ADVANCES IN ATMOSPHERIC SCIENCES, VOL. 31, JANUARY 2014, 131–138

Dynamic and Numerical Study of Waves in the Tibetan Plateau Vortex

CHEN Gong1 and LI Guoping∗2

1Institute of Plateau Meteorology, China Meteorological Administration, Chengdu 6100722College of Atmospheric Sciences, Chengdu University of Information Technology and The Key Laboratory of

Plateau Atmosphere and Environment of Sichuan Province, Chengdu 610225

(Received 16 October 2012; revised 10 February 2013; accepted 18 April 2013)

ABSTRACT

In terms of its dynamics, The Tibetan Plateau Vortex (TPV) is assumed to be a vortex in the boundary layer forced bydiabatic heating and friction. In order to analyze the basic characteristics of waves in the vortex, the governing equations forthe vortex were established in column coordinates with the balance of gradient wind. Based on this, the type of mixed wavesand their dispersion characteristics were deduced by solving the linear model. Two numerical simulations with triple-nesteddomains—one idealized large-eddy simulation and one of a TPV that took place on 14 August 2006—were also carried out.The aim of the simulations was to validate the mixed wave deduced from the governing equations. The high-resolution modeloutput data were analyzed and the results showed that the tangential flow field of the TPV in the form of center heating wascyclonic and convergent in the lower levels and anticyclonic and divergent in the upper levels. The simulations also showedthat the vorticity of the vortex is uneven and might have shear flow along the radial direction. The changing vorticity causesthe formation and spreading of vortex Rossby (VR) waves, and divergence will cause changes to the motion of the excitationand evolution of inertial gravity (IG) waves. Therefore, the vortex may contain what we call mixed inertial gravity–vortexRossby (IG–VR) waves. It is suggested that some strongly developed TPVs should be studied in the future, because of theireffects on weather in downstream areas.

Key words: Tibetan Plateau Vortex, thermal forcing, tangential flow field, mixed inertial gravity–vortex Rossby waves

Citation: Chen, G., and G. P. Li, 2014: Dynamic and numerical study of waves in the Tibetan Plateau Vortex. Adv. Atmos.Sci., 31(1), 131–138, doi: 10.1007/s00376-013-1035-5.

1. Introduction

Vortex motion is a very common kind of atmosphericmovement; vortices commonly arise and often persist forlengthy intervals in the atmosphere, especially in circum-stances influenced by the Earth’s rotation and stable densitystratification (McWilliams et al., 2003). Like all the com-mon vortices, the flow field of the Tibetan Plateau Vortex(TPV) is mainly tangential and approximately axisymmetric(McWilliams, 1989); however, it differs in that its formationis mainly due to thermal forcing and the boundary layer con-ditions of the Tibetan Plateau (Chen et al., 1996).

Some strongly developed atmospheric vortices can al-ways form spiral bands. Researchers generally agree that thespiral shape reflects some inner features of vortex dynamicsthat are closely related to atmospheric waves, and obtaininga clear picture of the developing process of spiral bands isimportant for understanding vortex evolution (Tao and Li,2008). Most studies on spiral rain bands have concentratedon tropical cyclones, and have raised two theories to explain

∗ Corresponding author: LI GuopingE-mail: liguoping@cuit.edu.cn

their cause: inertial-gravity wave theory (Tepper, 1958; Kuri-hara, 1976; Huang and Chao, 1980; Chow et al., 2002) andvortex Rossby wave theory (Macdonald, 1968; Montgomeryand Kallenbach, 1997; McWilliams et al., 2003).

Researchers in China have also studied the spiral rainbands of typhoons (Yu, 2002; Zhu et al., 2002; Zhang, 2006),as well as waves in typhoon systems (Deng et al., 2004; Kanget al., 2007) in detail. However, the spiral cloud bands of theTPV have received little attention since they were first men-tioned by Ye and Gao (1979). Qian et al. (1984) analyzedNational Oceanic and Atmospheric Administration (NOAA)satellite data and established that some strongly developedTPVs have spiral cloud bands and that there is less cloud,or no cloud, in the center of the vortex. Qiao (1987) laterpointed out that the cloud structure of the TPV in summeris obviously spiral in form, and similar to tropical cyclones.However, all these studies lack theoretical explanation, andmany questions remain unanswered. For instance, how arethe spiral cloud bands of the TPV formed, and what is thelink between the TPV itself and the spiral bands? What isits dynamic mechanism and which wave characteristics doesit reflect? The fact that these fundamental and important is-sues have not yet been properly addressed is a reflection of

