Meridional energy transport extremes and the general circulation of NH mid-latitudes: dominant weather regimes and preferred zonal wavenumbers

. The extratropical meridional energy transport in the atmosphere is fundamentally intermittent in nature, having extremes large enough to affect the net seasonal transport. Here, we investigate how these extreme transports are associated with the dynamics of the atmosphere at multiple scales, from planetary to synoptic. We use ERA5 reanalysis data to perform a wavenumber decomposition of meridional energy transport in the Northern Hemisphere mid-latitudes during winter and summer. We then relate extreme transport events to atmospheric circulation anomalies and dominant weather regimes, identified by 5 clustering 500hPa geopotential height fields. In general, planetary-scale waves determine the strength and meridional position of the synoptic-scale baroclinic activity with their phase and amplitude, but important differences emerge between seasons. During winter, large wavenumbers ( k = 2 − 3 ) are key drivers of the meridional energy transport extremes, and planetary and synoptic-scale transport extremes virtually never co-occur. In summer, extremes are associated with higher wavenumbers ( k = 4 − 6 ), identified as synoptic-scale motions. We link these waves and the transport extremes to recent results on exception-10 ally strong and persistent co-occurring summertime heat waves across the Northern Hemisphere mid-latitudes. We show that these events are typical, in terms of dominant regime patterns associated with extremely strong meridional energy transports.

clustering 500hPa geopotential height fields.In general, planetary-scale waves determine the strength and meridional position of the synoptic-scale baroclinic activity with their phase and amplitude, but important differences emerge between seasons.
During winter, large wavenumbers (k = 2 − 3) are key drivers of the meridional energy transport extremes, and planetary and synoptic-scale transport extremes virtually never co-occur.In summer, extremes are associated with higher wavenumbers (k = 4−6), identified as synoptic-scale motions.We link these waves and the transport extremes to recent results on exception-

Introduction
The latitudinal gradient in incoming net solar radiation is the main trigger of atmospheric and oceanic dynamics (Peixoto and Oort, 1992).Indeed, the resulting energy imbalance induces an atmospheric circulation that causes divergence of moist-static energy at low latitudes and convergence at high latitudes.
In the low latitudes, a key role is played by the zonally averaged circulation, dominated by the Hadley circulation, and the energy transport embedded in the mass streamfunction (Holton and Hakim, 2012).In the mid-latitudes, eddies are the most significant contributors to the overall transport.Conventionally, the eddy contribution is partitioned into a transient and a stationary component, with the former identified as the instantaneous deviation from long-term climatology, and the latter as the climatological departure from the zonal mean transport (e.g.Starr and White (1954); Lorenz (1967)).Energy transports associated with transient eddies have been found to exhibit a large variability, with a number of sporadic extreme events exceeding the mean values by a few orders of magnitude (Swanson and Pierrehumbert, 1997;Messori andCzaja, 2013, 2015).This emphasizes the non-linear nature of baroclinic activity and its interactions at different wave-scales and with the zonalmean circulation (cfr.Kaspi and Schneider (2013); Messori and Czaja (2014); Novak et al. (2015)).
The conventional transient-stationary decomposition, separating spatio-temporal averages and anomalies, mixes different spatio-temporal scales and does not allow to identify how specific features of the multiscale atmospheric dynamics in the midlatitudes are linked to meridional energy transports.An alternative approach uses a Fourier decomposition of eddy modes, to isolate the contribution of different zonal wavenumbers to the overall transport (Graversen and Burtu, 2016).It has recently been extended, by means of a wavelet decomposition, to the investigation of regional features, such as extratropical cyclones (Heiskanen et al., 2020).Fourier decomposition has enabled to separate synoptic and planetary-scale contributions, and their respective roles in engendering extreme meridional energy transports (Lembo et al., 2019).While synoptic-scale eddies always allow for baroclinic conversion, and thus systematically contribute to a poleward transports, planetary-scale eddies can occasionally oppose the total transport.These results point towards the importance of modes of low-frequency variability in modulating the energy transport by eddies (Messori and Czaja, 2015;Messori et al., 2017) and the emergence of preferred weather regimes in the occurrence of intermittent meridional energy transport extreme events (cfr.Nie et al. (2008); Ruggieri et al. (2020)).In a quasi-geostrophic context, the conversion of available potential energy into kinetic energy (Lorenz, 1955) supports interpreting the energy transfers in terms of modes of atmospheric variability, although the limits of predictability often challenge our understanding of low frequency variability and weather patterns associated with it.Particularly, blocking events in mid-latitudes have proven to be very complex aspects of the circulation, so that understanding the mechanisms behind them (Woollings et al., 2018;Lucarini and Gritsun, 2020) and reproducing them in state-of-the-art models (Davini and D'Andrea, 2016;Schiemann et al., 2020) is still an open issue.Through recurrent and persistent blockings, low frequency variability manifests itself, especially in summer, in terms of heat waves (e.g. the 2010 summer event over Russia, Dole et al. (2011)), whose nature of intermittent and extreme events has been recently studied with different methodologies, such as rare events algorithms (Ragone andBouchet, 2020, 2021) and large deviation theory (Gálfi et al., 2019;Galfi and Lucarini, 2021;Gálfi et al., 2021).Here, we leverage the Fourier decomposition approach of Graversen and Burtu (2016) to analyse the circulation anomalies and weather regimes associated with meridional energy transport extremes.We select the extremes with a rigorous methodology based on Extreme Value Theory (EVT) (Gnedenko, 1943).We then link the meridional structure of the wavenumberdecomposed extreme distribution to the emergence of anomalous weather regimes.
