Introduction
Atmospheric equatorial Kelvin waves (hereafter KWs), first discovered in the
stratosphere , are nowadays observed and studied over a
broad range of spatial and temporal scales. A broad wavenumber–frequency
spectrum can be traced to the spatiotemporal nature of tropical convection
which generates KWs along with a spectrum of other equatorial waves.
The atmospheric wave response to the stochastic nature of convection was studied
by and who made a distinction between
(i) projection or vertical response to short-term heating fluctuations (e.g.
daily convection) and (ii) the barotropic or horizontal response to seasonal
convective heating. For KWs, the vertical response gives rise to a broad
frequency spectrum of vertically propagating KWs that radiate outward into
the stratosphere where they drive zonal-mean quasi-periodic flows such as the
quasi-biennial oscillation QBO;. The horizontal
response to seasonal transitions in convective heating gives rise to
planetary-scale disturbances with a half-sinusoidal vertical structure
confined to the troposphere. A part of this response remains stationary over
the convective hotspot; its shape resembling a classic “Gill-type” KW
solution . The other part of the response intensifies and
advances over the Pacific, representing a transient component of the Walker
circulation .
Both components of the KW response received increased attention in the
scientific community over the last decades in terms of the role they play in
the (intra-)seasonal variability in the tropical tropopause layer (hereafter
TTL), defined as a transition layer between the typical level of convective
outflow at ∼ 12 km, where the Brunt–Väisälä frequency is at
its minimum, and the cold point tropopause at ∼ 16–17 km
. Within the TTL, temperature variations
play an important role in controlling the stratosphere–troposphere exchange
of various species such as ozone and water vapour, thereby aiding in the
dehydration process of air entering the stratosphere. The two parts of the KW
response modulate the TTL differently on different timescales
; their relative
contribution to TTL dynamics varies with season and is not yet fully
understood. The present study contributes to this topic by applying a novel
multivariate analysis of KW seasonal variability in model-level
analysis data.
Seasonal variations in KW dynamics in the TTL have been previously studied using temperature data derived from satellites
such as SABER Sounding of the Atmosphere using Broadband Emission Radiometry;,
HIRDLS High Resolution Dynamics Limb Sounder; and GPS-RO
Global Positioning System Radio Occultation;. For example, reported
a clear seasonal cycle around 16–17 km (∼ 100 hPa) in KW temperature observed by HIRDLS, coinciding closely with variations in background stability.
A widely used method for the KW filtering from gridded data is the space-time spectral analysis introduced by .
Space-time spectral filtering assumes that the linear adiabatic theory for equatorial waves on a resting atmosphere is applicable
.
Filtering operates on single variable data and it has been widely used to diagnose equatorial waves in the outgoing longwave
radiation OLR, e.g. and climate model outputs e.g.. Based on 40-year ECMWF
reanalysis (ERA-40) data, found that the temperature component of KWs tends to peak at 70 hPa while
the zonal wind peaks at lower altitudes, i.e. at 100 and 150 hPa in the eastern and western hemisphere, respectively.
On the equatorial β-plane, shallow-water linear wave theory describes the KW geopotential height (hkw) and
zonal wind (ukw) perturbations propagating zonally with phase speed c as the following :
hkw(x,y)=cgukw,whereukw(x,y)=u0exp(-βy22c)cosk(x-ct).
Here, u0 is the zonal wind amplitude at the equator, g is gravity, y is the distance from the equator
and β=df/dy, f being the Coriolis parameter.
The dispersion relationship between the wave frequency ν and the zonal wavenumber k is ν=kc.
The gravity wave speed in a layer of homogeneous fluid with mean depth D is given by c=gD .
The KW e-folding decay width ae, known as the equatorial radius of
deformation, is given by ae=(c/2β)1/2. By prescribing D, the
horizontal structure of KW is defined by Eq. () for any k and can be
used to simultaneously analyse wind and geopotential height perturbations due
to KWs on a single horizontal level. Such analysis was carried out by
for the lower stratosphere for the ERA-15 data in
the 1981–1993 period. Their results suggested that KWs contribute approximately 1 K2
to the temperature variance on the equator with peak activity occurring
during solstice seasons at 100 hPa, during December–February at 70 and
at 50 hPa it occurs during the easterly to westerly QBO phase transition. used ae as the
fitting parameter for the projection of the ERA-15 data on the meridional
structure of the KW and other equatorial waves. They found that the best fit
trapping scale within 20∘ N–20∘ S is around 6∘. The multivariate
projection of data on the horizontal structures of equatorial waves including
KWs on the equatorial β-plane was
performed also for the short-range forecast errors of the ECMWF model .
For example, found that forecast errors within the belt 20∘ N–20∘ S
project onto KWs significantly more
in the easterly QBO phase than in the westerly phase.
In this paper we extend the linear KW analysis based on the
shallow-water equation theory on the equatorial β-plane to the sphere.
Second, we extend the KW filtering on individual horizontal levels or
vertical planes to the three-dimensional (3-D) KW analysis simultaneously in
wind and temperature fields. This study thus explores seasonal variability in
KWs in the TTL in a multivariate fashion using most of the information
on the vertical wave structure available in recent operational ECMWF
analyses.
On the spherical Earth, the Kelvin mode is the slowest eastward-propagating eigensolution of the shallow-water equations
(or Laplace tidal equations)
linearized around a state of rest e.g.. In the continuously
stratified atmosphere, the depth D becomes
the “equivalent depth” of a given baroclinic mode and we need to solve Laplace tidal
equations for a range of D from large (corresponding to the barotropic structure)
to rather small (for high baroclinic modes)
in order to consider the spectrum of KWs e.g..
In contrast to the KW trapping on the equatorial β-plane,
which is controlled by ae, i.e. by the equivalent depth,
the degree of the KW equatorial confinement on the spherical Earth is in addition controlled by the zonal wavenumber
. As shown by , even barotropic KW with D around 10 km
are on the sphere, confined within the tropical belt.
In Sect. we present a methodology which diagnosis 3-D
KWs in spherical datasets. Section presents the KW
energetics in wavenumber space focusing on the seasonal cycle.
Section presents seasonal KW variability in several frequency bands
both for the horizontal as well as for the vertical projection KW response.
Conclusions and outlook are given in Sect. 5.
Data and methodology
The KWs are filtered using the normal-mode function (NMF) decomposition derived by
and formulated as the MODES software package by .
Here the methodology is briefly summarized followed
by the method for the computation of the KW temperature perturbations and by
examples of the 3-D KW structure in global data.
