IOD influence on the early winter tibetan plateau snow cover:diagnostic analyses and an AGCM simulation
Chaoxia Yuan • Tomoki Tozuka • Toshio Yamagata
Received: 2 June 2011 / Accepted: 19 September 2011 / Published online: 30 September 2011
� Springer-Verlag 2011
Abstract Using diagnostic analyses and an AGCM simu-
lation, the detailed mechanism of Indian Ocean Dipole (IOD)
influence on the early winter Tibetan Plateau snow cover
(EWTPSC) is clarified. In early winter of pure positive IOD
years with no co-occurrence of El Nino, the anomalous
dipole diabatic heating over the tropical Indian Ocean excites
the baroclinic response in the tropics. Since both baroclinic
and barotropic components of the basic zonal wind over the
Arabian Peninsula increase dramatically in early winter due
to the equatorward retreat of the westerly jet, the baroclinic
mode excites the barotropic Rossby wave that propagates
northeastward and induces a barotropic cyclonic anomaly
north of India. This enables the moisture transport cycloni-
cally from the northern Indian Ocean toward the Tibetan
Plateau. The convergence of moisture over the plateau
explains the positive influence of IOD on the EWTPSC. In
contrast, the basic zonal wind over the Arabian Peninsula is
weak in autumn. This is not favorable for excitation of the
barotropic Rossby wave and teleconnection, even though the
IOD-related diabatic heating anomaly in autumn similar to
that in early winter exists. This result explains the insignifi-
cant (significant positive) partial correlation between IOD
and the autumn (early winter) Tibetan Plateau snow cover
after excluding the influence of ENSO. The sensitivity
experiment forced by the IOD-related SST anomaly within
the tropical Indian Ocean well reproduces the baroclinic
response in the tropics, the teleconnection from the Arabian
Peninsula, and the increased moisture supply to the Tibetan
Plateau. Also, the seasonality of the atmospheric response to
the IOD is simulated.
Keywords Indian Ocean Dipole � Winter Tibetan
Plateau snow cover � Wave-activity flux � Ray tracing �Teleconnection � Barotropic mode � Baroclinic mode �AGCM simulation
1 Introduction
The Tibetan Plateau is the highest and biggest plateau in
the world; it occupies an area of around 1,000 by 2,500 km,
and has an average elevation of over 4,000 meters. Owing
to these unique geographical features, it plays an essential
role in the atmospheric circulation of the Northern
Hemisphere.
The mechanical effects of the plateau on the atmo-
spheric circulation have been examined since the late
1940s mostly to explain the asymmetry of atmospheric
circulation (e.g., Charney and Eliassen 1949; Bolin 1950).
The plateau is located right in the path of the midlatitude
westerly jet in autumn and winter. When hitting the pla-
teau, the westerlies are forced partly to ascend and partly to
detour (Trenberth and Chen 1988). Thus, large-scale quasi-
stationary waves are induced, contributing to the asym-
metry of zonal circulation. The resulting trough over East
Asia limits the precipitation upstream of the trough, and
causes an extensive arid climate there (Manabe and Broc-
coli 1990; Broccoli and Manabe 1992).
The thermal effects of the Tibetan Plateau have also
received much attention so far for their importance to
C. Yuan (&) � T. Tozuka � T. Yamagata
Department of Earth and Planetary Science,
Graduate School of Science, The University of Tokyo,
Tokyo 113-0033, Japan
e-mail: [email protected]
T. Tozuka
e-mail: [email protected]
T. Yamagata
e-mail: [email protected]
123
Clim Dyn (2012) 39:1643–1660
DOI 10.1007/s00382-011-1204-0
various aspects of the Asian climate (e.g., Reiter and Gao
1982; Hsu and Liu 2003; Duan and Wu 2005; Duan et al.
2005; Wang et al. 2008; Bao et al. 2010; Li et al. 2011).
The plateau is a huge heat source in the middle troposphere
in summer months (March-September) and a heat sink in
winter months (October-February) (e.g., Flohn 1957; Yeh
et al. 1957; Ye and Wu 1998). The heating (cooling) of the
plateau in summer (winter) months causes a strong
ascending (descending) motion of airflows over the plateau
and a corresponding convergence (divergence) in the lower
troposphere. This helps the seasonal reversal of atmo-
spheric circulation over the Asian-Australian monsoon
regions (Wu et al. 2007). Also, it influences the onset of the
Asian and Indian summer monsoons; the increase of air
temperature over the eastern plateau and southern China in
May reverses the land-sea thermal contrast and triggers the
onset of the southeast Asian summer monsoon; the increase
of air temperature over Iran and the western plateau in June
leads to the onset of the Indian summer monsoon (e.g., He
et al. 1987; Yanai et al. 1992).
The heating of the plateau is mainly contributed by the
sensible heat flux, especially during the pre-monsoon sea-
son (Li and Yanai 1996; Ye and Wu 1998). Hence, it is
greatly influenced by surface thermal conditions. In winter
months, the ground is frozen, and snow is the main form of
precipitation (Sato 2001). With the presence of snow, the
surface albedo is dramatically increased, and more
incoming solar radiation is reflected. The surface albedo of
fresh snow can reach 0.9, much higher than the globally
average one of 0.3. Also, extra solar energy is used to melt
the snow and to evaporate the water, rather than to heat the
ground (e.g., Shukla 1984; Shukla and Mooley 1987;
Yasunari et al. 1991). The consequent lower surface tem-
perature reduces the amount of sensible heat flux to the
overlying atmosphere and results in a decrease of the
overlying air temperature. In this sense, Yasunari (2007)
and Turner and Slingo (2010) regard snow cover as the
most important factor for the surface thermal condition
over the Tibetan Plateau.
The anomalous snow accumulation in winter over the
Tibetan Plateau experiences a strong interannual variation
(Yuan 2011; Yu et al. 2011). Due to the high altitude of
the Tibetan Plateau, the winter snow anomaly keeps a
significant positive correlation with the snow anomaly in
the subsequent spring and summer. Shaman and Tziperman
(2005) showed the significant positive correlation between
winter and the subsequent summer snow depths. The early
winter snow cover also has a long-lasting positive corre-
lation with the snow cover from winter to the subsequent
early summer (Yuan 2011). Therefore, the winter snow
anomaly influences not only the winter climate but also the
subsequent summer climate via its long-lasting influences
on the surface thermal condition. This has in fact been
noticed for a long time. Blanford (1884) hypothesized a
negative correlation between the winter snow accumulation
over the Himalayas (southern edge of the Tibetan Plateau)
and the subsequent summer monsoon rainfall over the
western India. Since then, especially after the 1970s, when
the satellite observations of snow cover over the Eurasian
continent were first available, many studies have been
devoted to the lagged impacts of the winter snow anomaly
on the subsequent summer climate (e.g., Hahn and Shukla
1976; Barnett et al. 1989; Fasullo 2004). In this sense,
deeper understanding on the interannual variability of
winter snow accumulation over the Tibetan Plateau not
only improves our understanding of winter atmospheric
circulation but also benefits the seasonal predictability of
the Asian summer climate.
