on the bogusing of tropical cyclones in numerical models...

Meteorol. Atmos. Phys. 65, 153-170 (1998) Meteorology, and Atmospheric

Physics �9 Springer-Verlag 1998 Printed in Austria

Bureau of Meteorology Research Centre, Melbourne, Victoria, Australia

On the Bogusing of Tropical Cyclones in Numerical Models: The Influence of Vertical Structure

Yuqing Wang

With 14 Figures

Received May 27, 1997

Summary

In this study, idealised conditions are used to study the influence of vertical structure of the bogus vortex on its motion in numerical models by comparing the resultant forecast tracks. Two vortices were used: one has a cyclonic circulation throughout the troposphere and the other has an upper tropospheric anticyclone. Both vortices have the same structure in the middle and lower troposphere. The two vortices were inserted into four different environmental flows on a beta-plane: (a) a resting atmosphere; (b) a uniform flow; (c) a horizontal shear flow and (d) a vertical shear flow. The results show that the forecast tracks are very sensitive to the vertical structure of the bogus vortex, especially when the environmental flow is very weak, or is westerly and has a cyclonic horizontal shear. However, this sensitivity is reduced in moderate vertical shear. This motion sensitivity is found to arise from the vertical coupling mechanism by which the upper- and lower-level circulations interact with each other when a horizontal displacement occurs between them.

The vertical structure of the bogus vortex can also affect the intensity of the model cyclone, depending on the configuration of the environmental flow. In general, the bogus vortex without an upper-level anticyclone will intensify quicker and will develop more intense than the one with an upper-level anticyclone, The vertical coupling mechanism can result in different asymmetric rainfall pattern in cyclone core region depending on the vertical structure of the bogus vortex. The asymmetric divergent flow associated with these convective asymmetries may in turn further influence the vortex motion. It is suggested that care needs to be taken in determining the vertical structure of the bogus vortex in numerical models.

1. Introduct ion

At the resolut ions current ly in use, and with the sparse data coverage over the tropical oceans, numer ica l analyses cannot adequate ly represent t ropical cyc lone circulat ions for use in numer ica l weather predic t ion (NWP) models (Leslie and Holland, 1995). At mos t N W P centers a " b o g u s i n g " scheme is thus em p lo y ed to force a tropical cyc lone vor tex into the numer ica l analysis. This is typical ly done by using a vor tex with suitable hor izontal and vert ical structure to derive a set of bogus observat ions for inclusion in the analysis /assimilat ion cycle (Elsberry, 1987). Bogus ing methods vary be tween the centers but mos t involve an ax isymmetr ic vor tex with some added a sy m m et ry to take into account current m o v e m e n t of the cyc lone and envi ronmenta l flow (e.g., Ueno, 1989, 1995; Mathur, 1991; Davidson and Puri, 1992; Kurihara et al., 1993, 1995).

There are basical ly three approaches that are current ly used in operat ional models , as sum- mar ized by Peng et al. (1993). The first is to bogus observat ional data before the object ive analysis is carr ied out. Examples o f this type of bogusing are those used in the US National Center for Envi ronmenta l Predic t ion (NCEP) global forecast model (Lord, 1991), in the US N a v y Operat ional Global Atmospher ic Predic-

154 Y. Wang

tion System (NOGAPS) (Fiorino et al., 1993; Goerss and Jeffries, 1994), and in the UK Meteorological Office global model (Radford, 1994; Heming et al., 1995). The second approach is to add a more complete vortex circulation defined by an analytical expression after the objective analysis but before the model initialization. Examples of this type of bogusing are those used in the Quasi-Lagrangian Model (QLM) of the US NCEP (Mathur, 1991) and the Typhoon Model of the Japan Meteorological Agency (JMA) (Ueno, 1989, 1995). The third approach is to bogus a "spinup" vortex gener- ated by the same forecast model, instead of using an analytical one. Examples of this are the multiply nested tropical cyclone model of the GFDL (Kurihara et al., 1993, 1995) and the typhoon-Track Forecast System (TFS) of the Central Weather Bureau (CWB) in Taiwan (Peng et al., 1993). In addition to the different methods, both the horizontal and vertical structures of the axisymmetric vortex vary considerably between the centers even for the same method (Serrano and Und6n, 1994; Leslie and Holland, 1995).

Leslie and Holland (1995) have made a comparison of four commonly used and refer- enced bogus vortex profiles in a barotropic framework, including the modified Rankine vortex, as used in the US Navy global model (Goerss and Jeffries, 1994), the UK global model (Heming et al., 1995) and as tested in the European Centre for Medium-Range Weather Forecasts (ECMWF) global spectral model (Andersson and Hollingsworth, 1988; Serrano and Und~n, 1994); the Fujita (1952) profile, as used in JMA typhoon model (Ueno, 1989, 1995) and in the US NCEP QLM (Mathur, 1991); the Holland (1980) profile, as used in the Australian Tropical Analysis Prediction System (TAPS) (Davidson and McAvaney, 1981), barotropic tropical cyclone forecast model (Holland et al., 1991), and storm-surge model (Hubbert et al., 1991); and the profile used by DeMaria (1987) and DeMaria et al. (1992) in their barotropic tropical cyclone forecast models. Without the added complications associated with the presence of baroclinic effects, Leslie and Holland (1995) compared these four profiles in a forecast barotropic model. They have established some of the sensitivities that need to be addressed in developing a tropical cyclone bogus for opera-

tional numerical models, such as sensitivities to the vortex profiles, to the initial vortex positions, and the influence of the bogus vortex on its environment.

