JOURNAL OF GEOPHYSICAL RESEARCH: ATMOSPHERES, VOL. 118, 9048–9063, doi:10.1002/jgrd.50709, 2013
Role of atmospheric waves in the formation and maintenance
of the Northern Annular Mode
Yuhji Kuroda1 and Hitoshi Mukougawa 2
Received 8 March 2013; revised 4 August 2013; accepted 5 August 2013; published 30 August 2013.
[1] We examined the roles of stationary, synoptic, and medium-scale atmospheric waves
in the formation and maintenance of the Northern Annular Mode (NAM) in winter by
analyses of zonal momentum and wave energy based on six-hourly reanalysis data from
the European Centre for Medium-range Weather Forecasts (ECMWF ERA-Interim).
Medium-scale waves have periods shorter than about two days and their effect has been
overlooked in previous research on the NAM. The effect of medium-scale waves on the
NAM is about 10% of that of total eddies. Although their effect on the NAM is of less
importance than their effect on the Southern Annular Mode (SAM), it is still significant in
the Northern Hemisphere. Our analysis also suggests that synoptic, medium-scale, and
stationary waves provide positive feedback to the zonal-mean zonal wind of the NAM. In
particular, energy transfer from synoptic and low-frequency transient waves to stationary
waves plays a key role in sustaining the stationary waves that drive zonal winds associated
with the NAM.
Citation: Kuroda, Y., and H. Mukougawa (2013), Role of atmospheric waves in the formation and maintenance of the
Northern Annular Mode, J. Geophys. Res. Atmos., 118, 9048–9063, doi:10.1002/jgrd.50709.
1.
Introduction
[2] Weather and climate are controlled by various types of
atmospheric wave in the troposphere. Among these, synoptic
waves are the most important because they are intimately
related to weather in the extratropics. Medium-scale waves
have recently begun to attract the attention of the climate
research community. A series of studies on medium-scale
waves [Sato et al., 1993; Sato et al., 2000, and references
therein] have shown that they are distinct from synoptic
waves in having wavelengths of about 2100 km with
barotropic structure in the vertical direction and eastward
phase speeds of about 22 ms1, twice the speed of synoptic
waves. They also found that medium-scale waves coexist
with synoptic waves in the extratropics of both hemispheres. Kuroda and Mukougawa [2011] showed that
medium-scale waves account for almost one third of the
variability of the Southern Annular Mode (SAM), which
is the dominant contributor to climate variability in the
extratropical Southern Hemisphere.
[3] The Northern Annular Mode (NAM), sometimes called
the Arctic Oscillation [Thompson and Wallace, 1998], is the
most prominent contributor to climate variability at high
latitudes in the Northern Hemisphere [Limpasuvan and
Additional supporting information may be found in the online version of
this article.
1
Meteorological Research Institute, Tsukuba, Japan.
2
Disaster Prevention Research Institute, Kyoto University, Uji, Japan.
Corresponding author: Y. Kuroda, Meteorological Research Institute,
1-1 Nagamine, Tsukuba, Ibaraki, 305-0052, Japan. ([email protected])
©2013. American Geophysical Union. All Rights Reserved.
2169-897X/13/10.1002/jgrd.50709
Hartmann, 1999]. The NAM is considerably more zonally
asymmetric than the SAM and is most active in the North
Atlantic. Unlike the SAM, activity of the NAM is much enhanced in winter.
[4] The recently established importance of medium-scale
waves in the formation of the SAM [Kuroda and
Mukougawa, 2011] has raised the question: How do
medium-scale waves contribute to the NAM? This is the motivation for this study. Additionally, as the importance of stationary waves and wave breaking of transient waves for the
NAM has been noted in previous studies [e.g., DeWeaver
and Nigam, 2000a, 2000b; Limpasuvan and Hartmann,
2000; Lorenz and Hartmann, 2003; Franzke et al., 2004;
Kuroda, 2005], we extended our study to cover the effect of
stationary and synoptic waves as well as medium-scale waves.
[5] We focused on how atmospheric waves force zonalmean zonal wind variations associated with the NAM, and
how these waves acquire energy from the zonal-mean fields.
Our examination is based on zonal momentum and wave energy equations and shows that the interactions of these waves
with the zonal-mean field sustain NAM variability through
positive feedback. Our analysis also shows that mediumscale waves contribute to NAM variability.
[6] Section 2 of this paper describes the data we used and
our analysis method. Section 3 presents our results, section
4 provides discussion of our results, and section 5 presents
our conclusions.
2.
Data Used and Analysis Methods
2.1. Data Selection
[7] The data we used in this study are the same as those
used by Kuroda and Mukougawa [2011]: 21 years of
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KURODA AND MUKOUGAWA: ROLE OF ATOMOSPHERIC WAVES ON NAM
six-hourly reanalysis data from the European Centre for
Medium-range Weather Forecasts (ECMWF ERA-Interim)
[Dee et al., 2011] from 1 January 1989 to 31 December
2009. However, we confined most of our analysis to the
20 winters from December to March of 1989/1990 to
2008/2009, as explained below. We analyzed the finestscale horizontal version of the data available for nonECMWF member states; the data are represented on a
1.5° × 1.5° longitude-latitude grid with 37 pressure levels
in the vertical direction.
[8] Although most of our analysis was based on monthly
means, second-order or higher-order quantities such as
Eulerian wave forcings were calculated first at 6 h intervals
and then averaged over each month. We calculated frictional
forcing and diabatic heating as residuals of three-dimensional
momentum and thermodynamic equations using the sixhourly reanalysis data.
[9] The NAM is defined as the dominant mode of variability
of sea level pressure (SLP) during the Northern Hemisphere
winter. To extract the NAM pattern, we applied Empirical
Orthogonal Function (EOF) analysis to the monthly averaged
SLP from December to March for the region north of 20°N as
specified by Thompson and Wallace [1998]. Although the
NAM appears in all seasons, we restricted our analysis to winter because the NAM has greater seasonal dependence than
SAM and its maximum activity is in winter. EOF analysis
showed that the dominant variability, the NAM, explains
21.7% of the total variance and greatly exceeds that of the second most dominant factor (14.2%). The NAM index is defined
by standardized month-to-month time coefficients.
[10] Synoptic and medium-scale waves were extracted
from the six-hourly data using a Lanczos band-pass filter
with a window width of 31 days [e.g., Hamming, 1977].
The same filter was used by Kuroda and Mukougawa
[2011]. We defined synoptic waves as those with periods of
two to six days and medium-scale waves as those with
periods of less than 1.75 days, according to the definition of
Sato et al. [2000]. As the frequency ranges of medium-scale
waves and tidal waves overlap, after time filtering, we
removed the tidal waves by discarding zonal wave number
components from zero to two. Stationary waves were
extracted by applying a 31 day running mean to the dailymean data, which imitates monthly averaging and corresponds to a loose low-pass filter with a cutoff period of about
50 to 90 days. In the following, we use 70 days for the typical
cutoff period
pffiffiffi for stationary waves as its transfer function becomes 1= 2 for a period of 70 days. Transfer functions of the
filters used in this study are shown in Figure S1.
[11] To examine the relationships between NAM variability and the three types of atmospheric waves, we performed
regression analysis of the NAM index with various physical
quantities after removing seasonal cycles.
2.2. Diagnostic Equations
[12] The model we used to evaluate the balance of zonalmean momentum is the same as that used by Kuroda and
Mukougawa [2011] and is described as follows.
