Tropical cyclones (TCs) encountering the terrain of Taiwan usually experience prominent track deflection, resulting in uncertainty in TC track forecasts. The underlying mechanisms of TC deflection are examined to better understand the pattern of TC tracks under various flow regimes. In this study, idealized experiments are carried out utilizing the Advanced Research version of the Weather Research and Forecasting (WRF) Model. This study investigates the motion of a TC that is deflected southward while moving westward toward an idealized terrain similar to Taiwan. An analysis of both the flow asymmetries and the potential vorticity tendency (PVT) demonstrates that horizontal advection contributes to the southward movement of the TC. The track deflection is examined in two separate time periods, with different mechanisms leading to the southward movement. Changes in the background flow induced by the terrain first cause the large-scale steering current to push the TC southward while the TC is still far from the terrain. As the TC approaches the idealized topography, the role of the inner-core dynamics becomes important, and the TC terrain-induced channeling effect results in further southward deflection. Asymmetries in the midlevel flow also develop during this period, in part associated with the effect of vertical momentum transport. The combination of the large-scale environmental flow, the low-level channeling effect, and asymmetries in the midlevel flow all contribute to the southward deflection of the TC track.
Taiwan experiences an average of three to four tropical cyclones (TCs) every year, which are usually accompanied by heavy rainfall and strong winds. With an average elevation of 2000 m, the Central Mountain Range (CMR) has a significant influence on TC tracks through modification of the background flow and a direct impact on the TC structure. Accurately predicting the track of a TC as it is near landfall is essential to increasing warning times for coastal communities. Many previous studies have focused on the orographic effect on TC track, circulation, and precipitation (Wu and Kuo 1999; Wu 2013).
Both observational and numerical studies have shown that TCs are prone to significant changes in intensity, structure, and movement when approaching Taiwan. Observational studies have examined the behavior of previous TCs and provided statistical analyses of TC tracks influenced by the CMR (Brand and Blelloch 1974; Wang 1980; Yeh and Elsberry 1993a; Hsu et al. 2013). Brand and Blelloch (1974) and Wang (1980) showed that westbound TCs tend to exhibit cyclonic movement around the northern part of the CMR. Wang (1980) discussed the cyclonic track observed when typhoons in the vicinity of Taiwan are embedded in a nonuniform background flow passing around the terrain. The deflection of the mean steering flow upstream of the CMR was proposed to explain deflections in the TC track. Yeh and Elsberry (1993a) researched west-moving TCs that made landfall in Taiwan from 1947 to 1990, indicating that the track deflection is more prominent for slow-moving and weak TCs.
A limitation of these observational studies is that they are limited by the quality of observational data, particularly for long-term climatologies. Numerical experiments, including real case simulations (Wu 2001; Jian and Wu 2008; Huang et al. 2011) and idealized experiments (e.g., Chang 1982; Bender et al. 1987; Yeh and Elsberry 1993a,b; Lin et al. 1999; Kuo et al. 2001; Wu 2001; Lin et al. 2005; Lin 2007; Huang et al. 2011; Lin and Savage 2011; Wu et al. 2015; Lin et al. 2016), have been conducted to address this issue. Wu (2001) simulated Typhoon Gladys (1994), which was deflected northward and slowed down when approaching Taiwan. An analysis of the potential vorticity budget suggested that convective heating on the windward side was the major factor contributing to the deflection of Gladys. Jian and Wu (2008) conducted a simulation of Typhoon Haitang (2005), which had a looping track before making landfall in Taiwan. The looping track was attributed to the low-level northerly jet that developed between the terrain and the typhoon center. This so-called channeling effect enhanced the wind speed in the western inner core, causing asymmetries in the tangential wind field as Haitang approached Taiwan. In their experiments the deflection became less apparent as the height of the topography was reduced, indicating that height plays a key role in TC track deflection. Huang et al. (2011) utilized MM5 with a finest grid spacing of 3 km to simulate Typhoon Krosa (2007), showing that the mechanism of track deflection was identical to that described by Jian and Wu (2008).
Using primitive equations involving friction and adiabatic effects, Chang (1982) found that the TC moves faster and is deflected northward when approaching the terrain. The track deflection of a TC approaching topography can be attributed to the low-level background flow. As the flow moves past the topography, a ridge forms upstream and a trough downstream. Bender et al. (1987) used idealized simulations with a finest resolution of 1/6° to compare the effect of topography on TC track deflection in 5 and 10 m s−1 background flow. The TC in the 5 m s−1 background flow was deflected to the north when approaching the topography, whereas there was no northward movement in the 10 m s−1 simulation, demonstrating that the TC track is sensitive to background flow speed. Yeh and Elsberry (1993a,b) simulated a westward-moving vortex approaching terrain with 45-km resolution, showing that the deflection is less pronounced for stronger vortices with a faster translational speed. For TCs where deflection was observed, the western side of the vortex was shown to weaken when the vortex moved within 250 km of the idealized topography. The unbalanced inner core and subsequent asymmetries in the flow were proposed to cause the vortex to deflect northward.
