The atmosphere transports energy polewards by circulation cells and eddies. To the present day, there has been a knowledge gap regarding the preferred spatial scales and physical mechanisms of eddy energy transport. To fill the gap, we separate the meridional atmospheric energy transport in the ERA5 reanalysis by spatial scales and into quasi-stationary and transient flow patterns and latent and dry components.

Baroclinic instability is the major instability mechanism in the transient synoptic scales and is responsible for forming cyclones, anticyclones, and small-scale Rossby waves. At the planetary scales, circulation patterns are often induced by other mechanisms such as flow interaction with orography and land–sea heating contrasts. However, a separation between circulation patterns at the synoptic and planetary scales has yet to be established. We find that both baroclinically induced and transient energy transport is predominantly associated with eddies at wavelengths between 2000 and 8000 km. The maxima in both types of transport occur at wavelengths around 5000 km, in good agreement with linear baroclinic theory. Since these results are independent of latitude, we adapt the scale separation of the energy transport to be based on the wavelength instead of the previously used wavenumber. We define the synoptic transport by the wavelength band between 2000 and 8000 km.

We analyse the annual and seasonal mean in the energy transport components and their inter-annual variability. The scale-separated transport components are fairly similar in both hemispheres.
Transport by synoptic waves is the largest contributor to extra-tropical energy and moisture transport, mainly of a transient character, and is influenced little by seasonality. In contrast, transport by planetary waves depends highly on the season and has two distinct characteristics. (1) In the extra-tropical winter, planetary waves are important due to a large transport of dry energy. This planetary transport features the largest inter-annual variability of all components and is mainly quasi-stationary in the Northern Hemisphere but transient in its southern counterpart. (2) In the sub-tropical summer, quasi-stationary planetary waves are the most important transport component, mainly due to moisture transport, presumably associated with monsoons.
In contrast to transport by planetary and synoptic waves, only a negligible amount of energy is transported by mesoscale eddies (

Atmospheric motions reduce the thermal contrast created by differential solar heating between high and low latitudes

Different separation methods of the vertically integrated, zonal-mean, northward transport of energy from ERA5 as a mean over the years 1979 to 2018.

The characteristics of the energy transport differ among latitudinal zones

Recent studies demonstrate the usefulness of separating the energy transport by spatial scales into planetary and synoptic components. For instance, eddies at these two scales impact the Arctic differently

So far, the energy transport across all latitudes has only been separated by a fixed wavenumber as shown in Fig.

This study proposes a revised partitioning by spatial scales based on wavelength to circumvent the above-mentioned problems associated with separation by wavenumber. With this, we partition the transport into planetary, synoptic, and mesoscale components to understand their role in transporting energy poleward. In addition, we apply the conventional decomposition of the transport into stationary and transient parts (Fig.

The new scale-separation method is employed to analyse meridional energy transport by the global atmospheric circulation. Previous studies found that transport by quasi-stationary waves is important in the NH but almost negligible in the SH

The following summarises the main research questions posed in this study:

At what scales does the atmosphere transport energy, and how does the scale-separation method compare to the conventional separation method?

What characterises the atmospheric energy transport in different meridional bands?

These questions are investigated in Sects.

The atmospheric energy transport for the period 1979–2021 is analysed with ERA5

The zonal integral of the ERA5 energy transport (Fig. S1a) confirms that found in previous studies using datasets with lower spatial resolution

For the calculation of convergence of energy transport, a 2

The atmospheric energy transport and its components are characterised by a large day-to-day variability

We define the vertically integrated, zonal-mean, time-mean, meridional transport of energy as

Firstly, the total atmospheric energy transport,

Secondly, the total energy transport,

Thirdly, the total energy transport,

To be precise, the Fourier decomposition is applied on the mass flux,

Based on this Fourier decomposition, the time-mean, zonal-mean energy transport can be written as

Note that the cross terms

The first term in Eq. (

The second term in Eq. (

The transient eddy part,

Having shown the relation of the terms in the Fourier decomposition with the transient and quasi-stationary terms in the conventional decomposition, we now introduce the scale separation of the eddy transport.
The instantaneous zonal-mean transport by wave

The annual-mean, zonal-mean Fourier-decomposed poleward transport of energy from ERA5 by each wave at all latitudes. Decomposition of the

To separate the energy transport between two scales based on a predefined wavelength,

The wavenumber of separation between planetary and synoptic eddies,

The partitioning of Eqs. (

An underlying interpretation is that at a longitude circle with for example 20 000 km extent (at a latitude of about 60

This continuous partitioning of the transport by the first wave smaller than 8000 km leads to the synoptic scale including less transport than the application of a strict separation (Fig. S2).
Hence, waves at a wavelength around and larger than 8000 km are associated with the planetary scale, whereas the synoptic scale constitutes waves strictly smaller than 8000 km. Spectra depicting the separation into the scale components at different latitudes are provided in Fig. S3, and a detailed illustration of the separation is provided in Sect. S3 in the Supplement. It should be noted that

Generally, the scale separation based on the Fourier decomposition is non-local, implying that the whole latitude circle influences the obtained eddies

Baroclinic instability is recognised as the single dominant instability of the synoptic scale

A wavelength band between 2000–8000 km appears appropriate to capture the majority of the transport associated with baroclinically induced synoptic eddies for three reasons.
(i) Cyclones and anticyclones feature some variability in their size but with a typical diameter between 1000 and smaller than 4000 km.
(ii) Short, synoptic Rossby waves are considered to occur at zonal wavelengths within this band, with meridional amplitudes of around half a wavelength, as further discussed in Sect.