∂u
¼ 2Ω v sin ϕ þ F 1 þ F 2 þ F n þ X ;
∂t
1 ∂Φ
¼ J;
2Ωu sin ϕ þ
a ∂ϕ
(1a)
(1b)
∂Φ
RT
¼
;
∂p
p
(1c)
∂T
Γ ω ¼ Q1 þ Q2 þ Qn þ S;
∂t
(1d)
1
∂
∂ω
¼ 0;
ðv cosϕ Þ þ
a cosϕ ∂ϕ
∂p
(1e)
where overbars represent zonal means and where the terms
1
∂
u′v′ cos2 ϕ ;
a cos2 ϕ ∂ϕ
1 ∂
ρ u′w′ ;
F2 ¼ ρ0 ∂z 0
1
∂
Q1 ¼ v′T ′ cosϕ ;
a cosϕ ∂ϕ
1 ∂
ρ w′T ′ ;
Q2 ¼ ρ0 ∂z 0
F1 ¼ (2)
are eddy mechanical forcings F 1 þ F 2 and thermal forcings
Q1 þ Q2 with suffix 1 (2) signifying forcing from meridional
(vertical) convergence; X and S are zonal-mean zonal frictional
forcing and diabatic heating, respectively; Γ = ∂ T0/
∂ p + κT0 /p is the stability of the basic atmosphere at temperature T0( p); Ω is the angular velocity of the Earth; z is
log-pressure height; ϕ is latitude; a is the radius of the Earth;
ρ0(z) is the basic air density; and other terms follow the usual
conventions [e.g., Andrews et al., 1987]. Here, nonlinear advection termsF n and Qn are defined by the following equations:
‾
u
∂‾
u ‾
v ∂‾
u‾
v
ω þ
tanϕ;
∂p
a ∂ϕ
a
‾
T
∂‾
T κ
∂‾
T κT
v∂‾
ω
þ ω‾
Γ ω:
Qn ≡ Tþ þ
∂p p
∂p
p
a ∂ϕ
Fn ≡ (3)
[13] The violation of balanced wind J is defined by equation (1b). We used Γ(z) as the climatological stability
obtained from monthly averaged temperature north of 30°N
in an extended winter from November to April.
[14] As equations (1a) to (1e) can be expressed as an elliptical differential equation of ω:
1 ∂ cosϕ ∂ω
4Ω2 a2 p ∂2 ω
þ
2
cosϕ ∂ϕ sin ϕ ∂ϕ
RΓ ∂p2
"
!#
2Ωap ∂ cosϕ ∂
J˙
(4)
¼
F1 þ F2 þ Fn þ X RΓ cosϕ ∂ϕ sinϕ ∂p
2Ω sinϕ
1
∂ cosϕ ∂ Q
þ
Q
þ
Q
þ
S
;
2
n
Γ cosϕ ∂ϕ sin2 ϕ ∂ϕ 1
the meridional circulation can be calculated from equations
(4) and (1e) with suitable boundary conditions. As equation
(4) is completely linear with respect to the forcings F i , Qi ,
X , S, and J , the meridional circulation due to each forcing
is evaluated separately. Acceleration of zonal winds due to
each forcing can be directly evaluated from equation (1a)
using the obtained meridional wind.
[15] To evaluate zonal-mean zonal wind acceleration due
to each wave forcing, it is also necessary to evaluate
nonlinear advection terms F n and Qn , because the meridional
circulation induced by wave forcing inevitably creates
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KURODA AND MUKOUGAWA: ROLE OF ATOMOSPHERIC WAVES ON NAM
(a)
(e)
(b)
(c)
(f)
(d)
(g)
Figure 1. December to March means of (a) total zonal-mean zonal wind, and zonal-mean amplitudes of
(b) stationary, (c) synoptic, and (d) medium-scale waves, each shown as height-latitude sections; and
December to March means of 300 hPa level amplitudes in the Northern Hemisphere of (e) stationary, (f )
synoptic, and (g) medium-scale waves. Zonal-mean amplitudes in Figures 1b to 1d are the square root of
the squared mean of the geopotential height anomaly at a given parallel of latitude. Amplitudes at the
300 hPa level in Figures 1e to 1g are the square root of the squared mean of the geopotential height anomaly
for a given spatial point. Contour intervals are 5 m s1 in Figure 1a, 20 m in Figure 1b, 10 m in Figures 1c
and 1d, 50 m in Figure 1e, and 10 m in Figures 1f and 1g. Shading indicates the month-to-month standard
deviations of deseasonalized variations: light, medium, and dark shading indicates standard deviations of 1,
2, and 3 m s1 in Figure 1a; 5, 10, and 20 m in Figure 1b; 1, 2, and 5 m in Figures 1c and 1d; 10, 20, and 50
m in Figure 1e; and 5, 10, and 15 m in Figures 1f and 1g.
nonlinear terms. Preliminary analysis showed that meridional
circulation and zonal wind acceleration due to nonlinear terms
alone are smaller than those from Coriolis and wave forcings,
so we evaluated them by an iterative method as follows. First,
only wave forcing terms were included in equation (4) to provide a first guess of the meridional circulation. Then, a first
guess of nonlinear terms was calculated from the observed
wind and temperature with the first-guess meridional circulation. These nonlinear terms, as well as wave forcings, were
again put into equation (4) to provide more accurate meridional circulation. These iterations were repeated three times to
achieve sufficient convergence. These calculations were
performed for every day using daily averaged wave forcings.
Note that the effects of nonlinear terms were ignored in the
previous study of Kuroda and Mukougawa [2011].
[16] This model has the same resolution as that of Kuroda
and Mukougawa [2011]: 100 vertical levels at intervals of 10
hPa and 121 horizontal grids of equal intervals of the sine
of latitude. The Appendix of Kuroda and Kodera [2004]
presents more details on solving these equations.
2.3. Energy Transfer Between Zonal Fields and Eddies
[17] The model we used to evaluate energy transfer from
zonal fields to atmospheric waves was the same as that used
by Kuroda and Mukougawa [2011]. We used the equation
for energy conversion between the zonal-mean field and an
eddy by Holton [1975]:
n
o n
o
d
ðK′ þ P′Þ ¼ ‾
K; K′ þ ‾
P; P′ þ W þ D;
dt
(5)
where K ′ and K are the eddy and zonal-mean kinetic energies, P ′ and P are the eddy and zonal-mean available
potential energies, {K , K ′} is the energy conversion from
K to K ′, {P, P ′} is the energy conversion from P to P ′, W
is the surface contribution, and D is the external forcing or
dissipation term.
[18] The integrands ε(K, K ′) and ε (P, P ′) of {K, K ′} and
{P, P ′} are explicitly written as
u
∂‾
u
1 ∂‾
v
‾ ; K′ ¼ ρ0 u′v′ 1 ∂‾
þ u′w′ þ v′2
ε K
a ∂ϕ
∂z
a∂ϕ
∂‾
v
tanϕ
tanϕ þv′w′
þ‾
u u′v′
‾
v u′2
;
∂z
a
a
and
9050
(6)
KURODA AND MUKOUGAWA: ROLE OF ATOMOSPHERIC WAVES ON NAM
(a) All
(b)
(e )
(c)
(f)
(d)
(g )
Figure 2. Height-latitude sections of December to March means of accelerations of zonal-mean zonal wind
due to (a) all wave forcings; (b) stationary waves, (c) synoptic waves, (d) medium-scale waves; (e) frictional
forcing; (f ) diabatic heating; and (g) the sum of all types of forcings. Accelerations were based on daily
calculations for each forcing. Contour intervals are 0.5 m s1 day1 in Figures 2a and b, 0.2 m s1 day1
in Figure 2c, 0.1 m s1 day1 in Figure 2d, and 0.5 m s1 day1 in Figures 2e to 2g. The zero contour is
shown as a thin solid line; dashed lines indicate negative values. Shading indicates the month-to-month standard deviations of deseasonalized variations: light, medium, and dark shading indicate standard deviations of
0.2, 0.3, and 0.5 m s1 day1 in Figures 2a and 2b; 0.05, 0.1, and 0.2 m s1 day1 in Figure 2c; 0.02, 0.05,
and 0.1 m s1 day1 in Figure 2d; and 0.1, 0.3, and 0.5 m s1 day1 in Figures 2e to 2g.
