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Northern Hemisphere planetary waves exhibit an abrupt change in early summer and a significant impact on East Asian summer monsoon rainfall. Although great achievements have been made toward understanding the characteristics and maintenance of planetary waves during winter and summer, the transition of planetary waves during the abrupt-change period is less well understood. This study aims to assess the relative contribution of harmonic waves to the planetary wave transition and mechanism from the perspective of full nonlinear responses to the mountains of Asia (above 500 m) during May and June, with a primary focus on the largest positive geopotential height anomaly over northeastern Asia. The largest positive geopotential height anomaly over northeastern Asia is primarily contributed by wavelengths of around 7000 km, which corresponds to zonal wavenumber 3. The mid–high latitudes planetary waves mainly consist of wavelengths of around 10,000 km (zonal wavenumber 2, roughly) and 7000 km, which are in-phase (out-of-phase) with each other over the Western (Eastern) Hemisphere. Wavelengths of around 10,000 km weaken and displace eastward, while those of 7000 km magnify and hence contribute to the largest positive geopotential height anomaly over northeastern Asia. The full nonlinear response to the forcing by the mountains of Asia provides a considerable contribution to the largest geopotential height anomaly over northeastern Asia. Such a positive contribution comes mainly from the full nonlinear response to sensible heating associated with the mountains over Asia, which is partially offset by the full nonlinear response to dynamical forcing of the Asian mountains.
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Vol.:(0123456789)
1 3
Climate Dynamics
https://doi.org/10.1007/s00382-021-06048-5
Intraseasonal transition ofNorthern Hemisphere planetary waves
andtheunderlying mechanism duringtheabrupt‑change period
ofearly summer
ZuoweiXie1 · BuehCholaw1· YiDeng2· BianHe3· ShengLai1,4
Received: 10 June 2021 / Accepted: 7 November 2021
© The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2021
Abstract
Northern Hemisphere planetary waves exhibit an abrupt change in early summer and a significant impact on East Asian
summer monsoon rainfall. Although great achievements have been made toward understanding the characteristics and main-
tenance of planetary waves during winter and summer, the transition of planetary waves during the abrupt-change period is
less well understood. This study aims to assess the relative contribution of harmonic waves to the planetary wave transition
and mechanism from the perspective of full nonlinear responses to the mountains of Asia (above 500m) during May and
June, with a primary focus on the largest positive geopotential height anomaly over northeastern Asia. The largest positive
geopotential height anomaly over northeastern Asia is primarily contributed by wavelengths of around 7000km, which cor-
responds to zonal wavenumber 3. The mid–high latitudes planetary waves mainly consist of wavelengths of around 10,000km
(zonal wavenumber 2, roughly) and 7000km, which are in-phase (out-of-phase) with each other over the Western (Eastern)
Hemisphere. Wavelengths of around 10,000km weaken and displace eastward, while those of 7000km magnify and hence
contribute to the largest positive geopotential height anomaly over northeastern Asia. The full nonlinear response to the forc-
ing by the mountains of Asia provides a considerable contribution to the largest geopotential height anomaly over northeastern
Asia. Such a positive contribution comes mainly from the full nonlinear response to sensible heating associated with the
mountains over Asia, which is partially offset by the full nonlinear response to dynamical forcing of the Asian mountains.
Keywords Planetary waves· Abrupt change· Northeastern Asia· GMMIP· Harmonic analysis
1 Introduction
Stationary waves, also known as stationary eddies, often
refer to the zonally asymmetric anomalies of the time-aver-
aged atmospheric circulation (Held etal. 2002; Nigam and
DeWeaver 2015). The asymmetric features of stationary
waves are rooted in the asymmetries of the lower bound-
ary conditions, such as land–ocean contrasts and mountain
terrain. Stationary waves can also be derived from the daily
meteorological field using a spatiotemporal spectral analysis
(Hayashi 1977; Watt-Meyer and Kushner 2015). Such daily
stationary waves fluctuate in amplitude from day to day and
are also referred to as planetary waves, which are consid-
ered as small wavenumbers of atmospheric waves (Holton
and Mass 1976; Hayashi 1977). Planetary waves not only
contribute directly to meridional fluxes of momentum and
heat, but also act as a background flow providing energy for
the barotropic and baroclinic instabilities of both extreme
weather systems and teleconnection patterns (Charney 1947;
Eady 1949; Simmons etal. 1983; Li and Ji 1997; Xie etal.
2019).
Planetary waves exhibit a drastic change during the tran-
sition seasons between winter and summer (Ye etal. 1958;
Tao etal. 1958; Ting etal. 2001). The abrupt change in June
* Zuowei Xie
xiezuowei@mail.iap.ac.cn
1 International Center forClimate andEnvironment Sciences,
Institute ofAtmospheric Physics, Chinese Academy
ofSciences, Beijing100029, China
2 School ofEarth andAtmospheric Sciences, Georgia Institute
ofTechnology, Atlanta, GA30332, USA
3 State Key Laboratory ofNumerical Modeling
forAtmospheric Sciences andGeophysical Fluid Dynamics,
Institute ofAtmospheric Physics, Chinese Academy
ofSciences, Beijing100029, China
4 Present Address: Climate Center ofGuangxi Zhuang
Autonomous Region, Nanning, Guangxi530022, China
Z.Xie et al.
1 3
is more evident than that in October and concurrent with the
onset of the well-known “plum rainfall” over central China
and Japan (Ye etal. 1958). During this period from May to
June, Chyi etal. (2021) showed that the largest change in
planetary waves in the Northern Hemisphere is characterized
by a warm high anomaly over northern Asia. The onset tim-
ing of such anticyclonic anomalies exerts a significant influ-
ence on the position and amount of plum rainfall over cen-
tral China (Chen etal. 2021; Chyi etal. 2021). Aside from
the significant climate and weather impacts of this abrupt
change in June, it is hugely challenging for atmospheric
global climate models to simulate. For instance, Ting etal.