A natural extension of the work done by Leslie and Holland (1995) is to study the influence of vertical structure of the bogus vortex in numerical models. As noted by Serrano and Und~n (1994), the vertical structure of the bogus vortex does substantially diverge in numerical models currently in use, in particular, with or without the outflow layer. For example, in the typhoon model of JMA and the QLM of NCER the bogus cyclone includes an anticyclonic circulation in the upper-troposphere, while in most of the global models such as those used by the US Navy, the UK Meteorological Office and the US NCER bogus observations representing a tropical cyclone are included by inserting a cyclonic circulation extending from the surface to about 400 hPa and nothing above this level in the data assimilation phase (Goerss and Jeffries, 1994; Heming et al., 1995; Lord, 1991). Note that although a forecast model during assimilation can develop an outflow region, it takes longer time than the short-term forecast length (6 h in most forecast/assimilation systems) of a data assimilation cycle. That means that the outflow layer of a real tropical cyclone cannot be well represented at the initial time of the forecast model. The questions arise as to whether, how, and to what degree the vertical structure of the bogus vortex influences the cyclone motion in three-dimensional models. Recent theoretical studies by Wang et al. (1993), Holland and Wang (1995) and Wang and Holland (1996 a, b, c) have shown that baroclinic vortex motion can be very different for vortices with different vertical structures.

In the present study we have focused on the potential impact of vertical structure of the bogus vortex on its motion. In order to isolate this issue from the possible influences of the uncertainties in observations or objective analyses of the environmental flow surrounding a tropical cyclone, numerical experiments presented in this study are all performed under idealized conditions. The next section describes the numerical model used and the strategy of our numerical experiments. Influences of vertical structure of the bogus vortex on its motion on a beta-plane in

On the Bogusing of Tropical Cyclones in Numerical Models 155

an environment at rest, and in a variety of environmental flows are evaluated in section 3. Our major findings are summarized and discussed in section 4.

2. Experimental Design

2.1 The Numerical Model

The numerical model used in this study is a modified version of the one designed and used by Wang (1995a), Wang and Holland (1996a, b). It is a limited-area, hydrostatic, primitive equation model on either an f-plane or a /3-plane formulated with Cartesian coordinates in the horizontal and a o--coordinate in the vertical [or = (p - Pt)/(Ps - Pt), where p is the pressure, p, the surface pressure, and Pt the pressure at the top of the model, which is taken to be 100hPa]. The model consists of 16 layers in the vertical from 0 = 0 to 1, with the interfaces or=0.0, 0.054, 0.114, 0.181, 0.25, 0.328, 0.397, 0.472, 0.546, 0.618, 0.688, 0.754, 0.816, 0.872, 0.922, 0.965, 1.0. All the vertically dependent variables, such as horizontal velocity, potential temperature and specific humidity, are defined in the middle of each layer but, the vertical velocity 6- is stag- gered. For upper and lower boundary conditions, we required that fluid particles do not cross the cr = 0 and cr = 1 surfaces. The horizontal mesh of the model consists of 141 • 141 grid points with a uniform spacing of 40km. All variables are defined at the same grid point on the cr surfaces. Sponge layers are applied to the north and south boundaries, and all variables are cyclic in the zonal direction. Both the horizontal and vertical resolutions of the model are chosen to be representative of those currently in operational use (e. g., the Quasi-Lagrangian Model of the US NCEP),

A two-time-level, explicit time-split scheme similar to that used by Leslie and Purser (1991) is used for the model integration (Wang, 1995a; Wang and Holland, 1996a,b). The procedure consists of an advection stage of time step AtA, followed by N adjustment steps with time step of AtL = AtA/N. The full integration is concluded with a physical process stage of time step AtA. The forward-in-time upstream advection scheme developed by Wang (1996) is adopted for the time integration of the advection stage. This

advection scheme has third-order accuracy for t ime-dependent and non-uniform flow, and possesses very weak dissipation, very small phase errors and good shape-preserving proper- ties. The adjustment stage is accomplished by the forward-backward scheme with the Coriolis force term implicitly treated.

For the horizontal differencing, we use a centred finite difference scheme with fourth- order precision. The vertical differencing scheme is identical to that used by Arakawa and Lamb (1977). For the horizontal resolution chosen in this study, an adjustment time step A t e = 120 seconds was used and the number of adjustment steps per advection step was chosen to be N = 3. The calculation of physical processes is sum- marised below.

The large-scale condensation is calculated explicitly with the method used in Leslie et al. (1985). Subgrid-scale cumulus convection is parameterized following Kuo (1974) with mod- ifications suggested by Anthes (1977). Evapora- tion of precipitation has been included in both the large-scale precipitation and the subgrid- scale precipitation, following the method of Kessler (1969). Subgrid-scale horizontal diffusion of momentum, heat and moisture is calculated in the manner given by Smagorinsky et al. (1965). The vertical eddy fluxes of momentum, heat and specific humidity are accomplished by the method proposed by Louis (1979). The important feature of the scheme is the dependence of the diffusion coefficients on the static stability of the atmosphere. Surface turbulent fluxes of momentum, and both sensible and latent heat are calculated by the bulk aero- dynamic method. The exchange coefficients are determined from the formula given by Kondo (1975) for neutral conditions and modified to be Richarson number-dependent following Louis (1979).

