Numerical prediction of tropical cyclone tracks has improved enormously over the past few decades, but there is little skill in forecasting the storm’s intensity change (Elsberry et al. 1992) and inner-core structures (Liu et al. 1997). In fact, hurricane intensity change is closely related to the evolving three-dimensional structures of the hurricane. The difficulties in the prediction of hurricane intensity and inner-core structure are associated with insufficient observations over the oceans and with the limitations of forecast models, such as low-resolution, hydrostatic dynamics, crude physical parameterization, and the inability to treat multiscale interactions. Recently, hurricane forecast models at high resolution have greatly improved as a result of advances in computer architecture. More sophisticated models have been developed and used for hurricane study and forecast. The Florida State University atmospheric global circulation model was run at a resolution as high as T213, which can rebuild some mesoscale signatures of the observed hurricane features with the help of satellite data using physical initialization (Krishnamurti et al. 1995). The well-known Geophysical Fluid Dynamics Laboratory (GFDL) hurricane model has been running operationally with a multiply nested movable mesh system at a grid resolution as high as 6 km, and a very sophisticated model initialization scheme (Bender et al. 1993; Kurihara et al. 1995; Ross and Kurihara 1995). The Pennsylvania State University–National Center for Atmospheric Research (Penn State–NCAR Mesoscale Model version 5 MM5) was also employed to simulate the development of Hurricane Andrew of 1992 (Liu et al. 1997) and Hurricane Felix of 1995 (Zou and Xiao 2000). It was run at a grid spacing of less than 10 km with explicit microphysics.
By contrast, advances in hurricane initialization have been relatively slow. With the sparse data coverage over the oceans, numerical analyses cannot adequately represent the initial circulations of tropical cyclones (Leslie and Holland 1995). Hurricane initialization becomes a necessary step before making a prediction. There are several approaches for hurricane initialization: (i) substitute a specified vortex circulation defined by an analytical expression for the analyzed vortex into the initial conditions (Mathur 1991; Ueno 1989; Serrano and Unden 1994; Leslie and Holland 1995), (ii) implant a“spinup” vortex generated by the same forecast model into the initial conditions (Kurihara and Ross 1993; Kurihara et al. 1995; Peng et al. 1993; Liu et al. 1997); and (iii) improve the initial conditions by making use of satellite–rain gauge based measurements of rainfall through a physical initialization procedure (Krishnamurti and Ross 1993, 1995, 1997, 1998). Although bogusing schemes are employed by many NWP centers, they do not always work well for a large range of tropical cyclones (Wang 1998). In order to minimize the effects of the “initial shock” resulting from the ad hoc assumptions in these bogus schemes, a procedure is usually needed to balance the model initial state. For example, the National Centers for Environmental Prediction (NCEP) global model generates bogus observations, which are run through the multivariate analysis scheme. This ensures that the initial state will be balanced. In the GFDL model, a quasi-balanced initial state is generated using a simplified version of the model in the bogus procedure (Kurihara and Ross 1993).
In the recent work of Zou and Xiao (2000), a variational bogus data assimilation (BDA) scheme was proposed to generate the structure of a tropical hurricane in the initial condition of a high-resolution mesoscale model. In the scheme, a specified surface low based on a few observed parameters was incorporated into the model’s initial conditions through a variational approach in which the forecasting model serves as a strong constraint. The initial vortex obtained by the proposed method contains a more realistic hurricane structure in all model fields and is also well adapted to the prediction model. Such an initialization procedure is not only objective, but also flexible for the inclusion of any available observations due to its variational formulation.
The BDA scheme worked well for the numerical simulation of Hurricane Felix (1995), a hurricane that made a recurvature prior to its landfall (Zou and Xiao 2000). In this paper, we further test the performance of the BDA scheme for the numerical simulations of Hurricane Fran (1996) during its landfall, which occurred from 0000 UTC 3 September to 0600 UTC 6 September 1996. We extend the work of Zou and Xiao (2000) to examine the BDA scheme’s sensitivity to model resolution, to the size of the specified vortex, and to the specification of bogused sea level pressure (SLP) versus wind. The advantage of studying this case is that there were extensive observational analyses after 0000 UTC 3 September 1996 that are available from the National Oceanic and Atmospheric Administration’s Hurricane Research Division (NOAA/HRD) for forecast verification, such as Weather Surveillance Radar-1988 Doppler (WSR-88D) reflectivities and surface wind analysis from before the landfall of Fran. These data are not available for Hurricane Felix (1995).