© Institute of Atmospheric Physics/Chinese Academy of Sciences, and Science Press and Springer-Verlag Berlin Heidelberg 2014

132 WAVES IN THE TIBETAN PLATEAU VORTEX VOLUME 31

the deficiency at present in dynamic studies of the TPV.The TPV is a major weather system that causes precipi-

tation in summer over the Tibetan Plateau. It usually gener-ates in the western part of the plateau and disappears in theeast. One noteworthy feature is that a small number of TPVscan develop and move eastward out of the Tibetan Plateauwhen conditions are favorable, leading to heavy rain, thun-derstorms and other severe weather processes in the plateau’scatchment area (Ye and Gao, 1979; Luo, 1992; Qiao andZhang, 1994). When the vortex moves out of the TibetanPlateau, it forms a weather situation featuring a trough inthe north and vortex in the south, which is the major rea-son behind subsequent heavy rainfall in the northwest ofChina. Eastward-moving TPVs mixing with cold air onthe ground often cause regional heavy rain processes overSichuan Province in summer, and when a vortex moves far-ther eastward out of Sichuan Province, it can also cause heavyrain over the middle and downstream regions of the YangtzeRiver, as well as over the Yellow River and Huaihe River, andeven over North China. For example, during the flooding ofthe Yangtze River in 1998, the TPV was one of the systemsthat played a key role in causing the heavy precipitation.

In the above context, the present study aims to establishthe governing equations of the TPV in column coordinateswith the balance of gradient wind, and a study of the wave dy-namics of the vortex is then carried out by solving the equa-tions. We also report upon numerical simulations carried outto verify the theoretical results. Through this research wehope to provide a better understanding of the inner structureof the TPV, as well as the basic dynamics of the evolutionaryprocess of the vortex.

2. Governing equations

Based on the results of former research (Liu and Li, 2007)and basic features of the TPV, the vortex was assumed as vor-tices in the boundary layer forced by diabatic heating andfriction. The governing equations for the vortex were thenestablished in column coordinates (r,λ ,z) with the balanceof gradient wind. It should also be noted that the vortexsystem being described is incompressible and axisymmetric(∂/∂λ = 0). The origin of the coordinates is at the center ofthe vortex, and these simultaneous equations are:⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

∂u∂ t

+u∂u∂ r

+w∂u∂ z

− v2

r= − 1

ρ0

∂ p∂ r

+ f v

∂v∂ t

+u∂v∂ r

+w∂v∂ z

+uvr

= − f u

0 = − 1ρ0

∂ p∂ z

−gρρ0

1r

∂ (ru)∂ r

+∂w∂ z

= 0

θθ0

= − ρρ0

=TT0

ddt

(g

θθ0

)+N2w =

gcpT0

Q

. (1)

In this model, r is radius, z is height, and t is time. The de-pendent variables are the radial, azimuthal and vertical ve-locity components u, v and w, respectively. θ is potentialtemperature, ρ is the air density, and T is air temperature.The subscript “0” represents the state of the stationary back-ground atmosphere. Meanwhile, f is the Coriolis parameter,g is gravitational acceleration, Q is the diabatic heating rate,cp is the specific heat at constant pressure, and N is Brunt–Vaisala frequency.

As they stand, these equations can already describe theTPV almost completely, but it remains hard to study the vor-tex dynamics, and thus it needs to be simplified. In orderto study the vortex dynamics more conveniently, the sim-plification will focus on 1st, 2nd, 4th formula of the simul-taneous Eq. (1), which relate to the kinematics. Note thatwe assume ph = constant, here h means the upper bound-ary of the homogeneous incompressible atmosphere and phis the pressure at h. First, we integrate the equation of staticequilibrium ∂ p/∂ z = −ρg from z = 0 to z = h and obtainp = ph + gρ(h− z). This means pressure decreases linearlywith height, and so we obtain ∂ p/∂ r = gρ∂h/∂ r. We alsointegrate the 4th formula of equations (1) from z = 0 to z = h,and after all transformation we obtain the following simulta-neous equations:

⎧⎪⎪⎪⎪⎪⎪⎨⎪⎪⎪⎪⎪⎪⎩

∂u∂ t

+u∂u∂ r

− v2

r= −g

∂h∂ r

+ f v

∂v∂ t

+u∂v∂ r

+uvr

= − f u

∂h∂ t

+u∂h∂ r

+hr

∂ ru∂ r

= 0

. (2)

These equations represent the simplified model for studyingthe dynamics of the TPV. This model is similar to some ex-isting models used for studying tropical cyclones (Huang andZhang, 2008) and tropical cyclone–like vortices (Nolan andMontgomery, 2002), which have been widely used and suc-cessful because the model can better describe the vortex mo-tion.

3. Wave dynamics

The method used for linearization is that of small pertur-bation, in which we let u = u′,v = v + v′, and h = H(r)+ h′.Taking note that the basic tangential flow field satisfies thegradient wind balance, i.e., v2/r+ f v = gdH/dr, and the tan-gential flow field has radial shear that is v = v(r), we finallyobtain the small perturbation equations as follows:

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎨⎪⎪⎪⎪⎪⎪⎪⎪⎩

∂u′

∂ t−

(2vr

+ f)

v′ = −g∂h′

∂ r

∂v′

∂ t+

(dvdr

+vr

+ f)

u′ = 0

∂h′

∂ t+ H

∂u′

∂ r+

(dHdr

+Hr

)u′ = 0

. (3)

JANUARY 2014 CHEN AND LI 133

We assume that the simultaneous Eq. (3) have the wave solu-tion and let u′ = U(r)e−iωt ,v′ = V (r)e−iωt , h′ = H(r)e−iωt .We then substitute these into Eq. (3), after which we obtainthe following ordinary differential equation:⎧⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎩

iωU +(

2vr

+ f)

V = gdHdr

iωV −(

dvdr

+vr

+ f)

U = 0

iωH − HdUdr

−(

dHdr

+Hr

)U = 0

. (4)

Eliminating Eqs. (4) can obtain:

− HB

d2Vdr2 +

(2β∗H

B2 − 2B

dHdr

− HBr

)dVdr

+(2vgr

+fg− ω2

Bg− 2β 2∗ H

B3 +AHB2 +

2β∗B2

dHdr

+

Hβ∗B2r

− 1B

d2Hdr2 − 1

BrdHdr

+H

r2B

)V = 0. (5)

In this equation,

A =1r

d2vdr2 − 2

r2dvdr

+2vr3 ,

B =dvdr

+vr

+ f = ζz + f ,

and β∗ = dζz/dr. d3v/dr3 has been omitted from the equa-tion, which means the third-order shear is not considered be-cause of its small quantities.

Obviously, Eq. (5) is too complicated to be solved di-rectly, and so it needs to be simplified. First, we analyzethe dimension of Eq. (5) and reserve the maximum and thesecond largest items in it. Next, we multiply the equationby Br2 and divide it by H. Notice that in Eq. (5) there isdH/dr = v 2/gr + f v/g. Finally, Eq. (5) is simplified to thefollowing form:

r2 d2Vdr2 +

(ω2r2

gH− β∗r

B− Ar2

B

)V = 0. (6)

Based on the basic characteristics of the TPV, we can con-clude the boundary condition of Eq. (6); that is, when r = R(at the edge of the vortex), velocity equals zero; and whenr = 0, it is bounded. So, the solution of Eq. (6) can be writ-ten in the form of sin (x) when β∗,A,B, H and r are constants,which means the following condition is satisfied:

sin

⎛⎝

√(ω2

gH− β∗

Br− A

B

)R

⎞⎠ = 0. (7)

After some simple mathematical derivation, we can obtainthe wave circular frequency as:

ω = ±√

gH(ζz + f )

√n2π2(ζz + f )/R2 +β∗/R+A (n ∈ Z).