2.2 Strategy o f Experiments

As has been indicated in section 1, the main purpose of this study is to address the potential impact of the vertical structure of the bogus vortex on its motion, and not to reach an optimal one for the operational use. The numerical experiments conducted in this study are all idealized but hopefully representative of real

156 Y. Wang

situations so that possible influences of uncertainties from observations and objective analyses of the environmental flow in which a tropical cyclone is embedded are excluded.

Two bogus vortices are used and designated as A and B, respectively. Vortex A has a deep cyclonic circulation throughout the troposphere, whose tangential flow is defined by

Vr(r, cr)=-Vm(~)expIl-(~m) 1 sin (7o) (1)

where r denotes radial distance from the vortex center, and Vm (30 m/s) is the maximum azimuthal wind at the radius of rm (120kin). An anticyclonic calculation in the upper troposphere, similar to that used by Wang and Holland (1996a), was introduced to vortex B:

VTA ( F, 0")

= {-V~ exp/~[ l - (~)21 ) sin@~e)E(cr)'

0,

r<re;

r~re

(2)

(3)

where

E(cr) = 1, cr~Crc; Crc J

0 , o-> cre.

Values of V0, ra, re, CrmA and o-c used in this study are 10ms -1, 260km, 1000km, 0.12 and 0.4, respectively.

The tangential wind profiles for the two vortices used in this study are shown in Fig. 1. Both vortices have the same structure in the middle-lower troposphere. This allows us to make issues of whether, how and to what degree of the vertical structure of the bogus vortex affects numerical predictions of tropical cyclone motion. Since the anticyclonic circulation in the upper troposphere is a common feature of real tropical cyclones (Frank, 1977), the vortex B can be referred to as a tropical cyclone-like vortex. It should be pointed out here that although the vortex A has no upper-level anticyclonic circulation at the initial time, an anticyclone is also developed during the model integration due to the presence of diabatic heating which plays a role to transport anticyclonic (cyclonic) potential vorticity (PV) to the upper (lower) troposphere.

0.0

0.I

0.2

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~ 0 . 5

0.6

0.7

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0.1

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0.3

0.4

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0.6

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'7

A

Radia l d i s t a n c e ( lOOkm) 0 I 2 3 4 5 6 7

I ~ ' , , . f ~ �9 I I " I �9 ] �9 I

l - / r - ' - - . \ \ - , , - - . . , , ,

B

Fig. 1. Azimuthal wind profiles for the two vortices (upper panel: A; lower panel: B) at the initial time used in this study. Contour interval is 2 m s -1

However, the resultant upper-level anticyclonic circulation in vortex B is stronger than that in vortex A during the later model forecast (see section 3).

The two vortices are embedded in a variety of environmental flows, including a uniform flow, a barotropic flow with linear horizontal shear and a horizontally uniform flow with linear vertical shear. Fourteen numerical experiments are performed with each of the vortices (A and B) embedded in each of the environmental flows (section 3). All the environmental flows satisfy the hydrostatic and geostrophic balances on a beta-plane, centred at 20~ The mass and


thermal structure of the initial vortex was obtained by the nonlinear balance equation described in Wang (1995b). The background surface pressure for a resting environment is set at constant of 1008.7 hPa. The thermal structure consists of the temperature profile of Stevens et al. (1977), with an initial relative humidity that is 5% higher than the mean cloud cluster environment of Gray et al. (1975) and is horizontally uniform. Sea surface temperature (SST) is taken to be constant at 28.5 ~

3. Numerical Results

3.1 The Environment at Rest

Motion and evolution of a tropical cyclone-scale vortex in an environment at rest on a beta-plane (the so-called beta-drift) have been extensively studied using both barotropic and baroclinic models (e. g., Chan and Williams, 1987; Fiorino and Elsberry, 1989; Wang and Li, 992; Li and Wang, 1994; Wang These studies show vortex will develop

and Holland, 1996a, b). that an initially symmetric a pair of counter-rotating

gyres (beta gyres) with anticyclonic to the northeast and cyclonic to the southwest of the vortex center in the Northern Hemisphere. The flow between the two gyres over the vortex core advects the vortex poleward and westward (Fiorino and Elsberry, 1989). The radial structure of the initial vortex influences the vortex motion by changing the amplitude and orientation of the beta-gyres (Li and Wang, 1994). Implications of such a sensitivity to radial profiles of the bogus vortex in numerical models have been discussed by Leslie and Holland (1995) using a barotropic model.

The vertical structure of the model vortex influences the baroclinic vortex motion by changing the vertical mean relative angular momentum (Wang and Li, 1992) or by vertical coupling mechanism (Wu and Emanuel, 1993; Flatau et al., 1994; Jones, 1995; Wang and Holland, 1996a, b), by which the circulations at different vertical levels can interact with each other by vertical penetration (Hoskins et al., 1985; Raymond, 1992). For a tropical cyclone- like vortex in a quiescent environment on a beta-plane, although the deep cyclonic vortex propagates poleward and westward, the large

upper tropospheric anticyclonic circulation drifts equatorward and westward relative to the lower cyclonic vortex due to the Rossby wave dispersion (Flatau et al., 1994; Wang and Holland, 1996a, b). Downward penetration of the upper- level anticyclonic circulation may reduce the westward motion component of the surface vortex by directly deflecting the lower level vortex and indirectly rotating the lower-level beta gyres anticyclonically (Wang and Holland, 1996b). In this case, vortices with stronger upper-level anticyclones will move slower and less westward than those with weaker or without upper-level anticyclones (Wang and Holland, 1996a, b).

