Coupling Development : An Efficient Mechanism for the

December 1991 I. Takayabu 609

"Coupling Development" : An Efficient Mechanism

for the Development of Extratropical Cyclones

By Izuru Takayabu

Meteorological Research Institute, Tsukuba, Ibaraki 305, Japan

(Manuscript received 23 January 1991, in revised form 28 August 1991)

Abstract

"Coupling development", or the rapid cyclogenesis with a coupling process of the upper and the lower tropospheric vortices is studied numerically using a ,*plane channel, dry primitive equation model. The "coupling development" occurred when a lower vortex is initially located at the latitude of the

jet axis, and an upper vortex to the northwest of the lower vortex. We displayed the following three stages of the "coupling development".

1) Deformation of the upper vortex associated with the "upper-level frontogenesis" (from day 0-day 2).

2) The . northward penetration of the lower vortex through advection of surface high-PV (from day 2-day 3).

3) Continuous rapid growth of the vortex near the surface triggered by the "coupling" of the upper and the lower vortices (day 2.5-day 3.5).

We have also made a brief data analysis of the 25-28 April 1986 cyclone developed around the Japan Islands. We observed the following two characteristics in that cyclone.

1) The northward penetration of the lower vortex before the "coupling".

2) The downward intrusion of the upper vortex along the sloping isentropic surface, and the "coupling" with the lower vortex at the beginning of the rapid development.

These observed features are consistent with our numerical results, which indicate the importance of the "coupling development" mechanism in the mid-latitudinal cyclone development.

1. Introduction

Extratropical cyclones are the dominant phenom-ena controlling mid-latitudinal weather. Therefore, for an accurate weather forecast, it is crucial to un-derstand precisely the development mechanism of the extratropical cyclones. It is widely accepted that unstable normal modes of a zonally homoge-neous baroclinic westerly flow (Charney,1947; Eady, 1949) represent the structure of the synoptic scale extratropical cyclones well. However, extratropical cyclones often have a relatively large amplitude prior to the development stage. At that time, their struc-ture also differs from that of the unstable normal modes. Furthermore, the observed frequent "rapid cyclogenesis" , or the growth rate of the observed cyclones frequently exceeds that predicted by the baroclinic instability theory. To explain these dis-crepancies, some effects other than the baroclinicity

c1991, Meteorological Society of Japan

of the basic field need to be introduced. A number of studies have been done on this problem discussing the effects of the latent heat release, the surface sen-sible and latent heat fluxes, mountains and upper tropospheric disturbances. Among them, some ob-servational studies suggested that the coupling of the upper and the lower tropospheric vortices was one of the important mechanisms responsible for the rapid cyclogenesis in various situations (e.g. Nitta et al., 1973; Buzzi and Tibaldi, 1978; Mullen, 1983; Uccellini et al., 1985 and Ogura and Juang, 1990). Here, we name this process the "coupling develop-ment" and describe its mechanism in detail.

1.1 Linear and weakly non-linear theories The upper trough seems to play an important

role in the process of the "coupling development". There exist two kinds of approaches when analyz-ing the baroclinic instability under the influence of the upper trough. One method is to regard the up-

per trough as the basic field and calculate normal

610 Journal of the Meteorological Society of Japan Vol. 69, No. 6

modes on this zonally inhomogeneous basic flow. The other one is to consider the upper trough as a finite-amplitude disturbance, and discuss its evo-lution as an initial value problem.

In the former case, the upper trough is repre-sented as the stationary jet streak. Pierrehumbert

(1984) assumed the horizontal scale of the jet streak to be far larger than that of the disturbance, and applied the WKB method. He showed that the cy-clone activity is confined in the exit region of the jet streak, which is called the "local mode" or the "regional cyclogenesis" .

However, the interaction between the upper tro-

pospheric jet streak and the local mode is not fully included in these models. We cannot apply their results to the "coupling development", because in the "coupling development" the upper trough also moves and undergoes some structural changes. Therefore, it is better to treat the upper trough as one of the disturbances. Then, the structure of ini-tial disturbances seems to play an important role in the process of the "coupling development" . So, we treat the problem as an initial value problem.

Farrell (1984) studied the evolution of a shal-low rear-surface disturbance when an upper distur-bance overtakes it. He succeeded in showing the rapid transient development of a normal modes-continuous modes mixed type disturbance in a nar-row baroclinic zone (the width of the baroclinic zone is represented as a parameter in his two-dimensional model). Through its development, the normal modes components develop rapidly, adjust-ing the boundary conditions which tend to be broken through the change of the structure of the continu-ous modes components.

However, these two-dimensional models have a limitation. All variables are meridionally constant, except for the constant temperature gradient. Thus, both the basic field and the disturbance are degen-erated in the meridional direction. This leads to an unrealistic horizontal structure for the simulated cy-clone. It is very important for us to reproduce a re-alistic cyclone when we try to clarify the mechanism of the "coupling development" through the analysis of the results of numerical experiments. We cannot offer here a full discussion of the problems with the two-dimensional models.

1.2 Forecasting experiments The non-linear effect is another essential factor for

reproducing a realistic extratropical cyclone. Thus, we cannot eliminate non-linear terms in the three-dimensional model. It is fag easier to use numerical models than theoretical models, when the structure of the initial disturbances differs greatly from that of the normal modes.

There have been many papers aimed at clarify-ing the development mechanism of extratropical cy-

clones with forecasting experiments. Most of them consist of a series of parameter studies. To discuss the effect of the upper tropospheric disturbance di-rectly, it is desirable to design experiments with and without the upper trough. Chen et al. (1983) stud-ied the role of the upper trough on the develop-ment of a maritime cyclone over the East China Sea during the AMTEX'75. They took away the upper trough from the initial disturbance in one of their experiments in order to discuss the role of the upper disturbance on the development of the cy-clone. In the experiment without upper trough, the disturbance at the surface was not organized suffi-ciently to become a deep cyclone. These results indi-cate that the upper tropospheric forcing is necessary for the "coupling development" . Recently, Zupanski and McGinley (1989) performed an experiment for the case of an Alpine lee cyclone. They eliminated the upper-level jet streak by reducing the upper-level wind maxima and showed a tendency for the reduction of the deepening rate of the lee cyclone. However, it is very difficult to control the effect of the upper tropospheric forcing independent of other parameters in such forecasting experiments. There-fore, we need simpler numerical models to distin-

guish the effects of various parameters.