(2001) showed that the lowest performance of the Geophysi-
cal Fluid Dynamics Laboratory general circulation model
in simulating the mid-level tropospheric planetary waves
occurs during May and June.
Harmonic decomposition of planetary waves has revealed
that large-scale fluctuations in boreal winter primarily con-
sist of westward (e.g. zonal wavenumbers 1–2) and east-
ward (e.g. zonal wavenumber 4) propagating planetary
waves (Pratt and Wallace 1976). Similar to the change in
zonal wavenumber, Sun etal. (2019) discovered an appar-
ent change in the meridional structure of planetary waves
from winter to summer by applying harmonic analysis to
both zonal and meridional waves. Xie etal. (2017) isolated
daily planetary waves using spherical harmonic analysis and
decomposed winter planetary waves into six groups based
on the cluster-mean daily planetary waves. Considering the
abrupt change of Northern Hemisphere circulation during
the period from May to June with the largest positive geo-
potential height over northeastern Asia, the contributions
of harmonic waves and how planetary wave patterns vary
remain unclear.
Orography, diabatic heating, transient eddy and nonlin-
ear interactions among them jointly form planetary waves
(Charney and Eliassen 1949; Ting etal. 2001; Held etal.
2002). The seminal paper by Charney and Eliassen (1949)
revealed the vital role of midlatitude mountains in deter-
mining the planetary wave of 45°N using a linear shallow-
water model. Much of the literature using linear models has
given us a tremendous wealth of knowledge regarding the
relative contributions of topography, diabatic heating, and
transient eddies to planetary waves (e.g. Hoskins and Karoly
1981; Ting and Held 1990). However, Ting etal. (2001)
and Held etal. (2002) emphasized an important role of the
nonlinear wave-wave interactions among the waves forced
by orography, diabatic heating and transient eddies in plan-
etary waves, which contributes more to winter than summer
planetary waves. This nonlinearity is primarily contributed
by the interaction between the flows forced by diabatic heat-
ing and orography and generates an anticyclonic circulation
around Lake Baikal in summer. Chang (2009) showed that
extratropical (north of 25° N) diabatic heating and Tibetan
Plateau forcings explain most of the planetary waves in
model simulations. Garfinkel etal. (2020) illustrated that
the strength of a planetary wave response to a given forc-
ing depends on the background-state temperature field set
by each forcing. As pointed out by Held etal. (2002), prior
studies have mainly analyzed the response to heat sources as
obtained from observations or general circulation models,
rather than first determining the diabatic heating distribution
generated from the lower boundary conditions. Although
some studies have proposed a driving air-pump mechanism
of the sensible heating determined by the Tibetan Plateau,
they focused on its role in regulating the East Asian mon-
soon circulation (Wu etal. 2007; He etal. 2019b).
In spite of the great achievements regarding the charac-
teristics and maintenance mechanism of planetary waves in
the winter and summer seasons, there remains several open
questions with respect to the intraseasonal variability of
planetary waves and the underlying mechanisms, especially
regarding the abrupt change during June, with the largest
positive geopotential height anomaly over northeastern Asia.
The specific questions that the current study seeks to address
are as follows:
(1) How do planetary waves of different wavelength con-
tribute to the intraseasonal change in planetary waves
from May to June?
(2) How many types of planetary wave pattern are there
from May to June?
(3) To what extent do the full nonlinear responses to the
mountains over Asia contribute to the intraseasonal
change of planetary waves from May to June?
Since the maintenance of planetary waves is separated
into the Sverdrup regime in the tropics and the Rossby
regime in the mid–high latitudes (Chen 2005), we restrict
our attention to the mid–high latitudes to answer these three
questions. This study refers planetary waves to the 500-hPa
geopotential height (Z500), including the latitudinal shear
of zonal mean Z500. We decompose the planetary waves
over the latitudinal belt encompassing the largest positive
geopotential height anomaly into different wavelengths using
Morlet wavelet analysis to assess the relative contribution
of each wavelength. Meanwhile, using a self-organizing
map (SOM), we classify daily planetary waves during May
and June into four clusters and then construct the planetary
wave patterns based on the cluster-mean planetary waves. To
reveal the mechanism underlying the intraseasonal change in
planetary waves, we adopt Global Monsoons Model Inter-
comparison Project (GMMIP) Tier-3 experiments to probe
the relative roles of sensible heating and dynamical forcing
associated with the mountains of Asia (above 500m).
Intraseasonal transition ofNorthern Hemisphere planetary waves andtheunderlying mechanism…
1 3
The structure of the paper is as follows: Sect.2 describes
the data and methods; Sect.3 presents the intraseasonal vari-
abilities of planetary waves; Sect.4 discusses the responses
of planetary waves to Asian mountain forcing; and Sect.5
provides a summary of the key findings and some further
discussion.
2 Data andmethods
2.1 Reanalysis data
We use the ERA5 global reanalysis datasets provided by
the European Center for Medium-range Weather Forecasts
(Hersbach etal. 2020). We obtain hourly and monthly 500-
hPa geopotential on a regular 2.5° longitude–latitude grid.
The daily mean Z500 is derived by averaging the hourly
data divided by 9.8m s−2. Since the outputs of the GMMIP
Tier-3 experiments are available over 1979–2014, we adopt
the ERA5 reanalysis data for the same time period. The tran-
sitional season in this study refers to the period from 1 May
to 30 June of each year (61days).
2.2 CMIP6 data
The Chinese Academy of Sciences’ Flexible Global
Ocean–Atmosphere–Land System model (FGOALS-f3-L)
model is participating in phase 6 of the Coupled Model
Intercomparison Project (CMIP6) and has already carried
out the historical Atmospheric Model Intercomparison Pro-
ject (AMIP) simulation and GMMIP Tier-3 experiments (He
etal. 2019a, 2020). We use the AMIP r1i1p1f1 simulation as
a control result, in which the model integrates from 1 Janu-
ary 1970 using the observational SST and sea-ice concentra-
tion and provides the outputs over 1979–2014 for analysis.