Because vortex B in Fig. 1 has an upper-level anticyclonic circulation at the initial time while vortex A does not, the upper-level anticyclonic circulation developed during the model time integration in vortex B is stronger than that in vortex A (Fig. 2). Thus, it is expected that vortex A would move faster and more westward than vortex B. This is verified by the 72-h tracks in Fig. 3 for the two vortices on a beta-plane in an environment at rest. Although the difference between the two tracks was small during the first 48-h, it became larger afterward. For example, the position difference after 48-h of integration was only 50km, but increased to 150km after 72-h. This occurred because the upper-level anticyclone developed in vortex B is stronger and larger than that in vortex A (Fig, 2), which displaced southwestward relative to the lower- level cyclone due to the Rossby wave dispersion (Fig. 4). It is the downward penetration of this stronger upper-level anticyclonic circulation that reduced the northwestward component of vortex B and deflected it eastward relative to vortex A, especially after 48 h of integration. This concurs with the findings of Flatau et al. (1994) and Wang and Holland (1996b).

The intensity change predicted by the numerical model also depends on the vertical structure of the bogus vortex (Fig. 5). The initial sudden drop in maximum wind for both vortices is due to the lack of the boundary layer of the initial vortex. However, the subsequent intensification is very different. Vortex A developed quicker than vortex B and reached its maximum intensity at 54 h of time integration (Fig. 4a), while vortex B reached its maximum intensity by the end of

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Fig. 2. Axisymmetr ic azimuthal (left) and radial (right) wind profiles for vortex A (upper panels) and vortex B (middle panels) after 24 h of t ime integration on a beta-plane in an environment at rest. The lower panels give the corresponding difference fields between vortex B and vortex A. Contour intervals are 4 m s -1 and 2 m s -1 in the upper left two panels and the upper right two panels, respectively, and 1 m s -1 in the lower two panels

the model run (Fig. 4b). Such a dependence of the intensification of model tropical cyclone on the vertical structure of the initial vortex has been also well documented in several other studies (e.g., Rosenthal, 1971; Kurihara and Tuleya, 1981; DeMaria and Pickle, 1988). Note that the intensity difference only changes the inner structure of the vortices, but not the outer structure in the middle, lower troposphere (Fig. 2). Studies by Fiorino and Elsberry (1989a, b) indicated that vortex motion is very sensitive to the outer structure of the initial vortex, but not the inner structure. Since the two vortices have very similar outer structure (outside 200 km from the vortex center) in the middle, lower troposphere (Fig. 2), the

difference in vortex motion is mainly a result of the vertical coupling mechanism discussed above, and is little attributed to the difference in vortex intensity.

The response of rainfall rate of the two vortices for the above vertical coupling and intensity change is also different (Fig. 6). The rainfall for vortex A was mainly enhanced on the equatorward side with a small oscillation in position of the rainfall maxima (Fig. 6a). However, the rainfall pattern for vortex B is quite different. It was initially enhanced on the equatorward side, similar to that for vortex A, and then rotated cyclonically around the vortex center (Fig. 6b). Note also that the degree of


u ' I ' I ' I ~ ] ' I

A

4

o 3 o v

2

0 , I , I , I , I ; I ,

- 6 - 5 - 4 - 3 - 2 - 1 0

X ( 1 0 O K M )

Fig. 3 .72-h tracks of the two vortices on a beta-plane in an environment at rest, with 12-h positions indicated

predicted cyclone track in a quiescent environment or in a very weak environmental flow. Such a bias will increase with increasing the forecast time, and also reduce the meandering tendency of the cyclone tracks. On the other hand, vertical structure of the bogus vortex may also influence the model cyclone intensity and the rainfall patterns in the inner core region of the model cyclone. This occurs because of the difference in vertical shearing effect induced by the downward penetration flow of the upper-level circulation over the lower-level vortex.

3.2 Horizontally and Vertically Uniform Flow

Although uniform flow has no effect on the propagation of a barotropic vortex t (Wang and Li, 1995), the baroclinic vortex motion can be affected indirectly by surface friction and asymmetric heat fluxes from the ocean (Jones, 1977;

T=24h T=48h T=72h a)

-12 .5 - 1 2 . ~ . ~ . . ~ 12, 5

b) Fig. 4, Potential vorticity fields at 200hPa after 24, 48, and 72h of integration for vortex A(a) and vortex B(b) on a beta-plane in an environment at rest. Contour interval is 2.5• 1 0 - a K k g m 2 s -1. The cross hairs indicate the corresponding surface cyclone centers and the domain shown in each panel is 3200km• 3200 km

asymmetry in rainfall rate is larger in vortex B than in vortex A. This may be responsible for a small oscillation in the track of vortex B (Fig. 3).

This result implies that bogus vortices without an upper-level anticyclone in the numerical models will lead to a northwestward bias of the

1In his shallow water model, Willoughby (1994) found a propagation to the right of a spatially uniform geostrophic environmental flow on an f-plane. He attributed such a propagation to the potential vorticity (PV) gradient due to the slope of the fluid surface associated with the geostrophic flow. Such a PV gradient's effect can be amplified by superposition of the vortex on the geostrophic gradient.

