Rare event algorithm study of extreme warm summers and heat waves over Europe
aa r X i v : . [ phy s i c s . a o - ph ] O c t manuscript submitted Rare event algorithm study of extreme warm summersand heatwaves over Europe
F. Ragone , , and F. Bouchet Univ Lyon, Ens de Lyon, Univ Claude Bernard, CNRS, Laboratoire de Physique, Lyon, France Earth and Life Institute, Universit´e catholique de Louvain, Louvain-la-Neuve, Belgium Royal Meteorological Institute of Belgium, Brussels, Belgium
Key Points: • The rare event algorithm increases by several orders of magnitude the number ofwarm summers and heatwaves sampled by the model. • Warm summers over either France or Scandinavia are linked to wavenumber 3 hemi-spheric teleconnection patterns. • Warm summers in Scandinavia show bimodality due to different distribution of sub-sequent subseasonal heatwaves.
Corresponding author: Francesco Ragone, [email protected] –1–anuscript submitted
Abstract
The analysis of extremes in climate models is hindered by the lack of statistics due tothe computational costs required to run simulations long enough to sample rare events. Wedemonstrate how rare event algorithms can improve the statistics of extreme events in state-of-the-art climate models. We study extreme warm summers and heatwaves over Franceand Scandinavia with CESM1.2.2 in present-day climate. The algorithm concentrates thesimulations on events of importance, and shifts the probability distributions of regional tem-peratures such that warm summers become common. We estimate return times of extremesorders of magnitude larger than what feasible with direct sampling, and we compute sta-tistically significant composite maps of dynamical quantities conditional on the occurenceof the extremes. We show that extreme warm summers are associated to wavenumber 3hemispheric teleconnection patterns, and that the most extreme summers are related to thesuccession of rare subseasonal heatwaves.
Plain Language Summary
The impact of extreme climatic events is often dominated by the rarest events. Theseevents have return times (a measure of how often they occur on average) of hundreds ofyears or more, but they could, and do, happen anytime. These events are poorly understoodbecause of lack of statistics. Climate models are computationally expensive, and can not berun for long enough to study events with return times longer than a few decades. We use anew computational technique that allows simulations to focus only on trajectories leadingto extreme heatwaves over a target region, optimizing the use of computational resources.We thus gather robust statistics for seasonal heatwaves with return times of hundreds orthousands of years, and observe even rarer events impossible to observe otherwise. Wefind that extreme warm summer over France or Scandinavia are synchronised with extremewarm summers in specific regions of Asia and North-America by a teleconnection patternextending over the entire Northern hemisphere. We also find suggestions that extreme warmsummers over Scandinavia may occur in two distinct ways. This new method can be usedto better study the impact of global warming on the risk of catastrophic events, and toimprove their predictability.
Recent decades have seen a number of exceptionally warm summers and record break-ing heatwaves at the Northern hemisphere midlatitudes (Luterbacher et al., 2004; Garc´ıa-Herrera et al., 2010; Barriopedro et al., 2011; Otto et al., 2012; Agha Kouchak, 2012; IPCC,2012; Russo et al., 2015; Coumou & Rahmstorf, 2012). The Intergovernmental Panel onClimate Change (IPCC) has concluded that hot days and heavy precipitation events havebecome more frequent since 1950 (IPCC, 2013). The precise extent to which heat extremeswill become more common in the future and under the target scenarios of +1.5 o C and+2 o C global surface temperature with respect to preindustrial levels is an active field ofresearch (Mueller et al., 2016; Dosio et al., 2018; Suarez-Gutierrez et al., 2018).A phenomenological theory exists on the causes of heatwaves (Schubert et al., 2014;Perkins, 2015; Horton et al., 2016), including large scale atmospheric circulation patterns,(Della-Marta et al., 2007; Cassou et al., 2005; Jezequel et al., 2018), lack of precipitationand soil moisture (Vautard et al., 2007; Zampieri et al., 2014; D’Andrea et al., 2016), andsea surface temperature anomalies (Della-Marta et al., 2007; Cassou et al., 2005), withdifferent levels of importance in different regions (St´efanon et al., 2012). Long lastingheatwaves and warm