1.S Idealized numerical experiments and aims of this study

There are many simple numerical models which used idealized basic flows in the three-dimensional

*-plane channel . However, most of them assumed the amplitude of the initial disturbances to be in-finitesimally small. Furthermore, they did not fo-cus on the effect of upper tropospheric forcing (e.g. Mudrick, 1974; Hoskins and West, 1979; Takayabu, 1986). The only exception is Bleck (1990). He adopted a finite-amplitude upper tropospheric dis-turbance (about 10K in temperature anomaly) ac-companied by tropopause folding and succeeded in simulating the cyclone development associated with upper tropospheric forcing. However, he put no ini-tial disturbance near the surface. Thus, model sim-ulation of the "coupling development" was not per-formed.

In this study, we reproduce the "coupling devel-opment" using a simplified three-dimensional model with finite amplitude initial disturbances. Through analysis of numerically simulated cyclones, we try to clarify when and how the "coupling development" occurs in the mid-latitude westerly jet. The model will be described in Section 2. In Section 3, the initial disturbance effective for the development is introduced. The results of a fine-grid experiment will be presented in Section 4, where the mechanism of the "coupling development" reproduced using a 100 km grid model will be discussed in detail. Sec-tion 5 will be devoted to discussions and remarks.


A summary is given in Section 6.

2. Model description

2.1 Equations

We use dry primitive equations in the sigma (*) coordinate system, the same as that in Takayabu (1986). * is the normalized pressure,

where Atop is the pressure at the upper boundary

of the model atmosphere and Ps is the surface pres-

sure. x and y are horizontal coordinates oriented

to the eastward and northward direction, respec-

tively. Primitive equations consist of a mass conser-

vation equation, horizontal momentum equations,

thermodynamic equation and the hydrostatic rela-

tion. They are written as follows.

2) Convective adjustment. The critical lapse rate is set at -9.8*/km (dry

adiabatic) throughout the model atmosphere.

3) Newtonian cooling. The relaxation time is 20 days.

4) Horizontal non-linear momentum diffusion. This is introduced mainly to suppress compu-

tational noises at high frequency.

2.2 Calculation domain and boundary conditions The *-plane channel with a width of 8100 km and

with a length of 10500 km is used here. The cyclic boundary condition is adopted in the zonal direc-tion. The northern and southern lateral boundaries are regarded as a stress-free wall, i. e.,

at lateral boundaries. (7)

The sigma velocity vanishes at the upper and the

lower boundaries, i. e.,

where *=ps -ptop, u, v, T and * have their stan-dard meanings and * is the vertical velocity in the sigma coordinate. * is the geopotential height; * is the potential temperature and x=T/8. In this model, the fl-plane approximation is used, i, e., the Coriolis parameter f is

yo corresponds to 45*N, coincides with the center of the channel in this model

The following processes are added in our experi-

ments.

1) Vertical momentum diffusion (the coefficient Km).

2.3 Finite difference scheme We adopt the finite difference scheme proposed

by Arakawa and Mints (1974). The distribution of the horizontal grid follows Arakawa's C scheme with the grid spacing of 100 km. The model has 16 levels up to 25 hPa. Time integration is performed by the leap-frog scheme except for the dissipation term (the time increment is 90s) . The Euler-backward scheme is also adopted periodically for computational sta-bility.

2.4 Basic field We choose a simple baroclinic westerly jet as the

basic flow. The meridional cross section of the basic state is shown in Fig. 1. The basic flow is zonally ho-mogeneous and meridionally symmetric around the center of the channel. The temperature decreases by 6.5*/km with height in the troposphere and is con-stant in the stratosphere. Of course, the potential temperature rapidly increases with height through the stratosphere. The tropopause is set at 200 hPa at the middle of the channel. The zonal wind in-creases linearly with height through the troposphere with its maximum at the tropopause. It then de-creases linearly with height in the stratosphere. It has a sine-square profile in the meridional direction (the half width is 3150 km). The center of the jet is located at 45*N, and its maximum value is about 38 m/s. The . above features are the same as those


Fig. 1. Meridional-height cross sections of the basic state adopted in the model. Contours of potential

temperature are dashed and drawn every 5K and those of westerly wind are continuous and drawn

every 4 m s- 1 .

chosen in Takayabu (1986), and approximates well the westerly jet profile in winter.

We have calculated normal modes on this basic field following the linear instability theory (see Fig. 2). The growth rate is largest when the horizon-tal scale (defined as 1/2 times wavelength) of the disturbance is 1800-2000 km. The e-folding time is about 2 days. This mode was adopted as the initial disturbance in Takayabu (1986).

3. Initial disturbances

3.1 Horizontal scale We adopt an initial disturbance with a horizontal

scale smaller than the most unstable normal mode. The preliminary study confirms that the scale de-pendency of the cyclone development rate with finite amplitude initial disturbance coincides with that of the normal modes (Takayabu, 1991). This study aims to discuss the vortex-vortex or vortex-basic flow interactions which dominate the transient de-velopment of cyclones. Therefore, it is desirable to examine a case where the growth rate of an unsta-ble normal mode itself is relatively small. We choose 900 km, which is 3/5 of the horizontal scale of the most unstable linear wave, as the horizontal scale of the initial disturbance. As indicated in Fig. 2, the growth rate of the most unstable normal mode has a minimum around 900 km (the e-folding time is about 5 days).

3.2 Vertical structure We adopt a vertical structure similar to that of

observed cyclones. An example of such a cyclone will be shown in Section 5.1 (The 25-28 April 1986 cyclone developed around the Japan Islands; see Fig. 20). The vertical-meridional sections of the initial disturbances are indicated in Fig. 3. In this case, the initial lower vortex is placed 1200 km to the south and 1500 km to the east of the upper vortex. Their characteristic features are summarized as follows.

Fig. 2. Growth rate of the most unstable nor-

mal mode of the basic flow as shown in

Fig. 1, as a function of the horizontal scale

of the disturbance. The horizontal scale is

defined as a half of the wave length.

1) The upper vortex: An upper cold vortex is accompanied by the tropopause folding. We

put a positive temperature anomaly above the tropopause and a negative temperature

anomaly around the upper troposphere. Max- imum/minimum values of the anomaly are

9K/-9K.

