1) Model

The GFDL multiply nested movable mesh hydrostatic model originally described by Kurihara and Bender (1980) is used for the model hurricane forecasts, with additional model details presented in Tuleya et al. (1984), Bender et al. (1987), Bender et al. (1993, hereinafter BRTK), and Tuleya (1994). The model is a primitive equation model formulated in latitude, longitude, and sigma coordinates, with 18 levels in the vertical (Table 1 of Kurihara et al. 1990). The integration domain spans 75° latitude by 75° longitude, and has a triply nested grid system with resolutions of 1°, ¹/₃°, and ¹/₆° (Table 1 of BRTK). The outermost domain extends from 10°S to 65°N in the meridional direction, and varies in the zonal direction, depending on the storm’s location at each forecast time. (In the case of this study, it is fixed between 85° and 160°E in the zonal direction.)

The model physics includes a cumulus parameterization scheme described by Kurihara (1973) with some modifications (appendix C of Kurihara and Bender 1980), a Monin–Obukhov framework for the interactions at the surface, and the Mellor and Yamada (1974) level 2 turbulence closure scheme for the vertical diffusion with a background diffusion coefficient added. In addition, as described by Tuleya (1994), the Schwarzkopf and Fels (1991) infrared and Lacis and Hansen (1974) solar radiation parameterizations are incorporated, including interactive radiative effects of clouds and a diurnal radiation cycle, along with land surface temperature computed by an energy equation containing a soil layer. The sea surface temperature is specified and held fixed to the initial value throughout the integration.

2) Initialization

The initial condition for each forecast experiment is determined from the hurricane model initialization scheme described in Kurihara et al. (1993) and Kurihara et al. (1995, hereinafter KBTR). As initial input data, this scheme uses the National Centers for Environmental Prediction (NCEP) T126 global analysis, as well as the tropical cyclone message file containing the specific storm location, intensity, and structure information. Using a simple smoothing technique (as described in BRTK), the flow field is separated into a mean and disturbance component. The region (r₀; 700 km in this study) containing the hurricane vortex resolved in the NCEP global analysis is identified in the disturbance field. Using an optimal interpolation and merging scheme, the background environmental field is reconstructed across the region r₀, while the flow field outside of the storm domain remains unchanged. According to KBTR, this technique successfully removes the hurricane disturbance in the global analysis within the r₀ region, while retaining most of the important environmental flow structure.

In the next step of the initialization system by KBTR, both symmetric and asymmetric components of the specified vortex are generated. First, an axisymmetric version of the GFDL hurricane model is integrated such that the tangential wind is forced toward a target flow field that resembles the observed hurricane wind profile obtained from the tropical cyclone message, which is distributed by the Joint Typhoon Warning Center (JTWC). Second, by using the tangential wind distribution obtained as input, a simplified version of a barotropic model (Ross and Kurihara 1992) is run in order to estimate the asymmetric flow due to the beta gyre (pair of vortices produced from the advection of planetary vorticity). The combination of the axisymmetric and asymmetric flow fields generates a hurricane vortex that has a much higher resolution than the vortex in the original global analysis and is consistent with the GFDL model. It is reinserted into the environmental flow field in the correct position to produce the initial wind and moisture field. A static initialization is then employed to recover the mass field. KBTR demonstrated improvement in the performance of the GFDL hurricane model forecasts using this approach.

3) Integration

The integration for each simulation was run for 72 h using the lateral boundary values specified from the forecasts of the NCEP global spectral model, linearly interpolated in time to hourly values (Kurihara et al. 1989).

1) Synoptic features

Figure 1 shows the comparison of forecast track with the best track analyses from both the CWB and the JTWC. In general, the analyses between CWB and JTWC are in agreement with each other. The control numerical experiment shows a fairly accurate track simulation for Gladys, especially in the first 54 h, though the model storm moves too slowly between about 27 and 39 h. The position error compared to that of the JTWC analysis is 82 and 151 km for the 24- and 48-h forecasts, respectively. The model storm in experiment B slows down between 27 and 39 h compared with the observed storm position, makes landfall at 46 h, and leaves Taiwan at 51 h, compared with the observed times of 39 and 42 h, respectively. This error may be in part related to the inaccurate prognosis of the large-scale environmental flow upstream of the high terrain, and in part due to the incorrect storm structure such as the vertical extent of the vortex. After 54 h, the model storm of experiment B turns westward while the best track continued northwestward, and the position error at 72 h increases to 350 km. The analysis of the simulated deep-layer (850–200 mb) mean flow indicates that the track of Gladys agrees very well with the deep-layer mean flow at 24 and 42 h (Figs. 4a and 4b), but not very well at 60 h (Fig. 4c). Since the vertical extent of Gladys became much shallower after passing over Taiwan, instead of using the deep-layer mean wind, we also examine the steering flow as defined by the lower- to middle-level (850–500 mb) mean flow (Fig. 4d). It is shown that the lower- to middle-level mean flow agrees reasonably well with the storm motion. This result is consistent with Dong and Neumann (1986), indicating that the height of the best steering level or the depth of the best deep-layer steering should increase in proportion to storm intensity. This concept is practically useful for predicting storms over topography when their intensities and structures undergo dramatic changes. The mean flow analysis also indicates that after Gladys departs Taiwan, the high pressure center over China (Fig. 4d) is located to the west of the observed center, causing the model track to deviate to the south of the best track.