In terms of sensitivity experiments, we chose an orographic
perturbation experiment that removes the topography above
500m over Asia (TIP; Fig.1) and a thermal perturbation
experiment that removes the sensible heating topography
above 500m in the Asian continent (TIP_nosh). In these two
experiments, the model integration also starts on 1 January
1970, similar to the AMIP r1i1p1f1 simulation.
The simulated daily and monthly geopotential height data
from FGOALS-f3-L are obtained from the data portals of
the Earth System Grid Federation. To be more comparable
with the ERA5 reanalysis, a bilinear interpolation scheme
is used to interpolate the data from the native grid to the
regular 2.5° longitude–latitude grid.
2.3 Morlet wavelet analysis
The Morlet wavelet is generally used for time–frequency
analyses to detect localized variations of power within a time
series. Here, we apply the Morlet wavelet to the mean Z500
within the latitudinal belt of 50°–70° N to investigate zonal
wavelengths. The wavelet transform is given by (Torrence
and Compo 1998)
where the term
𝜓(j)=𝜋
1
4
e
i6j
e
j
22
is the wavelet function,
a is the scale, b is the longitudinal position, and f(j) is a
longitude-series Z500. Since the wavelet analysis reflects
regional wavenumbers, we use the wavelength to depict the
wave structure. Considering the 2.5° equally spaced data,
the wavelength for each scale is derived by multiplying the
scale by the grid length and its corresponding series is the
real part of the wavelet transform. The wavelet power spec-
trum is defined as
|
|
|
W𝜓(a,b)
|
|
|
2
and the significance is evalu-
ated based on the sum of the power spectrum over a particu-
lar latitude using a red-noise process with lag(− 1)
autoregression. Given that a longitude-series Z500 is cyclic,
the cone of influence for all scales is negligible.
2.4 Planetary waves
We apply spherical harmonic analysis to the daily Z500
to isolate the daily planetary waves of the Northern Hem-
isphere in a slight adaptation of the method in Xie etal.
(2017). The spherical harmonic expansion of Z500 considers
both the zonal and meridional wavenumbers simultaneously,
and is defined as
(1)
W
𝜓(a,b)=𝜋12f(j)𝜓
(
j
b
a
)
dj
,
(2)
Z
500 =
M
m=0
N
n=m
[
Z500m
nPm
n(sin 𝜑)eim𝜆
],
Fig. 1 Topography heights (shaded; unit: m) in the no TIP topogra-
phy experiment. The thick contours are 500m and denote the modi-
fied topography
Z.Xie et al.
1 3
where λ is longitude, φ is latitude, and
Pm
n(sin
𝜑
)
are the
normalized associated Legendre functions:
Since the data are on a 2.5° longitude–latitude grid, M
and N are 72. To focus on the Northern Hemisphere, a sym-
metrical distribution of the daily Z500 about the equator
is assumed to calculate the coefficients. Unlike Xie etal.
(2017) in which a triangular truncation was used, we adopt
an analogue rhomboid truncation with (m = 5, n = m + 6),
in which zonal wavenumbers (m) no more than 5 and
meridional wavenumbers (
nm
2
) no more than 3 are retained
(Table1). In addition, we remove the total wavenumber 0
(i.e. m = 0, n = 0), which represents the areal mean of Z500
over the Northern Hemisphere. By removing this compo-
nent, the planetary waves are more comparable in different
time periods.
2.5 Clustering planetary waves
In comparison with K-means and hierarchical clustering, an
SOM groups high-dimensional data into a small number of
SOM patterns in a geometrical similarity neurons structure
(Kohonen 2001). The truncated daily Z500 of 4752 grid
points over (0°–357.5° E, 10°–90° N) are converted to a row
vector for 2196days (61days × 36years). The 2196 row vec-
tors are input into a batch SOM to obtain the SOM patterns
by implementing the SOM toolbox version 2.0 (http:// www.
cis. hut. fi/ proje cts/ somto olbox/ about). Initially, a number of
random nodes/neurons are specified with a weight vector and
a position in the two-dimensional grid, and are then updated
by averaging the data samples in the neighborhood of the
‘‘best matching unit’’ in each training step. The output is
(3)
P
m
n(sin 𝜑)=
(2n+1)(nm)
2(n+m)!
12
1sin2𝜑
m2
2nn!
×
d(m+n)
dsin(m+n)𝜑
sin2𝜑1
n
.
an SOM with a prescribed number of nodes that represent
cluster-mean spatial patterns (i.e., best matching units) of
the input truncated daily Z500. The optimum number of
SOM patterns should be large enough to accurately capture
the planetary wave patterns but small enough to sufficiently
differ from each other. To determine the optimum number
of SOM nodes, the SOM is repeated with the grid numbers
from 1 × 2 to 1 × 20. We calculate average pattern correla-
tions between each row vector of truncated daily Z500 and
their corresponding centroids (Lee and Feldstein 2013) and
the mean distance between each cluster pair in a slight adap-
tation of Ward’s distance (Ward 1963; Lee etal. 2017).
The SOM clustering indices are determined by finding
the "best matching units" to the truncated daily Z500. These
indices are used to composite the truncated daily Z500 to
construct the planetary wave patterns, which are analogues
of the time mean.