2) The lower vortex: A shallow vortex is concen- trated in the lower troposphere (up to 700 hPa).

The disturbance is accompanied by a positive temperature anomaly (4K at the surface).

Wind and temperature fields are related through the thermal wind relation for each disturbance. Peak values of the relative vorticity (*) are *=1.4 *


Fig. 3. Meridional-height section of the initial upper disturbance, superposed on the ba-

sic field. Contours of potential temperature (dashed line, contour interval 5K)

and relative vorticity (solid line, contour interval 2.0*10*5 s-1). Thin shaded ar-

eas indicate the upper vortex region (relative vorticity greater than 2*10-5 s-1) and the lower vortex region 1500 km to the east of this cross section (relative vorticity

exceeds 1*10-5 s-1) .

10-4 s-1 for the upper vortex and *=3.5*10-5 s-1 for the lower vortex as indicated in Fig. 3. These disturbances can be interpreted as a high potential vorticity anomaly (HPVA) near the tropopause and at the surface (Thorpe, 1985).

3.3 Design o f the comparative experiments In the "coupling development" experiment (the

control experiment), the initial upper vortex is placed 1200 km to the north of the basic jet axis. The initial lower vortex is placed on the jet axis and 1500 km to the east of the upper vortex (see Fig. 3). The choice of this particular configuration is based on the result of the preliminary experi-ments (Takayabu,1991). Besides the control experi-ment (Case C), we have performed 9 experiments as shown in Table 1, to examine the effect of the initial conditions. Cases E1 and E2 are the single vortex experiments with an initial vortex in either the up-per or lower troposphere. Cases E3*E6 are a series of experiments in order to determine the role of the meridional displacement between the upper and the lower vortices. Cases E7*E9 are the linear super-position of the results of single vortex experiments (time integration is not performed in these exper-iments). These three experiments are prepared to discuss the strength of the interaction between the upper and the lower vortex by comparing with Cases

Table 1. Summary of experiments, performed to study the mechanism of the "coupling development" . A

100 km grid model is used here.

* Zonal displacement between upper and lower vortex are 1500 km in

Case C, 1700 km in E5 and 1900 km in E3 (upper vortex to the west of the lower vortex).

* Character "N" denotes that the vortex center is 1200 km to the

north of the jet axis. Character "o" denotes that the vortex center exists on the jet axis.

* In E7*E9 , the basic field is subtracted before the superposition. After the superposition, the basic field is superposed on it once

more.


E1, E3 and E5, respectively. Differences in zonal

displacement among Cases E1, E3 and E5 are due

to the difference in basic zonal wind speeds around

these vortices.

4. Results

4.1 Time evolution of the surface vorticity First, we compare the time evolutions of the sur-

face vorticity in ten prescribed experiments. As an index of the cyclone strength, we adopt the value of the relative vorticity near the surface. Here, since we focus on the vortex center directly re-lated to the initially given upper vortex, we ne-glect the disturbances appearing at the edge of the wave packet in the analysis even though such dis-turbances may sometimes develop rapidly (this hap-pens in Case E4).1

Time evolution of the surface vorticity in each of the ten experiments is given in Fig. 4. Figure 4a in-dicates that the relative vorticity increases suddenly at day 3 in the "coupling development" experiment (Case C). At day 3.5, the vorticity strength greatly exceeds the value of Case E7 (mere superposition of the results of two single vortex experiments). The surface pressure decrease of the cyclone in Case C reaches 9 hPa per 24 hours from day 2.5-day 3.5 (which corresponds to 0.46 bergerons). On the other hand, when we put the lower vortex 1200 km to the north of the jet axis, and the upper vortex right to the west of the lower vortex (E5), time evolutions of the vorticity strength become quite different (see Fig. 4b). In Case E5, a temporary amplification at day 3 is completely explained by the superposition of two vortices (E8). When we put two vortices on the jet axis, as in Case E3 in Fig. 4c, development of the cyclone at the surface is about the same with that of Case E6 (lower vortex experiment) . These results indicate that,

1) Non-linear interaction is occurring in the "coupling development" experiment (Case C).

2) The meridional displacement between two initial vortices is critical for the occurrence of the "coupling development".

4.2 Overall feature o f Case C Figures 5*6 indicate the evolution of the extra-

tropical cyclone of Case C at day 2 and day 4 (the structure of the initial vortices was already discussed in Section 2). By day 2 (Fig. 5), a horizontal circu-lation associated with the upper vortex appears at

1As already indicated by Simmons and Hoskins (1979a), an initially isolated disturbance evolves to form a wave packet. In their paper, the wave packet was explained as a mere superposition of unstable normal modes of various wave lengths and independent of the vertical structure of the initial disturbances.

Fig. 4. Development of relative vorticity at * =0.97. (a) Cases C, E1, E2 and E7. (b)

Cases E1, E5, E6 and E8. (c) Cases E2, E3, E4 and E9.

the surface to the north of the lower vortex. By day 4, (Fig. 6), these two vortices merge and form a comma shaped vorticity pattern. Trajectories of the vortex center superposed on Fig. 6 indicate the prominent northward penetration of the lower vor-tex from day 2 to day 4. The drastic change in the structure of the cyclone occurring between day 2 and day 4 is accompanied by the rapid increase of the amplitude of the relative vorticity (see Fig. 4a). This is due to the non-linear effect of the "coupling development". The process of the "coupling development" can be

described with the following three stages.


Fig. 6. Surface pressure at day 4 of Case C

(the contour interval is 4 hPa). Relative vorticity at a=0.97 greater than 4*10-5 s-1 is stippled. Trajectories of the vortic-

ity centers at *=0.97 (*) and a =0.44 (*) with every 0.5 day interval from day 0 to

day 4 are superposed on it.

Fig. 5. Wind and potential temperature fields of Case C at day 2. Relative vorticity

greater than 4*10-5 s-1 are stippled. (a) At *=0.44. The contour interval is 4K.

(b) At *=0.97. The contour interval is 4K.

1) Deformation of the upper vortex (initial-day 2).

2) Northward penetration of the lower vortex (day 2-3).

3) Acceleration of the development of the cyclone near the surface (day 2.5-3.5).

In the subsequent subsections, we will elaborate on the mechanism of the "coupling development" at each of the above three stages.