From 0000 UTC 3 September through 0600 UTC 6 September 1996, Hurricane Fran moved in a northwest direction in the western Atlantic, north of the Caribbean, and made landfall on the North Carolina coast around 0030 UTC 6 September (Fig. 1). At landfall, the minimum central SLP of Fran was estimated as 954 hPa and the maximum sustained surface winds were 51.7 m s−1. The strongest winds occurred in streaks within the deep convective areas north and northeast of the center. Hurricane Fran was responsible for 34 deaths. The storm surge on the North Carolina coast destroyed or seriously damaged numerous beachfront houses. Extensive flooding caused additional damage in the Carolinas, Virginia, West Virginia, Maryland, Ohio, and Pennsylvania. Fran was responsible for an estimated $3.2 billion in damage to the United States (Pasch and Avila 1999).
This paper is organized as follows: The next section describes the experimental design, including a brief description of the hurricane variational initialization scheme. The BDA generated initial hurricane structure and the subsequent forecast are discussed in sections 3 and 4. Section 5 presents the sensitivity of the forecasted hurricane’s track and intensity to the size of initial vortex. The importance of bogused SLP versus wind fields in the BDA scheme is also tested in section 5. Finally, a summary and conclusions are provided in the last section.
2. Experimental design
a. The numerical model
The numerical model used in this study is an improved version of the Penn State–NCAR nonhydrostatic, movable, triply nested grid, 3D mesoscale model (Dudhia 1993; Grell et al. 1994). The model consists of 27 layers in the vertical (the model top is defined at 100 hPa). The 27 half-σ levels are 0.025, 0.070, 0.110, 0.150, 0.190, 0.230, 0.270, 0.310, 0.350, 0.390, 0.430, 0.470, 0.510, 0.550, 0.590, 0.630, 0.670, 0.710, 0.750, 0.790, 0.830, 0.870, 0.910, 0.945, 0.970, 0.985, and 0.995. All variables except vertical velocity w are defined on the half-σ levels. In the horizontal direction, the model has three nested domains A, B, and C, with horizontal resolutions of 54, 18, and 6 km, respectively. The coarsest domain A is fixed, but the intermediate domain B and the fine domain C moved along with the hurricane track (Fig. 1). The model variables are staggered horizontally such that u and υ are defined on the midpoints of all other quantities. The (x, y) dimensions are 76 × 85, 112 × 130, and 109 × 127 for domains A, B, and C, respectively. The time step for the coarsest domain A is 120 s and complies with the ⅓ rule for the intermediate domain B and fine domain C. To reduce the computational cost, domain C is activated into integration at 66 h, when Hurricane Fran is near its landfall. We activate this fine mesh so as to obtain a more detailed hurricane structure and compare it to the observed radar reflectivity and surface winds during the landfall of Fran.
The model water cycle processes include parameterization of shallow convection for all domains, the Grell (1993) cumulus parameterization and the Dudhia’s simple ice explicit moisture scheme for domain A, the Kain–Fritsch cumulus model and the Reisner mixed-phase explicit moisture scheme for domain B, and the Reisner graupel explicit moisture scheme for domain C. The more sophisticated model physics was used for the higher-resolution model domain. According to Zhang et al. (1988) and Molinari and Dudek (1992), convective parameterization could be bypassed for a grid size of 6 km. Other model physics include a modified version of Blackadar (1979) PBL parameterization (Zhang and Anthes 1982) and a simple radiative parameterization in which the radiation effects due to clouds are considered and calculated every 20 min. The SST data come from the NCEP global analysis and are kept unchanged in the model integration. However, the land surface temperature is predicted using surface energy budget equations in which the effects of short- and longwave radiation and cloud radiation are included. The model also includes three-dimensional Coriolis force. Surface heat and moisture fluxes are taken into account. To deal with the acoustic waves, an upper radiative boundary condition is applied. The reader can refer to Dudhia (1993) and Grell et al. (1994) for a more detailed description of the model.
b. The BDA scheme
The variational initialization scheme includes two parts. The first step is vortex specification. The second step is a minimization procedure forcing the forecast model to generate the hurricane vortex. The vortex specification applies to a few model variables and the minimization procedure produces fields for all model variables, objectively satisfying the dynamic and physical constraint for the atmosphere.
