The QBO-like oscillation is a robust feature, not sensitive to the choice of model configuration such as domain size and horizontal resolution, or boundary conditions such as prescribed
Trang 1We re-examine the internal oscillation dynamically analogous
to the equatorial quasi-biennial oscillation (QBO) that was firstly
obtained by Held et al (1993; hereafter HHR93) as a radiative-
convective quasi-equilibrium state in a highly-idealized two-
dimensional regional model with explicit moist convections under
a periodic lateral boundary condition without Coriolis effects A
QBO-like oscillation with a period of 120.6 days is obtained for
the control experiment with a similar configuration as HHR93
The QBO-like oscillation is a robust feature, not sensitive to the
choice of model configuration such as domain size and horizontal
resolution, or boundary conditions such as prescribed zonal wind
at the top and sea surface temperature
The obtained QBO-like oscillations show downward
propa-gation of the zonal mean signals in the stratosphere as revealed
by observations and wave-mean flow interaction theories, while
unlike the observed equatorial QBO, they have a clear signal in
the zonal mean zonal wind and temperature in the troposphere
The zonal mean precipitation also varies in accordance with the
oscillation, though its day-to-day fluctuation is very large
com-pared to the long-period oscillation
(Citation: Yoden, S., H.-H Bui, and E Nishimoto, 2014: A
minimal model of QBO-Like oscillation in a
stratosphere-tropo-sphere coupled system under a radiative-moist convective
qua-si-equilibrium State SOLA, 10, 112−116,
doi:10.2151/sola.2014-023.)
1 Introduction
The quasi-biennial oscillation (QBO) of the equatorial
strato-sphere is considered as an internal oscillation due to wave-mean
flow interactions under a zonally periodic boundary condition (see
e.g., Baldwin et al 2001) Classical QBO theories (Lindzen and
Holton 1968; Holton and Lindzen 1972) assumed the separation
of the troposphere where waves are generated, from the
strato-sphere where interactions take place, by specifying time-constant
wave forcing at the bottom boundary near the tropopause In a
laboratory analogue of the QBO, a standing internal gravity wave
was forced mechanically at the bottom boundary (Plumb and
McEwan 1978) or at the top (Otobe et al 1998) of an annulus of
salt-stratified water The separation is a theoretical idealization
under an assumption of “independent stratospheric variations” in
stratosphere-only models (Yoden et al 2002)
In the real atmosphere, however, there is no such a clear
boundary separating the stratosphere and the troposphere
Dynam-ical coupling between them in the extra-tropics has drawn much
attention over recent years (see, e.g., Yoden et al 2002), whereas
relatively little attention has been paid to the coupling in the
trop-ics, in particular, to the downward influence of the stratosphere
to the troposphere Only a few observational studies have shown
some evidence of the downward influence of the stratospheric QBO Gray (1984) pointed out an apparent influence of the QBO
on Atlantic tropical cyclone activity for the period of 1950−1982, although such a statistically significant relationship was not obtained for a longer dataset including the period of 1983−2008 (Camargo and Sobel 2010) By analyzing the records of outgo-ing long-wave radiation and highly reflective cloud index over decades, Collimore, et al (1998, 2003) showed a relationship between the QBO and tropical deep convection through the mod-ulations of tropopause height and cross-tropopause zonal wind shear