The paper is organised as follows: in Sect. 2 we describe the data, the methodology for extreme events selection and for the clustering of weather regimes.In Sect.3a distributions of meridional energy transports, their wavenumber decomposition and their extremes as a function of latitude are described, while in Sect.3b clustering of geopotential heights is related to composites of extreme events and dominant wavenumbers.In Sect. 4 an interpretation of these results is given, in light of composite mean anomaly patterns of geopotential height fields associated with extreme transports, while Sect. 5 summarises the findings and outlines limitations and future perspectives.

Data
Data for meridional energy transport and atmospheric circulation analyses are obtained from the ERA5 Reanalysis (Hersbach et al., 2020), retrieved from the Copernicus Data Storage (CDS).The data used covers December-January-February (DJF) and June-July-August(JJA) from 1979 to 2012, with a 6-hourly temporal resolution, a horizontal spatial resolution of 1 • ×1 • and 137 vertical levels.We deem the 6-hourly sufficient to encompass the synoptic and larger modes of variability, as evidenced in recent analyses (Lembo et al., 2019).The choice of seasons is aimed at avoiding conflating regimes that are representative of the warm and cold seasons, as may happen in spring and autumn.The analysis is focused on the mid-latitudinal Northern Hemisphere channel, i.e. latitudes in the 30 • N-60 • N range.For the computation of moist static energy, specific humidity (q), air temperature (T), and geopotential height (z) are considered.For the retrieval of the weather regimes and the k-means clustering, daily geopotential height at 500 hPa (z500) is used.

Meridional energy transports and wavenumber decomposition
The instantaneous meridional energy transport (or, more correctly, the enthalpy transport, cfr.Ambaum (2010); Lucarini and Ragone (2011)) is obtained as the scalar product of the meridional velocity v and the total energy E, including the kinetic energy and the moist static energy H, defined as: where q is the specific humidity, T is the air temperature, z is the geopotential height, L v , c p and g are the latent heat of vaporization, the specific heat at constant pressure, and the gravity acceleration, respectively.latitude is computed with the vertical and zonal integration: where p s is the surface pressure and V is the horizontal velocity vector.The sign convention is that transport is positive when northward directed, and negative when southward directed.The wavenumber decomposition is extensively discussed in Graversen and Burtu (2016), and in Lembo et al. (2019).We briefly summarize it here, recalling that the meridional energy transport as a function of zonal wavenumber k can be written as: where a and b are the Fourier coefficients defined as: where Ψ is either v or E, D = 2πR cos(ϕ) with R being the Earth's radius, k being the zonal wavenumber, and t, ϕ, λ the time, latitude and longitude, respectively.The highest zonal wavenumber N is set to 20, given that the spatial and temporal resolution of the ERA5 outputs poses a constraint to the modes of variability that can be resolved, and since it has been shown that the transport associated with wave number 0 to 20 constitute almost entirely the total transport (Graversen and Burtu, 2016).For sake of conciseness, we group wavenumbers into: k=0, reflecting zonal mean transports, k=1−5 for planetary-scale transports, k=6−10 for synoptic-scale transports and k=11−20 as mesoscale and lower spatial scale transports.The meridional circulation includes a zonal mean mass transport in opposite direction at different altitudes.However, at small temporal scales a vertical mean mass transport across latitudes may be encountered, which may transport a large amount of energy.This latter component of the enthalpy transport has to be subtracted from wave zero transport, in order to obtain the energy transport by the mean meridional circulation (Liang et al., 2017), which is done following Lembo et al. (2019).The instantaneous zonal mean and vertical mean meridional-circulation energy transport component is thus written as: with { } denoting the vertical mean, [ ] the zonal mean and † the departure from the vertical mean.Note that the wave zero energy transport component is given by the first term on the r.h.s. of Eq. 7.