Input ECMWF operational analyses cover approximately 6.5 years from January
2007 until June 2013. The dataset starts after two important updates in the
ECMWF assimilation cycle: a resolution update on 1 February 2006 and the
introduction of GPS-RO temperature profiles in the assimilation on 12
December 2006. The data ends at the next update in vertical resolution from
L91 to L137 on 25 June 2013. The data horizontal resolution is 256×128
points in the zonal and meridional directions (regular Gaussian grid N64),
respectively, on 91 irregularly spaced hybrid model levels up to around
0.01 hPa (around 80 km). The temporal resolution is 6 h, i.e.
4 times per day at 00:00, 06:00, 12:00, and 18:00 UTC. A case study of the large-scale KW in July
2007 in this dataset by showed that the NMF method
provides information on the 3-D wave structure and its vertical propagation in
the stratosphere. Another case study from the same month demonstrated how the
vertical KW structure improves as the number of vertical levels increased
.
Filtering of KWs by 3-D normal-mode function expansion
The basic assumption behind the NMF expansion is that a global state of the
atmosphere described by its mass and wind variables at any time can be
considered as a superposition of the linear wave solutions upon a predefined
background state. The NMF decomposition derived by uses
the σ vertical coordinate and linearization around the state of rest
and realistic vertical temperature and stability stratification. The 3-D wave
solutions of linearized primitive equations are represented as a truncated
time series of the Hough harmonic oscillations and the vertical structure
functions. The assumption of separability leads to separate equations for the
vertical structure and horizontal oscillations. The latter are known as
shallow-water equations on the sphere or Laplace tidal equations without
forcing. The two systems are coupled by a separation parameter D which is
called the equivalent height . Eigenmodes of the global
shallow-water equations are known as Hough harmonics. They describe two types
of wave motions: Rossby waves and inertio-gravity waves which obey their
corresponding dispersion relationships on the spherical Earth.
The expansion of a global input data vector
X(λ,φ,σ)=(u,v,h)T can be represented by a
discrete finite series as
u(λ,φ,σ)v(λ,φ,σ)h(λ,φ,σ)=∑m=1MSm∑n=1R∑k=-KKχnk(m)Hnk(λ,φ;m)Gm(σ).
The input data vector contains wind components u,v and the transformed
geopotential height h defined as h=g-1P, where g is the gravity and
P is defined as P=Φ+RT0ln(ps); that is, it is the sum of
geopotential Φ and a surface pressure, ps, term. Two other variables
represent the specific gas constant for dry air (R) and the
globally-averaged vertical temperature profile (T0(σ)). The zonal and
vertical truncations (K and M, respectively) define maximal numbers of
zonal waves at a single latitude (wavenumber k) and a maximal number of
vertical modes (denoted m), respectively. For every vertical structure
eigenfunctions Gm(σ), Hough harmonic functions,
Hnk(λ,φ), describe non-dimensional oscillations in
the horizontal plane of the fluid with the mean depth equal the equivalent
depth Dm. The parameter Dm appears in Eq. () in the
diagonal matrix Sm
with elements (gDm)1/2, (gDm)1/2
and Dm, which normalizes the input data vector after the vertical
projection and thereby removes dimensions. Parameter R is the total number
of meridional modes which is a sum of the eastward inertio-gravity waves
(EIG), westward inertio-gravity waves (WIG) and Rossby waves. Linearization
about the state of rest is not a drawback of the method as wave frequencies
are used solely for the formulation of the projection basis and not for
studying wave propagation properties. As shown by (see
also its Corrigendum) the meridional structures of the Hough functions for
large scales are not significantly different if the linearization is
performed around the non-zero mean zonal flow. The impact of latitudinal
shear on the KWs was shown to be negligible by . Further
details of the NMF projection procedure are given in .
For each zonal wavenumber, the Kelvin mode is the lowest eastward-propagating
latitudinal Hough function. In Eq. (), the KW is
represented by the non-dimensional complex expansion coefficients
χnk(m) with the meridional index n=1. However, to follow often-used
notation, we shall denote the KW in the remainder of this study as
the n=0 EIG mode, i.e. the KW wind and geopotential height are
represented by coefficients χkw=χ0k(m). The truncation values
are K=85 and M=60. This means that the KW signal in 3-D circulation at a
single time instant consists of 5100 waves, 85 waves in every shallow-water
equation system. Higher vertical modes were left out as their equivalent
depth is smaller than 2 m and their contribution to the total KW signal
is negligible in the outputs in the TTL and the stratosphere. The relation
between the truncation parameters and the normal-mode projection quality is
discussed in and references therein.
Once the forward projection is carried out and coefficients χnk(m) are produced, filtering of KWs in physical space can be performed through
Eq. () after setting all χ, except those representing the KWs, to zero. The result of filtering are fields
ukw, vkw and hkw,
which provide the KW zonal wind, meridional wind and geopotential height perturbations.
Notice here that in contrast to the equatorial β-plane, KWs on the sphere have a small meridional wind component
which is thus left out from the discussion .
The KW temperature perturbation, Tkw, can be derived from the hkw fields on σ levels using the
hydrostatic relation in σ coordinates:
Tkw=-gσR∂hkw∂σ.
The orthogonality of the normal-mode basis functions provides KW energy as a
function of the zonal wavenumber and vertical mode. After the forward
projection, the energy spectrum of total (potential and kinetic) energy for
each KW can be computed using the energy product for the kth and
mth normal modes as
Ikw(k,m)=12gDmχkw[χkw]*.
The units are J kg-1. The KW global energy spectrum as a function of the zonal wavenumber is obtained by summing energy in all vertical modes:
Ikw(k)=12∑m=1MgDmχkw[χkw]*.
Examples of 3-D structure of KWs in L91 analyses
The horizontal structure of KWs in the ECMWF analysis data on 25 July 2010 at (a) 100 and (b) 150 hPa.
The geopotential height perturbations (hkw) are shown by black contours, every 20 m, whereas temperature perturbations (Tkw)
are coloured red (every 1 K). Dashed contours represent negative and full line contour positive perturbations. Zero lines are omitted.
KWs are shown in Figs. – for
a few days in July 2010 to introduce and illustrate
their properties as filtered by the NMF methodology.
Figure illustrates the meridional structure of KWs
on 25 July 2010 on 2 levels. KW activity was found largest in the
zonal wind component at 150 hPa over the Indian Ocean. The geopotential
dipole structure is centred over the convective hotspot over the Maritime
Continent. At 100 hPa, we find the largest amplitude of KW temperature
perturbations up to 4 K positioned above the zonal wind maxima at 150 hPa.
The meridional wind component of the KW is non-zero in spherical
coordinates, but is at most 0.22 m s-1 at 100 hPa, which is negligible
compared to the zonal wind component (maximum 12.5 m s-1) making the KW
wind field primarily zonal. Note that the presented horizontal structure at a
single level is a superposition of 60 vertical modes, i.e. 60 shallow water
models with equivalent depths from about 10 km to a couple of metres.