1) Vortex specification
The assigned pressure Po and wind fields Vo values in the domain Ω are used as “observations” data to modify the MM5 analysis through a variational procedure, which is described below.
2) Minimization procedure
For simplicity, the background error covariance
In order to minimize (3), a forward model and its adjoint are required. In this paper, the MM5 adjoint system (Zou et al. 1997) is used as a tool to minimize the cost function J for the purpose of obtaining the optimum hurricane initial conditions. The hurricane variational initialization is carried out on the coarsest 54-km domain (domain A) and/or the intermediate 18-km domain (domain B). The model initial conditions for the 6-km domains (domain Ci) are interpolated from that of the 18-km domain.
The dynamic structure of the MM5 adjoint system is the same as the MM5 forecast model described above. However, the physical processes that were employed in the minimization procedure are different. These processes are the bulk aerodynamic planetary boundary layer parameterization, surface friction, surface fluxes, dry convective adjustment, Kuo-type cumulus parameterization, and large-scale precipitation process. The forward MM5 model and the backward adjoint version use the same set of model physics. The gradient is checked with a procedure suggested by Navon et al. (1992).
The limited-memory quasi-Newton method of Liu and Nocedal (1989) is used to minimize the objective function in this study. The background Xb (the standard MM5 analysis X(0)) is used as the first guess of X for the minimization procedure. In all experiments, 30 iterations are performed to minimize the cost function J. After the minimization, the model fields, not only pressure and wind fields, but also temperature and humidity fields, are adjusted. The new adjusted fields are taken as the model initial conditions for the subsequent simulation.
c. Numerical experiments
We conducted nine forecast experiments for the 78-h simulation of Hurricane Fran (1996) using the two-way interactive, triply nested, and movable mesh MM5. The differences between these experiments are in the initial conditions (listed in Table 1). CTL is the control experiment, which starts from MM5 analysis (NCEP 2.5° × 2.5° global analysis enhanced by rawinsondes and surface observations) without the variational initialization procedure. All other experiments use an initial condition obtained by the BDA procedure in which a bogused surface low and/or the corresponding balance wind are assimilated into the model initial conditions. These experiments differ in the horizontal resolution of the assimilation model, the size of the bogus vortex, and the bogus variables specified. Specifically, B80 is an experiment in which the BDA procedure was carried out at 18-km resolution (domain B) with 80-km RMW. A80, A100, A140, A180, A220 and A260 are experiments in which the BDA scheme was carried out at 54-km resolution (domain A) and with the radius R of 80, 100, 140, 180, 220 and 260 km. These experiments were designed to test the sensitivity of the hurricane forecast to the specification of the vortex size in the BDA scheme. The experiments A220P and A220V were carried out to test the relative effectiveness of SLP and wind information for the hurricane initialization and simulation. The BDA scheme in A220P minimizes Jb + Jp, and that of A220 V minimizes Jb + Jυ [see Eq. (4)].
3. Results from the BDA scheme
a. Efficiency of the technique
We performed 30 iterations of the minimization procedures in all the BDA experiments. Figure 3 shows the variations of the three terms in the cost function, Jb, Jp, and Jυ, during the 30 iterations for B80. The performance of the minimization for the other experiments was similar. As expected, the pressure and wind terms decreased at the expense of the background term increase. Since Xb is used as the initial point of the minimization, the background term is equal to zero at the beginning of the minimization and increases with the number of iterations. The figure indicates that the minimization converged very quickly in the first five iterations. After the background term was increased to a value close to the “observational” terms, the adjustment in the model’s initial condition became smaller. Usually 15 iterations were enough to obtain the optimal initial condition with a reasonable accuracy.
