European heatwaves: Link to large‐scale circulation patterns and intraseasonal drivers

This study examines the European heatwaves' predictability at subseasonal timescales. Land surface feedbacks and tropical convection, due to their variability at intraseasonal timescales, are taken into consideration and their potential role in extending the predictability beyond the medium range (10 days) is explored. A classification of European heatwaves into five heatwave types is used to discriminate the effects of surface feedbacks and of tropical variability among the different heatwave types. The classification is computed in terms of circulation patterns. By inferring the near‐surface temperature through atmospheric circulation, we aim to identify the predictable component of the heatwave events. All five heatwave circulation patterns are characterized by persistent anticyclonic anomalies located over the region with maximum temperatures. We show that soil moisture deficit is not a required precondition for the occurrence of heatwaves over most of Europe. However, heatwave events over southern Europe exhibit some sensitivity to dry conditions. We use a simplified index to describe the dominant mode of tropical convection at intraseasonal timescales. The index, based on precipitation anomalies, represents the evolution of the Boreal Summer Intraseasonal Oscillation (BSISO). We find that episodes with strong BSISO amplitudes characterized by enhanced convection over India, Bay of Bengal and China sea favour the occurrence of heatwave events over Russia. The results highlight the role of tropical intraseasonal variability in enhancing the predictability of some extreme temperature events over Europe.


| INTRODUCTION
Extreme weather conditions such as heatwaves (HWs) have very severe consequences for our society (Brimicombe et al., 2021). They impact our health leading to fatalities such as during the 2003 HW over western Europe that was responsible for over 70,000 additional casualties across 16 European countries (Robine et al., 2008). The 2010 HW and the extreme drought conditions in Russia lead to a reduced crop production and extreme wildfires threatening urban areas. The 2010 HW was predicted about 9 days in advance (Matsueda, 2011).
Subseasonal predictions (between 10 and 60 days) are crucial for the development of early warnings. Since 2013 the Subseasonal to Seasonal (S2S) Prediction project, established by the World Weather Research Programme/ World Climate Research Programme, has been promoting research activity on the subseasonal timescale with special emphasis on high-impact weather. However, subseasonal predictability is intermittent and it depends on the effect of local and remote anomalies evolving on intraseasonal timescales. Therefore, to improve and understand subseasonal forecasts for HW, it is important to identify the sources of their predictability. On seasonal scale, sea surface temperature conditions over the tropical Pacific and Atlantic in spring (Cassou et al., 2005;O'Reilly et al., 2018) have been documented as important drivers for heatwaves. Many synoptic studies have documented the mechanisms behind the day-to-day evolution of heatwaves (e.g., Pfahl & Wernli, 2012). In contrast, the processes that, at intraseasonal timescale, may favour the occurrence of heatwaves have received less attention. The goal of this study is to explore the physical processes that can play a role in extending the predictability of HWs at subseasonal timescales. Since land surface feedbacks and tropical convection exhibit considerable variability at intraseasonal timescales, we focus on the effects of these two processes.
HWs are characterized by persistent anticyclones (Pfahl & Wernli, 2012;Sousa et al., 2018;Stefanon et al., 2012). The clear-sky conditions allow for increased incoming shortwave radiation to diabatically warm the air. Air parcels within the anticyclone experience further warming through subsidence. More recent studies focusing on the Lagrangian perspective highlight the importance of diabatic warming of air parcels through surface sensible heat flux, especially for continental HWs (e.g., Russia; Zschenderlein et al., 2019). The coupling with the land surface is important, as in wet conditions latent heat flux through evapotranspiration dominates over sensible heat flux, leading to a cooling of the surface. During low soil moisture conditions however, latent cooling through evapotranspiration is inducing positive feedback which further enhances maximum temperature extremes (Ferranti & Viterbo, 2006;Hirschi et al., 2011;Miralles et al., 2014;Miralles et al., 2019).
Tropical intraseasonal variability has been shown to be an important source of predictability for boreal winter extratropical weather (Cassou, 2008;Ferranti et al., 1990;Lin et al., 2009, among many others). During the boreal summer, the role of intraseasonal tropical variability in enhancing predictability of extreme weather over Europe is less clear and not widely documented. The dominant mode of tropical intraseasonal variability consists of an eastward propagating pattern of alternately intense and weak tropical convection and precipitation primarily over the Indo-Pacific region (Madden & Julian, 1971, 1972. During boreal winter it is known as the Madden-Julian Oscillation (MJO). During the boreal summer it assumes a more complex structure and it is referred to as the Boreal Summer Intra-Seasonal Oscillation (BSISO) (Kiladis et al., 2014;Lee et al., 2013). Apart from the eastward propagation, the BSISO also propagates poleward over the Indian Ocean and the western North Pacific, with the northern branch being significantly stronger than the southern branch (Lawrence & Webster, 2002). The northward propagating BSISO component influences the active and break periods and even the onset of the East Asia summer monsoon.
Anomalous diabatic heating, associated with this dominant tropical mode, excites global-scale Rossby wave (RW) trains that propagate across Southeast Asia and the extratropics (Matthews et al., 2004;Stan et al., 2017). During the boreal winter, those wave trains project onto the Pacific North America and North Atlantic Oscillation patterns (Ferranti et al., 1990;Scaife et al., 2017). Since those are teleconnection patterns (Wallace & Gutzler, 1981) explaining a sizeable portion of the extratropical winter variability, the tropical-extratropical interactions are well defined and therefore largely documented. There are studies documenting the effect of tropical heating anomalies on the atmospheric circulation over extratropical North Atlantic leading to temperature anomalies over Europe (Cassou et al., 2005;O'Reilly et al., 2018). In contrast, during boreal summer, the tropical-extratropical interactions on intraseasonal timescale have attracted less interest. It is therefore relevant investigating the role of tropical heating in initiating and/or maintaining HW events.