!
R2
1 ∂‾
T
∂‾
T
‾
þ w′T ′
;
ε P; P′ ¼ ρ0 2 2 v′T ′
a ∂ϕ
∂z
N H
(7)
where the prime denotes the eddy component. The integrand
ε(D) of D is explicitly written as
R2 ρ
‾′ þ ‾
‾′;
εðDÞ ¼ ρ0 u′X
v′Y ′ þ 2 02 S′T
H N
(8)
where X ′, Y ′, and S ′ are the eddy components of zonal friction, meridional friction, and diabatic heating, respectively.
[19] In computing the energy conversion rate of waves, a
31 day running average of zonal-mean temperature over the
region from 30°N to 80°N was used as the basic state
temperature T1(z). The squared buoyancy frequency N2 was
calculated from T1.
[20] To obtain accurate conversion rates, we neglected the contribution under orography as follows. To evaluate v′T ′∂T=∂ϕ,
a three-dimensional distribution of v′T ′∂T =∂ϕmðxÞ is zonally
averaged. Here, m(x) represents a masking function of x,
defined by 0 (1) at the spatial point x which is located under
(over) orography. For consistency, we applied a similar zonal
averaging to the evaluation of wave forcings.
3.
Results
3.1. Climatological Features
[21] Figure 1 shows climatological parameters averaged
over the winter season (December to March) and their
month-to-month variabilities. Zonal winds attained their
peak of 42 m s1 at 200 hPa and 30°N (Figure 1a), and the
stationary, synoptic, and medium-scale waves (Figures 1b
to 1d) attained their peaks of about 172, 71, and 20 m at
250, 300, and 350 hPa and 50°N, poleward of the polar jet
stream at 40°N. All of these peaks occurred around the tropopause and the altitudes of the peaks decreased with increasing
frequency. The synoptic maps of atmospheric waves at the
300 hPa level (Figures 1e to 1g) show pronounced peaks in
the amplitude of stationary waves over Europe (240 m) and
the Far East (300 m). The peak over the Far East (Europe)
corresponds to the trough (ridge) of stationary waves (not
shown). The amplitudes of synoptic and medium-scale
waves show peaks of 95 m and 25 m, respectively, over the
Pacific sector and peaks of 100 m and 28 m, respectively,
over the Atlantic sector. The peaks of medium-scale waves
are downstream of those of the synoptic waves.
[22] Figure 2 shows climatological zonal-mean zonal wind
acceleration due to various forcings and their month-to-month
variabilities during the winter season. The acceleration of
zonal winds due to all waves (Figure 2a) shows two maxima:
1.7 m s1 day 1 at 30°N and 400 hPa, and 2.3 m s1 day 1 at
45°N and the surface. These peaks correspond well to the jet
stream core of westerly winds extending from 30°N and 400
hPa to 45°N and the surface. Although the acceleration due
to stationary waves (Figure 2b) is particularly dominant
around the subtropical jet stream core and the lower troposphere, synoptic and medium-scale waves play an important
9051
KURODA AND MUKOUGAWA: ROLE OF ATOMOSPHERIC WAVES ON NAM
(a)
(b)
(c)
Figure 3. Height-latitude sections of December to March means of
total energy
transfer
from zonal-mean
fields to (a) stationary, (b) synoptic, and (c) medium-scale waves (ε K; K’ þ ε P; P’ of equations (6) and
(7)). Contour interval is 5 × 105 W m3. Shading indicates month-to-month standard deviations of
deseasonalized variations: light, medium, and dark shading indicates 1 × 105, 2 × 105, and 5 × 105 W m3,
respectively. Zero contour is plotted as a thin solid line and dashed lines indicate negative values.
role in zonal wind acceleration at 40°N in the middle and
lower troposphere (Figures 2c and 2d). It is interesting to note
that the main contributor to acceleration of the subtropical jet
stream around 30°N and 200 hPa is from stationary wave forcing (Figure 2b), and the forcing associated with diabatic
heating decelerates the jet stream there (Figure 2f). Clearly,
the speed of the subtropical jet stream is determined by the balance of these forcings. It is also noteworthy that a prominent
quadrupole structure of zonal wind acceleration appears in
the tropics due to diabatic heating. Acceleration of zonal winds
due to atmospheric waves is well balanced with that associated
with frictional forcing and diabatic heating (Figures 2e to 2g).
[23] Figure 3 shows the climatological winter mean of total
energy transfer
from
the
zonal
field to each atmospheric
wave type (ε K; K′ þ ε P; P′ of equations (6) and (7)), and
month-to-month variabilities. The energy transfer for stationary
waves (Figure 3a) was stronger in the extratropical lower
troposphere and peaked at 8.0 × 104 W m3 at 60°N and the
surface. Synoptic and medium-scale waves (Figures 3b and
(a)
3c) show the largest total energy transfer in the lower
troposphere at around 40°N, with peaks of 4.9 × 104 and
1.3 × 104 W m3, respectively, decreasing with increasing
altitude. Medium-scale waves have a much smaller total energy
transfer rate than stationary and synoptic waves (Figure 3c).
The climatological zonal-mean meridional circulation in winter
induced by various forcings is shown in Figure S2.
3.2. NAM Variability and Factors Contributing
to Variability
3.2.1. NAM Variability
[24] Figure 4 shows SLP, zonal-mean zonal wind, and the
Eulerian mass stream function associated with NAM variability, calculated by regression with respect to the NAM index.
SLP shows a seesaw pattern between the polar cap and midlatitudes with centers over the Atlantic and Pacific (Figure 4a).
The polar-cap signal is oval shaped with a peak of about
7.0 hPa east of Iceland, whereas the Atlantic center extends
from the Atlantic to the Middle East with a peak of about 3.7
(b)
(c)
Figure 4. Regression patterns with respect to the NAM index of (a) sea level pressure in the Northern
Hemisphere, and height-latitude sections of (b) zonal-mean zonal wind and (c) the Eulerian mass stream
function. The heavier shading indicates statistical significance at the 95% level (correlation higher than
0.30) according to Student’s t test with an effective sample size of 42, which is derived from a sample size
of 80 with a lag-one autocorrelation of 0.31 [e.g., Trenberth, 1984]. Contour intervals are 1 hPa in
Figure 4a, 0.5 m s1 in Figure 4b, and 5 × 108 kg s1 in Figure 4c. The zero contour line is shown as a thin
solid line and dashed lines indicate negative values.
