The global atmospheric energy transport analysed by a wavelength-based scale separation
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Weather Clim. Dynam., 4, 1–17, 2023
https://doi.org/10.5194/wcd-4-1-2023
© Author(s) 2023. This work is distributed under
the Creative Commons Attribution 4.0 License.
The global atmospheric energy transport analysed by a
wavelength-based scale separation
Patrick Johannes Stoll1 , Rune Grand Graversen2,3 , and Gabriele Messori4,5,6,7
1 Department of Mathematics and Statistics, Arctic University of Norway, Tromsø, Norway
2 Department of Physics and Technology, Arctic University of Norway, Tromsø, Norway
3 Norwegian Meteorological Institute, Tromsø, Norway
4 Department of Earth Sciences, Uppsala University, Uppsala, Sweden
5 Centre of Natural Hazards and Disaster Science (CNDS), Uppsala, Sweden
6 Department of Meteorology, Stockholm University, Stockholm, Sweden
7 Bolin Centre for Climate Research, Stockholm, Sweden
Correspondence: Patrick Johannes Stoll (patrick.stoll@uit.no)
Received: 26 April 2022 – Discussion started: 10 May 2022
Revised: 13 October 2022 – Accepted: 4 November 2022 – Published: 3 January 2023
Abstract. The atmosphere transports energy polewards by scale-separated transport components are fairly similar in
circulation cells and eddies. To the present day, there has both hemispheres. Transport by synoptic waves is the largest
been a knowledge gap regarding the preferred spatial scales contributor to extra-tropical energy and moisture transport,
and physical mechanisms of eddy energy transport. To fill the mainly of a transient character, and is influenced little by sea-
gap, we separate the meridional atmospheric energy trans- sonality. In contrast, transport by planetary waves depends
port in the ERA5 reanalysis by spatial scales and into quasi- highly on the season and has two distinct characteristics.
stationary and transient flow patterns and latent and dry com- (1) In the extra-tropical winter, planetary waves are impor-
ponents. tant due to a large transport of dry energy. This planetary
Baroclinic instability is the major instability mechanism transport features the largest inter-annual variability of all
in the transient synoptic scales and is responsible for form- components and is mainly quasi-stationary in the Northern
ing cyclones, anticyclones, and small-scale Rossby waves. At Hemisphere but transient in its southern counterpart. (2) In
the planetary scales, circulation patterns are often induced the sub-tropical summer, quasi-stationary planetary waves
by other mechanisms such as flow interaction with orogra- are the most important transport component, mainly due to
phy and land–sea heating contrasts. However, a separation moisture transport, presumably associated with monsoons. In
between circulation patterns at the synoptic and planetary contrast to transport by planetary and synoptic waves, only a
scales has yet to be established. We find that both baro- negligible amount of energy is transported by mesoscale ed-
clinically induced and transient energy transport is predom- dies (< 2000 km).
inantly 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 lin-
ear baroclinic theory. Since these results are independent of 1 Introduction
latitude, we adapt the scale separation of the energy trans-
port to be based on the wavelength instead of the previously Atmospheric motions reduce the thermal contrast created
used wavenumber. We define the synoptic transport by the by differential solar heating between high and low lati-
wavelength band between 2000 and 8000 km. tudes (Hadley, 1735). Hence the atmospheric circulation
We analyse the annual and seasonal mean in the energy transports large amounts of energy polewards (Oort and
transport components and their inter-annual variability. The Peixóto, 1983) and has thereby a fundamental role in control-
ling the local weather and climate (e.g. Holton and Hakim,
Published by Copernicus Publications on behalf of the European Geosciences Union.
2 P. J. Stoll et al.: Scales in energy transport
2013; Vallis, 2017). The energy is primarily transported in lengths can be interpreted to represent different spatial scales.
the form of warm air (dry energy: comprising mainly en- Such a partitioning by wavenumber thus has two caveats:
thalpy and potential energy) and water vapour (latent energy) (i) towards the poles, all eddy transport converges to the plan-
which releases energy when condensating before precipita- etary scale (Fig. 1b). (ii) In the sub-tropics, wavenumbers 1–
tion (Peixoto and Oort, 1992). 3 appear to miss parts of planetary transport, as can be in-
The characteristics of the energy transport differ among ferred from quasi-stationary eddies in the sub-tropical SH
latitudinal zones (Trenberth and Stepaniak, 2003a). In the (Fig. 1a) being considerably larger than the planetary trans-
tropics and sub-tropics, where the Coriolis effect is small, port captured by wavenumbers 1–3 (Fig. 1b).
energy is predominantly transported by a zonally symmetric This study proposes a revised partitioning by spatial scales
meridional overturning circulation, known as the Hadley cell based on wavelength to circumvent the above-mentioned
(Hadley, 1735), and monsoon systems organised by quasi- problems associated with separation by wavenumber. With
stationary cells (Fig. 1a). In the extra-tropics, eddies trans- this, we partition the transport into planetary, synoptic, and
port the majority of the energy further poleward. Atmo- mesoscale components to understand their role in transport-
spheric eddies exist on a large range of scales, from plan- ing energy poleward. In addition, we apply the conventional
etary Rossby waves (Rossby, 1939) and transient synoptic decomposition of the transport into stationary and transient
Rossby waves, which vertically interact with synoptic cy- parts (Fig. 1a), as well as dry and latent components (Peixoto
clones (Bjerknes, 1919), to mesoscale disturbances, such as and Oort, 1992).
polar lows (Businger and Reed, 1989). Conventionally, the The new scale-separation method is employed to anal-
eddy transport is separated into a quasi-stationary compo- yse meridional energy transport by the global atmospheric
nent and a transient component (Fig. 1a), with the former rep- circulation. Previous studies found that transport by quasi-
resenting monthly-mean eddies and the latter faster-varying stationary waves is important in the NH but almost negli-
deviations from this mean (Oort and Peixóto, 1983). Tran- gible in the SH (e.g. Peixoto and Oort, 1992). Such quasi-
sient eddies dominate the extra-tropical energy transport in stationary transport is often associated with the planetary
both hemispheres (Fig. 1a), whereas quasi-stationary waves scale, which appears to imply that planetary transport is irrel-
transport a considerable amount of energy in the higher lati- evant in the SH (e.g. Trenberth and Stepaniak, 2003a). How-
tudes of the Northern Hemisphere (NH) and the sub-tropics ever, this is not the case since planetary waves are strongly
of both hemispheres. However, they are less relevant in the represented in the SH as shown in Fig. 1b. In contrast, trans-
extra-tropical Southern Hemisphere (SH). port by transient eddies is often associated with baroclinic
Recent studies demonstrate the usefulness of separating eddies at the synoptic scale (e.g. Trenberth and Stepaniak,
the energy transport by spatial scales into planetary and syn- 2003a). However, transport at other scales could be transient
optic components. For instance, eddies at these two scales as well. In this study, we underscore that the separation of
impact the Arctic differently (Baggett and Lee, 2015; Gra- transport into a quasi-stationary and transient contribution
versen and Burtu, 2016). The scale separation of the merid- differs from a separation into planetary and synoptic scales.
ional energy transport by a zonal Fourier decomposition be- However, a correlation exists between the two, especially for
came popular in recent years. It was applied to study the the NH.
mechanisms and impacts of energy transport in the Arctic The following summarises the main research questions
region (Papritz and Dunn-Sigouin, 2020; Graversen et al., posed in this study:
2021; Rydsaa et al., 2021; Hofsteenge et al., 2022) and the
1. At what scales does the atmosphere transport energy,
NH mid-latitudes (Lembo et al., 2019). Further, numerous
and how does the scale-separation method compare to
studies investigated the atmospheric dynamics in terms of
the conventional separation method?