Because accurate predictions of HW events are linked with the ability to forecast the time evolution of the atmospheric flow. Predictions beyond 2 weeks are more likely to capture the circulation patterns associated with temperature extremes than to represent the real extend of anomalous surface weather (Ferranti et al., 2018;Mastrantonas et al., 2021). Since the focus is to explore the HW predictability at intraseasonal time range, the HW events are characterized using atmospheric circulation patterns. The HW predictability is then explored by considering the role of local surface feedbacks and tropical convection (BSISO) in initiating and/or maintaining those patterns.
Section 2 describes the data and methodology used for the HW definition. Section 3 presents the results of the HW identification and the connection to the largescale circulation. Section 4 investigates the role of local land-surface and tropical intraseasonal variability. Section 5 summarizes the main findings and discusses the potential outcomes of this study.

| DATA AND METHODS
This study uses the ECMWF ERA5 reanalysis data (Hersbach et al., 2020) covering the May-September period from 1979 to 2020. Daily mean values of 2-m temperature (2mT), daily maximum and minimum temperature and daily geopotential height at 500 hPa (Z500) are used to characterize the HWs structures that typically occur over the European region (30 -80 N, 25 W-60 E). The analysis is based on a horizontal resolution for the surface variables of 0.25 × 0.25 and a resolution of 1 × 1 for the Z500, as it describes the large-scale circulation.
The volumetric soil water, available for evapotranspiration, is used to explore the land surface feedbacks. The evapotranspiration efficiency depends on vegetation. If the soil water content decreases below the permanent wilting point (PWP), the plants wilt. Consequently, when the soil water content is below the PWP, there is no transpiration and little to no evaporation. The field capacity (CAP) is the maximum amount of water that the soil can hold. Based on the above considerations, the soil wetness index (SWI) is defined as It represents the fraction of volumetric soil water available for evapotranspiration with Sm being the soil moisture in the layer of soil considered (Barbu et al., 2011). Between PWP and CAP evapotranspiration efficiency increases linearly from nil as the volumetric soil moisture increases, to reach 100% at CAP. Above CAP, evapotranspiration efficiency will stay at 100% as the exceeding water is converted as runoff and not available for evaporation. The SWI is computed for a soil layer of 1 m depth. ERA5 reproduces variability in soil moisture well with limitations over inhomogeneous soil and topography making it suitable for soil moisture considerations (Li et al., 2020).
Since intraseasonal tropical variability is characterized by large-scale patterns of organized convection and enhanced tropical rainfall, it is widespread practice to use variables such as precipitation, outgoing longwave radiation (OLR) and upper-level divergence over a tropical band to describe it (Kiladis et al., 2014;Lee et al., 2013;Madden & Julian, 1972). Total precipitation between 30 N and 30 S is used to represent the variability of tropical convection associated with BSISO and monsoon circulation. To isolate the intraseasonal component, the extended summer mean total precipitation of each year is removed as well as the seasonal cycle as done in Lee et al. (2013). Five-day means are used to reduce the noisiness of the precipitation field. The resulting anomalies are used as input for an empirical orthogonal function (EOF) analysis.
Total precipitation from ERA5 short-range forecast has already been used in numerous studies (De Luca et al., 2020;Mastrantonas et al., 2021). Mastrantonas et al. (2021) showed that ERA5 and E-OBS dataset (Cornes et al., 2018) give equivalent results. Hersbach et al. (2020) also compared ERA5 precipitation data with the TRMM Multi-satellite Precipitation Analysis 3B43 dataset. The authors showed that ERA5 dataset suffers from larger errors over the Intertropical Convergence Zone. The total precipitation is calculated following the approach by Mastrantonas et al. (2021) by using the accumulation of the forecast steps 7-18 for the models initiated at 1800 UTC of the previous day, and at 0600 UTC of the day in question. This reduces errors from spin-up of the forecast model outputs (Dee et al., 2011).

| Heatwave detection
For the detection of HW events we follow the method described by Stefanon et al. (2012) and use the daily mean 2mT. The climatological distribution for a given grid-value and for a given day (d) is estimated by sampling the corresponding grid-value over a window of d − 5 to d + 5 for the years 1979-2020. In this way, for a given grid-point, a sufficient sample (11 days window × 42 years = 462 values) is used to represent the climatological distribution of temperatures.
An individual HW event is identified when for a radius of 500 km at least 90% of the grid points exceed the 90th percentile of the climate distribution (described above) for at least four consecutive days. The minimum persistence of 4 days is in line with previous studies (Stefanon et al., 2012;Zschenderlein et al., 2019) and generates large enough sample of heatwaves to perform significant statistical analysis.