3 Planetary wave features
3.1 Intraseasonal transition ofplanetary waves
Figure2 displays the climatological mean Z500 and eddies
in May and June and their differences. The planetary wave
structure in May is primarily characterized by a wavenumber
2 with ridges over western North America and Europe and
troughs over eastern Asia to the North Pacific and northeast-
ern North America (Fig.2a). The ridge and trough pair over
the Eastern Hemisphere is broader than that over the Western
Table 1 The zonal and
meridional wavenumbers for
the truncation of spherical
harmonic analysis
Meridional wavenumber
Zonal wavenumber (0, 0)
(1, 0)
(0, 1) (2, 0)
(1, 1) (3, 0)
(0, 2) (2, 1) (4, 0)
(1, 2) (3, 1) (5, 0)
(0, 3) (2, 2) (4, 1)
(1, 3) (3, 2) (5, 1)
(2, 3) (4, 2)
(3, 3) (5, 2)
(4, 3)
(5, 3)
Intraseasonal transition ofNorthern Hemisphere planetary waves andtheunderlying mechanism…
1 3
Hemisphere. The polar vortex is meridionally elongated with
a center over the Taymyr Peninsula. Although the mid- and
high-latitude planetary wave structure in June resembles that
in May, the polar vortex displaces northward and a moderate
ridge appears over northeastern Asia (Fig.2b), which is the
strongest change between June and May (Fig.2c). Mean-
while, the circumpolar contours have drifted poleward and
are confined to the north to 30° N. In the subtropical region,
a closed high over northern Africa is more pronounced and a
trough over the Bay of Bengal is further deepened. Since the
Sverdrup regime and Rossby regime are separated by the jet
stream (Chen 2005), we limit our attention to the planetary
waves over mid and high latitudes.
Giventhat the most prominent change is over north-
eastern Asia, we average the Z500 within the latitudinal
belt of 50°–70° N, which encompasses this largest positive
Z500 anomaly. Since the mean Z500 of the latitudinal belt
of 50°–70° N does not include the latitudinal shear, we
investigate the planetary wave feature in term of eddies
relative to the zonal mean. Figure3 displays a Hovmӧller
diagram of the climatological mean Z500 eddies averaged
between 50° N and 70° N. Inspection of Fig.3 shows that
Fig. 2 Climatological mean
Z500 (contours; unit: gpm) and
the corresponding latitudinal
deviation field (shading) in a
May and b June, as well as c
the difference between June and
May. The contours are drawn
every 50 and thin lines indicate
zero. The lowest point in each
panel is drawn at (90° E, 10° N)
Fig. 3 Hovmӧller diagram of
the Z500 latitudinal devia-
tion field (unit: gpm) averaged
within the latitudinal belt of
50°–70° N. The top panel shows
the topographic features over
50°–70° N
Z.Xie et al.
1 3
the annual cycle of planetary waves consists of two major
periods: the boreal summer (June–August) and winter
(November–March) seasons, which are separated by two
transitional periods. The planetary waves are primarily
characterized by wavenumber 2, with the largest ampli-
tudes in winter and the smallest amplitude in summer.
Aside from the change in wave amplitude, the planetary
wave phase displaces eastward in summer with respect to
winter. The planetary waves weaken from April and turn
to be a typical summer pattern in June, with a moderate
positive anomaly dominating over the Eurasian continent
and a trough confined to the Bering Sea. In contrast, the
ridge over western North America exhibits stationary
with weaker amplitude and the trough over eastern North
America extends to the North Atlantic.
As noted above, the planetary waves exhibit different
spatial features over the Northern Hemisphere, we adopt
Morlet wavelet analysis to decompose the planetary waves
into different wavelengths and corresponding power spec-
tra. Figure4 shows the real coefficients and power spec-
tra of planetary waves in May and June, respectively. The
planetary waves in May are dominantly contributed by
wavelengths of around 10,000km, which corresponds
to zonal wavenumber 2 (Fig.4a). In contrast, the over-
all power spectrum of planetary waves in June exhibits
a bimodal pattern with new significant wavelengths of
around 7000km (Fig.4b), which corresponds to wave-
number 3. The wavelengths of around 10,000km in June
not only drastically weaken in amplitude but also displace
slightly eastward with respect to May, while the wave-
lengths of around 7000km amplify and shift slightly west-
ward. The wavelengths of around 7000km are stronger
and in-phase with the wavelengths of around 10,000km
in the Western Hemisphere, whereas they are out-of-phase
with the wavelengths of around 10,000km in the Eastern
Hemisphere. Therefore, the planetary waves exhibit a dras-
tic change in the Eastern Hemisphere, particularly over
northeastern Asia, where the positive height anomaly of
wavelengths of around 7000km is superior to the nega-
tive height anomaly of wavelengths of around 10,000km.
3.2 Cluster‑mean planetary wave patterns
As mentioned in the introduction, planetary waves can also
be obtained from the daily Z500 using spatiotemporal spec-
tral analysis (Hayashi 1977; Watt-Meyer and Kushner 2015).
The planetary wave variability discussed above is based
on the monthly mean, but, to a certain extent, such a time
period is somewhat subjective. In this section, we apply the
SOM, which outputs consecutive spatial patterns, to daily
Fig. 4 Wavelet power spectra
(shading) and real coefficient
(contours; unit: gpm) of the
average Z500 within the latitu-
dinal belt of 50°–70° N during
a May and b June. The global
wavelet power spectra (blue
line) with the 95% confidence
level (dashed red line) using the
corresponding red-noise spectra
are shown to the right
Intraseasonal transition ofNorthern Hemisphere planetary waves andtheunderlying mechanism…
1 3
truncated Z500 to construct the planetary wave patterns
based on the cluster mean. Since we focus on the planetary-
scale structures, daily synoptic waves are discarded before
the SOM is produced to remove their potential influence on
the clustering.
3.2.1 Planetary wave clustering
As introduced in Sect.2.5, the SOM is repeatedly generated
with grid numbers varying from 1 × 2 to 1 × 20 to determine
the optimum separation of planetary wave patterns. Figure5
displays the mean correlation coefficient between the daily
truncated Z500 and the corresponding cluster centroid, as
well as the mean distance between each pair of cluster cen-
troids. The distance increases smoothly from 1 × 20 to 1 × 4,
and then drastically to 1 × 3 and 1 × 2, suggesting that the
four clusters differ considerably from each other and can-
not be merged further. In contrast, the change in correlation
coefficient is relatively smooth. According to the distance
measure, we consider the 1 × 4 SOM grid as the optimum
cluster number. Since we try to isolate planetary wave pat-
terns varying in one direction (i.e. from 1 May to 30 June),
we prefer the 1 × 4 SOM grid to the 2 × 2 grid, in which all
SOM patterns are connected with each other.