To show the effectiveness of the BDA minimization procedure, Table 2 lists values of the central SLP and the low-level maximum wind of the initial vortex in all the experiments. The observed hurricane central pressure and maximum wind are also listed in Table 2. We can see that the BDA technique was, in general, capable of producing an initial hurricane with an intensity very close to the observed value. The central SLP of the hurricane center was 1008 hPa from the standard MM5 analysis. After the BDA procedures, the SLP decreased at least 20 hPa for all the experiments except A220V. The observed low-level maximum wind reached 38.8 m s−1, while the MM5 standard analysis was only 15.0 m s−1. After BDA, the low-level maximum winds increased by at least 20 m s−1 for all the variational experiments. We thus notice that the assimilation of the specified SLP adjusted the wind field to a great extent, but the assimilation of the bogused wind data alone did not make significant changes in the SLP field. The proposed BDA scheme is quite robust with respect to the specifications of the vortex size and has great skill in reproducing the observed initial hurricane intensity. An additional advantage of the BDA scheme is its ability to produce dynamically and physically consistent hurricane structures of all model fields, which are shown in the following subsection.
b. The thermodynamic structure of the initial hurricane obtained by B80
During the BDA procedure, the temperature and humidity fields are also modified so as to balance the pressure and wind adjustment within the hurricane area. Figure 4 shows the cross section of the temperature and humidity fields before and after the initialization in experiment B80. It can be seen that the NCEP analysis (Figs. 4a,b) lacked the structure that a mature hurricane has in the temperature and humidity fields. The temperature and humidity contours were flat above the cyclone. Since there are few, or no, radiosonde observations over the open ocean, the hurricane temperature and humidity fields were nearly the same as the environmental fields in the global analysis (Fig. 4a). After BDA, the hurricane temperature and humidity fields were modified and the temperature above the hurricane center increased (Fig. 4c). In the lower troposphere, the water vapor content also increased (Fig. 4d). The temperature and moisture structures in Figs. 4c and 4d indicate a mature hurricane structure with a warm, moist core. However, in the BDA scheme, surface temperature is not a control variable. It is, therefore, not adjusted after the initialization. That is why the lower air temperature in the eye is much greater than the (SST). Further work is needed to incorporate surface temperature into the BDA scheme to overcome this unrealistic feature.
The shaded areas in Figs. 4c and 4d are the BDA analysis increments of the temperature and specific humidity. The temperature increases are as large as 6°C at 700 and 200 hPa. The maximum increase in the humidity field occurred in the lower troposphere above the hurricane center (Fig. 4d), with a 6 g kg−1 increase observed near 850 and 700 hPa. Such an adjustment in the temperature and specific humidity are a result of the model’s fit to the bogus data constraint. There was no direct information on the temperature and specific humidity in the bogus data and no structure function in the background term. The hurricane warm-core structure was formed with the use of the BDA scheme. Moisture increase in the lower troposphere is very important for hurricane development (Liu et al. 1997). Such a modification will facilitate the triggering of deep convection associated with the storm and reduce the spinup problem of model integration.
4. Experimental results from the simulation of Hurricane Fran (1996)
According to the real-time surface wind analyses prepared by NOAA/HRD Atlantic Oceanographic and Meteorological Laboratory (AOML), Hurricane Fran had an RMW of close to 80 km at 0000 UTC 3 September 1996. Two experiments, A80 and B80, which both had an RMW of 80 km (close to the observed one), were carried out to examine the performance of the BDA scheme on the initialization and simulation of the landfall of Hurricane Fran while studying the sensitivities of the numerical results to the horizontal resolution of the assimilation model used in BDA.
Figure 5 shows the predicted hurricane tracks of Fran (1996) from CTL, A80, and B80, starting from 0000 UTC 3 September 1996. The NHC observed best track (OBS) is also plotted for comparison. Starting from 0000 UTC 3 September, the observed storm moved north-northwestward and landed at about 0030 UTC 6 September on the North Carolina coast. The CTL-simulated hurricane track is on the west side of the observed track and the position error at 78 h is about 352 km (see also Table 3). The landing time predicted by CTL had a 6-h delay. On the contrary, the hurricane tracks from A80 and B80 were on the east side of the observed track. The errors in both the movement and landing time were much reduced (Fig. 5 and Table 3). At 78 h of model integration, the track forecast made by B80 has about a 96.5-km position error. The forecasted landing time was about 1 h earlier than the observed one. This demonstrates the positive impact of the BDA scheme on the hurricane track prediction.