After some testing, we find that a radius of 500 km is a reasonable choice to filter out the smaller spatial scales and to represent the synoptic structures. To obtain a sufficiently large sample, we use the 90th percentile of the climate distribution. We tested the scheme requesting that either 80%, 90% or 99% of the grid points exceed the given temperature threshold. Noting a large sensitivity to this parameter, we choose 90% because the sample obtained with this value is comparable with results from other studies (Stefanon et al., 2012). Additionally, the propagation of heatwaves is accounted for by including neighbouring regions that match the three criteria and overlap by at least 60% over the original region. Consequently, if neighbouring regions have simultaneous heatwaves, they are considered as one.
This methodology filters out small-scale and shortlifespan events. The time persistence and homogeneous spatial structure of these events allows for them to be predicted at the extended forecast range (Vitart & Robertson, 2018) and have an impact on society. Over the 42 extended summer periods, 120 HW events including 798 HW days are identified.
The robustness of the results is assessed by applying the same methodology for daily maximum and minimum 2mT. Daily maximum is widely used to define HWs (Frich et al., 2002;Russo et al., 2015;Stefanon et al., 2012;Zschenderlein et al., 2019). Daily minimum temperature is a proxy for night-time temperature. Elevated night-time temperatures are one of the key ingredients in causing heat-related illnesses and mortality (Fischer & Schär, 2010;Gabriel & Endlicher, 2011;Murage et al., 2017). For an easier comparison between attributions, we compare heatwave days. By using daily maximum temperature, 1057 HW days are detected and 70% coincide with the daily mean temperature HWs. By using the daily minimum temperature, a smaller amount of HW nights (726) are identified and 85% coincide with the daily mean temperature sample. Considering the above results, we decided to focus on the analysis of the HW sample based on daily mean temperature since it represents the major HW in both day and night-time.

| Classification of heatwave patterns
A K-means clustering algorithm is applied to the HW days using Z500 anomalies to characterize typical HW circulation patterns for the European region. Cluster analysis is a conventional tool in atmospheric sciences used to objectively identify midlatitudes weather patterns (Hannachi et al., 2017;Michelangeli et al., 1995, among many others). The K-means clustering algorithm is widely used (Straus et al., 2007). For a given number K, through several iterations, it identifies the optimal partition of the data into K clusters. The optimal partition is the one that maximizes the ratio of the variance among cluster centroids to the average intracluster variance, using the Euclidean distance.
Since clustering techniques are more effective when applied in a reduced dimensional phase space, the HW days are projected onto a lower dimensional coordinate system represented by EOFs. The clustering is carried out in the phase space defined by nine leading EOFs of Z500 explaining about 80% of the total HW days variance. Clustering is applied to the 120 HW events (defined as the average of the uninterrupted sequence of HW days). Based on the spatial scale of the HW and the domain of interest, a maximum of six clusters are explored. Using the Davies-Bouldin score (Davies & Bouldin, 1979), defined as the ratio of within-cluster to between-cluster distances, we obtain that five is the optimal number of clusters. The robustness of the classification has been evaluated by a cross-validation procedure. Clustering is applied 100 times to a random subset of 80% of the elements. Each new set of clusters is associated to the original clusters using the Euclidean distance and a visual inspection of the composites (similar to Figure 1) confirms the similarity between the original and new clusters. This allows to compare which events are correctly attributed and avoids overfitting. The results show that more than 80% of the events are classified in the same clusters as in the original classification.
The resulting clusters are then used as reference spatial structures to compute daily indices.
The HW events, as identified in section 2.1, are characterized by a sequence of days with extreme temperatures representing therefore just the mature stage of the HW event. In order to have a realistic representation of the HW evolution, some additional days representing the onset and decay phases are included. The onset/decay definition is based on daily indices (daily projections onto the reference spatial structures). Determining the onset of the HW is key to identify the triggering processes of HWs. The indices are standardized projections of the daily 2mT anomaly field onto the composite 2mT anomaly of each cluster (Michel & Rivière, 2011). The onset (decay) is defined as the first set of three (two) days before (after) the mature phase of a HW with a positive (negative) derivative of the corresponding index.
Daily circulation indices specific to each cluster are created in the same way but using the nine EOFs. The indices give us an indication of the daily state of the atmosphere relative to the circulation patterns.
Each day is classified in either one of the HW circulation patterns using the indices. The largest projection of the day is selected and if exceeding the standard deviation, the corresponding pattern is attributed to the day. If none of the indices exceed the standard deviation, this day is categorized as a "no regime" day which indicates that none of the patterns are well defined. This categorical attribution allows us to investigate the relationship between HWs and their associated circulation patterns.

| HEATWAVE TYPES AND THEIR RELATION TO CIRCULATION PATTERNS
The results of the clustering are discussed in the following sections. The aim is to investigate the relationship between the main HW types and their corresponding atmospheric circulation, and the role of the latter as predictor for HWs. Figure 1 shows the five HW patterns obtained by clustering. The patterns are represented as composites of 2mT and Z500 anomaly of events of each cluster. Each cluster is named based on the location of the 2mT anomaly besides the Tripole cluster, which is named based on the atmospheric circulation, characterized by two anticyclonic and one cyclonic anomalies in between.

