A Numerical Study on the Effect of an Extratropical Cyclone on the Evolution of a Midlatitude Front

The extratropical transition (ET) of a tropical cyclone (TC) is a common phenomenon when TCs move poleward into midlatitude regions. In satellite imagery, an ET is characterized by a decrease in deep convection, the appearance of a comma-shaped cloud pattern or frontal structure, and the exposure of the low-level circulation center (Merrill, 1993). Although TCs experiencing ET lose their tropical characteristics, an extratropical cyclone may also produce extreme disasters, such as large waves and intense rainfall, posing serious threats to land and maritime activity. In particular, when a TC interacts with the midlatitude environment, the TC characteristics change dramatically (e.g., Foley and Hanstrum, 1994; Klein et al., 2000; Kitabatake, 2002; Atallah and Bosart, 2003). The inner core of a TC loses its symmetric appearance, and the precipitation around the TC center evolves into a wide asymmetric distribution and expands spatially. Regions of significant precipitation are typically embedded in the large cloud shield, which is related to the upper-level outflow into the midlatitude westerlies.

In previous studies, a great deal of research has focused on the influence of midlatitude systems on TC characteristics during the ET process. A major concern is extratropical cyclone reintensification under the influence of midlatitude systems. (Hanley et al., 2001) constructed composites of TCs that experienced ET through interaction with upper-level troughs. The composite of TCs that experienced reintensification indicates that a deep and wide upper-level potential vorticity (PV) anomaly approaches the TC center from the northwest. During the early stage of the interaction between the upper-level PV anomaly and the TC, vertical shear can inhibit the intensity of the TC (DeMaria, 1996). In the later stage of the ET process, vertical shear is essential for the reintensification of an extratropical system because of the presence of baroclinity. Using PV inversion techniques, (McTaggart-Cowan et al., 2001) also demonstrated that the upper-level trough played a crucial role in the reintensification of Hurricane Earl (1998) in the extratropics. (Klein et al., 2002) examined the sensitivity of ET to the lower-level thermal processes associated with a decaying TC and upper-level midlatitude dynamic processes. TC reintensification was found to occur when the remnant TC circulation interacted with the lower-tropospheric baroclinic zone, and the upper-level TC outflow was enhanced in the equatorward entrance region downstream of the TC. Moreover, weak cold air originating from midlatitude systems can be advected by the TC circulation into the TC's core, which may cause the ET cyclone to reintensify through energy conversion and energy transport (e.g., DiMego and Bosart, 1982).

The approach of midlatitude systems can exert a significant influence on TC structure during ET stage, leading to the erosion of the barotropic core of the cyclone and the establishment of a baroclinic cyclone (e.g., Thorncroft et al., 1993; Harr and Elsberry, 2000). (Harr and Elsberry, 2000) found that the final structural characteristics of the ET cyclone differ greatly from those of the TC, depending on the character of midlatitude circulation into which the TC moves. When the TC and midlatitude circulation meet to form a northwest pattern, the coupling of the TC remnants with the eastward-moving midlatitude trough located northwest of the TC is so vigorous that an intense extratropical cyclone with well-defined frontal characteristics forms. In contrast, when a weaker trough exists upstream of the TC in a northeast pattern, the coupling between the midlatitude trough and the TC is weakened, and only weak warm frontogenesis occurs to the northeast of the TC. Therefore, the structural changes of the TC are often linked to frontal evolution. (Keyser et al., 1988) examined the changes in the vector frontogenesis function that can quantify frontal development. This vector frontogenesis function consists of scalar and rotational components. Based on the lower-tropospheric equivalent potential temperature (θ_e) distribution, characteristics of TCs and their environments, (Kitabatake, 2008) classified ET cases into three categories. These three categories include seclusion-occlusion types, cold advection types and open-wave types. (Kitabatake, 2008) examined the differences in extratropical cyclone structure and frontal evolution among these three categories.