Rossby waves at different spatial scales (e.g. Wirth et al.,
2018; Röthlisberger et al., 2019). 2. What characterises the atmospheric energy transport in
So far, the energy transport across all latitudes has only different meridional bands?
been separated by a fixed wavenumber as shown in Fig. 1b
and presented by Graversen and Burtu (2016). The separa- These questions are investigated in Sects. 3 and 4. The
tion between planetary and synoptic scales has often been main results are then summarised and discussed in Sect. 5.
established between waves 3 and 4 (Baggett and Lee, 2015; However, first, we present the utilised data and methods.
Heiskanen et al., 2020). For investigation of the scale of the
transport at a specific latitude or a small zonal band, such 2 Data and methods
a separation by wavenumber is appropriate. However, the
wavelength associated with a given wavenumber is latitude 2.1 ERA5 reanalysis
dependent, which needs to be accounted for when defining
the wavenumber separating spatial scales (Heiskanen et al., The atmospheric energy transport for the period 1979–2021
2020). For instance, wave 4 corresponds to a wavelength of is analysed with ERA5 (Hersbach et al., 2020), the fifth at-
8200 km at 35◦ but only to 2600 km at 75◦ . These two wave- mospheric reanalysis from the European Centre for Medium-
Weather Clim. Dynam., 4, 1–17, 2023 https://doi.org/10.5194/wcd-4-1-2023
P. J. Stoll et al.: Scales in energy transport 3
Figure 1. Different separation methods of the vertically integrated, zonal-mean, northward transport of energy from ERA5 as a mean over
the years 1979 to 2018. (a) The conventional partitioning into the meridional overturning circulation (meri), quasi-stationary (q-s), and
transient (tran) eddies, as performed by Oort and Peixóto (1983). (b) A decomposition into transport by different spatial scales defined by
wavenumbers as suggested by Graversen and Burtu (2016). Transport by wave 0 provides the meridional overturning circulation. The sum of
transport by waves 1–3 is often associated with planetary transport, whereas waves with larger wavenumbers are considered to be of synoptic
scale.
Range Weather Forecasts (ECMWF). ERA5 provides hourly (Fig. S1b), different from the maximum zonally integrated
fields at a spectral truncation of T639, equivalent to a grid transport peaking at 41◦ .
spacing of 30 km, and with 137 vertical hybrid-sigma levels. For the calculation of convergence of energy transport, a
For this study, fields of air temperature, specific humidity, 2◦ running-mean filter is used along the meridional dimen-
geopotential height and horizontal wind components at all sion before computing the meridional derivatives.
hybrid levels, and surface pressure and surface topography
are used on a 0.25◦ × 0.25◦ horizontal grid spacing. Since 2.3 Decomposition of the energy transport
reanalysis data are prone to include mass-flux inconsisten-
cies (Trenberth, 1991), a barotropic mass-flux correction is The atmospheric energy transport and its components are
applied to the wind field before calculating the energy trans- characterised by a large day-to-day variability (Swanson and
port (Graversen, 2006). Pierrehumbert, 1997; Messori and Czaja, 2013). Here we fo-
cus on the annual-mean and seasonal-mean energy transport,
firstly to investigate the time-mean behaviour of the atmo-
2.2 Zonal mean versus zonal integral
spheric circulation and secondly to compare the newly in-
troduced separation of the eddy transport based on spatial
The zonal integral of the ERA5 energy transport (Fig. S1a) scales – described below – with the conventional separa-
confirms that found in previous studies using datasets with tion into quasi-stationary and transient transport introduced
lower spatial resolution (Peixoto and Oort, 1992; Tren- by Oort and Peixóto (1983) and commonly used in the lit-
berth and Caron, 2001; Graversen and Burtu, 2016). For in- erature (e.g. Trenberth and Stepaniak, 2003a, b; Kaspi and
stance, the zonally integrated poleward transport peaks at Schneider, 2013). The conventional separation obtains quasi-
4.8 × 1015 W in the NH and 5.6 × 1015 W in the SH at a lat- stationary eddies from monthly-mean fields; hence a compar-
itude of 41◦ in both hemispheres. By computing the zonal ison is only possible from a time-mean perspective. Quasi-
integral of the energy transport, which depends on the length stationary eddies could be derived differently, for example,
of the longitude circle, the transport becomes small at high by application of a temporal low-pass filter. This would en-
latitudes since the longitudes converge (Fig. S1a). However, able the comparison of the separation method by scale and
the local transport, expressed by the zonal mean, is consid- by quasi-stationary and transient components without taking
erable also in the polar regions (Fig. S1b). Hence, to com- time averages. However, it would prevent a direct compar-
pare the local importance of the atmospheric energy transport ison with the literature and require a new ad hoc analysis,
across all latitudes, we take a zonal-mean perspective which which is beyond the scope of this study.
provides the transport through an atmospheric column with
1 m width. The latitude of maximum zonal-mean transport,
namely the location at which the largest local meridional
transport occurs, is at a latitude of 45◦ in both hemispheres
https://doi.org/10.5194/wcd-4-1-2023 Weather Clim. Dynam., 4, 1–17, 2023
4 P. J. Stoll et al.: Scales in energy transport
We define the vertically integrated, zonal-mean, time- Thirdly, the total energy transport, vE,
f is separated into
mean, meridional transport of energy as transport by eddies at the planetary scale, vE f p ; the synop-
tic scale, vE sy ; and the mesoscale, vE ms , as well as the
f f
Zps meridional circulation, vEf md . For the partitioning into spa-
f = [vE] dp ,
vE (1) tial scales, a Fourier decomposition is applied along each
g
0 latitude, φ; at each vertical model level; and at every time
step for E and v 1 following Graversen and Burtu (2016). The
where v is the meridional wind, E is the atmospheric energy, Fourier series of E yields
p is pressure, ps is surface pressure, g is the gravitational
∞
a0E X
constant, · denotes a monthly time average, and [·] denotes E n2π x E n2π x
E= + an cos + bn sin , (4)
a zonal average. We decompose the total atmospheric energy 2 d d
n=1
transport, vE,
f in three ways that can be applied in succession:
Firstly, the total atmospheric energy transport, vE,
f is par- where x is the zonal coordinate, d = 2π a cos(φ); a =
titioned into latent energy transport, vQ, and dry energy
f 6371 km (Earth’s radius); and the Fourier coefficients, anE
transport, vD,f following Oort and Peixóto (1983). This is and bnE , are given as
achieved by separating the total atmospheric energy, E, in I
2 n2π x
Eq. (1) into its latent component, Q, and dry component, D, anE = E cos dx,
which comprises the enthalpy, cp T ; potential energy, gz; and d d
2
I
kinetic energy, v2 , as 2 n2π x
bnE = E sin dx, (5)
d d
v2
E = Q + D = Lq + cp T + gz + , (2) where n is zonal wavenumber. The Fourier coefficients for
2 the meridional wind, v, anv and bnv , are derived in a similar
with q being specific humidity, L being the latent heat release manner.
