A New View of Heat Wave Dynamics and Predictability over the Eastern Mediterranean

Skillful forecasts of extreme weather events have a major socio-economic relevance. Here, we compare two complementary approaches to diagnose the predictability of extreme weather: recent developments in dynamical systems theory and numerical ensemble weather forecasts. The former allows us to define atmospheric configurations in terms of their persistence and local dimension, which inform on how the atmosphere evolves to and from a given state of interest. These metrics may be used as proxies for the intrinsic predictability of the atmosphere, which depends exclusively on the 15 atmosphere’s properties. Ensemble weather forecasts inform on the practical predictability of the atmosphere, which primarily depends on the performance of the numerical model used. We focus on heat waves affecting the Eastern Mediterranean. These are identified using the Climatic Stress Index (CSI), which was explicitly developed for the summer weather conditions in this region and differentiates between heat waves (upper decile) and cool days (lower decile). Significant differences are found between the two groups from both the dynamical systems and the numerical weather prediction perspectives. Specifically, heat 20 waves show relatively stable flow characteristics (high intrinsic predictability), but comparatively low practical predictability (large model spread/error). For 500 hPa geopotential height fields, the intrinsic predictability of heat waves is lowest at the event’s onset and decay. We relate these results to the physical processes governing Eastern Mediterranean summer heat waves: adiabatic descent of the air parcels over the region and the geographical origin of the air parcels over land prior to the onset of a heat wave. A detailed analysis of the mid-August 2010 record-breaking heat wave provides further insights into the 25 range of different regional atmospheric configurations conducive to heat waves. We conclude that the dynamical systems approach can be a useful complement to conventional numerical forecasts for understanding the dynamics of Eastern Mediterranean heat waves. 30 https://doi.org/10.5194/esd-2020-37 Preprint. Discussion started: 8 July 2020 c © Author(s) 2020. CC BY 4.0 License.


Introduction
Heat waves are recognized as a major natural hazard (e.g., Easterling et al., 2000), causing detrimental socio-economic impacts 35 (e.g., Feeling the heat 2018) including excess mortality (e.g., Batisti and Naylor 2009;Benett et al., 2014;Peterson et al., 2013;Ballester et al., 2019), agricultural loss (e.g., Deryng et al., 2014) and ecosystem impairment (e.g., Williams, 2014;Caldeira et al., 2015). Moreover, heat waves are projected to increase in frequency, intensity and persistence under global warming (e.g., Meehl and Tebaldi, 2004;Stott et al., 2004;Fischer and Schär, 2010;Seneviratne et al., 2012;Russo et al., 2014). The Eastern Mediterranean has experienced several extreme heat waves in recent decades (e.g., Kuglitsch et al., 2010) and their 40 frequency and intensity are expected to increase in the coming decades (e.g., Giorgi 2006; Seneviratne et al., 2012;Lelieveld used operationally by the Israel Meteorological Service, and the boundary layer height, which is a major factor influencing the summer weather conditions over the Eastern Mediterranean (Ziv et al., 2004). Saaroni et al. (2017)  The analysis described in the next sections is specifically implemented for extremes of the CSI index, i.e., days during which 135 the CSI exceeds the 90 th percentile of the July and August climatological distribution (hereafter: 'upper 10% of CSI' or heat waves) versus days when the CSI is below the 10 th percentile of the July and August distribution (hereafter 'lower 10% of CSI' or cool days). The onset of a heat wave (cool days) is taken to be the first day in which the CSI exceeds (subceeds) the 90 th (10 th ) percentile threshold at 12UTC (0 h time in the Figures), which ought to roughly match the time of maximum daily temperature. Alpert et al. (2004b) have argued that July and August represent the mid-summer months, in which the Persian 140 Trough occurs on more than nine out of eleven days. For additional details on the computation of the CSI index and its evaluation, the reader is referred to Saaroni et al. (2017).