The use of general circulation models (GCMs) of the at-mosphere provides a complementary means to explore possible stratosphere-troposphere coupling mechanisms relating to the QBO Takahashi (1996) first succeeded in GCM simulation of a QBO-like oscillation for realistic sea surface temperature (SST) and surface topography, whereas Horinouchi and Yoden (1998) performed an idealized “aqua-planet” experiment for analyzing wave-mean flow interactions associated with the QBO Recently, four models in the Coupled Model Intercomparison Project Phase
5 (CMIP5) simulated the QBO realistically and projected its future change (Kawatani and Hamilton 2013) Even though these high-end numerical models might include the coupling process associated with the QBO, no attempt has been made to analyze possible downward influence deep in the troposphere, as far as
we know, perhaps due to too weak signals or limitation in spatial resolutions of these global models Any parameterization schemes
on cumulus convections and/or small-scale gravity waves, which are considered as major sources of model uncertainty, are neces-sary to simulate the QBO
Regional cloud-resolving models (CRMs) have been used to investigate convectively generated stratospheric gravity waves (Fovell et al 1992; Alexander et al 1995) and their possible role
in forcing the QBO in the equatorial stratosphere (Alexander and Holton 1997) However, downward influence of the QBO
to the troposphere has been beyond the scope of these studies Held et al (1993, hereafter HHR93) introduced another type of two-dimensional CRM with a periodic lateral boundary condition and obtained a QBO-like oscillation with a period of about 60 days in a radiative-moist convective quasi-equilibrium state, though they did not report much about the oscillation without any description about the dynamical coupling between the stratosphere and the troposphere
In this study, we reexamine the HHR93 results by performing much longer time integrations up to 2 years of a state-of-the-art regional CRM to describe the oscillation characteristics more precisely We also study robustness of the QBO-like oscillation
in a series of experiments by changing some model parameters
We focus on the phenomenological description in this letter, and detailed dynamical analyses of the oscillation, including a mo-mentum budget analysis, will be reported in a separated paper
2 Model and experimental design
The Advanced Research WRF (ARW) version 3 (Skamarock
et al 2008) is used to conduct a series of two-dimensional regional simulations of the tropical troposphere and stratosphere
A Minimal Model of QBO-Like Oscillation
in a Stratosphere-Troposphere Coupled System under a Radiative-Moist Convective Quasi-Equilibrium State
Shigeo Yoden1, Hoang-Hai Bui1, 2, and Eriko Nishimoto1
1Departmemt of Geophysics, Kyoto University, Kyoto, Japan
2Hanoi University of Science, Vietnam National University, Hanoi, Vietnam
Corresponding author: Shigeo Yoden, Kyoto University, Department of
Geophysics, Kitashirakawa Oiwake-cho, Sakyo-ku, Kyoto 606-8502,
Japan E-mail: yoden@kugi.kyoot-u.ac.jp ©2014, the Meteorological
Society of Japan
Trang 2Convective parameterization is turned off in all experiments WRF Single-Moment 6-class (WSM6) scheme is used for cloud microphysics to represent explicit moist convection As for the references for this scheme, see Skamarock et al (2008, Section 8.1.5) For radiation schemes, the Rapid Radiative Transfer Model
(RRTM) (ibid., Section 8.6.1) is used for longwave radiation, and MM5 (Dudhia) (ibid., Section 8.6.5) for shortwave radiation We
set the solar declination to the equinox condition and fix the solar insolation to the daily averaged value (436 W m−2) Planetary
boundary layer scheme is Yonsei University (YSU) PBL (ibid.,
Section 8.5.2) with surface fluxes based on Monin-Obukhov similarity theory, and the 1.5 order prognostic TKE closure option
(ibid., Section 4.2.4) is used for the eddy viscosities.