160 Y. Wang

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965 I [ I 1 I I I I I ... I I 9 6 0

6 12 18 2 4 3 0 3 6 4 2 4 8 5 4 6 0 6 6 7 2 Time (hours)

Fig. 5. Central sea surface pressure and maximum wind at the lowest model level as functions of time for (a) vortex A and (b) vortex B on a beta-plane in an environment at rest

Flatau et al., 1994; Wang, 1995a). These effects can result in convective asymmetries in vortex core region and thus a propagation to the right of the environmental flow due to the asymmetric divergent flow crossing the vortex center in the middle, lower troposphere (Wang, 1995a). Since these processes occur mainly in the planetary boundary layer, one may expect that motion of the vortices with similar structure in the lower troposphere, such as those in Fig. 1, would not be sensitive to the upper-level structure. This is not true because the vertical coupling between the lower- and upper-levels may also change the lower-level asymmetric structure. As was indicated in section 3.1, the equatorward and westward displacement of the upper-level anticyclone relative to the lower level vortex can produce different responses for the asymmetric rainfall and thus the asymmetric divergent flow over the vortex core. This effect is a function of

the vertical structure of the vortex as well as the direction of the environmental flow.

To demonstrate the above argument, four experiments were performed with each of the two vortices embedded in either a westerly or an easterly environmental flow with a magnitude of 5 m s -1. The tracks for these experiments are shown in Fig. 7, which shows a relative motion tendency to the right of the environmental flow since the northward displacement of the vortex in an environment at rest (Fig. 3) is reduced in westerly flow (Fig. 7a) and increased in the easterly flow (Fig. 7b). This occurs because the rainfall is relatively enhanced on the right side when facing down the environment current (not shown) due to asymmetric friction and both the latent and sensible heat fluxes from the ocean, in agreement with the findings of Wang (1995a). Comparing the motion of the two vortices, we can see that the motion is very sensitive to the


a)

T=24h

b) T=24h

6 T = 4 8 h T=4Bh

T=72h T--72h

Fig. 6. Rainfall rate at 24-h intervals in experiments for vortices A (left panels) and B (right panels) on a beta-plane in an environment at rest. Contour interval is 2 .5mmh i. The domain shown in each panel is 560km x 560kin. Cyclone symbol and arrow indicate the position and motion of the vortices

vertical structure of the bogus vortex in a westerly flow (Fig. 7a), while it is insensitive to the vertical structure of the bogus vortex in an easterly flow (Fig. 7b). By solving for instanta- neous motion tendencies using the equivalent barotropic vorticity equation, Holland (1983) found that eastward moving cyclones are quite sensitive to the small imposed perturbations in either the environmental flow or short-lived asymmetries in vortex circulation. Our results obtained above reveal that it is westerly flow that provides the most sensitivity for imposed perturbations in vertical structure of the bogus vortex.

Since tropical cyclones in the low latitudes typically experience an easterly flow, the forecast tracks will not be significantly influenced by the vertical structure of the bogus vortex. However, for those cyclones that recurve into the mid-

6 ~ ' l ' t ~ l ' l 1 ' 1 ' 1 ' 1 ' 1 ' 1 ' 1 ' 1 ' 1 ' 1 I ' 1 ' 1 1

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Fig. 7.72-h tracks of the two vortices m a uniform westerly (a) and in a uniform easterly (b) of 5ms -1, with 12h positions indicated

latitude westerlies, detailed vertical structure of the bogus vortex in numerical models may improve the model forecasts. This may partially account for relatively larger forecast errors by most operational global models for cyclones that are entering the midlatitude westerlies after recurvature (Ueno, 1994). Ueno (1994) verified tropical cyclone track forecasts during 1988- 1993 by four operational global models, including the global models of JMA, UK Meteorolog- ical Office, ECMWF and BMRC (Bureau of Meteorology Research Centre). The results (in his tables 3 and 4) have shown that except for the JMA model, which had similar forecast accuracy for cyclones after recurvature to that of those before recurvature, the other three models all had larger errors for cyclones after recurvature than those before recurvature. Note that in both the ECMWF and the BMRC models, no tropical cyclone bogusing had been made, while both the JMA and UK models have included bogus vortices below 500 and 300hPa, respectively, during the objective analysis/assimilation cycle.

In addition to the sensitivity of the forecast tracks to the vertical structure of the bogus vortex in the westerly flow, the intensity change of both vortices in the westerly (Fig. 8a) was also different from that in the easterly flow (Fig. 8b). We can see from Fig. 8b that the intensity

162 Y. Wang

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Time ( h o u r s )

C 9 7 0 . r - q

9 6 5 Fig. 8. Central sea surface pressure as a function of time for vortex A (solid) and vortex B (dashed) on a beta-plane in a uniform westerly flow (a) and in a uniform easterly flow (b)

change of the two vortices in the easterly is very similar to that in the resting environment shown in Fig. 5. However, in the westerly flow, vortex A was still continuing to intensify by the end of the model forecast (solid line in Fig. 8a), but vortex B reached its maximum intensity after 50 h of integration (dashed line in Fig. 8a). By 72, the difference in minimum sea level pressure at the vortex center between the two vortices reached 15hPa. Since the upper-level circulations for either vortex A or vortex B in the westerly and easterly flows (not shown) were similar to those shown in Fig. 4 for a quiescent environment, the large difference in vortex intensity may also have a small contribution to the motion difference.