3.2.2 Planetary wave patterns
Figures6 and 7 display the composite truncated daily Z500
and anomalies relative to the climatological mean of May
and June and the intraseasonal time series of occurrence
number for the four planetary wave patterns, respectively.
Wavenumbers 1–5 of the climatological mean circula-
tions consist with the unfiltered climatological mean flows
but with smoother contours (Figs.2a, b, 6a, b). The four
planetary wave patterns vary progressively from the struc-
ture resembling the climatological mean flow of May to
June. The anomalous fields relative to the climatological
Fig. 5 Mean correlation between the daily truncated Z500 and the
corresponding cluster centroid (closed circles) and the mean distance
between each pair of cluster centroids (open circles)
Fig. 6 Climatological mean daily truncated Z500 (contours; unit:
gpm) and the corresponding latitudinal deviation field (shadings) in
a May and b June. Composite daily truncated Z500 (contours) and
corresponding anomalies relative to climatological mean in May (left
column) and June (right column) for cluster 1 (c, d), cluster 2 (e, f),
cluster 3 (g, h) and cluster 4 (i, j) of planetary waves. The contours
are drawn every 50 and thin lines indicate zero. The lowest point in
each panel is drawn at (90° E, 10° N)
Z.Xie et al.
1 3
mean feature a positive phase of the Northern Annular
Mode (NAM) to a negative phase of the NAM. The occur-
rence number of the four planetary wave patterns peaks in
sequence (Fig.7).
The first planetary wave pattern is characterized by a pos-
itive phase of the NAM, suggesting a deepened polar vortex
and stationary troughs (Fig.6c, d). The polar vortex slides
toward the Taymyr Peninsula. This pattern primarily occurs
in the leading three weeks of May and then declines drasti-
cally to zero in early June (Fig.7). The second and third
planetary wave patterns are intermediate patterns between
the climatological mean flows in May and June, and their
anomalies exhibit a negative NAM and a positive NAM rela-
tive to May and June, respectively (Fig.6e–h). Such anoma-
lous circulation indicates amplifications of stationary ridges
and attenuations of stationary troughs and the polar vortex.
The polar vortex exhibits a fanning structure from Greenland
to the Taymyr Peninsula. Considering the second pattern
(Fig.6e, f), the ridge over western North America extends
northward to the Arctic Ocean. This pattern mainly occurs
over the period from mid-May to early June (Fig.7). In
comparison, a new moderate ridge is seen over northeastern
Asia, with the most prominent positive anomaly change with
respect to planetary waves in May for the third planetary
wave pattern (Fig.6g, h), which takes place from late May
to mid-June (Fig.7). Considering the fourth planetary wave
pattern (Fig.6i, j), the anomalies relative to the planetary
waves in May and June both resemble a negative phase of
the NAM. The polar vortex is reduced in size to Greenland,
suggesting amplifications of ridges over northeastern Asia
and western North America. This fourth pattern occurs in
roughly the last three weeks of June(Fig.7).
To test the sensitivity of our results to the clustering
method employed, we apply the K-means method to the daily
truncated Z500 fields with K = 4 (i.e., the same input data
used in creating the SOM clustering results). The spatial pat-
terns derived using the K-means approach closely resemble
those obtained from the SOM clustering, in which the spatial
pattern correlation coefficients are 0.998, 0.997, 0.994 and
0.998, respectively. Unlike the SOM clustering result, the
planetary wave patterns obtained from the K-mean method
exhibit more overlaps in their occurrence dates. For exam-
ple, the number of days associated with the second planetary
wave pattern is relatively high (around 10days) in the first
week and reaches one of maxima with 20days in the second
week of June (Figure not shown).
In comparison with prior studies that considered plan-
etary waves as the monthly or seasonal mean, the planetary
waves in this study include the latitudinal shear of the zonal
mean. The planetary wave patterns identified here exhibit
pronounced intraseasonal variabilities in both amplitude and
spatial structure. This is also in contrast with the daily plane-
tary wave isolated by spatiotemporal spectral analysis, which
primarily fluctuates in the amplitude of the planetary waves.
To calculate time scales of the four planetary wave pat-
terns, we first construct daily planetary wave pattern indices
by projecting each daily Z500 (Zdaily) on planetary wave pat-
terns (Zplanetary) using a pattern amplitude projection (Deng
etal. 2012):
where A represents the area over (10°–90° N, 0°–360° E), a
is the mean radius of the Earth, and λ and ϕ are the longitude
and latitude, respectively. Then, we apply the e-folding time
scale procedure provided by Gerber etal. (2008) to the time
series of daily indices of each planetary wave pattern. The
result shows that the four planetary wave patterns have time
scales of 7.7–14.1, 7.3–11.2, 7.7–18.2 and 7.5–12.9days,
respectively. The time scale analysis of planetary wave pat-
terns illustrates that variability of planetary wave is intra-
seasonal in nature.
We again apply Morlet wavelet analysis to the Z500 aver-
aged within the latitudinal belt of 50°–70° N to examine
each phase and amplitude of different wavenumbers for
the four planetary wave patterns. Figure8 displays the real
coefficients and power spectra for the four planetary wave
patterns. The overall impression from Figs.4 and 8 is one
of similarity in wavelengths of around 10,000km, which
weaken gradually and displace eastward. However, there
is an interesting difference in the wavelengths of around
7000km in that they intensify first and then weaken in
amplitude. Wavelengths of around 10,000km dominate in
the first pattern and decline roughly by half in amplitude for
the second pattern, while the amplitude of wavelengths of
around 7000km increases and turns to be significant at the
95% confidence level (Fig.8a, b). Although the second pat-
tern is predominated by wavelengths of around 10,000km,
the wavelengths of around 7000km are out-of-phase with
(4)
Planetary wave pattern index
=
A
1
Aa
2
ZdailyZplanetary cos 𝜙d𝜆d
𝜙
A1
A
a2
(
Z
planetary)
2cos 𝜙d𝜆d𝜙
Fig. 7 Time series of the occurrence number of four planetary wave
clusters
Intraseasonal transition ofNorthern Hemisphere planetary waves andtheunderlying mechanism…
1 3
Fig. 8 As in Fig.4 but for a
cluster 1, b cluster 2, c cluster
3 and d cluster 4 of planetary
waves
Z.Xie et al.
