day periods preceding the major heat waves, a reduction of precipitation by approximately 30% was found, with minor differences between the three events. The amount of net solar radiation in ERA-Interim was higher by approximately 20% on average and evaporative fraction was reduced, suggesting a lack of soil moisture, especially during the 2006 and 2015 events.

Table 2 Characteristics of major heat waves and associated precipitation, shortwave radiation, evaporative fraction and western and southern flows over Central Europe
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The average western flow component was reduced while an increase was observed in the southern flow component, indicating enhanced warm south-easterly advection during the major heat waves (both flow component anomalies were largest in 2015). Positive anomalies of vorticity were found, which suggests the presence of an SLP field with no distinctive patterns over Central Europe during major heat waves (considering mean negative vorticity in summer, Table 3, final row).

Table 3 Evaluation of RCM simulations
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4 EURO-CORDEX RCM simulations

The ensemble mean captured the number of major heat waves and their total extremity index relatively well but large differences were found among individual RCM simulations (Table 3). As described in Sect. 3, observed major heat waves are associated with favourable circulation conditions and lack of available soil moisture for latent cooling. Those RCM simulations that considerably underestimated the total extremity index of major heat waves (or no major heat wave was simulated) failed to reproduce this mechanism. The three lowest values of total extremity index in DMI-HIRHAM-ICHEC, IPSL-WRF-IPSL, and SMHI-RCA-MPI were probably linked to substantially overestimated summertime precipitation (>300 mm, Table 3) and this deficiency was amplified by no soil drying during major heat waves (Table 4). In addition, DMI-HIRHAM-ICHEC simulated an increased zonal flow and IPSL-WRF-IPSL exhibited positive values of vorticity (indicating cyclonic conditions) during major heat waves (Table 4; Fig. 5). However, the mechanisms associated with an underestimation of major heat waves were not fully consistent across all RCM simulations. For example, the total extremity index in CLM-CCLM-MPI (101.6 °C) was close to E-OBS, but its summertime climatology of precipitation, net shortwave radiation, and evaporative fraction suggests rather cold and moist summertime conditions and the model overestimated mean westerly advection (Table 3). These deficiencies are probably compensated by a substantial increment of net shortwave radiation (138%, largest among the RCM simulations) and the largest increase of southern and decrease of western flow components during major heat waves (Table 4).

Table 4 Intensity of major heat waves and changes of precipitation, net shortwave radiation, evaporative fraction and atmospheric circulation during major heat waves in the RCM simulations
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Fig. 5
figure 5

Composite maps of sea level pressure (hPa) during major heat waves in EURO-CORDEX RCMs and ERA-Interim. N number of major heat waves, D total duration of heat waves (days), Ihw total extremity index of heat waves (°C)

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By contrast, those RCM simulations that substantially overestimated the total extremity index of major heat waves tended to simulate too-low evaporative fraction and predominant easterly advection during the summer season, which created high potential for the occurrence of major heat waves. The average circulation characteristics were primarily given by driving GCMs. For example, all simulations driven by HadGEM had a negative mean western flow component, while those driven by MPI exhibited quite strong westerly advection in summer (Table 3). Individual RCMs seemed to be capable, however, of modifying the large-scale flow inside their domains.

Although the three highest values of total extremity index were found in the RCA RCM simulations, mechanisms associated with the development of major heat waves were probably different, as discussed below. SMHI-RCA-CNRM and SMHI-RCA-HadGEM suffered from extensive drying during major heat waves (Table 4), resulting in the driest soil conditions among all model simulations (despite too much precipitation during the major heat waves), which probably contributed to the overestimated total magnitude of major heat waves. This behaviour was not observed in SMHI-RCA-IPSL, which simulated soil moisture conditions more realistically.

In addition to the lack of soil moisture during major heat waves, pronounced south-eastern flow and anticyclonic conditions were found in SMHI-RCA-CNRM during these events (Table 4; Fig. 5) and this combination probably resulted in the largest total extremity index (211.8 °C) among all RCM simulations. Favourable circulation conditions were present also in SMHI-RCA-IPSL, which simulated the third largest total extremity index of major heat waves (159.3 °C). By contrast, only minor changes in circulation during major heat waves were found in SMHI-RCA-HadGEM, indicating that soil–atmosphere interactions play an important role in the major heat waves’ development in this simulation, similarly to CLM-CCLM-HadGEM and to a limited extent KNMI-RACMO-HadGEM. The importance of soil–atmosphere interactions in the RCMs driven by HadGEM possibly originates from the prevailing summertime easterly advection in this GCM, which means that atmospheric circulation is predominantly favourable to high temperature extremes and thus the most extreme major heat waves are mainly triggered by an amplifying effect of the soil moisture deficit.