In summary, both observational and numerical studies demonstrate that slow-moving and weak TCs experience greater track deflection as they approach Taiwan (Yeh and Elsberry 1993a ,b). Previous work also demonstrates that changes in the background flow as it passes around topography will affect the movement of a TC (Brand and Blelloch 1974; Wang 1980; Chang 1982). There are discrepancies between these studies, however. Some early studies documented northward track deflection for TCs approaching Taiwan (Brand and Blelloch 1974; Wang 1980; Chang 1982; Bender et al. 1987; Yeh and Elsberry 1993a,b; Wu 2001). Later on, modern radar observations have documented sudden southward track deflection or looping motion in TCs about to make landfall in Taiwan. Numerical models have shown their ability to reproduce such unique track changes in real TCs with idealized designs (Jian and Wu 2008; Huang et al. 2011; Wu et al. 2015).
Various mechanisms have been proposed to explain this observed track deflection, including background flow, convective heating, and the channeling effect.
Lin et al. (2005) conducted idealized experiments using a 30-km-resolution model without the effects of moisture or surface friction. Six nondimensional parameters were used to evaluate TC track deflection under different flow regimes—the Froude number (Fr = Vmax/Nh for the vortex and Fr = U/Nh for the basic flow), the Rossby wave (Ro = Vmax/fR for the vortex and Ro = U/fLx for the basic flow), R/Ly (the ratio of the vortex scale to the topography scale in the y direction), and h/Lx (the gradient of the topography). The deflection of the TC track is larger, and the track tends to be discontinuous with small Vmax/Nh, U/Nh, R/Ly, U/fLx, Vmax/fR, and large h/Lx. The parameters Vmax/Nh and U/Nh determine the extent of track deflection, while R/Ly controls the direction of deflection. When R/Ly is smaller, the track turns to the south, possibly as a result of the channeling effect (Lin et al. 1999; Jian and Wu 2008; Huang et al. 2011). However, southward deflection was rarely observed in other studies (e.g., Chang 1982; Bender et al. 1987; Yeh and Elsberry 1993a), indicating that high resolution is essential for accurate representation of inner-core processes.
Lin and Savage (2011) studied the tracks of vortices placed at different initial latitudes and moving in different directions, utilizing the same dry model as Lin et al. (2005). Based on an analysis of the vorticity budget, they showed that the deflection of a TC track as it approaches terrain is primarily due to vorticity advection, while the deflection after landfall is related to the effect of vorticity stretching. Since the model used in Lin et al. (2005) and Lin and Savage (2011) does not include the effects of latent heat release or surface friction, the validity of these results in the real atmosphere requires further investigation. Wu et al. (2015) investigated the tracks of TCs in different flow regimes and attempted to clarify the role of the channeling effect in southward deflection. Using MM5, a vortex was simulated approaching Taiwan. The southward deflection of the vortex was attributed to asymmetries in the midlevel flow. This mechanism is distinct from the channeling effect and changes in the background flow induced by the topography, and is worthy of further investigation. Lin et al. (2016) proposed that for a high Froude number, a TC moves anticyclonically over a mesoscale mountain range. The southward deflection of the TC can be explained by subgeostrophic flow caused by the deceleration of the easterly mean flow, which advects the TC to the southwest. The orographically generated mesoscale high pressure also contributes to the anticyclone movement over the mountain range.
To better understand the physical mechanisms responsible for determining the track of a TC as it approaches topography, this study presents an analysis of potential vorticity tendency (PVT). A vortex can be treated as a positive potential vorticity anomaly, which is linked to the PVT. Wu and Wang (2000) simulated a vortex on a β plane with no background flow, showing that the motion of a symmetric TC vortex is correlated with the positive wavenumber-1 PVT. By using this PVT diagnosis, the direction of vortex propagation can be estimated with reasonable accuracy. The importance of individual physical processes can also be quantitatively estimated from the PVT by examining their relative contributions to the wavenumber-1 component of PVT. This approach can be applied to observations or numerical simulations. Wu and Wang (2001) demonstrated that two processes associated with convective heating affect TC motion. The first is the advection of symmetric potential vorticity (PV) by heating-induced asymmetric flow. The second is the direct generation of positive PV tendency by asymmetric heating, which induces TC motion in the direction of the region of maximum negative gradient in asymmetric heating.
This study builds on the work of Wu et al. (2015) and aims to further study the discrepancies in understanding of mechanisms causing TC deflection in the aforementioned studies. The model configuration and experiment design are presented in section 2. In section 3, the results of the control experiment and sensitivity experiments are described. Conclusions are given in section 4.