Figure

The composite of the anomalous poleward energy transport by individual waves (

The latitudinal independence of the wavelength of the baroclinically induced transport anomaly provides a major argument for using a wavelength threshold to separate between the synoptic and planetary scales rather than a wavenumber threshold. It is surprising that the scale of maximum baroclinically induced transport anomaly is independent of the latitude since the Rossby deformation radius,

We note that processes other than baroclinic instability may contribute to the formation of the here-defined synoptic eddies, such as heating contrasts. A future study will further investigate the drivers of eddy transport at different scales.

In the following, we show that the partitioning at a wavelength of 8000 km approximately captures our intuitive understanding that synoptic cyclones and synoptic Rossby wave packets are transient by nature, whereas most quasi-stationary eddies are at planetary scales since they may be constrained by large-scale orography and semi-stationary thermal forcing, such as heating contrasts between ocean and land

Indeed, the spectral decomposition of the annual-mean energy transport,

For the transient energy transport, the wavenumber of maximum transport is 6 or 7 in the sub-tropics and decreases towards the poles such that the corresponding wavelength of maximum transient transport is around 5000 to 6000 km for all latitudes. Also in the moisture transport, the transient component reaches its maximum around 5000 km (Fig. S5), which is in good agreement with

The preferred wavenumber and wavelength of the quasi-stationary transport,

The separation of synoptic and planetary waves at a wavelength of 8000 km captures our intuitive understanding that (i) most transient transport occurs at the synoptic scale, whereas (ii) most quasi-stationary transport is at the planetary scale. The inverse is valid for the former but not the latter:
planetary waves at a wavelength larger than 8000 km can be both transient and quasi-stationary (Fig.

The fraction of the quasi-stationary part of the transport by planetary and synoptic waves as a function of latitude in ERA5.

In contrast to planetary transport, the inverse of (i) above, that synoptic transport is mainly (70 %–100 %) of a transient nature, is valid at almost all latitudes (Fig.

We conclude that the conventional decomposition of the transport into stationary and transient parts

Previous studies performing a wave decomposition qualitatively agree on the separation at a wavelength of 8000 km:

Firstly,

Secondly, their separation into planetary and synoptic eddies by wavenumber is similar to the here-applied partitioning by wavelength at a latitude of 53

Thirdly, at 70

In conclusion, separating at wavelengths of 8000 km is consistent with previous interpretations of planetary-scale and synoptic-scale transport. However, as mentioned earlier, a sharp threshold likely does not exist. Therefore, the separation wavelength of 8000 km is compared to wavelengths of 10 000 and 6000 km in the Supplement (Fig. S7). The main results of this study are not affected by the exact choice of the separation wavelength, as shortly discussed in the Supplement.

In this section, we analyse the atmospheric energy transport from ERA5 by utilising the scale-separation method.
The applied latitudinal bands used in this study are provided in Table

The applied terms to describe latitudinal bands in this study.

The meridional atmospheric energy transport features considerable similarities in the two hemispheres in most components and for most climate zones. Hence, to simplify the comparison of the two hemispheres, we display the poleward transport of both hemispheres at different latitudes on a common

The annual-mean, zonal-mean poleward energy transport,

The energy transport,

Despite the total energy transport,

The total annual-mean moisture transport,

The dry transport,

Synoptic-scale waves dominate the energy transport in the mid-latitudes of both hemispheres (Fig.

Extra-tropical synoptic waves transport approximately two-thirds of their energy in dry form and one-third in latent form (Fig.

The planetary energy transport is similar in both hemispheres, different from quasi-stationary transport which is mainly relevant in the NH (Figs.

In both hemispheres, the planetary transport is similar in the sub-tropics and lower mid-latitudes. In the higher mid-latitudes and polar region of the SH, it is approximately 20 % weaker than in the corresponding NH regions. Hence, eddies at similar spatial scales are transporting the energy in both hemispheres (see also Fig.

Generally, two patterns of planetary transport are identified:

In the sub-tropics, most planetary transport is associated with quasi-stationary moisture transport,

In the extra-tropics, planetary eddies mainly transport dry energy and only little moisture. In the polar regions, this planetary energy transport is almost as important as synoptic transport. The peak in energy transport by planetary waves,

The meridional overturning circulation,

In the mid-latitudes, the meridional circulation,

In contrast to synoptic and planetary waves, mesoscale waves,

Some transport patterns become more apparent when seasons are analysed separately. The NH summer and the SH winter are defined as June to August, and the NH winter and the SH summer are December to February. In spring and autumn the energy transport is mainly similar to the annual-mean transport (Figs.