Shaman and Tziperman (2005) examined the role of sea
surface temperature (SST) anomaly related to the El Nino/
Southern Oscillation (ENSO) in the tropical Pacific on the
interannual variability of winter snow depth over the
Tibetan Plateau, and claimed a positive influence of ENSO.
Since the ENSO and the Indian Ocean Dipole (IOD, Saji
et al. 1999) sometimes co-occur, Yuan et al. (2009) ana-
lyzed the respective influences of IOD and ENSO. In
marked contrast to Shaman and Tziperman (2005), they
found that the IOD rather than the ENSO is related to an
increase of the early winter Tibetan Plateau snow cover
(EWTPSC). The positive IOD event is associated with a
barotropic cyclonic anomaly north of India. The barotropic
cyclonic anomaly transports extra moisture from the
northern Indian Ocean to the Tibetan Plateau, and results in
an increase of precipitation and snow cover there (Lang
and Barros 2004; Ueno 2005).
However, in Yuan et al. (2009), the detailed mechanism
leading to the barotropic cyclonic anomaly north of India in
early winter has not been clarified yet. In fact, no research
to date has systematically described the circulation anom-
aly related to the IOD in early winter. Therefore, in this
study, based on the observational data, various diagnostic
methods are applied to investigate the circulation anomaly
generated by the IOD-related diabatic heating in early
winter. This completes the key step in understanding the
influence of IOD on the EWTPSC. Then, an atmospheric
general circulation model (AGCM) is adopted to reproduce
this circulation anomaly to provide us a deeper insight into
the IOD-EWTPSC relationship. In most AGCMs, the land
surface scheme is not sophisticated enough to resolve
interannual variations of the regional snow cover (e.g., Frei
and Gong 2005; Khan et al. 2008). Therefore, attentions
are paid to the circulation anomaly related to the IOD in
early winter that has been attributed to increase the mois-
ture supply to the Tibetan Plateau.
The content of the present work is organized as follows.
In Sect. 2, the data and diagnostic methods used in the
1644 C. Yuan et al.: IOD influence on the early winter tibetan plateau snow cover
123
study are introduced. Based on the observational data, Sect.
3 analyzes the atmospheric response to the IOD in early
winter, and explains the mechanism generating the baro-
tropic cyclonic anomaly north of India. In Sect. 4, the
AGCM is applied to reproduce the observed circulation
anomaly related to the IOD and to confirm the mechanism
of the positive IOD-EWTPSC relationship. The final sec-
tion summarizes and discusses the main results.
2 Description of the data and diagnostic methods
2.1 Data
The monthly data from Hadley Centre sea ice and sea
surface temperature (HadISST, see Rayner et al. 2003) and
that of atmospheric fields from the National Centers for
Environmental Prediction and National Center for Atmo-
spheric Research Reanalysis Project (NCEP/NCAR
reanalysis, see Kalnay et al. 1996) are used for a period
from January 1960 to December 1999.
To be consistent with Yuan et al. (2009), the Dipole
Mode Index (DMI) in the present work is defined as the
peak period (September-November) SST anomaly differ-
ences between the western (40�–60�E, 10�S–10�N) and
eastern (90�–110�E, 10�S–Equator) poles of IOD to reflect
its interannual variation. However, conclusions are basi-
cally the same if a conventional definition of DMI is
adopted (Saji et al. 1999). The index of ENSO is also the
peak period (November–January) Nino-3 (90�–150�W,
5�S–5�N) SST anomaly.
2.2 Partial correlation and regression
The partial correlation and regression analyses are applied
to separate the influence of IOD from that of ENSO. The
formula of partial correlation is the same as in Yuan et al.
(2009). All time series used for the partial correlation
analysis are linearly detrended. The anomalous field par-
tially regressed on the IOD after excluding the influence of
ENSO is calculated by product of the partial correlation
coefficient between the field and IOD and one standard
deviation of the field.
2.3 Matsuno-Gill model
Matsuno (1966) studied the atmospheric response to a
sinusoidal diabatic forcing along the Equator. He showed
that, without a basic state, the dominant circulation
anomaly is trapped in the tropics with a pair of cyclonic
(anticyclonic) anomalies that straddle the Equator to the
west of the positive (negative) heating as the stationary
Rossby wave response and an easterly (westerly)
anomaly along the Equator to the east of the positive
(negative) heating as the stationary Kelvin wave
response. The circulation anomaly in the upper tropo-
sphere is opposite to that in the lower troposphere due to
the assumption of the pure baroclinic response in the
tropics (Gill 1980; Geisler and Stevens 1982; Kasahara
and Puri 1981).
The IOD-related SST anomaly remains significant in both
its western and eastern poles in early winter (Fig. 1). Above
the SST anomaly, a considerable diabatic heating anomaly is
induced in the tropics, as revealed by the outgoing longwave
radiation (OLR) anomaly in Fig. 2a. Hence, following
Matsuno (1966) and Gill (1980), the Matsuno-Gill model is
used in this study to diagnose the tropical atmospheric
response to the IOD-related diabatic heating.
In the Matsuno-Gill model (see 2 in Appendix 1), the
heating rate Q is set as a dipole along the Equator to mimic
the diabatic heating anomaly related to the IOD. It is
depicted in Fig. 3a and expressed as
Q ¼ Qþ þ Q� ; ð1aÞ
Qþ ¼0 x\� 3L�cosðkxÞeð�1
4y2Þ �3L� x� � L
0 x [ � L; k ¼ p
2L;
8<
:
ð1bÞ
Q� ¼0 x\L�cosðkxÞeð�1
4y2Þ L� x� 3L
0 x [ 3L; k ¼ p
2L:
8<
:
ð1cÞ
Here, Q? (Q-) denotes the western heating (eastern cool-
ing). The description of the Matsuno-Gill model and the
solutions to the dipole diabatic heating are shown in
Appendix 1.
In reality, the diabatic heating anomaly related to the
IOD is not exactly symmetric about the Equator; the neg-
ative heating anomaly over the eastern pole is shifted to the
Southern Hemisphere. However, a small deviation of the
diabatic heating from the Equator does not dramatically
change the pattern of atmospheric response; it only leads to
an asymmetry in amplitude with the larger amplitude in the
hemisphere to which the heating is shifted (Gill 1980;
Kasahara 1984).
2.4 Wave-activity flux
The atmospheric response to the tropical diabatic heating is
not confined to the tropics. In the presence of zonal wind
with vertical shear, the barotropic mode is excited (Lim
and Chang 1986; Kasahara and Dias 1986). The resulting
barotropic mode with the same phase as the upper part of
the baroclinic mode propagates poleward, and transports
wave energy to mid-high latitudes (Lee et al. 2009).