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KURODA AND MUKOUGAWA: ROLE OF ATOMOSPHERIC WAVES ON NAM
(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)
(i)
Figure 5. Height-latitude sections showing regression patterns with respect to the NAM index for (a to c)
Eulerian meridional circulation, and (d to f) acceleration of zonal-mean zonal wind. The latitudinal trends
of surface pressure changes (g to i) are also shown. The left column is for eddy forcings, the central column
is for frictional forcings, and the right column is the sum of all forcings. Arrowheads in Figures 5a to 5c
indicate velocities on the meridional plane. The contour interval is 5 × 108 kg s1 for Figures 5a to 5c,
0.1 m s1 day1 for Figures 5d to 5f, and the ordinate units for Figures 5g to 5i are 1 × 102 hPa day1.
Shading is as described in caption of Figure 4. Small vectors were ignored.
hPa west of Portugal. The Pacific center has a smaller peak of
1.8 hPa northeast of Japan. These features are similar to those
obtained in previous studies [Thompson and Wallace, 2000],
although the Pacific center we identified is somewhat smaller.
The zonal-mean zonal wind pattern (Figure 4b) exhibits a
meridional dipole with centers on the 300 hPa level at 55°N
(2.5 m s1) and 30°N (1.5 m s1). Anomalous positive
winds at higher latitudes increase with altitude up to the
middle stratosphere and are observed even at 1 hPa. The
Eulerian mass stream function pattern (Figure 4c) shows a
clear meridional dipole structure with anticlockwise circulation at higher latitudes and clockwise circulation at lower
latitudes. Upwelling over the polar cap corresponds closely
to anomalous low pressure there, and downwelling at 40°N
corresponds to the anomalous high pressure zone there. The
Eulerian mass stream function at higher latitudes peaks at
6.8 × 109 kg s1 at 650 hPa and 60°N and at lower latitudes
it peaks at 4.8 × 109 kg s1 at 700 hPa and 25°N.
3.2.2. Effect of Atmospheric Waves on Variations
of the Zonal-Mean Field
[25] We first examined the overall features of zonal-mean
variations associated with the NAM. Figure 5 shows the
results of regression analyses with respect to the NAM index
of changes induced by total eddies, friction, and the sum of
all forcings for Eulerian-mean meridional circulation, zonal
wind acceleration, and zonally averaged surface pressure
change. The contribution of all forcings was obtained by linearly adding the contribution due to each forcing, including
nonlinear terms, as was done by Kuroda and Mukougawa
[2011]. We included nonlinear effects in evaluating the contribution of total eddies and friction. To evaluate the effect of
zonal-mean friction, we included extrapolated frictional data
under the topography where they are specified the same as
those just on the topography. Without this procedure, the
frictional effect cannot be well reproduced by our model
due to the assumption of a flat lower boundary.
[26] The total meridional mass flux driven by all wave forcings is 4.1 × 109 kg s1 (Figure 5a). Frictional forcing drives
the meridional mass flux with a peak of 3.4 × 109 kg s1 in
the lower troposphere (Figure 5b), which counteracts the zonal
wind anomaly associated with NAM variability. For diabatic
heating, nonlinear and violation of balanced wind terms,
meridional circulation is significant only in the tropics (not
shown). The meridional circulation induced by all forcings
9053
KURODA AND MUKOUGAWA: ROLE OF ATOMOSPHERIC WAVES ON NAM
(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)
(i)
Figure 6. Height-latitude sections showing regression patterns with respect to the NAM index for (a to c)
zonal-mean wave amplitudes, and wave amplitudes in the Northern Hemisphere (d to f) at the 300 hPa level
and (g to i) at the 1000 hPa level. The left column is for stationary waves, the central column is for synoptic
waves, and the right column is for medium-scale waves. Contour intervals are 1 m in Figures 6a to 6c, 5 m
in Figures 6d and 6g, and 2 m in Figures 6e, 6f, 6h, and 6i. Shading is as described in caption of Figure 4.
(Figure 5c) is almost the same as that obtained in Figure 4c. In
fact, the peak values of 7.0 × 109 kg s1 and 4.8 × 109 kg s1
in the lower troposphere for all forcings (Figure 5c) are almost
the same as those of the Eulerian mass stream function
(Figure 4c). These results confirm the accuracy of our
diagnostic modeling.
[27] The acceleration of zonal wind due to all atmospheric
waves (Figure 5d) is 0.44 m s1 day1 at 60°N in the lower
troposphere, which is about one third of the maximum value
of mechanical forcing (1.5 m s1 day 1 at 55°N and 250 hPa
level; not shown). Frictional forcing (Figure 5e) decelerates
the zonal wind through the troposphere between 40°N and
70°N. The contributions of diabatic and other forcings are
small (not shown). The sum of all forcings (Figure 5f) shows
that zonal wind acceleration is almost negligible.
[28] Atmospheric waves reduce surface pressure over the
polar cap and increase it at 50°N (Figure 5g). Frictional
forcing has the opposite effect (Figure 5h). Contributions
from diabatic and other forcings are small at all latitudes
(not shown). Consequently, the surface pressure change
outside the polar cap is negligible due to the balance between
eddies and friction, again confirming the accuracy of our
modeling (Figure 5i).
[29] We next examined the influence of stationary, synoptic, and medium-scale waves on variations of the NAM.
Figure 6 shows the results of regression analyses with respect
to the NAM index of zonally averaged wave amplitudes and
horizontal variations of wave amplitudes at the 300 and 1000
hPa levels. Comparison of zonal-mean wave amplitudes
shows that the behavior of stationary waves is quite different
from the others. Both synoptic and medium-scale waves
exhibit barotropic dipole structures with centers at 60°N
and 30°N (Figures 6b and 6c), whereas stationary waves
show a quadrupole meridional structure in the middle troposphere that is out of phase with those of synoptic and
medium-scale waves (Figure 6a). The peak value of the correlation coefficient of zonal-mean amplitude for mediumscale waves with the NAM index is 0.78 (not shown), which
is higher than those of both synoptic waves (0.63) and stationary waves (0.60). Regressed zonally averaged peak wave
amplitudes are 1.9 m at 350 hPa and 60°N for medium-scale
waves (Figure 6c), 3.3 m at 250 hPa and 60°N for synoptic
waves (Figure 6b), and 9 m at 1000 hPa and 70°N for stationary waves (Figure 6a). Stationary waves show another prominent negative peak of 7 m at 300 hPa and 70°N
(Figure 6a). These higher latitude peaks reside poleward of
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KURODA AND MUKOUGAWA: ROLE OF ATOMOSPHERIC WAVES ON NAM
(a)
(b)
(c)
(d)
(e)
(f)
Figure 7. Height-latitude sections showing regression patterns with respect to the NAM index for
Eulerian wave forcings: (a to c) mechanical and (d to f) thermal forcings. The contour interval is
0.1 m s1 day1 in Figures 7a to 7c and 0.02 K day1 in Figures 7d to 7f. Shading is as described
in caption of Figure 4.
the climatological peaks at around 50°N (Figures 1b to 1d).
The horizontal amplitude variations of synoptic and medium-scale waves (Figures 6e, 6f, 6h, and 6i) associated with
the NAM reach maxima over Europe, downstream of the
climatological peak over the Atlantic (Figures 1f and 1g),
and their variations are almost barotropic.