The hurricane track predicted by A80 with the BDA scheme carried out on 54-km resolution (domain A) was slightly degraded. The simulated track was farther to the east and slightly faster than that of B80.
Figure 6 depicts the time variation of the minimum central pressure (Fig. 6a) and the maximum low-level winds (Fig. 6b) from CTL, B80, and A80. The observed minimum central pressures and the maximum low-level winds from observations are also shown as a reference in the figure. The simulated maximum low-level wind is the highest value of the averaged 25th and 26th model level winds calculated at each grid point. Without the variational initialization procedure, model simulation (CTL) did not capture the intensity of Hurricane Fran, either in the central pressure or the maximum low-level winds. The errors from the B80 and A80 simulations initialized with the BDA technique were significantly smaller compared to CTL. The spinup problem seen during the first 6-h integration of A80 and B80, reflected in the central pressure jump during that interval in Fig. 6a, is probably due to the use of triply nested domains for predication and a single domain for initialization.
According to the HRD real-time surface wind analysis and NHC aircraft reconnaissance (Pasch and Avila 1999), Hurricane Fran had its maximum wind streak from the east to the north-northeast of the hurricane center. Figure 7 shows the surface analyses of the streamlines and isotachs (kt) at 0100 and 0700 UTC 5 September 1996 using the available observations and the aircraft reconnaissance by NOAA/HRD. The maximum winds are observed to the northeast of the hurricane center. The maximum surface wind at 0100 UTC is 95 kt (49.1 m s−1). It is 90 kt (46.5 m s−1) at 0700 UTC 5 September 1996. The simulations of the hurricane surface wind fields at 0100 and 0700 UTC 5 September 1996 are shown in Figs. 8a and 8b, respectively. We can see that the simulated maximum wind streaks were located in the northeast quadrant. The maximum surface wind was 49.6 m s−1 at 0000 UTC 5 September and 56.3 m s−1 at 0600 UTC 5 September 1999. The simulated wind features resemble the HRD real-time surface wind analysis. However, the simulated RMW is slightly smaller than the observations.
To show the structures of the simulated Hurricane Fran, the vertical cross sections of temperature, specific humidity, horizontal wind, and vertical velocity of the B80 simulated 49-h hurricane along line AB in Fig. 8a are given in Fig. 9. The temperature field had an evident warm core above the hurricane (Fig. 9a) because of compensating descent inside the hurricane eye. The maximum value of specific humidity occurred near the surface in the hurricane center (Fig. 9b). The regions of maximum moisture were in the eyewalls from lower to middle troposphere. The hurricane center area was not as moist as the eyewall regions from 600 to 950 hPa. As seen in Fig. 8a, the cross sections are along the direction of the most asymmetric wind. Therefore, the wind fields in Fig. 9c also depict the asymmetric characteristics in the vertical distribution. The radius of the maximum wind increases with the height. It is noted that the ascending motion (Fig. 9d) was also not axisymmetric. The axes of the ascending motion in the eyewall and the compensating descent in the hurricane eye were tilted. The maximum ascending vertical motion occurred between 400 and 500 hPa in the eyewall.
From the simulated results we can summarize the following characteristics of the hurricane’s flow and its thermodynamic structure. 1) The tangential or swirling wind of the hurricane is strongly asymmetric. The maximum wind speed occurred around 900 hPa. 2) The ascending vertical motion around the eye increases the moisture in that region, while the descent inside the eye makes the area of the hurricane center drier in the lower to middle troposphere. Near the surface at the hurricane center, the specific humidity reaches its maximum value. 3) The compensating descent inside the hurricane eye is the main reason for the formation of the warm core. Because the temperature increase does not occur in the eyewall where the convective latent heating release takes place, we suspect that convective latent heating release is not the main reason for the formation of the hurricane’s warm core.