(8)

The wave dispersion relationship [Eq. (8)] is, to a certain ex-tent, quite complicated. However, notice that the relationshipdescribed by Eq. (8) contains the items

√gH and β∗, which

clearly means the TPV may contain mixed waves and that thewaves are mixed with inertial gravity (IG) and vortex Rossby(VR) waves. We thus need to explain the item β∗ and the VRwave. β∗ = dζz/dr and ζz = dv/dr+ v/r is the key part of thewave mechanism of VR waves. Like the β effect of planetaryRossby waves, here β∗ can explain the basic vertical vorticitydistribution in the radial (r) direction to be uneven; if air par-ticles in the r direction have generated little disturbance, inorder to maintain conservation of total vorticity the perturba-tion vorticity must change, making the air particles oscillatein the r direction.

We are naming this mixed wave the inertial gravity–vortex Rossby (IG–VR) wave, as it contains the character-istics of both IG and VR waves. It can further be categorizedas a “type II” mixed wave (Lu et al., 2007), which refers tospecial waves that possess the characteristics of some basicwaves simultaneously, and cannot be separated. It only gen-erates in some specific background conditions. In the phys-ical quantity field that contains type II mixed waves, we canfind the coexistence of vortex and convergence–divergencemotion.

The mechanism of the mixed wave can be explained bythe law of conservation of potential vorticity. From Eq. (3),we can derive the following equation:

∂ζ ′z

∂ t+( f + ζz)D′ +u′

dζz

dr= 0. (9)

Here, ζ ′z is the vertical vorticity perturbation ζ ′

z = ∂v′/∂ r +v′/r and D′ is the horizontal divergence perturbation D′ =∂u′/∂ r + u′/r. With Eqs. (3) and (9), we can finally derivethe following equation:

(∂∂ t

+u′∂∂ r

)(ζz +ζ ′

z + fH +h′

)= 0. (10)

This is the law of conservation of potential vorticity. Underthe constraints of this law, a changing environmental poten-tial vorticity will lead to both vortex motion and convergenceand divergence movement changes. The changes in vorticitycause the formation and spreading of the VR wave, and di-vergence will cause changes to the motion of the IG wave’sexcitation and evolution.

4. Idealized simulation

Having studied the dynamics of the TPV, we found thatit might contain a mixed wave. The key condition is that, inthe vortex, there is uneven and shear basic flow vorticity anddivergence. Following this, the next step was to carry out anidealized numerical experiment to validate the results of thedynamics, at least to a certain extent, and study how the vor-tex flow field looks and how it forms. This idealized numer-ical experiment was carried out with the Weather Research

134 WAVES IN THE TIBETAN PLATEAU VORTEX VOLUME 31

and Forecasting (WRF) model, which was developed by Na-tional Centers for Environmental Prediction–National Centerfor Atmospheric Research NCEP–NCAR and is a convenienttool for studying various problems in the atmospheric sci-ences. It can not only carry out simulations with real data, butalso possesses a number of inbuilt ways to perform idealizedtests, 3D quarter-circle shear supercell simulations, 3D baro-clinic wave simulations, 3D large eddy simulations, and soon. For example, Rotunno et al. (2009) used the WRF modelto simulate a case of an idealized tropical cyclone, and stud-ied the role of turbulence effects in the cyclone. In the presentstudy, we took advantage of advances in computing power touse the method of 3D large eddy simulation to model the gen-eration process of an idealized TPV.

The default WRF large-eddy test produces a large-eddysimulation (LES) of a free convective boundary layer (CBL),in which the environmental wind (or the initial wind profile)is set to zero. The turbulence of the free CBL is driven by thesurface heat flux, which is specified in the WRF’s namelistas “tke heat flux” (“tke” is short for turbulent kinetic energy)and is equal to 0.24 (in MKS units). A random perturbation isinitially imposed on the mean temperature field at the lowestfour grid levels to start the turbulent motion. A double pe-riodic boundary condition is used in both x and y directions.It takes at least 30 minutes of simulation time to spin up theturbulent flow field, and only after the spin-up can the turbu-lence inside the CBL be considered to be well established.

After understanding the default case of WRF large-eddysimulation, and having considered the importance of thermaleffects on the formation of the TPV, it was clear that we onlyneeded to make very slight changes in order to approach ourproblem, i.e., to simulate the formation process of the TPVand the flow field of the vortex.