To sum up, the soil moisture deficit seems to play an important role in the major heat waves’ development inasmuch as the five largest values of total extremity index and duration of major heat waves were associated with the substantial decrease of evaporative fraction during these events (except for SMHI-RCA-IPSL, Tables 3, 4). This lack of soil moisture was also quite well linked to amplified average daily Tmax excesses during major heat waves, while moister conditions were associated with relatively low Tmax excesses (Table 4).

Various patterns of SLP and Z500 were simulated during major heat waves by individual RCMs (Figs. 5, 6). In ERA-Interim, major heat waves were related to a high-pressure system situated north of the Central European domain, causing a warm south-easterly advection, with relatively minor differences between the three major heat waves (particularly the two most severe in 1994 and 2015, cf. Fig. 4, middle row). The SLP pattern was associated with Z500 contours with a wavy pattern, exceeding 5,800 m over Central Europe.

Fig. 6
figure 6

Composite maps of 500 hPa geopotential height (m) during major heat waves in EURO-CORDEX RCMs and ERA-Interim. N number of major heat waves, D total duration of heat waves (days), Ihw total extremity index of heat waves (°C)

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This circulation pattern was reproduced with difficulties, because many RCM simulations had a marked anticyclone (in the SLP field) over Europe (> 1,020 hPa), especially RCMs driven by the CNRM GCM. The position of this high-pressure system determined the origin of major heat waves: CLM-CCLM-CNRM simulated these events with rather a radiative nature (strong negative vorticity), while major heat waves in SMHI-RCA-CNRM were rather driven by advective processes (strong eastern and southern flow). These anticyclones were probably not developed throughout the troposphere, because Z500 was not substantially elevated compared to ERA-Interim.

The Z500 pattern associated with major heat waves was reproduced relatively well in the majority of RCMs (Fig. 6). High-amplitude waves in Z500 contours, resembling a developed Ω-blocking pattern, were present in simulations driven by the MPI GCM. This shape of Z500 contours was linked to the overestimated southerly advection during major heat waves that probably compensated too-moist conditions in these simulations. By contrast, waves in Z500 contours in SMHI-RCA-HadGEM had only low amplitude during major heat waves, suggesting a crucial role of soil–atmosphere interaction in this model simulation. DMI-HIRHAM-ICHEC simulated a pronounced meridional SLP gradient that was linked to anomalous westerly advection during major heat waves (Table 4; Fig. 5), and this pattern was also captured in the Z500 map (Fig. 6).

5 Discussion

5.1 Observed major heat waves and associated meteorological factors

The summer of 2015 was exceptional even at the European scale (Russo et al. 2015), and many stations across Central Europe recorded the highest numbers of very hot days (Tmax ≥35 °C, Hoy et al. 2016). The summer was anomalous also from the hydrological perspective; Orth et al. (2016) reported that it was even drier in Central Europe than the well-known 2003 and 2010 summers, according to cumulative precipitation. The previous 1994 and 2006 major heat waves were the most distinctive since the beginning of temperature measurements in Central Europe (1775 in Prague, according to the sum of Tmax excesses above 30 °C; Kyselý 2010). Together with the 2015 major heat wave this clearly illustrates that recent decades have been exceptional as to summer temperature conditions in Central Europe over the whole period of observed records.

Although Central European heat waves are associated with several circulation patterns (e.g. Kyselý 2008; Tomczyk and Bednorz 2016), all major heat waves analysed in the present study are linked to a similar pattern dominated by positive anomalies of SLP and Z500 centred north to northeast from the Central European domain. This circulation pattern may be preferred for major heat waves’ development due to its persistence, and it is probably related to the so-called Scandinavian blocking, associated with Rossby waves’ breaking events (Michel et al. 2012). In accordance with previous studies (Fischer et al. 2007; Stéfanon et al. 2014), all observed major heat waves were preceded by a precipitation deficit that amplifies Tmax through a reduced cooling effect of latent heat.

Duchez et al. (2016) hypothesised that a North Atlantic cold ocean anomaly in 2015 and the resulting strong meridional sea surface temperature gradient could have triggered a propagating Rossby wave train, causing a stationary jet stream position that favoured the development of positive 850 hPa geopotential height anomaly and temperature extremes over Central Europe during the summer of 2015. A heat wave’s life cycle seems to be more complex, however, since Plavcová and Kyselý (2016) showed that anticyclonic circulation types (with dominant radiative heating due to clear-sky conditions) prevail before the onset of heat waves while southerly and easterly types (in which warm advection plays a more important role) become dominant during heat waves and support their development and persistence.

5.2 Simulated major heat waves and their associated meteorological factors

The joint effect of favourable and persistent circulation and reduced soil-moisture, which is important for the development of major heat waves, was simulated with difficulties. Some RCMs tended to establish a soil moisture-limited regime across Central Europe. This behaviour was reported by Stegehuis et al. (2013) using a previous generation of ENSEMBLES RCMs driven by reanalysis, indicating that this deficiency was not fully solved. The inconsistency is probably linked mainly to biases in the simulation of convective precipitation and surface fluxes in RCMs that use parameterizations and do not resolve these processes explicitly (Jin et al. 2010; Rauscher et al. 2010).