Dynamical systems metrics
A novel method blending extreme value theory with Poincaré recurrences allows estimating the instantaneous properties of 145 chaotic dynamical systems (Lucarini et al., 2016;Faranda et al., 2017a). A temporal succession of two-dimensional maps of a given atmospheric variable -for example daily latitude-longitude maps of sea-level pressure (SLP) over the Eastern Mediterranean -is interpreted as a long trajectory in phase space. Each 2-D map corresponds to a single point along this trajectory, for which instantaneous properties are calculated. The analysis focuses on two metrics: the local dimension d and the persistence θ -1 . 150 The local dimension d is based on recurrences of the system around a state of interest, for example, a specific daily field of SLP. It originates from the result that the cumulative probability distribution of properly defined recurrences of the system converges to the exponential member of the Generalized Pareto Distribution (Freitas et al., 2010;Lucarini et al., 2012). In practical terms, d reflects the geometry of the trajectories in a small region (neighborhood) of the system's phase space around the state of interest. It is therefore related to the number of degrees of freedom that the system can explore about the state; in 155 other words, it informs on the way the system evolves around the state of interest.
The persistence (θ -1 ) of a state is obtained by estimating the extremal index (Moloney et al., 2019), here calculated using the Süveges (2007) estimator. −1 quantifies the persistence of the system in the neighborhood of the state of interest, and tends to https://doi.org/10.5194/esd-2020-37 Preprint. Discussion started: 8 July 2020 c Author(s) 2020. CC BY 4.0 License. be very sensitive to small changes in the state of the system. Nevertheless, Hochman et al. (2019) found that relative differences in −1 may be related to relative differences in the persistence of different weather regimes. For more details on the estimation 160 of the dynamical systems metrics, the reader is referred to Lucarini et al. (2016) and Faranda et al. (2017a, 2019a. The dynamical systems perspective has been fruitfully applied to a range of climate fields and datasets (e.g. Faranda et al., 2017a, b;Messori et al., 2017;Rodrigues et al., 2018;Faranda et al., 2019a, b, c;Faranda et al., 2020;Hochman et al., 2019Hochman et al., , 2020bDe Luca et al., 2020). In particular, it has been explicitly shown that d and θ -1 can offer an objective characterization of synoptic systems over the Eastern Mediterranean (Hochman et al., 2019) and the North Atlantic (Faranda et al., 2017a;165 Messori et al., 2017;Rodrigues et al., 2018).
In this study, we compute d and θ -1 for daily and 6-hourly 500 hPa geopotential height (Z500) and SLP fields from the NCEP/NCAR reanalysis over the Eastern Mediterranean placing Israel in the middle of the domain (27.5°N-37.5°N; 30°E-40°E; Fig. S1). To understand the differences between heat waves and cool days, we analyze both the CDFs (Cumulative Distribution Functions) and the mean temporal evolution of the two groups of days in terms of d and θ -1 . The Wilcoxson Rank-170 Sum (comparing the medians) and Kolmogorov-Smirnov (comparing the CDFs) tests are used for estimating the differences between the upper and lower 10% of CSI days at the 5% significance level. A bootstrap sampling test is used to evaluate the 95% confidence intervals of the mean temporal evolutions.
Previous studies have shown that the dynamical systems metrics d and θ -1 , have a strong seasonal cycle (Faranda et al., 2017a, b;Rodrigues et al., 2018). Thus, we remove the seasonal cycle before comparing the various events. The seasonal cycle is 175 estimated by averaging the metrics for a given time step (e.g., 15 August at 12UTC) over all years, repeating this for all time steps within the year and ultimately smoothing the series with a 30-day moving average.