Nine experiments (2)−(10) as summarized in Table 1 are carried out to investigate sensitivity of the QBO-like oscillation obtained in Control case (1) to model configurations, boundary conditions, or cloud microphysics
3 Results
Figure 1 shows vertical profiles of the zonal mean temperature
in quasi-equilibrium state for Control case (black line behind green line) and the nine other cases of the experiments, together with the initial state (gray solid line) In all the experiments except for Warm rain case with Kessler scheme (Skamarock et al 2008, Section 8.1.1), QBO-like oscillations are obtained as described below (Figs 2 and 3) The zonal mean temperature for the nine cases (1)−(9) shows similar lapse rate (7.7 K km−1) as the observed climatology (i.e., the initial state), and has lower values about 5−10 K than the climatology through the troposphere; SST_30 case (orange line) is about 5 K lower, SST_25 (dark blue line) and Fine (gray dashed line) cases are the lowest over 10 K, and the others are in between The tropopause for the nine cases is located
at 11−13 km, several km below the climatology In Hitop cases (red line and black dashed line), temperature in the stratosphere is much lower than the climatology because of the lack of shortwave heating due to ozone
Note that the Warm rain experiment has a very different vertical profile of the zonal mean temperature (red dashed line) In this quasi-equilibrium state without QBO-like oscillation, moist convections are not very active and much smaller lapse rate of 3.2 K km−1 is maintained up to the elevated tropopause at the height of 24 km just below the Rayleigh damping layer The changed lapse rate would be a consequence of the very different spatial distributions of clouds and moisture that give different diabatic heating by the atmospheric radiation and cloud micro-physics
A periodic boundary condition is assumed in the zonal direction
so that the zonally averaged winds are free to evolve The Coriolis
parameter is set to zero
The control experiment has a similar configuration as HHR93;
640 km domain width with 5 km horizontal resolution and 130
vertical levels up to 26 km from the surface at the initial state At
the bottom boundary, SST is uniform and constant at 27°C At the
top boundary, a traditional Rayleigh damping layer is introduced
for 5 km depth to absorb vertically-propagating gravity waves by
relaxing dependent variables to the reference state given as the
initial condition
An idealized zonally uniform initial condition is given by the
climatological profiles of temperature and moisture on the equator
(gray solid line in Fig 1 for temperature) that were created from
the ERA-Interim reanalysis dataset (Dee et al 2011) and a
con-stant zonal wind of 5 m s−1 in the entire domain Time integrations
are made for two years with a time increment of Δt = 10 s.
Fig 1 Vertical profile of temperature at the initial state (gray solid line)
and those of the zonal mean temperature (°C) in quasi-equilibrium states
for ten sensitivity experiments The statistical equilibrium states are
ob-tained as time averages for complete cycles of the obob-tained QBO-like
oscillations, for Control case (black line behind green and light blue lines)
and the nine other cases of experiments (color lines as shown inside the
figure)
Table 1 List of the ten experiments performed in this study The first two columns are case number and name, and
the third one gives brief description of the difference from Control case (1) given as; time step, Δt = 10 s;
horizon-tal resolution, Δx = 5 km and grid number, Nx = 128 for the domain width of 640 km; vertical resolution, ∆z~200
m and grid number, Nz = 130 for the domain height Ztop = 26 km at the initial state; prescribed zonal wind at the top
boundary, Utop = 5 m s−1; SST = 27°C; and WRF Single-Moment 6-class scheme for cloud microphysics The fourth
and fifth columns are the mean and the standard deviation of the oscillation period in the unit of days, both of which
are calculated with the periods estimated from the zonal mean zonal winds for all the levels below the Rayleigh
damping layer Four cycles of the oscillation are used for the estimation except for Fine case (3), in which only one
cycle is used for the estimation (denoted by *)
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
Control Control_0 Fine Coarse Wide Hitop Hitop_0 SST_25 SST_30 Warm rain