Selection of the extreme events
We adopt in this work a rigorous methodology for the detection of meridional energy transport extremes based on the "peak over threshold" approach of Extreme Value Theory (EVT) (Balkema and Haan, 1974;Pickands, 1975).The main advantage of this methodology is that the properties of the data themselves determine the threshold used to define extreme events instead of arbitrary threshold choices.Furthermore, the probability distribution of extreme values is given by EVT, thus no subjective decisions are needed considering the shape of this distribution.An overview of this approach is hereby drawn, based on Coles et al. (2001), and of the convergence algorithm also presented in Gálfi et al. (2017).Full theoretical and technical details can be found therein.
We first consider a series of independent identically distributed random variables X 1 , X 2 , ... with common probability distribution F (X), X denoting an arbitraty term in the series X i .Under appropriate conditions (discussed generally below, for a comprehensive and rigorous description see Leadbetter (1974); Leadbetter et al. (1989); Coles et al. (2001)), the threshold exceedances y of a large enough threshold u, y = X − u with X > u, are asymptotically distributed according to the Generalized Pareto Distribution (GPD) family as: with 1 + ξy/σ > 0 for ξ ̸ = 0, y > 0, and σ > 0. The shape parameter ξ determines the shape of the distribution and the tail behavior.If ξ = 0 the tail of the distribution decays exponentially, if ξ > 0 the tail decays polinomially, while, if ξ < 0, the distribution is bounded.
In order to apply EVT to meridional energy transport data, one has to make sure that the conditions of independence and homogeneity are fulfilled, and thus the data can be modelled based on a stationary stochastic process (Leadbetter, 1974).While both conditions are, strictly speaking, unrealistic in case of geophysical data, the problem can be approached from a practical perspective.First, we detect linear long-term trends for the 1979-2012 period, and we test their significance according to a Mann-Kendall test at the 95% significance level (Mann, 1945;Forthofer and Lehnen, 1981), then we remove trends only at those latitudes where they are found to be significant, i.e., for DJF, north of 37.5 • N, for JJA in the 40 convergence to the limiting distribution (Coles et al., 2001).To avoid this, we decluster, where necessary, the time series before estimating the parameters by using the "intervals" declustering method (Ferro and Segers, 2003) based on the "extremal index" defined in Gálfi et al. (2017).
We then test the applicability of the theory by looking at the convergence of the selected extremes to the limiting GPD distribution.This is done by plotting the estimated shape parameter ξ(u) as a function of an increasing threshold u.The lowest threshold u * at which the shape parameter "plateaus", i.e. does not change with further threshold increases, provides the optimal parameter estimate.This estimate has a lower uncertainty than for u > u * , and at the same time provides an estimated distribution which is equivalent to the limiting GPD considering the estimation uncertainty given by the confidence intervals.In order to achieve a latitude-independent definition of extremes, we express the threshold in terms of fraction of data points above the threshold.
This threshold selection procedure applies in case of extremes located in the right tail of the transport's probability density function (pdf), hereafter referred to as "poleward" extreme energy transports.Similarly, we refer to extremes located in the left tail of the pdf as "equatorward" extreme energy transports.These extremes are weaker than the median transports, and sometimes slightly negative.The procedure for equatorward extremes is the same as described above for poleward extremes.
Hence, we search for a stable shape parameter as function of a decreasing threshold, equivalent to a decreasing fraction of data points below the threshold.
For illustrative purposes, Figure 1 shows the behavior of the shape parameter ξ as a function of the threshold u at different latitudes.We notice that the shape parameter is almost everywhere negative, evidencing that the extreme value distribution is bounded.In other words, Figure 1 provides a graphical explanation of the convergence methodology, justifying the following choice of the thresholds: -DJF, equatorward: 10% of data below the threshold (10% percentile); -DJF, poleward: 14% above the threshold (86% percentile); -JJA, equatorward: 14% below the threshold (14% percentile); -JJA, poleward: 7% above the threshold (93 % percentile); We notice that, while ξ is systematically negative for this choice of the thresholds, σ is positive and slightly increasing with latitude, denoting an increasingly large spread of extremal values (Fig. 1a, b).

Weather regimes
The Weather Regimes (WRs) are computed from the daily geopotential height at 500 hPa (z500), using the WRtool Python package (Fabiano et al., 2021).We summarise the methodology here; for more details and discussion the reader is referred to the Methods section in Fabiano et al. (2020).We focus on latitudes between 30 • and 90 • N and three different longitudinal sectors: the Euro-Atlantic (EAT, from 80°W to 40°E), the Pacific-North American (PAC, from 140°E to 80°W) and the whole Northern Hemisphere mid-latitudes (NH).The original data were first interpolated to 2.5 • ×2.5 • horizontal resolution; since the WR diagnostic aims at capturing largescale configurations, this step does not alter the results of the analysis.Before computation, the daily mean seasonal cyclesmoothed with a 20-day running mean -is removed from the data to obtain daily anomalies.
