Meteorol. Atmos. Phys. 65, 153-170 (1998) , and Springer-Verlag 1998 Printed in Austria

Bureau of Meteorology Research Centre, Melbourne, Victoria, Australia

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

Yuqing Wang

With 14 Figures

Received May 27, 1997

Summary 1. Introduction

In this study, idealised conditions are used to study the At the resolutions currently in use, and with the influence of vertical structure of the bogus vortex on its sparse data coverage over the tropical oceans, motion in numerical models by comparing the resultant forecast tracks. Two vortices were used: one has a cyclonic numerical analyses cannot adequately represent circulation throughout the troposphere and the other has an tropical circulations for use in numerical upper tropospheric . Both vortices have the prediction (NWP) models (Leslie and same structure in the middle and lower troposphere. The Holland, 1995). At most NWP centers a two vortices were inserted into four different environmental "bogusing" scheme is thus employed to force a flows on a beta-plane: (a) a resting atmosphere; (b) a vortex into the numerical uniform flow; (c) a horizontal shear flow and (d) a vertical shear flow. The results show that the forecast tracks are very analysis. This is typically done by using a vortex sensitive to the vertical structure of the bogus vortex, with suitable horizontal and vertical structure to especially when the environmental flow is very weak, or is derive a set of bogus observations for inclusion in westerly and has a cyclonic horizontal shear. However, this the analysis/assimilation cycle (Elsberry, 1987). sensitivity is reduced in moderate vertical shear. This Bogusing methods vary between the centers but motion sensitivity is found to arise from the vertical coupling mechanism by which the upper- and lower-level most involve an axisymmetric vortex with some circulations interact with each other when a horizontal added asymmetry to take into account current displacement occurs between them. movement of the cyclone and environmental flow The vertical structure of the bogus vortex can also affect (e.g., Ueno, 1989, 1995; Mathur, 1991; Davidson the intensity of the model cyclone, depending on the and Puri, 1992; Kurihara et al., 1993, 1995). configuration of the environmental flow. In general, the There are basically three approaches that are bogus vortex without an upper-level anticyclone will intensify quicker and will develop more intense than the currently used in operational models, as sum- one with an upper-level anticyclone, The vertical coupling marized by Peng et al. (1993). The first is to mechanism can result in different asymmetric rainfall bogus observational data before the objective pattern in cyclone core region depending on the vertical analysis is carried out. Examples of this type of structure of the bogus vortex. The asymmetric divergent bogusing are those used in the US National flow associated with these convective asymmetries may in turn further influence the vortex motion. It is suggested that Center for Environmental Prediction (NCEP) care needs to be taken in determining the vertical structure global forecast model (Lord, 1991), in the US of the bogus vortex in numerical models. Navy Operational Global Atmospheric Predic- 154 Y. Wang tion System (NOGAPS) (Fiorino et al., 1993; tional numerical models, such as sensitivities to Goerss and Jeffries, 1994), and in the UK the vortex profiles, to the initial vortex positions, Meteorological Office global model (Radford, and the influence of the bogus vortex on its 1994; Heming et al., 1995). The second approach environment. is to add a more complete vortex circulation A natural extension of the work done by Leslie defined by an analytical expression after the and Holland (1995) is to study the influence of objective analysis but before the model initiali- vertical structure of the bogus vortex in numer- zation. Examples of this type of bogusing are ical models. As noted by Serrano and Und~n those used in the Quasi-Lagrangian Model (1994), the vertical structure of the bogus vortex (QLM) of the US NCEP (Mathur, 1991) and does substantially diverge in numerical models the Typhoon Model of the Meteorological currently in use, in particular, with or without the Agency (JMA) (Ueno, 1989, 1995). The third layer. For example, in the typhoon model approach is to bogus a "spinup" vortex gener- of JMA and the QLM of NCER the bogus ated by the same forecast model, instead of using cyclone includes an anticyclonic circulation in an analytical one. Examples of this are the the upper-troposphere, while in most of the multiply nested tropical cyclone model of the global models such as those used by the US GFDL (Kurihara et al., 1993, 1995) and the Navy, the UK Meteorological Office and the US typhoon-Track Forecast System (TFS) of the NCER bogus observations representing a tropical Central Weather Bureau (CWB) in (Peng cyclone are included by inserting a cyclonic et al., 1993). In addition to the different methods, circulation extending from the surface to about both the horizontal and vertical structures of the 400 hPa and nothing above this level in the data axisymmetric vortex vary considerably between assimilation phase (Goerss and Jeffries, 1994; the centers even for the same method (Serrano Heming et al., 1995; Lord, 1991). Note that and Und6n, 1994; Leslie and Holland, 1995). although a forecast model during assimilation Leslie and Holland (1995) have made a can develop an outflow region, it takes longer comparison of four commonly used and refer- time than the short-term forecast length (6 h in enced bogus vortex profiles in a barotropic most forecast/assimilation systems) of a data framework, including the modified Rankine assimilation cycle. That means that the outflow vortex, as used in the US Navy global model layer of a real tropical cyclone cannot be well (Goerss and Jeffries, 1994), the UK global model represented at the initial time of the forecast (Heming et al., 1995) and as tested in the model. The questions arise as