Longitude–pressure cross section of the Kelvin wave (KW) zonal wind (red-blue shaded contours) and temperature (red contours)
perturbations along 0.7∘ N on (a) 25 July, (b) 28 July and (c) 31 July 2010. Temperature is shown every 1 K,
starting at 2 K. Zonal winds are drawn every 4 m s-1. Zero lines are omitted.
Figure illustrates day-to-day filtered KW fields along
the equator on three separate July days in 2010, namely 25, 28 and
31. Both zonal wind (blue-to-red shades) and temperature fields (red
contours) are shown. Without any predefined constrains on the KW propagation,
one can observe a rich variety of KW behaviour occurring in time: from the
quasi-stationary dipole patterns centred at 160 hPa to a wave package of
free-propagating wave structures in the stratosphere transiting from the
western into the eastern hemisphere.
In the stratosphere, the uppermost easterly wind component in blue shades
around 30–50 hPa moves in eastward and downward directions, demonstrating
the upward transport of KW energy . KW amplitudes were
largest over the eastern hemisphere with temperatures up to 4 K and zonal winds
up to 12 m s-1. The large amount of KW activity occurred during the
easterly phase of the QBO with strong easterly winds present between 30 and
80 hPa (not shown), providing favourable conditions for strong KW activity.
Between 100 and 200 hPa during the second half of July, there was
low-frequency KW activity present in the form of a stationary and robust
“wave-1” pattern with strong KW easterly winds up to 24 m s-1 in the eastern
hemisphere and KW westerly winds up to 10 m s-1 in the western
hemisphere. The high vertical resolution within the TTL resolves shallow KW
structures and a typical slanted structure towards the east in KW easterlies
as well. The appearance and strength of horizontal KW response coincides with
the presence of strong easterly winds in the TTL in the eastern hemisphere
during this period (not shown). Figure also shows that
below 300 hPa the KW activity decreases and we shall not discuss levels under
300 hPa in this paper.
The zonal wind and temperature components are coupled through Eq. (),
which states that the amplitude of the negative KW temperature
perturbation is proportional to the negative vertical gradient in
geopotential (and vice versa), as well as in the zonal wind since the zonal
wind and geopotential are in phase. Horizontally, the cold anomaly is always
located between the westerly and the easterly phase of the zonal wind
component. Vertically, maximal positive temperatures are observed between
easterly winds below and westerly winds above. An estimate of the vertical
wavelength can be made based on alternating zonal wind minima and maxima. For
example, on 25 July a well-developed KW package extending into the
stratosphere moved from the western into the eastern hemisphere. A
quasi-stationary component of the wave package is observed around
60∘ E with easterly winds located at 50 (∼21.5 km) and 150 hPa (∼13.5 km), implying a vertical wavelength of around 8 km.
More examples based on a daily basis filtered data from the 10-day deterministic forecast of the ECMWF can
be found on the MODES website.
Six-year average of the zonal wind and static stability fields of the ECMWF operational analyses. Both fields are
latitudinally averaged over 5∘ S–5∘ N, and have been low-pass filtered a priori with a cut-off period of
90 days to highlight seasonal variability. (a) Longitude–height section and (b) longitude–time section at 100 hPa.
Zonal winds are coloured by blue-to-red contours, each 5 m s-1, whereas and static stability is shown in red contours,
each (a) 1×10-4 s-2 and (b) 0.5×10-4 s-2. Zero lines are omitted.
Other data and impact of the background state
In addition to the outputs from modal decomposition, full zonal wind and
temperature fields from ECMWF analyses are used to compute the background
fields based on the same N64 grid and over the same period (January
2007–June 2013). Zonal wind U and static stability N are latitudinally averaged in
the belt 5∘ S–5∘ N on all model levels to produce their zonal
structure.
Static stability profiles are estimated through
N2=g2Θ∂Θ∂ϕ
in units of s-2 and are defined on hybrid model levels on which the
geopotential field ϕ and the potential temperature field Θ are
derived a priori from the input data. Both fields are shown in Fig. .
The zonal wind field has the largest values on average in the TTL around 150 hPa
with westerly winds peaking in the western hemisphere over the Pacific
Ocean and easterly winds peaking in the eastern hemisphere over the Indian
Ocean and Indonesia. It represents a typical time-averaged outflow pattern in
response to tropical convection e.g.. Throughout
the seasons there is a longitudinal shift of this pattern following the
convective source which is most clearly observed at 150 hPa. Such a seasonal
shift is visible up to 100 hPa in Fig. b where winds are
weaker compared to 150 hPa. In northern winter, zonal winds are strongest
over Indonesia and the eastern Pacific with the zonal wind maxima position
and strength similar compared to the longer ERA-40 dataset used by
. During boreal summer, easterly winds mainly prevail over
the Indian Ocean, which is linked to the Indian monsoon season.
At 100 hPa, the static stability illustrates the strongest seasonal cycle
with values ranging from near-tropospheric values of 3×10-4 m s-2 during northern winter towards stratospheric values of
5–6 ×10-4 m s-2 during boreal summer. Note also the resolved local maxima
in static stability at 80 hPa above the warm pools, known as the tropical
inversion layer (TIL) and which is possibly wave-driven
. Figure b suggests that the
TIL descends down to 100 hPa during boreal summer months peaking over the western
Pacific, in agreement with the cycle found in GPS-RO observations by
.
KWs are subject to wave modulation in changing background
environments. Along its trajectory, the potential energy of the KW changes
with varying background winds and stability which can be largely described by
linear wave theory as long as waves are not near their critical level
involving breaking and dissipation . For simplification,
KW modulation can be examined for the case of pure zonal as well as pure
vertical wave propagation based on the wave modulation analysis performed by
. A few key points on their local wave action conservation
principle are summarized in the following.
In the tropical atmosphere, zonal modulation is the dominant process for KWs
propagating in the stratosphere and in all non-easterly winds in the TTL.
Vertical modulation becomes important in the presence of easterly winds
within the TTL. Zonal modulation is found to affect both ukw and
Tkw components and their amplitudes are proportional to the
Doppler-shifted phase speed by (c-U)1/2 in the case of a pure zonal
propagation direction. This means that KWs diminish in amplitude
over regions with westerly winds and become more prone to dissipative
processes, while amplify over regions with easterly winds. In the case
of pure vertical modulation, the change in wave potential energy mainly
fluctuates with the temperature component of the KW. Along the rays'
vertical path, the waves amplitude is proportional to the
Brunt–Väisälä frequency as ∝N3/2, and to the
Doppler-shifted phase speed as ∝(c-U)-1/2, such that N is
expected to play a primary role above 120 hPa where its value starts
increasing rapidly (see Fig. ).
showed through wave modulation principles that temporal
variations in zonal-mean N indeed are correlated with observed KW
amplitudes at 16 km (approx. 100 hPa). A more extensive wave modulation
analysis was described by using the full ray-tracing
equations to demonstrate that zonal winds in the TTL not only modulate KWs
locally but also create a lasting modulating effect on wave activity
through ray convergence in the stratosphere. In particular, the seasonal
cycle of the upper tropospheric easterlies (on average located over the
western Pacific), that acts as an escape window for KWs throughout
the year and largely explains the longitudinal structure of KW zonal
wind and temperature climatology.