To retain only the large-scale component and reduce dimensionality, an Empirical Orthogonal Function (EOF) decomposition is performed, separately for each considered longitudinal sector.The minimum number of EOFs that explain at least 90% of the total variance is retained: this corresponds to 16, 19 and 41 EOFs during DJF for the EAT, PAC and NH, respectively; for JJA 22, 25 and 57, respectively.The WRs are then computed by applying a K-means clustering algorithm to the selected Principal Components (PCs).For all sectors and seasons, we set the number of regimes to 4. This choice is widely documented in literature for the EAT and PAC winter circulation (Michelangeli et al., 1995;Cassou, 2008;Weisheimer et al., 2014;Hannachi et al., 2017;Straus et al., 2017), although different numbers of clusters have been used in other studies (e.g.Pasquier et al., 2019;Strommen et al., 2019;Hochman et al., 2021).Each day is assigned to one of the regimes and a set of 4 regime centroids is obtained.The regime pattern is defined as the composite of all anomalies assigned to a certain regime.
We refer to JJA regimes (right column) as xCn, with "x" being EAT, PAC or NH, and n = 1, . . ., 4 the index denoting the cluster.Thus, for the EAT domain: EAT C1 features a zonally spread blocking extending from the Eastern Atlantic to Scandinavia, EAT C2 closely resembles the NAO+ pattern, EAT C3 can be referred to as a Greenland blocking, while EAT C4 features a dipole structure, with an Eastern Atlantic low and a Scandinavian high (cfr.Guemas et al. (2010); Yiou et al. (2011)).
Concerning PAC and NH, all regimes feature anomalies that are much weaker than DJF regimes, given that the circulation as a whole is weaker in the JJA season.P ACC1 features a weak blocking south-west of Alaska, while P ACC2 is somehow similar to the BR pattern, although much weaker.P ACC3 and P ACC4 appear to mirror each other.N HC1 exhibits a Siberian high, while N HC2 features a number of highs surrounding the North Pole; N HC3 features a Greenland blocking and N HC4 closely resembles EAT C1.
For each cluster, the absolute frequency is computed within the population of all events, then the ratio of absolute frequency in the population of extreme events to the absolute frequency in the overall population is obtained, for each tail of the distribution and in each season.Specifically, the relative variations in absolute frequencies are retrieved as ∆f ′ x = f ′ x fx − 1, where f x is the absolute frequency of occurrence of the cluster x for the overall population, and f ′ x is the frequency of occurrence of extreme events in cluster x relative to the total extreme population.Hence a positive ∆f ′ x indicates that cluster x include a higher fraction of extreme events compared to its fraction of all events, i.e. cluster x is more favourable for extreme events.In https://doi.org/10.5194/wcd-2021-85Preprint.Discussion started: 4 January 2022 c Author(s) 2022.CC BY 4.0 License.order to assess whether the variation in absolute frequencies is significant, a bootstrapping is performed, through 300 random resamplings of the original population with the same number of events as the number of extreme events in the respective tail.
The hypothesis test is performed at the one-sided 95% significance level.
In order to link the weather regimes characterisation of extremal transports to the wavenumber decomposition illustrated in Sect.3.1, we focus on the zonal wavenumber effecting the largest share of the meridional energy transport anomaly.First, at each latitudinal band, for each assigned weather regime, in each season and for each tail of the distribution, we compute the contribution of each individual wavenumber to the meridional energy transport anomaly wrt. the average across the extreme events in the selected subset.Then, the dominant wavenumber for the specific event is assigned, as the one whose contribution to the transport is largest.Finally, the average of the dominant wavenumbers across the subset of extreme events assigned to the specific regime and occurring at the selected latitudinal band is computed.

The PDFs of meridional energy transports and their wavenumber decomposition
We start our analysis by looking at the PDFs of the total and wavenumber-decomposed meridional energy transports and their extremes.
The normalized PDFs (filled contour plots) of the total zonally averaged meridional energy transport are computed for each latitude in the 30 • -60 • latitudinal channel, as shown in the top panels of Figures 3 and 4 (for DJF and JJA, respectively).In DJF, the PDF peaks at about 42.5 • N, with a value of 6.5×10 15 W , and then steeply decays towards the high latitudes.In JJA, the PDF shows a weaker variability across latitudes, with a mean/median value oscillating between 2.0 and 2.5×10 15 W , and a moderate decrease towards the high latitudes.PDFs in DJF are mildly positive-skewed (with higher skewness at the edges of the midlatitudinal channel, amounting to 0.96-1.09,and lower skewness in the midlatitudes, about 0.85).The low latitudes in JJA clearly reflect a positively skewed distribution, whereas the PDF is more symmetric in the high latitudes data (with skewness ranging between 1.28 in the low latitudes and 0.96 in the high latitudes).
The tails of the distributions, encompassing the extreme events selected according to the methodology described in Sect.