to whether, how, European Centre for Medium-Range Weather and to what degree the vertical structure of the Forecasts (ECMWF) global spectral model bogus vortex influences the cyclone motion in (Andersson and Hollingsworth, 1988; Serrano three-dimensional models. Recent theoretical and Und~n, 1994); the Fujita (1952) profile, as studies by Wang et al. (1993), Holland and used in JMA typhoon model (Ueno, 1989, 1995) Wang (1995) and Wang and Holland (1996 a, b, and in the US NCEP QLM (Mathur, 1991); the c) have shown that baroclinic vortex motion can Holland (1980) profile, as used in the Australian be very different for vortices with different Tropical Analysis Prediction System (TAPS) vertical structures. (Davidson and McAvaney, 1981), barotropic In the present study we have focused on the tropical cyclone forecast model (Holland et al., potential impact of vertical structure of the bogus 1991), and -surge model (Hubbert et al., vortex on its motion. In order to isolate this issue 1991); and the profile used by DeMaria (1987) from the possible influences of the uncertainties and DeMaria et al. (1992) in their barotropic in observations or objective analyses of the tropical cyclone forecast models. Without the environmental flow surrounding a tropical added complications associated with the pre- cyclone, numerical experiments presented in this sence of baroclinic effects, Leslie and Holland study are all performed under idealized condi- (1995) compared these four profiles in a forecast tions. The next section describes the numerical barotropic model. They have established some of model used and the strategy of our numerical the sensitivities that need to be addressed in experiments. Influences of vertical structure of developing a tropical cyclone bogus for opera- 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 advection scheme has third-order accuracy for environmental flows are evaluated in section 3. time-dependent and non-uniform flow, and Our major findings are summarized and dis- possesses very weak dissipation, very small cussed in section 4. phase errors and good shape-preserving proper- ties. The adjustment stage is accomplished by the forward-backward scheme with the Coriolis 2. Experimental Design force term implicitly treated. For the horizontal differencing, we use a 2.1 The Numerical Model centred finite difference scheme with fourth- The numerical model used in this study is a order precision. The vertical differencing scheme modified version of the one designed and used by is identical to that used by Arakawa and Lamb Wang (1995a), Wang and Holland (1996a, b). It (1977). For the horizontal resolution chosen in is a limited-area, hydrostatic, primitive equation this study, an adjustment time step Ate= 120 model on either an f-plane or a /3-plane seconds was used and the number of adjustment formulated with Cartesian coordinates in the steps per advection step was chosen to be N= 3. horizontal and a o--coordinate in the vertical The calculation of physical processes is sum- [or = (p - Pt)/(Ps - Pt), where p is the pressure, marised below. p, the surface pressure, and Pt the pressure at the The large-scale condensation is calculated top of the model, which is taken to be 100hPa]. explicitly with the method used in Leslie et al. The model consists of 16 layers in the vertical (1985). Subgrid-scale cumulus convection is from 0=0 to 1, with the interfaces or=0.0, parameterized following Kuo (1974) with mod- 0.054, 0.114, 0.181, 0.25, 0.328, 0.397, 0.472, ifications suggested by Anthes (1977). Evapora- 0.546, 0.618, 0.688, 0.754, 0.816, 0.872, 0.922, tion of has been included in both 0.965, 1.0. All the vertically dependent variables, the large-scale precipitation and the subgrid- such as horizontal velocity, potential temperature scale precipitation, following the method of and specific , are defined in the middle Kessler (1969). Subgrid-scale horizontal diffu- of each layer but, the vertical velocity 6- is stag- sion of momentum, heat and moisture is cal- gered. For upper and lower boundary conditions, culated in the manner given by Smagorinsky et al. we required that fluid particles do not cross the (1965). The vertical fluxes of momentum, cr = 0 and cr = 1 surfaces. The horizontal mesh of heat and specific humidity are accomplished by the model consists of 141 • 141 grid points with a the method proposed by Louis (1979). The uniform spacing of 40km. All variables are important feature of the scheme is the depen- defined at the same grid point on the cr surfaces. dence of the diffusion coefficients on the static Sponge layers are applied to the north and south stability of the atmosphere. Surface turbulent boundaries, and all variables are cyclic in the fluxes of momentum, and both sensible and zonal direction. Both the horizontal and vertical latent heat are calculated by the bulk aero- resolutions of the model are chosen to be dynamic method. The exchange coefficients are representative of those currently in operational determined from the formula given by Kondo use (e. g., the Quasi-Lagrangian Model of the US (1975) for neutral conditions and modified to be NCEP), Richarson number-dependent following Louis A two-time-level, explicit time-split scheme (1979). similar to that used by Leslie and Purser (1991) is used for the model integration (Wang, 1995a; Wang and Holland, 1996a,b). The procedure 2.2 Strategy of Experiments consists of an advection stage of time step AtA, As has been indicated in section 1, the main followed by N adjustment steps with time step of purpose of this study is to address the potential AtL = AtA/N. The full integration is concluded impact of the vertical structure of the bogus with a physical process stage of time step AtA. vortex on its motion, and not to reach an optimal The forward-in-time upstream advection scheme one for the operational use. The numerical developed by Wang (1996) is adopted for the experiments conducted in this study are all time integration of the advection stage. This idealized but hopefully representative of real 156 Y. Wang