As to the intensity forecast, the comparisons of the maximum surface wind with the analyses from both the CWB and the JTWC are shown in Fig. 3. Both the CWB and JTWC analyses show that Gladys reached its maximum intensity at 0000 UTC 1 September [about 10 h before landfall, which is consistent with the statistics of 12 h from Brand and Blelloch (1974) and the result of 10 h from the idealized simulation with a 5 m s⁻¹ background wind in Bender et al. (1987)]. Yet a large difference exists between the two analyses. For example, as Gladys reaches its maximum intensity, the maximum surface wind speed indicated by the analysis from the JTWC (85 kt) is 30% higher than that from the CWB (65 kt). This difference results in part from the different definition of the surface wind (i.e., the JTWC uses the 1-min-average wind, while the CWB uses the 10-min-average wind). Although the GFDL hurricane model forecast underestimates Gladys’s intensity throughout the forecast period, the model can capture the evolution of Gladys’s intensity, especially the weakening during landfall. Nevertheless, as the intensity of a typhoon is affected by large and complex arrays of physical processes governing the interaction of the storm (both the eyewall and mesoscale dynamics) with the underlying ocean and the atmospheric environment, the uncertainty of the intensity prediction remains a big challenge for dynamical hurricane models (Bender and Ginis 2000; Wu et al. 2000).

2) Mesoscale structures

3) PV budget

To obtain more insight on the role of advective, diabatic, and frictional processes in affecting the storm evolution, the PV budget is calculated here based on the same formulation as by Wu and Kurihara (1996); that is, we formulate our calculation of the PV budget on the π coordinate [Exner function: π = C_p(p/p₀)^κ]. The approximate definition of Ertel’s PV in π coordinates is

View Expanded

where κ = R_d/C_p, p is the pressure, η is the vertical component of absolute vorticity, and θ is the potential temperature. The PV budget is

View Expanded

where ω* ≡ dπ/dt, and the terms on the right represent the local change of PV due to the horizontal and vertical advection, and the effect from diabatic heating (dθ/dt, including the condensational and radiative heating) and friction (F), respectively. It should be noted that the analysis may reduce numerical accuracy due to the interpolation from the model’s sigma coordinate to the π coordinate. However, as will be shown later, the effect from both the vertical motion and condensational heating is predominent in the inner part of Gladys. It is anticipated that the effects due to the above terms are predominant in the PV budget analysis in any of the π, sigma, or θ coordinates. It can be assumed that a major feature of the PV budget is captured from this analysis.

At 36 h, the distribution of condensational heating (Fig. 11a) is consistent with that of upward motion (Fig. 5b). The result suggests that the condensation occurs mainly on the resolvable scale in the model since we have also conducted simulations with the cumulus parameterization turned off, and have produced similar heating profiles. (No absolute convective instability occurs in these no-convective-adjustment simulations, probably due to the effect of strong vertical mixing within the vortex.) The maximum condensational heating (about 65 K h⁻¹) occurred on the western flank of the eyewall at about 650 mb, while the values for the eastern flank were 60 K h⁻¹ at 400 mb. This condensational heating profile causes the redistribution of PV in the vertical direction (Fig. 11b) by creating a negative PV anomaly in the upper troposphere [at a rate of about −4 PVU (12 h)⁻¹ at 350 mb] and a positive PV anomaly in the lower troposphere [8 PVU (12 h)⁻¹ at 600 mb].

In the entire troposphere, there is a very weak positive horizontal PV advection to the downshear side of Gladys, and a very weak negative one to the upshear side (figures not shown). This horizontal PV advection is much weaker compared to those terms associated with the condensational heating. The local change in the PV tendency due to the vertical advection (Fig. 11c) is strongest at Gladys’s center. Physically, the strong updraft near the hurricane center carries the high-PV air from the middle troposphere to the upper troposphere and the low-PV air from the lower troposphere to the middle troposphere, thus producing a maximum positive PV tendency of 1 PVU (12 h)⁻¹ at about the 350-mb level, and a negative PV tendency [about −0.3 PVU (12 h)⁻¹] in the lower and middle troposphere. The frictional effect on PV is very small (Fig. 11d), and is mainly present near the hurricane center, where large horizontal wind shear exists.