| Heatwave types description
All five clusters are characterized by a strong anticyclonic anomaly over the positive temperature anomaly. The Scandinavian cluster (SC) has a strong 2mT anomaly (>5 K) over Scandinavia and includes the July 2003 and 2018 HWs (Spensberger et al., 2020). The south European cluster (SE) has a larger spread but weaker 2mT anomaly (3-4 K) over south central to east of Europe. The Russian cluster (RU) is characterized by a strong 2mT anomaly (>5 K) over Russia and exhibits a remarkably similar structure to the 2010 HW included in this cluster. The western Europe (WE) cluster is defined by a 2mT anomaly (4-5 K) spread across France and the British Isles. Both 2003 HWs (June and August) are part of this cluster (Schär et al., 2004). The Tripole cluster stands out with a strong 2mT anomaly (>5 K) over southern Russia and a weaker anomaly over the Iberian Peninsula (2 K). The structures of the circulation patterns related to the HWs are similar to blocking anticyclone structures such as omega (RU, WE, Tripole) and diffluent blockings (SC, SE). This can be seen by extending the domain eastward (Tripole, RU) and westward (WE; not shown). This is consistent with previous studies highlighting the relationship between summertime warm temperature extremes and blocking anticyclones (Pfahl, 2014;Pfahl & Wernli, 2012;Sousa et al., 2018). Figure 2 summarizes the results for the HWs with their full life cycle. The number of HWs across the clusters is evenly distributed, with SC, Tripole, SE and WE clusters grouping 22, 21, 22 and 20 HWs, respectively. The RU cluster includes however 27 HWs and the largest amount of HW days with 473. The SC cluster groups a similarly large amount of HW days with 417 days, while Tripole, WE and SE clusters have only 377, 347 and 335 days, respectively. Differences are also visible in the length of the HWs (Figure 2c). The median length of HWs is slightly above 15 days, with the SC cluster standing out with 19 and with the largest spread. Figure 2d shows the distribution of HW days across the extended summer months for each cluster. The months of April and October are included as HWs with full life cycle can extend to late April and early October. Tripole HWs mostly occur at the end of the summer (August-September), while the SC HWs occur mainly in the middle of summer (July) and the SE HWs are more frequent in the early summer (May-July). The RU HW type has a more homogeneous distribution with only the month of May having more HW days. Lastly, WE HW days are mostly distributed in May, June and August. Using conditional probability, the relationship between the occurrence of HWs of different types is investigated. The probability of HWs to occur 2 weeks after another HW is assessed and compared with the probability of occurrence of HWs within a 2-week period ($5%). Following SE, WE and Tripole HWs, some HWs have a higher likelihood to occur (not shown). WE and SE have 10% chance to occur after a SE HW. SC HWs have 10% chance to occur after Tripole events. The more striking result is a 20% probability for RU HWs to follow WE HWs. This shows, compared to climatology, an increased likelihood for some HW types to occur after other HWs by up to four times. The link between HW types can be explained by the general eastward propagation due to the prevailing westerlies and by the geographically close location of some HW types. However, due to the limited sample size, the result is not statistically significant.
In the context of a warming climate, not only the shift towards warmer temperature but also the increased variability leads to an observed increase of frequency of HWs in Europe (Schär et al., 2004). In recent decades, Europe has experienced an exceptional number of pronounced HWs (Alexander et al., 2006;Meehl & Tebaldi, 2004), which can be attributed to anthropogenic global warming. Figure 3a shows the climatological distribution of HW days across the study period of 1979-2020. A positive trend is apparent. During the first two decades the European region recorded on average 21 HW days per year compared to 72 in the last decades. This trend is however not homogeneous as WE and RU clusters show no significant trend (using a 2-tailed test at 95th percentile) with an increase by a factor of 2 while the SE shows the strongest increase with HW days being 7 time more frequent. This inhomogeneous increase in HW frequency is confirmed by other studies and in line with climate projections (Fischer & Schär, 2010). Figure 3b shows the extended summer 2mT difference between the last and first two decades. The differences highlight an inhomogeneity in summer temperature increase. The southern and more continental part of Europe shows the highest warming, corresponding with the stronger HW days frequency increase over SE. The SWI shows similar patterns with stronger decrease of SWI (i.e., stronger drying) over southern and continental Europe, indicating a strong link between 2mT and land surface conditions. Because the HW detection is based on temperature anomalies with respect to a climate averaged over the whole 42 years period, we can assume that the HW days frequency increase is associated with the effect of the nonstationary climate.
Lastly, we look at the relationship between the distribution of HW days for each summer and the corresponding seasonal average temperature. The 2mT anomaly is integrated over our region of study and averaged over each summer. The correlation between the averaged summer temperature and the number of HW days is of 0.79. Out of the 10 warmest summers, 7 are among the top 10 years with the highest count of HW days. It follows that the frequency of HW days is closely related with the summer average temperatures.

| HW circulation patterns
In the following section, we analyse the relationship between HWs and their associated circulation patterns using the categorical attribution introduced in section 2.2.
This classification allows us to determine the climatological frequency of HW circulation patterns across the summer and their correlation to HWs. Figure 4a shows F I G U R E 3 HW climatology over the European region between 1979 and 2020 with cluster attribution.