At 66 h of model integration, the 6-km grid-spacing domain C was activated. Therefore, we obtain a detailed hurricane forecast structure that can be compared with the onshore radar reflectivity distribution observed during the landfall of Hurricane Fran. The radar reflectivity was estimated from the model cloud water, rainwater, and other ice particles such as graupel. The method for calculation of the model reflectivity was the same as that in Liu et al. (1997) and it was based on the R–Z relation of Jorgenson and Wills (1982) and Fujiyoshi et al. (1990). Contributions of cloud water to reflectivity were small and therefore neglected. For Hurricane Fran, the structure of the storm at landfall was well captured by the WSR-88D radar onshore at North Carolina (Fig. 10b). The radar-observed stronger reflectivity represents the deep convection that occurred in the north-northwest area of the hurricane center. The simulated reflectivities of Hurricane Fran immediately after its landfall (Fig. 10a) showed that the simulated strong reflectivities were also in the north-northwest section of the hurricane center. The model reproduced very well the intense precipitation in the north-northwestern direction of the hurricane center, in accordance with the radar observations onshore. The horizontal structure of radar reflectivities were highly asymmetric from both the simulation and observation. The simulated higher radar reflectivities were more intense over land, a feature consistent with observations from the onshore radar at 0028 UTC 6 September 1996.
It must be pointed out that the simulation of B80 has some shortcomings. The predicted hurricane intensity is still weak compared with observation. The spinup problem is not eliminated during the first 6-h integration. The simulated winds in the hurricane environment are weaker than the analysis from observations (cf. Fig. 7 with Fig. 8). It is necessary to conduct more experiments and case studies to improve the BDA scheme in the future.
5. Sensitivities of the BDA results to the model resolution, RMW, and bogus variable specification
The specification of the bogus vortex [see Eq. (1)] requires knowledge of the RMW. The RMW is not always known, nor can it be estimated exactly. Previous studies, such as Fiorino and Elsberry (1989), addressed the sensitivity of hurricane prediction to the RMW using barotropic models. In our study, however, the baroclinic effects were included through the use of the primitive-equation mesoscale model MM5. We will examine the influence of the specified RMW upon the prediction of hurricane track and intensity using BDA. In addition, we will also test the relative importance of specifying the bogused SLP versus wind in the BDA scheme for the hurricane initialization and prediction.
a. Influence of the model resolution and specified vortex RMW in BDA
Figure 11 gives the predicted hurricane tracks of Fran (1996) for a set of experiments, CTL, A80, A100, A140, A180, A220, and A260, all initialized at 0000 UTC 3 September 1996. All the experiments initialized with the BDA scheme produced hurricane tracks east of the observed track, except in the beginning 6 h of the model integration. The results show that the predicted hurricane track is sensitive to the specified RMW, that is, R in Eq. (1). For RMW greater than 100 km, the storm moved more westward with time as the radius increased. This is shown more clearly for the tracks beyond 48 h. This numerical result is consistent with the result of barotropic model simulation by Fiorino and Elsberry (1989). The baroclinic effects included in MM5 did not change the propagation tendency. However, the track predicted by A80 is more westward than those predicted by A100 and A140. We suspect that the 54-km grid spacing is not sufficient to resolve the initial hurricane structure with an 80-km RMW hurricane.
Figure 12 depicts the time variation of the minimum central SLP (panel a) and the maximum low-level winds (panel b) from simulations with different values of RMW. All the forecasts initialized with the BDA procedure matched Hurricane Fran’s intensity change well. The intensifying period from 0 to 48 h and weakening period after 48 h were predicted. However, the hurricane intensity forecast was sensitive to the specified RMW. For RMW larger than 100 km, the hurricane weakens as the RMW increases. An exception occurred to A80 for the reasons mentioned above. With BDA being carried out at 54-km resolution and RMW being equal to 180 km and 220 km, the forecasts performed better than the other experiments for both the hurricane track and intensity simulations. Their forecast performances are comparable to B80. In summary, both A180 and A220 simulated an intensity and intensity variation very close to the observed one, although these two experiments were done at the resolution of 54 km (instead of 18 km) and the RMW used in the BDA was larger than the observed one.
b. Relative importance of SLP versus wind information in specifying the initial vortex
The BDA experiments described above include two types of bogus data: the SLP and wind. In this section, we perform two additional experiments, one without the bogused wind (A220P) and the other without the bogused SLP (A220V). The BDA schemes of both experiments were performed at 54-km resolution (domain A) and the RMW was taken as 220 km, because A220 produced reasonably good simulations in both the hurricane track and intensity. We are interested in seeking an answer to the question: which type of bogused data is more important for the hurricane initialization and forecast using the variational approach?