Moreover, this deficiency probably originated not only from the RCMs, because a lack of soil moisture was present especially in those RCMs driven by the HadGEM GCM in our study. The reduced evaporative fraction in SMHI-RCA-HadGEM was surprisingly associated with the largest precipitation during major heat waves among all RCM simulations. Although we do not have a clear explanation for this behaviour, the discrepancy may originate from joint effects of (i) a tendency of the RCA RCM to overestimate precipitation during severe heat waves (Lhotka and Kyselý 2015b), and (ii) the prevailing summertime easterly advection along with low precipitation in simulations driven by the HadGEM GCM (Sect. 4). These contradictory factors may create non-standard interactions between convective and land-surface schemes in this RCM simulation.

Despite the fact that the Tmax excesses were overestimated, the mean magnitude of major heat waves was comparable to observed data. This is related to an underestimated mean number and duration of major heat waves in the RCM simulations, which is in contrast with Vautard et al. (2013) and Plavcová and Kyselý (2016), who concluded that RCMs tended to simulate too-persistent heat waves. These seemingly contrasting results are probably associated with different definitions of events. In our study, we analysed only major heat waves that lasted for roughly two weeks. They probably were related to atmospheric blocking events that are reported to be underestimated in climate models (Scaife et al. 2010), which may be associated with the underestimated duration and frequency of major heat waves in RCM simulations.

5.3 Possible limitations of major heat waves’ analysis

As the study deals with major heat waves, the results need to be discussed with caution due to a relatively small number of events (given the length of observed records and RCM simulations). Only three major heat waves occurred since 1950 in the observed data. The sample size would be larger (in observed as well as RCM-simulated data) with a lower threshold used to delimit events that are considered “major”, but this would draw the analysis from the focus on extreme heat waves (that deserve attention also because the society’s vulnerability to their impacts, which is much larger than in case of ordinary heat waves, Kharin et al. 2007). Similar limitations were encountered by Beniston (2004), who studied modelled events analogous to the 2003 heat wave in Western Europe, and by Barriopedro et al. (2011), who dealt with the 2003 and 2010 heat waves in RCMs.

In addition, main features of SLP and Z500 patterns may be faded in the composite maps due to an averaging of individual major heat waves, especially in those RCM simulations in which land–atmosphere interaction plays a vital role for the development of major heat waves. For example, three of five major heat waves in CLM-CCLM-HadGEM were associated with an enhanced eastern flow, while the other two were linked to westerly advection (not shown). This may contribute to the indistinct SLP field in the composite map in this RCM simulation.

6 Conclusions

Major Central European heat waves in an ensemble of EURO-CORDEX RCM simulations driven by GCMs were analysed. We evaluated their severity and associated meteorological factors against the observed major heat waves (1994, 2006, and 2015) using the E-OBS data set and the ERA-Interim reanalysis. The key findings can be summarized as follows:

  • The summer of 2015 was the most pronounced in Central Europe since 1950 according to the seasonal sum of the heat waves’ extremity index. The most severe heat wave during this summer persisted for 13 days between Aug 3 and Aug 15 and along with the 1994 and 2006 events, it represents one of the three major heat waves that are characterized by long duration and high extremity index. These events are probably exceptional in the context of observed records in Central Europe since 1775.

  • These major heat waves were related to circulation patterns resembling Ω-shaped blocking, which is characterized by reduced zonal flow, allowing meridional advection of warm air masses. Precipitation deficits were also observed during and before heat waves along with reduced evaporative fraction and increased net shortwave radiation.

  • The value of the total extremity index of major heat waves in the ensemble mean was close to observed data, but substantial differences were present in individual RCM simulations. These variations were linked to the representation of large-scale circulation and land–atmosphere interactions. Overestimation of the number and duration of major heat waves in some RCMs was related to a combination of strong south-easterly advection and depletion of soil moisture, while their underestimation was mainly associated with too-moist summertime conditions.

  • In some RCM simulations, the seemingly good reproduction of the total extremity index of major heat waves was erroneously achieved through unfavourable circulation conditions compensated by a substantial lack of available soil moisture and vice versa. Although these mechanisms seem to be physically realistic, no analogous situation was found in the observed data since the mid-twentieth century.

The last point emphasizes the importance of evaluating not only resulting climatological characteristics, but also their associated meteorological factors. It should be noted that successful representation of major heat waves’ driving mechanisms in historical climate does not guarantee a credible simulation of these events in the future climate, but it does provide some guidance for the selection of a suitable ensemble of RCM simulations for further analyses. Although the design of an objective performance metric for RCM simulations is beyond the scope of this article, the CCLM, RACMO, and RCA RCMs driven by the ICHEC-EC-EARTH GCM performed best in simulating the total magnitude of Central European major heat waves and their links to meteorological factors. In other words, the characteristics of major heat waves in these model simulations were most similar to what we observe in the real world.