As Fig.

Due to seasonal variations in the thermal contrast between the Equator and poles, more energy is transported poleward in the winter than in the summer hemisphere (Fig.

The location separating northward and southward total transport, the energy flux equator

In the extra-tropics of both hemispheres, the synoptic transport,

In the sub-tropics of the summer hemisphere, quasi-stationary planetary waves,

In this study, the inter-annual variability in the energy transport is computed by the standard deviation of the annual-mean transport.
The total energy transport,

(

In contrast to the total energy transport, the variability of the total moisture transport,

We hypothesise that the different co-variability of the scale contributions for the total energy and moisture transport is due to their different underlying mechanisms. Preliminary results point towards the annual-mean energy transport being induced by the meridional temperature gradient in the manner of a diffusion process with a globally almost constant diffusion coefficient. Hence, large transport in one component reduces the temperature gradient, leading to less transport in another. Differently, moisture is a tracer of the atmospheric circulation and, therefore, not described by a diffusion process such that the components do not compensate similarly to the total energy transport.

The tropics feature large inter-annual variability in the moisture transport,

In the extra-tropics, the planetary transport,

The extra-tropical moisture transport,

In this study, we analyse the global atmospheric circulation by separating the meridional energy transport of the years 1979–2021 in the ERA5 reanalysis by spatial scales, by moist and dry components, and by quasi-stationary and transient parts. For separating the energy transport by scales for all latitudes, we apply a new approach by using the wavelength instead of the wavenumber utilised previously

We demonstrate that separating transport by synoptic and planetary eddies at a wavelength of 8000 km reflects the physically grounded distinction between baroclinically induced and other eddies. Moreover, we show that the wavelength of 8000 km is reasonable for separating at all latitudes. This separation wavelength approximately agrees with the conventional separation between transient and quasi-stationary eddies, as most eddy transport smaller than 8000 km is transient, whereas most quasi-stationary transport occurs at the planetary scale larger than 8000 km. Despite the latter, a considerable amount of the planetary energy transport is transient, especially in the extra-tropical SH.

It should be noted that the scale separation is implemented continuously so that the largest eddy with a wavelength smaller than 8000 km is partitioned between the planetary and synoptic scales. This implies that the planetary transport includes waves of around 8000 km in size, whereas synoptic transport is by waves strictly smaller than 8000 km.

Eddies with a wavelength of almost 8000 km may appear as large for being part of the synoptic scale. However, most baroclinically induced and most transient energy transport organises at wavelengths around 5000 km at all latitudes (Figs.

Synoptic eddies are perceived as low- and high-pressure systems near the surface and small-scale Rossby waves that are often strongest around the tropopause. In the baroclinic development, near-surface pressure systems vertically interact with the upper-level Rossby waves.
One synoptic wave includes both a low- and a high-pressure system. Hence, a 2000–8000 km range implies that synoptic cyclones and anticyclones feature a typical diameter of between 1000 and smaller than 4000 km and that the typical distance between the cores of two independent (anti)cyclones is between 2000 and 8000 km. Both appear reasonable from comparison with weather maps. Even in situations of cyclone clusters, arguably situations where the distance between cyclones is unusually low, the spacing between cyclonic centres is around 2000 km

A single, sharp spatial separation between the synoptic and planetary scales may not exist in the real world. However, a spatial decomposition is helpful for better understanding the atmospheric circulation and its impact on regional climate

Different from the classical separation into quasi-stationary and transient energy transport, the spatial scales of the transport are quite similar in both hemispheres, pointing towards similarities in the contribution of active physical mechanisms. The most pronounced difference between the two separation methods is that planetary transport,

In the annual mean, most energy and moisture in the extra-tropics are transported by synoptic eddies,

The synoptic energy transport reveals to be influenced little by the season. In contrast, extra-tropical planetary transport,

Other known characteristics of the atmospheric circulation are reproduced in this study, such as the dominance of the Hadley circulation in the tropics for transporting energy,

In this study, the atmospheric transport is analysed on an annual-mean and seasonal-mean basis, whereas on shorter timescales, the transport can be highly sporadic and displays large deviations from climatology

The computed decomposition of the energy transport based on ERA5 and the code for the analysis are willingly provided on request.

The supplement related to this article is available online at:

RGG calculated the Fourier-decomposed energy transport. PJS performed further data processing and visualisation. PJS, RGG, and GM contributed to interpreting the results and writing the manuscript.

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.

Thanks go to ECMWF for providing access to data from the ERA5 reanalysis. The data were partly processed with the supercomputer Fram and stored at NIRD, both provided by the Norwegian Research Infrastructure Services (NRIS) Sigma2 AS (project nos. NN9348K and NS9063K, respectively). We also thank two anonymous reviewers and the editors for their constructive comments, which considerably improved the paper.

This research has been supported by the Research Council of Norway (NFR) under the projects “The role of the atmospheric energy transport in recent Arctic climate change” (no. 280727) and “Stability of the Arctic climate” (no. 314570).

This paper was edited by Camille Li and reviewed by two anonymous referees.