The Advanced Research version of the Weather Research and Forecasting (WRF) Model (ARW; version 3.5) is utilized to simulate a vortex moving toward idealized topography in a steady background flow. The experiment consists of three nested domains, with horizontal resolutions of 27, 9, and 3 km. The grid dimensions of each domain are 342 × 342, 313 × 313, and 559 × 559 points, with 40 terrain-following σ levels in all three domains. The inner domain covers 1677 km × 1677 km and is large enough to ensure that the vortex tracks remain within the domain. To avoid boundary perturbations and fluctuations, periodic boundary conditions are used in the x and y directions. Experiments conducted in f plane are located at 15°, with a sea surface temperature of 29°C and homogeneous throughout all regions. The Kain–Fritsch cumulus parameterization (Kain and Fritsch 1993; Kain 2004) is used in the coarsest domain. The parameterization schemes used in the simulations are as follows: the WRF single-moment 6-class microphysics scheme (WSM6; Hong and Lim 2006) with water vapor, cloud water, snow, graupel, and cloud ice hydrometers; the Yonsei University (YSU) PBL parameterization, the Dudhia radiation parameterization for shortwave radiation (Dudhia 1989), and the Rapid Radiative Transfer Model (RRTM; Mlawer et al. 1997) for longwave radiation.
In the control experiment, idealized topography is included in the domain to identify the effect of the topography of Taiwan on the TC track. In contrast, in ocean runs the topography is removed in order to facilitate the comparison of the TC tracks in cases with and without topography.
a. Control experiment
In the control (CTL) experiment, a vortex is embedded in an easterly background flow and continues moving westward until it makes landfall at the idealized terrain. To build up this idealized experiment, three steps are required: The prerun of a steady-state vortex, initialization of steady background flow with bell-shaped topography, and the insertion of the vortex into the background flow.
To obtain a vortex, a preliminary vortex simulation is conducted with no background flow. A bogus vortex with Vmax = 21 m s−1, a radius of maximum winds = 10 km, and an outer radius = 30 km is simulated until the vortex reaches a quasi-steady state. The idealized quasi-steady vortex has a maximum wind of 80 m s−1 and a minimum central pressure of 930 hPa. The radius of 17 m s−1 wind is 180 km, while the radius of maximum winds is 35 km.
By adding a forcing of 5 m s−1 easterly background flow without a vortex in the meshes every hour, the initial field of both with terrain (CTL) and without terrain (OC) are conducted. In the CTL experiment, the background flow enters a steady state after 72 h of integration. When the background flow reaches the idealized terrain, it splits into two components, which we refer to as the north and south components of the flow. A lee vortex is observed in the simulation, which is consistent with the results of previous studies (e.g., Smith and Smith 1995; Smolarkiewicz and Rotunno 1989). The average basic flow speed with/without terrain is about 3–4 m s−1.
An idealized bell-shaped terrain is used in this study:
where and . The parameter values used (hmax = 3000 m, a = 75 km, b = 200 km) are identical to those used in Wu et al. (2015).
The final step is to combine the vortex and the background flow with terrain, making an initial condition for the simulation. A simulation without terrain is also conducted using the same methodology. In the simulations with and without terrain, the implanted vortex is swiftly balanced in the background field. Initially, the vortex is placed 800 km from the center of the terrain, and the location of the vortex center is determined each hour by the circulation center of the 850-hPa streamlines. To ensure that using the 850-hPa streamline is an accurate method to define the TC center, we compare the results to the center as defined by the location of minimum sea level pressure (MSLP). The differences between the centers calculated by these two methods is 3.3 and 4.0 km in the x and y directions during the time that the vortex is affected by the terrain, demonstrating that the center can be accurately determined using the 850-hPa streamline.
Two commonly observed features when a vortex makes landfall are the vertical tilting of the vortex and the development of a lee vortex on the opposite side of the terrain. These effects complicate the situation and will be discussed in detail in this study.
b. Sensitivity experiments
By altering different parameters, such as the terrain height, the terrain width, the terrain length, and the initial vortex location, we can investigate the effect of terrain on a tropical cyclone track. An overview of the sensitivity experiments conducted is provided in Table 1.
To investigate the influence of topography height, sensitivity experiments are performed with a peak terrain height of 1000, 2000, and 5000 m, and are compared to the CTL experiment with a peak height of 3000 m. These simulations are named H10, H20, and H50, respectively. For these experiments, all other parameters are held constant.
Sensitivity experiments on the effect of the width of the terrain consist of two separate sets. Simulations with a terrain width of 75 and 300 km (compared to 150 km in CTL) are conducted to investigate the effect of slope on vortex motion. These are denoted as A75 and A300, respectively.
In the second set of experiments, three simulations with terrain length set at 200, 600, and 1000 km (compared to 400 km in CTL) are used to assess the impact of the north–south extent of the topography on a TC track. These are denoted B200, B600, and B1000, respectively.