summers are among the most relevant events in terms of impacts(Camargo & Seth, 2016; Trenberth, 2012). Although they are known to be related topersistent weather regimes (Lau & Kim, 2012; Teng et al., 2013; Hoskins & Woollings, 2015;Petoukhov et al., 2016; Boers et al., 2019; Kornhuber et al., 2019), their dynamics is notfully understood. Some studies show stronger increase with global warming of the frequency –2–anuscript submitted of persistent temperature extremes (Pfleiderer et al., 2019). However, the response of theglobal circulation to climate change is extremely complex and not well understood (Hoskins& Woollings, 2015), in particular for the type of rare dynamics that lead to extreme events.The impact of climate extremes is often dominated by the rarest events. For instance,the death toll of the Western European heatwave in 2003, about 70.000 casualties, exceededthe sum of the fatalities due to all other heatwaves during the last three decades (Barriopedroet al., 2011). Moreover, extreme events with very long return times (also called returnperiods) always occur. For instance, an extreme event with a return time of 1000 years, hasa chance 1/1000 to occur next year. Among the huge number of possible extreme eventswith a return time of 1000 years, a few of them will certainly occur somewhere sometimesnext year. It is thus crucial to study the most extreme and rare events However, the study ofsuch events faces strong scientific limitations: we can not rely on historical data for eventswith return times of 100 years or more, because often no similar events have ever beenobserved, and it is extremely difficult to study these events using climate models because ofthe required computational costs.In this paper we address the problem of computational cost limitations. In order toface this problem, we use a rare event algorithm that concentrates ensemble simulations ontrajectories of importance for the extreme events, optimizing the use of the computationalresources. Rare event algorithms have recently been applied to turbulence problems (Grafkeet al., 2015; Laurie & Bouchet, 2015; Ebener et al., 2019; Bouchet et al., 2019; Lestang etal., 2020) and climate applications (Ragone et al., 2018; Webber et al., 2019; Ragone &Bouchet, 2020; Plotkin et al., 2019). Based on the phenomenology of the dynamics for eachfamily of extreme events, an appropriated type of rare event algorithm should be carefullychosen. Here we use a genealogical algorithm (Ragone et al., 2018; Ragone & Bouchet,2020) adapted from (Del Moral et al., 2005; Giardina et al., 2011), that is efficient to studylong lasting events. This rare event algorithm has been used to study heatwaves with anintermediate complexity model (Ragone et al., 2018) in perpetual summer conditions. Herewe use it to sample rare heatwaves in CESM 1.2.2 (Hurrell et al., 2013), a fully realisticclimate model, in presence of daily and seasonal cycles.The goal of this paper is to demonstrate the applicability of rare event algorithms tostate-of-the-art climate models, and to highlight properties of extreme long lasting heat-waves that can not be assessed with traditional sampling strategies. We study extremewarm summers and heatwaves over France and Scandinavia in CESM1.2.2, in present-dayclimate. We compute return times orders of magnitude larger than what feasible with directsampling, and statistically significant composite maps of dynamical quantities. Our resultsshow that extreme warm summers are associated to wavenumber 3 teleconnection patternsin the Northern hemisphere, and suggest that the most extreme summers are related to thesuccession of multiple rare subseasonal heatwaves.
Model.
All simulations are performed with the Community Earth System Model(CESM) version 1.2.2 (Hurrell et al., 2013). We use an atmosphere and land only setup,whose active components are the Community Atmospheric Model version 4 (CAM4) andthe Community Land Model version 2 (CLM2). The model is run at statistically sta-tionary state, with sea surface temperature (SST), sea ice cover, and the concentration ofatmospheric CO2 and other greenhouse gases fixed at values representative of present dayclimate (year 2000). Contrary to (Ragone et al., 2018), the model features daily and sea-sonal cycle, and reproduces a fully realistic climate. See the SI for more details. We studythe statistics of a 1000 years long control run, and the statistics of several sets of simulationsusing the rare event algorithm. –3–anuscript submitted
Heatwaves and physical observable definition.