Forecast spread/skill
To obtain an ensemble forecast, a few numerical forecasts are performed with either different initial conditions, and/or 180 perturbation of physical parametrizations. Ensemble forecasts offer an efficient way of estimating uncertainty by computing the ensemble spread. This is quantified by estimating the standard deviation between ensemble members. The spread can be taken as an indicator of practical predictability: in a perfect ensemble, a small spread would generally indicate we can determine with a good degree of confidence the future weather, while a large spread would point towards a larger uncertainty (e.g., Buizza 1997). This type of approach is commonly used when investigating atmospheric predictability (e.g., Hohenegger et al., 2006;185 Ferranti et al., 2015).
An additional frequently used forecast diagnostic is the absolute error, which provides a measure of forecast skill. Here, we use the homogeneous station archive mentioned in Sect. 2.1 above as ground truth to estimate the forecasts' skill. In order to https://doi.org/10.5194/esd-2020-37 Preprint. Discussion started: 8 July 2020 c Author(s) 2020. CC BY 4.0 License. remove biases due to topographic differences between the model and that of the stations, the GEFS reforecast gridded data is bilinearly interpolated to the location of the stations. The bias computed over the whole period is then removed for each station. 190 The GEFS reforecasts are initialized at 00UTC and are available at three-hour intervals. Since our analysis focuses on heat waves, we estimate the spread/skill for maximum temperature and SLP at a lead-time of 69 hours, while the maximum temperature is defined between 45 h and 69 h. Given the three-hour interval of the forecast data, and bearing in mind that each station's maximum temperature is recorded between 20UTC and 20UTC of the next day, this time-window roughly corresponds to the definition of maximum temperature for the station data. Since the dynamical systems metrics offer 195 information on the temporal evolution of the atmosphere in the neighbourhood of a given reference state, we argue that using the time of forecast initialization as temporal coordinate when plotting spread and error is most indicative for comparing the dynamical systems and numerical forecasts. In the supplementary material, we also plot the spread/skill for the forecasts initialised 69 h before the marked time. Thus, the plots in the main text show forecast initialisation times, while those in the supplementary material show the forecast valid times. A bootstrap test is used to infer the 95% confidence interval of mean 200 forecast spread and error. The Wilcoxson Rank-Sum (comparing the medians) and Kolmogorov-Smirnov (comparing the CDFs) tests are used for comparing forecast diagnostics on different groups of days at the 5% significance level.

Air parcel tracking
In order to identify typical pathways of air masses leading to situations with high and low CSI values, ten-day backward 205 trajectories are computed using the Lagrangian Analysis Tool (LAGRANTO; Wernli and Davies, 1997;Sprenger and Wernli, 2015). The tracking of temperature and potential temperature along the trajectory further allows to quantify the contribution of adiabatic and diabatic processes to the anomalous temperatures. The vertical and horizontal wind components required for the trajectory computations are acquired from the ERA-Interim reanalysis (Dee et al. 2011, Sect. 2.1). The trajectories are initialized at 12UTC from the study region on the first day of a heat wave or cool days (Fig. S1). In order to analyze the near-210 surface air masses, i.e. those related to the hot and cool conditions, we consider trajectories that are initialized between the surface and 90 hPa above the surface. The reader is referred to Fig. 2 in Sprenger and Wernli (2015) for a schematic overview of the typical steps taken to compute trajectories.
