The Generation Mechanism of the Western Disturbances
over the Himalayas
Masayuki Hara∗ , Fujio Kimura,∗ and Tetsuzo Yasunari,∗∗Frontier Research Center for Global Change,
Japan Agency for Marine-Earth Science and Technology,
e-mail: hara.masayuki@jamstec.go.jp†‡

Institute of Geoscience, University of Tsukuba

Hydrospheric Atmospheric Research Center, Nagoya University

Abstract
A meso-α-scale quasi-stationary cyclone sometimes appears along the southern slope of the Himalayas. Thecyclone can be simulated reasonably well by a regional meteorological model and can be explained by the theoryof the topographic Rossby wave. The characteristics of the cyclone were also verified using an f-plane shallowwater equations model (SWEM). The model studies suggest that the cyclone is generated when a synoptic
trough passes over the Tibetan plateau. The southern part of the trough is cut off at the western side of theplateau and forms a cyclone. Although the generated cyclone is almost stationary and moves eastward very
slowly, the remaining northern part of the trough moves eastward faster than the subtropical westerlies. Theseproperties can also be seen in the results of the SWEM simulations. The vertical structure of the cyclone
is barotropic and extends up to the tropopause. The phase velocity and vertical/horizontal structure of thecyclone agree well with the theoretical solution of the topographic Rossby wave in a stratified quasi-geostrophic
fluid.

1mura and Doutani (1985) studied the cold surge aroundthe Tibetan plateau with a numerical model and indicated that the dynamics of the Kelvin wave and TRW
are some of the major factors responsible for the generation of the cold surge. Hsu (1987) studied storm
tracks around the major mountains in the world andstated that the statistical features of the storms propagating along the mountain ranges are similar to thoseof TRWs. However, the disturbances observed in theIntroduction

A meso-α-scale quasi-stationary cyclone sometimes appears along the southern slope of the Himalayas andoccasionally brings heavy snowfall. In the winter of1990/1991, the most tragic accident in the history ofmountaineering occurred in Meilixueshan in southeastern Tibet. Because of the abnormally heavy snowfall
for a full two-to-three-day period between January 1
and 3, 1991, a huge avalanche that was triggered near
the summit of the mountain hit an expedition campand killed seventeen climbers. The new snow that had
accumulated during the two-to-three-day snow period
was estimated to be more than two meters in depth;
however, the meteorological disturbance directly responsible for the heavy snowfall had not been clearly
detected in the synoptic weather chart (Sakai, 1991).
This study determined that the cyclone had been triggered by the trough to the west of the plateau and had
propagated very slowly as a topographic Rossby wave(TRW) along the southern periphery of the Tibetan
plateau and the Himalayan range.
In the ocean, TRWs are sometimes observed andhave been studied well (Rhines, 1969; Pedlosky, 1987).
Although TRWs can theoretically exist in the atmosphere as well, little observational evidence has beenpresented so far. TRWs can be explained by the conservation law of potential vorticity as an oscillation of
the relative vorticity caused by the bottom slope. On
the other hand, Rossby β-waves are explained as theoscillation of the relative vorticity contributed by theβ effect.
In the northeast region of the Tibetan plateau, a cold
surge is observed after a synoptic trough passes overthe plateau (Nakamura and Doutani, 1985). Naka-NCEP/NCAR reanal. 18Z29DEC1990
690060˚N40˚N
000
72750

20˚N60˚E80˚E 100˚E

Figure 1: Geopotential height at 400 hPa at 18 UTC December 29, 1990; NCEP/NCAR reanalysis dataset. The
shaded area indicates the area in which the topographicalheight is greater than 2500 m.