by condensation, cp being specific heat capacity at constant Based on this Fourier decomposition, the time-mean,
pressure, T being temperature, and v being the horizontal zonal-mean energy transport can be written as
wind vector. 1 1X ∞
Secondly, the total energy transport, vE, f expressing a [vE] = a0v a0E + a v a E + bnv bnE . (6)
4 2 n=1 n n
time-mean transport, Ris separated into transport by tran-
f tr = ps [v 0 E 0 ] dp ; quasi-stationary eddies,
sient eddies, vE 0 g Note that the cross terms anv and am
E with n 6 = m, and sim-
f q-s = ps [v ∗ E ∗ ] dp ; and the mean meridional circulation,
R
vE v E
ilarly bn and bm , vanish when computing a zonal average
0 g
f md = ps [v][E] dp , by partitioning the zonal-mean, time-
vE
R since the Fourier coefficients feature an orthogonal basis. In
0 g
the following, we show how this decomposition relates to
mean transport, [vE], in Eq. (1) according to Oort and the decomposition by Oort and Peixóto (1983) expressed in
Peixóto (1983) and Peixoto and Oort (1992) by Eq. (3).
The first term in Eq. (6) can be approximated by the first
[vE] = [vE] + [v 0 E 0 ]
term on the right-hand side (RHS) of Eq. (3):
∗
= [v][E] + [v ∗ E ] + [v 0 E 0 ], (3)
1 v E
a a = [v][E] = [v][E] + [v 0 ][E 0 ] ' [v][E] (7)
·0
with denoting anomalies from the time mean and denot- ·∗ 4 0 0
ing zonal anomalies from the zonal mean. The first equal- since [v 0 ][E 0 ], the time mean of the transient part of the
ity separates the time-mean transport into the transport by meridional circulation, is small. Hence, the time-mean trans-
the time-mean fields, [vE], and by faster-varying fluctua- port by the meridional overturning circulation can also be
tions, [v 0 E 0 ]. The second equality partitions the time-mean f md = ps 1 a v a E dp .
R
written as vE 0 4 0 0 g
term into a zonally symmetric transport component, [v][E],
∗ The second term in Eq. (6) is a time-mean transport by ed-
and a contribution by zonal waves, [v ∗ E ]. The duration
dies, [v ∗ E ∗ ], and can be separated into stationary and tran-
of the time mean, ·, for which eddies are considered quasi-
sient eddy transport:
stationary, is arbitrary. However, conventionally the mean is
taken over 1-month periods (e.g. Oort and Peixóto, 1983). ∞ n
1X o ∗
∗
Hereby, the quasi-stationary eddy transport, [v ∗ E ], provides anv anE + bnv bnE = [v ∗ E ∗ ] = [v ∗ E ] + [v 0 ∗ E 0 ∗ ]. (8)
2 n=1
the transport given by the monthly-mean eddies, and the
transient transport, [v 0 E 0 ], is the faster varying component. 1 To be precise, the Fourier decomposition is applied on the mass
The annual-mean energy transport partitioned in this conven- flux, v dp/g, since the thickness, dz, times density, ρ, providing the
tional manner is depicted in Fig. 1a. The transport of latent mass thickness of the model layers, dp/g = −ρdz, is non-constant
energy, vQ,
f and dry energy, vD, f is partitioned similarly. in hybrid-sigma coordinates.
Weather Clim. Dynam., 4, 1–17, 2023 https://doi.org/10.5194/wcd-4-1-2023
P. J. Stoll et al.: Scales in energy transport 5
The stationary eddy part is the second term on the RHS of separation depicted in Fig. 2 between the black curves at
Eq. (3) and can also be expressed by 2000 and 8000 km.
∞ n The partitioning of Eqs. (13)–(15) is applied to calcu-
∗ 1X v E
o
late the time-mean transport by planetary eddies, vE fp =
[v ∗ E ] = a vn a E
n + bn bn . (9)
2 n+1 R ps
∗ ∗ dp R ps
∗ ∗ dp
0 [v E ]p g ; synoptic eddies, vE sy = 0 [v E ]sy g ;
f
R ps dp
and mesoscale eddies, vE ∗ ∗
0 [v E ]ms g . It is in
f ms =
The transient eddy part, [v 0 ∗ E 0 ∗ ], is the difference between
a similar manner applied to calculate the transport by
the total transient transport, [v 0 E 0 ] (term 3 on RHS of Eq. 3),
quasi-stationary eddies at different scales, for instance
and the transient part of the meridional circulation [v 0 ][E 0 ], f q-s
the transport by quasi-stationary planetary eddies, vE p =
which is again small in the time mean, hence R ps ∗ ∗ dp
0 [v E ]p g . The transport by transient eddies at the dif-
[v 0 ∗ E 0 ∗ ] = [v 0 E 0 ] − [v 0 ][E 0 ] ' [v 0 E 0 ]. (10) ferent scales is simply obtained from the difference between
the time-mean transport and the quasi-stationary transport.
Having shown the relation of the terms in the Fourier de-
For instance, the transport by transient planetary eddies is
composition with the transient and quasi-stationary terms in f trp = vE f q-s
calculated as vE f p − vE p .
the conventional decomposition, we now introduce the scale
An underlying interpretation is that at a longitude circle
separation of the eddy transport. The instantaneous zonal-
with for example 20 000 km extent (at a latitude of about
mean transport by wave n is given by
60◦ ), wave 1 includes the transport at a scale of and larger
1 v E than the longitude cycle, wave 2 is between 10 000 and
[v ∗ E ∗ ]n = an an + bnv bnE . (11)
2 20 000 km, and so forth. Hereby, wave 3 with a wavelength of
6700 km provides the transport between its wavelength and
To separate the energy transport between two scales based 10 000 km and is therefore partitioned between the synop-
on a predefined wavelength, λsep , the latitude-dependent (φ) tic and planetary scales. Since the wavenumber of separation
wavenumber of separation, nsep , is computed: between the planetary and synoptic scale is np/s = 2.5 at a
latitude of 60◦ , this wave is equally partitioned between the
2π · a · cos(φ) two scales (second term in Eq. 13 and first term in Eq. 14).
nsep = . (12)
λsep This continuous partitioning of the transport by the first
wave smaller than 8000 km leads to the synoptic scale in-
The wavenumber of separation between planetary and syn-
cluding less transport than the application of a strict sepa-
optic eddies, np/s , is computed at each latitude from the
ration (Fig. S2). Hence, waves at a wavelength around and
wavelength λp/s = 8000 km (lower black solid line in Fig. 2).