2.2.2, are skewed towards either equatorward or poleward extreme transports in both seasons.Equatorward extremes attain smaller or even negative values at higher latitudes, where the mean transport is weaker, which emphasises the importance of such extreme events for setting the seasonal energy transport at high latitudes.The opposite occurs for the poleward extremes, with the largest extremes being stronger for those latitudes where the mean transport is stronger.This is in agreement with Lembo et al. (2019), who found that both poleward and equatorward extremes are related to the mean strength of the transport (cfr.their Figure 1d-g).
We next decompose the transport into its wavenumber components (panels c)-f) in Figures 3 and 4).Not surprisingly, in both seasons the most significant contribution to the overall transport comes from the planetary-scale and synoptic-scale of poleward extremes follows that of the median transport for the respective component, and attains large values when the median component is at its maximum.Equatorward extremes, on the other hand, only partly follow the median curve and attain near-zero values at almost all latitudes, especially regarding the synoptic contribution.During JJA, a significant share of planetary-scale equatorward extremes feature net negative transport in the middle latitudes, where the contribution to the transport is almost vanishing on average.This is consistent with planetary waves being able to act passively, transporting energy counter-gradient, and thus with no conversion of available potential energy into kinetic energy, as discussed in Baggett and Lee (2015); Lembo et al. (2019).Synoptic-scale waves, instead, almost everywhere share the positive sign and the meridional structure of the mean transport, although as in DJF, the most extreme events during JJA also attain near-zero values at almost all latitudes.

Weather regimes and zonal wavenumbers associated to extreme events
We now shift our attention to the detection of weather regimes in the population of extreme events, in order to investigate the relation between extreme transports and recurrent patterns of the large-scale circulation.
As discussed in Appendix B, conditioning on different extreme transport events yields different average values of the PCs of the leading EOFs, suggesting that the population of extreme events might exhibit a preferred development of specific weather regimes.Following from this hypothesis, we compute ∆f ′ x in the population of extreme events (as described in Sect.2.2.3), grouping extremes by 2-degrees wide latitudinal bins.Figures 5-6 display ∆f ′ x for each of the chosen regimes in the EAT, PAC and NH regions, for poleward (left) and equatorward (right) extreme events in DJF and JJA, respectively.DJF poleward extremes are characterized by anomalously negative z500 anomalies in the lower mid-latitudes and highlatitudinal blockings, especially over the Northern Atlantic, as denoted by the sharp increase in the frequency of NAO-, AO and PT regimes.Consistently, a significant reduction in the NAO+, BR and ALR modes is found.In JJA, NHC4/EATC2, characterised by a pattern similar to an Eastern Atlantic-Scandinavian blocking, is increasingly likely.EATC4 and PACC4, denoted by negative anomalies in the eastern boundaries of the Atlantic and Pacific oceans, are rarer, as well as NHC3, featuring a weak Pacific ridge and a Greenland blocking.In general, we observe that changes in absolute frequencies are coherent across neighbouring latitudes, consistently with what is observed for the energy transport extremes, often occurring concomitantly at several latitudes (compare to Fig. 1d-g in Lembo et al. (2019)).
DJF equatorward extremes largely mirror what is described for poleward extremes: NAO-, PT and AO modes become generally less frequent, whereas NAO+, PNA-, ALR and, to some extent, BR modes are more frequent.In other words, a more zonal North Atlantic regime and stronger Pacific blocking are associated with weaker meridional transports.This is in line with the opposite signs of PC fractional changes described in Appendix B. Looking at JJA, it clearly emerges that the P ACC4 pattern becomes more frequent, while P ACC3 and N HC3 (especially for extremes at high latitudes) are rarer.Remarkably, EAT C3 and EAT C1 become increasingly likely for extremes at low and mid-latitudes, respectively, EAT C2 for extremes at higher latitudes.This suggests a weakening and a northward shift of the centres of baroclinic activity, as the latitude at which the equatorward extremes are selected increases.We then focus our attention to the dominant wavenumber, as a function of the region and of the cluster to which extreme events are attributed.We remark that the spectrum of the meridional energy transports is now different from the one considered in Figures 3 and 4, as we focus on the wavenumber decomposition anomalies relative to their climatological contributions, rather than on their absolute values.For this reason, we limit our range of wavenumbers to 0 − 7, as no higher wavenumber appears to be dominant in any of the considered cases.