See the caption
Utop = 0 m s−1
Δt = 5 s, Δx = 2 km, Nx = 320
Δx = 10 km, Nx = 64
Ztop = 40 km, Nz = 200
Ztop = 40 km, Utop = 0 m s−1
SST = 25°C SST = 30°C Kessler microphysics
120.6 135.0 124.6*
121.3 112.3 134.8 132.8 111.9 133.2
−
3.0 1.7 3.1*
0.5 1.4 0.9 0.4 0.6 0.7
−
Trang 3Figure 2 shows QBO-like oscillations of the zonal mean zonal
wind for (a) Control, (b) Control_0, (c) Hitop, and (d) Hitop_0
cases All of the cases show clear oscillations both in the
strato-sphere and the tropostrato-sphere with a kink around the tropopause If
we look at zero-wind lines in the plot of Hitop_0 case as an
exam-ple, we can easily identify the downward propagation of the
oscil-lation from the bottom of the Rayleigh damping layer (~30 km) to
the tropopause (~13 km) at a mean speed of roughly 170 m day−1
(the descending time is about 100 days) The downward
propaga-tion is slower in Control_0 case with 120 m day−1 (about 65 days
for the height range from 20 km to 12 km) Downward
propaga-tion of the oscillapropaga-tion continues to the surface at a mean speed of
about 260 m day−1 (about 50 days from 13 km to 0 km) in Hitop_0
case
The QBO-like oscillation of the zonal mean zonal wind is
symmetric with respect to the zero wind in the cases with Utop =
0 m s−1 (Figs 2b, d), whereas positive wind phase is longer and its
maximum wind speed is larger in the cases with Utop = 5 m s−1 (Figs
2a, c) Dependence of the asymmetric nature of the oscillation
on the top boundary condition Utop is clear throughout the strato-sphere and the tropostrato-sphere
The oscillation period is not very different for all the cases as listed in Table 1 (the fourth column); from 111.9 days for SST_25
to 135.0 days for Control_0 The estimation of the mean period
of the oscillation is robust with small standard deviation, 3.1 days
at most, throughout the stratosphere and troposphere (the last column) Note that the oscillation period becomes longer as SST increases from 25 to 30°C, as opposed to the expectation of
short-er pshort-eriod due to more convections
Figure 3 shows the time mean and variations of the zonal mean zonal wind for eight cases The time mean (thick line) is almost 0 m s−1 in Control_0 (b) and Hitop_0 (f) cases with Utop =
0 m s−1 due to the symmetric nature of the oscillation as described above In the cases with Utop = 5 m s−1 except for Hitop case (e),
on the other hand, the time mean is greater than Utop in the strato-sphere and the upper tropostrato-sphere The variable range also shows
Fig 2 Time-height sections of the zonal mean zonal wind (m s−1) for four cases of (a) Control, (b) Control_0, (c) Hitop, and (d) Hitop_0 Negative values are shaded A pair of vertical lines in each plot indicates the interval of full four cycles of oscillation
Fig 3 Statistical values of the zonal mean zonal wind variations (m s−1); the time mean (thick line), the time mean plus/minus one standard deviation (gray box), and maximum/minimum values (thin whiskers), for (a) Control, (b) Control_0, (c) Coarse, (d) Wide, (e) Hitop, (f) Hitop_0, (g) SST_25, and (h) SST_30 All values are calculated from the four oscillation cycles starting from day 100
Trang 4an almost symmetric profile with respect to the zero wind in the
two cases with Utop = 0 m s−1 (Figs 3b, f), whereas it is
asymmet-ric in the cases with Utop = 5 m s−1, largely due to the non-zero
values of the mean zonal wind and skewness of the variations
These asymmetric features of the oscillation are attributable to
the artificial top boundary condition for the zonal wind and the
asymmetry becomes smaller if the top boundary is moved upward
(e)
The amplitude of the oscillation has two peaks as shown in
Fig 3; in Hitop cases it has the maximum in the stratosphere at
~24 km and the second maximum at ~11 km, a few km below the
tropopause with a local minimum at ~13 km In the other cases
with Ztop = 26 km, the stratospheric maximum is comparable to or
smaller than the tropospheric maximum due to the influence of the
top boundary damping
Some other aspects of the QBO-like oscillation in the
stratosphere-troposphere coupled system are shown in Fig 4 for
Hitop_0 case Time variation of the zonal mean zonal wind in the
mid-stratosphere is characterized by rapid transition to the
oppo-site sign and very gradual approach to one of the extreme values
alternatively, in similar way as the observed QBO On the other