To analyze the impact of the initial vortex location on terrain-induced deflection, experiments are conducted with vortices initialized north and south of the initial location in CTL. Simulations are conducted with vortices placed 50, 100, and 150 km to the north of their CTL counterpart, and are named N050, N100, and N150, respectively. Likewise, simulations with vortices placed to the south are named S050, S100, and S150, respectively. This set of simulations aims to assess the impact of initial latitude on the vortex track.
c. PVT diagnosis
PV tendency diagnosis (Wu and Wang 2000) is used to evaluate the contribution of individual physical process to the TC motion. A TC can be considered to be a positive potential vorticity anomaly relative to the environmental flow, with motion associated with the wavenumber-1 component of the PV tendency. Therefore, the PV tendency distribution can be used to determine the TC motion. This PV tendency analysis includes the effects of horizontal advection, vertical advection, diabatic heating, and friction. Such an analysis has been used in multiple previous studies (e.g., Chan et al. 2002; Hsu et al. 2013; Tang and Chan 2014, 2015, 2016).
The PV tendency equation in σ–p coordinates (Wu and Wang 2000) can be written as
where P is the PV, V is the horizontal wind, and Q is the diabatic heating rate.
The PV tendency of a vortex in a moving coordinate system is the sum of the PV tendency in a fixed coordinate system and the PV advection associated with the TC motion. The wavenumber-1 component of the PV tendency in a fixed reference frame is balanced by the advection of the symmetric PV component associated with the TC motion. Therefore, the formula becomes
where C is the location of the vortex center at different levels, and the motion of the vortex is determined by the maximum of the wavenumber-1 PV tendency.
The detailed derivation of the formula used in this study and the concept of PV tendency are described in Wu and Wang (2000). The results of the current study are presented in the following sections.
a. Control experiments
Figure 1 shows the tracks of the CTL and no-terrain (NT) simulations. In both CTL and NT, the vortex moves westward with consistent speed for the first 20 h. After 21 h, the vortex in CTL continues to move westward, while NT heads slightly to the north, on a west-northwest track, for a short period of time. This slight northward shift is probably due to the background flow, and it does not have a major influence on the overall track of NT, which remains westward throughout the simulation. In contrast, CTL moves toward the west prior to 39 h, after which it is suddenly deflected to the south. This deflection occurs when the center of the vortex is located at about 250 km from the eastern edge of the terrain. The southward deflection in CTL continues until its landfall at 57 h, with the vortex deviating to the south from its previous track by about 100 km. Before the vortex makes landfall, a lee-side vortex develops on the west side of the mountain range. Soon after the vortex makes landfall, the lee-side vortex replaces the original low-level center and becomes the new center. This discontinuity in the track causes the translational speed of the vortex to increase dramatically from 57 to 60 h, while the intensity drops as a result of the structural disorganization.
To validate the following analyses, the vertical alignment of the vortex is examined. Before the vortex makes landfall (57 h), the vortex is vertically aligned, with coincident circulation centers at 850, 700, 500, and 350 hPa. The vortex center becomes tilted after it makes landfall, with the upper-level center moving smoothly over the mountain, and the low-level center remaining to the eastern side of the terrain and gradually weakening. The lee vortex replaces the original center, and the vortices couple again as the system moves away from the idealized topography.
To analyze the movement, the TC is assumed to be a point vortex advected by the mean environmental flow. The translational speed and direction of a vortex can be estimated by calculating the mean environmental flow within a certain area. Chan and Gray (1982) found that the environmental flow within a radius of 5°–7° from the center dominates the track of a TC. Furthermore, Wu and Emanuel (1995a,b) suggested that the TC track is best represented by the inner-core mean flow.
The deep-layer (400–850 hPa) mean of the asymmetric flow is calculated within 100 km of the vortex center. Figure 2 demonstrates that in CTL before 39 h (the beginning of the southward deflection), the asymmetric flow generally corresponds to the track of the vortex, except at certain times when the steering deflects slightly to the north, possibly because of the background flow. After 40 h, the asymmetric steering flow develops a southward component, and the southward steering flow persists from 40 to 54 h. The tendency of the asymmetric flow is very similar to the observed track, demonstrating the link between the southward deflection of the vortex and the modification of the mean flow by the terrain.
In addition to the asymmetric flow analysis, PV tendency diagnosis is also used to examine the contributions of different physical processes to the vortex track. The track of the vortex is linked to maximum azimuthal wavenumber 1 of PV tendency, which is balanced by the advection of axially symmetric PV by TC motion (Wu and Wang 2000). It can be written as
The above equation indicates that the vortex movement is governed by the symmetric circulation that moves toward the region with the maximum azimuthal wavenumber-1 component of the PV tendency. It can also be written in the following form:
The components in the x direction Cx and y direction Cy may be calculated using least squares to minimize:
where N represents the number of grid points in a given domain. The corresponding Cx and Cy of the individual contribution can also be obtained.
In Fig. 3, it is seen that the PV tendency of the vortex is highly correlated with the track direction, capturing the southward trend before 54 h. At 58 h, the TC starts to turn to west-northwest, which is also captured by the PV tendency. At times the direction of motion does not coincide with the PV tendency (such as at 42, 56, and 58 h in Fig. 3, where there is large discrepancy between the vortex track and the PV tendency). However, these sporadic inconsistencies do not detract from the excellent agreement with the PV tendency overall.