situations so that possible influences of uncer- Radial distance (100km) tainties from observations and objective analyses 0 1 2 3 4 5 6 '7 of the environmental flow in which a tropical 0.0 I I cyclone is embedded are excluded. 0.1 A Two bogus vortices are used and designated as 0.2 A and B, respectively. Vortex A has a deep cyclonic circulation throughout the troposphere, 0.3 whose tangential flow is defined by 0.4 0.5 Vr(r,cr)=-Vm(~)expIl-(~m) 1 sin (7o) 0.6 (1) 0.7 where r denotes radial distance from the vortex O.B center, and Vm (30 m/s) is the maximum azimuthal 0.9 wind at the radius of rm (120kin). An anti- 1.0 cyclonic calculation in the upper troposphere, similar to that used by Wang and Holland (1996a), Radial distance (lOOkm) was introduced to vortex B: 0 I 2 3 4 5 6 7 B 0.0 I ~',,. f~ I I " I ] I VTA ( F, 0") 0.I l-/r-'--.\\- ,, --.., , , = {-V~ exp/~[l-(~)21 ) sin@~e)E(cr)' r cre. 0.a Values of V0, ra, re, CrmAand o-c used in this study 0.9 are 10ms -1, 260km, 1000km, 0.12 and 0.4, 1.0 respectively. Fig. 1. Azimuthal wind profiles for the two vortices (upper The tangential wind profiles for the two panel: A; lower panel: B) at the initial time used in this vortices used in this study are shown in Fig. 1. study. Contour interval is 2 m s-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 However, the resultant upper-level anticyclonic of the vertical structure of the bogus vortex circulation in vortex B is stronger than that in affects numerical predictions of tropical cyclone vortex A during the later model forecast (see motion. Since the anticyclonic circulation in the section 3). upper troposphere is a common feature of real The two vortices are embedded in a variety of tropical cyclones (Frank, 1977), the vortex B can environmental flows, including a uniform flow, a be referred to as a tropical cyclone-like vortex. It barotropic flow with linear horizontal shear and a should be pointed out here that although the horizontally uniform flow with linear vertical vortex A has no upper-level anticyclonic circula- shear. Fourteen numerical experiments are per- tion at the initial time, an anticyclone is also formed with each of the vortices (A and B) developed during the model integration due to embedded in each of the environmental flows the presence of diabatic heating which plays a (section 3). All the environmental flows satisfy role to transport anticyclonic (cyclonic) potential the hydrostatic and geostrophic balances on a (PV) to the upper (lower) troposphere. beta-plane, centred at 20~ The mass and On the Bogusing of Tropical Cyclones in Numerical Models 157 thermal structure of the initial vortex was upper tropospheric anticyclonic circulation drifts obtained by the nonlinear balance equation equatorward and westward relative to the lower described in Wang (1995b). The background cyclonic vortex due to the Rossby wave disper- surface pressure for a resting environment is set sion (Flatau et al., 1994; Wang and Holland, at constant of 1008.7 hPa. The thermal structure 1996a, b). Downward penetration of the upper- consists of the temperature profile of Stevens level anticyclonic circulation may reduce the et al. (1977), with an initial relative humidity that westward motion component of the surface is 5% higher than the mean cluster vortex by directly deflecting the lower level environment of Gray et al. (1975) and is vortex and indirectly rotating the lower-level horizontally uniform. beta gyres anticyclonically (Wang and Holland, (SST) is taken to be constant at 28.5 ~ 1996b). In this case, vortices with stronger upper-level will move slower and less westward than those with weaker or without 3. Numerical Results upper-level anticyclones (Wang and Holland, 1996a, b). 3.1 The Environment at Rest Because vortex B in Fig. 1 has an upper-level Motion and evolution of a tropical cyclone-scale anticyclonic circulation at the initial time while vortex in an environment at rest on a beta-plane vortex A does not, the upper-level anticyclonic (the so-called beta-drift) have been extensively circulation developed during the model time studied using both barotropic and baroclinic integration in vortex B is stronger than that in models (e. g., Chan and Williams, 1987; Fiorino vortex A (Fig. 2). Thus, it is expected that vortex and Elsberry, 1989; Wang and Li, 992; Li and A would move faster and more westward than Wang, 1994; Wang and Holland, 1996a, b). vortex B. This is verified by the 72-h tracks in These studies show that an initially symmetric Fig. 3 for the two vortices on a beta-plane in an vortex will develop a pair of counter-rotating environment at rest. Although the difference gyres (beta gyres) with anticyclonic to the between the two tracks was small during the first northeast and cyclonic to the southwest of the 48-h, it became larger afterward. For example, vortex center in the . The the position difference after 48-h of integration flow between the two gyres over the vortex core was only 50km, but increased to 150km after advects the vortex poleward and westward 72-h. This occurred because the upper-level (Fiorino and Elsberry, 1989). The radial structure anticyclone developed in vortex B is stronger of the initial vortex influences the vortex motion and larger than that in vortex A (Fig, 2), which by changing the amplitude and orientation of the displaced southwestward relative to the lower- beta-gyres (Li and Wang, 1994). Implications of level cyclone due to the Rossby wave dispersion such a sensitivity to radial profiles of the bogus (Fig. 4). It is the downward penetration of this vortex in numerical models have been discussed stronger upper-level anticyclonic circulation that by Leslie and Holland (1995) using a barotropic reduced the northwestward component of vortex model. B and deflected it eastward relative to vortex A, The vertical structure of the model vortex especially after 48 h of integration. This concurs influences the baroclinic vortex motion by with the findings of Flatau et al. (1994) and Wang changing the vertical mean relative angular and Holland (1996b). momentum (Wang and Li, 1992) or by vertical The intensity change predicted by the numer- coupling mechanism (Wu and Emanuel, 1993; ical model also depends on the vertical structure Flatau et al., 1994; Jones, 1995; Wang and of the bogus vortex (Fig. 5). The initial sudden Holland, 1996a, b), by which the circulations at drop in maximum wind for both vortices is due to different vertical levels can interact with each the lack of the boundary layer of the initial other by vertical penetration (Hoskins et al., vortex. However, the subsequent intensification 1985; Raymond, 1992). For a tropical cyclone- is very different. Vortex A developed quicker like vortex in a quiescent environment on a than vortex B and reached its maximum intensity beta-plane, although the deep cyclonic vortex at 54 h of time integration (Fig. 4a), while vortex propagates poleward and westward, the large B reached its maximum intensity by the end of 158 Y. Wang