The traditional theory believes the TPV is a vortex in theboundary layer of the Tibetan Plateau, and is a kind of shal-low vortex. So, the top of the model domains was set to 2 km

Fig. 1. Setup of the experimental domains.

and the vertical levels to 31 layers. The scale of the TPV isabout 500 km and some strongly developed ones can reach600 to 800 km. The size of the simulated region must there-fore meet the scale of the vortex. So, in this case, we usedtriple-nested square domains, with the coarsest having sidesof 900 km, followed by 300 km, and then 100 km. The levelsof resolution were thus 9 km, 3 km and 1 km, respectively. Inorder to consider the gradient of heat flux—that is to say, theneed to reflect the heterogeneity of non-adiabatic heating—each domain had a different “tke” heat flux (0.15, 0.25 and0.35 K m s−1, respectively). All the grid setups are shown inFig. 1. The initial basic flow pattern was zero, and did notconsider microphysical processes. This means that, by onlyconsidering the distribution of surface heat flux as the centralheating form, the plateau vortex flow could be generated. Thesimulation lasted for six hours.

After three hours of simulation, the resulting flow field isshown in Fig. 2. We can see that, at this time, the vortex was

Fig. 2. Stream line (simulated for 3 hours): (a) layer 9; (b) layer19.

JANUARY 2014 CHEN AND LI 135

not fully spun up and thus not completely established. Boththe cyclonic flow in the lower levels (Fig. 2a) and the anticy-clonic flow in the upper levels (Fig. 2b) were not clear. Theconvergence and divergence was also very weak in both thelower and upper levels.

However, after six hours of simulation, the vortex flowfield was completely established (Fig. 3). In the lower levels,it showed cyclonic (Fig. 3a) convergence (Fig. 4a) and in theupper levels it showed anticyclonic (Fig. 3b) divergence (Fig.4b). This feature was most notable in the central area. Thisresult reflects the belief that the TPV always develops in theearly afternoon and matures before evening (Jiang and Fan,2002; Pei et al., 2012). That is to say, when the situation isfavorable, a TPV can form in about six hours.

Furthermore, we were able to confirm that the flowfield is uneven and may have shear flow along the radial or

Fig. 3. Stream line (simulate for 6 hours): (a) layer 9; (b) layer19. The black box represents the central area.

tangential directions. Both the divergence (Fig. 4) and vortic-ity (Fig. 5) of the flow showed a positive or negative alternatedistribution in the upper and lower levels. The entire featuremeans that, at least in this idealized test, the vortex possessesthe conditions to generate mixed IG–VR waves.

5. Numerical simulation

To further verify the results of the dynamic study and ide-alized simulation, a numerical case study was examined andis reported in this section. The case was a TPV that was ac-tive on 14 August 2006, and it was chosen because it was aTPV that formed and developed strongly with an eye regionand spiral cloud band.

The numerical simulation was also carried out using theWRF model. NCEP 1◦ ×1◦ data were used as the initial andbackground fields. The domains were triple-nested (Fig. 6),with the innermost domain covering most of the TPV with a

Fig. 4. Divergence in the central area (simulated for 6 hours):(a) layer 9; (b) layer 19 (units: 10−5 s−1).

136 WAVES IN THE TIBETAN PLATEAU VORTEX VOLUME 31

(a)

(b)

Fig. 5. Vorticity in the central area (simulated for 6 hours): (a)layer 9; (b) layer 19 (units: 10−5 s−1).

grid size of 5 km and 28 levels in the vertical direction. Wethus expected the numerical solutions to capture some of theinner structure of the TPV, given sufficient resolution. Wechose the WRF Single-moment 6-class scheme (Hong andLim, 2006) for the microphysics, the Rapid Radiative Trans-fer Model scheme (Mlawer et al., 1997) for longwave radia-tion, the Dudhia scheme (Dudhia, 1989) for shortwave radi-ation, and the Mellor–Yamada–Janjic scheme (Janjic, 1994)for the planetary boundary layer. The simulation time wasfrom 0800 LST 14 August 2006 to 0800 LST 15 August 2006—a total of 24 hours, including the developing and matura-tion periods of the vortex.