No matter in which region the clustering is focused, DJF extreme events are associated with wavenumbers between 2 and 4 (Figure 7).In JJA (Figure 8), the situation is more diversified, with wavenumbers in the range of k = [2, . . ., 6] and a clearer dependence on the circulation cluster.The dominance of higher zonal wavenumbers is consistent with the finding that PC fractional changes in JJA occur mainly for higher order EOFs, as described in Appendix B. Poleward extremes generally peak at higher wavenumbers than equatorward extremes.Focusing on EAT C2 and N HC4, we also find that synoptic scales (k = 5 and k = 6) are co-located with latitudes featuring the largest frequency change (cfr.Figure 6).Interestingly, to some extent the same happens for EAT C4, P ACC4 and N HC3, where the latitudes featuring the largest frequency reductions are also characterised by relatively higher wavenumbers (compared to extremes in other clusters and in the same cluster but different latitudes), again k = 5 and k = 6.Dominant wavenumbers for equatorward extremes are less sensitive to frequency variations: events associated with P ACC4 and EAT C1 frequency increases are associated with a dominant k = 4 wavenumber.EAT C2 features a k = 3 dominant wavenumber in the high latitudes, whereas EAT C3 is characterised by a k = 2 wavenumber in the low latitudes.

Discussion
Composite mean z500 anomalies for the subset of extremes taken at different latitudes (Figures 9 and 10) support the message contained in the results above.Clearly, JJA and DJF differ in the fact that the higher zonal variability in the latter is related to a higher dominant zonal wavenumber.In both seasons, poleward extremes are characterised by a more marked meridional structure of the z500 anomalies compared to equatorward extremes, confirming that the zonality of the general circulation (and the dominant patterns denoting it) is related to the strength of the meridional energy exchanges.
Going into the details of the different seasons and tails of the distributions, we start from JJA equatorward extremes, given that they exhibit an a priori surprisingly large share of energy exchanges from the Pole toward the Equator.Lower latitudinal extremes are associated with widespread negative z500 anomalies, both on the main ocean basins and on land.For higher latitudinal extremes, a Euro-Scandinavian blocking pattern emerges, consistently with an increasing frequency of the EAT C2 pattern, with negative z500 anomalies confined at even higher latitudes, and with a dominant k = 2−3 wavenumber pattern.An interpretation of these features is provided in light of what described above (cfr.Figures 6 and 8).At lower latitudes (30-33 • N), the increased likelihood of the P ACC4 regime is consistent with co-located negative anomalies, especially over the Pacific, and a dominant k = 4 wave.Overall, this hints at the role of the planetary-scale contribution, that is particularly relevant when the total transport extreme is negative and the synoptic contribution is weak, especially at higher latitudes, as seen in Figure 4. Looking at the composites, we thus argue that, when the extreme transport is negative, the planetary-scale transport in the JJA poleward extremes also find a relatively straightforward interpretation in the z500 composites.For extremes located in the 30-33 band, negative z500 anomalies are widespread (although with very different patterns compared to the equatorward extremes), while at higher latitudes several blocking patterns emerge in the channel.Overall, the regime frequency changes (in particular the reduced frequency of the EATC4, PACC4 and NHC3 regimes) are consistent with this pattern, with the midlatitudinal negative anomalies being replaced by coexisting high geopotential ridges.Consistently with Figure 8, evidencing that these patterns are dominated by wavenumbers k = 5 − 6, Kornhuber et al. (2020) find that these modes of the general circulation are associated with the development of co-located heat waves in the NH Summer.We thus argue that heat waves may plausibly be related to the occurrence of extremely strong poleward meridional energy transports.
To heuristically test this hypothesis, we focus on poleward extreme transports in JJA for the year 2010, which was characterised by a number of concurrent heat waves developing in several regions of the NH mid-latitudinal channel, especially Central-Eastern North America and Russia (Dole et al., 2011).Figure 11 shows analogous results to those shown in Figures 6, 8 and 9, for JJA 2010 only.Extremes at the three chosen latitudinal bands are associated with a positive anomaly over Eastern Europe and Russia, particularly intense in the 45-47 latitudinal band.The composites are also consistent with an increased frequency of the EAT C2 and N HC4 patterns (Figure 11b), especially in the higher latitudinal bands.In addition to that, some frequency reductions, that are not as relevant in the rest of the extreme events population, are found for EAT C1, P ACC1 and N HC1, pointing towards a reduced occurrence of a NAO+ regime and of the so-called "Aleutinian ridge".Kornhuber et al. (2020) interpreted the 2010 heatwave as a case study of concomitant heatwaves over several regions of the Northern Hemisphere, a consequence of quasi-resonant amplification of stationary Rossby waves (Kornhuber et al., 2017;Petoukhov et al., 2013).They found that k = 5 − −7 were particularly favorable to the development of this pattern.Here, we show (Figure 11c) that more frequent regimes in the energy transport extremes population are associated with dominant wavenumbers ranging between k = 4 and k = 6.Overall, we thus argue that the 2010 event is "typical" of the more general circulation features associated with poleward meridional energy transport extremes in JJA, and that their occurrence is consistent with the explanation given by (Kornhuber et al., 2020) and the quasi-resonant amplification mechanism.The fact that the 2010 event captures a rare yet typically persistent fluctuation of the summer atmospheric fields in Eurasia has been discussed by Galfi and Lucarini (2021) using large deviation theory arguments.We also found (not shown) that the so-called "Dzud" event occurred in Winter 2010, characterized by intense and persistent cold outbreaks throughout parts of Asia, has been typical (in the sense described above) in terms of meridional energy transport extremes, and associated weather regimes.