A detailed breakdown of the components of the PV tendency shown in Fig. 4 shows that the horizontal advection (green arrow) makes the largest contribution to the PV tendency, while both the vertical advection (blue arrow) and diabatic heating (orange arrow) play relatively minor roles. The horizontal advection, which is associated with the asymmetric winds, correlates with the track of the TC. Therefore, the results of PV tendency diagnosis is consistent with the analysis of the asymmetric flow, demonstrating that the deflection of the vortex primarily results from the change of mean flow.
As the horizontal advection is the primary process contributing to the PVT, the impact of the asymmetric flow on horizontal advection is investigated in further detail. The asymmetric flow at different levels from 31 to 60 h is shown in Fig. 5. Prior to the track deflection (39 h), the asymmetric flow has a west-northwest component in the low and midlevels; however, there is a change in the vortex motion after 40 h. The southward deflection of the vortex can be attributed to changes in the low-level wind direction. At this time the low-level wind speed also increases by up to 7 m s−1, suggesting that changes in the low-level flow are responsible for the change in vortex track. In the later period of deflection, the midlevel wind vectors also develop large southerly components, indicating that the midlevel asymmetric flow also contributes to the deflection of the vortex.
The asymmetric flow in the inner-core region (about 100-km radius from the center) of the vortex plays an important role in determining the track of a TC. Although the symmetric flow is averaged over the whole column in this analysis, it is still necessary to investigate the wind structure at different levels. The vertical cross section of the meridional wind averaged 5 km to the north and south of the vortex is shown in Fig. 6. Prior to the deflection of the vortex (39 h), the meridional wind is symmetric, with the strongest wind found between 850 and 900 hPa. As the vortex gradually approaches the terrain, there are no obvious changes on the east side of the vortex; however, the meridional wind on the west side of the vortex strengthens substantially at low levels after 40 h. The enhanced low-level wind in the western inner core peaks at 48–52 h, coinciding with the time the vortex deflects to the south. This low-level northerly jet is similar to that described by Lin et al. (1999) and Jian and Wu (2008), who showed that the formation of the northerly jet is associated with orographic blocking and the channeling effect. In addition to the low-level jet, asymmetries in the midlevel (500–600 hPa) winds develop shortly prior to landfall. The southward deflection of TC caused by the channeling effect and midlevel asymmetric flow continues until landfall at 57 h. In contrast, the cross section of the wind profile in NT shows no discernible changes during the westward movement of the vortex (Fig. 7), with no northerly jet developing in the absence of terrain. Consequently, the changes in the vortex circulation can be attributed to the topography. These observed changes in the flow can also be identified in previous studies, such as the channeling effect as described by Huang et al. (2011) and the development of asymmetries in the midlevel flow as described by Wu et al. (2015).
To quantitatively assess the changes in the meridional wind at different levels, the evolution of the wind at 850, 700, 600, and 500 hPa (Fig. 8) is examined. To investigate changes in wind speed on opposite sides of the vortex, the winds are averaged within the western and eastern quarter circles to a radius of 100 km. The time series at both 850 and 700 hPa show similar results. The most significant change occurs at 40 h, coincident with the beginning of the deflection. Before 40 h, winds on opposite sides of the vortex are approximately equal; however, after this time asymmetries develop. On the western side of the vortex, the wind field broadens and the maximum wind speeds increase from 45 to 55 m s−1. Changes in the midlevel flow are not as clear, with asymmetric flow at 600 hPa evident only from 50 to 54 h.
In NT, a time series of changes in the meridional wind at different levels (not shown) show no obvious trend, suggesting that the differences between the tracks in CTL and NT can be attributed to the effect of the terrain.
The enhanced low-level winds in the western inner core and the development of asymmetries in the midlevel wind field are two important findings from the analysis. The simultaneous development of these two features was not observed in previous studies. The link between the channeling effect (below 700 hPa) and midlevel asymmetries remains unclear. The meridional wind budget is analyzed to determine which physical processes are responsible for this phenomenon.
The meridional wind budget equation can be written as follows:
The left-hand side of this equation represents the local change of meridional wind, while the terms on the right-hand side represent the vortex following change in meridional wind (including the Coriolis force, pressure gradient force, horizontal advection, and vertical advection). The calculation of meridional wind budget is averaged over 3 h to avoid noisy results. An evaluation of this budget during different time periods can help to identify the physical mechanisms responsible for the development of both the channeling effect–induced low-level jet and the asymmetric flow in midlevels. Note that in Figs. 9–11, blue coloring indicates that a term contributes to the increasing northerly wind on the western side of the vortex.
The averaged meridional wind budget is analyzed over three separate time periods: 38–40 (Fig. 9), 46–48 (Fig. 10) and 49–51 h (Fig. 11). These three time periods represent the vortex before deflection, during the initial stages of southward deflection, and during the later stages of deflection, respectively. The budget is averaged over the western sector of the vortex to a radius of 100 km and from ground level to 400 hPa.