.0270 .0270 m ",,..;2; ...... 2181 .2181

.4092 ~ .4092 110 .6003 .6oo3

.7914 ,7914 "-':-, H-.s

.9825 li|t,,tJkJ.'J,".,,""l/' /' I / ' I I .9825 012345878910 0 12345678910 .0270 .027O % ~, -10.30 o~176

.2181 .2181 o- L. 1,77 .409~ ~ .4092

.60o3 b~ .6003

.7914 .7914

,..'.': .2 ".-.. ";~2t'::)~.:::'a'.2D'.~. , , , , .9825 ,9825 Fig. 2. Axisymmetric azimuthal 0 1 2 3 4 5 6 7 8 9 10 0 1 2 3 4 5 6 7 8 9 10 (left) and radial (right) wind .0270 .027O ~(' !- ' ' '--6 ' ' ' profiles for vortex A (upper ;-, ,.'..: ,.,;-':.-, ,; ,,' ," panels) and vortex B (middle 0 o- .2181 .2101 panels) after 24 h of time inte- gration on a beta-plane in an .4092 ./ ...... 4092 environment at rest. The lower :' " ...... :;:''" C"~-o.J ""i ~ L-2~,s UO panels give the corresponding .6oo3 .eoo3 difference fields between vortex ',: H_.I~ B and vortex A. Contour inter- .7914 .7914 vals are 4ms -1 and 2ms -1 in i i I the upper left two panels and the L~:~:.,.,p, , , , , , , .9825 .9825 •T'•I I i I t i I I upper right two panels, respec- 0 12345878910 0 1 2 3 4 5 8 7 8 9 10 tively, and 1 m s -1 in the lower Radius (lOOkm) Radius (100kin) two panels

the model run (Fig. 4b). Such a dependence of difference in vortex motion is mainly a result of the intensification of model tropical cyclone on the vertical coupling mechanism discussed above, the vertical structure of the initial vortex has been and is little attributed to the difference in vortex also well documented in several other studies intensity. (e.g., Rosenthal, 1971; Kurihara and Tuleya, 1981; The response of rainfall rate of the two DeMaria and Pickle, 1988). Note that the intensity vortices for the above vertical coupling and difference only changes the inner structure of the intensity change is also different (Fig. 6). The vortices, but not the outer structure in the middle, rainfall for vortex A was mainly enhanced on lower troposphere (Fig. 2). Studies by Fiorino the equatorward side with a small oscillation and Elsberry (1989a, b) indicated that vortex in position of the rainfall maxima (Fig. 6a). motion is very sensitive to the outer structure of However, the rainfall pattern for vortex B is quite the initial vortex, but not the inner structure. different. It was initially enhanced on the Since the two vortices have very similar outer equatorward side, similar to that for vortex A, structure (outside 200 km from the vortex center) and then rotated cyclonically around the vortex in the middle, lower troposphere (Fig. 2), the center (Fig. 6b). Note also that the degree of On the Bogusing of Tropical Cyclones in Numerical Models 159

u ' I ' I ' I ~ ] ' I predicted cyclone track in a quiescent environ- ment or in a very weak environmental flow. Such A a bias will increase with increasing the forecast time, and also reduce the meandering tendency of the cyclone tracks. On the other hand, vertical 4 structure of the bogus vortex may also influence the model cyclone intensity and the rainfall patterns in the inner core region of the model o3 o cyclone. This occurs because of the difference in v vertical shearing effect induced by the downward 2 penetration flow of the upper-level circulation over the lower-level vortex.

3.2 Horizontally and Vertically Uniform Flow

0 , I , I , I , I ; I , Although uniform flow has no effect on the -6 -5 -4 -3 -2 -1 0 propagation of a barotropic vortex t (Wang and X(10OKM) Li, 1995), the baroclinic vortex motion can be

Fig. 3.72-h tracks of the two vortices on a beta-plane in an affected indirectly by surface friction and asym- environment at rest, with 12-h positions indicated metric heat fluxes from the ocean (Jones, 1977;

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

-12.5 - 12.~.~..~ 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• 10-aKkgm 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 1In his shallow water model, Willoughby (1994) found a prop- than in vortex A. This may be responsible for a agation to the right of a spatially uniform geostrophic environ- small oscillation in the track of vortex B (Fig. 3). mental flow on an f-plane. He attributed such a propagation to the This result implies that bogus vortices without potential vorticity (PV) gradient due to the slope of the fluid surface an upper-level anticyclone in the numerical associated with the geostrophic flow. Such a PV gradient's effect can be amplified by superposition of the vortex on the geostrophic models will lead to a northwestward bias of the gradient. 160 Y. Wang

(a) Vortex A 40] I I I i i I i I I._ I I ~ 10oo %" 35 ~---~---~-'''" ..... " --"l 995 / E 30 "" 990

"~ 25 - 985

~= 20 - 980 j~

15

~ 10 - 970.