Figure 13a presents the hurricane SLP and 850-hPa wind field after minimization of A220V. The pressure field after the BDA with bogused winds alone (Fig. 13a) is still weak and does not match well with the wind fields. The surface low was extended to the northeast compared to the NCEP global analysis (Fig. 13c), but the center was still located about 50 km southwest of the hurricane wind circulation (vortex). Only a 2-hPa change occurred to the central pressure value through the assimilation of wind data in A220V. In A220P (Fig. 13b), not only the bogused pressure field was assimilated into the model’s initial condition, but also the wind fields were significantly adjusted, showing a more compact, asymmetric distribution compared to the NCEP global large-scale analysis (see Fig. 13c). The maximum 850-hPa wind was in the northeastern quadrant of the hurricane cyclone, the same as that observed in B80. We notice that the BDA-generated pressure and wind fields in Fig. 13a (and Fig. 13b to some extent) do not necessarily satisfy the balance equation. The complete forecast model serves as the dynamic and physical constraint in the BDA scheme.
Figure 14 shows the predicted hurricane intensity variations of A220P and A220V for the 78-h simulations. As a comparison, the intensity changes of A220 and the NHC observations are also shown in Fig. 14, along with A220P and A220V. At the initial time, A220P had a hurricane central pressure of 976 hPa and a maximum low-level wind of 26.1 m s−1, while in A220V the central pressure was 1007 hPa and the maximum low-level wind was 34.6 m s−1. This implies that the assimilation of the bogused wind alone could not produce a hurricane SLP field with realistic intensity. On the contrary, the wind fields were significantly adjusted while assimilating the bogused SLP data. The subsequent 78-h model simulations show that A220V predicted a relatively weaker hurricane, although the forecasting skill in A220V is improved compared to CTL. The predicted hurricane central pressure and low-level maximum wind speed at 54 h were 982 hPa and 42 m s−1, respectively. It is interesting to note that, although the low-level maximum wind of A220V at the beginning was very close to the observation, the forecast became poorer as the time of integration increased. A precise specification of wind fields alone in the BDA scheme seems insufficient to obtain a prediction with a realistic intensity and intensity change if no related pressure field is also specified in the scheme. A220P had an overall better performance than A220V, although the wind fields at the initial time were slightly weaker and the model prediction suffered a 12-h spinup problem (Figs. 14a,b). It should be pointed out that the predicted hurricane low-level maximum winds in A220P were closer to the observation than in A220V, although the wind was not bogused into the model initial condition in A220P. From these experiments, we conclude that the pressure bogus is more efficient than the wind bogus in reproducing a realistic hurricane intensity forecast. This reconfirms the importance of the surface low information in the pressure field for the hurricane BDA initialization (Zou and Xiao 1999).
Figure 15 shows the adjustments of the temperature and humidity fields of A220P and A220V. The warm and moist core in the initial vortex of A220P (Figs. 15c,d), is not produced in the initial vortex of A220V (Figs. 15a,b). The temperature fields in Fig. 15a were similar to the CTL experiment (Fig. 4a). In A220P, however, the warm core is stronger than that in A220 (figure omitted). This may be part of the reason that A220P produced a stronger hurricane intensity forecast compared to A220. The stronger initial warm core in A220P resulted in a deeper hurricane central pressure in the model simulation and, hence, intensified the hurricane circulation (wind fields). Because no warm core was formed at the initial time in A220V, the simulated hurricane intensity was too weak.