hand, the time variation in the troposphere shows more gradual
increase and decrease
Figure 4b shows a time-height section of the zonal mean
temperature anomaly from the time mean In the stratosphere, the
descent of warm anomalies is clear around the timing of the rapid
transition of the mean zonal wind, suggesting the importance of
vertical turbulent mixing associated with the large vertical shear in
the transition phase Tropospheric temperature also shows periodic
variations associated with the QBO-like oscillation, though there
is little phase lag through the troposphere in contrast to the mean
zonal wind oscillation The zonal mean daily precipitation (Fig
4c) also shows the time variation associated with the QBO-like
oscillation in the low-pass filtered component (thick blue line),
though high frequency components are dominant and produce
quite irregular variations
4 Discussion
We demonstrated the QBO-like oscillations of the zonal mean zonal wind have a clear signal even in the troposphere, in which organized convective momentum transport (Lane and Moncrieff 2010) might be important because of tilted convective structures
by vertical shear of the mean zonal wind (not shown) We also showed the zonal mean temperature and precipitation vary periodically in accordance with the mean zonal wind oscillations Further investigation on the interrelation between the mean zonal wind oscillations and moist convections in the troposphere is under way
The present experimental framework is highly idealized and simplified if compared to the real atmosphere This is a two- dimensional model on a non-rotating plane without Coriolis effects, instead of the three-dimensional atmosphere on the rotat-ing spherical earth Clear features of the QBO-like oscillations
in the troposphere obtained in this model may be weakened or smeared by the influences of such complicated processes in the real atmosphere However, we think the use of a hierarchy of numerical models, including this type of idealized simple one, is useful to deepen our dynamical understanding of the equatorial QBO and to reduce the gap between an idealized theory and the complex real atmosphere (Hoskins 1983; Held 2005) We can regard the present model as a minimal model, or a maximally simplified model to study the dynamics of the stratosphere- troposphere coupling process associated with the equatorial QBO Takahashi (1993) made a unique experiment with a two- dimensional model along the equator derived from a GCM with-out the rotation of the earth, and obtained a QBO-like oscillation with a period less than 100 days, with clear signal even in the troposphere and associated change in the direction of precipitation movement (his Figs 1b and 3) The model resolution was very coarse with the truncation zonal wavenumber of 10, and the convective parameterization of Kuo scheme was retained Some aqua-planet experiments with three-dimensional GCMs show QBO-like oscillations with a hint of associated variations in the troposphere (Horinouchi and Yoden 1998) However, most of the analyses in these studies were focused on the stratospheric part of the oscillation It would be timely to reinvestigate the dynamics of the QBO-like oscillations obtained in these hierarchies of ideal-ized two- and three-dimensional global models from a viewpoint
of stratosphere-troposphere dynamical coupling in the tropics The experimental framework introduced by HHR93 was quite unique in the sense that a self-sustained radiative-moist convective quasi-equilibrium state was obtained in a CRM In this minimal model, Rayleigh damping layer placed at the top bound-ary plays an important role to sustain a quasi-equilibrium state by absorbing vertically-propagating gravity waves and preventing their artificial reflection (Klemp et al 2008) Only a very weak cooling trend is discernible in the stratosphere for the two year integrations as shown in Fig 4b The altitude of the top boundary and the prescribed reference value in the Rayleigh damping layer are also important to determine the oscillation amplitude and the downward propagation speed of the oscillation signals as shown
in Figs 2 and 3 High frequency gravity waves with a large vertical group velocity are artificially attenuated in this damping layer to influence the zonal-mean momentum budget in the layer and below As shown in Fig 1, the thermal structure near the top boundary is also influenced by the relaxation process of artificial cooling in Warm rain case and heating in the other cases