1 3
the wavelengths of around 10,000km over the Eastern
Hemisphere and thus weaken the negative anomaly of the
planetary waves over northeastern Asia.
Considering the third pattern (Fig.8c), wavelengths of
around 10,000km decline further by more than half in terms
of amplitude and displace slightly eastward in comparison
with the second pattern. In contrast, wavelengths of around
7000km magnify in amplitude and regress westward. The
amplitude of the wavelengths of around 7000km exceeds
that of the wavelengths of around 10,000km over northeast-
ern Asia (90°–150° E), rendering a positive anomaly over
that region. Unlike the second and third patterns, the ampli-
tudes of the wavelengths of around 10,000km and 7000km
both decrease in the fourth pattern (Fig.8d). Waves of wave-
lengths of around 10,000km displace further eastward by
about 10° and those of around 7000km shift westward, in
which they are in-phase with each other at around 240° E
but out-of-phase at around 60° E. Wavelengths of around
7000km show a positive center over northeastern Asia and
overlap with a node of wavelengths of around 10,000km,
delivering a positive anomaly of the stationary eddy in-situ.
In comparison with monthly mean planetary waves, the clus-
ter-mean planetary waves reveal that the planetary waves
exhibit rather different characteristics in June.
4 Planetary wave response toAsian
mountain forcing
Prior studies have shown an evident circulation response
over northeastern Asia to the Tibetan Plateau forcing (Ting
etal. 2001; Held etal. 2002; Chang 2009). The nonlinearity,
which represents nonlinear wave–wave interactions among
the waves forced by orography, diabatic heating and tran-
sient eddies, generates opposite circulations around Lake
Baikal during winter and summer (Ting etal. 2001). Such
circulations are substantially contributed by the nonlinear
wave-wave interaction between the flows forced by the orog-
raphy and diabatic heating. In light of these findings, we use
GMMIP Tier-3 experiments from a sophisticated model that
not only considers the sensible heating distribution associ-
ated with the mountains over Asia (above 500m), but also
nonlinear wave-wave interactions between the flows forced
by the orography and sensible heating (He etal. 2019a,
2020). Following Held etal. (2002), we refer to AMIP as
the total forcing that produce the simulation F(AMIP) and
F(AMIP) − F(TIP) as the full nonlinear forcing response to
the Asian mountains denoted by TIP. The full nonlinear forc-
ing to sensible heating and dynamical forcings associated
with the mountains of Asia are F(SH) = F(AMIP) − F(TIP_
nosh) and F(DYN) = F(TIP_nosh) − F(TIP), respectively.
Figure9 displays the monthly mean truncated Z500 for
the AMIP and full nonlinear responses to the mountains
of Asia. The simulated climatological mean Z500 in May
and June generally agree with the reanalysis over the mid
and high latitudes (Figs.2, 6a, b, 9a–c). The model suc-
cessfully reproduces the largest positive Z500 anomaly
over northeastern Asia but with a stronger amplitude and
a larger southeastward extension (Fig.9c). Meanwhile, the
model also yields larger positive Z500 anomalies over the
North Pacific, the Great Lakes and Great Britain. In terms
of the full nonlinear response to the mountains of Asia, it
mainly amplifies the climatological planetary waves, par-
ticularly over the Eastern Hemisphere (Fig.9d–f), which
agrees with prior studies (Held etal. 2002; Chang 2009).
The ridge from Scandinavia to Lake Baikal magnifies and
then extends northeastward to northeastern Asia, resulting
in a moderate positive Z500 anomaly there.
The full nonlinear response to the mountains of Asia is
then decomposed to full nonlinear responses to sensible
heating and dynamical forcings associated with the moun-
tains of Asia, respectively (Fig.9g–l). The noticeable feature
of this decomposition is the offset over East Asia and the
North Pacific between full nonlinear responses to sensible
heating and dynamical forcings associated with the moun-
tains of Asia, suggesting a major contribution of sensible
heating forcing associated with the mountains of Asia to the
largest Z500 anomaly over northeastern Asia. More specifi-
cally, the full nonlinear response to the sensible heating forc-
ing associated with the mountains of Asia is characterized
by positive Z500 anomalies over the mid and high latitudes
and negative Z500 anomalies over the subtropical region
(Fig.9g, h). A conspicuous positive Z500 anomaly center
elongates from the Tibetan Plateau to the Northeast Pacific
in May and withdraws toward northeastern Asia in June,
delivering the largest positive Z500 anomaly over northeast-
ern Asia (Fig.9g–i). In contrast, although the full nonlinear
response to dynamic forcing associated with the mountains
of Asia resembles that to the mountains of Asia, it features
a negative Z500 anomaly over East Asia to the North Pacific
in both May and June (Fig.9j–l). Therefore, the dynamical
forcing associated with the mountains of Asia exhibits a
detrimental influence on the formation and maintenance of
the warm ridge over northeastern Asia.
To focus on the largest positive Z500 anomaly over north-
eastern Asia, Fig.10 displays the deviation of Z500 averaged
within the latitudinal belt of 50°–70° N from the zonal mean
for the ERA5 reanalysis, the AMIP simulation and GMMIP
experiments. The planetary wave eddies of the AMIP simu-
lation are in good agreement with those of ERA5, which
are a wave of roughly wavenumber 2. The AMIP simulation
has a positive bias around Great Britain in May, where the
full nonlinear responses to the mountains of Asia all tend to
yield positive Z500 anomalies. Considering this deficiency
of the model, we narrow down our discussion to the region
over 0°–270° E.