The above two experiments indicate that the pressure field is more important than the wind field in generating hurricane structure using BDA. With the cost function (4b) included, the wind field is adjusted to keep (4b) small and force the pressure and wind field to a balanced state. Otherwise, the pressure field will change very rapidly during the model integration and the cost function (4b) may not be minimized. Although tropical cyclogenesis is emphatically not a simple process, our results from the BDA experiments indicate that collecting more information for formulating the bogused SLP field is effective in generating initial structures of a mature hurricane using the BDA technique. However, both pressure and wind observation data are necessary to obtain a better forecast, as is clearly shown from the results of this study. Ideally speaking, rotationally balanced wind and pressure vortex fields should be used as the data constraints in the assimilation. Then, the divergent circulation in the vortex will be generated during the data assimilation with a thermally active prediction model.
6. Summary and conclusions
One of the most challenging problems for the tropical cyclone forecaster and researcher is defining the structure of the tropical cyclone and the adjacent synoptic features with insufficient observations over the ocean. In this paper, the BDA scheme for hurricane initialization, proposed by Zou and Xiao (2000), is tested for the landfalling simulation of Hurricane Fran (1996). We studied the sensitivity of the BDA scheme to the model resolution, the radii of maximum SLP gradient for the specification of the bogus vortex, and the type of bogus data assimilated in the BDA. Numerical simulations of MM5 using the BDA scheme showed a remarkable forecast skill in reproducing the movement, intensity, and structure of Hurricane Fran near landfall. Sensitivity studies reveal many interesting features. The most important results are summarized as follows.
The BDA scheme is very efficient in recovering the initial structure of the hurricane using very little observational information. Because the hurricane forecast model was used as a strong constraint in the hurricane BDA scheme, all model fields were adjusted to fit the bogus data of the SLP low and the derived balance wind fields. For instance, a moist warm-core hurricane structure was found in the initial vortex after BDA. These are adjustments in the model variables not directly bogused. An automatic result of BDA is that the initial conditions were consistent with the hurricane forecast model.
The simulation of the hurricane track was sensitive to the model resolution on which the BDA scheme was performed. The predicted hurricane track was improved from the initialization with higher resolution. But the improvement from using higher resolution does not occur in the intensity forecast.
In the present case with the current model configuration, the RMW used in the BDA scheme is a sensitive parameter for the hurricane track and intensity forecast. If the selected domain grid mesh can resolve the specified bogus vortex, hurricanes with larger RMW have a larger component of westward motion and are usually weaker.
The sensitivity study shows that assimilation with the use of the bogused SLP field in the BDA scheme is more effective than the wind fields in recovering hurricane structure in all model variables. The hurricane simulation from the initial conditions produced by the use of bogused SLP low data is closer to observation than the use of bogused wind data only.
Despite the differences resulting from variations in bogus data and model resolution, all the forecast experiments initialized with the BDA scheme obtained reasonably good hurricane track forecasts, which were reflected in the landfall location and the landfalling time. It is of particular importance that the BDA scheme showed great capabilities in reproducing the intensity and intensity changes of Hurricane Fran.
The hurricane flow structure is simulated well using BDA and is in conformity with the structures illustrated by many authors such as Willoughby (1995). During the landing period of Fran, the model-simulated wind and reflectivity exhibited many structures similar to the observed wind and radar reflectivity distributions onshore.
This study is a natural extension of the work by Zou and Xiao (2000) where the BDA scheme was tested for the prediction of Hurricane Felix (1995). It is demonstrated that the BDA scheme works well, not only for a developing hurricane, but also for a mature hurricane simulation. The studies of the sensitivity of the BDA scheme to the model resolution, the RMW of the specified bogused SLP low, and the bogus variables in BDA increased our understanding of the performance of the BDA scheme in many aspects. Further experiments will be conducted to assess the capability, propriety, and feasibility of the proposed scheme for operational application.
This research has been supported by AFSOR under Grant F4920-96-C-0020 and NSF under grant ATM-9908938. Thanks to Drs. Z. Zhang at The Florida State University and L. Wu at the University of Hawaii for many helpful discussions. Thanks also to Dr. Y. Liu of McGill University for providing the diagnosis software for model radar reflectivity calculation. The authors gratefully acknowledge the Mesoscale and Microscale Meteorology Division and Scientific Computing Division, National Center for Atmospheric Research, for providing computing time on Cray machines.
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Hurricane central SLP and low-level maximum wind speed for all the initialization experiments.
Hurricane track errors for A80, B80, and CTL (km).