larger than 8000 km are associated with the planetary scale,
Synoptic and mesoscale eddies are separated at a wavelength
whereas the synoptic scale constitutes waves strictly smaller
of λs/m = 2000 km. In Sect. 3, we argue for the usage of
than 8000 km. Spectra depicting the separation into the scale
these two wavelengths for scale-separating the energy trans-
components at different latitudes are provided in Fig. S3,
port. The wavenumbers of separation, as defined here, are
and a detailed illustration of the separation is provided in
real numbers. To ensure a continuous separation (Fig. S2b),
Sect. S3 in the Supplement. It should be noted that Wolf and
instead of abrupt transitions (Fig. S2a), the transport by plan-
Wirth (2017) also applied a continuous scale separation for
etary, synoptic, and mesoscale eddies is defined by
the latitude-dependent detection of Rossby wave packages.
bn
X p/s c The same procedure of scale separation is applied to the la-
[v ∗ E ∗ ]p = [v ∗ E ∗ ]n tent and dry energy transport.
n=1 Generally, the scale separation based on the Fourier de-
+ np/s − bnp/s c · [v ∗ E ∗ ]dnp/s e , composition is non-local, implying that the whole latitude
(13)
∗ ∗ ∗ ∗ circle influences the obtained eddies (Heiskanen et al., 2020).
[v E ]sy =(dnp/s e − np/s ) · [v E ]dnp/s e Therefore the Fourier decomposition is useful if the trans-
bn
X s/m c port across the circle is governed by similar eddy scales,
+ [v ∗ E ∗ ]n which we can observe from meteorological weather maps
n=dnp/s e+1 along zonal bands. Arguably, the zonal and meridional scales
+ ns/m − bns/m c · [v ∗ E ∗ ]dns/m e , of atmospheric eddies match: from the investigation of me-
(14)
teorological weather maps, we know (i) that synoptic-scale
[v ∗ E ∗ ]ms = dns/m e − ns/m · [v ∗ E ∗ ]dns/m e
cyclones are circular to the first order and (ii) that the merid-
∞
X ional extent, i.e. the amplitude, of Rossby waves, appears to
+ [v ∗ E ∗ ]n , (15) roughly match the distance between a trough and a ridge in
n=dns/m e+1
the zonal direction. Hence, as many other studies (e.g. Gra-
with b·c denoting rounding to the integer part and d·e round- versen and Burtu, 2016; Lembo et al., 2019), we interpret
ing to the least integer. This provides the latitude-dependent
https://doi.org/10.5194/wcd-4-1-2023 Weather Clim. Dynam., 4, 1–17, 2023
6 P. J. Stoll et al.: Scales in energy transport
Figure 2. The annual-mean, zonal-mean Fourier-decomposed poleward transport of energy from ERA5 by each wave at all latitudes. Decom-
position of the (a) quasi-stationary and (b) transient energy transport. The wavenumbers corresponding to wavelengths of 2000, 4000, 6000,
and 8000 km are depicted by black curves. The first and last curve separate the transport into the mesoscale, synoptic scale, and planetary
scale. At each latitude the wave of maximal poleward energy transport is displayed with a grey dot. The dot is not displayed at latitudes
where this wave is responsible for less than 5 % of the total quasi-stationary/transient transport of the latitude with maximum transport.
the zonal wavenumber of an eddy, which is associated with a teract vertically and baroclinically with the synoptic Rossby
zonal wavelength at a given latitude, as its spatial scale. waves, generally recognised by upper-tropospheric oscilla-
tions of the jet stream. The theoretical scale (wavelength)
of baroclinic eddies is given by 3.9 times the Rossby defor-
3 Wavelengths utilised for scale separation mation radius, Ld , and hence estimated to be 4000 km by
Vallis (2017, p. 354) and 4800 km by Stoll et al. (2021) us-
Orlanski (1975) defines the mesoscale to be smaller than ing more exact values obtained from extra-tropical cyclones.
2000 km, which is commonly accepted and hence used in this Note that a low-pressure (high-pressure) system spans half a
study as the lower threshold for the synoptic scale. However, wavelength and has accordingly a typical diameter of around
a widely agreed separation between the planetary and syn- 2000 km.
optic scales is not established. Below, we argue for placing A wavelength band between 2000–8000 km appears ap-
the separation between the planetary and synoptic scales at propriate to capture the majority of the transport associated
a wavelength of 8000 km, based on the argument that baro- with baroclinically induced synoptic eddies for three rea-
clinic instability is the major instability and hence the physi- sons. (i) Cyclones and anticyclones feature some variability
cal mechanism of wave generation at the synoptic scale. The in their size but with a typical diameter between 1000 and
exact value is to some degree arbitrary. As previously pre- smaller than 4000 km. (ii) Short, synoptic Rossby waves are
sented, this partitioning is done continuously such that trans- considered to occur at zonal wavelengths within this band,
port at and around the wavelength of 8000 km is associated with meridional amplitudes of around half a wavelength, as
with the planetary scale, whereas synoptic waves are strictly further discussed in Sect. 3.4. (iii) The non-local Fourier de-
smaller than this threshold. composition of the energy transport in situations of localised
synoptic cyclones captures considerable transport at neigh-
3.1 Theoretical baroclinic argument bouring waves to the cyclone (Heiskanen et al., 2020, Fig. 3),
which may be considered a weakness of the Fourier decom-
Baroclinic instability is recognised as the single dominant position. However, the band of wavenumbers around the lo-
instability of the synoptic scale (Markowski and Richardson, calised eddy appears appropriate to capture the eddy.
2011, p. 4). Thus, the synoptic scale should include most of
the energy transports associated with eddies developing by 3.2 Statistical baroclinic argument
baroclinic instability. Synoptic eddies are typically identified
as cyclones and anticyclones in sea-level pressure, as well as Figure 3 depicts the anomalous daily energy transport by
shorter Rossby waves (Frederiksen, 1978) often referred to different waves at a lag time of 4 d after enhanced merid-
as transient synoptic Rossby waves (e.g. Röthlisberger et al., ional temperature gradients (90th percentile). Different lag
2019; Ali et al., 2021). The cyclones and anticyclones in- times (> 0) provide similar results (Fig. S4), and the pre-
Weather Clim. Dynam., 4, 1–17, 2023 https://doi.org/10.5194/wcd-4-1-2023P. J. Stoll et al.: Scales in energy transport 7
between the synoptic and planetary scales rather than a
wavenumber threshold. It is surprising that the scale of max-
imum baroclinically induced transport anomaly is indepen-
dent of the latitude since the Rossby deformation radius,
Ld = NH f , estimating the size of baroclinic eddies (Vallis,
2017), depends inversely on the Coriolis parameter, f , in-
creasing with latitude and depends linearly on the depth
of the troposphere, H , and the tropospheric static stability,
N , which rather decrease with latitude (Stoll et al., 2021).