[30] We next examined the role of each type of wave forcing on variations of the NAM. Figure 7 shows the results of
regression analyses with respect to the NAM index for
Eulerian mechanical forcings and thermal forcings for each
type of atmospheric wave. Eulerian mechanical forcings
have peaks of 0.66, 0.53, and 0.19 m s1 day1 at 250–300
hPa and 50°N to 60°N for stationary (Figure 7a), synoptic
(Figure 7b), and medium-scale waves (Figure 7c), respectively. The latitude of the peak of each mechanical forcing
corresponds well to that of the regressed zonal wind anomaly
(Figure 4b). Although the contributions from thermal forcing
of synoptic and medium-scale waves (Figures 7e and 7f) are
very small, that for stationary waves is very large (Figure 7d),
exhibiting a tripole pattern with prominent peaks of 0.1,
0.16, and 0.15 K day1 at 40°N, 55°N, and 75°N, respectively, in the lower troposphere, and another prominent peak
of 0.12 K day1 above the tropopause at 65°N (Figure 7d).
[31] The meridional circulation, zonal wind acceleration,
and surface pressure changes produced by each type of wave
associated with variations of the NAM are shown in Figure 8.
The induced meridional mass flux is 1.7 × 109 kg s1 for
stationary waves (Figure 8a), 1.7 × 109 kg s1 for synoptic
waves (Figure 8b), and 0.5 × 109 kg s1 for medium-scale
waves (Figure 8c).
[32] The acceleration of zonal-mean zonal wind due to stationary waves (Figure 8d) has peaks of 0.29 and 0.25 m s1
day1 in the lower and upper troposphere, respectively.
Peaks due to synoptic and medium-scale waves are 0.13 m s1
day1 (at 300 hPa) and 0.06 m s1 day1 (at 650 hPa) at
50°N (Figures 8e and 8f), respectively. Comparison of the
acceleration of zonal wind (Figure 8d) with mechanical forcing (Figure 7a) for stationary waves shows the former to be
relatively larger (~1/2.5) due to the additive contribution from
thermal forcing (Figure 7d). In contrast, the accelerations of
zonal wind for synoptic and medium-scale waves (Figure 8e
and 8f) are about one fourth to one third of their mechanical
forcings (Figures 7b and 7c). The zonal wind acceleration
due to all wave types (Figure 5d) shows that each of the three
wave types has an important role in the acceleration of the
zonal wind associated with NAM variability. In fact, the peak
of the westerly acceleration due to stationary, synoptic, and
medium-scale waves at 50°N to 60°N (Figures 8d and 8f)
coincides well with the high-latitude center of the zonal wind
variation (Figure 4b).
[33] The contribution from stationary and synoptic waves
(Figures 8g and 8h) explains most of the wave-induced surface pressure changes between 40°N and 60°N (Figure 5g).
It is also clear that about two third of the surface pressure
change poleward of 60°N (Figure 5g) comes from stationary
and synoptic waves (Figures 8g and 8h).
3.2.3. Effects of Waves of Various Periods
and Horizontal Scales
[34] We examined the effects of atmospheric waves on the
NAM not only for specific wave types but also considering
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KURODA AND MUKOUGAWA: ROLE OF ATOMOSPHERIC WAVES ON NAM
(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)
(i)
Figure 8. Height-latitude sections showing regression patterns with respect to the NAM index for (a to c)
Eulerian meridional circulation and (d to f) acceleration of zonal-mean zonal wind. The latitudinal trends of
surface pressure changes (g to i) are also shown. The left column is for stationary waves, the central column
is for synoptic waves, and the right column is for medium-scale waves. The contour interval is 3 × 108 kg s1
for Eulerian meridional circulation and 0.03 m s1 day1 for zonal wind acceleration. Shading is as described
in caption of Figure 4.
differences in wave periods and horizontal scales (wave
number) to develop a more comprehensive examination as
had been done by Kuroda and Mukougawa [2011]. We
applied a set of high-pass Lanczos band-pass filters to the
six-hourly data set to isolate wave components with periods
ranging from less than 1 day to 70 days.
[35] Figure 9 shows the regressed Eulerian mechanical
forcing, induced meridional circulation, zonal wind acceleration, and surface pressure changes associated with the
Eulerian wave forcings (mechanical plus thermal forcings)
for various wave periods. Mechanical forcing tends to increase with increasing period up to 6 days (Figures 9a to
9d). The peak value for waves with a period of less than 1
day is only 0.06 m s1 day1 (Figure 9a), but it increases
from 0.17 to 0.39 m s1 day1 as wave period increases from
1 to 6 days (Figures 9b to 9d). For waves with periods of
6–10 days, wave forcing and induced circulation are very
small (not shown). For the wave components with periods
between 10 days and that of stationary waves (low-frequency
transient waves; LFT), mechanical forcing reaches 0.29 m
s1 day1 around 70°N (Figure 9e). The thermal forcing
for each wave component (not shown) is very small, and it
reaches 0.05 K day1 for LFT.
[36] These results show that the meridional circulation centered at 50°N due to all wave types (Figure 5a) is produced
mainly by waves with periods of 1–6 days (Figures 9g to
9i). Moreover, the correlation between mechanical forcing
and the NAM index exceeds 0.5 for each type of wave for periods of less than 6 days. Thus, the small contribution to meridional circulation of waves of period less than 1 day reflects
the relatively small climatological variability of such waves.
[37] The peak value of zonal wind acceleration for wave
components with periods of 3–6 days (0.11 m s1 day1;
Figure 9n) is larger than that for wave components with
periods of 1–2 days (0.06 m s1 day1; Figure 9l) and 2–3
days (0.06 m s1 day1; Figure 9m), and less than those with
periods of 1 day (0.02 m s1 day1; Figure 9k). Note that the
effect of LFT is to decelerate the zonal-mean zonal wind at
55°N (0.1 m s1 day1; Figure 9o), which is similar to
the effect of frictional forcing (Figure 5e).
[38] The surface pressure changes at 40°N come primarily
from wave components with periods of 1–6 days (Figures 9q
to 9s), whereas LFT contribute a positive peak at 60°N and a
negative peak in the polar-cap region (Figure 9t). It is
noteworthy that the contribution of atmospheric waves to
surface pressure changes in the polar region increases with
9056
KURODA AND MUKOUGAWA: ROLE OF ATOMOSPHERIC WAVES ON NAM
(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)
(i)
(j)
(k)
(l)
(m)
(n)
(o)
(p)
(q)
(r)
(s)
(t)
Figure 9. Height-latitude sections showing regression patterns with respect to the NAM index for
different wave periods for Eulerian mechanical forcing (first row), induced meridional circulation (second
row), and zonal wind acceleration (third row). Regressions of thermal forcing are not shown. The latitudinal
trends of surface pressure changes (bottom row) are also shown. Wave periods range from less than 1 day
(left column) to between 10 days and stationary-wave period (right column). Contour intervals are 0.05 m s1
day1 in Figures 9a to 9e, 1 × 108 kg s1 in Figures 9f to 9j, and 0.02 m s1 day1 in Figures 9k to 9o.
Shading is as described in caption of Figure 4.
increasing period (note that the vertical scales of Figures 9s
and 9t are different from those of the other panels).
[39] We also examined the contributions of atmospheric
waves with different zonal wave numbers. Figure 10 shows
the contributions to Eulerian mechanical and thermal forcings and the induced meridional circulation and surface pressure changes for waves of different wave number. All wave
components except those of wave numbers 3 and 4 make
large contributions to mechanical forcing (Figures 10a to
10d). For thermal forcing, only wave components with wave
numbers 1 (Figure 10e) and 2 (Figure 10f) make significant
contributions. Wave components with wave numbers 1 and
2 show quasi-stationary behavior (not shown) and they will
be forced by geographical distribution around the Arctic.