3.3 Barotropic Flow with Linear Horizontal Shear

Recent studies by Williams and Chan (1994) and Wang and Li (1995) have shown that horizontally sheared environmental flow influences the barotropic vortex motion by changing the intensity and orientation of the asymmetric beta-gyres which determine the propagation of the vortex relative to the environmental flow. They found that vortices embedded in a zonal flow with cyclonic shear propagate slower than those embedded in an anticyclonic shear. However, the influence of such an environmental flow on a baroclinic vortex motion has not been documented.


6

~ 4

o 3 0

V >.,2

'i;'- 5 a

i

A

1

0 - 8 - 6 - 4 - 2 0

8

7

6

~'5

g4

' I ' I ' I ' I ' I ~ I ' I '

- A (b)

i

B

2

2

1 p

0 , I, I, I, ,I, I, ,

- 4 - 2 0 2 4

X(100KM) Fig. 9. 72-h tracks of the two vortices in a barotropic flow with linear cyclonic horizontal shear (a) and linear anticyclonic horizontal shear (b), with 12-h positions indicated

It has been indicated in section 3.1 that downward penetration of the upper-level anticyclonic circulation which is displaced southwestward relative to the lower-level vortex may reduce the northwestward drift of the surface vortex on a beta-plane in an environment at rest (Figs. 3 and 4). In the presence of a horizontal shear, the relative positions of the upper-level and the lower-level circulations may be changed by the shearing effect of the environmental flow. In this case, one can expect that a zonal flow with a moderate cyclonic shear would cause the upper-and lower-level circulations to be aligned

in a more meridional direction. Downward penetration of the upper-level anticyclonic circulation will reduce the westward motion component of the beta-drift. For the same reason, downward penetration of the upper-level anticyclonic circulation will reduce the poleward motion component of the beta-drift in a zonal flow with an anticyclonic shear. As a result, cyclones with stronger upper-level anticyclones will move less westward (poleward) in a zonal flow with cyclonic (anticyclonic) shear than those cyclones with weak upper-level anticyclones.

The above hypothesis was verified using experiments with either vortex A or B embedded in a zonal flow with either a cyclonic or an anticyclonic shear of 5.875• -1. In these experiments, the vortex started from where the zonal flow is zero. The tracks (Fig. 9) show that vortex B moved less westward than vortex A in the cyclonic shear (Fig. 9a) and tess poleward than vortex A in the anticyclonic shear (Fig. 9b). As was expected that the upper-level anticyclonic circulation (low potential vorticity region) was to the equatorward side of the surface vortex in the cyclonic shear (Fig. 10) and to the west to southwest in the anticyclonic shear (Fig. 11). Therefore, downward penetration of the upper- level anticyclonic circulation reduces the westward (poleward) motion component of a tropical cyclone in a zonal flow with a cyclonic (anticyclonic) horizontal shear. This effect is larger for cyclones that have stronger upper-level anticyclones, such as vortex B used in this study. The intensity change of both vortices in these experiments (not shown) was similar to that in the quiescent environment shown in Fig. 5 because the flow around the cyclones was very weak.

Note also that although the position differ- ences between the two vortices after 72h of integration are similar for both cyclonic and anticyclonic shear (126 km versus 116 kin), they may not only be caused by the horizontal shear, but may also be partially affected by the direction of the environmental flow, as discussed in section 3.2. Since the sensitivity of vortex motion to the vertical structure of the bogus vortex depends on the direction of the environmental flow, the above results imply that the vortex motion may be most sensitive to the vertical structure of the

164 Y. Wang

T=24h T=48h T=72h a)

b) Fig. 10. Potential vorticity fields at 200 hPa after 24, 48, and 72 h of integration for vortex A (a) and vortex B (b) on a beta-plane in a barotropic zonal flow with linear cyclonic horizontal shear. Contour interval is 2.5x10 -8 Kkgm2s -I. The cross hairs indicate the corresponding surface cyclone centers and the domain shown in each panel is 3200 kmx 3200 km

12.5 ~ 1 2 . 5 -

I 1

b)

T=48h T=72h T=24h a)

~ ' 5 ~ '2"s] lz.5 1 5 ~

- . - _,2

Fig. 11. Potential vorticity fields at 200 hPa after 24, 48, and 72 h of integration for vortex A (a) and vortex B (b) on a beta-plane in a barotropic zonal flow with linear anticyclonic horizontal shear. Contour interval is 2.5x 10 -8 Kkg m 2 s -1. The cross hairs indicate the corresponding surface cyclone centers and the domain shown in each panel is 3200 km x 3200 km

bogus vor tex in a wester ly flow with cyclonic shear.

Compar ing the tracks in Fig. 9a,b with those in Fig. 3, one can see that the po leward mot ion componen t o f the beta-drif t is reduced in the cyclonic shear flow (Fig. 9a), but it is increased

in the ant icyclonic shear flow (Fig. 9b). This concurs with the findings by Wil l iams and Chan (1994) and Wang and Li (1995). The results also demonst ra te that the hor izontal shearing effect o f the envi ronmenta l flow dominates to reduce (increase) the beta-drif t in a cyc lonic (anti-


cyclonic) shear even though for diabatic baroclinic vortices.