We shall present the seasonal variability in tropical convection by using the
OLR dataset with daily outputs from the NOAA
Interpolated OLR product . The OLR product, often used as
a proxy for convection, is extracted on a 2.5∘×2.5∘
grid and interpolated on a N64 grid. Latitudinal averages are derived over
a larger domain, namely over 15∘ S–15∘ N since organized
convection tends to happen more remote from the equator, especially during the
summer monsoon season over the Asian continent.
KW energetics
We start with a discussion of the KW energy distribution
among zonal wavenumbers as given by Eq. (), followed by seasonal
differences.
Energy distribution of KWs
The seasonal cycle in the energy–zonal-wavenumber spectra is shown in Fig. after summing up over all vertical modes. On average,
energy decreases as the zonal wavenumber increases as typical for atmospheric
energy spectra. As we deal with large scales, we show only the first 6
zonal wavenumbers with energy values shown separately for the annual mean and
the four seasons separately.
Figure shows that largest seasonal variations in KW
energy are found at the largest zonal scales. For all zonal wavenumbers,
above annual-mean energy values are observed during DJF and JJA seasons while
SON and MAM are below annual-mean energy. In the zonal wavenumber 1, total KW
energy varies between 200 J kg-1 in MAM season and somewhat over 300 J kg-1 in JJA. In wavenumber 2, values do not exceed 100 J kg-1 and
JJA still contains the largest energy. At higher wavenumbers, DJF season
becomes the most energetic. In k>4, total KW energy is under 20 J kg-1 and continue to reduce with k. The slope of the KW energy
spectrum is between -5/3 and -1 at planetary scales (not shown), similar
to the spectra presented in for July 2007 data. The JJA
spectra has on average the steepest slope compared to other seasons, in
particular the DJF spectra. The energy distribution on planetary scales is
mainly associated with large-scale tropical circulation established in
response to ongoing tropical convection. Therefore, the zonal distribution of
tropical convection may likely play a crucial role in explaining DJF and JJA
season differences of KW energy, which will be explored in the next section.
Kelvin wave (KW) energy (in J kg-1) as a function of the zonal wavenumber k for k=1 to 6. For each k, seasonal
averages are shown along with the total average as described by the legend.
Energy is vertically integrated over 60 vertical modes. Further details are in Sect. .
Seasonal cycle of KW energy
Figure illustrates more details on the seasonal cycle by
showing KW energy–time series at the largest scales represented by zonal
wavenumbers k=1, k=2 and remaining scales k>2. During most JJA seasons
and occasionally in DJF (e.g. 2008) the total amount of KW energy in k=1
can reach up to 600 J kg-1, or twice the JJA average. The minimum in
k=1 KW energy mainly occurs during October followed by April with values
dropping towards 100 J kg-1, or half the SON average. The temporal
pattern in k=2 is similar to the k=1 pattern, but with a less pronounced
semiannual cycle with maximum values up to 200 J kg-1 and minimum
values towards 30 J kg-1. On zonal scales k>2, KWs still show a
semiannual cycle with highest vertically integrated values of energy in DJF.
In particular, for zonal wavenumber k=1 one can distinguish inter-monthly in
addition to semiannual variability. Inter-monthly variability is most clearly
observed during JJA, for example in July 2011 where one can distinguish six
separate peaks of over 400 J kg-1 energy over a period of approximately
90 days resembling an average wave period of about 18 days. These are typical
periods for free-propagating KWs as observed in the TTL and lower
stratosphere e.g.. Note here again that our KW energy
is vertically integrated over the whole model depth. This means that the
observed inter-monthly variability in KWs appears to be dominated by the cyclic
process of free-propagating KWs entering the TTL, amplifying due to changing
environmental conditions, followed by wave breaking or dissipation.
Time series of the global total KW energy for various zonal wavenumbers over the following periods: (a) 2007–2009
and (b) 2010–2012. Labels on the x axis “A”, “J” and “O” refer to the first days of April, July and October, respectively.
Presented are the zonal wavenumbers k=1 (blue line), k=2 (green line) and
all smaller zonal scales, k>2 (red line). A 90 day low-pass filter has been applied (black lines) for each
time series in order to filter out high-frequency variability and to highlight seasonal variability.
The dominant scales of temporal variability in KWs are illustrated by a
frequency spectrum of k=1 in Fig. . The spectrum is
produced by the Fourier transform of energy time series of 6.5 years. The
resulting power spectrum has been smoothed by taking the Gaussian-shaped
moving averages over the raw spectrum by using the Daniell kernel three times
. The spectrum contains a peak at 1 day period associated
with the diurnal tide partially projecting on the KWs. After that, a
gradual increase in energy is seen towards the 16-day period with multiple
individual periods standing out. For periods longer than 20 days, individual
peaks are found close to 25, 43 and 59 days. After that, most KW energy is
contained by far in the semiannual cycle. The frequency spectrum provides a
useful starting point for the discussion in the next section when the
spatiotemporal patterns of KWs shall be examined in several spectral domains.
Returning to Fig. , a low-pass filter with 90-day cut off
has been applied on KW energy in order to keep only the two main spectral
peaks in Fig. . The result is visible as the thicker
black line in Fig. for all three zonal wavenumber groups.
A semiannual cycle for all zonal wavenumbers is evident with most energy
observed around January and July, while least energy is observed
approximately one month after the equinoxes. During the years 2007, 2010,
2011 and 2012, more k=1 KW energy is observed during JJA compared to the
follow-up DJF season. The DJF of 2009–2010 was, for example, above average with
energy values for k=1 above 350 J kg-1.
Kelvin wave (KW) frequency spectrum for the zonal wavenumber k=1. The 1-2-1 filter with a Daniell kernel has been used to
smooth the initial raw power spectra.
The year-to-year differences can be explained by many coupled factors. In
general, one expects the vertically integrated KW activity to increase when
background wind conditions become favourable, i.e. in the presence of easterly
winds. This occurs in the TTL in relation to strong convective outflow
during DJF and JJA
seasons mainly. Moreover, KW activity is enhanced whenever easterly QBO winds
are present down into the lower stratosphere or during El Niño . The
latter factor may partly explain a large difference in the KW energy during
the El Niño DJF of 2009–2010 and the below-average energy
level a year after, during the strong La Niña DJF period of
2010–2011. However, during the La Niña DJF of 2007–2008, the
amount of KW energy is above normal. That season, however, was characterized by
above-normal Madden–Julian Oscillation activity which often occurs during favourable easterly QBO
conditions in the stratosphere . During 2010–2011, DJF season
stratospheric winds were largely westerly thereby prohibiting KW activity.