(a) Distribution of the HW days across the study period with 5 years running mean (black line). (b) Difference in summer daily mean 2mT ( C) between the last two decades (2001-2020) and the first two decades  [Colour figure can be viewed at wileyonlinelibrary.com] the climatological summer frequency of each circulation pattern. Each of the circulation types account for 14%-16% of the atmospheric variability during summer. We observe however that only 20%-25% of the circulation days do coincide with HWs. In Figure 4b, the average persistence of the circulation patterns is shown stratified by whether they coincide with HWs or not. The persistence of circulation patterns is on average longer when coinciding with HWs. For example, the SC circulation type is on average twice as long, from less than 4 days outside HWs to more than 8 days when coinciding with HWs. Across all clusters we observe that outside HWs, the circulation patterns persist on average 3 days or less while when coinciding with HWs they persist for 5 days or longer. To investigate this further, Figure 5 compares the frequency of occurrence of the circulation patterns coinciding with HWs. The occurrences are displayed for the full sample, for the circulation patterns persisting for less than 4 days and for at least 5 days. Only 5% of HW events coincide with short-lived circulation patterns. In contrast, about 20% of HW events, more than 30% for the RU, Tripole and SC HWs coincide with long-lived circulation patterns. Longer circulation patterns are up to five times more likely to coincide with HWs. Longer persisting patterns account for only 33% or less of all patterns, therefore representing a significantly higher probability of HWs. The difference in frequencies between shortand long-lasting circulation patterns highlights the link between extreme warm temperatures anomalies and persisting local anticyclones, consistent with previous literature (Perkins, 2015;Pfahl, 2014;Sousa et al., 2018;Stefanon et al., 2012). An analysis of the trend of the different circulation patterns both in their frequency and persistence across the study period, identified no significant trend that could influence the increased frequency of HWs The categorical attribution of the different patterns showed that HWs are coinciding primarily with longer persisting circulation patterns, further highlighting the importance of persisting anticyclonic conditions (Perkins, 2015;Pfahl, 2014). This suggest that the identified circulation patterns could play the role of predictors.
Other sources of predictability can play an important role, such as local soil moisture conditions and tropical enhanced convection. These will be investigated in the following section.

| POTENTIAL SOURCES OF PREDICTABILITY AT INTRASEASONAL TIMESCALE
Many different processes influence HWs at longer timescales. Slow varying fields such as the sea surface temperature in the northern Atlantic (Cassou et al., 2005) and low-frequency modes, in particular ENSO (Schneidereit et al., 2012) and the NAO (Blunden & Arndt, 2012) influence the occurrence of HWs on a longer, seasonal range.
The following section explores potential HW drivers at subseasonal range. The two main processes with considerable variability at intraseasonal range that are known to affect the surface weather conditions over Europe are associated with the local land surface feedbacks and with the response to tropical convection via RWs.
Over Europe, previous studies have focused on the role of local soil moisture conditions. They find that low soil moisture conditions are responsible for extreme warm temperatures during summer (Seneviratne et al., 2006). Lorenz et al. (2010) further shows the role of reduced soil moisture in the increased persistence of HWs. The connection is especially relevant for very extreme warm temperatures such as during the 2003 HW over western Europe and the 2010 HW in Russia (Ferranti & Viterbo, 2006;Fischer et al., 2007;Miralles et al., 2014). This connection has however been shown to be event and region-dependent (Stefanon et al., 2012).
Considering the current state of the research this section focuses on land surface feedback (section 4.1) and on tropical heating variability (section 4.2). The aim is to assess their systematic influences across the identified HW types and their relevance at the extended range.

| Land surface
Soil moisture preconditioning has been shown in previous studies to have important interactions with HWs (Ferranti & Viterbo, 2006;Seneviratne et al., 2006). Using the SWI introduced in section 2, we investigate the systematic effect on HWs. The SWI is integrated over the regions of highest positive 2mT anomalies for the different clusters. Two regions are considered for the Tripole cluster (Iberian Peninsula and southern Russia). The integration allows to investigate the local effect of soil moisture on HWs. However, the fixed region of each cluster does not account for HW variability and in some rare cases could correlate HWs that do not overlap fully with the region. Figure 6 compares, for each HW type, the SWI distributions at onset, end of mature phases and outside HWs. A Gaussian kernel has been used to smooth the distribution. For all HW types, except for WE, the SWI distribution, at the end of the mature phase, is significantly shifted towards drier conditions compared to the climatology (see Table 1). This shows the effect of HWs on the surface conditions. At the onset, the shift towards drier conditions is less evident and region-dependent. In fact, only the Tripole and SE HW types exhibit drier F I G U R E 5 Frequency of occurrence of the five HW circulation patterns including only the days when the HW is on. The occurrences are displayed for the full sample (forward slash bar) and for the circulation patterns persisting for less than 3 days (dotted bars) and for at least 5 days (backward slash bars) [Colour figure can be viewed at wileyonlinelibrary.com] distributions with significantly lower median SWI compared to the climatology. The Tripole has the smallest shift among the two HW types. However, the integrated SWI is climatologically low in both distributions, indicating that in summer these regions are rather dry, limiting the evapotranspiration. This allows for feedback between land and atmosphere to occur during anticyclonic conditions. For SC HWs, local soil is close to saturation at onset. Areas where soil moisture conditions are close to saturation have a weak dependence between soil moisture and evaporation rate. The RU HWs have a small shift towards higher SWI values which could be explained by a majority of HWs starting in the early part of the summer (late April to early May; Figure 2d).
The results show that dry soil conditions, at onset, are not systematic and are region-dependent. During dry conditions, the temperature is sensitive to the atmospheric circulation (Quesada et al., 2012) integrated SWI of 0.3 at onset. For northern regions, evapotranspiration is rarely limited by soil moisture content; therefore, soil moisture preconditioning does not play a significant role in HW occurrence. Southern regions however show some sensitivity to drier conditions at onset. The regional dependence has been observed previously with southern Europe being more sensitive to land surface feedback (Perkins, 2015;Quesada et al., 2012;Stefanon et al., 2012). Soil moisture preconditioning can therefore not be used as predictor of HWs. It could be used, in conjunction with the occurrence of persistent anticyclones to provide warning of extreme warm conditions (Quesada et al., 2012). The more significant shift after HWs represents the impact of continued suppressed precipitation during anticyclones and increased temperature. This highlights the role of HWs, especially longer HWs, as contributor to droughts.