4.3 Dynamics of the "coupling development"

4.3.1 Deformation o f the upper vortex Figure 7a shows the meridional-height sections at

the western side of the upper vortex in Case C at day 2 (about 400 km to the west of the upper vortex

center). Comparing with Fig. 3 (initial condition), we can find that the upper vortex to the north of the jet axis bends and intrudes gradually into the lower troposphere below the jet axis as time passes. This is purely an upper tropospheric process and the lower vortex makes no contribution here. Actually, the same process is seen in Case El which has only an upper vortex initially (Takayabu, 1991). When an upper vortex is superposed on the westerly baro-clinic jet, a sharp jet streak forms to the south of the upper vortex center. This existence of the jet streak indicates the strong interaction between the upper vortex and the basic flow.

In order to look into the mechanism of the defor-mation, we examine potential vorticity (PV), a con-served quantity in the dry atmosphere. We utilize the potential vorticity with the hydrostatic approx-imation defined as,

where g is the gravitational acceleration; f, the Cori-olisparameter and

is the vertical component of relative vorticity on 0-surface. Since the static stability g*/*p is one or-der or more larger in the stratosphere than in the troposphere, the PV is also far larger in the strato-sphere when the atmosphere is at rest. The contour of 10-6 m2 s-1 K kg-1 approximates the boundary of the stratospheric air mass when f *1*10-4 s-1.


Fig. 7. (a) Meridional-height cross sections through the entrance region of the jet

streak at day 2 of Case C. Contours are potential temperature (dashed line, contour

interval 5K) and relative vorticity (solid line, contour interval 2*10-5 s-1). The shaded area indicates values of relative

vorticity greater than 2*10-5 s-1. Air flow along the cross section is indicated

by vectors (both zonal mean and meridional mean are subtracted) . Units of vec-

tors are indicated in the bottom left corner of the figures (5 ms-1 in the horizontal di-

rection and 5 cm s-1 in the vertical direction). The thick dot (J) denotes the cen-

ter of the baroclinic westerly jet. (b) The same cross section as that in (a). Thick

lines superposed on it are contours of potential vorticity (1.0*10-6 m2 kg-1 s-1K

= PV-unit) of day 0 (dotted line), day 1

(broken line) and day 2 (solid line) at the entrance region of the upper jet streak.

For convenience, we adopt 10-6 m2 s-1 K kg-1 as a "potential vorticity unit (PV unit)" after Hoskins

et. al. (1985). We superpose contours of PV at the western edge

of the upper vortex (day 0, day 1 and day 2) onto the flow pattern at day 2 (see Fig. 7b). Since PV is con-served following air parcels, the folding structure of the PV contour clearly shows that the deformation occurs with the downward advection of the high-PV air. Characteristics of this vertical circulation are as follows.

1) It appears at the entrance of the jet streak, which corresponds to the confluent region (not

shown).

2) The direction of the vertical motion is upward (downward) in the warmer (colder) side of the

baroclinic zone. It corresponds to the thermally direct circulation.

From the above points, we can conclude that the upper vortex deformation is associated with the sec-ondary direct circulation accompanying the fronto-genesis at the jet streak.

Initially, both the confluent flow and the trans-verse circulation is confined to the upper tropo-sphere in Case C. However, the transverse circu-lation at the upper troposphere gradually advects the high-PV air to the lower troposphere along the sloping isentropic surface (about 1.0 km/day). As a result, the confluent flow appears near the surface by day 2, and the cross-frontal circulation extends over the entire troposphere. Such a circulation does not develop when the baroclinicity of the basic field is confined either in the upper or in the lower tro-posphere (not shown).

The exit region of the jet streak (the eastern side of the upper vortex) is frontolytic, and a thermally indirect circulation occurs (not shown). Since the vertical air motion is upward to the north of the jet axis, the intrusion of the upper high-PV anomaly does not occur there.

4.3.2 The northward movement o f the lower vortex So far we have shown that the upper vortex gets

deformed through the "upper-level frontogenesis". The deformed upper vortex then begins to form cy-clonic horizontal circulation near the surface and the interaction with the lower vortex becomes apparent.

In Case C, the lower vortex shifted northward from day 2 to day 3 as shown in Fig. 6. On the other hand, in Case E2, the vortex moved eastward (not shown). It indicates that the upper vortex plays an important role in the northward movement of the lower vortex.

In order to elaborate the dynamics associated with the lower vortex movement, we estimate the vorticity budget near the surface with the following


equation.

where

and us the zonal velocity of the system (6.56 m/s in Case C). The meridional velocity of the system is neglected here. All variables are divided into the basic field (A) and deviations (A'). Distributions of terms (III) (advection by the disturbance) and (V) (stretching terms) in Case C at day 2 are shown in Fig. 8. Remaining terms are negligibly small and not shown here. The leading term is the stretching caused by the upward flow, and its maximum value is 2.7*10-9s-2. Advection by the disturbance is up to 0.4 *10-9s-2, which is 20-30% of the stretch-ing term. Another characteristic feature is that the area with large stretching effect is elongated in the meridional direction from the center of the northern (upper) vortex to the center of the southern (lower) vortex. This stretching leads to the apparent north-ward movement of the lower vortex.

The origin of the stretching is sought by examin-ing the upward air motion using the omega equation;

where *, the p-velocity; *g, the geostrophic wind; *', the deviation of geopotential height; f o, the mean value of Coriolis parameter; N2, the static stabil-ity. Equation (13) indicates that the upward air motion balances with the positive vorticity advec-tion aloft (term (I)), or with the warm air advection (term (II)). The p-velocity due to the vorticity ad-vection in the upper troposphere may also appear in Case E1. We here focus on the warm air advection near the surface (term (II)), because the distinction of * between Cases C and E1 must be due to this term. To confirm the above expectation, we examine the

relationship between the warm air advection and the

Fig. 8. Horizontal distribution of the terms of Eq. (11) at *=0.97 around the lower vor-

tex at day 2 of Case C. Centers of the upper and the lower vortex are indicated with

thick dots. (a) Advection by the anoma- lous wind (Term (III) of Eq. (11)). (b)

Summation of stretching terms (Term (V) of Eq. (11)). The contour interval is 1*

10-10 s-2 . Shaded areas indicate positive fields.

upward wind profile on the meridional-height cross sections. Figures 9*11 are meridional-height cross sections through the center of the lower vortex of Cases C, E1 and E2, respectively. Distributions of (a) relative vorticity, (b) vertical velocity and (c) meridional wind speed portrayed in the wind vectors and horizontal potential temperature gradient are


depicted. There are found four peaks of upward flow in Case C, marked with signs a, b, c and d in Fig. 9b. Among them, Peak c appears at the northern edge of the lower vortex and leads to the northward movement of the lower vortex through stretching.