3.4 Horizontally Uniform Flow with Linear Vertical Shear

The influence of vertical shear in the environmental flow on tropical cyclone motion has received considerable attention in recent years (e.g., Wu and Emanuel, 1993; Flatau et al., 1994; Jones, 1995; Wang and Holland, 1996c). These studies show that tropical cyclone-like vortices can propagate to the left of the vertical shear when facing down shear due to the vertical coupling mechanism similar to that discussed in sections 3.1, 3.3. In this case, the vertical shear displaces the upper-level anticyclonic circulation of a tropical cyclone downshear. Flow associated with the downward penetration of this downshear displaced anticyclone will deflect the surface vortex to the left of the vertical shear vector (Wu and Emanuel, 1993; Flatau et al., 1994). Diabatic heating in the vortex core and the development of convective asymmetries can enhance this propagation tendency (Wang, 1995a; Wang and Holland, 1996c).

To study whether vertical structure of the bogus vortex has a significant effect on the motion of model vortex in vertical shear, four experiments were performed with the two vortices embedded in a horizontally uniform flow with a linear vertical shear, with 8 m s -1 at the top of the model atmosphere and 0 at the surface. The tracks for these experiments are shown in Fig. 12a for westerly shear and Fig. 12b for easterly shear. We can see that the motion difference between the two vortices is small in both westerly shear and easterly shear (67 km versus 46 kin) compared to that in a resting atmosphere (Fig. 3). The propagation to the left of the vertical shear vector is evident in westerly shear for both vortices since the poleward displacement is larger for the vortex in westerly shear (Fig. 9a) than that in a resting atmosphere (Fig. 3). In this case, vortex B, which has a stronger upper-level anticyclone, has a larger leftward motion tendency than vortex A, reducing the motion difference between the two vortices in an environment at rest. One might expect that the motion difference between the two vortices should be enhanced in easterly shear since the

0 o

>.,

' I ' I ' I ' i ' i ' I ' I ' I ~ I ' ' I ' I

A (a)

2 B

I, # , , I,I

0 2 4 6 8 10 12 14

6

5

1

0 ' - 14

- (

- 12 -10 - 8 - 6 - 4 - 2 X(IO0~:M)

] d

]

0

Fig. 12. 72-h tracks of the two vortices in a horizontally uniform flow with linear westerly shear (a) and linear easterly shear (b), with 12-h positions indicated

stronger upper-level anticyclone of vortex B should further reduce the poleward motion tendency of the beta-drift. However, this did not happen. What occurred was that the easterly shear flow increased the westward displacement of the upper-level anticyclone relative to the lower-level vortex. As a result, the upper-level anticyclone was shifted far westward from the lower-level vortex and its influence on the vortex motion was therefore very limited (Fig. 13). In this case, the predicted motion is not sensitive to vertical structure of the bogus vortex.

An important issue which should be addressed here is that in addition to the dependence of the intensity of the model cyclone on the vertical structure of the bogus vortex as seen from the previous subsections, the intensity of the model cyclone also depends on the direction of the vertical shear (Fig. 14). Cyclones in westerly shear (Fig. 14a) developed stronger than those in easterly shear (Fig. 14b). Such a dependence of model cyclone intensity on the direction of vertical shear in the environmental flow has been studied in detail by Wang (1995a), who found that compared to a westerly shear, an easterly vertical shear may increase the westward dis-

166 Y. Wang

T = 2 4 h a)

-12.5 " 12.5

T=48h T=72h

-------" 12.5 .~______.. ! 2.5 ~ 12.5 ~.--- 12.5 ~

~)) 12.5- 1 2 . 5 ~ 1 2 . 5 t 12.5 12,5-- 12,5

Fig. 13. Potential vorticity fields at 200 hPa after 24, 48, and 72 h integration for vortex A (a) and vortex B (b) on a beta-plane in a horizontally uniform flow with linear easterly vertical shear. Contour interval is 2.5 x 10 -~ K kgm 2 s - ] . The cross hairs indicate the corresponding surface cyclone centers and the domain shown in each panel is 3200kin x 3200 km

(a) Westerly shear

1000 'I l i i I l i i i i i

9 9 5 1 - r

n. 9 9 0 -

9 7 5 -

9 6 0 1 I l, I I I I I I,, f I I / 0 6 12 18 24 30 36 42 4 8

T i m e ( h o u r s )

1000

9 9 5

99O

' 9 8 5

980

9 7 5 &

(b) Easterly s h e a r

54 60 66 72

t I I I I [ I I I I I I t

9 7 0 - , t , - q

965 - 9 6 0 I I I I I I I I I I I

0 6 12 18 24 30 36 42 48 54 60 6 6 72 T i m e ( h o u r s )

Fig. 14. Central sea surface pressure as a function of time for vortex A (solid) and vortex B (dashed) on a beta-plane in a horizontally uniform flow with linear westerly (a) and easterly (b) vertical shears


placement of the upper tropospheric outflow layer relative to the lower-level cyclone purely due to the Rossby wave dispersion, and increase the vertical tilt of the vortex and thus decrease the vortex intensity. The above result seems to be in contrast to the findings of Tuleya and Kurihara (1981), who found a bias toward easterly vertical shear in tropical cyclogenesis when the mean surface wind is easterly. We suggest that the strong cyclonic shear in the environmental flow for their numerical experiments played a role in keeping the outflow layer over the surface disturbance.

It should be pointed out that the above results are obtained from a linear vertical shear flow. Studies by Flatau et al. (1994) found potential impact of the vertical profile of the environmental flow on baroclinic vortex motion. In that case, the motion of the vortex is not only influenced by the shearing effect and vertical coupling mechanism, but also influenced by the horizontal potential vorticity gradients associated with the vertical shear in the environmental flow. Since the latter can be attributed to the gross beta-induced propagation (Shapiro, 1992), we do not intend to include its effect here.