Looking at DJF z500 composites (Figure 10), we note that the three latitudinal bands are characterised by a NAO-pattern, when poleward extremes are taken into account.In the Pacific-North American sector, a dipole structure, somewhat opposed to what found in JJA, emerges, with a strong trough in the Pacific and a ridge over the American continent at 45-47, moving westward and weakening at 57-60.The described pattern is consistent with what found in Figure 5, the NAO-, PT and AO weather regimes becoming more frequent for extremes at all latitudes.At the same time, the Pacific dipole structure is opposed at higher latitudes by negative anomalies, consistently with a reduction in high-latitudinal blockings over that region, as denoted https://doi.org/10.5194/wcd-2021-85Preprint.Discussion started: 4 January 2022 c Author(s) 2022.CC BY 4.0 License.by the decreased frequency of ALR and BR regimes.Composites are also consistent with k = 2−3 being the range of dominant wavenumbers for the DJF poleward extremes, as seen in Figure 7, with a relatively weak dependence on the weather regime assigned to the extreme event under consideration.The pattern for DJF equatorward extremes is to a certain extent reversed wrt.poleward extremes, with a clear NAO+ footprint in the poleward half of the mid-latitudinal channel, and a ALR-like pattern for extremes located in the 45-47 • channel.This reflects the fact that the dominant k = 2 − −4 wavenumbers do not change for the two classes of extremes, no matter the regime to what these are assigned (cfr.Figure 7).It is rather the phase and amplitude of ultra-long planetary-scale waves, carrying energy from the Equator towards the Pole for both poleward and equatorward meridional transport extremes (cfr.Figure 3c), that determine the strength and location of the overall baroclinic eddy activity.
In DJF, planetary and synoptic-scale transport extremes thus rarely co-occur (as already stressed in Lembo et al. (2019) and above in this work), and the planetary contribution to the extreme transport is less dependent on the median value of the transport than the synoptic contribution.In other words, in DJF the planetary-scale pattern, embedding higher-scale eddies, is dominant almost everywhere except at lower latitudes, and the synoptic scale contribution sharply weakens with the median transport as the latitude increases.Synoptic-scale eddies are thus modulated by the phase and strength of the underlying dominant planetary wave, as clearly suggested by the 500 hPa geopotential anomalies.On the contrary, the strengths of the planetary-and synoptic-scale contributions are comparable in JJA.The pattern highlighted by the composite analysis is thus a blend of the two competing factors, with synoptic-scales becoming dominant in central latitudes (for poleward extremes) or the two contributions canceling each other almost symmetrically at most latitudes, confining baroclinic activity where the extreme transports occur (for equatorward extremes).
Summarizing, the composite analysis illustrates qualitatively that the extremes in the overall transport are the result of the interference of high and low wavenumbers (see also the discussion in Messori and Czaja (2014) and Messori et al. (2017) on this topic).Such interference occurs in different ways in the two seasons, with the planetary-scale waves generally determining the latitude and strength of the baroclinic activity, but relative role of the synoptic and planetary waves being very different at different latitudes.The minima and maxima of the planetary and synoptic-scale transports are in fact located at the two edges of the mid-latitudinal channel in DJF, and at the centre of the channel in JJA (cfr.Figures 3c-d and 4c-d).

Summary and Conclusions
In this work, we analysed the zonally averaged meridional energy transports in the mid-latitudinal NH channel for the DJF and JJA seasons in ERA5 Reanalysis.We decomposed the transports depending on their zonal wavenumbers, and isolated four contributions: zonal mean (k = 0), planetary scales (k = 1 − −5), synoptic scales (k = 6 − −10) and higher scales (k = 11 − −20).We applied an EVT-based selection methodology to isolate extreme meridional energy transport events, labelled as "poleward", when the transport is stronger than average, "equatorward" when it is weaker.We adopted a clustering algorithm for the z500 anomalies associated with meridional energy transport extremes, and we looked for dominant patterns and preferred wavenumbers as a function of the latitudes at which the extremes are detected.We used this to support our interpretation of geopotential height composites of extreme transport events.We find that energy transport extremes emerge as a result of the growth of different wave types across the mid-latitudes, particularly synoptic and planetary scales depending on meridional location and season.Specifically, dominant patterns and preferred wavenumbers suggest that planetary scales determine the strength and meridional position of the synoptic-scale baroclinic activity with their phase and amplitude, exhibiting significant seasonal differences.In DJF, they modulate the synopticscale activity, which is generally stronger than the smaller scales, while in JJA they chiefly interfere with the latter being of similar magnitude, either constructively (poleward extremes) or destructively (equatorward extremes).Notably, equatorward extremes feature mainly negative-signed planetary-scale transports north of 42 • N.