Data : NCEP/NCAR reanalysis dat
Variable : Geopotential Height
Date : 18Z29DEC1990Level : 400 hPa

northeast of the Tibetan plateau can be explained asa mixed mode of coastal Kelvin waves and TRWs.
Coastally trapped waves (CTWs) in the atmosphere
are often observed and studied. For major mountains
1Realistic Numerical Simulation

The numerical model in the present study is a modified
RAMS (TERC-RAMS, Pielke et al., 1992; Yoshikaneet al., 2001; Sato and Kimura, 2003). NCEP/NCAR
reanalysis data was used as initial and lateral boundary
conditions. The lateral boundary conditions are interpolated 6-hourly from NCEP/NCAR reanalysis data.
The sea surface temperature is interpolated from themonthly mean data of Reynolds SST (Reynolds, 1994).
The horizontal grid interval is 100 km (100×100 gridpoints), while the vertical grid interval is 120 m in thelowest layer stretching gradually to increase up to 1000m in the upper layer (30 layers together). The numerical experiment started at 0 UTC December 27, 1990
and ran until 0 UTC January 1, 1991. Full physics areassumed in all of the three experiments.
Figure 2 shows the geopotential height at the levelof 400 hPa at every 30 hours from 6 UTC December 28
to 6 UTC December 29, 1990 simulated by the CONTROL run. In comparison with the reanalysis data,
the time evolution and spatial structure of the quasistationary cyclone seem to be reasonably simulated by
the CONTROL run. In the middle level of the troposphere, the synoptic trough is located in the west of theTibetan plateau (Fig. 2A, 6 UTC December 28, 1990).
When the synoptic trough hits the Tibetan plateau,
the southern part of the trough is cut off, and a cyclone is generated in the southwest area of the plateau(Fig. 2B, 18 UTC December 29, 1990). At the same(A) CONTROL 06Z28DEC1990
60˚N40˚N07350770

20˚N8050
60˚E80˚E 100˚E 120˚E(B) CONTROL 18Z29DEC1990
60˚N
50

2time, this cyclone causes snowfall along the Himalayas(no figure). The generated cyclone propagates eastward very slowly accompanied by precipitation along
the Himalayas and survives for a week (Fig. 2C, 6 UTC
December 31, 1990). Although the averaged westerly
in this area is estimated to be about 25 m/s in themiddle level in the troposphere, the eastward migration speed of the cyclone is only about 4 m/s.

73

around the world, such as the Rockies, the Alps, andSouthern Africa, there are many studies about CTWs
(Tory et al., 2001; Gross, 1994; Gill, 1977).
Meso-α-scale quasi-stationary cyclones, called Western Disturbances, are sometimes observed along thesouthern slope of the Himalayas. By means of astatistical analysis using the station data and theNCEP/NCAR reanalysis data, Lang and Barros (2004)
demonstrated that cyclones exist in the southwesternarea of the Himalayas in snow days in the central Himalayas, but they did not explain why cyclones occur
and stay in the area. In this paper, we will explain
why cyclones occur and stay in the southwestern areaof the Himalayas using the theory of TRWs.
Figure 1 shows the contours of the geopotential
height at the level of 400 hPa at 18UTC December
29, 1990, three days before the abovementioned accident, given by NCEP/NCAR reanalysis data (Kalnayet al., 1996). The early stage of the cyclone, which
later brought the disaster mentioned above, seems tobe one of the typical cases of the southwest cyclone. Acyclone exists in the southwestern side of the Tibetan
plateau. The horizontal scale of the cyclone extends
to 1400 km, and the cyclone has a barotropic vertical structure in the troposphere. Although the strong
subtropical westerly blows in this area, this cyclone
propagated eastward very slowly along the Himalayas
and survived for a week.

40˚N

L

7700

20˚N80560˚E080˚E 100˚E 120˚E(C) CONTROL 06Z31DEC1990
60˚N7350
40˚N

7700

L20˚N8050
60˚E80˚E 100˚E 120˚EData : NCEP/NCAR

Variable : Geopoten

Date : 06Z28DEC19Level : 400 hPa

Figure 2: Geopotential height at 400 hPa simulated by theTERC-RAMS/CONTROL run at (A) 6 UTC December 28,(B) 18 UTC December 29, and (C) 6 UTC December 31,
1990. The thick line indicates the location of the synoptic
trough, ’L’ shows the center of the cyclone, and the shaded
area indicates the area in which the orographic height isgreater than 2500 m.