Overall, the simulation results seemed to accurately rep-resent the TPV. Figure 7 depicts the 300-hPa flow field at1900 LST, in which we can clearly see the vortex showinganticyclonic flow. Figure 8 shows the time-averaged vortic-ity profile along 31◦N from 1700 to 2000 LST (cross sec-tion through the center of the TPV). This represents the ra-dial variation of vorticity, and we can see that from the vortex

eye region (31◦N, 86◦E) outward, the average vorticity in-creased slightly, with the maximum value appearing in theregion (86.3◦–86.4◦E). Thereafter, in the outer region, thevorticity gradually decreased. This radial gradient of aver-age vorticity is the root cause of the VR waves, i.e., the basicflow vorticity needs to be uneven and shear.

In order to further study the waves in the vortex, we cuta concentric circle with the vortex of 50 km radius to ana-lyze the wave conditions in the tangential direction. The bestevidence for the mixed wave was that both the vorticity anddivergence showed fluctuation in the circle. Figure 9 presentsthe vorticity and divergence profile in the azimuthal direc-tion at different times, and we can clearly see (Fig. 9a) therewas vorticity fluctuation; and, furthermore, in Fig. 9b it canbe seen that the divergence and convergence were changingalternately. In addition, we can infer from Fig. 9 that themoving tangential direction of waves was clockwise, and thespeed was about 8 km h−1.

Fig. 6. Setup of the model domains for the TPV on 14 August2006.

Fig. 7. The 300-hPa flow field at 1900 LST 14 August 2006.

JANUARY 2014 CHEN AND LI 137

Fig. 8. Time-averaged vorticity profile for the period 1700–2000 LST 14 August 2006 along 31◦N (units: 10−4 s−1).

The status in the radial direction was also analyzed and,in summary, the features of vorticity fluctuations in this direc-tion first spread inward, and then spread out after the maturestage of the vortex. Figure 10 shows the spreading processin the radial direction, demonstrating that the time between1900 and 2000 LST was the period of change in terms ofwhen the vorticity fluctuations spread inward and outward.The feature of divergence was not so clear in this period.

6. Summary and concluding remarks

Following a dynamic study, idealized simulation and casestudy of a TPV, we can draw the following preliminary con-clusions:

(1) TPVs possess both vortex motion and convergence anddivergence movement. Changes in the vorticity causethe formation and spreading of VR waves, and diver-gence will cause changes to the motion of IG wave ex-citation and evolution. Thus, the vortex may containmixed IG–VR waves.

(2) The idealized experiment not only confirmed the diver-gence and vorticity of the vortex is uneven and mayhave shear flow along the radial or tangential direc-tions, but also showed the flow field of the vortex iscyclonic and convergent in the lower levels and anticy-clonic and divergent in the upper levels.

(3) Having simulated a vortex case that took place on 15August 2006, we further confirmed the existence of themixed wave and, moreover, we found that the mixedwave spreads both in the tangential and radial direc-tions. The features of the wave spreading in the radialdirection involve an initial inward spread, and then aspreading out after the mature stage of the vortex.

Finally, it is important to note the significance of studyingwaves in the TPV, as has been done here, because it enables

Fig. 9. (a) 500-hPa vorticity profile of the azimuth (x-axis isazimuth; y-axis is vorticity). Angles: 0◦, 90◦, 180◦ and 270◦are for east, north, west and south, respectively. The lines withsmall circles (black), solid circles (green), small squares (yel-low) and solid squares (red) represent the vorticity profiles at1700, 1800, 1900 and 2000 LST 14 August 2006, respectively(units: 10−4 s−1). (b) 500-hPa divergence profile of the az-imuth.

Fig. 10. Perturbation vorticity zonal–time profile.

us to more precisely predict its influence on regional weather.Furthermore, the results of the present study serve to re-mind us that some strongly developed TPVs that do not move

138 WAVES IN THE TIBETAN PLATEAU VORTEX VOLUME 31

east also need to be studied in the future, because the wave-spreading process can also affect weather in downstreamareas. And this study attempts to investigate this type ofTPV other than eastward-moving TPVs that are most stud-ied. However, the present conclusions have their limitationsand need to be further tested.

Acknowledgements. This research was supported by the Na-tional Key Basic Research and Development Project of China(Grant No. 2012CB417202), the National Nature Science Fund ofChina (Grant No. 41175045), the Special Fund for Meteorologi-cal Research in the Public Interest (Grant Nos. GYHY201006014,GYHY201206042 and GYHY201106003), and the Sichuan Me-teorological Bureau Fund for Young Scholars (Grant No. 2011-YOUTH-02).

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