The role of these low-frequency atmospheric phenomena on KW seasonal
variability is a topic of further research.
Finally, Fig. also shows that KW activity in July 2007,
previously examined by , was exceptionally strong. A large
part of that energy, (somewhat more than half) belonged to zonal wavenumber
1. In spatiotemporal terms, it is associated with the presence of a strong
dipole structure in the TTL (as in Fig. ), which is
colocated with favourable easterly wind conditions in the TTL as well as in
the stratosphere (not shown). In fact, at 50 hPa the QBO was just at the
beginning of its easterly phase in July 2007.
A spatiotemporal view on KW seasonal variability
KW decomposition among wave periods
In this section, the spatiotemporal view of KWs shall be
presented over three dominant ranges of wave periods in Fig. ,
namely (i) the (semi)annual cycle using a low-pass
filter with cut-off period at 90 days, (ii) the intra-seasonal period using a
bandpass filter over periods between 20 and 90 days and finally (iii) the
intra-monthly period with bandpass filtered periods between 3 and 20 days. The
chosen periods, especially the intra-monthly periods, are similar to those
used in previous studies. In each case, mean 6-year fields as well as
seasonal means shall be presented.
Note that our temporal filtering operates on time series of KW signals at
every grid point. This is different from the commonly applied space-time
filtering following that applies KW dispersion relations.
Our filtered KWs can appear stationary or even westward-shifted due to
westward-moving sources of the KW amplification (e.g. easterly winds, high
static stability in the TTL).
Both KW components ukw and Tkw are Fourier-transformed to frequency
space where the spectral expansion coefficients χkw in domains
outside the desired frequency ranges are put to zero. Case (i) results in KW
components ukw,l and Tkw,l where l indicates the low-frequency
component. Case (ii) results in ukw,m and Tkw,m where m indicates
the intra-monthly period. Case (iii) results in fields ukw,h and
Tkw,h where h stands for the high-frequency component. Previous
studies have defined free-propagating KWs over similar ranges (3–20 days, ; 4–23 days, ) and similarly for
intra-seasonal periods (23–92 days, ). Next, seasonal
averages will be taken over the four seasons, resulting in variables
ukw,l‾s and Tkw,l‾s for the low-frequency
component and similarly for the other two cases. The superscript s
represents one of the four seasons: northern winter (s= DJF), spring
(s= MAM), summer (s= JJA) and autumn (s= SON).
Cases (ii) and (iii) contain purely subseasonal variability and therefore one
can expect their 6-year means to be zero-valued since variability beyond
90 days has been put to zero. Similarly, mean fields for each of the four
seasons result in ukw,h‾s≪ukw,l‾s and
ukw,m‾s≪ukw,l‾s and the same for the
temperature component. This reflects the fact that positive and negative
phases of the fast KW responses average out to approximately zero on seasonal
timescales (figure not shown). Therefore, the seasonal mean of the absolute
amplitudes of the zonal wind and temperature are examined instead, i.e.
|ukw,h|‾s and |ukw,m|‾s and similarly for
temperature. This describes seasonal fluctuations in subseasonal KW
amplitudes.
Longitude–pressure sections along 0.7∘ N of the KW zonal wind and temperature averaged
over the 6-year period for (a) low-frequency, (b) intra-seasonal and (c) intra-monthly periods.
The contouring is as follows: (a) zonal wind is coloured each 1.5 m s-1 and temperature
is shown by red contours each 0.5 K, with zero lines omitted;
(b) absolute amplitudes of the zonal wind and temperature
are shown in grey shades each 0.5 m s-1 and red contours, each 0.15 K, respectively and
(c) absolute amplitudes of the zonal wind are in grey shades each 0.25 m s-1 and temperature in
red contours (each 0.15 K).
Figure shows results for all three cases after taking means
over the whole period. The left panel resembles a dominant “wave-1” structure
with zonal wind maximized around 140 hPa. Easterly KW winds are strongest
around 60∘ E and westerly winds around the International Date Line. Note that two
stationary perturbations over African (30∘ E) and South American
(80∘ W) orography are the result of our terrain-following NMF
analysis. If one compares the KW zonal wind pattern with the climatological
zonal wind pattern in Fig. a, it can be observed that the
zonal wind pattern is located around 20∘ west of the climatological
pattern. Wave temperature perturbations are largest where the vertical
gradients in zonal wind are largest, which explains the quadrupole structure.
Warm and cold KW anomalies are located at 100 hPa in the eastern and western
hemispheres, respectively, and vice versa at 200–300 hPa.
The average low-frequency or seasonal KW structure has a significant
resemblance with the classical Gill-type KW solution
describing a steady-state linear wave response to convective forcing. The
Gill-type KW solution is characterized by westerly upper-troposphere winds
east of the large-scale convective source. In response to the seasonal cycle
of convection, the solution in Fig. a also illustrates, in addition
to a low-frequency KW variability in westerly winds, a considerable
low-frequency variability west of the convective outflow.
This part of the signal represents the wave modulation effect of the propagating KWs on seasonal timescales.
The middle panel of Fig. shows the average distribution of KW
activity on intra-seasonal timescales. The activity is largest in the eastern
hemisphere with average zonal wind maxima up to 3 m s-1 and temperature
maxima up to 0.7 K. Zonal wind activity is largest over a broad area between
90 and 150 hPa over the Indian Ocean and the Maritime Continent. Temperature
activity occurs slightly higher around 90–100 hPa. Intra-seasonal activity is
locally somewhat increased also around 120∘ W, west of the Andes
mountain range.
Finally, Fig. c illustrates the average distribution of
intra-monthly KWs. The eastern hemisphere again makes up for the larger KW
activity than the western hemisphere, but the maximum is located more upward
in comparison to the intra-seasonal scales, around 80 hPa. Zonal wind activity
peaks up to 3 m s-1 over a broad range of 70–110 hPa and temperature
peaks over a more narrow area around 76 hPa (up to 0.75 K). The main area for
KW activity is found over the Indian Ocean region, while least wave activity is
above the central Pacific. Towards the stratosphere, KW activity reduces and
becomes more uniform along the longitudinal direction.
Seasonally averaged longitude–pressure sections of the KW zonal wind (blue-to-red colour-filled
contours) and temperature (red contours) along 0.7∘ N. (a) DJF, (b) MAM, (c) JJA and (d) SON. Contouring of the
KW signal is the same as in Fig. a. A single static stability contour with value 5×10-4 s-2
is shown as a thick dotted black line to represent the seasonal movement of the tropical tropopause height. The average background
zonal wind is shown by blue contours (each 5 m s-1, starting from 15 m s-1). The background zonal wind and stability
fields are latitudinally averaged over 5∘ S–5∘ N. All fields are smoothed using a low-pass filter with the cut-off period of 90 days.