In addition to the impact of midlatitude systems on extratropical cyclones, the modification of upper-level circulation in the extratropics by TC circulation has also been investigated. (Uccellini and Kocin, 1987) found that, in regions of convection and latent heat release, the diabatic erosion associated with ET cyclones could separate the upper-level jet into two parts. The region between the two parts of the upper-level jet was characterized by enhanced divergence associated with the combination of the downstream jet entrance region and the upstream jet exit region. This enhanced divergence, in turn, created favorable conditions for rapid cyclogenesis in the midlatitude zone. Alternatively, the latent heat release can result in enhanced PV below the level of maximum heating and reduced PV in the upper troposphere. The diabatic reduction of PV in the upper troposphere can lead to enhanced ridging downstream of the system and thus a steepening of the tropopause (e.g., Massacand et al., 2001; Atallah and Bosart, 2003). In addition, the development of midlatitude upper-level systems can often be observed downstream of an extratropical cyclone through Rossby wave dispersion due to the PV gradient between a TC and the upper-level jet. [Ferreira and Schubert, 1999] examined downstream development in a shallow water model, showing that a cyclonic PV anomaly could indeed generate downstream trough development. In addition to downstream development at upper levels, smaller-scale developments can take place upstream at lower levels in association with disturbances growing on the low-level temperature gradient (e.g., Thorncroft and Hoskins, 1990; Wernli et al., 1999). The fact that the TC circulation's maximum amplitude occurs at low levels suggests that upstream development may be significant in some cases.

Compared to the influence of midlatitude systems on a TC during the ET stage, the extratropical cyclone modulation of the characteristics of midlatitude frontal systems within a baroclinic environment remains elusive. A midlatitude cold front with a spatial scale of several thousand kilometers can spread into a large-scale region within a few days and produce a considerable temperature drop and frontal precipitation. However, once the midlatitude system interacts with an ET cyclone, the evolution of the frontal system's features is not well understood. The evolution of these frontal systems can be further investigated by means of a numerical approach. Current high-resolution models are capable of accurately reproducing the interaction between frontal systems and are able to reveal the role of TCs in modulating the characteristics of midlatitude frontal systems by removing the TC vortex in a sensitivity experiment. Therefore, a typical case of a TC experiencing the ET process is chosen to compare the frontal structure and evolution in the presence and absence of a TC. The case chosen in this study is that of TC Haima (2004), which experienced reintensification and transformed into an extratropical cyclone during the interaction with a frontal system after making landfall. The objective of this study is to elucidate the influence of ET cyclones on frontal systems and to explore the underlying physical processes associated with these systems from dynamic and thermodynamic perspectives.

The paper is organized as follows. In section 2, an overview of TC Haima (2004) is given and the synoptic evolution during the ET stage is briefly introduced. In section 3, the model and experimental design are described. The numerical results are verified in section 4. The physical interpretations of the role of TCs in frontal evolution are presented in section 5. Finally, the conclusions are given in section 6.

Initially, TC Haima (2004) formed to the southwest of Taiwan as a low-pressure center at 1800 UTC 10 September 2004. Following the steering flow of the subtropical ridge, TC Haima (2004) was shifted northwestward and reached the strength of tropical storm, with a minimum central pressure of 996 hPa and a maximum surface wind speed of 18 m s^-1. At 0400 UTC 13 September, TC Haima (2004) made landfall over Wenzhou in Zhejiang Province. Similar to most TCs that make landfall, TC Haima (2004) began to weaken due to increased surface friction and reduced energy supply from the surface layer. After landfall, a potent midlatitude trough approached from the west and interacted with TC Haima (2004). As a result, TC Haima (2004) reintensified at 0000 UTC 14 September and underwent the ET process to become an extratropical cyclone. This extratropical cyclone crossed China from the south to the north, resulting in precipitation in Shangdong and Hebei Provinces.

This study utilized version 3.4 of the Advanced Research version of the Weather Research and Forecast (WRF) model. WRF is a three-dimensional, fully compressible, nonhydrostatic model formulated within a mass coordinate that follows the terrain in the vertical axis. The model's physics schemes include the Rapid Radiative Transfer Model (RRTM) for longwave radiation [Mlawer et al., 1997], the Goddard shortwave radiation scheme [Chou and Suarez, 1994], the Monin-Obukhov surface flux calculation over the ocean, the Rapid Update Cycle (RUC) land surface model [Smirnova et al., 1997], the Yonsei University (YSU) planetary boundary layer scheme [Hong et al., 2006], and the Kain-Fritsch cumulus parameterization scheme (Kain and Fritsch, 1990) for subgrid-scale deep convection.

