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 spatial
scales, from planetary to synoptic. We use the 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 clustering 500

The latitudinal gradient in incoming net solar radiation is the main trigger of atmospheric and oceanic dynamics

Meridional energy transports through eddies are increasingly recognized as communicating the climate change signal towards the high latitudes,
especially when taking into account the contribution by moisture

As an alternative to the usual transient–stationary eddy partitioning, a Fourier decomposition of eddy modes, isolating the contribution of
different zonal wavenumbers to the overall transport has been proposed

By separating synoptic and planetary scales as having wavenumbers

Here, we focus on meridional energy transports in the mid-latitudes, where the baroclinic activity is strongest. We decompose the transport using the
above-described zonal wavenumber decomposition approach of

The paper is organized as follows: in Sect.

Data for meridional energy transport and atmospheric circulation analyses are obtained from the ERA5 Reanalysis

The instantaneous meridional energy transport (or, more correctly, the enthalpy transport; cf.

The highest zonal wavenumber

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

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)

We first consider a series of independent identically distributed random variables

Meridional section for equatorward DJF meridional-energy-transport extremes of

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 modeled based on a stationary stochastic process

The asymptotic GPD shape parameter is not affected by the existence of clusters; its finite-size estimates however are biased due to the slow convergence.

as a result of a slower convergence to the limiting distributionWe 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

This threshold selection procedure applies in the 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 a function of a decreasing threshold, equivalent to a decreasing fraction of data points below the threshold.

For illustrative purposes, Fig.

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

The weather regimes (WRs) are computed from the daily geopotential height at 500

The original data were first interpolated to 2.5

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, and 22, 25 and 57, respectively, during JJA. An EOF-based dimensionality reduction is
a common first step in weather regime detection algorithms

For all sectors and seasons, we set the number of regimes to 4. This choice is widely documented in the literature for the EAT and PAC winter circulation

Clusters of zg500 geopotential height anomalies (in

Figure

We refer to JJA regimes (right column) as

As shown in Fig.

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

In order to link the weather regime characterization of extremal transports to the wavenumber decomposition illustrated in Sect.

We start our analysis by looking at the PDFs of the total and wavenumber-decomposed meridional energy transports and their extremes.

PDFs of total (filled contours) and extreme poleward (red contours) and equatorward (blue contours) DJF meridional energy transports over the 1979–2012 period in ERA5.

Same as in Fig.

Unbiased estimates of meridional-energy-transport skewness, as a function of latitude, for

The PDFs (filled contour plots) of the total zonally averaged meridional energy transport are computed for each latitude in the 30–60

The extreme transports for both equatorward and poleward tails of the distributions are identified from the PDFs of total zonally averaged transports,
following the methodology described in Sect.

We next decompose the transport into its wavenumber components in Figs.

Ratios of zonal (blue), planetary (red) and synoptic (yellow) wavenumber components for all events

To provide a clearer view of the relative importance of the different components, we show in Fig.

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.

Relative variations in absolute frequency of clusters

Same as in Fig.

As discussed in Appendix

DJF poleward extremes are characterized by anomalously negative z500 anomalies in the lower mid-latitudes and high-latitudinal blockings over the
northern Atlantic, as denoted by stronger frequency of NAO

DJF equatorward extremes largely mirror what is described for poleward extremes: NAO

We then focus our attention to the dominant wavenumber, as a function of the region and of the weather regime to which extreme events are
attributed. We remark that the spectrum of the meridional energy transports is now different from the one considered in Figs.

Time-averaged zonal wavenumber associated with meridional-energy-transport extremes (see text) for DJF clusters obtained in different regions, as a function of the latitude at which the extreme is found.

Same as in Fig.

No matter in which region the clustering is focused, DJF extreme events are associated with dominant wavenumbers between 2 and 4 (Fig.

The zonal wavenumber decomposition adopted here poses some challenges when trying to relate meridional-energy-transport extremes to specific
atmospheric circulation features. Above, we have adopted weather regimes as a tool to identify such circulation features, and we argue that they span
the diversity of patterns associated with these extremes. In order to further examine the population of extreme transport events and identify
persistent patterns in some regions of the domain, it is useful to complement the description of weather regimes and dominant wavenumbers with the
analysis of composite mean z500 anomalies. We stress that while the composite mean view is not informative of the intrinsic variability
associated with those extreme events, it allows already-evidenced aspects of the circulation associated with extreme transport
events to be better framed. Figures

Composite mean of z500 anomalies (in

Same as in Fig.