From 38 to 40 h (Fig. 9) the horizontal and vertical advection terms dominate the budget, while other terms, such as the pressure gradient and Coriolis force, play relatively minor roles. Within the area with a radius between 20 and 40 km, the maxima of both horizontal and vertical advection lie between 700 and 850 hPa. These two terms have opposite sign in areas where they are at a maximum, cancelling each other out. Near ground level the northerly wind clearly contributes to horizontal advection. The total of all terms (horizontal advection, vertical advection, pressure gradient force, and Coriolis force) is close to zero, and at this time the vortex moves toward the west without obvious track deviation. The left-hand-side term (representing the local change in the meridional wind) shares similar characteristics with the summation of all right-hand-side terms.
In 46–48 h (Fig. 10), as the vortex begins to deflect to the south, changes in the budget become apparent. While the horizontal and vertical advection terms in the area of radius between 20 and 40 km still have opposite sign, there is a noticeable increase in the low-level northerly horizontal advection that also expands from an area with a radius between 20 and 100 km. This increase of horizontal advection is associated with the channeling effect and leads to the enhanced wind speed on the western side of the vortex. The total of all the terms demonstrates an overall increase in the northerly wind at low levels, especially below 850 hPa. The local meridional wind shows a similar pattern, with enhanced northerly winds below 850 hPa.
During the later stages of deflection, from 49 to 51 h (Fig. 11), this tendency becomes even more pronounced. The horizontal advection term continues to contribute to intensification of the low-level northerly wind, while the vertical advection also helps to enhance the northerly wind in the western inner core. During this time, there is a clear increase in the speed of the northerly component of the wind between 20- and 40-km radius and from ground level to 500 hPa. This increase in vertical advection from 49 to 51 h helps transport the momentum upward from low levels, enhancing the midlevel northerly winds.
In summary, the physical mechanisms responsible for both the low-level northerly jet and the midlevel asymmetric flow are explained using the meridional wind budget. As the TC approaches the idealized terrain (46–48 h), the distance between the TC center and terrain decreases. Therefore, the flow is accelerated on the western side of the TC as a result of the channeling effect. During 49–51 h, momentum is transported from low to midlevels, resulting in the development of asymmetries in the midlevel flow.
b. Sensitivity experiments
To investigate the behavior of the vortex in varied flow regimes, experiments are conducted varying different parameters. By adjusting the terrain height, width, and length, the effects of different parameters on the vortex can be evaluated. In addition, experiments with different initial locations of the vortex allow the effects of the vortex making landfall at different locations of the topography to be studied. A detailed description of the parameters varied in each experiment is provided in Table 1, and the nondimensional parameters are presented in Table 2.
1) Sensitivity to terrain height
In contrast to CTL (3000 m), the maximum height of the topography is adjusted to 1000 (H10), 2000 (H20), and 5000 m (H50). The results of these simulations (Fig. 12) show that as the terrain height increases, the degree of deflection increases as the vortex approaches the idealized terrain. The comparison of the tracks of CTL, H10, H20, and H50 in Fig. 12 shows that these simulations have the same tendency to deflect slightly to the north 600 km upstream from the center of topography. The northward deflection continues until the vortex is 400 km upstream from the terrain. After this point, differences become apparent between the simulations. The two experiments with lower terrain height, H10 (blue line in Fig. 12) and H20 (green line in Fig. 12), are not deflected as far southward as CTL (black line in Fig. 12), but they still exhibit an overall southerly track. Similar to CTL, the track in H50 (red line in Fig. 12) turns to the south after passing 400 km upstream of the terrain center. A sharp southward deviation occurs when the vortex is very close to landfall. These results are consistent with Lin et al. (2005), who demonstrated that the track deflection increases as the Froude number decreases.
An analysis of the asymmetric flow at different levels in H10 and H50 can explain the discrepancies between these simulations. The southward deflection of H10, although less obvious than that observed in CTL and H50, starts from 37 h and continues to 55 h. In Fig. 13, a weak southerly component is detectable in the low-level (700–850 hPa) steering flow throughout the period of southward deflection. Shortly before the vortex makes landfall, the southward steering in low levels becomes more apparent. The southward deflection of H10 is primarily attributed to the low-level asymmetric flow, which is linked to the channeling effect. The cross section of the meridional wind (Fig. 14) in H10 shows only slight strengthening at low levels in the western part of the vortex as the vortex approaches the terrain. No asymmetries are observed in the midlevel, possibly because of the lower height of the terrain.
In contrast, the track in H50 is deflected south from 34 to 58 h. Prior to the deflection (34–50 h), the vortex deviates farther from its previous westward track compared with the track of H10. At low levels, the steering flow is noticeably stronger than in H10 at 7–8 m s−1, contributing to the larger southward deflection (Fig. 13). During the later stages of the deflection (55–58 h), the southward track is primarily attributed to asymmetries in the midlevel wind field, indicating that asymmetric flow at midlevels is responsible for the sudden change in the vortex track near the terrain.