Figure 9c shows the distributions of the warm air advection of Case C. We confirm from the figure that the southerly wind speed and the temperature gra-dient are both large near the peak c, resulting the strong northward warm air advection there. A com-bined effect of the upper and the lower vortices is necessary to cause strong northward warm air ad-vection. Each vortex produces:

1) the strong southerly wind induced by the downward penetration of the high-PV air,

2) the large temperature gradient at the northern edge of the initial lower vortex accompanied by

the warm air mass.

Since one of these two conditions is not satisfied in Cases E1 or E2 (experiments with one initial vor-tex), the strong warm air advection does not oc-cur. Actually in Case El (Fig. l0c), rather strong southerly wind is induced by the deformed upper vortex, but the temperature gradient is small there. In Case E2 (Fig. 11c), on the other hand, though a large temperature gradient at the northern edge of the lower vortex exists, no strong southerly wind ap-pears. As a result, Peaks a, b and d are also found in Cases E1 or E2, Peak c is not.

We can interpret the mechanism also from the standpoint of the PV advection. The region of high-PV near the surface (*0.6 PV-units) is indicated by the thick dotted line in Fig. 9a. The high-PV anomaly appears just to the north of the center of the lower vortex center, around the Peak c of the up-ward air motion. It clearly shows that near-surface

Fig. 9. Meridional-height cross sections through the center of the lower vortex at

day 2 of Case C. (a) Relative vorticity

(contour interval 1*10-5 s-1). Shaded area indicates values greater than 2*10-5

s-1. The thick dotted line is the contour of 0.6 PV-unit. (b) Vertical velocity (contour

interval 5*10-3 ms-1) . Shaded areas indicate values greater than 5*10-3 ms-1.

Four peaks of upward velocity are indicated by characters a, b, c and d. (c) Am-

plitude of the horizontal gradient of the potential temperature (*/*) (contour interval 0.5K/ 100 km). Shaded areas indi-

cate values greater than lK/100 km. Air motions along the cross section are indi-

cated by vectors.


Fig. 10. As in Fig. 9 except for Case El. The cross section is along the same zonal posi-

tion as in Case C. Two peaks of upward air motion are indicated by characters a and

b in (b).

Fig. 11. As in Fig. 9 but for Case E2. A peak of upward velocity is indicated by charac-

ter d in (b).

620 Journal of the Meteorological Society of Japan ' Vol. 69, No. 6

Fig. 12. Time series of maxima of upward air

motion at *= 0.7 of Cases C, E1 and E5.

The time series of relative vorticity at *

=0.97 of Case C is also indicated as thin

sold line.

high-PV anomaly is produced by the northward ad-vection of air parcels along the potential tempera-ture surface there. The reduced static stability pro-duces large relative vorticity.

4.3.3 Continuous rapid growth of the vortex As already shown in Fig. 4a, relative vorticity of

the vortex center near the surface increases rapidly from day 2.5 to day 3.5. It increases from 6.9 *10-5 s-1 at day 2.5 to 14.1*10-5 s-1 at day 3.5.

Figure 12 shows the time series of the peak val-ues of p-velocity at *=0.70 (approximately 700 hPa level) from Cases C, El and E5. A pronounced in-crease of the p-velocity is observed only in Case C, where the value doubles within 9 hours from day 2.25. In Case E1 (upper initial vortex only) or in Case E5 (no displacement in the meridional direc-tion between two vortices), such a rapid increase in w field does not occur. In Case C, a large value of * is maintained for more than a day. Therefore, we can confirm that the stretching associated with this large * contributed to the rapid increase of the vorticity near the surface.

At day 2.5, the "coupling" of the upper and the lower vortices is clearly seen. Figures 13 show the zonal-height sections at day 2 and day 2.5 at the lat-itudes between the upper and the lower vortex cen-ters (at day 2.5, the upper vortex center is located about 300 km to the north of the section, while the lower vortex is found about 500 km to the south of this section). Until day 2, the upper and the lower vortices are separate systems. At day 2.5, these two vortices connected together with the axis in-clining to the west with height. At the same time, a strong vertical circulation develops around these connected vortices, suggesting that there must be some close relationships between the "coupling" and

Fig. 13. Zonal-height cross sections of Case C at (a) day 2 and (b) day 2.5, through the

latitude between the upper and the lower vortices. Contours of potential tempera-

ture are thin broken and drawn every 5K and those of relative vorticity are thin con-

tinuous and drawn every 2*10-5 s-1. The thick broken line is the contour of 1.0 PV units around the upper troposphere and the thick dotted line 0.6 PV units near

the surface. Motions along the sections are indicated by vectors (zonal mean is

subtracted). Units of vectors are horizontally 5 m s-1 and vertically 5.0*10-2

ms -1. (indicated in the bottom left corner of the figures).

the increase of the upward wind velocity.

At this stage, the meridional displacement be-

tween the upper and the lower vortices become cru-

cial for the "coupling" . In practice, in Case E5,

where two vortices are initially at the same latitude,

the upward velocity around the lower vortex does


Fig. 14. Meridional-height cross sections through the center of the lower vortex at

day 2.5. Contours of potential temperature are thin broken and drawn every 5K.

Motions along the sections are indicated by vectors (zonal mean and meridional

mean are not subtracted here) . Units of vectors are horizontally 10 m s-1 and ver-

tically 1*10-1 ms-1 (indicated in the bottom left corner of the figures). Areas of the lower vortex at the same cross section, and the upper vortex 300 km to the west are shaded (values larger than 4*10-5 s-1).