Figure 1.  Infrared imagery (units: ℃) from the GEOS-9 satellite (a, b), and the 200-hPa geopotential height (solid, units: pgm) and 500-hPa vertical pressure velocity (shaded, units: Pa s^-1) from the FNL analysis (c, d) at 1200 UTC 13 September (a, c) and 14 September (b, d). The red triangle symbol denotes the TC center.

Two interactive nesting domains were set in the two experiments. The outermost domain had 210×180 grid points, with a horizontal grid spacing of 30 km. The innermost domain had 301×301 grid points, with a horizontal grid spacing of 10 km, and covered the region of interaction between the TC and the midlatitude trough. Considering that this study focuses on the system evolution on the synoptic scale, this resolution is sufficient to resolve the ET and the interaction process. The model's initial conditions and outmost lateral boundary conditions were obtained from the National Centers for Environmental Prediction (NCEP) global final (FNL) analysis dataset at 1° resolution and 6-h intervals. SST was taken from the NCEP real-time objective SST at the initial time and remained fixed because there was no significant variation and influence during the integration period.

Figure 2.  Sea level surface pressure (contour, units: hPa) and 850-hPa winds (vector, units: m s^-1) at 0000 UTC 13 September 2004 for (a) The FNL analysis, (b) the initial conditions in the CTL run incorporating the pre-run TC vortex, (c) the initial conditions in the NOTC run with the TC vortex removed and (d) the TC vortex removed from the CTL run.

Two main numerical experiments were performed in this study. One was the control run (CTL run), which was designed to reproduce the observations. However, the FNL analysis failed to capture the realistic intensity of TC Haima (2004) compared with the most accurate track from the China Meteorological Administration (CMA). This discrepancy was likely caused by the scarcity of conventional observations over the ocean and the coarseness of the FNL analysis resolution to resolve TC Haima's intensity. Therefore, it was necessary to incorporate a TC-like vortex with a realistic size and intensity into the initial conditions, which improved the simulation of the track and the strength of the TC. For this purpose, the model was initially integrated for 24 hours starting from 0000 UTC 12 September to spin up a realistic vortex. The pre-run output generated a vortex with dynamically balanced structure and realistic intensity, similar to the most accurate analysis at the model's initial starting point. Then, the vortex was extracted and merged into the FNL fields as the model's initial conditions, with the vortex center identical to that in the most accurate track analysis. In contrast to the incorporation of an artificial vortex with artificial axisymmetric structures, this procedure not only incorporates a realistic vortex structure but also avoids producing any notable "shocks" once the model is integrated. Thus, this procedure tends to be more compatible with the model dynamics than the use of an arbitrarily contrived vortex. After inserting the intensified vortex into the initial analysis, the initial model vortex was stronger than that in the FNL analysis (Figs. 2a and b). The minimum sea level pressure decreased from 1007 hPa in the FNL analysis to 998 hPa in the initial analysis, which is approximately 2 hPa higher than that in the most accurate TC track. Therefore, the initial fields in the CTL run improved the representation of the TC vortex.

The other run was designed to remove the TC circulation from the FNL analysis (NOTC run). The vortex removal algorithm was based on Kurihara et al. (1993, 1995). A simple smoothing operator was applied to the wind, geopotential height, temperature and specific humidity fields of the FNL analysis and was centered at the observed TC center. Figures 2c and d show the environmental fields without the TC vortex and with the removed TC circulation, respectively. As shown in Fig. 2d, the major proportion of strong cyclonic flow in the removed vortex is located in the eastern semicircle of the TC circulation, which is consistent with the observations, indicating that the asymmetric structure associated with TC circulation had been removed from the initial conditions.