5 - - 965 0 I I I I I I I I I I I 960 0 6 12 18 24 30 36 42 48 54 60 66 72 Time (hours)

(b) Vortex B 40 | I l n I I I I I I 1 I 1000 %" 35 995 co E 30 ..--~ 1 990 I:Z., v ,s 985 I:z., ~= 20 98O E E 9~5 E

~ 10 970 .t-q N Fig. 5. Central sea surface pressure and 5 965 maximum wind at the lowest model level as 0 I [ I 1 I I I I I ... I I 960 functions of time for (a) vortex A and (b) 0 6 12 18 24 30 36 42 48 54 60 66 72 vortex B on a beta-plane in an environment Time (hours) at rest

Flatau et al., 1994; Wang, 1995a). These effects the vertical structure of the vortex as well as the can result in convective asymmetries in vortex direction of the environmental flow. core region and thus a propagation to the right of To demonstrate the above argument, four the environmental flow due to the asymmetric experiments were performed with each of the divergent flow crossing the vortex center in the two vortices embedded in either a westerly or an middle, lower troposphere (Wang, 1995a). Since easterly environmental flow with a magnitude of these processes occur mainly in the planetary 5 m s -1. The tracks for these experiments are boundary layer, one may expect that motion of shown in Fig. 7, which shows a relative motion the vortices with similar structure in the lower tendency to the right of the environmental flow troposphere, such as those in Fig. 1, would not be since the northward displacement of the vortex in sensitive to the upper-level structure. This is not an environment at rest (Fig. 3) is reduced in true because the vertical coupling between the westerly flow (Fig. 7a) and increased in the lower- and upper-levels may also change the easterly flow (Fig. 7b). This occurs because the lower-level asymmetric structure. As was indi- rainfall is relatively enhanced on the right side cated in section 3.1, the equatorward and when facing down the environment current (not westward displacement of the upper-level anti- shown) due to asymmetric friction and both the cyclone relative to the lower level vortex can latent and sensible heat fluxes from the ocean, in produce different responses for the asymmetric agreement with the findings of Wang (1995a). rainfall and thus the asymmetric divergent flow Comparing the motion of the two vortices, we over the vortex core. This effect is a function of can see that the motion is very sensitive to the On the Bogusing of Tropical Cyclones in Numerical Models 161

a) b) 6~'l't~l'l 1'1'1'1'1'1'1'1'1'1 I'1'1 1 T=24h T=24h

0 ,l,l,IJl Ifl,l 0 2 4 6 8 I0 12 14 16 18

8 . '1'1 '1'1~1'/'1'1'1'1'1'1'1'1 I'l'l' . 6 7 (b) ,,.,6 B T=48h T=4Bh

~3 2 1 0 -,4 -,o -4 -2 o X(lOOKM) Fig. 7.72-h tracks of the two vortices m a uniform westerly T=72h T--72h (a) and in a uniform easterly (b) of 5ms -1, with 12h positions indicated

latitude , 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 Fig. 6. Rainfall rate at 24-h intervals in experiments for most operational global models for cyclones that vortices A (left panels) and B (right panels) on a beta-plane are entering the midlatitude westerlies after in an environment at rest. Contour interval is 2.5mmh i. recurvature (Ueno, 1994). Ueno (1994) verified The domain shown in each panel is 560km x 560kin. tropical cyclone track forecasts during 1988- Cyclone symbol and arrow indicate the position and motion 1993 by four operational global models, includ- of the vortices ing the global models of JMA, UK Meteorolog- ical Office, ECMWF and BMRC (Bureau of vertical structure of the bogus vortex in a Meteorology Research Centre). The results (in westerly flow (Fig. 7a), while it is insensitive to his tables 3 and 4) have shown that except for the the vertical structure of the bogus vortex in an JMA model, which had similar forecast accuracy easterly flow (Fig. 7b). By solving for instanta- for cyclones after recurvature to that of those neous motion tendencies using the equivalent before recurvature, the other three models all had barotropic vorticity equation, Holland (1983) larger errors for cyclones after recurvature than found that eastward moving cyclones are quite those before recurvature. Note that in both the sensitive to the small imposed perturbations in ECMWF and the BMRC models, no tropical either the environmental flow or short-lived cyclone bogusing had been made, while both the asymmetries in vortex circulation. Our results JMA and UK models have included bogus obtained above reveal that it is westerly flow that vortices below 500 and 300hPa, respectively, provides the most sensitivity for imposed pertur- during the objective analysis/assimilation cycle. bations in vertical structure of the bogus vortex. In addition to the sensitivity of the forecast Since tropical cyclones in the low latitudes tracks to the vertical structure of the bogus vortex typically experience an easterly flow, the forecast in the westerly flow, the intensity change of both tracks will not be significantly influenced by the vortices in the westerly (Fig. 8a) was also vertical structure of the bogus vortex. However, different from that in the easterly flow (Fig. for those cyclones that recurve into the mid- 8b). We can see from Fig. 8b that the intensity 162 Y. Wang

(a) Westerly 1000 / I t i i t i I I I I I "~ 995 9oh

I

980 ......

975 E ."4

~ C 970 -

965 -

96O I I I I I I I I I I I 0 6 12 18 24 30 36 42 48 54 60 66 72 Time (hours) (b) Easterly 1000 I I I I I I I I I 1 I 995

.r 99O 985 13., 98O

9'75 E

.r-qC 970

965 Fig. 8. Central sea surface pressure as a function of time for vortex A (solid) and 960 r r I l I 1 1 I I f I vortex B (dashed) on a beta-plane in a 0 6 12 18 24 30 36 42 48 54 60 66 72 uniform westerly flow (a) and in a uniform Time (hours) easterly flow (b)

change of the two vortices in the easterly is very 3.3 Barotropic Flow with Linear Horizontal similar to that in the resting environment shown Shear in Fig. 5. However, in the westerly flow, vortex A was still continuing to intensify by the end of Recent studies by Williams and Chan (1994) and the model forecast (solid line in Fig. 8a), but Wang and Li (1995) have shown that horizontally vortex B reached its maximum intensity after sheared environmental flow influences the baro- 50 h of integration (dashed line in Fig. 8a). By tropic vortex motion by changing the intensity 72, the difference in minimum sea level pressure and orientation of the asymmetric beta-gyres at the vortex center between the two vortices which determine the propagation of the vortex reached 15hPa. Since the upper-level circula- relative to the environmental flow. They found tions for either vortex A or vortex B in the that vortices embedded in a zonal flow with westerly and easterly flows (not shown) were cyclonic shear propagate slower than those similar to those shown in Fig. 4 for a quiescent embedded in an anticyclonic shear. However, environment, the large difference in vortex the influence of such an environmental flow on intensity may also have a small contribution to a baroclinic vortex motion has not been docu- the motion difference. mented. On the Bogusing of Tropical Cyclones in Numerical Models 163