Wave components with wave numbers 1 and 2 drive a larger
meridional circulation than the other wave components because both mechanical and thermal wave forcings contribute
to the formation of the meridional circulation of these waves
(not shown). These wave components also force large surface
pressure changes (Figures 10m and 10n). Wave components
with wave numbers 5–9 show wave forcings (Figures 10c
and 10g), meridional circulations (Figure 10k), zonal wind
accelerations (not shown), and surface pressure changes
(Figure 10o) that are similar to those due to synoptic waves
(Figures 7b and 7e, 8b, 8e, and 8h), but the contributions of
wave numbers 5–9 are slightly larger. This is because wave
numbers 5–9 and synoptic waves are represented by similar
wave components (not shown). The contribution of wave
components with wave numbers larger than 10 (Figures 10d,
10h, 10l, and 10p) is about twice that due to medium-scale
9057
KURODA AND MUKOUGAWA: ROLE OF ATOMOSPHERIC WAVES ON NAM
(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)
(i)
(j)
(k)
(l)
(m)
(n)
(o)
(p)
Figure 10. Height-latitude sections showing regression patterns with respect to the NAM index for selected
wave numbers (WNs) for mechanical forcing (first row), thermal forcing (second row), and induced meridional circulation (third row). Regressions for zonal wind accelerations are not shown. The latitudinal trends of
surface pressure changes (bottom row) are also shown. WNs range from 1 (left column) to greater than 10
(right column). Contour intervals are 0.1 m s1 day1 in Figures 10a to 10d, 0.05 K day1 in Figures 10e
to 10h, and 5 × 108 kg s1 in Figures 10i to 10l. Shading is as described in caption of Figure 4.
waves (Figures 7c and 7f, 8c, 8f, and 8i). This is because
waves with longer periods but smaller horizontal scales are beyond the parameters that define medium-scale waves.
3.3. Feedback Between Zonal Fields and Eddies
[40] Our analyses show that the three types of atmospheric
waves considered here amplify the zonal-mean zonal
wind anomaly associated with NAM variability. Previous
studies [DeWeaver and Nigam, 2000a, 2000b; Lorenz and
Hartmann, 2003] have also suggested that the NAM (or
North Atlantic Oscillation) is sustained by positive
feedback between atmospheric waves and zonal winds such
that the waves reinforce westerly zonal winds, which in
turn amplify the wave forcings. The addition of energy to
each wave amplifies its amplitude and wave forcings. To
examine how the waves are amplified by their interactions
with mean zonal-mean fields, wave-energy conversion
(equations (6) and (7)) for stationary, synoptic, and
medium-scale waves has been
Figure 11 shows
evaluated.
the regressed totalε K; K′ þ ε P; P′ and potential energy
conversion ε P; P′ with the NAM index. The patterns of total
energy transfer for all wave types (Figures 11a to 11c) show a
9058
KURODA AND MUKOUGAWA: ROLE OF ATOMOSPHERIC WAVES ON NAM
(a)
(b)
(c)
(d)
(e)
(f)
Figure 11. Height-latitude sections showing regression patterns with respect to the NAM index of total
wave energy transfer (a to c) and potential energy transfer (d to f) from zonal-mean fields to eddies. Left
column is for stationary waves, center column is for synoptic waves, and right column is for medium-scale
waves. Contour interval is 1 × 105 W m3 in Figures 11a and 11d and 0.5 × 105 W m3 in Figures 11b,
11c, 11e, and 11f. Shading is as described in caption of Figure 4.
meridional dipole structure with a positive peak at high latitude and a negative peak at lower latitude. The positive (negative) peak of 2.0 × 104 (0.8 × 104) W m3 for stationary
waves is at 65°N (45°N) in the lowermost troposphere
(Figure 11a). The corresponding peaks for synoptic and
medium-scale waves are 3.2 × 105 (2.4 × 105) W m3 at
55°N (40°N) in the middle troposphere, and 1.1 × 105
(0.9 × 105) W m3 at 50°N (40°N) in the lower troposphere, respectively. Our analyses also show that, except for stationary waves, the kinetic energy conversion rate is much
smaller than the potential energy conversion rate. Most of the
potential energy conversion is derived from the term that is
proportional to v′T ′∂T =∂ϕ in equation (7). The meridional
patterns of total energy conversion rate for each wave type
(Figures 11a to 11c) are very similar to those of their zonal wind
accelerations, especially in the lower and middle troposphere
(Figures 8d to 8f). Thus, our analysis shows that potential
energy conversion is the main contributor to the amplification
of each wave type, and there is a positive feedback process
between the zonal-mean zonal wind field and each wave type.
[41] We also performed lagged regression analyses of the
NAM index with 31 day running averaged zonal wind acceleration (Figure 12a) and total energy conversion (Figure 12b)
for each wave type. The specific part of the lower troposphere
covered in these analyses (950 to 800 hPa and 55°N to 60°N)
was selected because the highest correlation (>0.9) between
zonal-mean zonal wind and the NAM index (Figure 4b)
exists there. A positive lag means precedence of the NAM
variation. The zonal-mean zonal wind in this part of the
troposphere has the highest correlation with the NAM index,
with a lag of +1 day (not shown). Here, zonal wind acceleration was calculated using the lagged regression of wave forcings, as for Figure 8. The peaks of zonal wind acceleration of
0.23, 0.08, and 0.02 m s1 day1 appear at 11, 0, and +20
days for stationary, synoptic, and medium-scale waves, respectively (Figure 12a). For medium-scale waves, though
the peak time does not precede the NAM index, there is a
marked increase when the time lag approaches day 0. These
results show that each of the three wave types has a role in
driving NAM variations in this part of the troposphere, and
that the contribution from stationary waves is largest. The
number of days of precedence for each wave type should correspond to its time scale (period). The peak values for energy
conversion from the zonal field of 3.5 × 105, 2.3 × 105, and
0.6 × 105 W m3 appear at +6, +2, and +3 days for stationary, synoptic, and medium-scale waves, respectively
(Figure 12b). The peak for each wave type is lagged with respect to the NAM index, which indicates that wave generation tends to peak after the NAM has matured. Because the
generation of atmospheric waves accelerates the zonal-mean
zonal wind, the life span of the NAM is prolonged by this
positive feedback process.
[42] We conducted the same regression analyses for the entire extratropical region (Figures 12c and 12d). The part of
the troposphere we selected for these analyses (poleward of
45°N and from the surface to the 100 hPa level) corresponds
to the region of anomalous westerly winds associated with
the NAM (Figure 4b). The zonal wind acceleration for each
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KURODA AND MUKOUGAWA: ROLE OF ATOMOSPHERIC WAVES ON NAM
(b)
(a)
-20
0
20
-20
(c)
-20
0
20
0
20
(d)
0
-20
20
Figure 12. Lagged regressions with respect to the NAM index of (a) zonal-mean zonal wind acceleration
due to each wave type and (b) total energy transfer from zonal fields to each wave type averaged between
55°N and 60°N and between the 950 and 800 hPa levels. (c) Estimated power transferred from eddies to
zonal wind and (d) from zonal fields to eddies averaged for the area north of 45°N and below the 100
hPa level. Curves are blue for stationary waves, black for synoptic waves, and red for medium-scale waves.