Hence, baroclinic eddies would be expected to be smaller at
higher latitudes. A hypothesis for the latitude independence
of the baroclinic eddies is as follows. Most extra-tropical cy-
clones originate from the mid-latitudes, where the meridional
temperature contrast is the largest. The size of a cyclone is
set during the genesis stage when the fastest-growing mode
Figure 3. The composite of the anomalous poleward energy trans- is prevailing. Many cyclones propagate to higher latitudes
port by individual waves ([vE]n of Eq. 11) at different latitudes along the diagonal axis of the storm tracks (Shaw et al., 2016)
4 d after situations of anomalous high (90th percentile) meridional and may preserve their original size.
temperature contrasts around the latitude of energy transport. The We note that processes other than baroclinic instability
anomalies on a daily resolution are computed from the 21 d and 9-
may contribute to the formation of the here-defined synoptic
year running-mean climatology. The meridional temperature con-
eddies, such as heating contrasts. A future study will further
trast is computed by the difference between the zone 10◦ equa-
torward and 10◦ poleward of the latitude of interest. Hence, red investigate the drivers of eddy transport at different scales.
colours denote waves transporting more energy polewards 4 d af-
ter situations of enhanced meridional temperature differences. The 3.3 Transient and quasi-stationary eddies
wavenumbers corresponding to wavelengths of 2000, 4000, 6000,
and 8000 km are depicted by black lines. Wave 0 is corrected by In the following, we show that the partitioning at a wave-
the meridional mass flux to express the instantaneous zonal-mean length of 8000 km approximately captures our intuitive un-
transport according to Lembo et al. (2019). derstanding 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
sented one of 4 d is in good agreement with Fig. 1a of Baggett constrained by large-scale orography and semi-stationary
and Lee (2015). The separation between waves featuring en- thermal forcing, such as heating contrasts between ocean and
hanced and decreased transport as a response to the increased land (Vallis, 2017).
thermal contrast is at around 8000 km for all latitudes in the Indeed, the spectral decomposition of the annual-mean en-
extra-tropics. Waves whose energy transport is most closely ergy transport, vE,
f at different latitudes reveals that most ed-
associated with the increased temperature gradient have a dies smaller than 8000 km are of a transient nature, whereas
wavelength between 3000 and 8000 km with a maximum most of the quasi-stationary transport is at scales larger than
transport anomaly for wavelengths around 5000–6000 km. 8000 km (Fig. 2). This is in good agreement with Dell’Aquila
Since baroclinic instability is induced by a horizontal tem- et al. (2005), who found in the average of the extra-tropical
perature gradient, this provides strong statistical evidence NH, that wave 3, here defined as planetary scale, features a
that baroclinic instability is an important development mech- typical period of around a month, whereas smaller eddies,
anism for waves at wavelengths between 2000 and 8000 km, here associated with the synoptic scale, are characterised by
which is here defined as the synoptic scale. In the follow- weekly or daily periods.
ing, we refer to the anomalous energy transport 4 d after sit- For the transient energy transport, the wavenumber of
uations of enhanced meridional temperature gradients as a maximum transport is 6 or 7 in the sub-tropics and decreases
“baroclinically induced transport anomaly”. The strength of towards the poles such that the corresponding wavelength
the baroclinically induced transport anomaly by the synoptic of maximum transient transport is around 5000 to 6000 km
waves (Fig. 3 at a wavelength between 2000 and 8000 km) for all latitudes. Also in the moisture transport, the transient
is around a third of the time-mean energy transport of these component reaches its maximum around 5000 km (Fig. S5),
waves (Fig. 2). The mean meridional temperature contrast which is in good agreement with Lee et al. (2019). This
will also induce baroclinic waves transporting energy, which wavelength corresponds well to the preferred scale of baro-
is not captured by this methodology. clinic eddies (4000–5000 km: Vallis, 2017; Stoll et al., 2021)
The latitudinal independence of the wavelength of the and of baroclinically induced transport anomalies presented
baroclinically induced transport anomaly provides a ma- in the previous section. The latitudinal independence of the
jor argument for using a wavelength threshold to separate wavelength of maximum transient transport supports sepa-
https://doi.org/10.5194/wcd-4-1-2023 Weather Clim. Dynam., 4, 1–17, 20238 P. J. Stoll et al.: Scales in energy transport
the quasi-stationary contribution to the synoptic transport is
small (< 30 %) compared to its transient part. Hence, for sim-
plicity’s sake, the synoptic transport is not separated into a
transient and quasi-stationary contribution in the remainder
of this study. An exception for the transient character of syn-
optic transport is over Antarctica, which is characterised by
katabatic flows advecting cold air towards lower latitudes,
occurring at preferred locations of drainage, hence including
a large stationary component.
We conclude that the conventional decomposition of
Figure 4. The fraction of the quasi-stationary part of the transport the transport into stationary and transient parts (Oort and
by planetary and synoptic waves as a function of latitude in ERA5. Peixóto, 1983) is to some degree related but not equivalent
to a separation into planetary and synoptic waves.
rating the planetary and synoptic scale by using wavelength 3.4 Comparison to previous studies
instead of wavenumber.
The preferred wavenumber and wavelength of the quasi- Previous studies performing a wave decomposition qualita-
f q-s , are latitude dependent (Fig. 2a).
stationary transport, vE tively agree on the separation at a wavelength of 8000 km:
The wavelength of maximum quasi-stationary transport is Firstly, Baggett and Lee (2015) perform a Fourier de-
larger than 8000 km everywhere besides close to the North composition of energy characteristics for the entire NH and
Pole where the Fourier decomposition is not applicable and demonstrate different life cycle behaviour of long (plane-
around 40◦ S where the quasi-stationary transport is almost tary) and short (synoptic) waves for a separation between
negligible. A short analysis of the preferred scales of the waves 3 and 4. Ali et al. (2021) identify recurrent synoptic-
quasi-stationary transport is provided in Sect. S5. scale transient Rossby wave packets in the mid-latitudes at
The separation of synoptic and planetary waves at a wave- wavenumbers between 4 and 15. Wirth et al. (2018) note that
length of 8000 km captures our intuitive understanding that planetary-scale Rossby waves are typically characterised by
(i) most transient transport occurs at the synoptic scale, zonal wavenumbers 1–3, whereas higher wavenumbers char-
whereas (ii) most quasi-stationary transport is at the plane- acterise synoptic-scale Rossby waves.
tary scale. The inverse is valid for the former but not the lat- Secondly, their separation into planetary and synoptic ed-
ter: planetary waves at a wavelength larger than 8000 km can dies by wavenumber is similar to the here-applied parti-
be both transient and quasi-stationary (Fig. 2). In the latitude tioning by wavelength at a latitude of 53 ◦ , which is close
band between 70 and 30◦ S and poleward of 70◦ N, zones to the location of maximum eddy activity (Fig. 1). For
mainly characterised by open ocean, the transient compo- a hemisphere-wide separation into planetary and synoptic
nent within the planetary transport is larger than the quasi- eddies with a single wavenumber threshold as utilised by
stationary component (Fig. 4). At latitudes with more land, Baggett and Lee (2015) and Ali et al. (2021), it appears cru-
the quasi-stationary component is responsible for 50 %–80 % cial to capture the partitioning around this latitude.