C. Yuan et al.: IOD influence on the early winter tibetan plateau snow cover 1645
123
To examine the above, the analysis of wave-activity flux
is useful. The wave-activity flux vector is parallel to the
propagation direction of wave energy under both the quasi-
geostrophic approximation and the Wentzel-Kramers-
Brillouin (WKB) approximation. It can be used to diagnose
the generation, propagation, and absorption of wave
packets in a slowly varying basic flow. As in Yuan et al.
(2009), the formula of wave-activity flux vector W derived
by Takaya and Nakamura (2001) is used in this study.
2.5 Ray tracing
The wave-activity flux tracks the propagation of wave
energy of all waves with various wavenumbers as a whole,
and hence contains no phase information. In contrast, a ray
is defined to be in the direction of the local group velocity
of the wave with a specific wavenumber. By tracing the
ray, the propagation of wave energy of the specific wave
can be tracked. Readers are referred to Appendix 2
for details of the ray tracing method used in the present
work.
3 Atmospheric response to the IOD in early winter
3.1 Atmospheric response in the tropics
Figure 3b shows the steady atmospheric response in the
lower troposphere to the dipole heating located along the
Equator (Eq. 1, Fig. 3a) in the Matsuno-Gill model (Eq. 2)
with L = 1 and e ¼ 0:1. There is a clear pair of anticy-
clonic (cyclonic) anomalies straddling the Equator as the
Fig. 1 November–December SST anomaly (�C) partially regressed on the IOD, after excluding the influence of ENSO. Anomalies at a 90%
confidence level by the two-tailed t test are shaded
(a)
(b)
Fig. 2 November–December OLR anomalies (contour interval is
2 W m�2) obtained from a the partial regression on the IOD after
excluding the influence of ENSO with the NCEP/NCAR reanalysis
data and b the AGCM result for a pure positive IOD experiment
(P-IOD) as discussed in Sect. 4. Anomalies at the 90% confidence
level by the two-tailed t test are shaded
1646 C. Yuan et al.: IOD influence on the early winter tibetan plateau snow cover
123
stationary Rossby wave response. Poleward flow exists at
the western (eastern) edge of the pair of anticyclones
(cyclones). Along the Equator, easterlies (westerlies) lie
east (west) of the positive heating. Note that the easterlies
are stronger than the westerlies because the easterlies are
composed of the mixture of the easterlies associated with
the stationary Kelvin wave response to the positive heating
in the west and the stationary Rossby wave response to the
negative heating in the east. Due to an offset effect of the
stationary Kelvin wave response to the positive and nega-
tive heatings, no significant flow is seen along the Equator
to the east of the negative heating. Also, strong conver-
gence (divergence) and ascent (descent) occur over the
positive (negative) heating regions (Fig. 3c). Because of
the nature of the Matsuno-Gill model, the circulation
anomaly in the upper troposphere is assumed to be oppo-
site, forming the baroclinic structure in the vertical direc-
tion. In the observations, the streamfunction anomaly
related to the IOD at 850 hPa in the lower troposphere
shows a pair of anticyclonic (cyclonic) anomalies strad-
dling the Equator west of the negative (positive) heating
anomaly (Fig. 4a). Notice that the cyclone northwest to the
diabatic heating over the Arabian Peninsula is not as
apparent as in the Matsuno-Gill model. This is caused by
an offset effect of barotropic Rossby waves generated there
with opposite sign of anomaly, and will be discussed in the
following subsection. Northward flow is observed along the
western edge of the anticyclonic anomaly over the Bay of
Bengal. This carries the moisture toward the Indian sub-
continent, as shown later in Fig. 7a. At 250 hPa in the
upper troposphere, the anomalous pattern is reverse; a
cyclonic (anticyclonic) anomaly is seen over the Bay of
Bengal (Arabian Peninsula) (Fig. 4c). This baroclinic
response in the tropics becomes clearer in the zonal-verti-
cal sections of the streamfunction anomaly averaged over
5�–15�N and 5�–15�S in Fig. 5a, c. Also, ascending
(descending) motion prevails over the positive (negative)
heating regions consistent with the Matsuno-Gill model.
In general, the observed circulation anomaly related to
the IOD is consistent with the result of the Matsuno-Gill
model, confirming the baroclinic response to the IOD-
related diabatic heating anomaly. It is worth mentioning
that the basic flow in the Matsuno-Gill model is set to zero,
which is different from reality. Lau and Lim (1982) added
the basic flow to the model, and found that the anomalous
circulation pattern in the tropics doesn’t change much.
With the presence of westerly (easterly) lower tropospheric
winds, the Rossby wave response becomes stronger
(weaker) in amplitude but extends less (further) westward,
however, the Kelvin wave response becomes weaker
(stronger) but extends further (less) eastward. The pair of
Rossby wave response to the eastern diabatic heating
anomaly over the eastern tropical Indian Ocean are zonally
elongated probably due to the effects of the easterly basic
flow there (Fig. 4a).
3.2 Atmospheric response in mid latitudes
At 250 hPa, the center of the cyclonic anomaly north of the
Bay of Bengal is much farther north than that of the anti-
cyclonic anomaly over the Arabian Peninsula (Fig. 6a).
Therefore, the cyclonic anomaly is not just the upper-layer
counterpart of the lower-layer anticyclonic anomaly over
the Bay of Bengal. The meridional-vertical section of the
(a)
(b)
(c)
Fig. 3 Non-dimensionalized heating located along the Equator as
described by Eq. 1 and the steady atmospheric responses. a Dipole
diabatic heating. b Streamfunction (contour interval is 3 9 105) and
wind (vector) anomalies. c Velocity potential (contour interval is
3 9 105) and divergent wind (vector) anomalies. Winds with
magnitudes less than 0.04 in b and 0.02 in c are not shown
C. Yuan et al.: IOD influence on the early winter tibetan plateau snow cover 1647
123
streamfunction anomaly averaged over 80�–100�E shows
that the vertical structure is baroclinic from 10�N to about
28�N as the atmospheric response to the diabatic heating
anomaly in the tropics (Fig. 6c). However, from 28�N
northward, the vertical structure becomes barotropic. It is
by this barotropic cyclonic circulation anomaly north of
India that the moisture from the Arabian Sea, the Indian
subcontinent, and the Bay of Bengal is transported cycl-
onically to the Tibetan Plateau (Yuan et al. 2009; Fig. 7a),
explaining the positive influence of IOD on the EWTPSC.