Abscissas show the lag (days) against the NAM index. Ordinate units are 1 m s1 day1, 1 × 105 W m3,
1 × 1012 W, and 1 × 1012 W for Figures 12a, 12b, 12c, and 12d, respectively.
wave type was converted to power density P (W m3) by
the expression
∂‾
u
P ¼ ρ0 ‾
;
u
∂t e
(9)
where ∂‾
u=∂t e is estimated zonal wind acceleration for each
wave type (equation (1a)); its integration is shown in
Figure 12c. The peak values of 5.9 × 1012, 4.3 × 1012, and
0.8 × 1012 W appear with lags of +2, 10, and +4 days for
stationary, synoptic, and medium-scale waves, respectively.
However, the peaks for stationary and medium-scale waves
are very flat at around day 0. The zonal wind acceleration
due to synoptic waves in the entire extratropical region
(Figure 12c) is more important than that in the smaller region
(Figure 12a) and occurs very close to the time of the peak for
stationary waves in the smaller region (Figure 12a).
Precedence of the peak zonal wind acceleration with respect
to the NAM index is observed for only synoptic waves in the
extratropical region. Thus, synoptic waves have a primary
role in driving the zonal wind anomaly for the entire
extratropical region. Our analysis of the integrated energy
transfer rate from the zonal-mean zonal field to each wave
type in the entire extratropical region (Figure 12d) shows
peak values of 0.7 × 1012, 10.7 × 1012, and 2.1 × 1012 W with
lags of +11, +2, and 1 days for stationary, synoptic, and
medium-scale waves, respectively. The energy transfer from
the zonal-mean field to synoptic waves is much larger than
those to other wave types (Figure 12d). Thus, synoptic waves
play a dominant role in the interaction of atmospheric waves
with zonal-mean zonal wind flow in the entire extratropical
region. The overwhelming predominance of synoptic waves
is because the energy transfer to stationary waves occurs
mainly near the surface (Figure 11a), whereas those for synoptic and medium-scale waves occur over a broader range of
heights (Figures 11b and 11c). The large negative energy
transfer south of 55°N for stationary waves (Figure 11a) also
contributes to these differences.
[43] The small energy conversion from the zonal-mean field
to stationary waves (Figure 12d) suggests that stationary
waves do not significantly amplify and hence do not accelerate
it greatly. However, the acceleration that is present is
controlled mostly by stationary waves (Figure 12c), which
suggests that stationary waves obtain energy from other
sources. Because equation (5) is exactly satisfied when all
wave components are included in the eddy, when we consider
a particular wave type, additional terms representing the energy exchange between the other waves should be included
[Saltzman, 1957]. In the present case, the additional terms
representing energy exchange with other wave components include many terms (see equation (S3.6)). However, we decided
to evaluate the net effect of these terms as the residual of the
energy conservation equation for a specific wave component
because direct computation of all the terms in equation
(S3.6) would accumulate numerical errors due to the high
number of computational operations. We checked the accuracy of our numerical method by computing the energy budget
for all waves, which does not include any energy exchange
terms among the wave components. Table S4, listing each
component of the climatological energy budget for the region
north of 45°N and below 100 hPa, indicates that the discrepancy from energy conservation is negligible. The magnitude
of the discrepancy inferred from the residual (SUM) is only
5% of the smallest forcing term (DIAB; diabatic heating).
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KURODA AND MUKOUGAWA: ROLE OF ATOMOSPHERIC WAVES ON NAM
(a)
(b)
wave-wave interactions between stationary and other
waves, especially synoptic waves and LFT. However, further work is needed to obtain a more detailed understanding
of this phenomenon.
4.
-20
0
20
(c)
-20
0
20
0
20
(d)
-20
0
20
-20
Figure 13. Lagged regressions of changes of energy of (a)
stationary, (b) synoptic, (c) medium-scale waves, and (d)
LFT with respect to the NAM index over the entire
extratropical region (north of 45°N and below the 100 hPa
level). Curves are black for change of total energy, red for energy input from zonal fields, blue for energy flow from the
boundary of the area analyzed, and green for energy input
from other waves. Abscissas show the lag (days) against
the NAM index. Ordinate units are 1 × 1012 W.
[44] Figure 13 shows the results of lagged regressions with
respect to the NAM index of energy changes for each wave
type integrated over the entire extratropical region according
to equation (5), thus deriving the time derivative of wave energy d(K ′ + P ′)/dt, energy outflow at the boundary of the area
analyzed W,
rate from the zonal totalenergy
conversion
mean field K; K′ þ P; P′ , and the energy exchange rate
between wave types estimated by
Δ¼
n
o n
o
d
ðK′ þ P′Þ ‾
K; K′ ‾
P; P′ W D:
dt
(10)
[45] Contributions from diabatic heating and frictional
forcing D are relatively smaller and are not shown in
Figure 13. These analyses show that stationary waves
receive a very large energy input from other waves
(Figure 13a), whereas synoptic waves and LFT provide a
substantial output of energy to other waves. For mediumscale waves, there is a relatively small energy input from
other waves (note that the vertical scale of Figure 13c is
different from others). Although LFT tends to reduce the
zonal-mean zonal wind anomaly associated with NAM variability (Figure 9o), it also contributes energy to stationary
waves, especially during the growing stage of the NAM.
It is also noteworthy that energy conversion from the
zonal-mean field is quite small for LFT.
[46] The results of our analyses suggest that a positive
feedback between stationary waves and the zonal-mean
flow is established through the energy conversion of
Discussion
[47] We found that stationary, synoptic, and medium-scale
waves all tend to accelerate the zonal-mean zonal wind
anomaly associated with the NAM, and that the zonal-mean
field feeds energy to these waves. Thus, these two processes
constitute a two-way feedback mechanism that sustains
NAM variability. Previous studies [e.g., DeWeaver and
Nigam, 2000a, 2000b; Lorenz and Hartmann, 2003] have
suggested that both stationary and synoptic waves sustain
NAM variability through a positive feedback mechanism.
Here, we have shown that medium-scale waves (of shorter
period than synoptic waves) also sustain NAM variability
through a positive wave-mean flow interaction, although
their contribution is smaller than those of synoptic and stationary waves and constitutes about 10% of the zonal-mean
zonal wind acceleration. Our analysis also shows that although stationary waves are the most important drivers of
the zonal-mean zonal wind anomaly associated with NAM
variability, synoptic waves also play a significant role.
Synoptic waves not only directly drive zonal-mean flow,
but also feed energy to stationary waves, which in turn
accelerates the zonal-mean zonal wind anomaly.
[48] We used the NAM to represent the dominant variability of the zonal-mean field in the Northern Hemispheric winter. However, whether the NAM is really a “dynamical mode
of variability” is still controversial, which is not the case for
the SAM [e.g., Deser, 2000; Feldstein and Franzke, 2006;
Itoh, 2008]. We have undertaken the same analysis using
the North Atlantic Oscillation [e.g., Hurrell et al., 2003]
index, but the overall results remain the same. Hence, our
results are not crucially distorted as far as we discuss the
zonal-mean zonal wind variation in the Northern Hemisphere.
[49] We found that the contribution of stationary waves to
NAM variability is very important. Stationary waves tend to
accelerate the zonal-mean zonal wind anomaly associated
with the NAM, which is very different from the situation
for the SAM. Stationary waves in the Southern Hemisphere
have a climatological peak amplitude of 107 m, which is
about two third of that of stationary waves in the Northern
Hemisphere winter. Moreover, it has been shown that both
stationary waves and LFT tend to decelerate the zonal-mean
zonal wind anomaly associated with the SAM (not shown).