Local soil moisture preconditioning is not a systematic source of predictability. In the next section tropical convection is investigated as source of predictability.

| The boreal summer intraseasonal oscillation index
European HW events have been linked to the effect of tropical convective activities. For example, Cassou et al. (2005) discussed how warm conditions over western Europe could be associated with convective anomalies over the Caribbean via RW train patterns.
Increased heating over the Tropics is linked with changes in the RW activity (Scaife et al., 2017). ENSO and MJO can enhance RW activity (Lee et al., 2019). RWs are considered teleconnection pathways involved in regime transitions (Michel & Rivière, 2011) and more particularly in blocking establishment and maintenance (Masato et al., 2012). Atmospheric blockings have been shown to be key drivers of HWs (Pfahl & Wernli, 2012;Sousa et al., 2018;Stefanon et al., 2012) highlighting the importance of analysing tropical precipitation in relation with HW occurrence. Several authors (Di Capua et al., 2021;Lau & Kim, 2012) highlighted the link between enhanced convection over Pakistan with the persistence of the Russian extreme hot event in 2010. In this section we investigate the link between the BSISO evolution in conjunction with the occurrence of the HW types previously identified.
The BSISO index, used in this study, is a simplified version of the one used by Lee et al. (2013) and it is based on the first two leading EOFs (explaining 6% of the variance) of detrended total precipitation from ERA5 (see section 2). Both EOF patterns exhibit a large-scale coherent structure over the Indian Ocean, Indonesia and across the Equatorial Pacific. The correlation between the two corresponding time coefficients (not shown) indicates that the maximum modulus of correlation exists with a lag/lead of about 10 days, suggesting that EOF1 and EOF2 describe an oscillation with an average period of 40 days.
The BSISO cycle described by the two EOFs is shown in Figure 7. The strong precipitation anomalies over Indian Ocean (Figure 7a) propagate eastwards towards Indonesia, New Guinea and northwards over India (Figure 7b). Subsequently, with the precipitation propagating north, the anomalies develop into a North-South dipole structure with enhanced convection to the north and decreased convection to the south (Figure 7c). During the last phase of the BSISO cycle ( Figure 7d) the precipitation anomalies start to develop over the Indian Ocean while dry anomalies develop over India.
The BSISO life cycle in Figure 7 is consistent with the description given by the multivariate BSISO1 index by Lee et al. (2013). In particular, the BSISO1 phases P2, P4, P6 and P8 depicted in their fig. 9 exhibit similar spatial structures to the ones in Figure 7. The BSISO1 average period is about 40 days (Lee et al., 2013) consistent with the one estimated by our BSISO index. The spatial structures of the two leading EOFs used to describe the BSISO cycle also match well the ones found by Kiladis et al. (2014). Although their analysis was limited to 20 N-20 S, by considering the whole longitudinal domain they showed the BSISO structures over the Central and East Pacific. Features of particular interest are the link between anomalous suppressed/enhanced convection North of the Equator around 120 -80 W with the enhanced/suppressed convection over India and maritime continent (Figure 7b,d) and the longitudinal extend of the wet anomalies of the North-South dipole structure (Figure 7c) reaching the Central Pacific.

| How some BSISO phases could favour the occurrence of heatwaves
To investigate whether the HW occurrences can be associated with the variability of tropical convection, we examine the BSISO daily evolution during the 14 days preceding HW onset. Figure 8 shows the time evolution of the daily precipitation anomalies in the twodimensional phase space defined by the two leading EOFs used to define the BSISO cycle. This simple view is widely used to monitor the time evolution of intraseasonal tropical variability (Lee et al., 2013;Wheeler & Hendon, 2004). The BSISO evolution preceding the HW onset is computed for all the HW events. The BSISO cycle follows anticlockwise trajectories around the origin, indicating systematic eastward and northward propagation of convection/precipitation. Large amplitudes (values outside the ellipse) signify strong BSISO cycles while the lines near the origin indicate weak BSISO activity. The BSISO exhibits large amplitudes for many of the RU HW events (Figure 8a) with the BSISO staying in phases 2 and 3 for 7 and 14 days preceding HW onset. Excluding the cases with small amplitudes (cases inside the ellipse), 13 out of the 17 HW onset days (stars) are in the upper and lower right quadrant. Looking at 7 days before the HW onset, 9 out of 15 cases (square) are in the lower right quadrant. While 14 days preceding the onset (triangles), 8 out of 16 cases are in the lower left quadrants. Although those cases are not necessarily sequential, they indicate BSISO phases 2 and 3 as the predominant BSISO phases during the days preceding the HWs over Russia. The nine trajectories (coloured lines) provide further evidence that for one third of the RU HWs, during the preceding 14-7 days, the BSISO is strong and tends to be in phases 2 and 3. For the other HW types (Figure 8b-e) the BSISO amplitudes are, in comparison smaller. However, there are still few HW events that can be associated with strong BSISO activity. Excluding the weak BSISO cases, 7 out of 10 SC HWs (Figure 8b) populate the lower half of the plot. Cases in the lower left quadrant tend to follow a similar evolution to RU cases, while the others are stationary or subside. Eight out of nine WE cases are concentrated in the lower and upper right quadrants and exhibit little propagation, except for the June 2003 case. For SE, 8 out of 12 cases are spread across the lower right and upper left quadrants and exhibit a limited propagation except for the 2015 event. Lastly, the Tripole HWs show an almost even distribution within each quadrant. The upper left quadrant is slightly more populated with 5 out of 13 events.