Low-frequency KW variability
The seasonal patterns of the low-frequency components of the KW is presented
as pressure–longitudinal cross sections along the equator (at 0.7∘ N)
of the KW seasonal means, given by [ukw,l]‾s and
[Tkw,l]‾s in Fig. .
The largest amplitudes are found during the JJA months. A strong dipole
“wave-1” pattern is evident in the TTL. The strongest zonal winds are found
close to 150 hPa with easterlies up to -12 m s-1 centred over the Indian
Ocean and westerlies up to 6 m s-1 over the western Pacific. Negative
temperature KW anomalies at 110 hPa are strongest as well during JJA with
values up to 1.5 K over the Indian Ocean and annually averaged value of -0.5 K
over the western Pacific.
During DJF, the dipole pattern has shifted more eastward and upward compared
to JJA and has a more slanted structure. Easterly (westerly) KW winds are
located more east over the Maritime continent (central Pacific) and are
centred at 130 hPa. The upper temperature dipole pattern is found higher up
at approximately 90 hPa. Values are somewhat weaker compared to Northern Hemisphere
summer with easterlies up to -6 m s-1 and westerlies up to 5 m s-1.
Finally, SON and MAM season months are transition seasons with respect to the
strength and position of the KW dipole as it moves west- and downward towards
JJA and east- and upward towards DJF. Season MAM has the weakest KW dipole with
slightly stronger westerly winds up to 5 m s-1.
The longitudinal position and the strength of the low-frequency KWs have been
linked to the seasonal patterns of the background winds in the TTL
representing the upper level monsoon and Walker circulations
. The average background winds maximize at 150 hPa as
shown in Fig. a. In Fig. , one can see how
the KW easterlies in the eastern hemisphere are strongest during JJA in
relation to the Indian and South Asian monsoon circulation. Background easterlies
as strong as -30 m s-1 are located approximately 10∘ east of the
KW maximum easterlies. Season DJF has the strongest background westerlies in
relation to the upper-level circulation of the western Pacific anticyclones.
Season MAM shows similar background wind patterns compared to DJF but with weaker
circulation. Season SON shows similar patterns with JJA but with weaker winds.
Further details on longitudinal position and interannual variability in the
low-frequency KW response at its maximum value at 150 hPa are illustrated by
the Hovmöller diagram in Fig. . For comparison, tropical
convection is represented as well through the OLR proxy variable averaged
over 15∘ S–15∘ N latitudes. All fields have been filtered
with a 90-day cut-off low-pass filter in order to highlight the seasonality.
As a result, one can observe enhanced or reduced KW activity during the same
individual seasons as seen from the time series in Fig. .
Above-average seasonal KW activity with stronger dipole structures occurred
during the summer of 2007 (mainly through its easterlies at 60∘ E)
and during the winters of 2006–2007 and 2009–2010. In these winters, El Niño
was active and a clear longitudinal eastward shift is observed in OLR and in the
background circulation (not shown), as well as in the dipole KW structure.
The El Niño winter of 2009–2010 was followed by a strong La Niña winter with
an increase in tropical convection over the Maritime Continent (note OLR
values below 195 Wm-2).
Longitude–time section at model level 45 (∼153 hPa) of the KW zonal wind
along 0.7∘ N (blue to red shaded contours every 2 m s-1 with zero line omitted) and the outgoing longwave
radiation (OLR) averaged over the latitude belt 15∘ S–15∘ N (red contours each 10 Wm-2 starting at 225 Wm-2).
Both fields have been filtered a priori using a low-pass filter with a cut-off period of 90 days.
The vertical seasonal movement of the KW dipole has been linked with the
seasonal movement of the tropical tropopause height . The position of the tropical tropopause height (represented by a
static stability value of 5×10-4 s-2 in Fig. ) is found at approximately 85 hPa during DJF and descends
towards 100 hPa in JJA, similar to values obtained from GPS-RO observations
by . In particular, during JJA, one can notice how the
asymmetry in the tropical tropopause height over the Indian Ocean around
60∘ E coincides with increasing temperatures by the KW dipole up to
1.5 K. Such deformation of the tropical tropopause is also evident during DJF
and SON seasons.
Seasonally averaged longitude–pressure sections for (a, c) DJF and (b, d) JJA. (a–b) KW
temperature, Tkw‾s,
(blue-to-red shades every 0.25 K) and static stability field, N2‾s (black contours, each 1×10-4 s-2,
starting at 2×10-4 s-2). (c–d) KW static stability anomaly, Nkw2‾s (blue-to-red, each
0.2×10-4 s-2), and static stability anomaly with respect to the zonal mean, N′2‾s (red contours,
each 0.4×10-4 s-2).
Figure a and b illustrate
seasonal-mean KW temperatures Tkw,l‾s in relation to the
tropical tropopause layer defined by static stability N2. Seasonal
variations in KW temperatures are colocated with the position of the
tropopause, descending down from its highest position during DJF to its
lowest position during JJA. Temperature amplitudes are observed to decline
roughly above N2=5-6×10-4 s-2. Within this zonal-mean
seasonal picture, zonal asymmetries in N2 exist and are found: (i) near
the International Date Line with values of 8×10-4 s-2 at 80 hPa during DJF
and 7×10-4 s-2 at 90 hPa during JJA and (ii) lower at 100 hPa
over the Indian Ocean during JJA. Particularly during JJA, the
deformation of the zonal-mean static stability field colocates strongly with
the position of a strong KW temperature anomaly over the Indian Ocean. A rough
estimation is made on the contribution of the KW anomaly to the zonal
deformation of the tropopause layer by removing zonal-mean parts of both
fields. First, static stability zonal anomalies, N′2‾s, are
derived by subtracting zonal-mean values of N2 from the full N2 field
per time step and at every pressure level, followed by seasonal averaging.
Next, we can estimate the static stability change associated with the KW
anomaly, using the relation Nkw2=gθ‾∂θkw∂z, followed
by seasonal averaging as well, i.e. Nkw2‾s.
As a result, Fig. c and d show how
both static stability anomalies are overlapping. During DJF, the structure of
the zonal anomaly N′2‾s has a positively valued tilt eastward
which stretches up to 80 hPa, while during JJA a strong static stability
anomaly is found more localized over the Indian Ocean region with values in the
TTL up to N′2‾JJA=±0.8×10-4 s-2. The
anomaly associated with the KW temperature is found to peak up to
+0.6×10-4 s-2 during JJA and up to +0.4×10-4 s-2 during DJF. Finally, by dividing both fields with each other, the
resulting contribution of the quasi-stationary KW to the observed
deformation of the tropical tropopause layer is estimated up to 60% during
JJA and 80% during DJF.