We consider the surface temper-ature T s ( ~r, t ), where ~r is the space variable and t is time, and define the mean surfacetemperature E ( T s ) ( ~r, t ), which varies in time (because of the seasonal cycle) and in space.In practice, E ( T s ) will be approximated by the climatological average of T s computed from a1000 years long control run. We study the statistics of the spatially and temporally averagedsurface temperature anomaly defined by a ( t I ) = 1 T Z t I + Tt I A ( t )d t where A ( t ) = 1 |D| Z D ( T s − E ( T s )) ( ~r, t ) d ~r, (1)where A ( t ) is the instantaneous spatial average, D is a spatial domain area, t I is the startingdate of the time average, T is the averaging time, for instance several days up to one season.Heatwaves will be defined as extreme values of the observable a ( t I ), as heatwave indicesdeveloped for dynamical studies often use anomalies rather than absolute values (Perkins,2015). We are specifically interested in long events, for instance warm summers with T =3months. For summer anomalies, we consider a JJA defined by (1) with t I being June 1stand t I + T August 29. In the following, we consider D as the area over either France orScandinavia (see the SI for the definition of the areas). Rare event algorithm experiments and importance sampling.
Rare event algo-rithms allows a numerical model to produce very efficiently rare trajectories of importancefor the study of extremes. We simulate an ensemble of N model trajectories, and at constantintervals of a resampling time τ we perform trajectory selection, pruning and cloning trajec-tories in order to favour those leading to the extreme events. See the SI for a more detaileddescription and (Ragone et al., 2018). The algorithm also allows to compute probabilitiesfor the obtained trajectories. Let ~X ( t ) be the vector of values of all the model variables attime t (which includes but is not limited to the temperature T s defined above). We considerthe trajectory n ~X ( t ) o , with all values of X along all the interval t a ≤ t ≤ t a + T a , where t a isthe starting date and T a the trajectory duration in the algorithm. We denote P k (cid:16)n ~X ( t ) o(cid:17) the probability distribution function of the trajectories obtained in the algorithm. Then therare event algorithm produce trajectories distributed according to P k (cid:16)n ~X ( t ) o(cid:17) = e k R ta + Tata A ( u ) d u Z P (cid:16)n ~X ( t ) o(cid:17) , (2)where P (cid:16)n ~X ( t ) o(cid:17) is the probability distribution function of the trajectories in the modelclimate, Z is a normalization term computed by the algorithm, A is the selection function(with the dependance on the trajectory implicit for simplicity, A ( t ) = A (cid:16)n ~X ( t ) o(cid:17) ), and k controls the strength of the algorithm selection. Equation 2 is called an importance ratioformula. Using equation 2 we can compute the actual probabilities of the rare trajectoriesobtained in the simulations with the algorithm. See the SI and (Ragone et al., 2018) formore details.We use as selection function A the same function used to define a heatwave in formula(1). We see from equation (2) that if the parameter k is positive, then trajectories with largevalues of the time average of the surface temperature anomaly will be much more probable insimulations obtained with the algorithm rather than in simple simulations with the model.The larger k , the stronger the selection, and the more probable trajectories with extremevalues of the time averaged surface temperature. We analyse extremely warm summers overFrance and Scandinavia. For each case, we perform K = 10 ensemble simulations with thealgorithm, each with N =100 trajectories, biasing parameter k =30, with T a =90 days fromJune 1st to August 29th, and resampling time τ =5 days (see the SI). A 1000 years longcontrol run is used to provide initial conditions for the experiments with the algorithm,and as a benchmark for the statistics. The computational cost of the experiments with thealgorithm is equivalent to simulating 1000 summers in the control run, but they allow togather a much richer statistics for the extreme events of interest. –4–anuscript submitted The main goal of the algorithm is to perform importance sampling for the distributionof the summer temperature anomalies over the target region. Figures 1a and 1b show theprobability distribution functions of the summer temperature anomalies a JJA for the controlrun and the rare event algorithm. The control distribution shows a similar variance ofabout 1 o K for both France and Scandinavia. The algorithm is very effective in performingimportance sampling and populating the upper tails of the distributions. The typical valueof the seasonal anomaly a JJA in the rare event algorithm experiments is around 4 o K forboth cases, which are values never observed in the control run. Thanks to the algorithmmost of the computational power is indeed used to simulate extremely warm summers, ratherthan trajectories belonging to the bulk of the