of the planetary transport, meaning that also at these lati- Thirdly, at 70◦ N, a wavelength of 8000 km is associated
tudes a considerable proportion of the planetary transport with a separation number nsy = 1.7, meaning that 70 % of
is transient. Also the moisture transport, vQ, f comprises a wave 2 is associated with the planetary scale and 30 % is as-
planetary component that features both transient and quasi- sociated with the synoptic scale. Accordingly, the lead–lag
stationary contributions, similar to the total energy transport, regression of the Arctic temperature on the latent transport
f (Fig. S6).
vE presented in Fig. 6 of Graversen and Burtu (2016) shows a
In contrast to planetary transport, the inverse of (i) above, clear difference between wave 1, leading to heating of the
that synoptic transport is mainly (70 %–100 %) of a transient Arctic, and waves 3 and larger, having a baroclinic signal.
nature, is valid at almost all latitudes (Fig. 4). This coincides Wave 2 appears to share characteristics of both wave groups,
with the transient character of synoptic cyclones and Rossby in agreement with the here-applied partitioning of wave 2 at
waves of short wavelengths. The small quasi-stationary con- 70◦ N. Also Heiskanen et al. (2020) find a good attribution
tribution (0 %–30 %) to the synoptic transport is attributed of the meridional energy transport by an idealised cyclone to
to preferred spatial locations for synoptic activity. For in- the synoptic scale if the separation between the planetary and
stance, the NH Atlantic sector features more cyclonic activity synoptic scales is performed at rather small wavenumbers,
than other longitudes, resulting in increased quasi-stationary even though they do not test a separation between waves 2
transport in the time mean. This can be inferred from Rydsaa and 3.
et al. (2021), who show a large time-mean synoptic trans- In conclusion, separating at wavelengths of 8000 km is
port in the Atlantic sector for strong latent transport events consistent with previous interpretations of planetary-scale
in winter at 70◦ N. However, in a zonal-mean perspective, and synoptic-scale transport. However, as mentioned earlier,
Weather Clim. Dynam., 4, 1–17, 2023 https://doi.org/10.5194/wcd-4-1-2023P. J. Stoll et al.: Scales in energy transport 9
Table 1. The applied terms to describe latitudinal bands in this Despite the total energy transport, vE,
f appearing seam-
study. less, different transport mechanisms are important in the dif-
ferent climate zones, as reflected by considerable variations
Climate zone Latitude band across latitudes in the moisture and dry transports (Fig. 5b
Equatorial region < 10◦ and c) and the scale components of the transport.
Tropics < 23◦ The total annual-mean moisture transport, vQ, f of both
Sub-tropics 23–35◦ hemispheres features equatorward extremes at around 10◦
Extra-tropics 35–90◦ (Fig. 5b), poleward maxima at around 40◦ , and decaying
Mid-latitudes 35–60◦ tails towards the poles. This leads to moisture divergence
Polar boundary Around 60◦ in the non-equatorial tropics and sub-tropics, whereas mois-
Polar regions 60–90◦ ture converges in the equatorial regions and extra-tropics
(Fig. 5e). The moisture transport is generally stronger in
the Southern Hemisphere than Northern Hemisphere due to
a sharp threshold likely does not exist. Therefore, the sepa- more evaporation on the water surfaces of the SH. Further,
ration wavelength of 8000 km is compared to wavelengths of some moisture is transported across the Equator from the SH
10 000 and 6000 km in the Supplement (Fig. S7). The main to the NH, leading to the highest convergence of moisture at
results of this study are not affected by the exact choice of around 7◦ N, which is in the annual mean the approximate
the separation wavelength, as shortly discussed in the Sup- location of the intertropical convergence zone (ITCZ).
plement. The dry transport, vD,
f is plateau-like between a latitude of
◦
10–65 (Fig. 5c) and decays towards the Equator and poles.
Hence, it is mainly responsible for divergence in the equa-
4 Organisation of the global energy transport torial regions and convergence in the polar regions (Fig. 5f).
However, the scale components have different roles in the
In this section, we analyse the atmospheric energy transport
different climate zones.
from ERA5 by utilising the scale-separation method. The
applied latitudinal bands used in this study are provided in
4.1.2 Synoptic transport
Table 1.
4.1 Annual-mean transport Synoptic-scale waves dominate the energy transport in the
mid-latitudes of both hemispheres (Fig. 5a). However, syn-
4.1.1 Overview optic transport is around 40 % stronger in the SH than in
the NH. This is in broad agreement with the finding of
The meridional atmospheric energy transport features con- Peixoto and Oort (1992) that transient transport is more rel-
siderable similarities in the two hemispheres in most com- evant in the SH, but it should be kept in mind that some of
ponents and for most climate zones. Hence, to simplify the the transient transport occurs at the planetary scale (Fig. 4).
comparison of the two hemispheres, we display the poleward Despite a broad spectrum of possible waves, most energy
transport of both hemispheres at different latitudes on a com- is transported by eddies at wavelengths between 2000 and
mon x axis (Fig. 5a–c). 8000 km, demonstrating the dominant role of synoptic waves
The annual-mean, zonal-mean poleward energy transport, for the mid-latitudinal energy transport (Fig. S7). This pro-
f is seamless in the sense that it resembles half of a sine
vE, vides a different perspective from previous studies finding
curve for both hemispheres (black lines in Fig. 5a) as noted that transient eddies are responsible for the majority of mid-
by Trenberth and Stepaniak (2003b). However, in the sub- latitudinal energy transport (e.g. Peixoto and Oort, 1992),
tropics and mid-latitudes, the energy transport is ∼ 15 % since planetary waves may also be transient. The peak trans-
larger in the SH than in the NH. The difference is approx- port by synoptic waves is at a latitude of around 45◦ , the loca-
imately balanced by more oceanic transport in the NH (Tren- tion of the climatological storm tracks (Hoskins and Hodges,
berth and Caron, 2001). 2002, 2005), and coincides with the zone of largest total en-
The energy transport, vE,
f leads to an annual-mean diver- ergy transport. Hence, synoptic waves transport energy from
gence of around 40 W m−2 in the tropics and sub-tropics the sub-tropics (< 40◦ ) to the extra-tropics (Fig. 5d).