The thick solid line is the contour of relative vorticity (8*10-5 s-1) at the center

of the upper vortex. The thick broken line and thick dotted line are contours of poten-

tial vorticity (broken line; 1.0 PV-units at the cross section of the upper vortex cen-

ter, dotted line; .0.6 PV-units at the cross section of the lower vortex center).

not increase when the upper vortex overtakes the lower one (see Fig. 12). To make the difference be-tween Case C and Case E5 clear, we investigate the meridional-height sections of both Cases C and E5 at day 2.5, at the center of the lower vortices (Figs. 14 and 15). The area of the upper vortices 300 km to the west of the lower ones are projected on the sections. In Case C, the center of the upper vortex appears about 300 km to the west and 800 km to the north of the lower vortex. A high-PV anomaly is in-duced at the northern part of the lower vortex (the thick dotted line), which is overtaken by the upper air high-PV anomaly aloft, accompanying the up-per vortex (thick broken line) (see also Sub-section 4.3.2). It results in a strong vertical air flow to the north of the lower vortex center, and the lower vor-tex connects with the upper vortex on the same po-tential vorticity surface. On the other hand, in Case E5, since the high-PV anomaly near the surface is

Fig. 15. As in Fig. 14 but for Case E5.

formed far to the north of the upper air high-PV anomaly, the vertical circulation of these two vor-tices did not couple (Fig. 15). Evolution of Case E5 corresponds to the result of the mere superposition of two boundary waves in the two-dimensional linear model (not shown).

5. Discussion

5.1 Observational analysis and comparison with the "coupling development"

5.1.1 Observational facts It is widely said among the weather forecast pro-

fessionals that some of the rapid development of the cyclones around the Japan Islands is associated with the upper trough. For example, Nikaidou (1986b) described cyclone development associated with an upper vortex at 40*N using potential vorticity on the isentropic surface. In this section, we show an example of the "coupling development" in the real atmosphere in the period from 25 through 28 April 1986. Figures 16 and 17 show the surface weather maps

and GMS infrared images at 00GMT 26 April and 00GMT 28 April. On 26 April, we can find two dis-

tinct low pressure centers, one in the north-eastern part of the Asian Continent, and the other near the Korean Peninsula. Each of them is accompanied by a cloud system. By 28 April, these two cyclones merged and developed to the north-east of the Japan Islands. The comma-shaped cloud pattern shows that this cyclone is in its mature stage at this time.

Figure 18 shows the tracks of the northern and southern vortices superposed on the time mean westerly jet axis (averaged from 16 to 30 April). The northern vortex (*) moved eastward along 45°N, about 5 degrees to the north of the main branch of the westerly jet axis, while the southern vortex (*) first appeared under the southern branch of the


Fig. 16. Surface weather maps of East Asia.

(a) At 00GMT 26 April 1986. The center of the northern and the southern lows before the coupling are denoted by charac-

ters LN and LS . (b) At 00GMT 28 April 1986. The center of the cyclone developed

through the coupling is denoted by character Lc. (From JMA global objective anal-

ysis data)

westerly jet (around 30*N) and moved north-eastward till it reached the latitude of the main branch of the westerly jet axis. The northern vortex was associated with a cold vortex aloft (*). The coupling of these two vortices occurred in the pe-riod from 00GMT to 12GMT 27 April. As indi-cated in Fig. 19, relative vorticity near the surface increased suddenly through the "coupling" , suggest-ing the importance of the coupling of vortices for the development of this cyclone. The surface pres-sure changed from 994 hPa (12z 27) to 974 hPa (12z

Fig. 17. GMS infrared images of the same

time and area as Fig. 16.

28) in 24 hours (1.02 bergerons). The meridional-height cross sections of these two vorticities before the "coupling" (00GMT 25 April) are shown in Fig. 20. The following characteristics are indicated;

1) The northern vortex (Fig. 20a) : It had the structure of an upper cold vortex. The hor-

izontal scale of the vortex was 800 * 900 km. The maximum amplitude of the relative vortic-

ity anomaly (*) and the temperature anomaly

(zT) are *=1.3 x 10-4 s-1 and *=*10K.

2) The southern vortex (Fig. 20b): A shallow lower vortex was seen at 30*N from the surface up to

700 hPa, while the horizontal scale was 800 ti 900 km. *=0.3*10-4 s-1 and *= +3K

The center of the southern vortex was located at 15 degrees to the south and 12.5 degrees to the east of


Fig. 18. Trajectories of the 25-28 April cyclone are drawn in 12-hour segments from 00GMT 25 to 12GMT 28 April 1986. *, *, and denote the center of the southern surface vortex center, northern surface vortex center and the northern vortex center at 400 hPa, respectively. Two baroclinic jet axes are

also indicated by thin continuous lines with arrows. The region where the wind velocity around the tropopause exceeds 30 m/s is stippled.

the northern vortex. Considering above features of the two vortices, we call the northern vortex "the upper vortex" , and the southern vortex "the lower vortex". Next, the meridional-height cross sections of

the cyclone at the earlier stage of the "coupling" (00GMT 27 April) are shown in Fig. 21 We can see that the upper vortex bent along the sloping isentropic surface (Fig. 21a) and connected with the lower vortex located to the east (Fig. 21b). The cy-clone began to develop rapidly at this time.

We also perform a brief statistical analysis of the extratropical cyclones developed around the Japan Islands. In 1986, 151 extratropical cyclones were observed along three tracks (30*N, 40*N and 50*N at 140*E; These tracks corresponds to those pointed out by Umemoto, 1982 and Asai, Kodama and Zhu, 1988). The statistics show that there were 7 cases of the "coupling development" out of 39 well-developed cyclones (maximum deepening rates greater than 7 hPa/12 hours) along 40*N and 50*N tracks (see Fig. 22). Most of them appeared in spring, late autumn and early winter. In all 7 cases upper vortices moved from northeastern part of Asian continent to Japan Islands, coupled with shallow lower cyclones born

Fig. 19. Time series of relative vorticity asso-

ciated with the 25-28 April cyclone. •,

* and * indicate values of relative vor-

ticity at the centers of the southern vor-

tex at 850 hPa, the northern vortex at 850

hPa and the northern vortex at 400 hPa,

respectively.

around 30*N of the east coast of Asian continent.

5. 1.2 Comparison with the observed cyclone

In Sections 3 and 4, we use a simple numerical

model with idealized disturbances and basic flow.