The barotropic cyclonic anomaly north of India may be
generated by the northeastward propagation of the sta-
tionary Rossby wave from the Arabian Peninsula. Due to
the equatorward retreat of the westerly jet over the Eur-
asian continent in early winter (Fig. 8a), the Arabian
Peninsula is covered by the westerly at 250 hPa. As a
result, both barotropic and baroclinic components of the
basic zonal wind increase dramatically, as represented by
the dramatic increase of sum and difference of the clima-
tological zonal wind at 250 and 850 hPa averaged over
(20�-80�E, 15�-20�N), respectively. As seen in Fig. 9a, the
baroclinic (barotropic) component reaches 25 m s�1
ð15 m s�1Þ in December. This sets up the environment to
generate the barotropic component (Lim and Chang 1986;
Kasahara and Dias 1986). The resulting barotropic mode
with the same phase as the upper part of the baroclinic
mode propagates poleward, and transports wave energy to
higher latitudes (Lee et al. 2009). To show this wave
energy transport, the wave-activity flux at 250 hPa is cal-
culated. As shown in Fig. 10a, a significant amount of
wave-activity flux emanated from the Arabian Peninsula
propagates northeastward, and mostly converges north of
India. This confirms that the barotropic mode is indeed
generated over the Arabian Peninsula in early winter, and
transports the wave energy to the north of India.
Since the wave-activity flux does not contain the phase
information during the propagation, the ray tracing method
is applied to confirm the generation of the cyclonic
anomaly north of India by the anticyclonic anomaly over
the Arabian Peninsula. As introduced in Appendix 2, the
ray tracing not only tracks the ray but also marks the phase
change along the ray. It is often conducted at the upper
troposphere for the stationary Rossby wave, and the cli-
matology of zonal wind there is then used as the basic state
(b)
(d)
(a)
(c)
Fig. 4 November–December streamfunction (contour interval is
3� 105 m2 s�1) and velocity (vector, m s�1) anomalies at a, b 850
and c, d 250 hPa obtained from (left panels) the partial regression on
the IOD after excluding the influence of ENSO with the NCEP/NCAR
reanalysis data and (right panels) the P-IOD. Velocity anomalies at
the 90% confidence level by the two-tailed t test are shown only.
Streamfunction anomalies at 90 and 99% confidence levels are
shaded
1648 C. Yuan et al.: IOD influence on the early winter tibetan plateau snow cover
123
(Karoly 1983; Shaman and Tziperman 2005). Therefore,
November–December climatology at 250 hPa is used as the
basic state for the ray tracing in this study. Figure 11a, c
and e show the horizontal distributions of zonal wind ( �U),
meridional derivative of the absolute vorticity ( �Qy), and the
stationary wavenumber (Ks). It is seen that the midlatitude
westerly jet demarcates the zonal maximum bands of both�Qy and Ks. According to the wave-guide theory (Hoskins
and Ambrizzi 1993), the zonal maximum band of Ks acts as
a wave-guide; once the ray enters the wave-guide, it will be
trapped and propagate in the downstream direction because
rays tend to be refracted toward the larger Ks.
The origin of ray is set at (55�E, 18�N) over the Arabian
Peninsula. The initial zonal wavenumber k is chosen as 5 to
satisfy the WKB approximation because Ks at the origin is
around 7. The ray is integrated until the first phase change
of p and marked at one hour interval. As shown in Fig. 12a,
the ray starts from the Arabian Peninsula, propagates
northeastward, and has the first phase change of p north of
India. This is not surprising because the observed wave
pattern from the Arabian Peninsula to the north of India has
the zonal wavenumber around 5. Therefore, the result
confirms that the anticyclonic anomaly over the Arabian
Peninsula can lead to the barotropic cyclonic anomaly
north of India by the propagation of stationary Rossby
wave. This result is not sensitive to a small shift of the
origin as long as the shift is about ±5� (10�) in meridional
(zonal) direction and a small change in the initial k. With
the initial k of 6, the ray still has the first phase change of pnorth of India (Fig. 12c), but the angle of the ray to the
zonal direction becomes smaller compared with the case
of k = 5 owing to the increase of k and the fixed value of
Ks.
3.3 Seasonality of the atmospheric responses
The SST anomaly and the corresponding OLR anomaly in
September–October in the tropics related to the IOD are
very similar to those in early winter, except that the
anomalies over the eastern pole are stronger in September–
October than in early winter (not shown). By the diabatic
heating anomaly, the anticyclonic anomaly over the Bay of
Bengal extends farther westward and covers most of the
northern tropical Indian Ocean at 850 hPa (not shown). At
250 hPa (Fig. 13a), the cyclonic anomaly is seen from the
Bay of Bengal to India, but much weaker than the one in
(b)
(d)
(a)
(c)
Fig. 5 November–December streamfunction (contour interval is
3� 105 m2 s�1) and velocity (vector, m s�1) anomalies in zonal-
vertical sections averaged over a 5–15�N and c 5�–15�S partially
regressed on the IOD after excluding the influence of ENSO with the
NCEP/NCAR reanalysis data, and b Equator–15�N and d Equator–
15�S in the P-IOD. Velocity anomalies at the 90% confidence level by
the two-tailed t test are shown only. Streamfunction anomalies at 90
and 99% confidence levels are shaded
C. Yuan et al.: IOD influence on the early winter tibetan plateau snow cover 1649
123
early winter (Fig. 6a). In addition, it is confined to the
upper troposphere in the tropics as the upper-layer coun-
terpart of the lower-layer anticyclonic anomaly (Fig. 13c).
Since no barotropic cyclonic anomaly is observed north of
India, the teleconnection from the Arabian Peninsula to the
north of India by the propagation of the barotropic sta-
tionary Rossby wave is not present in September–October.
Although the IOD-related diabatic heating anomaly over
the tropical Indian Ocean in autumn is similar to that in
early winter, the induced atmospheric response is quite
different owing to a significant seasonal variation of the
basic state, as revealed by the seasonal march of westerly
jet (Fig. 8a). The barotropic component of the basic zonal
wind over the Arabian Peninsula is easterly in September
and vanishes in October; the baroclinic component changes
sign from September to October (Fig. 9a). This basic state
is certainly not favorable for generation of the barotropic
Rossby wave and the consequent teleconnection from the
Arabian Peninsula. The result is consistent with the partial
correlation between IOD and the Tibetan Plateau snow
cover after excluding the effects of ENSO. As shown in
Yuan et al. (2009), the partial correlation coefficient
between IOD and September-October Tibetan Plateau
snow cover is -0.1, insignificant; that between IOD and
November–December Tibetan Plateau snow cover is 0.4 at
a 95% significant level by the two-tailed t test for the data
set from 1973 to 1999.