Yoden and Holton (1988) studied symmetric or asymmetric features of a QBO-like oscillation in a simple stratosphere-only model, and showed that time variation of the zonal mean zonal wind is symmetric if the wave forcing is symmetric (or, a standing wave) at the bottom boundary, whereas it is not if the wave forcing
is not symmetric In this study with the minimal model of QBO-like oscillation, we demonstrated some examples of asymmetric time variations due to asymmetric (i.e., nonzero) zonal wind forcing given by the top boundary condition in Control and Hitop cases (Figs 2a, c) On the other hand, in Control_0 and Hitop_0
Fig 4 Several aspects of the QBO-like oscillation in Hitop_0 case; (a)
time variations of the zonal mean zonal wind (m s−1) at the heights given
by gray thin lines, (b) time-height section of the anomaly of the zonal
mean temperature (K) from the time mean, and (c) time variation of the
zonal mean daily precipitation (mm) and its 21-day running mean (thick
blue line)
Trang 5cases with the symmetric forcing, the time variation of the zonal
mean zonal wind is almost symmetric (Figs 2b, d), which is
im-plicitly indicative of symmetric nature of wave momentum fluxes
generated by moist convections in a statistical sense
5 Conclusions
We reexamined the QBO-like oscillation reported by Held
et al (1993), and robustly reproduced such oscillations in the
nine cases (Table 1) except for Warm rain case with Kessler cloud
microphysics The oscillation period is from 111.9 to 135.0 days,
which is not that sensitive to the choice of experimental
parame-ters The QBO-like oscillations show downward propagation of
zonal mean signals in the stratosphere, similar as the observations
(Fig 2) Even in the troposphere, the zonal mean temperature and
precipitation are also modulated in association with the QBO-like
oscillation of the zonal mean zonal wind (Fig 4)
The present model can be regarded as the minimal model that
can produce a QBO-like oscillation in the stratosphere-troposphere
coupled system under a radiative-moist convective
quasi-equilib-rium state, and the model would be useful for better understanding
the QBO dynamics Detailed dynamical analyses including
mo-mentum budget in the oscillation will be reported in a separated
paper
Acknowledgements
We thank Dale Durran for his helpful discussion and
com-ments on our numerical expericom-ments This work was supported
by JSPS KAKENHI (S) Grant Number 24224011 The stay of
HHB as a research fellow was supported by Kyoto University’s
Global COE Program ‘‘Sustainability/Survivability Science for a
Resilient Society Adaptable to Extreme Weather Conditions’’ for
FY2009-13
References
Alexander, M J., and J R Holton, 1997: A model study of zonal
forcing in the equatorial stratosphere by convectively
in-duced gravity waves J Atmos Sci., 54, 408−419.
Alexander, M J., J R Holton, and D R Durran, 1995: The
grav-ity wave response above deep convection in a squall line
simulation J Atmos Sci., 52, 2212−2226.
Baldwin, M P., L J Gray, T J Dunkerton, K Hamilton, P H
Haynes, W J Randel, J R Holton, M J Alexander, I
Hirota, T Horinouchi, D B A Jones, J S Kinnersley, C
Marquardt, K Sato, and M Takahashi1, 2001: The quasi-
biennial oscillation Rev Geophys., 39, 179−229.
Camargo, S J., and A H Sobel, 2010: Revisiting the influence of
the quasi-biennial oscillation on tropical cyclone activity J
Climate, 23, 5810−5825.
Collimore, C C., M H Hitchman, and D W Martin, 1998: Is
there a quasi-biennial oscillation in tropical deep
convec-tion? Geophys Res Lett., 25, 333−336.
Collimore, C C., D W Martin, M H Hitchman, A Huesmann,
and D E Waliser, 2003: On the relationship between the
QBO and tropical deep convection J Climate, 16, 2552−
2568
Dee, D P., S M Uppala, A J Simmons, P Berrisford, P Poli,
S Kobayashi, U Andrae, M A Balmaseda, G Balsamo,
P Bauer, P Bechtold, A C M Beljaars, L van de Berg,
J Bidlot, N Bormann, C Delsol, R Dragani, M Fuentes,
A J Geer, L Haimberger, S B Healy, H Hersbach, E V
Hólm, L Isaksen, P Kållberg, M Köhler, M Matricardi, A P McNally, B M Monge-Sanz, J.-J Morcrette, B.-K Park,
C Peubey, P de Rosnay, C Tavolato, J.-N Thépaut, and F Vitart, 2011: The ERA-Interim reanalysis: configuration and
performance of the data assimilation system Q J R Meteor
Soc., 137, 553−597, doi:10.1002/qj.828.