distribution. In the case of Scandinavia thealgorithm statistics in figure 1b shows a bimodality that we will discuss in section 3.3.In figures 1c,d we compare return times of a JJA in the control run and in the experi-ments with the rare event algorithm. A description of the computation of return times bothfor direct sampling and importance sampling using formula (2) is presented in (Lestang etal., 2018). The black curves are obtained from the control run using 1000 years of data. Inorder to estimate uncertainty ranges, we compute also an estimate dividing the control runin K =10 samples of 100 years each, computing 10 estimates of the return times curve. Wethen take their average (blue curves), and compute the empirical standard deviation (blueshaded areas). The red line and shaded areas are obtained in the same way, but using theestimates from K = 10 independent experiments with the algorithm.With the rare event algorithm we reach return times up to 10 -10 years with uncer-tainty ranges comparable with the ones with the control run for return times of order 10 years. Given the large value of k we chose, we have a small range of overlap for estimates ofthe return times from the control run and the rare event algorithm. When they do overlap,the values are consistent with each other within the uncertainty ranges. After about 10 -10 years the return time curves reach a plateau. Such plateaux are due to undersampling, asdiscussed in the SI and in (Lestang et al., 2018). A full demonstration of the reliability ofthe results obtained with the rare event algorithm in similar simulations can be found in(Ragone et al., 2018; Ragone & Bouchet, 2020). We study the dynamical properties of extremely warm summers with return time largerthan 100 years (called 100-year warm summers or seasonal heatwaves from now on). Wecompute composite maps of anomalies of the local JJA surface temperature and 500 hPageopotential height conditional on the occurrence of 100-year warm summers, for the controlrun and the rare event algorithm experiments. One of the key advantage of the rare eventalgorithm is that it gives much better results than the control run for composite statisticsfor large return times. Moreover the rare event algorithm gives access to composite statisticsfor return times larger than 1000 years, which is impossible with the control run.Figure 2a shows composite statistics of surface temperature and 500 hPa geopotentialheight of 100-year warm summers over France in the control run. The map hints at thepresence of a wavenumber 3 teleconnection pattern for both observables. However, howmuch of these patterns, which were obtained by averaging over only 10 warm summers, isstatistically significant? Figure 2b shows the t -value map for the geopotential height (seethe SI for details). Only the geopotential height anomalies over Europe pass a statisticalsignificance test with | t | >
2, which means then we can not really assess the reality of theteleconnection pattern using a 1000 years control run: we just do not have enough data.Figures 2c,d show the same composite maps and statistical significance analysis for 100-yearwarm summers over France, but computed using the rare event algorithm. The algorithm –5–anuscript submitted results are globally significant, except over the northern part of the Pacific area. Transitionareas between cyclonic and anticyclonic anomalies have a | t | value smaller than 2, becausethey have a low value of the conditional average. They are however rather narrow, so thattheir location can be still considered rather precise. The rare event algorithm thus allows toproperly assess the existence of teleconnections of warm summers in Europe, North Americaand Central Asia.The algorithm also gives a much better estimate of the amplitude of the anomalies, sinceit gives access to large amplitude events unavailable in the control run, because they are toorare. In the same way, the rare event algorithm gives also access to composite statistics thattotally unavailable with the control run. For instance figure 3a shows composite statisticsof surface temperature and 500 hPa geopotential height for 1000-year warm summers overScandinavia, which also show a teleconnection pattern with a different spatial pattern butsimilar broad stroke features.Based on the rare event algorithm results, we obtain a better overview of the character-istics of the synoptic dynamics occurring during extremely warm summers in the consideredregions. A warming pattern centered over the target region is present, encompassing alarger area on a spatial scale of a few thousands km, which coincide with central-WesternEurope for France and Northern-Eastern Europe for Scandinavia. Persistent anticyclonicsynoptic scale structures centered over the target area are associated to this warming pat-tern. Locally these structures are consistent with the observed synoptic conditions for theoccurrence of European heatwaves. In particular, for the North Atlantic and European area,the local patterns are very