6 in a more meridional direction. Downward penetration of the upper-level anticyclonic cir- 5 'i;'-a culation will reduce the westward motion

i component of the beta-drift. For the same reason, ~4 A downward penetration of the upper-level anti- o3 cyclonic circulation will reduce the poleward 0 motion component of the beta-drift in a zonal V>.,2 flow with an anticyclonic shear. As a result, cyclones with stronger upper-level anticyclones 1 will move less westward (poleward) in a zonal flow with cyclonic (anticyclonic) shear than 0 those cyclones with weak upper-level anti- -8 -6 -4 -2 0 cyclones. The above hypothesis was verified using experiments with either vortex A or B embedded 8 ' I ' I ' I ' I ' I ~ I ' I ' in a zonal flow with either a cyclonic or an 7 - A (b) anticyclonic shear of 5.875• -1. In these

i experiments, the vortex started from where the 6 B zonal flow is zero. The tracks (Fig. 9) show that 2 vortex B moved less westward than vortex A in ~'5 the cyclonic shear (Fig. 9a) and tess poleward than vortex A in the anticyclonic shear (Fig. 9b). g4 As was expected that the upper-level anticyclonic circulation (low potential vorticity region) was to the equatorward side of the surface vortex in the 2 cyclonic shear (Fig. 10) and to the west to southwest in the anticyclonic shear (Fig. 11). 1 p Therefore, downward penetration of the upper- level anticyclonic circulation reduces the west- 0 , I, I, I, ,I, I, , ward (poleward) motion component of a tropical -4 -2 0 2 4 cyclone in a zonal flow with a cyclonic (anti- X(100KM) cyclonic) horizontal shear. This effect is larger for cyclones that have stronger upper-level anti- Fig. 9. 72-h tracks of the two vortices in a barotropic flow cyclones, such as vortex B used in this study. The with linear cyclonic horizontal shear (a) and linear anti- cyclonic horizontal shear (b), with 12-h positions indicated 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 It has been indicated in section 3.1 that weak. downward penetration of the upper-level anti- Note also that although the position differ- cyclonic circulation which is displaced south- ences between the two vortices after 72h of westward relative to the lower-level vortex may integration are similar for both cyclonic and reduce the northwestward drift of the surface anticyclonic shear (126 km versus 116 kin), they vortex on a beta-plane in an environment at rest may not only be caused by the horizontal shear, (Figs. 3 and 4). In the presence of a horizontal but may also be partially affected by the direction shear, the relative positions of the upper-level of the environmental flow, as discussed in section and the lower-level circulations may be changed 3.2. Since the sensitivity of vortex motion to the by the shearing effect of the environmental flow. vertical structure of the bogus vortex depends on In this case, one can expect that a zonal flow with the direction of the environmental flow, the a moderate cyclonic shear would cause the above results imply that the vortex motion may upper-and lower-level circulations to be aligned be most sensitive to the vertical structure of the 164 Y. Wang

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

Fig. 10. Potential vorticity fields b) 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 in- dicate the corresponding surface cyclone centers and the domain shown in each panel is 3200 kmx 3200 km

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

12.5 ~12.5-

I 1

Fig. 11. Potential vorticity fields b) at 200 hPa after 24, 48, and 72 h of integration for vortex A (a) ~'5~ '2"s] lz.5 1 5~ and vortex B (b) on a beta-plane in a barotropic zonal flow with -.- _,2 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 vortex in a westerly flow with cyclonic in the anticyclonic shear flow (Fig. 9b). This shear. concurs with the findings by Williams and Chan Comparing the tracks in Fig. 9a,b with those in (1994) and Wang and Li (1995). The results also Fig. 3, one can see that the poleward motion demonstrate that the horizontal shearing effect component of the beta-drift is reduced in the of the environmental flow dominates to reduce cyclonic shear flow (Fig. 9a), but it is increased (increase) the beta-drift in a cyclonic (anti- On the Bogusing of Tropical Cyclones in Numerical Models 165 cyclonic) shear even though for diabatic baro- ' I ' I ' I ' i 'i ' I ' I' I ~ I ' ' I ' I clinic vortices. A (a) 2 B