Our calculation clearly shows that the local change in PV due to other nonconservative processes (including both the radiative heating and friction) is more than an order of magnitude smaller than that due to the condensational heating. In other words, condensational heating is the primary nonconservative factor affecting Gladys’s PV evolution. The local change of PV due to all terms (figure not shown), including the total advection, heating, and friction, indicates that there existed a PV source in the middle to lower troposphere, and a sink in the upper troposphere at Gladys’s center.

Similar results are also found at other forecast times before landfall. For example, at 42 h the condensational heating term indicated a 35 K h⁻¹ heating rate (Fig. 12a) at about 400 mb, which is associated with the updraft on the western side of the storm center. Such heating results in a PV sink of −2 PVU (12 h)⁻¹ at 350 mb and a PV source of 3.5 PVU (12 h)⁻¹ at 550 mb (Fig. 12b). The vertical advection of PV still shows an upward transportation of PV air and, thus, leads to a PV tendency of 1 PVU (12 h)⁻¹ at 400 mb, −0.8 PVU (12 h)⁻¹ at 650 mb, and −0.4 PVU (12 h)⁻¹ at 800 mb. The frictional effect remains insignificant (Fig. 12d) even though Gladys is near the Taiwan terrain.

Once Gladys is already located inland over Taiwan (e.g., at 48 h in Fig. 13), strong condensational heating is still found over the mountains, with a peak heating rate reaching 80 K h⁻¹ at 500 mb (Fig. 13a), which is consistent with the distribution of the vertical velocity. However, because of the disintegration of the PV structure (Fig. 7a) over the terrain, the PV change due to condensational heating (Fig. 13b) is quite different from the typical dipole patterns (positive tendency below and negative above) found in earlier hours (cf. Figs. 11b and 12b). The pattern of upward transport of high-PV air seen in Figs. 11c and 12c is not found in Fig. 13c. Meanwhile, Fig. 13d indicates that the frictional effect becomes larger and results in PV tendencies of −2 PVU (12 h)⁻¹ (about the same order of magnitude as the other processes) both near the surface and at about 350 mb. As a result, the net PV tendency due to all processes shows a complicated pattern (figure not shown). The result suggests that the detailed PV redistribution processes are more complicated for a storm, such as Gladys, which made landfall over Taiwan terrain, than for the oceanic storms, for example, Hurricane Bob (1991) in Wu and Kurihara (1996). Note that our analysis shows that some frictional dissipation of PV exists over the surface (e.g., Fig. 13d), and can significantly affect the PV evolution of Gladys after its landfall. It is well recognized that a tropical storm decays quickly after making landfall, mainly due to the cutoff of water vapor supply from ocean, as well as the effect of the friction-induced Ekman spindown process. Our analysis provides a PV view of the frictional effect on a landfalling typhoon, even though the direct mechanical effect of the surface drag on the momentum budget is not estimated separately.

Overall, the PV budget analysis clearly demonstrates that vertical advection and the effect of condensational heating are the two dominant processes causing the local change in PV for Gladys. However, when compared with the PV budget analysis of Hurricane Bob (1991) in Wu and Kurihara (1996), some differences are found. First, as Gladys is a much weaker storm, it appears that the PV tendency due to vertical advection is weaker, and cannot compensate for the stronger PV redistribution due to the condensational effect; second, the PV distribution near the storm center over the topography is less organized than that over the ocean, and thus even though the model demonstrates strong updraft and condensational heating in the eyewall region, the PV budget appears to be very noisy. The result indicates the difficulty in interpreting the PV budget when the storms are over the mountains. Nevertheless, consistent with Wu and Kurihara (1996) is that our results also indicate that the diabatic heating effect plays a crucial role in the evolution of the PV field in typhoons. It also suggests the importance of accurate representation of the heating profile in typhoon models when the storm encounters topography. Finally, it should be stressed that because any new eddy from PV generation may lead to the track deflection or affect the storm development, more case studies and more detailed analyses are needed in order to better understand the dynamics of the effect of the Taiwan terrain on typhoons based on PV budget analysis.