To verify that the simulation can reasonably reproduce the evolution of synoptic systems, the comparison of the simulation with the observations, in terms of the TC track, intensity and precipitation, is described briefly in this section. The centers of the simulated TC are defined as the minimum surface pressure within the TC circulation. As shown in Fig. 3, the model accurately reproduces the observed track because of the position adjustment of the artificial vortex at the initial time of integration. The simulated TC moves north-northwestward, consistent with the observed track, although it has a comparatively slow displacement and shifts in a more westward direction compared to the observed track. After the incorporation of the artificial vortex, the simulated minimum surface pressure appears to be somewhat lower than the observed surface pressure during most of simulation period. However, the model captures the intensity change well. In particular, after 1200 UTC 13 September, TC Haima (2004) progressively intensifies because of its interaction with the midlatitude trough. Similar to the relationship between the final central pressure of an ET event and the type of midlatitude circulation pattern found by [Klein et al., 2000], the midlatitude trough located to the northwest of the TC in this study causes TC reintensification. The ET process is complete after 0000 UTC 15 September, and the simulated TC decay is in agreement with the observed TC decay.

The three-day precipitation accumulation during the integration period appears to peak in Shangdong Province (Fig. 4), in agreement with the precipitation distribution found by [Chen, 2011]. However, the simulated precipitation encompasses a broader area compared with the recorded rainfall at observation stations obtained from the CMA (Fig. 4a). This expansion of the rainfall region may be attributed to a stronger TC intensity and a deficiency of related physical parameterizations in the model. The precipitation over the is closely linked to the abundant moisture transport east of the TC. Despite ocean (not shown in Fig. 4a) the disparities described above, the consistency of the main rainfall region implies that the simulation can reasonably capture the major features of the interaction between TC Haima (2004) and the midlatitude frontal system.

Figure 3.  The observed track of TC Haima (2004) (solid) and the simulated track (dash) from 0000 UTC 13 September to 0000 UTC 16 September 2004 are presented in the upper panel. The observed and simulated sea level pressure (units: hPa) during the model integration are presented in the lower panel.

The differences in the midlatitude frontal evolution between the two runs clearly demonstrate the role of the ET cyclone in modulating the frontal structure. Figure 5 depicts the simulated outgoing longwave radiation (OLR) and the 850-hPa wind fields. It is apparent that the frontal system drastically changes in the CTL run compared with that in the NOTC run. At 0000 UTC 14 September, the two isolated convection regions correspond to the midlatitude frontal system and the TC circulation in the CTL run. Accompanied by the northward-shifting TC, the low-level maximum winds are observed to the east and north of the TC center, creating favorable conditions for transporting moisture northwestward from the ocean (Fig. 5a). In contrast, the frontal system exhibits distinctly different features in the NOTC run (Fig. 5c). On the one hand, the frontal system in the NOTC run has greater meridional extension than its counterpart in the CTL run. This disparity can be attributed to the evident northerly flow to the west of the TC center. The northerly flow associated with the TC cyclonic circulation can increase cold advection over the southwestern portion of the front (Fig. 5a). As a result, the enhancement of cold advection suppresses the development of convection and reduces the meridional extent of convection in the CTL run.

Figure 4.  (a) The observed station precipitation and (b) simulated total precipitation during the integration period from 0000 UTC 13 September to 0000 UTC 16 September (units: mm).

On the other hand, the midlatitude frontal system expands more zonally and shifts further eastward in the NOTC run than in the CTL run. The zonal range of the frontal system can be modified significantly by the downstream circulation pattern. Due to the presence of the TC in the CTL run, the easterly flow north of the TC can enhance the horizontal convergence at the eastern edge of the front. Through the dynamic convergence and thermal contrast between the two systems, the frontal system tends to condense the frontal zone and contract its zonal extent. In addition, the potent easterly flow ahead of the front can also slow down the eastward-migrating midlatitude system through an advective effect.