3.4 Horizontally Uniform Flow with Linear 0 Vertical Shear o >., The influence of vertical shear in the environ- mental flow on tropical cyclone motion has received considerable attention in recent years I, # , , I,I (e.g., Wu and Emanuel, 1993; Flatau et al., 1994; 0 2 4 6 8 10 12 14 Jones, 1995; Wang and Holland, 1996c). These 6 studies show that tropical cyclone-like vortices - ( can propagate to the left of the vertical shear 5 ] when facing down shear due to the vertical d coupling mechanism similar to that discussed in ] sections 3.1, 3.3. In this case, the vertical shear displaces the upper-level anticyclonic circulation 1 of a tropical cyclone downshear. Flow associated 0 ' with the downward penetration of this downshear -14 -12 -10 -8 -6 -4 -2 0 X(IO0~:M) displaced anticyclone will deflect the surface vortex to the left of the vertical shear vector (Wu Fig. 12. 72-h tracks of the two vortices in a horizontally and Emanuel, 1993; Flatau et al., 1994). Diabatic uniform flow with linear westerly shear (a) and linear heating in the vortex core and the development of easterly shear (b), with 12-h positions indicated convective asymmetries can enhance this propa- gation tendency (Wang, 1995a; Wang and Holland, 1996c). stronger upper-level anticyclone of vortex B To study whether vertical structure of the bogus should further reduce the poleward motion vortex has a significant effect on the motion of tendency of the beta-drift. However, this did model vortex in vertical shear, four experiments not happen. What occurred was that the easterly were performed with the two vortices embedded shear flow increased the westward displacement in a horizontally uniform flow with a linear of the upper-level anticyclone relative to the vertical shear, with 8 m s -1 at the top of the lower-level vortex. As a result, the upper-level model atmosphere and 0 at the surface. The anticyclone was shifted far westward from the tracks for these experiments are shown in Fig. lower-level vortex and its influence on the vortex 12a for westerly shear and Fig. 12b for easterly motion was therefore very limited (Fig. 13). In shear. We can see that the motion difference this case, the predicted motion is not sensitive to between the two vortices is small in both vertical structure of the bogus vortex. westerly shear and easterly shear (67 km versus An important issue which should be addressed 46 kin) compared to that in a resting atmosphere here is that in addition to the dependence of the (Fig. 3). The propagation to the left of the intensity of the model cyclone on the vertical vertical shear vector is evident in westerly shear structure of the bogus vortex as seen from the for both vortices since the poleward displace- previous subsections, the intensity of the model ment is larger for the vortex in westerly shear cyclone also depends on the direction of the (Fig. 9a) than that in a resting atmosphere (Fig. vertical shear (Fig. 14). Cyclones in westerly 3). In this case, vortex B, which has a stronger shear (Fig. 14a) developed stronger than those in upper-level anticyclone, has a larger leftward easterly shear (Fig. 14b). Such a dependence of motion tendency than vortex A, reducing the model cyclone intensity on the direction of motion difference between the two vortices in an vertical shear in the environmental flow has been environment at rest. One might expect that the studied in detail by Wang (1995a), who found motion difference between the two vortices that compared to a westerly shear, an easterly should be enhanced in easterly shear since the vertical shear may increase the westward dis- 166 Y. Wang

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

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

Fig. 13. Potential vorticity fields at 200 hPa after 24, 48, and 72 h integration for vortex A (a) and ~)) 12.5- 12.5~12.5 t 12.5 12,5-- 12,5 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 indi- cate 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 9951- r n. 990-

975-

960 1 I l, I I I I I I,, f I I / 0 6 12 18 24 30 36 42 48 54 60 66 72 Time (hours)

(b) Easterly shear 1000 t I I I I [ I I I I I I t 995

99O '985 980 & 975

,t,-q 970- Fig. 14. Central sea surface pressure as a 965 - function of time for vortex A (solid) and vortex 960 I I I I I I I I I I I B (dashed) on a beta-plane in a horizontally 0 6 12 18 24 30 36 42 48 54 60 66 72 uniform flow with linear westerly (a) and Time (hours) easterly (b) vertical shears On the Bogusing of Tropical Cyclones in Numerical Models 167 placement of the upper tropospheric outflow that one is cyclonic throughout the troposphere layer relative to the lower-level cyclone purely and the other has an extra anticyclone in the due to the Rossby wave dispersion, and increase upper troposphere. The results show that the the vertical tilt of the vortex and thus decrease forecast tracks as well as the intensity can be the vortex intensity. The above result seems to be very sensitive to the vertical structure of the in contrast to the findings of Tuleya and Kurihara bogus vortex, especially when the environmental (1981), who found a bias toward easterly vertical flow is very weak, or westerly and has cyclonic shear in tropical when the mean shear. However, this sensitivity is reduced in surface wind is easterly. We suggest that the moderate vertical shear. This motion sensitivity strong cyclonic shear in the environmental flow is found to arise from the vertical coupling for their numerical experiments played a role in mechanism by which the upper- and lower-level keeping the outflow layer over the surface circulations interact with each other when a disturbance. horizontal displacement occurs between them. It should be pointed out that the above results This vertical coupling can also result in devel- are obtained from a linear vertical shear flow. opment of convective asymmetries in the vortex Studies by Flatau et al. (1994) found potential core region. The asymmetric divergent flow in impact of the vertical profile of the environ- the lower troposphere associated with these mental flow on baroclinic vortex motion. In that convective asymmetries may in turn further case, the motion of the vortex is not only influence the vortex motion by deflecting the influenced by the shearing effect and vertical vortex to the region with maximum convection. coupling mechanism, but also influenced by the On a beta-plane in an environment at rest, the horizontal potential vorticity gradients associated upper-level anticyclonic circulation drifts equa- with the vertical shear in the environmental flow. torward and westward relative to the lower Since the latter can be attributed to the gross cyclonic vortex due to the Rossby wave disper- beta-induced propagation (Shapiro, 1992), we do sion. Downward penetration of this upper-level not intend to include its effect here. anticyclonic circulation reduces the poleward and westward motion of the surface vortex. As a result, the cyclone without an upper-level anti- 4. Discussion and Conclusions cyclone in the initial bogus vortex in a numerical Despite the progress made in the performance of model will move faster and more westward than numerical weather prediction models, the lack of the one which has an upper-level anticyclone. adequate data over the tropical oceans limits the The motion sensitivity to the vertical structure of accuracy of analyses and forecasts of tropical the bogus vortex in a uniform easterly flow is cyclones. Bogusing techniques of tropical cyclones mainly caused by the vertical coupling mecha- in numerical models, therefore, have been widely nism by which the downward penetration of the used in operational forecasting and research upper-level anticyclonic circulation exerts a models to improve tropical cyclone analysis shearing effect on the lower cyclonic portion of and model performance. The usual procedure is the cyclone, changing the distribution and to define a synthetic data distribution based on an intensity of convection and thus the vortex analytically prescribed vortex, which is passed to motion. The horizontal shear affects the baro- the analysis scheme as a set of high quality clinic vortex motion by a shearing effect which observations, or inserted into the analysed field makes the upper-level anticyclone to be located as the initial conditions of the forecast models. In to the equatorward (westward to southwestward) this procedure, the structure of the bogus vortex side of the surface vortex. In this case, the is prescribed based on some characteristics of the cyclone initially without an upper-level anti- tropical cyclones to be forecasted. cyclone will move more westward (poleward) in In this study, idealised conditions are used to a cyclonic (an anticyclonic) shear than that with study the vertical structure of the bogus vortex on an upper-level anticyclone. The insensitivity of its motion in numerical models by comparing the model cyclone motion to the vertical structure of forecasted tracks for two vortices which have the bogus vortex in vertical shear results mainly different vertical structures at the initial time in from the fact that in a westerly vertical shear 168 Y. Wang