The cross section of the meridional wind in H50 (Fig. 15) shows that in the early stages of track deflection (34–50 h), the wind speed gradually strengthens west of the vortex while remaining constant in the east. This unbalanced meridional wind structure causes the vortex to turn toward the south. From 50 to 55 h it is worth noting that the west side of the vortex is weaker than the east side, causing the vortex motion to change from south-westward to westward. As the vortex turns sharply to the south in the later stages of the deflection (55–58 h), asymmetric flow develops in the midlevels, especially between 300 and 600 hPa. This asymmetry causes the vortex to deflect sharply to the south, identical to the physical mechanism responsible for track deflection in CTL.
2) Sensitivity to terrain width and length
In the sensitivity experiments varying the terrain width, the width of the terrain is adjusted from 150 km in CTL to 75 (A75) and 300 km (A300) (Fig. 16). When the terrain width is narrower (and hence the gradient is steeper), the vortex deviates from its previous position by about 50 km. On the other hand, when the width is larger (and the gradient is smaller), the vortex is deflected around 100 km. Lin et al. (2005) indicated that a vortex encountering terrain with a steeper gradient would experience more pronounced track deflection. However, Wu et al. (2015) proposed that the width of terrain has little effect on the track of the vortex. The results of this study are consistent with Wu et al. (2015), suggesting that terrain width and the nondimensional parameter (h/Ly) play only a minor role in determining the track of the vortex.
Experiments are conducted with the length of the terrain varied from 400 km in CTL to 200 (B200), 600 (B600), and 1000 km (B1000) to investigate the impact of changing the north–south length of terrain (Fig. 17). These three simulations all show different degrees of southward track deflection. The extent of the track deflection in B200, B600, and B1000 is 70, 120, and 80 km in distance, respectively. In Lin et al. (2005), as R/Ly becomes larger, a vortex approaching the terrain has a tendency to deflect to the north. However, Wu et al. (2015) argued that terrain length does not have an impact on the vortex track. The simulations in this study show southward deflection in sensitivity experiments with varying terrain length. This result is consistent with Wu et al. (2015), suggesting that terrain length has little effect on the degree of southward vortex deflection.
3) Sensitivity to initial positions
By placing the vortex 50 (N050), 100 (N100), and 150 km (N150) north of and 50 (S050), 100 (S100), and 150 km (S150) south of the initial position in CTL, it is possible to investigate the differences in vortex structure and track as it approaches different regions of the idealized terrain (Fig. 18). Two important observations can be made from these simulations: 1) vortices approaching the southern end of the topography experience larger deflection than vortices approaching the north and 2) the simulated vortices start to deflect at a distance of approximately 350–400 km from the center of the topography. Two questions therefore arise: 1) Why do vortices approaching the southern end of the topography experience greater deflection, and 2) why do vortices start to deflect when they are still far from the terrain?
Unlike in CTL, where the track deflection begins when the vortex is around 250 km from the idealized terrain, S100 starts to deflect 400 km upstream from the terrain. Since the vortex is of medium size (~150-km radius), it is clear that the deflection is not caused by terrain–vortex interaction at this point. One factor that could influence the vortex track is the background flow. The relationship between the topography, vortex, and background flow is nonlinear. To simplify the question of how topography affects vortex track, previous studies have focused only on the interaction between the vortex and topography; however, it is important to investigate whether the early southward turn of S100 can be attributed to the background flow.
To demonstrate that the large-scale background flow influences the vortex track in S100, the asymmetric flow averaged over a 300-km radius is shown in Fig. 19. Calculation of the steering flow to this radius ensures that the contribution from the background flow is included. In CTL and N100, the asymmetric steering flow within a 300-km radius is primarily westward when the vortex deflects to the south, indicating that the vortex track change is due to the inner-core dynamical process. However, the asymmetric flow below 600 hPa in S100 has a clear southward component throughout the deflection of the vortex, suggesting that the large-scale background steering flow impacts the vortex track of S100.
The role of the background flow in S100 can also be investigated by considering the 400–850-hPa-averaged wind speed in the western quadrant of the vortex (Fig. 20). In this quadrant, a tendency of radial wind speed expansion outside the radius of 80 km starts from about 30 h, while the inner core of the vortex maintains a constant intensity, further suggesting that the track deflection is primarily due to the background flow. It is unclear, however, whether the observed changes in the background flow are due to the vortex itself or the effect of the topography. Regardless, it is clear that the background flow is an important factor in determining the vortex track deflection. This may also explain the discrepancies in previous studies, as in addition to inner-core dynamics, the large-scale environmental flow should also be taken into consideration.