Fovell, R., D Durran, and J R Holton, 1992: Numerical simula-tions of convectively generated stratospheric gravity waves
J Atmos Sci., 49, 1427−1442.
Gray, W M., 1984: Atlantic seasonal hurricane frequency Part I: El Niño and 30 mb quasi-biennial oscillation influences
Mon Wea Rev., 112, 1649−1668.
Held, I M., 2005: The gap between simulation and understanding
in climate modeling Bull Amer Meteor Soc., 86, 1609−
1614
Held, I M., R S Hemler, and V Ramaswamy, 1993: Radiative- convective equilibrium with explicit two-dimensional moist
convection J Atmos Sci., 50, 3909−3927.
Holton, J R., and R S Lindzen, 1972: An updated theory for the
quasi-biennial cycle of the tropical stratosphere J Atmos
Sci., 29, 1076−1080.
Horinouchi, T., and S Yoden, 1998: Wave-mean flow interaction associated with a QBO-like oscillation simulated in a
simpli-fied GCM J Atmos Sci., 55, 502−526.
Hoskins, B J., 1983: Dynamical processes in the atmosphere and
the use of models Quart J Roy Meteor Soc., 109, 1−21.
Kawatani, Y., and K Hamilton, 2013: Weakened stratospheric quasibiennial oscillation driven by increased tropical mean
upwelling Nature, 497, 478−481, doi:10.1038/nature12140.
Klemp, J B., J Dudhia, and A D.Hassiotis, 2008: An upper
gravity-wave absorbing layer for NWP applications Mon
Wea Rev., 136, 3987−4004.
Lane, T P., and M W Moncrieff, 2010: Characterization of momentum transport associated with organized moist
con-vection and gravity waves J Atmos Sci., 67, 3208−3225
Lindzen, R S., and J R Holton, 1968: A theory of the quasi-
biennial oscillation J Atmos Sci., 25, 1095−1107.
Otobe, N., S Sakai, S Yoden, and M Shiotani, 1998: Visual-ization and WKB analysis of the internal gravity wave in
the QBO experiment Nagare: Japan Soc Fluid Mech., 17
[Available online athttp://www.nagare.or.jp/mm/98/otobe/ index.htm]
Plumb, R A., and A D McEwan, 1978: The instability of a forced standing wave in a viscous stratified fluid: A
laborato-ry analogue of the quasi-biennial oscillation J Atmos Sci.,
35, 1827−1839
Skamarock, W C., J B Klemp, J Dudhia, D O Gill, D M Barker, M G Duda, X.-Y Huang, W Wang, and J G
Powers, 2008: A description of the advanced research WRF
version 3 NCAR technical note, NCAR/TN–475+ STR, 113
pp
Takahashi, M., 1993: A QBO-like oscillation in a two-dimensional
model derived from a GCM J Meteor Soc Japan, 71, 641−
654
Takahashi, M., 1996: Simulation of the stratospheric quasi-
biennial oscillation using a general circulation model
Geo-phys Res Lett., 23, 661−664.
Yoden, S., and J R Holton, 1988: A new look at equatorial quasi-
biennial oscillation models J Atmos Sci., 45, 2703−2717.
Yoden, S., M Taguchi, and Y Naito, 2002: Numerical studies
on time variations of the troposphere-stratosphere coupled
system J Meteor Soc Japan, 80, 811−830.
Manuscript received 25 March 2014, accepted 19 June 2014 SOLA: https://www.jstage.jst.go.jp/browse/sola/