The trajectories are calculated from 6-hourly ERA-Interim data and remapped to a 1° regular latitude-longitude grid. Thus, the analyzed wind field does not resolve sub grid-scale processes such as Lagrangian transports due to sub grid-scale convective 215 3. Results 220

Dynamics of heat waves over the Eastern Mediterranean
We first analyze the differences between heat waves (upper 10% CSI values) and cool days (lower 10% CSI values). From an atmospheric dynamics' standpoint, the main difference between the two groups is that heat waves days are associated with an upper level ridge (Fig. 1a) while cool days are associated with an upper level trough (Fig. 1b). The SLP patterns are quite similar in both groups, but the heat waves show lower SLP in the south-west and a higher SLP in the north-east compared to 225 the cool days sample (Fig. 1c). This reveals that the large-scale configuration is an important factor in the generation of a heat wave over the Eastern Mediterranean. The backward trajectory air parcel analysis illustrates that the flow preceding an extreme heat wave has a roughly meridional orientation when traveling over the Eastern Mediterranean and originates over the European continent (Fig. 2a). On the other hand, the air parcels for cool days often originate over the Atlantic, and take a more zonal pathway across the Eastern Mediterranean (Fig. 2b). The initial potential temperature of the heat wave air masses is 230 about 7 K higher than that for the cool days (Fig. 2e). The differences in potential temperature between the two groups can mainly be attributed to the more continental origin of the air parcels for the heat waves, thus transporting potentially warmer air masses that descend on their path to the target region. Their descent, which is stronger than for cool days (Fig. 2c), is accompanied by a temperature increase of more than 25 K during the ten-day period (Fig. 2d). The potential temperature remains nearly constant until the final stages of the descent except for the diurnal cycle (Fig. 2e). Thus, we conclude that the 235 extreme heat is related to an adiabatic descent of the air parcels over the Eastern Mediterranean rather than to diabatic heating.
In other words, the warm air parcels are transported towards the Eastern Mediterranean with the governing westerlies rather than heated up locally over several days. This supports the findings of Harpaz et al. (2014), who argued that extreme summer heat waves over the Eastern Mediterranean are mostly regulated by mid-latitude disturbances rather than by the Asian Monsoon, as previously proposed by Ziv et al. (2004). An additional important difference between the two sets of CSI events 240 is that, unlike for the heat waves (Fig. 2a, f), the specific humidity of the cool days increases by 2 g kg -1 around t = -48 h, due to the longer stretch the latter air parcels follow over the Mediterranean Sea (Fig. 2b, f).
From a dynamical systems point of view, the upper and lower 10% of CSI also exhibit substantial differences. Fig. 3 shows a phase-plane diagram for d and θ computed on Z500 and SLP for the heat waves and cool days. θ is significantly lower at both levels for heat waves with respect to cool days, i.e., the former are generally more persistent systems. Statistically significant 245 differences in the median local dimensions (d) of the two groups are found only for the Z500 variable, for which the heat waves typically display a lower local dimension (d) than the cool days (Fig. 3a). The clear separation between the two groups, especially at upper level (cf. Fig. 3a and Fig. 3b) correlates well with the atmospheric dynamics' viewpoint, which also shows more pronounced differences at Z500 (Fig. 1). This points to the importance of using different variables at different pressure levels to obtain a comprehensive picture of the dynamics of heat waves. 250 https://doi.org/10.5194/esd-2020-37 Preprint. Discussion started: 8 July 2020 c Author(s) 2020. CC BY 4.0 License. Fig. 4 displays the average temporal evolution of d and θ during the selected events, again computed for Z500 and SLP. Zero denotes the first day of the event at 12UTC. Substantial differences are found between the time evolutions of the upper and lower 10% of the CSI events. For Z500, the temporal evolution of d and θ for heat waves are in phase with each other, and show a minimum with below climatology values in the 24 h preceding the event onset (Fig. 4a). In general, persistent highpressure systems have better predictability than low pressure systems (Ceppa and Colucci, 1989). Therefore, the minimum of 255 d and θ at Z500 may be explained by the positioning of the upper level ridge, seen in Figure 1a, between lower pressure regions. While there is still a considerable spread around the mean, even the upper bounds of our confidence intervals are well below zero in the build-up to the events. Instead, cool days display weak positive anomalies of d and θ, but these are almost never significantly different from 0 (Fig. 4b). The dynamical systems metrics computed on SLP provide a completely different picture: heat waves typically display a weak above-climatology d, which increases towards the event onset and then decreases 260 ( Fig. 4c). θ displays a slightly below-climatology persistence (i.e. positive anomalies) and decreases towards the event onset ( Fig. 4c). However, the very large spread in the composite evolution, and in particular in d, suggests some caution in overinterpreting the details of these evolutions. Cool days are characterized by higher positive anomalies of d and θ in the days preceding the event. The build-up towards this type of event is characterized by an increase in θ (decrease in persistence) and a decrease in d (Fig. 4d). The cool days also appear to have a more coherent evolution (lower spread around the mean) than 265 the heat waves for SLP.