close to the observed patterns for the Western-European and theScandinavian heatwave clusters obtained from reanalysis data in (St´efanon et al., 2012).The application of the rare event algorithm allows to assess in a statistically robust waythat these local dynamics are part of hemispheric structures of approximately wavenumber3, which induce a temperature teleconnection pattern, with persistent regional temperatureanomalies of alternating signs around the hemisphere. The patterns for the two regionsare in broad strokes similar, although they differ in the exact location of positive andnegative anomalies. Warm summers over France occur systematically with warm summersover Siberia and North-East America. The corresponding tripolar structure of anticyclonicanomalies is accompanied by a localized low over Central-Asia and a general lower pressureover the Arctic, with minimum over Greenland. The structure related to Scandinavianwarm summers is similar on the North-Atlantic sector, but over Asia it is quite different,with a negative temperature anomaly (and related low pressure) extending from SouthernEurope to the whole central Asia, with the positive anomaly constrained over the far East.The circulation over the Arctic is also different, with a strong low over the Pole. Figure 1b a bimodality of the Scandinavia summer temperatures in the rare eventalgorithm data. This suggests that two types of distinct dynamical events might lead toScandinavian extreme summers. We note that, because of the nonlinear relation (2), abimodality in the algorithm distribution does not necessarily imply a bimodality in thetail of the model distribution. Still it is interesting to test the hypothesis of two types ofdynamics.Figure 3a shows composite statistics of surface temperature and 500 hPa geopotentialheight for 1000-year warm summers over Scandinavia. Figures 3b and 3c show the compositemaps from the rare event algorithm computed separately for a JJA < . o K and a JJA > . o K ,where 4.2 o K corresponds to the local minimum between the two peaks of the distributionin red in figure 1b. While the overall structure is the same as the total composite mapin figure 3a, the map of the first range (figure 3b) shows a weaker teleconnection pattern,and an anticyclonic anomaly over the North-Atlantic that is not present in the map of thesecond range (figure 3c). The Scandinavian warm summer dynamics is compatible with a –6–anuscript submitted northward shift of the jet stream along the entire hemisphere. In the case of the first range(figure 3b), this shift is less clear over the North-Atlantic, where a different dynamics seemsto be in place. It is however likely that, if two distinct types of dynamics are occurring, aselection based only on the range of seasonal regional temperature fluctuations is not enoughto differentiate between different dynamics, and therefore simple composite maps show fromthat point of view mixed information.The study of relation between subseasonal fluctuations of surface temperature andextreme warm summers can give an explanation of this bimodality. To visualize this relation,we look at the genealogical structure of the trajectories in an experiment with the rare eventalgorithm for Scandinavia in figure 4a. The black lines correspond to trajectories belongingto the first range ( a JJA < . o K), while the red lines to trajectories belonging to the secondrange ( a JJA > . o K). In the experiment represented in figure 4a, trajectories belongingto each of the two ranges of the bimodal distribution coexist. In figure 4b, we show thesame genealogical tree, but indicate with different colors the values of the 5-days temperatureanomaly in each segment. These values are computed using equation 1 with T =5 days and t I corresponding to the date of each resampling event. In particular red segments indicate a 5-day anomaly above 4.5 o K. The chosen threshold of 4.5 o K is the median of the distribution ofthe 5-day temperature anomalies rare event algorithm experiments for Scandinavia (shownin the SI). This value corresponds to the 96.6th percentile of the distribution of the 5-day temperature anomalies in the control run. We can thus consider 5-days periods withtemperature anomaly larger than this threshold as heatwave periods, and a succession of 2or more consecutive heatwave periods as a subseasonal heatwave.With this definitions, during warmer summers belonging to the second range (red infigure 4a), we see a first subseasonal heatwave that lasts about 20 days in late June-earlyJuly, and then a second subseasonal heatwave that last again about 15 days in August. Lessextreme summers (black in figure 4a) have instead only one subseasonal heatwave in June-July. The bimodality of the algorithm statistics therefore corresponds to two qualitativelydifferent types of warm summer, with either one or two subseasonal heatwaves. We note thatthe 2003 warm summer in France was characterized by two separate subseasonal heatwavesin June and August (Garc´ıa-Herrera et al., 2010).