To explain the relationship between stationary eddies and
the zonal-mean flow anomaly associated with the NAM,
Kimoto et al. [2001] proposed a “tilted-trough” mechanism,
in which the anomalous zonal wind changes the meridional
structure of stationary waves, which in turn causes a wave
forcing to accelerate the anomalous zonal wind. This mechanism explains well why the stationary wave amplitude at
60°N in the tropopause does not increase for the NAM
(Figure 6a). However, from the energetics point of view,
acceleration of zonal wind accompanies energy transfer from
stationary waves to the zonal-mean field. So some energy
input is needed to maintain the energy of stationary waves.
Amplification of waves and the associated energy transfer
associated with NAM variability in the troposphere
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KURODA AND MUKOUGAWA: ROLE OF ATOMOSPHERIC WAVES ON NAM
(Figures 6a and 11a) will partly contribute to this. The energy
transfer from synoptic waves and LFT to stationary waves is
therefore important for the maintenance of stationary waves,
as suggested by our analysis.
[50] Comparison of the difference between the fast transient waves of NAM and SAM (Figures 9 and 8 of Kuroda
and Mukougawa [2011]) shows that the largest energetic
waves in the NAM have periods from 3 to 6 days
(Figure 9d), but these periods are 1 to 2 days in the SAM
(Figure 8b of Kuroda and Mukougawa [2011]). This
difference reflects the climatological difference of the
frequency-wave number structures of the two hemispheres;
high-frequency waves are of lower amplitude in the Northern
Hemisphere. Correspondingly, the climatological amplitudes
of medium-scale waves in the Northern Hemisphere (20 m)
are about two third of those of the Southern Hemisphere (28
m), which explains why the effect of medium-scale waves
on the NAM is smaller than their effect on the SAM.
However, the maximum correlation of medium-scale wave
amplitude (and of other parameters associated with mediumscale waves) with the NAM index tends to be higher than
those of other waves. This is demonstrated by the increase
with decreasing wave period of the area in which the correlation is greater than 0.30 (Figure 9), indicating that the activity
of medium-scale waves is more strongly controlled by zonal
winds. It seems logical that the faster, shorter waves would
be more strongly controlled by the jet and less able to
propagate away from it [Hoskins and Ambrizzi, 1993].
Comparison of the maximum acceleration of zonal winds
attributed to medium-scale waves with that attributed to all
wave types indicates that the contribution to NAM variability
of medium-scale waves amounts to about 10% of the contribution of all wave types. Though this is not a large contribution,
it is too big to ignore.
[51] Kuroda and Mukougawa [2011] concluded that in the
Southern Hemisphere synoptic and medium-scale waves
have typical growth time scales of 3.9 and 8.0 days, respectively. We calculated the corresponding growth time scales
in winter in the region north of 20°N from the surface to
the 100 hPa level and found that the growth time scales of
synoptic and medium-scale waves there are typically 3.5
and 8.3 days, respectively. Therefore, synoptic waves in the
Northern Hemisphere are a little less stable than those of
the Southern Hemisphere, and medium-scale waves in the
Northern Hemisphere are a little more stable than those in
the Southern Hemisphere. These differences reflect in part
differences of the climatological distributions of synoptic
and medium-scale waves; those of lower (higher) frequency
tend to be more dominant in the Northern Hemisphere
(Southern Hemisphere). Further research is needed to determine the origin of these differences.
[52] The magnitude of the meridional circulation associated
with the NAM due to all wave types as derived in two previous
studies [Kuroda, 2005, 2007] is only about 80% of that
presented here. If only waves with wave numbers larger than
4 are considered, that percentage drops to 40. These differences clearly reflect a lack of fast waves in the daily data used
in the previous studies and indicate that six-hourly data are the
minimum requirement for the capture of important fast frequency waves, including medium-scale waves.
[53] Our evaluation of the acceleration of zonal wind due to
atmospheric waves is more accurate than that of Kuroda and
Mukougawa [2011] due to our inclusion of nonlinear terms
and our use of daily calculations, which allowed us to evaluate
the significance of calculated variables. Comparison of our results with and without the inclusion of nonlinear terms showed
that their inclusion tended to reduce the calculated acceleration
of zonal winds by less than about 8%. For example, acceleration due to total eddy was reduced from 0.41 to 0.38 m s1
day1 at the 300 hPa level at 55°N (Figure 5d). Because this
improvement is small, reasonable comparisons can still be
made with the results of the previous study of Kuroda and
Mukougawa [2011].
[54] We compared the amount of energy conversion associated with NAM variability with that associated with climatological values. For the energy conversion from zonal fields
to atmospheric waves, the total integrated climatological
values poleward of 45°N from the surface to the 100 hPa
level for stationary, synoptic, and medium-scale waves are
1.4 × 1014, 6.3 × 1013, and 7.3 × 1012 W, respectively. In
comparison, energy conversion associated with the NAM
with no time lag (Figure 12d) represents 0, 17, and 29% of
their climatological values. These results show that the
variability of medium-scale waves is large and much of
the energy variation of medium-scale waves is controlled
by NAM variability. If we consider the much smaller
climatological energy conversion of medium-scale waves
(Figure 3c), the large effect of medium-scale waves on the
NAM is surprising. This relationship reflects the very close
relationship between zonal winds and medium-scale waves,
as was implied by the highest correlation shown in
Figure 6c. Further research is needed to better define the
close relationship of medium-scale waves to zonal wind.
5.
Conclusions
[55] We used a six-hourly reanalysis data set to examine
the effect of atmospheric waves on the NAM. Our major findings are as follows.
[56] 1. About 60% of the acceleration of zonal winds and
40% of meridional circulation driven by eddies in the NAM
is due to stationary waves. The remaining contribution is
from synoptic and medium-scale waves.
[57] 2. Although the amplitude of climatological variability in the Northern Hemisphere is much smaller than that of
the Southern Hemisphere, the contribution of medium-scale
waves to the formation of the NAM in winter is about 30%
of that of synoptic waves. As a result, about 10% of wave
driving in the NAM from total eddies is from mediumscale waves.
[58] 3. Our analysis implies the existence of a positive
feedback process between the NAM anomaly and stationary,
synoptic, and medium-scale waves. Of these, the contribution of stationary waves to the acceleration of zonal
winds is the largest, consistent with previous studies [e.g.,
DeWeaver and Nigam, 2000a, 2000b; Limpasuvan and
Hartmann, 2000; Lorenz and Hartmann, 2003]. In contrast,
synoptic waves receive the largest amount of energy from
the zonal field, and though their ability to directly accelerate
zonal winds is secondary, they still play a key role in the
transfer of the energy that sustains stationary waves.
[59] 4. The subtropical jet stream in winter is driven by stationary waves, whereas it is decelerated by the circulation
that results from diabatic heating in the tropics.
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KURODA AND MUKOUGAWA: ROLE OF ATOMOSPHERIC WAVES ON NAM
[60] 5. Low-frequency transient waves, which have periods between 10 and 70 days, tend to decelerate zonal winds
associated with the NAM, consistent with the studies of
Lorenz and Hartmann [2003]. They play a role in sustaining
stationary waves through energy transfer as synoptic waves.
[61] Although stationary waves are the primary drivers of
the NAM, the role of synoptic and other waves in sustaining
stationary waves is also very important. The relationships
between atmospheric waves and the zonal fields of the
NAM are much more complex than those of the SAM.
More research is needed to clarify these relationships.
[62] Acknowledgments. We thank the anonymous reviewers for insightful comments. This research was supported in part by Grant-in-Aid
(23340141) for Science Research from the Ministry of Education, Culture,
Sports, Science, and Technology of Japan.
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