4 AGCM simulation of the IOD influence on the snow
cover over the Tibetan Plateau in early winter
4.1 Description of the model and experiments
The AGCM adopted here is Frontier Atmospheric Model
(FrAM) version 1.1. It was originally developed at the
Climate Variation Research Program of Frontier Research
Center for Global Change, Japan Agency for Marine-Earth
Science and Technology (JAMSTEC). The model has 28
vertical levels from the surface to 10 hPa in the hybrid
vertical coordinate system; the sigma (isobaric) coordinate
is used at the surface (stratosphere). It is horizontally
truncated at T42, corresponding to a horizontal resolution
of 2.8125�. Various parameterizations are used for the
model physics; the cumulus convection scheme is based on
Emanuel (1991), the land surface scheme is based on
Viterbo and Beljaars (1995), the longwave radiation
scheme is after Shibata (1989) and Shibata and Aoki
(1989), and the shortwave radiation scheme is after Lacis
and Hansen (1974). The model has successfully simulated
(b)
(d)
(a)
(c)
Fig. 6 November–December streamfunction anomalies (contour
interval is 5� 105 m2 s�1) at a, b 250 hPa, and in c 80�–100�E and
d 70�–90�E meridional-vertical sections obtained from (left panels)
the partial regression on the IOD after excluding the influence of
ENSO with the NCEP/NCAR reanalysis data and (right panels) the
P-IOD. Topography is indicated by black shading. Streamfunction
anomalies at 90 and 99% confidence levels by the two-tailed t test are
shaded
1650 C. Yuan et al.: IOD influence on the early winter tibetan plateau snow cover
123
(a)
(c)
(b)
(d)
Fig. 7 November–December
vertically integrated anomalies
of a, b moisture flux (vector,
Kg m�1 s�1) and c, d its
convergence (shading interval
is 3� 105
Kg m�2 s�1) obtained
from (left panels) the partial
regression on the IOD after
excluding the influence of
ENSO with the NCEP/NCAR
reanalysis data and (rightpanels) the P-IOD. Moisture
flux anomalies at the 90%
confidence level by the two-
tailed t test are thickened
(b)
(a) Fig. 8 Seasonal march of the
south flank of westerly at 250
hPa from July–August to
November–December obtained
from a the NCEP/NCAR
reanalysis data and b the
AGCM result for the control
experiment (CTRL) as
discussed in Sect. 4
C. Yuan et al.: IOD influence on the early winter tibetan plateau snow cover 1651
123
the IOD-related climate variations in many studies such as
the summer atmospheric circulation in the tropics (Guan
et al. 2003), the summer monsoon precipitation in India
(Ashok et al. 2004), and the winter moisture supply to the
Arabian Peninsula (Chakraborty et al. 2006).
Two experiments are conducted. Each has 20 ensemble
members starting from different initial conditions, and is
integrated for one calendar year from May 1st to April 30th
in the following year. The same set of initial condition is
used for the two experiments. The control experiment
(CTRL) is forced by the monthly climatology of HadISST
as the lower boundary condition to remove the interannual
variability of SST. The sensitivity experiment (P-IOD) is
aimed to simulate the atmospheric circulation anomaly in a
pure positive IOD year with no co-occurrence of El Nino.
Hence, the P-IOD is forced by the monthly climatology of
HadISST plus the SST anomaly partially regressed on the
IOD after removing the impact of ENSO. The SST
anomaly is only applied within the tropical Indian Ocean
from 20�S to 20�N. At the open boundaries in the north,
south and east, additional 10� buffer regions are added.
The ensemble mean of CTRL is used as the model cli-
matology, and validated against the climatology of NCEP/
NCAR reanalysis. The anomaly of P-IOD is defined as the
mean deviation of the 20 ensemble members of P-IOD
from the model climatology. Zonal mean fields for the
zonal wind and the geopotential height are further removed
to highlight a zonal wave pattern. The two-tailed t test is
used to check the statistical significance of the anomaly.
4.2 CTRL experiment
Prior to investigating the impact of IOD on the atmospheric
circulation, it is necessary to check the performance of the
present model. The CTRL well simulates the equatorward
retreat of westerly jet over the Eurasian continent from
summer to winter (Fig. 8b) The dramatic increase of both
barotropic and baroclinic components of the zonal wind
over the Arabian Peninsula from summer to winter is also
reproduced rather well (Fig. 9b). Note that in early winter,
the southern edge of the midlatitude westerly jet in the
CTRL at 250 hPa extends farther southward than that in the
NCEP/NCAR reanalysis. This results in a stronger baro-
clinic component of the zonal wind by 5 m s�1 over the
Arabian Peninsula and the coverage of westerly over
Somalia. The horizontal distributions of zonal wind ( �U),
meridional derivative of the absolute vorticity ( �Qy), and
stationary Rossby wavenumber (Ks) in early winter at 250
hPa are shown in Fig. 11b, d, and f. When compared to
those obtained from the NCEP/NCAR reanalysis, the
CTRL well captures the location and strength of the wes-
terly jet in the midlatitudes, the maximum bands of both �Qy
and Ks along the jet, and the distribution of equatorial
easterly. These basic state conditions are crucial for the
teleconnection related to the IOD in early winter, as dis-
cussed in Sect. 3 Therefore, the good correspondence
between the climatologies of model and the NECP/NCAR
reanalysis assures that this model can provide useful
insight into the atmospheric circulation anomaly related to
the IOD in early winter.
4.3 P-IOD experiment
4.3.1 Circulation anomaly in the tropics
The simulated OLR anomaly in the early winter of P-IOD
is consistent with the reanalysis data (Fig. 2). The negative
OLR anomaly extends from Eastern Africa to the central
tropical Indian Ocean, indicating the enhanced convective
activity associated with the positive SST anomaly in the
western pole of IOD. The positive OLR anomaly is over
(b)
(a)
Fig. 9 Seasonal march of barotropic (blue line) and baroclinic (red
line) components of the basic zonal wind (m s�1) over the Arabian
Peninsula represented by sum and difference of the climatological
zonal wind at 250 and 850 hPa averaged over (20�–80�E, 15�–20�N)
from a the NCEP/NCAR reanalysis data and b the CTRL
1652 C. Yuan et al.: IOD influence on the early winter tibetan plateau snow cover
123
the eastern tropical Indian Ocean, and indicates the sup-
pressed convection there due to the negative SST anomaly
in the eastern pole. However, the simulated OLR anomaly
over the western (eastern) tropical Indian Ocean is stronger
(weaker) than the observed one, suggesting that the con-
vection activity over the western (eastern) tropical Indian
Ocean in the FrAM may be more (less) sensitive to a small
SST anomaly than in reality.
The dipole convective anomaly induces a pair of anti-
cyclonic (cyclonic) anomalies straddling the Equator in the
lower troposphere (Fig. 4b), as in the reanalysis data
(Fig. 4a). Owing to the stronger (weaker) convective
anomaly in the western (eastern) tropical Indian Ocean in
the simulation, the simulated cyclonic (anticyclonic)
anomaly over the Arabian Peninsula (Bay of Bengal) is
stronger (weaker) than the observed one. Hence, the
anomalous airflow is advected to the Indian subcontinent
mainly by the cyclone over the Arabian Peninsula rather
than the anticyclone over the Bay of Bengal, in contrast to
the reanalysis data. At 250 hPa in the upper troposphere
(Fig. 4d), the circulation anomaly in the tropics is almost
reverse to that at 850 hPa (Fig. 4b), except that an easterly
anomaly extends westward from the northwestern tropical
Pacific to the eastern tropical Indian Ocean. This easterly
anomaly is related to the anticyclone in the northwestern
tropical Pacific, which may be generated by the stationary
Rossby wave propagation from the north of India, as will
be discussed later. Also, the center of the simulated
anticyclonic anomaly in the upper troposphere is located
around Somalia, about five degrees southwestward to that
of the observed. This southwestward shift of the simulated
anticyclone may be due to the further southward extension
of westerly jet in early winter of the CTRL (Fig. 8b).