Many studies (Gill, 1980;Hoskins & Karoly, 1981;Sardeshmukh & Hoskins, 1988) have shown that tropical diabatic heating source can excite RWs that, propagating into the midlatitudes, can significantly modulate the extratropical circulation. The lower/upper-level convergence/divergence, induced by tropical convection, produces an anomalous vorticity source in the Tropics. The upper-level component of this vorticity source triggers a RW train.
For the HW characterization, upper-level synopticscale RWs are particularly relevant, since they interact with cyclones and anticyclones, impacting extreme temperatures at lower levels (Fragkoulidis et al., 2018;Wirth et al., 2018). Schubert et al. (2011) underlines the key role F I G U R E 8 (Continued) of stationary RWs in the monthly temperature variability and specifically in the 2003 and 2010 HWs. RW breaking is also known to be a key process in blocking occurrence (Masato et al., 2012).
To illustrate the link between the summer tropical convection anomalies, associated with the BSISO activity, and the HW circulation patterns in the extratropics, we examine the RU HW initiated on the August 11, 2007. This case exhibits the strongest BSISO evolution. Figure 9 shows the daily mean geopotential height anomalies at 250 hPa and precipitation anomalies for the August 4, 2007. To highlight both eastward and westward propagation of RWs, the geopotential height has been filtered by retaining only the first six zonal wave numbers. In fact, considering the barotropic RW dispersion relation, the summer climatology is such that, for large zonal wave numbers, westward propagation is allowed (Hoskins & Ambrizzi, 1993;O'Reilly et al., 2018). Figure 9 indicates RWs from India propagating northward and westward and from Equatorial East Pacific moving eastward. The spatial distribution of precipitation anomalies, with wet conditions over India, Vietnam and Philippines, is consistent with the BSISO in transition from phase 2 to 3. We have analysed several strong BSISO cases (not shown) and, in all of them, we detect wave trains propagating northward and westward stemming from either India, Bay of Bengal or the China sea depending on the BSISO transition state between phase 2 and 3. Consistent with Cassou et al. (2005), most of the cases present also RWs propagating eastward originating from East Pacific and Caribbean. The case in Figure 9 illustrates how the BSISO phases 2 and 3 during the preceding 7 days of the HW onset can play a role in sustaining persistent high-pressure systems. Although the BSISO signal is stronger during RU HWs comparing with the other HW types, the tropical convection anomalies can influence the development of any HW types (Cassou et al., 2005).
To highlight the role of tropical convection as source of predictability, we have considered the ensemble spread from a set of ECMWF reforecasts (https://confluence. ecmwf.int/display/FUG/Forecast+User+Guide) in operation between April and September 2019. The advantage of using reforecast data versus the real-time forecast is that we are dealing with the same forecasting system for all the predictions. Each reforecast is an ensemble of 11 members: one control and 10 perturbed members. The forecast is produced twice per week. The ensemble spread is an indicator of forecast uncertainty therefore the rate at which the ensemble spread grows can be viewed as a predictability estimate (Ferranti et al., 2018). When the ensemble spread grows slowly/rapidly with lead time, the predictability is higher/lower. As RU HWs show the strongest link with specific BSISO phases, namely BSISO phase 2 and 3 (see Figure 8), the impact of the BSISO on predictability for RU HWs is investigated further. Figure 10 shows the ensemble spread in terms of the circulation index at different lead time, for two groups of RU HWs. The first group includes forecasts for five HWs with the strongest BSISO activity, while the second group consist of forecasts for five HWs with inactive BSISO. All forecasts initial conditions, targeting the first HW group, exhibit considerable tropical anomalies consistent with an active BSISO state. In contrast, the second HW group predictions are initialized during a nonactive BSISO. Therefore, the source of predictability, associated with the BSISO, is likely to play a role only in the first group of forecasts. The ensemble spread computed as the standard deviation among the ensemble members is evaluated at each HW's onset and during the successive 3 days. The ensemble spread beyond Day 7 is, on average, reduced for the HWs with strong BSISO (Figure 10a) compared with the HW cases during inactive BSISO (Figure 10b). The difference between both groups is significant at 95th percentile level at lead time of 14 and 21 days. This result suggests that the enhanced predictability level in the first group of HWs forecast is associated with the BSISO large-scale tropical anomalies. Although the signal is not statistically significant, we also find that the root-mean-square errors (RMSE) of the predictions with strong BSISO are smaller than the ones with inactive BSISO (not shown). We have noticed that the forecast ensembles for the 2007 HW case (see Figure 9) exhibit low uncertainties, but that their RMSE is greater than the RMSE average value. This case should be further explored since it could provide some insight about model error associated with tropicalextratropical interactions.