Sample sizes for extremes in each of the latitudinal circles chosen for the composite mean maps in Figs.

JJA equatorward extremes are particularly interesting, given that they account for an a priori surprisingly large share of energy transport from the
pole toward the Equator. As shown in Fig.

JJA poleward extremes also find a relatively straightforward interpretation in the z500 composites. For extremes located in the 30–33

To heuristically test this hypothesis, we focus on poleward extreme transports in JJA for the year 2010, which was characterized by a number of
concurrent heat waves developing in several regions of the NH mid-latitudinal band, especially central-eastern North America and Russia

Looking at DJF z500 composites (Fig.

In DJF, planetary- and synoptic-scale transport extremes rarely co-occur (as already stressed in

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

In this work, we analyze the zonally averaged meridional energy transports in the mid-latitudinal NH band for the DJF and JJA seasons in ERA5
Reanalysis. We decomposed the transports depending on their zonal wavenumbers and isolated four contributions: zonal mean (

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 amplitude, exhibiting significant seasonal
differences. In DJF, they modulate the synoptic-scale activity, being generally stronger than all other 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

Understanding meridional-energy-transport extremes is key to identifying mechanisms through which diabatic heating and temperature gradients are
balanced. We demonstrated that some preferred circulation regimes favor 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 and cooling, as already stressed before regarding
the influence of synoptic-scale eddy activity on Arctic weather (cf.

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

Here, we estimate 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

Finally, a possible outcome of this analysis, which 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 (cf.

Figures

Patterns of the four leading EOFs for DJF: EAT (first row), NH (second), PAC (third).

Patterns of the four leading EOFs for JJA: EAT (first row), NH (second), PAC (third).

We investigate here changes in the PCs of the population of extremes, compared to the population of all days. For the sake of simplicity, we restrict
ourselves to the four leading EOFs, computed in DJF and JJA over the three regions of interest: EAT, PAC and NH. Fractional changes in the mean of the PC
distribution relative to the climatological standard deviation (Fig.

Fractional change (relative to climatological standard deviation) of the PC mean for the first four leading EOFs, as functions of the region of interest, for

In DJF, significant shifts are found for the first PC, corresponding to the positive phase of the Arctic Oscillation (AO) pattern for NH

The choice of the threshold for the separation between planetary and synoptic scales, as well as the best indicator to consider the different scales,
is the topic of an ongoing scientific discussion

Synoptic-scale waves defined in this way are remarkably homogeneous across latitudes and seasons so that the only appreciable change is in the
position of the peak. This is broadly coherent with our approach, considering

Ultra-long planetary waves play a dominant role in shaping the extremes in DJF, consistent with Figs.

The regrouped wavenumbers support the conclusion that the strength of the extremes is in all cases dependent on the shape of the median
meridional section. The

Same as in Fig.

ERA5 Reanalysis data are publicly accessible via Copernicus Data Storage (

VLe, VLu and GM designed the analysis and wrote the manuscript. RG performed the wavenumber decomposition of meridional energy transports, VMG conceived the algorithm for extreme-event detection and carried out the convergence analysis, and FF performed the EOF and

The contact author has declared that none of the authors has any competing interests.

Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Gabriele Messori has received funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation program (grant agreement no. 948309, CENÆ project). Valerio Lucarini acknowledges the support received from the EPSRC project EP/T018178/1 and from the EU Horizon 2020 project TiPES (grant no. 820970). The work is also associated with the Norwegian Science Foundation (NFR) project no. 280727.

This research has been supported by the European Research Council (ERC) and a Research Innovation Action (RIA) under the European Union’s Horizon 2020 research and innovation program (grant nos. 948309 and 820970) and the Norwegian Science Foundation (NFR; project no. 280727).

This paper was edited by Pedram Hassanzadeh and reviewed by two anonymous referees.