4. Discussion and Conclusions

Despite the progress made in the performance of numerical weather prediction models, the lack of adequate data over the tropical oceans limits the accuracy of analyses and forecasts of tropical cyclones. Bogusing techniques of tropical cyclones in numerical models, therefore, have been widely used in operational forecasting and research models to improve tropical cyclone analysis and model performance. The usual procedure is to define a synthetic data distribution based on an analytically prescribed vortex, which is passed to the analysis scheme as a set of high quality observations, or inserted into the analysed field as the initial conditions of the forecast models. In this procedure, the structure of the bogus vortex is prescribed based on some characteristics of the tropical cyclones to be forecasted.

In this study, idealised conditions are used to study the vertical structure of the bogus vortex on its motion in numerical models by comparing the forecasted tracks for two vortices which have different vertical structures at the initial time in

that one is cyclonic throughout the troposphere and the other has an extra anticyclone in the upper troposphere. The results show that the forecast tracks as well as the intensity can be very sensitive to the vertical structure of the bogus vortex, especially when the environmental flow is very weak, or westerly and has cyclonic shear. However, this sensitivity is reduced in moderate vertical shear. This motion sensitivity is found to arise from the vertical coupling mechanism by which the upper- and lower-level circulations interact with each other when a horizontal displacement occurs between them. This vertical coupling can also result in development of convective asymmetries in the vortex core region. The asymmetric divergent flow in the lower troposphere associated with these convective asymmetries may in turn further influence the vortex motion by deflecting the vortex to the region with maximum convection.

On a beta-plane in an environment at rest, the upper-level anticyclonic circulation drifts equatorward and westward relative to the lower cyclonic vortex due to the Rossby wave dispersion. Downward penetration of this upper-level anticyclonic circulation reduces the poleward and westward motion of the surface vortex. As a result, the cyclone without an upper-level anticyclone in the initial bogus vortex in a numerical model will move faster and more westward than the one which has an upper-level anticyclone. The motion sensitivity to the vertical structure of the bogus vortex in a uniform easterly flow is mainly caused by the vertical coupling mechanism by which the downward penetration of the upper-level anticyclonic circulation exerts a shearing effect on the lower cyclonic portion of the cyclone, changing the distribution and intensity of convection and thus the vortex motion. The horizontal shear affects the baroclinic vortex motion by a shearing effect which makes the upper-level anticyclone to be located to the equatorward (westward to southwestward) side of the surface vortex. In this case, the cyclone initially without an upper-level anticyclone will move more westward (poleward) in a cyclonic (an anticyclonic) shear than that with an upper-level anticyclone. The insensitivity of model cyclone motion to the vertical structure of the bogus vortex in vertical shear results mainly from the fact that in a westerly vertical shear

168 Y. Wang

vortex with a stronger upper-level anticyclone has a larger leftward motion tendency to the vertical shear vector and thus reduces the motion difference in a resting atmosphere, while in an easterly vertical shear the upper-level anticyclonic circulation is shifted far westward relative to the lower-level vortex so that its influence on vortex motion is largely reduced.

Our main purpose in this study has not been to reach an optimal vortex structure for operational use. Rather, we have addressed the potential impact of vertical structure of the bogus vortex on its motion in a numerical model. However, our results indicate that vortices which lack an anticyclone in the upper troposphere would move quite differently in some environmental config- urations. We suggest that care needs to be taken in determining the vertical structure of the bogus vortex in numerical models. Note that our numerical experiments have started from vortices with no radial flow or secondary circulation. But the results seem not to be significantly influenced by this treatment, except that spinup of the vortex takes about 12-h of integration.

The influence of vertical structure of the bogus vortex has been tested here using only very simple environmental flows. Holland and Wang (1995) have shown potential sensitivity of recurving tropical cyclones to vertical structure of model vortices. Wang and Holland (1995) have indicated that binary interaction of tropical cyclones can also be very sensitive to the vertical structure of model vortices. These studies indicate that more sensitivity of tropical cyclones to vertical structure of the bogus vortex may occur in more complicated environmental flow and in situations of multiple tropical cyclones.

In order to study the potential influence of vertical structure of the bogus vortex on its motion, we have not considered the impact of parameterization schemes of model physics. Although many previous studies have indicated that successful forecast of tropical cyclones should be also gained by improving the planetary boundary layer formulation and the convection scheme of the numerical models (Heckley et al., 1987; Krishnamurti et al., 1989; Puri and Miller, 1990; Lazid, 1993), we expect that the findings of sensitivity to vertical structure of the bogus vortex in this study are not significantly changed by using different physical parameterization

schemes. Our preliminary numerical experiments have shown that different parameter izat ion schemes give different vertical heating profiles and thus result in different vertical structure of the model cyclone. As a result, the motion difference is directly caused by the changes in vertical structure of the model cyclone. Further studies are needed to understand the dynamics by which the physical parameterization schemes of the numerical models influence the performance of tropical cyclone forecast by numerical models.

Acknowledgment

The author is grateful to Dr. Greg Holland for carefully reading an early version of the manuscript and for valuable comments. This study has been benefited from discussions with Drs. Greg Holland and Noel Davidson. Part of this work has been supported by the U. S. Office of Naval Research under grand N-00014-94-I-0556.

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Author's address: Dr. Yuqing Wang, BMRC, GPO Box 1289K, Melbourne, VIC 3001, Australia.

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