Intraseasonal transition ofNorthern Hemisphere planetary waves andtheunderlying mechanism…
1 3
The full nonlinear response to the mountains of Asia
in May provides a pronounced contribution to two ridges
over Europe and North America and a moderate contri-
bution to the trough from East Asia to the North Pacific
(Fig.10a). The contribution to the ridge is mainly from
the full nonlinear response to dynamical forcing associated
with the mountains of Asia. In contrast, the full nonlinear
response to sensible heating associated with the moun-
tains of Asia deepens the trough over the North Pacific
and yet offsets the trough over northeastern Asia. In June
(Fig.10b), the full nonlinear response to the mountains
of Asia exhibits a sizeable contribution to the planetary
waves over Eurasia and a moderate contribution to the
planetary waves over the North Pacific and North America.
Although there is more offsetting between the full nonlin-
ear responses to sensible heating and dynamical forcings
associated with the mountains of Asia over northeastern
Asia, the full nonlinear response to sensible heating forc-
ing associated with the mountains of Asia is superior to
its dynamical forcing counterpart. Therefore, a discernible
stationary ridge rides over northeastern Asia. The contri-
bution of the full nonlinear response to sensible heating
forcing associated with the mountains of Asia also plays
Fig. 9 Climatological mean
Z500 (contours; unit: gpm) and
the corresponding latitudinal
deviation field (shading) in a
May and b June, as well as c
the difference between June and
May for the AMIP simulation.
The full nonlinear responses
in Z500 to (df) the mountains
of Asia, gi sensible heating
forcing associated with the
mountains of Asia, and jl
dynamical forcing associated
with the mountains of Asia. The
left, middle and right columns
refer to May, June and the dif-
ference between June and May,
respectively. The contours are
drawn every 50 and thin lines
indicate zero. The lowest point
in each panel is drawn at (90°
E, 10° N)
Z.Xie et al.
1 3
a dominant role in the largest positive Z500 anomaly in
planetary waves over northeastern Asia (Fig.10c).
The results in Sect.3 showed that the planetary waves
can be separated into four patterns on the intraseasonal
time scale from May to June, and the largest positive Z500
anomaly over northeastern Asia appears first in the third
planetary wave pattern. It is of interest to examine the
intraseasonal variability of the planetary waves associated
with the forcings of the mountains of Asia. Since the full
nonlinear responses to each forcing are derived in terms
of anomalies, it is hard to determine their corresponding
planetary wave clusters. As an alternative, we construct a
planetary wave pattern index by projecting each daily trun-
catedZ500 (
) of F(AMIP), F(TIP) and F(TIP_nosh)
on each planetary wave pattern (
Zstationary
) using Eq.4. Fig-
ure11 displays the probability density functions (PDFs) of
planetary wave pattern indices for the AMIP simulation,
and the full nonlinear responses to the mountains of Asia
[F(AMIP) – F(TIP)], sensible heating forcing associated
with the mountains of Asia [F(AMIP)-F(TIP_nosh)], as
well as dynamical forcing associated with the mountains
of Asia [F(TIP_nosh) – F(TIP)]. The PDFs of the AMIP
simulation are generally above 0.9, indicating good perfor-
mance of the model in simulating the intraseasonal plan-
etary wave patterns.
In terms of the first and second planetary wave pat-
terns (Fig.11a, b), the mountain forcing tends to produce
more index values that are relatively larger and fewer
that are relatively smaller. Such a distribution is mainly
contributed by the full nonlinear response to dynamical
forcing associated with the mountains of Asia, indicating
that dynamical forcing likely produces the first and sec-
ond planetary wave patterns. In contrast, the full nonlinear
response to sensible heating forcing associated with the
mountains of Asia increases the amount of larger index
values for the third and fourth planetary wave patterns
(Fig.11c, d). Despite the more index values that are larger
for the fourth planetary wave pattern induced by sensible
heating forcing associated with the mountains of Asia, it
is offset to a greater extent by dynamical forcing associ-
ated with the mountains of Asia. Therefore, the full non-
linear response to the mountains of Asia tends to result
more in the generation of the third planetary wave pattern
and thus induces the largest positive Z500 anomaly over
northeastern Asia. This is also inferred when comparing
Figs.6 and 9, in that the response to the sensible heating
forcing associated with the mountains of Asia is a positive
anomaly over the mid and high latitudes, mimicking the
fourth planetary wave pattern. However, the response to
dynamical forcing associated with the mountains of Asia
offsets that to the sensible heating forcing associated with
the mountains of Asia, particularly from East Asia to the
North Pacific. Therefore, the full nonlinear response to
the mountains of Asia tends to produce the third planetary
wave pattern more than the fourth planetary wave pattern.
5 Summary anddiscussion
In this study, we have examined the intraseasonal transi-
tion of planetary waves in terms of Z500 over the Northern
Hemisphere during May and June, when the so-called abrupt
change of planetary waves takes place. Unlike prior studies
in which the zonal mean was removed to define the plan-
etary waves, the planetary waves considered here include
the latitudinal shear of the zonal mean. The abrupt change
of planetary waves is characterized by the largest positive
Fig. 10 Deviation of Z500 averaged within the latitudinal belt of
50°–70° N from the zonal average during a May and b June in ERA5
(gray), AMIP (black), the full nonlinear response to the mountains of
Asia (blue), and the full nonlinear responses to sensible heating (red)
and dynamical forcings (purple) associated with the mountains of
Asia. c is the difference between (b) and (a)
Intraseasonal transition ofNorthern Hemisphere planetary waves andtheunderlying mechanism…
1 3
Z500 anomaly over northeastern Asia. Morlet wavelet analy-
sis was applied to the Z500 averaged within the latitudinal
belt of 50°–70° N, which encompasses the largest positive
Z500 anomaly over northeastern Asia, to assess the relative
contribution of each wavelength to the intraseasonal change
in planetary waves. The intraseasonal change in planetary
waves is further discussed based on the cluster mean derived
by applying an SOM to the daily truncated Z500 of wave-
numbers 1–5. Orographic perturbation experiments from
GMMIP were adopted to investigate the relative contribu-
tions to the largest positive Z500 anomaly over northeastern
Asia from the full nonlinear response to the forcing by the
mountains of Asia.