and convergence poleward of a latitude of 40◦ of up to Extra-tropical synoptic waves transport approximately
100 W m−2 in the polar regions (Fig. 5d) in good agreement two-thirds of their energy in dry form and one-third in latent
with Trenberth and Stepaniak (2003a). The smaller diver- form (Fig. 5b, c). The latent contribution is slightly higher
gence close to the Equator is due to oceanic currents trans- in the mid-latitudes close to the sub-tropics and lower in the
porting heat to the sub-tropics, creating a cold tongue of sea- polar regions, where the cold atmosphere cannot hold much
surface temperatures over the equatorial Pacific (Trenberth water vapour. Despite transporting more dry than moist en-
and Stepaniak, 2003b). ergy, synoptic eddies are responsible for most extra-tropical
moisture transport. Especially in the polar regions, almost all
https://doi.org/10.5194/wcd-4-1-2023 Weather Clim. Dynam., 4, 1–17, 202310 P. J. Stoll et al.: Scales in energy transport
Figure 5. (a) Annual-mean, zonal-mean poleward atmospheric energy transport from ERA5. The transport of the Northern Hemisphere
and Southern Hemisphere are depicted in solid and dashed lines, respectively. The total energy transport (black) is divided into the zonally
symmetric meridional overturning circulation (blue) and wave components at the planetary (orange, waves ≥ 8000 km) and synoptic scales
(green, < 8000 km). The quasi-stationary contribution of the planetary transport on a monthly scale is depicted in red. (b, c) As panel (a)
but for the latent and dry energy transport components, respectively. (d–f) Resulting convergence of atmospheric energy from the transport
components presented in panels (a)–(c) but for simplicity omitting the convergence of quasi-stationary planetary transport. The latitudes on
the x axis are scaled to represent equal surface areas such that the integrated convergence in each component becomes zero.
moisture transport is by synoptic waves, whereas dry trans- in agreement with Trenberth and Stepaniak (2003a), under-
port in the polar regions occurs at both synoptic and planetary scoring that quasi-stationary transport is a primary factor in
scales. the extra-tropical NH. The latter study associates this quasi-
stationary transport with the planetary scale, albeit without
4.1.3 Planetary transport proof – a hypothesis confirmed by this study (Fig. 4). A new
finding that could partly be inferred from Fig. S3 of Lembo
The planetary energy transport is similar in both hemi- et al. (2019) is the near-symmetric structure of the plane-
spheres, different from quasi-stationary transport which is tary energy transport in both hemispheres. This symmetry
mainly relevant in the NH (Figs. 1a, 4, 5a). The latter is could not have been anticipated by considering only quasi-
Weather Clim. Dynam., 4, 1–17, 2023 https://doi.org/10.5194/wcd-4-1-2023P. J. Stoll et al.: Scales in energy transport 11
stationary transport since the planetary transport in the SH is 53◦ . The Ferrel cell is almost twice as strong in the SH than
mainly transient (Fig. 4), in agreement with Mo (1986). NH. The transport by the Ferrel cell is mainly in the form of
In both hemispheres, the planetary transport is similar in dry energy, which is to a small extent compensated by ther-
the sub-tropics and lower mid-latitudes. In the higher mid- mally direct moisture transport. In the NH, the eddy-driven
latitudes and polar region of the SH, it is approximately 20 % Ferrel cell (Vallis, 2017), spans the whole extra-tropics, in-
weaker than in the corresponding NH regions. Hence, eddies cluding the Arctic. In the SH, a thermally direct polar cell is
at similar spatial scales are transporting the energy in both evident in the dry transport, vD
f md , which is primarily driven
hemispheres (see also Fig. 2), likely due to similar phys- by katabatic flow from Antarctica as noted by Trenberth and
ical mechanisms in both hemispheres forming the energy- Stepaniak (2003a). Different to previous studies by for ex-
transporting eddies. ample Peixoto and Oort (1992) a NH polar cell is not evident
Generally, two patterns of planetary transport are identi- in the here-utilised ERA5 dataset, neither in the annual mean
fied: nor in the summer or winter season (Sect. 4.2). In the Arc-
tic, energy is transported by synoptic and planetary eddies
1. In the sub-tropics, most planetary transport is associated favouring the formation of a Ferrel cell, whereas zonal sym-
with quasi-stationary moisture transport, vQf q-s
p . These metric katabatic flows, as observed in the Antarctic, do not
waves presumably represent sub-tropical high-pressure develop due to the lack of a large ice dome centred over the
and monsoon systems, which can prevail for several pole.
weeks. The planetary moisture transport leads to hu-
midity divergence in the tropics and convergences in the
sub- and extra-tropics (Fig. 5e). 4.1.5 Mesoscale transport
2. In the extra-tropics, planetary eddies mainly transport In contrast to synoptic and planetary waves, mesoscale
dry energy and only little moisture. In the polar re- waves, vEf ms , at scales smaller than 2000 km, are only re-
gions, this planetary energy transport is almost as im- sponsible for a negligible part of the energy and moisture
portant as synoptic transport. The peak in energy trans- transport at all latitudes (Figs. 2, S7), in accordance with Gra-
port by planetary waves, vE f p , is at the polar bound- versen and Burtu (2016), who show that wavenumbers 0–10
ary at a latitude of around 60◦ in both hemispheres are responsible for the majority of the energy transport at all
(Fig. 5a, c), hence further poleward than the peak in latitudes. Atmospheric models may have larger challenges
synoptic transport at 45◦ . Thus, the planetary dry trans- in reproducing mesoscale eddies as compared to eddies at
port, vD
f p , leads to energy divergence in the sub-tropics larger scales. However, ERA5 at a horizontal grid spacing
and mid-latitudes and convergence in the polar regions equivalent to 30 km can reproduce mesoscale cyclones, such
(Fig. 5f). These planetary waves are mainly transient as polar lows (Stoll et al., 2021), and hence the negligible
(Fig. 4: 70 %) in the mid-latitudinal SH, whereas the importance of mesoscale eddies for the total energy transport
quasi-stationary component dominates (60 %) in the appears trustworthy. Due to its negligible role, we include
corresponding NH region, which agrees with Peixoto the mesoscale into the synoptic transport for the remainder
and Oort (1992). However, in the high latitudes of the of this study such that the sum of all scale components yields
SH, a considerable fraction of the planetary transport is the total transport.
quasi-stationary.
4.1.4 Meridional overturning circulation 4.2 Seasonal transport
The meridional overturning circulation, vE f md , and its role Some transport patterns become more apparent when seasons
in transporting energy poleward have long been known (e.g. are analysed separately. The NH summer and the SH winter
Hadley, 1735; Lorenz, 1967; Peixoto and Oort, 1992). The are defined as June to August, and the NH winter and the SH
Hadley circulation in the tropics dominates the energy trans- summer are December to February. In spring and autumn the
port in that region. The total energy transport, vE
f md , by the energy transport is mainly similar to the annual-mean trans-
Hadley circulation is small compared to the thermally direct port (Figs. 5, S8).
dry component, vD f md , and to the thermally indirect latent Due to seasonal variations in the thermal contrast between
component, vQ f md , since the latter largely compensates the the Equator and poles, more energy is transported poleward
former (Fig. 5a–c). Further, the annual-mean transport by in the winter than in the summer hemisphere (Fig. 6a, d)
the Hadley circulation is small since transport into the tropi- in good agreement with previous studies (e.g. Peixoto and
cal winter hemisphere originates from the equatorial summer Oort, 1992). The seasonality in the transport is larger in the
hemisphere, leading to compensation of summer and winter NH than the SH, as also noted by Trenberth and Stepaniak
cells (see Sect. 4.2). (2003a). This is affected by a larger annual temperature cy-
In the mid-latitudes, the meridional circulation, vE
f md , fea- cle in the NH due to its large continents having a smaller
tures the thermally indirect Ferrel cell with a peak around heat capacity than the oceans in the SH. Still, the two hemi-
https://doi.org/10.5194/wcd-4-1-2023 Weather Clim. Dynam., 4, 1–17, 202312 P. J. Stoll et al.: Scales in energy transport
Figure 6. As Fig. 5a–c but for the seasonal-mean transport of (a–c) winter and (d–f) summer for (a, d) the total energy transport, (b, e) its
latent component, and (c, f) its dry component.
spheres share many characteristics in the atmospheric energy agreement with results from wavenumber separated transport
transport regarding seasonality. of the NH mid-latitudes in Lembo et al. (2019) and with tran-
The location separating northward and southward total sient transport in Trenberth and Stepaniak (2003a). In con-
transport, the energy flux equator (Adam et al., 2016), is at trast, the planetary transport, vE
f p , has a strong seasonality,
around a latitude of 10◦ in the summer hemisphere (Fig. 6d). being highly relevant in winter but almost absent in summer.