The differentiation between the two samples is thus more pronounced when computing the metrics on Z500 than on SLP (Fig.   4), as also shown in the daily distributions (Fig. 3). Moreover, the variability in the temporal evolution of the dynamical systems metrics is smaller in Z500 than in SLP (Fig. 4). This points to: i) coherent, and very different, upper level conditions which engender the two sets of CSI days; and ii) a comparatively wide range of possible near-surface patterns which all lead 270 to severe heat waves. The latter may be explained by the fact that, given initially warm upper-level air parcels and upper-level subsidence leading to rapid adiabatic warming, the occurrence of a heat wave is then relatively insensitive to the details of the We analyze next numerical ensemble forecasts from the GEFS reforecast dataset for both sets of events. Substantial differences are again found between the two groups (Fig. 5). Both the ensemble spread and the absolute error are significantly higher for heat waves than for cool days (Fig. 5). The model spread and absolute error increase before the onset of the heat wave, peaking at around 24-48 hours negative lags (Fig. 5). The pattern somewhat resembles the temporal evolution of d computed on SLP 280 (cf. Fig. 5e and Fig. 4c), but stands in stark contrast to the pattern computed on Z500 (cf. Fig. 5a, c, e and Fig. 4a). The reforecasts computed for the individual stations (not shown) resemble the average forecast spread/skill (Fig. 5). The The Z500 and SLP patterns for 15 th August 2010 are comparable with the average configuration of a heat wave, but show a stronger upper level ridge and meridionally-oriented isobars (cf. Fig. 6a and Fig. 1a). From a dynamical systems point of view, the 2010 heat wave was also an uncommon extreme, especially for the metrics computed on Z500. The dynamical systems 290 metrics' anomalies computed on this field range between -0.9 and -1.4 for d, and -0.14 and -0.2 for θ (Fig. 6b). This situates the heat wave in the lower 10% of the respective distributions (see also red dots in Fig. 3a). During its evolution, the event displays an increase in both d and θ computed on Z500 and a decrease (increase) in θ (d) computed on SLP (Fig. 6b, c). While the Z500 d and θ evolution is roughly comparable to that identified for heat wave days (cf. Fig. 4a and 6b), the SLP d and θ evolutions show profound differences. This may simply reflect the larger spread in dynamical systems properties across the 295 different heat waves for SLP than for Z500. We further hypothesize that differences between the single case and the climatology may be related to the relatively small day to day variations during summer over the Eastern Mediterranean (Ziv et al., 2004), which make it challenging to depict the exact onset of a heat wave.