Fig. 20. Meridional-height sections through the center of (a) the upper vortex (100*E) and (b) the lower vortex (112.5*E) at

00GMT 25 April 1986. Contours of potential temperature are thin broken and drawn every 5K and those of relative vorticity are thin solid and drawn every 2 * 10-5 s-1. The vortex region is roughly indicated by the stippled area. Contours of potential vorticity are the thick broken line

(1.0 PV units). Air flows along the cross section are also indicated by vectors (zonal

mean and meridional mean are not subtracted). Units of vectors are horizontally

10 ms-1 and vertically 1*10-1 ms -1.

Nevertheless, when we compare the experimental re-sults with the observational facts (Section 5.1.1), we still can find many common features among them.

a) Northward movement o f the lower vortex In the 25-28 April cyclone, the basic field showed

the double jet profile around 100*E, where distur-bances first appeared. However, near the longitude

Fig. 21. As in Fig. 20 except for cross sections at 00GMT 27 April, through the center of

(a) the upper vortex (122.5*E) and (b) the lower vortex (130*E).

where the "coupling development" occurred, only one jet axis was found (Fig. 18). Hence we consider that it is appropriate to compare the results with the model results.

In the 25-28 April cyclone, the upper vortex first appeared about 500 km to the north of the jet axis, accompanied by a jet streak at the southern edge and moved eastward along the northern edge of the westerly jet. The shallow lower vortex first appeared beneath the southern branch of the baroclinic west-erly jet, and moved northeastward till it reached the latitude of the northern branch of the baroclinic jet flow. This northward movement of the lower vor-tex, which is a key process in the "coupling develop-ment" , corresponds well to that which seen in Case C. Such behavior of the lower vortices was also re-ported by Mullen (1983), Sanders (1986) and Ogura and Juang (1990).


Fig. 22. Trajectories of cyclones developed through coupling of two vortices. All seven cases occurring

around the Japan Islands in 1986 are indicated. Maps of sea level pressure are used here. Trajectories are drawn in 12-hour segments. Positions where northern and southern vortices first appear are indicated

by * and *, respectively.

b) Intrusion of the upper vortex In the 25-28 April cyclone, the upper vortex bent

along a sloping isentropic surface and connected with the lower vortex at 00GMT 27 April (see Fig. 21). Coupling of two vortices led to the accelera-tion of the cyclone development. This process cor-responds well to that occurred in Case C. Intrusion of the upper vortex to the lower troposphere preced-ing the development of the cyclone was also pointed out by Uccellini et al. (1985,1987), Bleck (1990) and Ogura and Juang (1990).

As described above, characteristic features associ-ated with the "coupling development" we have pic-tured can also be found associated with some ob-served cyclones. Therefore, we can confirm that the mechanism of the "coupling development" re-ally works in the mid latitudes.

5.2 Comparison with the existing models of cyclogenesis through upper level processes

In this study, the downward intrusion of a large amplitude upper vortex is indispensable for the "coupling development" . The frontogenetical trans-verse circulation at the western edge of the upper vortex corresponds well to that represented by the Sawyer-Eliassen equation (Sawyer, 1956; Eliassen,

1962). The downward intrusion of the lower strato-spheric air associated with the secondary circula-tion is also reproduced in two-dimensional frontoge-nesis models (e.g. Hoskins and Bretherton, 1972). Uccellini and. Johnson (1979) studied the three-dimensional circulation around a jet streak in de-tail. The circulation pattern around the jet streak in Case C is in good agreement with their results. They also investigated the relationship between the upper tropospheric jet streaks and severe convective storms which frequently developed in the warm sec-tor of the extratropical cyclones. They pointed out that the strong southerly wind embedded in the in-direct (frontolytic) circulation around the exit of the upper tropospheric jet streak contributes to the oc-currence of severe convections. It may correspond to the second stage of our "coupling development".

The main effect of the lower disturbance on the "coupling development" is to prepare strong baro-

clinicity near the surface. Therefore, when we put a zonally symmetric baroclinic zone near the sur-face instead of the shallow vortex, the initial con-dition corresponds to that of Type B of Pettersen and Smeybe (1971), or cyclogenesis induced by the upper air high-PV anomaly proposed by Hoskins et al. (1985). Bleck (1990) simulated cyclogenesis fol-


lowing Hoskins et al.'s model. However, there ex-ists a large difference between our study and their models. In our study, the shallow, near surface baroclinic zone is separated from the main west-erly jet aloft. Through the thermal wind relation, it inevitably produces a strong horizontal shear zone near the surface. This basic field seems to be more realistic, because there are many kinds of shallow disturbances around the cyclogenesic field in the mid-latitudes. For example, thermally or orograph-ically induced vortices and coastal fronts. Recently, Thorncroft and Hoskins (1990) succeeded in simu-lating a cyclone developed through the interaction between a surface cold front and an upper air high-PV anomaly. The development processes described in their study correspond well to those of the "cou-pling development" . It indicates that the mecha-nism of the "coupling development" works also in some cases of frontal cyclogenesis.

5.3 The origin of the upper and the lower vortices In this study, we do not investigate where the ini-

tial vortices we adopted come from in the real at-mosphere. In this subsection, we discuss the possi-Me origin of these vortices referring to the previous studies.

5.3.1 The lower vortex There are many forecasting experiments and ob-

servational studies examining the formation process of the vortex near the surface. In the case of mar-itime cyclones, the sensible and/or the latent heat supply from the sea surface reduced the stability of the atmosphere at the lower troposphere, which in-duced a shallow lower vortex there (e.g. Chen et al., 1983; Orlanski, 1986; Reed and Albright, 1986 and Gyakum and Barker, 1988). In the case of shallow lower vortices formed over the continent, not only the heating, but also the dynamical forcing becomes important in the process of formation. Accumula-tion of a cold air mass by mountains (e.g. Pagnotti and Bosart, 1984), formation of a low static stabil-ity region downstream of mountains (e.g. Buzzi and Tibaldi, 1978) and formation of shear line down-stream of mountains (Murakami and Nakamura, 1983 and Nakamura and Murakami, 1983) can all generate a vortex in the lower troposphere. Sur-face frontogenesis (e.g. Mullen, 1983 and Ogura and Juang, 1990) or the instability along a front (Moore and Peltier, 1987, Joly and Thorpe, 1990) also pro-duces a vortex near the surface either over the con-tinent or over the ocean. The lower vortices in the previously mentioned, 1986's seven cases correspond well with the "subsequent phase" of Himalayan lee cyclogenesis discussed in Murakami and Nakamura (1983). Above studies indicate that the lower vortices can be generated through various kinds of processes ei-ther over the continent or over the ocean.