Figure 3 shows a longitude-vertical cross section of
the meridional wind and relative vorticity at 18 UTC
December 29, 1990. The vertical distribution of the relative vorticity and the meridional wind at the center ofthe cyclone indicates that the cyclone has a barotropic Since it is estimated to be about 4.5 × 104 m, the vertistructure.
cal structure of the TRW should almost be barotropic
in the troposphere. In estimating the phase speed of
the TRW, we use the height of the tropopause as thedepth of fluid because the observed disturbance can beseen only below the tropopause. The vertical structure shown by Fig. 3 does not conflict with this theory. These facts indicate that the cyclone along theHimalayas is a TRW.
In order to discuss the formation mechanism of theTRW cyclone, we also conducted some numerical simulations using a simple f-plane shallow water equations
system (SWEM). In the equations system, there are nowaves except for topographic Rossby waves and gravFigure 3: Vertical-longitude cross section at 34 ◦ N of the ity waves. The equations system used in SWEM is as
meridional wind and relative vorticity of the CONTROL follows,
run at 18 UTC December 29, 1990. The contours indicate
meridional wind, and the gray shaded area indicates thearea in which the relative vorticity is greater than 0.5×10−4s−1 .

3Discussion

The structure of TRWs in the ocean has been revealed
in studies by Rhines (1969) and Pedlosky (1987). In
the stratified quasi-geostrophic fluid, the phase speedof TRWs over the bottom is given asc = u0 −s · f0 1· 2,h0K(1)where c is the phase speed of TRWs, f0 , the Coriolis
parameter, s, the gradient of the bottom slope, h0 ,the averaged depth of fluid, K, the horizontal wave
number, and u0 , the mean meridional wind velocity.
The vertical scale of TRWs depends on its horizontal
scale and phase speed. The vertical e-folding scale ofTRWs (d) in a nearly neutral state is given as follows,
d=1 f0· ,K N

(2)

where N is the Brunt-Väisälä frequency.
The phase speed of TRWs in a shallow-water equations system can also be estimated by Equation (1).
From theoretical Equation (1), the phase speed of
the TRW is estimated to be about 20 m/s westward,
and the phase speed of the TRW against the earth is estimated to be 5 m/s eastward. This value almost agrees
with the 4 m/s estimated by the numerical model. By
the linear theory, the phase speed of the Rossby β-wave
in this region is 0.26 m/s westward against the atmosphere. The Rossby β-wave cannot explain the cyclone
along the Himalayas because it is too slow.
The vertical scale of the TRW can be theoreticallyestimated with the Coriolis parameter and the atmospheric static stability. After the theory assuming astratified fluid and a quasi-geostrophic approximation,
the vertical scale of the TRW is related with the horizontal scale of the TRW, as given by Equation (2).

∂u∂t∂v∂t∂h∂t∂u∂u∂h+v− f0 v = −g ∗(3)
∂x
∂y∂x
∂v
∂v
∂h+ u+v+ f0 u = −g ∗(4)∂x∂y∂y∂u · (h − hB ) ∂v · (h − hB )++= 0, (5)
∂x
∂y+ u

where h is the level of the water surface, hB is the elevation of the bottom, g ∗ is the reduced gravity whichis assuming to be 1.0 m/s2 , and f0 is the Coriolis parameter. The orography is assumed to be a cigar-shapewhose width is 10,000 km along the meridional direction and 3,000 km in the latitudinal direction and maximum height is 3,000 m (shaded area in Figure 4). After the mountain waves achieved a stationary state,a trough is artificially created in the windward of themountain. The trough is meridionally uniform and has
been adjusted to be geostrophic balance.
Figure 4 shows the elevation of the water surface
simulated by SWEM at every 30 hours after the startof the simulation. The initial state is shown in Figure
4A. When the trough passes through the orography,
the trough is divided into two parts by the orography (Figure 4B), and two cyclonic circulation patterns
appear in the northern and southern side of the orography (Figure 4C). The northern cyclone moves fasterthan the speed of the westerly, but the southern cyclone
moves very slowly and seems to be almost stationary.
These properties of the cyclones agree with observationand the realistic simulation shown above.
As well as the numerical model with full physics,
SWEM can also almost completely simulate formation
process in which a cyclone is separated from a synoptic
trough by the Tibetan plateau and propagates slowly
eastward along the southern slope of the Himalayas.
The model experiments also show that the cyclone
along the southern slope can exist only when the phasespeed of the TRW is slower than the wind speed of
the westerly. This demonstrates the existence of thethreshold westerly velocity. When the westerly is lessthat the threshold, any disturbances induced by thetrough cannot propagate to the southern side of theorography. Since the threshold velocity is roughly esti-