The 2010 heat wave was also uncommon in terms of the large-scale flow and Lagrangian trajectories (Fig. 7). Between -10 to -5 days prior to the event, the majority of air parcels were transported in an easterly flow on the southern flank of an anticyclone 300 located over Russia. Thus, air parcels came from the Zagros Plateau of Northern Iran, rather than from central Europe as in the climatology (cf. Fig. 7a, b and Fig. 2a) Mediterranean and Israel (Fig. 7a, b and Fig. 8). For the last five days (Fig. 7b), the parcel's trajectories resemble more closely the climatology of heat waves (Fig. 2a). Furthermore, the initial potential temperature and temperature of the air parcels are respectively about 2K and 7K higher than the climatology of heat waves (cf. Fig. 7d, e and Fig. 2d, e). Accordingly, the hot air masses in the mid-August 2010 heat wave are transported to the Eastern Mediterranean and undergo adiabatic heating, rather than being heated up locally. This is in line with the climatology discussed in Sect. 3.1, and heat waves in other parts of 310 the world (e.g., Quinting and Reeder, 2017; Zschenderlein et al., 2019). Fig. 9 shows the temporal evolution of the forecast spread/skill for the mid-august 2010 heat wave compared to the heat wave climatology. Throughout the lead up and early phases of the event, the forecast displays a lower spread and error than for other heat waves. A large decrease in the practical predictability occurs as the event develops, i.e., an increase in the spread/skill for maximum temperature (Fig. 9a, b). This mirrors the increase in d and θ computed on Z500 and for d computed on SLP (cf. Fig. 9a, b with Fig. 6b, c). Indeed, the decay phase of the Russian heat wave was characterized by low practical predictability (Matsueda 2011), which may have influenced the predictability over the Eastern Mediterranean. However, it should be noted that the spread computed on maximum temperature for the mid-August 2010 heat wave does not correlate well with the spread computed on SLP (cf. Fig. 9a with Fig. 9c). Moreover, some striking differences are displayed between the ensemble forecast of this single event and the climatology of forecasts for heat waves. These discrepancies may be related to the fact that we are 320 analyzing a single event, whose error may not reflect the practical predictability of the atmosphere even for a perfect ensemble

Summary and conclusions 325
Heat waves are a major weather-related hazard, especially in an era of rapid climate change. We define heat waves over the Eastern Mediterranean according to a state-of-the-art 'Climatic Stress Index' (CSI; Saaroni et al., 2017), developed specifically for the region's summer weather conditions. We use a combination of dynamical systems theory, numerical weather forecasts and air parcel back-trajectories to investigate the evolution and predictability characteristics of heat waves (high CSI) and cool days (low CSI) for the region. 330 The main conclusions are as follows: significant differences are found between heat waves and cool days from both a dynamical systems and numerical weather prediction perspectives. Heat waves show relatively low practical predictability (large model spread/low skill) in the ensemble reforecast dataset used here, in spite of the relatively stable flow characteristics (high intrinsic predictability) compared to the cool days. When considering Z500, the intrinsic predictability of heat waves over the Eastern Mediterranean is highest, i.e., low local dimension (d) and high persistence (low θ), in the 24 h preceding the 335 onset of the event, and lowest in the decay phase of the event. Indeed, Lucarini and Gritsun (2020) recently argued that atmospheric blocking over the Atlantic also displays such characteristics. The persistent upper level ridge that characterises the heat waves may explain the high intrinsic predictability during the onset phase. The dynamical systems metrics computed on SLP show a different temporal evolution to their Z500 counterparts, emphasizing the different characteristics of the atmospheric flow at the different vertical levels. Specifically, there is a very large spread across different heat wave events. 340 We argue that this may be associated with the delicate interplay between the Subtropical High and the Persian Trough at surface levels (Alpert et al., 1990), which can lead to a range of different SLP configurations all leading to a heat wave.
Based on the Lagrangian air parcel analysis, we conclude that the physical processes governing Eastern Mediterranean summer heat waves relate to adiabatic descent of the air parcels over the region rather than diabatic heating, in agreement with previous findings (e.g., Ziv et al., 2004). In other words, the air parcels are transported horizontally and vertically towards the Eastern 345 Mediterranean with the governing westerlies rather than heated up locally over consecutive days. We further conclude that the origin of the air parcels over land in the days before the onset of a heat wave takes an important part in its generation.