We have shown how simulations with the algorithm produce hundreds of times moreextremes than a control run for the same computational cost, and allow us to estimatereturn times of extreme events orders of magnitude larger. This allows to compute preciselystatistically significant composite maps of dynamical quantities for warm summers withextremely strong seasonal surface temperature anomalies. In this way we are able to identifyrigorously the occurrence of persistent teleconnection patterns of wavenumber 3 during verywarm summers. These patterns and the related dynamics can not be properly studiedwith direct sampling, as the corresponding local anomalies of temperature and geopotentialheight are statistically significant only over the target region. The improved statistics givenby the rare event algorithm instead allows to obtain statistically significant maps and a veryclear signal also away from the target region.Teleconnection patterns similar to what we have obtained here were observed in thefirst application of the rare event algorithm to a climate model (Ragone et al., 2018). In thatcase the model was an intermediate complexity model, run in perpetual summer setup, andthe target area was the whole Europe. In this case we use a much more realistic model withseasonal cycle, calibrated to reproduce present day climate, and we target areas consistentwith observed heatwave clusters (St´efanon et al., 2012) and recent cases of very intenseheatwaves or warm summer, like the heatwave over France of 2003 and the warm summerover Northern Europe of 2018. It is striking that we obtain similar qualitative results.This supports the idea that these teleconnections at seasonal scale and the corresponding –7–anuscript submitted wavenumber 3 dynamics are robust features, mainly dynamical and little affected by thedetails of the physical parameterizations.Comparison with observations is not straightforward, due to the lack of data and thefact that most studies have focused on events at subseasonal scale. Several authors have re-cently highlighted the role of Rossby waves in determining teleconnection of extreme events(Schubert et al., 2011; Lau & Kim, 2012; Petoukhov et al., 2013, 2016), with particularemphasis on strong heatwaves, e.g. cases over the central USA (Teng et al., 2013), Al-berta (Petoukhov et al., 2018) and Western Europe (Kornhuber et al., 2019). These studiestypically find patterns with wavenumber 5 to 7 and analyse subseasonal temperature fluctua-tions. Several different detection methods are used in the literature to identify the dynamicsleading to heatwaves, including projections of heatwave states on typical variability patternsobtained with cluster analysis (Cassou et al., 2005) or empirical orthogonal functions (Tenget al., 2013), spectral analysis (Petoukhov et al., 2018; Kornhuber et al., 2019) and/or indi-cators based on resonance models (Petoukhov et al., 2013, 2016). Merging these approacheswith rare event simulations should lead to very promising future studies, aimed at investi-gating the relation between the seasonal scale structures we find here and the possible roleof higher wavenumber stationary Rossby waves proposed in the literature, as well as thepossible multimodality in the way of occurrence of some extreme events.
Acknowledgments
This work was granted access to the HPC resources of CINES under the allocation 2019-A0070110575 made by GENCI. The computation of this work were partially performedon the PSMN platform of ENS de Lyon. This work has received funding through theACADEMICS grant of the IDEXLYON, project of the Universit´e de Lyon, PIA operatedby ANR-16-IDEX-0005. The research leading to these results has received funding from theEuropean Research Council under the European Union’s seventh Framework Programme(FP7/2007-2013 Grant Agreement No. 616811). The data related to the figures presented inthis paper have been uploaded with the submission for review purposes. We are discussingwith CINES the long term storage and open access of the full dataset of our simulationsaccording to the Enabling FAIR data Project guidelines. –8–anuscript submitted
Figure 1.
Distribution of seasonal JJA temperatures anomalies averaged over France (a) andScandinavia (b) from the control run (black) and the rare event algorithm (red). Return timesfor the seasonal temperature anomalies for France (c) and Scandinavia (d), from the control run(black) and the rare event algorithm (red). The shaded areas, light blue for the control run andlight red for the algorithm, correspond to 1 standard deviation of the sample used to compute theestimate (see SI). –9–anuscript submitted a) b)c) d)
Figure 2.
Northern hemisphere composite maps (conditional statistics) for the JJA anomaliesof the surface temperature (colors) and 500 hPa geopotential height (contours) for 100-year warmsummers over France, in the control run (a) and in the rare event algorithm statistics (c). Panels b)and d) show for the control run and the rare event algorithm respectively the corresponding mapsof the t values of the 500 hPa geopotential height anomalies (see the SI).–10–anuscript submitted a)b) c) Figure 3.
Composite maps for the anomalies of the surface temperature (colors) and 500 hPageopotential height (contours) for warm summers over Scandinavia with return times larger than1000 years (a). Panel b) and c) show respectively composite maps for the same variables with thecondition of JJA temperature anomaly smaller or higher that 4.2 o K.–11–anuscript submitted a)b)
Figure 4.
Panel a) shows the genealogical tree of a rare event algorithm experiment, with N = 100 ensemble members, for selection of Scandinavia seasonal heatwaves. Each broken line,composed by one trunk and its branches up to the last leave, represents a trajectory. The horizontalaxis represents time in blocks of τ = 5 days. The genealogical trees have been created with thehelp of the ETE Python toolkit (Huerta-Cepas et al., 2016). Black lines represent trajectories with a JJA < . o K, red lines trajectories with a JJA > . o K. Panel b): the same, but with different colorsfor each 5 day period: blue corresponds to negative 5-day time averaged anomalies, black between0 and 4.5 o K, and red above 4.5 o K. –12–anuscript submitted
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