Seasonally averaged longitude–pressure sections along 0.7∘ N of the intra-seasonal
KW zonal wind (white-to-black shades, each 0.5 m s-1) and temperature
(red contours, each 0.2 K). (a) DJF, (b) MAM, (c) JJA and (d) SON. The averaging is performed for
the absolute values of both zonal wind and temperature perturbations. The background zonal wind (shown
by blue contours) and the tropical tropopause height (single thick dotted contour) are defined as in Fig. .
Intra-seasonal KW variability
The seasonality of intra-seasonal KW variability is shown in Fig. and shall be briefly discussed here. The DJF
stands out as the most active season for KW activity, located mainly in the
eastern hemisphere centred at 100∘ E and with maximum activity at 110 hPa for zonal wind and temperature with a
second maximum in temperature at 90 hPa. Values observed are up to 0.8 K for KW temperature and 5 m s-1 for
KW zonal wind. During the MAM season, the KW activity fields are weaker but
spread over a larger area in the eastern hemisphere and in the TTL with
maximum activity centred at 120 hPa (90 hPa) for the zonal wind
(temperature) component. Both JJA and SON seasons have KW activity positioned
at lower altitudes and more westward. In both seasons, KW zonal wind activity
is split up between two structures with an eastward tilt with height: one
with a maximum around 110∘ E and one pattern starting from 100 hPa
and extending towards 60∘ E. Note also the increase in KW activity in
the western hemisphere below 150 hPa in the east Pacific. The maximum KW
activity in the temperature component for both seasons is positioned near 100 hPa
approximately on the tropical tropopause contour with a value 5×10-4 s-2.
The eastward tilted structure is observed throughout all seasons except MAM
when background easterly winds are nearly absent in the eastern hemisphere.
In all other seasons one can observe how the tilted structure is locked to
the background easterlies with maximum amplitudes located slightly above and
west of it. Such eastward tilt with height has been frequently observed, for
example over a radiosonde station Medan at 100∘ E during the early
stage of Madden–Julian Oscillation development .
As in Fig. but for the intra-monthly KWs.
The zonal wind (white-to-black shades) is drawn every 0.25 m s-1.
Intra-monthly KWs
The seasonal variability in intra-monthly KWs, represented by their
absolute amplitudes |ukw,h′|‾s and
|Tkw,h′|‾s, shall be examined in relation to the background
conditions. Figure illustrates favourable regions
for KW activity. In general, KW activity increases upward from around 120 hPa
towards its zonal-mean peak value at 76 hPa. The largest values are observed
in the eastern hemisphere in a region from 30 to 150∘ E.
The temperature component in particular has a constant maximum peak (up to
0.8 K) located around 76 hPa throughout the year, where the largest
increase in N2 also occurs as shown in Fig. . Above 70 hPa, KW
activity continuously decreases in the stratosphere.
The longitudinal structure of the KW zonal wind shows two distinct peaks in
the TTL, one consistently located at 76 hPa and another around 100–110 hPa in
the eastern hemisphere, which is mainly present during solstice seasons. The
first maximum coincides with the temperature distribution, which can be
explained by their balance relationships and free horizontal propagation in
the stratosphere. Below the tropopause, KW activity is coupled to convective
processes alternating the tropospheric vertical wave structures as discussed
by .
The secondary maximum around 110 hPa in Fig. is
present mainly during solstice seasons in the eastern hemisphere and it is
associated with the seasonal movement of the background wind.
The maximum of KW wind and the background wind maximum move eastward from DJF
to JJA seasons similar to the low-frequency variability.
A day-by-day comparison of the KW activity and background wind confirms that
propagating KWs amplify while approaching a region of strong easterlies,
forming a folding structure around it while the individual KWs dissipate
towards the centre of easterly winds. In Fig. one can notice
a fast reduction of KW amplitudes eastward of its
maximum towards the centre of the background easterlies. It is likely related
to dissipation and wave breaking processes as observed over Indonesia
(120∘ E) by . Within such regions, the
KW–background-wind interaction becomes complex and the linearity assumption
breaks .
A comparison with the previous study by using ERA-40
data shows that the L91 data contain stronger KW activity in the vicinity of
the background easterlies in the eastern hemisphere, and more fine-scale
details, which can be explained by better analyses based on more observations
and improved models including increased resolution. For example,
used 5 levels of ERA-40 data between 50 and 200 hPa
whereas the present study considers 25 model levels between 50–200 hPa.
Maxima of the KW temperature signal appear in similar locations and strength,
except for a small offset in vertical position (70 hPa in
, versus 80 hPa in Fig. ) and a
larger zonal asymmetry in our results.
Intra-monthly KW zonal wind and temperature composites as a function of
longitude and month in a calendar year at (a–b) model level 40 (∼110 hPa) and
(c–d) model level 49 (∼200 hPa) along 0.7∘ N.
The waves are accumulated from different years into a single calendar year to highlight
seasonal behaviour. Only the most energetic signals are shown:
(a, c) zonal wind, |ukw′|, each 0.5 m s-1, and (b, d) temperature |Tkw′|,
each 0.1 K. For comparison, the background zonal wind field is presented by red contours, each 5 m s-1.
On the right side of each panel, blue lines with circles denote maximal amplitude of the
KW zonal wind occurring anywhere along the equator averaged over the 6-year period
for each calendar month. This highlights seasonality in the maximum amplification of propagating KWs.
Another view of the seasonal cycle of free-propagating KWs is illustrated in
Fig. , which focuses on the spatiotemporal distribution of
individual KW tracks. Hovmöller diagrams are illustrated for KW zonal wind and
temperature at levels 110 and 200 hPa cumulated from different years into
a single calendar year along with the background zonal wind. In addition, the
monthly-mean values of daily maximum KW amplitudes occurring in longitude are
added on the right side of each diagram. It represents seasonality in the KW
maximum amplitudes in a similar fashion to Fig. 6 in ,
which is based on HIRDLS satellite data.
The individual wave tracks at 110 hPa illustrate KWs with amplitudes
exceeding 3 m s-1 and 0.6 K, which are propagating throughout the year
in the eastern hemisphere, during June–October months only over the Pacific,
and all except DJF months in most of the western hemisphere. Typical wave
tracks start east of the 0∘ (30∘ W) meridian during winter
(summer) and largely disappear west of 120∘ E. The largest wave
amplitudes are observed between 50 and 100∘ E prior to
regions of easterly winds in agreement with Fig. .