A detailed analysis of the record-breaking mid-August 2010 heat wave provides further insights in this respect, by underscoring how the parcels which contributed to the heat wave were warmer than those of the climatology of heat waves as early as 10 days prior to the event. Interestingly, the onset of the heat wave over the Eastern Mediterranean was related to the decay phase 350 of the Russian heat wave (Quandt et al., 2019) and we conclude that the anti-cyclonic Rossby wave breaking over Russia contributed to the onset of the Eastern Mediterranean heat wave. The 2010 heat wave showed both differences and similarities to other heat waves, highlighting the range of possible atmospheric and dynamical developments leading to high CSI values. This is compounded by the general difficulty of analyzing the life-cycle of heat waves, since there is little agreement as to what exactly a heat wave is and when it starts and ends (e.g., Shaby et al., 2016). 355 We conclude that the instantaneous dynamical systems metrics of local dimension (d) and persistence (θ -1 ) do provide complementary information on extreme summer heat waves compared to the conventional analysis of numerical weather forecasts. The discrepancy between the practical and the intrinsic predictability of the heat waves reflects this complementarity.
For example, we interpret a very persistent system as being intrinsically highly predictable, yet the numerical forecasts we analyse display larger spread and error for the more persistent atmospheric configurations. In this respect, having an a-priori 360 measure of the persistence of an atmospheric configuration from dynamical systems can be a useful complement to the numerical forecast. As a caveat, the comparison of the practical and intrinsic predictability still carries some interpretation challenges. Although the differences between the two can be partly ascribed to the different characteristics of the two measures, they may also be subject to the shortcomings of the GEFS ensemble data. In particular, the spread of the GEFS ensemble data, as most NWP ensemble forecasts, does not always reflect the practical predictability of the atmospheric flow (e.g., Kuene et 365 al., 2014). Moreover, our interpretation of the dynamical systems metrics may also be imperfect. Indeed, the metrics provide local information in phase space, while the spread and error of an ensemble forecast presumably reflect the longer-term evolution of the atmospheric flow. Similar interpretation challenges for the practical vs. intrinsic predictability have emerged when studying cold spells (Hochman et al., 2020a).
Notwithstanding these ongoing challenges, we believe that the novel view presented here, which leverages a dynamical 370 systems approach for diagnosing extreme weather events, outlines an important avenue of research. We trust that it may be successfully applied to other regions and weather extremes in the future. indicating days (from 10 days before onset to onset), trajectory density 10 days before onset (number of trajectories per 1000 650 km² in shading), and trajectory density for the indicated time lags (5, 2, 1 days before onset, contours denote a density of 20 trajectories per 1000 km²). Streamlines of 800 hPa winds averaged between -5 to -1 days are included. Median evolution of (c) pressure (hPa) (d) temperature (K) (e) potential temperature (K) (f) specific humidity (g kg⁻¹) of air parcels. Heat waves are indicated in red and cool days in blue. The inter-quartile range is plotted for the physical properties of the air parcels. 0 h corresponds to the first day of CSI ≥ 90% or CSI ≤ 10% and at 12UTC. 655 https://doi.org/10.5194/esd-2020-37 Preprint. Discussion started: 8 July 2020 c Author(s) 2020. CC BY 4.0 License. Figure 4 The average temporal evolution of the dynamical systems metrics (d and θ) for heat waves (upper 10% of CSI) and cool days (lower 10% of CSI) events. The dynamical systems metrics were computed for: (a, b) Z500 and (c, d) SLP. The events are centered (0 h) on the first day of CSI ≥ 90% or CSI ≤ 10% and at 12UTC. A 95% bootstrap confidence interval is plotted in shading. 665 https://doi.org/10.5194/esd-2020-37 Preprint. Discussion started: 8 July 2020 c Author(s) 2020. CC BY 4.0 License. Figure 7 Backward trajectory air parcel tracking for the mid-August 2010 heat wave initialized on 15.8.2010 at 12UTC with (a) circles indicating days (from -10d to -6d before 15.8.2010 at 12UTC), trajectory density 10 days before onset (number of trajectories per 1000 km² in shading), stream lines of 800-hPa wind (averaged between -10d to -6d before 15.8.2010 at 12UTC).
(b) as in (a), but for -5d to -1d and trajectory density 5 days before onset (number of trajectories per 1000 km² in shading).