Meteorol. Atmos. Phys. 65, 153-170 (1998) Meteorology, and Atmospheric Physics 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 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 cyclone circulations for use in numerical upper tropospheric anticyclone. Both vortices have the weather 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 tropical cyclone 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 Japan Meteorological currently in use, in particular, with or without the Agency (JMA) (Ueno, 1989, 1995). The third outflow 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 Taiwan (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 storm-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 precipitation has been included in both 0.965, 1.0.