The simulated baroclinic response in the tropics and the
strong ascent (descent) over the western (eastern) tropical
Indian Ocean is clearly seen in the zonal-vertical sections
(Fig. 5b, d). To show a better view, these sections are
averaged over Equator–15�N (Equator–15�S) in the P-IOD
rather than 5�–15�N (5�–15�S) in the reanalysis data by
taking the model bias into account.
4.3.2 Circulation anomaly in mid latitudes
The barotropic cyclonic anomaly north of India is also
reproduced in the P-IOD (Fig. 6b, d). In Sect. 3, it is shown
that the anomaly is generated through the teleconnection
from the Arabian Peninsula in early winter, when both
barotropic and baroclinic components of the basic zonal
wind there increase dramatically and enable generation of
the barotropic mode and the consequent teleconnection.
This is confirmed by the model. First, the CTRL well
captures the significant increase of both barotropic and
baroclinic components of the basic zonal wind (Fig. 9b).
This sets up the environment for generating the barotropic
mode (Lim and Chang 1986; Kasahara and Dias 1986; Lee
et al. 2009). The resulting barotropic mode propagates
(a)
(b)
Fig. 10 Wave-activity flux
(vector, m�2 s�2) calculated
from the November–December
streamfunction anomalies
(contour interval is
5� 105 m2 s�1) at 250 hPa
obtained from a the partial
regression on the IOD after
excluding the influence of
ENSO with the NCEP/NCAR
reanalysis data and b the P-IOD.
Fluxes less than 0:2 m�2 s�2 in
a and 0:1 m�2 s�2 in b are not
shown. Streamfunction
anomalies at 90 and 99%
confidence levels by the two-
tailed t test are shaded
C. Yuan et al.: IOD influence on the early winter tibetan plateau snow cover 1653
123
poleward, and transports the wave energy to higher
latitudes.
As shown in Fig. 10b, the wave-activity flux is ema-
nated from Somali and the Arabian Peninsula, propagates
northeastward, and mostly converges north of India. This
indicates that, in the P-IOD, the barotropic mode is indeed
generated over Somalia and the Arabian Peninsula, prop-
agates northeastward, and transports the wave energy to the
north of India to sustain the circulation anomaly there.
Notice that the cyclonic anomaly north of India in the
P-IOD is located southwestward to the observational one
due to the southwestward shift of the anticyclonic anomaly
over Somali and the Arabian Peninsula. The wave-activity
flux to the north of India also comes from the upstream of
the waveguide along the midlatitude westerly jet. Strong
fluxes start from the midlatitudes over the Atlantic Ocean,
propagate eastward to the Mediterranean Sea region, and
then bifurcate there (Fig. 10b). One branch propagates
northeastward to the high latitudes of the Eurasian conti-
nent; the other branch turns southeastward, propagates
along the waveguide, and mostly converges north of India.
The remaining fluxes propagate further to the northwestern
tropical Pacific, and may generate the anticyclonic anom-
aly there. As mentioned above, the anticyclone extends
westward to the eastern tropical Indian Ocean, and destroys
the baroclinic response there related to the eastern cooling
pole of the IOD.
In the P-IOD, forcing of the SST anomaly is confined to
the tropical Indian Ocean, but in reality, the significant SST
anomalies are found in other ocean basins such as in the
tropical Atlantic (Fig. 1). The positive SST anomaly there
and the resulting diabatic heating anomaly can generate a
strong teleconnection that crosses the northern Atlantic
Ocean and turns to the northern Eurasian continent, as
suggested by Hoskins and Ambrizzi (1993) and shown in
Fig. 10a. Since the atmospheric response over the northern
Atlantic Ocean to the interannual SST anomaly in the
tropical Atlantic may exceed that in the tropical Indian
Ocean, the Rossby wavetrain and wave energy propagation
along the midlatitude westerly jest in the P-IOD is not
clearly seen in the observations. However, the influence of
IOD is seen over regions at the rim of the Indian Ocean. It
(a) (b)
(c) (d)
(e) (f)
Fig. 11 November–December climatologies of a, b zonal wind
(contour interval is 10 m s�1), c, d meridional derivative of the
absolute vorticity (contour interval is 2� 10�11 m�1 s�1), and (e, f)
stationary Rossby wavenumber from 4 to 8 at 250 hPa from (left
panels) the NCEP/NCAR reanalysis data and (right panels) the
CTRL. Easterlies in the tropics are indicated by thick enclosed blacklines in a, b, e, and f
1654 C. Yuan et al.: IOD influence on the early winter tibetan plateau snow cover
123
is fair to say that the P-IOD captures to some extent the
observed teleconnection from around the Arabian Penin-
sula to the north of India.
Figure 12b, d show the ray tracing from around the
Arabian Peninsula. The ray starting from the origin at
(50�E, 15�N) with both initial zonal wavenumber 5 and 6
extends northeastward, and has the first phase change of pnorth of India. Therefore, the anticyclonic anomaly over
the Arabian Peninsula indeed leads to the generation of the
barotropic cyclonic anomaly north of India through the
propagation of the stationary Rossby wave. The result of
ray tracing is not sensitive to a small change in both origin
and initial zonal wavenumber.
Another important aspect of the above atmospheric
response suggested by the observation is that it is season-
ally dependent. As shown in Fig. 13b, no significant anti-
cyclonic anomaly exists around the Arabian Peninsula in
September-October of P-IOD. The significant cyclonic
anomaly from the Bay of Bengal to the northern India is
confined in the upper troposphere as the counterpart of the
anticyclonic anomaly in the lower troposphere, forming the
baroclinic response to the eastern cooling of IOD
(Fig. 13d). Therefore, no teleconnection appears from the
Arabian Peninsula to the north of India in autumn, which is
consistent with the observations (Fig. 13a, c).