vortex with a stronger upper-level anticyclone schemes. Our preliminary numerical experiments has a larger leftward motion tendency to the have shown that different parameterization vertical shear vector and thus reduces the motion schemes give different vertical heating profiles difference in a resting atmosphere, while in an and thus result in different vertical structure of easterly vertical shear the upper-level anti- the model cyclone. As a result, the motion cyclonic circulation is shifted far westward difference is directly caused by the changes in relative to the lower-level vortex so that its vertical structure of the model cyclone. Further influence on vortex motion is largely reduced. studies are needed to understand the dynamics by Our main purpose in this study has not been to which the physical parameterization schemes of reach an optimal vortex structure for operational the numerical models influence the performance use. Rather, we have addressed the potential of tropical cyclone forecast by numerical models. impact of vertical structure of the bogus vortex on its motion in a numerical model. However, our results indicate that vortices which lack an Acknowledgment anticyclone in the upper troposphere would move The author is grateful to Dr. Greg Holland for carefully quite differently in some environmental config- reading an early version of the manuscript and for valuable comments. This study has been benefited from discussions urations. We suggest that care needs to be taken with Drs. Greg Holland and Noel Davidson. Part of this in determining the vertical structure of the bogus work has been supported by the U. S. Office of Naval vortex in numerical models. Note that our Research under grand N-00014-94-I-0556. numerical experiments have started from vortices with no radial flow or secondary circulation. But the results seem not to be significantly influenced References by this treatment, except that spinup of the vortex Andersson, E., Hollingsworth, A., 1988: Typhoon bogus takes about 12-h of integration. observations in the ECMWF data assimilation system. The influence of vertical structure of the bogus ECMWF Research Department Tech. Memo. No. 148, ECMWF, Reading, UK, 25 pp. vortex has been tested here using only very Anthes, R. A., 1977: A cumulus parameterization scheme simple environmental flows. Holland and Wang utilizing a one-dimensional cloud model. Mon. Wea. Rev:, (1995) have shown potential sensitivity of 105, 270-286. recurving tropical cyclones to vertical structure Arakawa, A., Lamb, V. R., 1977: Computational design of of model vortices. Wang and Holland (1995) the basic dynamical process of the UCLA general circula- have indicated that binary interaction of tropical tion model. Methods in Computational Physics, 17, 173- 265. cyclones can also be very sensitive to the vertical Chan, J. C.-L., Williams, R. T., 1987: Analytical and numer- structure of model vortices. These studies ical studies of the beta-effect in tropical cyclone motion. indicate that more sensitivity of tropical cyclones Part I: Zero mean flow. J. Atmos. Sci., 44, 1257-1265. to vertical structure of the bogus vortex may Davidson, N. E., McAvaney, B. J., 1981: The ANMRC occur in more complicated environmental flow tropical analysis scheme. Aust. Meteor. Mag., 29, 155- 168. and in situations of multiple tropical cyclones. Davidson, N. E., Puri, K., 1992: Tropical prediction using In order to study the potential influence of dynamical nudging, satellite-defined convective heat vertical structure of the bogus vortex on its sources, and a cyclone bogus. Mon. Wea. Rev., I20, motion, we have not considered the impact of 2501-2522. parameterization schemes of model physics. DeMaria, M., 1987: Tropical cyclone track prediction with a Although many previous studies have indicated barotropic spectra model. Mon. Wea. Rev., 115, 2346- 2357. that successful forecast of tropical cyclones DeMaria, M., Aberson, S. D., Ooyama, K. V., Lord, S. J., should be also gained by improving the planetary 1992: A nested spectral model for hun'icane track fore- boundary layer formulation and the convection casting. Mon. Wea. Rev., 120, 1628-1643. scheme of the numerical models (Heckley et al., DeMaria, M., Pickle, J. D., 1988: A simplified system of 1987; Krishnamurti et al., 1989; Puri and Miller, equations for simulation of tropical cyclones. J. Atmos. Sci., 45, 1542-1554. 1990; Lazid, 1993), we expect that the findings of Elsberry, R. L., 1987: Tropical cyclone motion. In: Elsberry, sensitivity to vertical structure of the bogus R. L. (ed.) A Global View of Tropical Cyclones. Arlington, vortex in this study are not significantly changed VA: Marine Meteorology Program, US Office of Naval by using different physical parameterization Research, 185 pp. On the Bogusing of Tropical Cyclones in Numerical Models 169

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