This is close to the ascending branch of the Hadley circula- Hence, the summer is dominated by synoptic transport, vE f sy .
tion (Vallis, 2017, p. 514). In the tropics, the meridional over- Differently, in winter, both planetary and synoptic waves are
turning circulation, vE f md , is most important (Fig. 6, blue). highly relevant for the energy transport. In the NH winter,
It transports energy from the summer tropics to the winter planetary waves, vEf p , contribute to more transport than do
sub-tropics, whereas moisture, vQ f md , is transported in the synoptic waves, mainly by their quasi-stationary component,
opposite direction. f q-s
vE p . In the SH winter, planetary transport is also important
In the extra-tropics of both hemispheres, the synoptic f trp , whereas its stationary
but mostly in its transient form, vE
transport, vE
f sy , is little influenced by seasonality, in broad
part is small as noted previously (Oort and Peixóto, 1983).
Weather Clim. Dynam., 4, 1–17, 2023 https://doi.org/10.5194/wcd-4-1-2023P. J. Stoll et al.: Scales in energy transport 13
In the sub-tropics of the summer hemisphere, quasi- (Fig. 7a). This is remarkable since the annual-mean plan-
f q-s
stationary planetary waves, vE p , are among the largest con- etary transport is mainly smaller (Fig. 5) than the synop-
tributors to poleward energy transport (Fig. 6d). These waves tic transport, vE
f sy . Consequently, the planetary transport,
f q-s
are transporting energy mainly in the form of moisture, vQ p vE p , varies from year to year by approximately 10 % in the
f
(Fig. 6e), presumably reflecting the summer monsoon and mid-latitudes and 15 %–20 % in the polar regions. In con-
long-lasting sub-tropical high-pressure systems. trast, the synoptic transport, vE
f sy , varies only by around
5 %. The large planetary variability is mainly attributed to
4.3 Inter-annual variability its quasi-stationary component, vEf q-s
p , whereas its transient
tr
component, vE p , is much less variable (not shown). This
f
In this study, the inter-annual variability in the energy trans- demonstrates the “quasiness” of the quasi-stationary trans-
port is computed by the standard deviation of the annual- port, being the transport component that varies most from
mean transport. The total energy transport, vE,f is only vary-
year to year. This presumably reflects the role of (inter-
ing by a few percent between years for all latitudes (Fig. 7a). )annual modes of climate variability in favouring different
However, the inter-annual variability in the individual com- quasi-stationary circulations and planetary transports in dif-
ponents is up to 3 times larger than the variability in the to- ferent years.
tal transport, especially in the extra-tropics (Fig. 7a). Hence, The extra-tropical moisture transport, vQ,
f is varying ap-
large transport in one component is typically compensated proximately equally for planetary, vQf p , and synoptic waves,
by smaller transport in another, as noted by Trenberth and f sy (Fig. 7b). Since synoptic waves are responsible for
vQ
Stepaniak (2003a) and Lembo et al. (2019).
most of the moisture transport in the extra-tropics (Fig. 5b),
In contrast to the total energy transport, the variability of
the variability fraction is considerably higher for the plane-
the total moisture transport, vQ,
f is larger than the variabil-
tary than the synoptic moisture transport.
ity of its individual scale components (Fig. 7b). Hence, the
moisture transport components are not compensating each
other in the same manner as the total energy transport com- 5 Discussion and conclusion
ponents. Instead, the compensation of the components of the
total energy transport is in the form of dry energy (Fig. 7c). In this study, we analyse the global atmospheric circulation
We hypothesise that the different co-variability of the scale by separating the meridional energy transport of the years
contributions for the total energy and moisture transport is 1979–2021 in the ERA5 reanalysis by spatial scales, by moist
due to their different underlying mechanisms. Preliminary and dry components, and by quasi-stationary and transient
results point towards the annual-mean energy transport being parts. For separating the energy transport by scales for all
induced by the meridional temperature gradient in the man- latitudes, we apply a new approach by using the wavelength
ner of a diffusion process with a globally almost constant dif- instead of the wavenumber utilised previously (e.g Graversen
fusion coefficient. Hence, large transport in one component and Burtu, 2016).
reduces the temperature gradient, leading to less transport in We demonstrate that separating transport by synoptic and
another. Differently, moisture is a tracer of the atmospheric planetary eddies at a wavelength of 8000 km reflects the
circulation and, therefore, not described by a diffusion pro- physically grounded distinction between baroclinically in-
cess such that the components do not compensate similarly duced and other eddies. Moreover, we show that the wave-
to the total energy transport. length of 8000 km is reasonable for separating at all lat-
The tropics feature large inter-annual variability in the itudes. This separation wavelength approximately agrees
moisture transport, vQ,f and approximately equally large with the conventional separation between transient and
variability in the dry transport, vDf (Fig. 7b, c). The large quasi-stationary eddies, as most eddy transport smaller than
total variability in the moist and dry energy transports is al- 8000 km is transient, whereas most quasi-stationary transport
most entirely due to variability in the meridional overturning. occurs at the planetary scale larger than 8000 km. Despite the
This is not surprising since the meridional overturning is re- latter, a considerable amount of the planetary energy trans-
sponsible for most of the moist and dry energy transport in port is transient, especially in the extra-tropical SH.
the tropics (Figs. 5b, c, 6b, c, e, f). However, the variability It should be noted that the scale separation is implemented
in total transport, vE,
f is only a fifth of the moisture transport continuously so that the largest eddy with a wavelength
variability (Fig. 7a, b). Hence, a Hadley circulation causing smaller than 8000 km is partitioned between the planetary
a larger-than-usual thermally direct dry energy transport in a and synoptic scales. This implies that the planetary transport
single year also causes a larger-than-usual thermally indirect includes waves of around 8000 km in size, whereas synoptic
latent energy transport in that year. This explains that the to- transport is by waves strictly smaller than 8000 km.
tal energy transported by the Hadley circulation is more or Eddies with a wavelength of almost 8000 km may ap-
less constant between years. pear as large for being part of the synoptic scale. However,
In the extra-tropics, the planetary transport, vE f p , is the most baroclinically induced and most transient energy trans-
component exhibiting the largest inter-annual variability port organises at wavelengths around 5000 km at all lati-
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