1) Experiment NT

Comparing the control experiment (expt B) with experiment NT, in which the Taiwan topography is removed, it is clear that the presence of the topography results in the deceleration of Gladys’s translation speed from 27 to 39 h, and then its acceleration from 39 to 46 h as it approached Taiwan (Fig. 14a). Decomposition of the storm movement into the zonal velocity (Fig. 14b) and meridional velocity (Fig. 14c) indicates that when Gladys is about 300 to 200 km away from Taiwan (27–39 h), the deceleration due to the presence of the Taiwan terrain is mainly on the zonal speed, which is consistent with the result of zonal deceleration at region B as indicated in Fig. 27 of Yeh and Elsberry (1993a). As shown in Fig. 8b, the northeasterly boundary flow associated with Gladys is blocked at the northeast coast of Taiwan, and some deflected and reversed flow inland of northeastern Taiwan is also found. Therefore we believe that the zonal deceleration should be principally associated with the barrier blocking (Wang 1980; Lin et al. 1999) of the background mean flow. Small southward deviation (Fig. 14c) also exists between 12 and 33 h, which is consistent with Yeh and Elsberry (1993a,b), though no explanation was given then. A possible mechanism for such southward deviation is the so-called channeling effect in which the air is forced southward by the ageostrophic pressure gradient when the storm circulation impinges on the topography (e.g., Huang and Lin 1997; Lin et al. 1999).

When the storm is within 100 km of Taiwan (i.e., from 39 to 46 h), both the zonal and meridional translation speed increased, thus leading to a northwestward track, which is in agreement with the statistics of Wang (1980), and the result of Chang (1982), Bender et al. (1987), and Yeh and Elsberry (1993a,b). Note that the magnitude of acceleration in this case is smaller than that in Chang (1982) and Bender et al. (1987), which is likely to be because Gladys is originally moving at an average speed of 8 m s⁻¹, which is faster than the 5 m s⁻¹ background flow used in both Chang (1982) and Bender et al. (1987). Bender et al. (1987) argued that the storm is advected by the accelerated mean flow due to the influence of the topogaphy on the mean flow and the extra southerly flow induced by the interaction of the storm circulation with the topography, though further explanation on why this occurred was not discussed.

In the simulation of a vortex passing a bell-shaped topography under a uniform background flow (Lin et al. 1999, see their Fig. 13), the vortex deviated southward before landfall, then turned northward after passing the central axis of the topography. This track pattern is consistent with the response of an idealized flow over an isolated topography on the f plane (Peng et al. 1995). It is interesting to ask why our model track turned northward before landfall, instead of after passing the central axis of the terrain, as found in Lin et al. (1999). One likely answer is that this is related to the moist dynamics. Note that Lin et al. (1999) used a dry model without considering the moisture effect. In our full-physics simulation, right before landfall (e.g., 42 h), the upslope lifting of the moisture-laden air produces heavy precipitation (see Fig. 10a) over the northwest quadrant of Gladys. Meanwhile, to the southwest of Gladys, as shown in Fig. 8b, downslope dry air is dominant, which tends to inhibit the development of convective activity. Therefore, the moist dynamics appears to play an important role in favoring new convection and diabatically generating potential vorticity to the northwest quadrant of Gladys. We believe such an asymmetric feature can lead to a different storm track as compared to the theoretical result from the dry model. Our reasoning above appears to fill the gap in interpreting the inconsistency between Bender et al. (1987) and Lin et al. (1999).

As to the intensity simulation (Fig. 2), the control experiment (expt B) indicates rapid weakening after 36 h as Gladys approaches and makes landfall on Taiwan. Meanwhile, experiment NT (with no topography) indicates that the intensity of Gladys remains the same as that in experiment B up to 36 h. After 36 h, the intensity of NT remains at 65 kt for another 18 h until 54 h, 3 h before landfall in southern China. Without the drying effect or the topographic blocking shown in the control experiment, experiment NT thus simulates a storm of sustained intensity while passing Taiwan with flat terrain.

2) Experiment B2

The last experiment (B2), with a stronger and larger bogus vortex, shows that the motion of such a vortex is affected by a stronger beta effect (Fiorino and Elsberry 1989) and, thus, leads to a more northwestward track (Fig. 1) and does not make landfall on Taiwan. As such, the resulting wind and precipitation distribution is significantly different from the control experiment. Nevertheless, the motion of the B2 vortex is clearly affected by the Taiwan terrain and makes a distinct cyclonic turn as it passes through the region offshore from northern Taiwan. The above result indicates that the improper specification of the typhoon vortex in the model can affect the track forecast significantly, especially when the typhoon vortex encounters high terrain. Therefore, accurate representation of the typhoon vortex is needed to understand the typhoon–topography interaction problem.