N100 is also examined to assess the effect of the environmental flow. An analysis of the background flow within a 300-km radius of the vortex center (Fig. 19) shows constant easterly winds between 400 and 850 hPa (the levels that are associated with the vortex track) throughout the time period of the deflection. Figure 20 demonstrates that in N100, the 400–850-hPa-averaged wind speed in the western quadrant of the vortex does not expand radially as in S100. The wind speed in the inner core of the vortex (within 50 km) strengthens as the vortex turns to the south, suggesting that this is the cause of the deflection. From the cross section of meridional winds in N100 (Fig. 21), in addition to the increased wind speeds in the western part of the vortex, midlevel asymmetric flow develops as the vortex is about to make landfall. Consequently, the physical mechanisms responsible for the southward deflection in N100 are identical to that of CTL, both involving inner-core intensification and midlevel asymmetric flow.
Multiple factors, including the large-scale environmental flow and TC inner-core dynamics, play a role in TC track deflection. The large-scale background flow splits into two components as it flows around topography, with even more complicated effects when a TC is included. When the TC is placed in different initial positions and the asymmetric flow is investigated within a radius of 300 km from the vortex center, the TC track is clearly affected by adjustments to the environmental flow induced by the topography. The background flow affects TC movement while the TC is 350–400 km from the terrain, causing the TC to deviate from its previous path. As the TC approaches the terrain, the role of inner-core dynamics becomes increasingly important in determining the vortex track. An evaluation of the asymmetric flow and PVT at a radius of 100 km from the TC center show that they are highly correlated with the TC track. PVT analysis further demonstrates horizontal advection is the dominant physical process in determining the TC track, while vertical advection and diabatic heating play relatively minor roles. Previous studies have shown that asymmetric diabatic heating is an important factor in determining the track of a TC approaching Taiwan, since the terrain-induced redistribution of PV can influence TC movement. However, this study provides different results, suggesting that the effect of horizontal advection is more important in causing the southward TC track deflection in our simulations.
The mechanisms of TC deflection in different flow regimes are examined in two separate time periods. The first period is while the terrain-induced change in the vortex structure is subtle or does not have a substantial impact on the TC motion, and the second is when TC comes very close to the terrain. While the TC is still far from the terrain, the southward track deviation is attributed to the adjustment to the large-scale environmental flow to the presence of the topography. At this stage, the southward component of the low-level background flow is enhanced and slowly pushes the TC southward. The low-level wind field gradually expands radially on the western side of the TC while remaining constant on the eastern side. The observed increase in wind speed on the western side results largely from horizontal advection, which can be attributed to the environmental flow. During the second period of investigation, the TC is located about 100 km from the eastern coastline of the terrain and the vortex’s inner core is directly influenced by the topography. The wind speed on the western side of the vortex increases significantly, especially in the inner core (20–40 km from the TC center). This increase in the inner-core wind speed is attributed to the channeling effect. In addition to the low-level wind speed increase, asymmetries also develop in the midlevel wind field shortly prior to landfall. The increase in midlevel inner-core winds on the western side of the vortex is due to momentum being transported from low to midlevels.
A set of sensitivity experiments are carried out with varying different control parameters. Consistent with earlier studies (Lin et al. 2005; Jian and Wu 2008; Huang et al. 2011; Wu et al. 2015), the track deflection increases with increased terrain height. In H10, CTL, and H50, characteristic low-level flow asymmetries caused by the channeling effect are clearly observed as the TC comes near to the topography. In CTL and H50, the large terrain height favors vertical momentum transport, leading to the development of asymmetries in the midlevel flow. In contrast, no such asymmetries are observed in H10. Aside from terrain height, the length and width of the terrain in each experiment is also varied. However, our results indicate that the TC track is not sensitive to either of these parameters.
Sensitivity experiments of TC in different initial locations are also carried out. Large-scale background flow plays an essential role in the southward movement of S100, rendering an earlier deflection compared to CTL and N100. In contrast, the inner-core processes in CTL and N100, including the channeling effect and midlevel asymmetries, become vital as the vortices approach the coastline. Therefore, the mechanisms of TC track deflection varied in different flow regimes.
In summary, as the TC approaches the topography, it experiences southward track deflection possibly as a result of the background flow, the channeling effect within the inner core of the TC, and the development of asymmetries in the midlevels in response to vertical momentum transport. TC track deflection can be explained by different mechanisms in varied scenarios, and the circumstances become even more complicated when other factors are taken into consideration (e.g., beta effect, vertical shear, and unbalanced TC structure). Predicting the track of a TC approaching Taiwan remains challenging, and previous studies have attempted to understand the mechanisms of track deflection using case studies or idealized simulations. In this study, several possible factors are discussed that help to explain the discrepancies between previous studies (e.g., Huang et al. 2011; Wu et al. 2015). However, many other parameters, including TC size, intensity, and translational speed, also have complicated and unpredictable effects on the TC track, and thus further studies will be required.
This work is supported by the Ministry of Science and Technology of Taiwan under Grant MOST 106-2111-M-002-013-MY3. The comments from Anna Vaughan, the editor, and three anonymous reviewers helped improve the quality of the manuscript and are highly appreciated.