The largest positive Z500 anomaly over northeastern
Asia during the period from May to June results from the
interaction between wavelengths of around 10,000km
and 7000km, which correspond to zonal wavenumbers 2
and 3, respectively. Although the monthly mean planetary
waves provide an overview of the intraseasonal variability
of each wavenumber belt, the time period in deriving the
planetary waves is somewhat subjective. The SOM applied
to the daily truncated Z500 identifies four planetary wave
patterns that occur in sequence from May to June. The
anomalous fields relative to the climatological mean fea-
ture a positive phase of the NAM to a negative phase of
the NAM. Meanwhile, a positive change over northeastern
Asia amplifies gradually from the second to the fourth
planetary wave pattern. Considering the planetary waves
averaged within the latitudinal belt of 50°–70° N, wave-
lengths of around 10,000km and 7000km are in- and out-
of-phase with each other over the Western Hemisphere and
Eastern Hemisphere, respectively. Therefore, the planetary
waves maintain the phase over the Western Hemisphere
during May and June. Wavelengths of around 10,000km
weaken in amplitude and displace eastward, while those of
around 7000km magnify gradually from the first to third
pattern and weaken in the fourth pattern. Therefore, the
largest positive Z500 anomaly over northeastern Asia is
primarily contributed by wavelengths of around 7000km
and the third planetary wave pattern.
The full nonlinear response to the forcing by the moun-
tains of Asia, particularly that associated with sensible heat-
ing forcing associated with the mountains of Asia, provides a
considerable contribution to the largest positive Z500 anom-
aly over northeastern Asia. The full nonlinear response to
the Asian mountains forcing acts to intensify the stationary
ridge and trough over the Eastern Hemisphere. The full non-
linear responses to sensible heating and dynamical forcings
associated with the mountains of Asia offset each other over
East Asia. The positive anomaly response to sensible heating
forcing associated with the mountains of Asia over north-
eastern Asia enhances from May to June, while the negative
height anomaly response to dynamical forcing associated
with the mountains of Asia over northeastern Asia weakens.
Fig. 11 The PDFs of projec-
tion indices of planetary wave
patterns for a cluster 1, b cluster
2, c cluster 3 and d cluster 4 in
AMIP (gray). The anomalous
PDFs of projection indices of
planetary wave patterns for the
full nonlinear response to the
mountains of Asia (blue), and
the sensible heating (red) and
dynamical forcings (purple)
associated with the mountains
of Asia
Z.Xie et al.
1 3
Consequently, the full nonlinear response to the combina-
tion of sensible heating and dynamical forcings associated
with the mountains of Asia contributes to the largest positive
Z500 anomaly over northeastern Asia. The full nonlinear
response to dynamical forcing associated with the mountains
of Asia in Z500 is mainly wavenumber 2 and thus overpro-
duces the first and second planetary wave patterns. In con-
trast, the full nonlinear response to sensible heating forcing
associated with the mountains of Asia is characterized by
positive anomalies over the mid and high latitudes, which is
more likely to produce the third and fourth planetary wave
patterns. Given the offsetting responses over northeastern
Asia between sensible heating and dynamical forcings
associated with the mountains of Asia, the full nonlinear
response to the mountains of Asia overproduces the third
planetary wave pattern rather than the fourth planetary wave
pattern.
In terms of the transient eddy feedback forcing, we
speculate that its contribution to planetary waves mimics
that of the dynamical forcing associated with the mountains
of Asia. The response to the transient eddy feedback forc-
ing is generally characterized by two major dipoles, with
negative anomalies poleward to positive anomalies over
the North Pacific and the North Atlantic (Held etal. 2002).
Chang (2009) demonstrated that the orographic forcing of
the Tibetan Plateau substantially suppresses the activity of
transient eddies over the continents. Therefore, the response
to transient eddy feedback forcing over East Asia bears some
resemblance with that to the dynamical forcing of the moun-
tains of Asia, which offsets the positive Z500 anomaly over
northeastern Asia. From May to June, the response to the
transient eddy feedback forcing weakens and thus the offset-
ting of the positive Z500 anomaly over northeastern Asia
reduces.
It has been noted by Chyi etal. (2021) that the forma-
tion of a warm anticyclone anomaly over northeastern Asia
in early June is associated with snowmelt in Eurasia. We
acknowledge a potential positive contribution from snow-
melt to the largest Z500 anomaly over northeastern Asia.
The snowmelt over northern Asia increases the water vapor
in the atmosphere by receiving more solar heating in June.
The upward motion of water vapor condenses in the tropo-
sphere and thereby releases latent heat to the atmosphere,
which could provide a discernible positive contribution to
the warm ridge over northeastern Asia.
Prior studies regarding the transition of the seasons have
primarily focused on the onset of the East Asian monsoon.
In contrast, we limited our attention to investigating the larg-
est positive Z500 anomaly over northeastern Asia. It has
been well established that such a positive Z500 anomaly over
northeastern Asia exports Rossby wave energy southward
in the mid and high troposphere and induces the Northeast
China cold vortex or the well-known Mei-yu trough (e.g.
Bueh etal. 2008). This study simply uses the orographic per-
turbation experiment from GMMIP; more suitable experi-
ments will be conducted in future work.
Acknowledgements We would like to thank two anonymous review-
ers and Prof. Liren Ji for instructive comments and helpful sugges-
tions, and Prof. Edwin P. Gerber for providing us the code of time
scale analysis. This research was funded by the National Natural Sci-
ence Foundation of China (41630424, 41861144014 and 41875078)
and the National Key Research and Development Program of China
(2018YFC1507101). Yi Deng is in part supported by the U.S. National
Science Foundation (NSF) through Grant AGS-2032532 and by the
U.S. National Oceanic and Atmospheric Administration (NOAA)
through Grant NA20OAR4310380. We acknowledge the Copernicus
Climate Change Service for providing the ERA5 reanalysis datasets
(https:// cds. clima te. coper nicus. eu/ cdsapp# !/ datas et/ reana lysis- era5-
press ure- levels? tab= overv iew).
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