Here, presented details show that the most notable waves appear during the Asian
monsoon period with upper-level easterlies prevailing from June into
September. The largest KW amplitudes appear to be confined to the June and July
months followed by a rapid drop in August. In fact, a local minimum in the
number of KWs as well as in wave amplitudes occurs in August before the KW
activity increases slightly during autumn.
At 200 hPa, the favourable area for KW propagation shifts to the western
hemisphere and high KW activity is observed west of the South American
continent throughout the year (west of 80∘ W) with a westward
extension over the Pacific during JJA. Another set of wave tracks starts over
equatorial South America around 30∘ W and continues until
60∘ E during JJA. During DJF these wave tracks shift more east and
start at 5∘ W and continue until 90∘ E. The seasonal shifts of
approximately 30∘ in KW tracks colocate with similar shifts in the
prevailing TTL winds.
The amplitude of KWs undergoes a clear annual cycle with a small secondary
peak present during DJF, as represented by the monthly-means of daily maximum
amplitudes on the right side of Fig. . The largest
amplitudes are found at 110 hPa during JJA with monthly-mean zonal wind
(temperature) values up to 8.5 m s-1 (1.8 K) in June. During the DJF
months KWs amplify more eastward with monthly-mean zonal wind
(temperature) values up to 7.8 m s-1 (1.6 K) in December. Our result
matches well with the observed seasonal pattern in maximum KW temperatures at
16 km (∼ 100 hPa) from the HIRDLS satellite observations Fig. 6. At 200 hPa, KW amplitudes are on average lower with a
yearly-averaged amplitude reduction around 55% in temperature and 35%
in zonal wind.
The semiannual cycle in maximum amplitudes remains visible up until 70 hPa.
Above 70 hPa, where the KW activity remains large in the eastern hemisphere
(Fig. ), the semiannual cycle is replaced by an
interannual cycle in line with the dominant impact of the QBO.
Discussion and conclusions
We have applied a multivariate decomposition of the ECMWF operational
analyses during the period 2007–2013 when the operational data assimilation
and forecasting were performed on 91 model levels. The applied normal-mode
function decomposition simultaneously provides the wind components,
geopotential height and temperature perturbations of Kelvin waves (KWs) on many
scales without any prior data filtering. The three-dimensional KW
structure in the upper troposphere and lower stratosphere is composed of
KW solutions of 60 linearized shallow-water equation systems on the
sphere with equivalent depths from 10 km up to about 3 m. As the KW
meridional wind component is very small it is not discussed here. We showed
that large-scale KWs readily persist in the data despite analysing selected
processing times independently.
The KW is a normal mode of the global atmosphere and our 3-D-orthogonal
decomposition allows for the quantification of its contribution to the global energy
spectrum and variability. We have presented the total (kinetic + potential)
energy of KWs in the L91 data as a function of the zonal wavenumber in
different seasons. The zonal wavenumber k=1 contains the largest portion of
KW energy in all seasons. There is almost one-third more energy in JJA than
in MAM in k=1. In k=2 there is 50 % less energy than in k=1 but season JJA
still contains most energy. In all larger zonal wavenumbers, the most
energetic season is DJF.
We focused on the spatiotemporal features of the KW temperature and zonal
wind components in the four seasons. The KW seasonal cycle in the
tropical tropopause layer (TTL) was compared with seasonal variability in the
outgoing longwave radiation (OLR), and the background wind and stability
fields, which are believed to play an important role in KW variability.
Our results of the seasonal KW variability complement previous studies which
applied different methods for the KW filtering and different datasets. The
frequency spectrum has revealed a semiannual cycle as well as inter-seasonal
and intra-monthly variability. Three ranges of wave periods were analysed:
3–20, 20–90 and longer than 90 days. This choice was partly
deliberate in order to compare our results with several previous studies of
KW variability. First we demonstrated that the low-frequency KW dipole
pattern in the TTL, with westerly winds in the western hemisphere and with
easterly winds in the eastern hemisphere, partly resembles a
seasonal-averaged Gill-type “wave-1” pattern and contains partly
low-frequency modulation of vertically propagating KWs. The quadrupole-shaped
temperature component represents a thermally adjusted pattern with respect to
the zonal wind component, and contributes to seasonal warming above 100 hPa
in the western and cooling in the eastern hemisphere. The largest KW
amplitudes are observed during JJA and DJF seasons. From boreal summer
towards winter,
KW perturbations move eastward (from the Indian Ocean basin towards the Maritime Continent) and upward
(e.g. zonal wind component moves up from 150 towards 120 hPa). The KW zonal wind amplitude varies
between 12 m s-1 strong easterlies over the Indian Ocean near 150 hPa in JJA and 6 m s-1
over the western Pacific. Over the Indian Ocean
in JJA, the KW easterlies thus make up almost half of the total wind vector.
The associated KW temperature perturbations are from 1.5 K over the Indian Ocean in JJA to -0.5 K over the western Pacific.
The zonal modulation of KWs is found to be locked with respect to
the seasonal movement of convection and the convective outflow in the TTL.
The modulation effect is strongest for the low-frequency KWs during
the summer monsoon season, when strong easterly winds are present at 150 hPa, resulting in the largest KW zonal wind and temperature anomalies, of
which the latter results in deformation of the tropical tropopause over the Indian Ocean.
Intra-seasonal (periods 20–90 days) activity is strongest in DJF with maxima
up to 0.8 K for KW temperature and up to 5 m s-1 for KW zonal wind centred
at 120∘ E. Both temperature and zonal wind activities have an eastward
tilt with height. In comparison to a previous study by using
ERA-40 data, the slanted structure in the present data continues to extend
more upward and eastward, which is likely due to the increased number of
vertical model levels compared to ERA-40. The importance of vertical model
resolution for the KW structure and amplitude was demonstrated in
and .
For periods 3–20 days, the seasonal cycle of KWs is clearly seen in the
wave amplitude. In the zonal-mean perspective, the largest amplitudes are
located between 70 and 100 hPa for both zonal wind and temperature but it
is modulated by the seasonal movement of the TTL. A major zonal asymmetry was
found in KW activity: around 110 hPa the KW undergoes
amplification mainly in the eastern hemisphere during the solstice seasons,
while at 200 hPa a secondary region of the KW amplification occurs in the
western hemisphere during boreal summer. The inter-monthly KWs show largest
amplitudes in the vicinity of the strongest easterlies preferably west and
above the centre of the easterlies. The applied novel methodology makes it
possible to observe such dynamics on a daily basis whenever easterlies are
strong in the TTL. A nearly real-time representation of the KW activity is
available at http://modes.fmf.uni-lj.si (last access: 12 June 2018).
In summary, our seasonal variability analysis shows that the background wind
in the TTL linked with convective outflows play a dominant role in the
longitudinal position where the zonal modulation of KWs is
preferred, while the tropical tropopause and its seasonal vertical movement
determine the vertical extent of the KW modulation processes.