Within this section, the impact of subseasonal sources of predictability, local soil moisture conditions and tropical enhanced convection, has been investigated for European HWs. Dry soil, by favouring the amplification of warm temperature, has been long considered as a source of predictability for HWs (Dirmeyer et al., 2018). Forecast initialized with the correct land surface conditions can represent better the severity of the warm temperature anomalies (Ferranti & Viterbo, 2006). However, the land surface feedbacks are not necessary in the development and maintenance of HWs (Quesada et al., 2012). It follows that not all HW events exhibit dry soil condition at the onset. The role of tropical convection in enhancing the HW predictability has been less explored. By looking at the BSISO activity for some HWs, we can trace RWs originating in the Tropics and propagating into Europe. Like the land surface feedbacks the tropical convection can, in some cases, be relevant for the HW development. Since land surface feedbacks and the effect of BSISO activity on the extratropic are processes that work on the intraseasonal timescale, both are potential sources of predictability for subseasonal predictions.

| CONCLUSIONS
The focus of this study is to explore the European HW predictability at the intraseasonal timescale. For this reason, we limit the analysis to the effects of land- atmosphere feedbacks and tropical intraseasonal variability. A classification of European heatwaves into five HW types is used to discriminate the effects of surface feedbacks and of tropical variability among the different HW groups. The identification of HW events, based on 2mT, is such that only HW events lasting for at least 2 days with a spatial scale of the order of 1000 km are considered. Since, at the extended range, the predictable signal for severe and persistent extremes is better exploited using flow patterns (Ferranti et al., 2018;Mastrantonas et al., 2021), the HW types are classified in terms of circulation patterns, using Z500. By inferring the surface temperature through circulation, we aim to identify the predictable component of HW events. In addition, by using HW circulation patterns, we can directly highlight the effect of tropical-extratropical teleconnections. All five HW circulation patterns are characterized by persistent anticyclonic anomalies located over the region with maximum temperatures. Using indices, a categorical attribution of the identified patterns allowed to quantify their relation to the HWs. Longer persisting circulation patterns coincide with HWs up to five times more than shorter circulation patterns. This highlights the importance of persisting anticyclonic conditions (Perkins, 2015;Pfahl, 2014;Sousa et al., 2018;Stefanon et al., 2012) for HW occurrence and therefore their role as predictors.
The distribution of HW frequency across the 42 years period shows an increase during the most recent 20 years. Most of the increase is observed over the southeastern part of the European domain consistent with the stronger warming of the recent two decades.
The probability of HWs within 2 weeks after another HW has been investigated. This showed an increased probability for some HW types to occur after other HWs. Specifically, RU HWs have a four times higher probability compared to climatology to occur after WE HWs. This can be explained by the eastward propagation due to prevailing westerlies. These results, even if their significance is limited, could be used to add confidence in the prediction of some HWs.
By comparing the distribution of local soil water content at the onset of HWs with the corresponding climatological values, we find that drier than normal soil conditions are typical precursors for southern European HWs. For the other HW types the evidence of land surface being a precursor for HWs is weak. In contrast, all HW types lead to drier conditions, thanks to persistent anticyclonic conditions preventing precipitation and to prolonged warm temperatures. This latter result highlights the possibility that particularly prolonged HWs can favour the occurrence of droughts.
We have constructed a BSISO index, based on tropical precipitation, to explore the relationship between HWs and the different BSISO phases. Looking at the time evolution of the BSISO index, during the days preceding the HW onset, we notice that for many of the HWs over Russia the BSISO is particularly strong and coherent. In addition, during the preceding 7-14 days of the onset, we identify a preferred BSISO state. For one third of all RU HW events, the BSISO is strong and, during the preceding 7-14 days of the onset, tends to be in BSISO phases 2 and 3. The transition between BSISO phase 2, characterized by enhanced precipitation over India and Maritime continent, to phase 3, defined by enhanced precipitation over Bay of Bengal and China sea, favour the occurrence of HWs over Russia. These results are consistent with studies that documented the importance of enhanced convection over northern India and Pakistan for the Russian HW in 2010 (Di Capua et al., 2021;Lau & Kim, 2012).
The BSISO cycle is significantly stronger and more coherent for RU HWs and, to some extent, for the SC HWs compared with the BSISO evolution during the SE, WE and Tripole HWs. However, among each HW type, there are few events that stand out for their large values. This indicate that the effect of tropical-extratropical interaction, although not systematically present, could still play a role for any of the HW types.
We use the RU HW of August 2007 to illustrate the effect of BSISO phases 2 and 3 on the extratropical circulation via RW trains. For most of the strong BSISO cases, including the non-Russian HW types, we can detect wave trains propagating mainly northward and westward stemming from either India, Bay of Bengal or the China sea depending on the BSISO phase. Consistent with Cassou et al. (2005), for fewer cases, such as the HW in 2003, RW propagating eastward originated over East Pacific and Caribbean are found.
We further investigate the role of the BSISO as source of predictability by comparing the forecast of five HWs with an active BSISO in the initial conditions with five HWs without an active BSISO. The comparison shows a reduced spread at lead times 14 and 21 days for active BSISO events which highlights the higher predictability of HWs influenced by strong tropical convection. The active cases also correlate with lower RMSE; however, this result is not statistically significant.
Our results indicate that the tropical intraseasonal variability plays a role in the predictability of the HW events. Episodes with strong BSISO amplitudes characterized by enhanced convection favour the occurrence of HW events over Russia. When assessing the risk of HW occurrence over Europe, monitoring the BSISO evolution is helpful in adding confidence to extended range forecast probabilities for persistent high-pressure systems, specifically over Russia.