4.3.3 Anomalous moisture transport to the Tibetan Plateau
Despite some discrepancies between the model results and
observations, the P-IOD well reproduces the baroclinic
response in the tropics and the teleconnection from around
the Arabian Peninsula to the north of India. This circulation
anomaly in the tropics advects moisture from the tropical
Indian Ocean to the Indian subcontinent (Fig. 7b). Note
that there is a difference between the simulated and
observed moisture transport to the Indian subcontinent; in
the former (latter), the moisture is advected mostly by the
strong cyclonic (anticyclonic) anomaly over the Arabian
Peninsula (Bay of Bengal) in the lower troposphere. By the
barotropic cyclonic anomaly north of India, the moisture in
the Indian subcontinent together with the moisture from the
Bay of Bengal is transported cyclonically further to the
Tibetan Plateau. Also, due to the southwestward shift of
the simulated cyclonic anomaly north of India, the
(a)
(c)
(b)
(d)
Fig. 12 Ray tracings for the stationary Rossby wave at 250 hPa
superimposed to the November–December streamfunction anomalies
(contour interval is 5� 105 m2 s�1) obtained from (left panels) the
partially regressed on the IOD, after excluding the influence of ENSO
and (right panels) the P-IOD. The ray with the origin (55�E, 18�N)
and initial zonal wavenumber a 5 and c 6 in left panels and the ray
with the origin (50�E, 15�N) and initial zonal wavenumber b 5 and d6 in right panels are integrated until the first phase change of p. Blackdots indicate the starting and ending points of the ray and green dotsmark 1 h integration. Streamfunction anomalies at 90 and 99%
confidence levels by the two-tailed t test are shaded
C. Yuan et al.: IOD influence on the early winter tibetan plateau snow cover 1655
123
simulated anomalous pattern of moisture flux is corre-
spondingly shifted southwestward to the observed one.
Nevertheless, the resulting convergence of moisture over
the plateau increases the possibility of precipitation and
snow cover (Fig. 7d). This supports our earlier hypothesis
that the positive IOD increases the EWTPSC.
5 Conclusions and discussions
The EWTPSC (early winter Tibetan Plateau snow cover)
has a prolonged cooling effect on the surface and overlying
air temperature from winter to the subsequent spring and
early summer, and hence plays a very important role on the
Asian summer climate. Yuan et al. (2009) have shown the
positive influence of IOD on the EWTPSC. In this study,
the detailed mechanism of the IOD influence on the EW-
TPSC is clarified by using various diagnostic methods and
the AGCM simulation.
In the early winter of pure positive IOD years, the dipole
diabatic heating anomaly over the tropical Indian Ocean
excites the baroclinic response in the tropics. In the lower
troposphere, a pair of stationary anticyclonic (cyclonic)
anomalies straddle the Equator as the stationary Rossby
wave response to the negative (positive) heating anomaly.
The anticyclonic anomaly over the Bay of Bengal induces
the northward flow along its western edge, and carries extra
moisture to the Indian subcontinent. Since both baroclinic
and barotropic components of the basic zonal wind over the
Arabian Peninsula increase dramatically in early winter, it
becomes more favorable for the excitation of the barotropic
mode (Lim and Chang 1986; Kasahara and Dias 1986; Lee
et al. 2009). The resulting barotropic Rossby wave propa-
gates northeastward, and induces a barotropic cyclonic
anomaly north of India. This transports the moisture
already advected to the Indian subcontinent from the
tropical Indian Ocean together with the moisture from the
Bay of Bengal and the Arabian Sea cyclonically toward
the Tibetan Plateau. The convergence of moisture over the
plateau increases the possibility of precipitation and snow
cover, and explains the positive influence of IOD and the
EWTPSC.
We note that the above atmospheric response to the IOD
is seasonally dependent. In contrast to early winter
(November-December), both barotropic and baroclinic
components of the basic zonal wind are weak over the
Arabian Peninsula in autumn (September–October). This is
not favorable for generation of the barotropic mode and the
consequent teleconnection. Therefore, the teleconnection
starting from the Arabian Peninsula, the barotropic cyclo-
nic anomaly north of India, and the increased moisture
supply to the Tibetan Plateau are not present, even though
the IOD-related diabatic heating anomaly in autumn is
similar to that in early winter. This result is consistent with
(a)
(d)
(b)
(c)
Fig. 13 As in Fig. 6, but for September-October
1656 C. Yuan et al.: IOD influence on the early winter tibetan plateau snow cover
123
the insignificant (significant positive) partial correlation
between IOD and September–October (November–
December) Tibetan Plateau snow cover after excluding the
influence of ENSO, as shown in Yuan et al. 2009.
We have used the AGCM of FrAM (Frontier Atmo-
spheric General Circulation Model) to reproduce the
observed circulation anomaly related to the IOD and to
explain the positive influence of IOD on the EWTPSC. In
the sensitivity experiment P-IOD, the FrAM is forced by
the SST climatology in all basins and the SST anomaly
within the tropical Indian Ocean related to the pure positive
IOD with no co-occurrence of El Nino. The convective
activity is enhanced (suppressed) over the western (eastern)
tropical Indian Ocean. This dipole convective anomaly
induces the baroclinic atmospheric response in the tropics.
In the lower troposphere, the cyclonic (anticyclonic)
anomaly is seen over the Arabian Peninsula (Bay of Ben-
gal), transporting extra moisture toward the Indian sub-
continent. The teleconnection from around the Arabian
Peninsula and the consequent generation of the barotropic
cyclonic anomaly north of India are also reproduced. By
the barotropic cyclonic anomaly, the extra moisture over
the Indian subcontinent together with the moisture from the
Bay of Bengal is transported cyclonically to the Tibetan
Plateau. The convergence of the moisture anomaly over the
plateau supports the positive correlation between IOD and
EWTPSC. In addition, the seasonality of the circulation
anomaly related to the IOD is also seen in the P-IOD; the
teleconnection from around the Arabian Peninsula to the
north of India is not present in autumn owing to the sig-
nificant seasonal variation of the basic state.
The IOD-related circulation anomaly in early winter not
only influences the EWTPSC but also the Indian winter
monsoon. The warm and humid air is advected from the
tropical Indian Ocean to the Indian subcontinent by the
anticyclonic anomaly over the Bay of Bengal in the lower
troposphere (Fig. 4a). These wind anomalies oppose the
climatological wind pattern in early winter in the Indian
subcontinent, and hence the Indian winter monsoon is
weakened. This supports Yang et al. (2010), who have
found that a positive IOD tends to decrease the Indian
winter monsoon. The increased moisture supply and con-
vergence over the central and southern China by the warm
and humid southwesterlies (Fig. 7a) may increase the
winter precipitation and even snowstorms there. The
extremely heavy snowstorm that hit the central and
southern China in January 2008 caused a huge economic
loss. This was closely related to these southwesterly
anomalies (Wen et al. 2009). More studies are certainly
needed to understand thoroughly the role of IOD in the
winter climate variation from both scientific and societal
viewpoints.
Acknowledgments We thank Drs. H. Nakamura, T. Hibiya, Y.
Masumoto, and I. Yasuda for fruitful discussions. The present
research is supported by the Japan Society for Promotion of Science
(JSPS) through Grant-in-Aid for Scientific Research (B) 20340125
and Sumitomo Foundation. The first author has been supported by the
Research Fellowship of JSPS for Young Scientists.