of their genesis, growth, and decay is essential for theprediction and prevention of snow disasters in theseregions.
References[1] Hsu, H.-H. (1987), Propagation of Low-Level Circulation Features in the Vicinity of Mountain Ranges, Mon.
Wea. Rev., 115, 1864–1892.
[2] Gill, A. E. (1977), Coastally Trapped Waves in the Atmosphere, Quart. J. R. Met. Soc., 103, 431–440.
[3] Gross, B. D.(1994), Frontal Interaction with Isolated
Orography, J. Atmos. Sci., 51, 1480–1496.
[4] Kalnay, E. and co-authors (1996), The NCEP/NCAR
40-Year Reanalysis Project, Bull. Amer. Meteor. Soc.,
77, 437–472.
[5] Lang, T. J. and A. P. Barros (2004), Winter Storms inthe Central Himalayas, J. Meteor. Soc. Japan, 82, 829–844.
[6] Nakamura, H. and T. Doutani (1985), A Numerical
Study on the Coastal Kelvin Wave Features about theCold Surges around the Tibetan Plateau, J. Meteor. Soc.
Japan, 63, 547–563.
[7] Pedlosky, J. (1987), Geophysical Fluid Dynamics, 2nded., 710 pp., Springer-Verlag, New York.
[8] Pielke, R. A. and co-authors (1992), A Comprehensive
Meteorological Modeling System RAMS, Meteorol. Atmos. Phys., 49, 69–91.

Figure 4: Fluid height of the SWEM in (A) 36 hours, (B)72 hours, and (C) 108 hours. The contour lines indicate
the fluid height, and the shaded area indicates the area inwhich the orographic height is greater than 2500 m.

[9] Reynolds, R. W. and T. M. Smith (1994), Improved
Global Sea Surface Temperature Analysis Using Optimum Interpolation, J. Climate, 7, 929–948.
[10] Rhines, P. B. (1969), Slow Oscillations in an Oceanof Varying Depth Part1. Abrupt Topography, J. Fluid
Mech., 37, 161–189.

mated to be about 20 m/s in the Himalayas, the TRW
cyclone forms in the case of relatively strong westerly. [11] Sakai, T. (1991), The Assault on Meilixueshan andTragic Loss of Seventeen Climbers, SANGAKU (TheThe threshold velocity depends on the size of the TRW
Journal of the Japanese Alpine Club), 86, 104–111 (inand the steepness of the slope.
Japanese with an English abstract).

4Summary[12] Sato, T. and F. Kimura (2003), A Two-dimensional
Numerical Study on Diurnal Cycle of Mountain Lee Precipitation, J. Atmos. Sci., 60, 1992–2003.

A quasi-stationary cyclone was observed over thesouthern slope of the Himalayas. This cyclone can be [13] Sumi, A. (1985), A Study on Cold Surges Around theexplained as a TRW along the Himalayan slope sinceTibetan Plateau by Using Numerical Models, J. Meteor.
it can be simulated well by full-parameterized numerSoc. Japan, 63, 377–396.
ical models as well as by a simple SWEM. The phasespeed and vertical and horizontal structure of the cy- [14] Tory, K. J., P. L. Jackson, and C. J. C. Reason (2001),
Sensitivity of Coastally Trapped Disturbance Dynamics
clone agree well with the linear theory of TRWs.
to Barrier Height and Topographic Variability in a NuSimilar cyclones have been observed at least threemerical Model, Mon. Wea. Rev., 129, 2955–2969.
times (February 8 to 12 1996, February 23 to 25 1998,and December 5 to 10 1999) from 1995 to 1999. All cy- [15] Yoshikane, T., F. Kimura, and S. Emori (2001), Nuclones were observed in winter and slowly propagatedmerical Study on the Baiu Front Genesis by Heating
Contrast between Land and Ocean, J. Meteor. Soc.
along the southern slope of the Tibetan plateau. SinceJapan, 79, 671-686.
these cyclones sometimes bring heavy snowfall along
the Himalayan range and the southern part of the Tibetan plateau, further understanding of the dynamics