5.3.2 The upper vortex On the other hand, there are not so many stud-

ies focusing on the origin of the vortices around the tropopause. An observational study using a Q-map (map of potential vorticity on the isentropic surface) was done by Hoskins et al. (1985). They studied the behavior of the disturbances around the tropopause, tracing the PV anomaly on the isentropic surface. They concluded that there are many, long-lived vor-tices around tropopause, advected eastward on the baroclinic westerly jet. In some cases, the vortex reaches the surface, but in other cases there ap-pear no horizontal circulations near the surface as-sociated with the upper disturbances. These vor-tices seemed to be isolated disturbances rather than a crest of wave packets. However, the generalized method to represent the isolated vortex theoretically is not yet established. How to distinguish the iso-lated disturbances from the basic field in the real atmosphere is also a very difficult problem to be solved (Fourier analysis is inadequate to pick up this kind of disturbance) . We cannot clearly say where the upper vortex comes from, until we solve these technical problems.

6. Conclusion

Using a *-plane dry primitive equation model, we have succeeded in reproducing the "coupling devel-opment" of an extratropical cyclone. We clarified the necessary conditions for the "coupling develop-ment" and described its dynamical process.

The following three conditions are essential for the "coupling development".

1) The initial upper disturbance which is accompanied by a high-PV anomaly around the upper troposphere appears on the northern side of the

baroclinic zone to form a jet streak to the south of the disturbance.

2) The initial lower disturbance exists as a warm air mass confined near the surface. It is accom-

panied by a strong surface front at the northern edge.

3) The location of the initial lower disturbance is to the south-east of the initial upper distur-

bance.

We can summarize the mechanism of the "coupling development" as follows;

1) A jet streak forms in the upper troposphere between the jet axis and the northern upper tropospheric vortex. Then transverse ageostrophic

circulation associated with the upper-level frontogenesis around the entrance region of the jet

streak deforms the upper vortex from day 0 to day 2. As a result, the upper vortex bends along


a sloping isentropic surface, and intrudes into the lower troposphere beneath the jet axis.

2) This upper vortex induces a strong southerly around the lower vortex. Since an air mass

with the warm temperature anomaly accompa- nies the lower vortex, a large -* • * area is

formed at the northern edge of the lower vortex. It yields a strong upward flow, and hence

stretching results there. Afterwards, positive vorticity tends to be produced at the northern

edge of the lower vortex, so that the lower positive vortex center moves northward from day 2

to day 3.

3) Around day 2.5, the upper air high-PV anomaly overtakes the high-PV anomaly near the sur-

face, and the rapid amplification of upward p- velocity occurs in the middle troposphere. At the same time, the upper vortex and the lower

vortex come into contact along the sloping isentropic surface. The intensified upward velocity

produces a large positive vorticity through the stretching effect, and the cyclone continues to develop rapidly from day 2.5 to day 3.5.

Movement of the lower vortex, and the intrusion of the upper vortex into the lower troposphere corre-spond well to the 25-28 April 1986 cyclone devel-oped around the Japan Islands. This indicates that the development mechanism summarized above oc-curs in the real atmosphere. The origin of both the upper and the lower vortices is also an interesting problem left for future studies.

Acknowledgements

The author wishes to express his gratitude to Prof. T. Asai of the Ocean Research Institute, Uni-versity of Tokyo, for his guidance and encourage-ment throughout this study. He also wishes to ex-press his particular thanks to Dr. Hajime Naka-mura of the Japan Meteorological Agency for his guidance and suggestion for the numerical model used in this study. He is also grateful to Prof. K. Gambo for much useful advice. He also wishes to express his thanks to Prof. T. Matsuno and Prof. A. Sumi of the Center for Climate System Research, University of Tokyo, Dr. Ko. Masuda and Dr. Y.Y. Hayashi of the Department of Earth and Planetary Phisics, University of Tokyo, and Prof. R. Kimura and Dr. K. Nakamura of the Ocean Department of Earth and Planetary Physics, University of Tokyo, for their very willing co-operation. He is also grate-ful to Prof. H.C. Davies, ETH and Dr. R.T. Pierre-humbert, GFDL/NOAA, of Princeton University for comments on the earlier version of Section 3 of this study. Finally, he is much obliged to Prof. Y. Ogura of the Japan Weather Association, Dr. M. Yoshizaki

and Dr. M. Nagata of the Meteorological Research Institute, Dr. Hisashi Nakamura of the University of Washington, Ms. Y.N. Takayabu of the National Institute for Environmental Studies and the referees of this journal for reading the manuscript and giving valuable comments.

The computation was done by the HITAC M-200, M-280, M-680 and *-810/20 computers at the Com-puter Center, University of Tokyo. The Graphic Utility Library of NCAR was used in this study.

This work was accomplished as a doctoral thesis submitted to University of Tokyo.

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「カップリング発達」の研究=温帯低気圧の効率的発達のメカニズム

高藪出

(気象研究所)

「カップリング発達」一対流圏上層と下層の二つの渦のカップリングにともなう低気圧の急発達一を、β一

平面チャネルの水無しプリミティブ方程式系モデル(16層、格子間隔100km)を用いて数値的に調べた。

カップリング発達を再現する適切な初期条件を探った結果、下層渦をジェット軸上に、上層渦をその北西

方に置いたときに「カップリング発達」が生ずることが判った。この「カップリング発達」は次の三ステー

ジからなる。1)上層フロントゲネシスがもたらす上層渦の変形(初期一2.0日目)。2)下層渦位の移流がも

たらす下層渦の北上(2.0-3.0日目)。3)上下の渦の「カップリング」に伴う下層渦の発達加速(2.5-3.5

日目)。いずれのステージにおいても、渦と渦、あるいは渦と偏西風ジェットの相互作用が重要な役割を果

たしている。

本論文では、日本列島周辺で1986年4月25-28日にかけて発達した低気圧についての簡単な解析も行っ

た。この低気圧については次の二点の特徴が確認された。1)カップリングに先立つ下層渦の北上。2)傾いた

等温位面に沿った上層渦の下方侵入と、急発達開始期の下層渦との「カップリング」。数値実験の結果はこれ

らの諸特徴をよく再現しており、「カップリング発達」のメカニズムが中緯度で重要であることを示している。

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