Understanding meridional energy transport extremes is key to identify mechanisms through which diabatic heating and temperature gradients are balanced.We demonstrated that some preferred regimes favour extreme transports, and that they reflect to some extent preferential modes of variability related to specific zonal wavenumbers.This has clear implications for high latitude warming/cooling, as already stressed before regarding the influence of synoptic-scale eddy activity on Arctic weather (cfr.Ruggieri et al. (2020)) or dynamical patterns related to extreme near-surface temperatures over the Arctic (cfr.Messori et al. (2018); Papritz (2020)).
The emergence of dominant zonal wavenumbers associated with extreme meridional energy transports also has implications for teleconnections.Investigations based on large deviation theory have shown that persistent weather extremes are associated with very large scale atmospheric features Gálfi et al. (2019); Galfi and Lucarini (2021); Gálfi et al. (2021).We emphasized here the similarity between our results and the concurrent emergence of heat waves across the Northern Hemisphere associated with a persistent k = 5 − −7 Rossby wave pattern, as found by Kornhuber et al. (2020).Our results emphasize that the modes related to energy transport extremes are hemispheric in scale, and suggest that regional features such as the NAO or PNA trigger co-variability of weather in remote regions Thompson and Wallace (1998); Branstator (2002).Analysing the aggregated effect of wave packets on meridional energy transports in association with weather regimes provides a thermodynamic background to the concept of quasi-resonant amplification Petoukhov et al. (2013); Coumou et al. (2014); Kornhuber et al. (2017) for the development of weather extremes, potentially linking local events to anomalies in the general circulation.
Here, we estimated the extremal index with the aim to decluster the energy transport time series in order to accelerate the convergence of extreme value statistics.The extremal index itself, however, contains valuable information related to the persistence of extreme states, as it is the inverse of the mean cluster size of extremes Coles et al. (2001).In future studies, one could concentrate more on the persistence of extreme (and non-extreme) events in meridional energy transport based on the extremal index.The persistence of individual states together with the local attractor dimension can be used as a dynamical proxy of the general circulation.This approach has already successfully been applied to dynamical features of the atmosphere (Faranda et al., 2017;Messori et al., 2021)), but never, to the best of our knowledge, to thermodynamic features.
Finally, a possible outcome of this analysis, that is left for future work, is the study of meridional energy transport extremes, their zonal wavenumber decomposition and the underlying dynamical drivers, in numerical climate simulations.Assessing the statistics of these events against reanalysis-based data would provide an important background for the study of the climate response to external forcing and how changing statistics in extreme events related to baroclinic eddies can affect future weather predictability in the mid-latitudes (cfr.Scher and Messori (2019)).
• N-47.5 • N and 54.5 • N-58.5 • N latitudinal bands.By analysing summer and winter separately, we eliminate another source of dependence and heterogeneity due to the seasonal cycle.Furthermore, we verify for every latitude the decay of the auto-correlation function.Despite the fact that several consecutive values in our times series are correlated, the chaotic nature of atmospheric motions allows that two values being far away in time from each other are nearly independent, meaning that the auto-correlation function decays to 0 at a finite time lag.Looking at the auto-correlation functions, we find that JJA (DJF) daily data require the removal of the climatological JJA (DJF) season at every latitude (south of 45 • N).Once this is achieved, the GPD parameters may be computed.Even in the absence of long-range correlations, however, one may encounter clusters of data exceeding the threshold consecutively in time.Those are clearly correlated and would lead to biased GPD parameters 1 as a result of a slower https://doi.org/10.5194/wcd-2021-85Preprint.Discussion started: 4 January 2022 c Author(s) 2022.CC BY 4.0 License.
contributions.The equatorward and poleward extremes largely overlap in the zonal mean component, and both attain negative values.Very different patterns emerge at the planetary and synoptic scales.During DJF and at both these scales, the magnitude https://doi.org/10.5194/wcd-2021-85Preprint.Discussion started: 4 January 2022 c Author(s) 2022.CC BY 4.0 License.

Figure 1 .Figure 2 .
Figure 1.(Top) Meridional section for equatorward DJF meridional energy transport extremes of: a. Shape parameter ξ; b.Scale parameter σ; c.Threshold value [10 15 W].The colours in a and b denote parameter estimates corresponding to the threshold values shown in c.The blue lines denote the final shape and scale parameter estimates based on the blue threshold values.(Bottom) Shape parameter as function of threshold (in terms of fraction of data points below the threshold) at different latitudes.The uncertainty range is defined based on 95% maximum likelihood confidence intervals.The orange vertical line denotes the selected fraction of data for the specific tail, which is chosen to be the same at all latitudes.