Appendix 1: Steady atmospheric responses to a dipole
diabatic heating located along the Equator
in the Matsuno-Gill model
The Matsuno-Gill model is a set of shallow water equations
non-dimensionalized by a length scale of the equatorial
Rossby radius ðc2bÞ12 and a time scale ð2bcÞ�
12: Here, b is
the meridional derivative of the Coriolis parameter f ; cð¼ffiffiffiffiffiffiffigHp
Þ is the long gravity wave speed, g is the gravity
acceleration, and H is the equivalent depth. If H is adopted
as 400 m, the length scale is about 10�, and the time scale is
about one quarter of a day. When the basic state is of no
motion, the governing equations for a disturbance are
eu� 1
2yvþ op
ox¼ 0 ; ð2aÞ
1
2yuþ op
oy¼ 0 ; ð2bÞ
epþ ou
oxþ ov
oy¼ �Q : ð2cÞ
Here, p is the geopotential height of the disturbance, u and
v are the zonal and meridional velocities of the disturbance,
e is the linear damping rate, and Q is the diabatic heating
rate. Note that the linear damping term in the meridional
momentum equation (2b) is removed due to the long wave
approximation (Gill 1980).
Since the Matsuno-Gill model is a linear model, the
atmospheric response to the dipole diabatic heating along
the Equator (Eq. 1, Fig. 3a) can be linearly decomposed to
the response to each monopole forcing. Readers are
referred to (Gill 1980) for detailed processes of calculation
treating the monopole forcing. Here, only the results are
given.
The steady response to the western heating is
pþ ¼1
2qþ0 þ qþ2 1þ y2
� �� �e �
14y2ð Þ ; ð3aÞ
uþ ¼1
2qþ0 þ qþ2 �3þ y2
� �� �e �
14y2ð Þ ; ð3bÞ
vþ ¼ 4eqþ2 þ Qþð Þye �14y2ð Þ ; ð3cÞ
wþ ¼1
2eqþ0 þ
1
2eqþ2 1þ y2
� �þ Qþ
� �
e �14y2ð Þ ; ð3dÞ
C. Yuan et al.: IOD influence on the early winter tibetan plateau snow cover 1657
123
where
ðe2 þ k2Þqþ0
¼0 x\� 3L
ksinkxþ ecoskx� ke�eðxþ3LÞ �3L� x� � L
�kð1þ e�2eLÞe�eðxþLÞ �L\x
;
8><
>:
ð4aÞ
ð9e2 þ k2Þqþ2
¼�kð1þ e�6eLÞe3eðxþ3LÞ x\� 3L
�ksinkxþ 3ecoskx� ke3eðxþLÞ �3L� x� � L
0 �L\x
:
8><
>:
ð4bÞ
The steady response to the eastern cooling is
p� ¼1
2q�0 þ q�2 1þ y2
� �� �e �
14y2ð Þ ; ð5aÞ
u� ¼1
2q�0 þ q�2 �3þ y2
� �� �e �
14y2ð Þ ; ð5bÞ
v� ¼ 4eq�2 þ Q�ð Þye �14y2ð Þ ; ð5cÞ
w� ¼1
2eq�0 þ
1
2eq�2 1þ y2
� �þ Q�
� �
e �14y2ð Þ ; ð5dÞ
where
ðe2 þ k2Þq�0
¼0 x\L
�ksinkx� ecoskxþ keeðL�xÞÞ L� x� 3L
�kð1þ e�2eLÞeeð3L�xÞ 3L\x
;
8><
>:ð6aÞ
ð9e2 þ k2Þq�2
¼kð1þ e�6eLÞe3eðx�LÞ x\L
ksinkx� 3ecoskxþ ke3eðx�3LÞ L� x� 3L
0 3L\x
:
8><
>:ð6bÞ
Therefore, the total steady response of atmosphere is
p ¼ pþ þ p� ; ð7aÞu ¼ uþ þ u� ; ð7bÞv ¼ vþ þ v� ; ð7cÞw ¼ wþ þ w� : ð7dÞ
In the present work, we tentatively adopt L = 1 (about 10�)
and e ¼ 0:1 (about 0.4 day-1).
Appendix 2: Ray tracing
The ray is defined to be in the direction of the local group
velocity of the wave with a specific wavenumber. By ray
tracing, the propagation of wave energy of the specific
wave can be tracked as in the following:
x ¼Z
ugdt þ x0 ; ð8aÞ
y ¼Z
vgdt þ y0 : ð8bÞ
Here, (x, y) is the ray, (x0, y0) is the origin of the ray, and ug
and vg are the zonal and meridional group velocities. The
phase change along the ray is governed by
h ¼ �Z
xdt þZ
kdxþZ
ldyþ h0 ; ð9Þ
where h and h0 are the phase after and before the ray
tracing, x is the frequency, and k and l are the zonal and
meridional wavenumbers.
From the dispersion relation of Rossby wave under both
the quasi-geostrophic approximation and the WKB
approximation, the frequency can be given by
x ¼ �Uk þ �Vlþ �Qxl� �Qyk� �
= k2 þ l2� �
; ð10Þ
and the group velocities are expressed as
ug ¼ �U þ k2 � l2� �
�Qy � 2kl �Qx
� �= k2 þ l2� �2
; ð11aÞ
vg ¼ �V þ k2 � l2� �
�Qx þ 2kl �Qy
� �= k2 þ l2� �2
: ð11bÞ
Here, suffixes x and y denote the partial derivative, overbar
denotes the variables of the basic state, �U and �V are the
zonal and meridional components of the basic-state
velocity, �Qð¼ r2 �wþ f Þ is the basic-state absolute
vorticity, and �w is the basic-state streamfunction. If the
basic state varies slowly in space, changes in k and l along
the ray are governed by
dgk
dt¼ � ox
ox
¼ �k �Ux � l �Vx
þ �Qxyk � �Qxxl� �
= k2 þ l2� �
; ð12aÞ
dgl
dt¼ � ox
oy
¼ �k �Uy � l �Vy
þ �Qyyk � �Qxyl� �
= k2 þ l2� �
: ð12bÞ
Therefore, by use of Eqs. 8, 11 and 12, the ray under the
quasi-geostrophic approximation and the WKB approxi-
mation can be traced.
For the case of stationary Rossby wave (x = 0), if the
basic state is nearly zonally symmetric, Eq. 10 is reduced to
�U � �Qy=K2s ¼ 0 ð13Þ
where
�Qy ¼ b � �Uyy : ð14Þ
1658 C. Yuan et al.: IOD influence on the early winter tibetan plateau snow cover
123
Here, b is the meridional derivative of f, and Ksð¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffik2 þ l2p
Þ is the local total wavenumber of stationary
Rossby wave. Therefore, along the ray of stationary Rossby
wave, the total wavenumber must satisfy
Ks ¼� �Uyy þ b
�U
12
: ð15Þ
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