Twelve hours later, the two systems merge and develop into a comma-shaped cloud in the CTL run, which is typical of an ET pattern (Fig. 5b). The low-level flow forms a clear cyclonic circulation with a relatively larger radius than that in Fig. 5a, indicating that TC Haima (2004) experiences reintensification during the ET stage. The appearance of convective asymmetry and a broad cloud shield located north of the TC center suggests that the TC's structure loses its tropical characteristics under the influence of the baroclinic system and that the TC begins to transform into an ET cyclone with an occlusion pattern. By comparison, because of the removal of the TC in the NOTC run, the midlatitude system in that run retains its frontal characteristics and shifts eastward (Fig. 5d). Ahead of the cold front is the uniform southeasterly flow, which can transport warm and moist air northwestward and maintain a meridionally elongated frontal band. However, in contrast to the circumstances 12 hours earlier, the frontal convection appears to be weakened.

Figure 5.  The distribution of simulated OLR (shaded, units: W m^-2) and 850-hPa winds (vector, units: m s^-1) for the CTL run (a, b) and the NOTC run (c, d) at 0000 UTC (a, c) and 1200 UTC 14 September (b, d).

Figure 6 depicts the midlevel structure of temperature, vertical velocity and temperature advection in the CTL and NOTC runs. The major differences lie in the strength of vertical motion and temperature advection between the two runs. At 0000 UTC 14 September in the CTL run (Fig. 6a), the strong easterly flow associated with the TC circulation to the north of the TC is directed against the temperature gradient, generating a broad region of warm advection. Potent cold temperature advection is present near the trough base, suppressing convection in the southern portion of the front. Meanwhile, the simulated TC center is coincident with the warm core, indicative of a barotropic-like structure. In association with warm temperature advection, the rising of warm, moist air induces the primary ascending motion to the northwest of the TC. In the NOTC run (Fig. 6c), due to the absence of the TC warm region and of the easterly flow north of the TC, warm and cold temperature advection is reduced significantly. As a result, weakened upward motion and a diluted temperature gradient are observed in the vicinity of the front.

Figure 6.  The simulated temperature (solid, units: K); vertical velocity (dash, starting from 0.1 m s^-1 at intervals of 0.05 m s^-1) at 500 hPa; and temperature advection (shaded, units: K d^-1) averaged between 925 and 300 hPa for the CTL run (a, b) and the NOTC run (c, d) at 0000 UTC (a, c) and 1200 UTC 14 September (b, d). For clarity, the fields are nine-point smoothed. The triangle symbol denotes the simulated minimum surface pressure center.

At 1200 UTC 14 September, when TC Haima (2004) is displaced northwestward in the CTL run (Fig. 6b), the midlevel warm core shifts away from the TC surface center, representing the baroclinic transition of the TC vertical structure. The warm core penetrates into the northern part of the cold front, creating a frontal trough axis in a northwest-southeast orientation. Along with the cyclonic flow related to the ET cyclone, cold advection is dominant to the south of the comma-shaped convection region, and consequently, a broad cloud-free region is observed in the southern part of the ET cyclone, consistent with OLR distribution shown in Fig. 5b. In comparison, temperature advection and vertical motion are substantially lower in the NOTC run (Fig. 6d).

Figure 7.  The potential vorticity (solid, units: PVU, 1 PVU=10^-6 K kg^-1 m² s^-1, starting from 2 PVU at intervals of 2 PVU); divergence (dash, starting from 5×10^-6 s^-1 at intervals of 5×10^-6 s^-1); wind (vector, units: m s^-1); and wind at 250 hPa for the CTL run (a, b) and the NOTC run (c, d) at 0000 UTC (a, c) and 1200 UTC 14 September (b, d). For clarity, the fields are nine-point smoothed. The triangle symbol denotes the simulated minimum surface pressure center.

To describe the three-dimensional structure of the frontal system during the ET stage, Figures 8a-d depict the distributions of θ_e, in-plane flow and vertical velocity in the vertical sections along the main precipitation region, perpendicular to the front. At 0000 UTC 14 September, theθ_e contours become dense and tilt vertically due to the proximity of the two systems in the CTL run (Fig. 8a), implying an enhancement of frontogenesis. Concurrently, two ascending maxima appear near the frontal zone. One of these ascending maxima is located along the eastern edge of the front. When the air is advected northwestward by the easterly flow north of the TC, it can be lifted along the steep θ_e surfaces to initiate and sustain deep convection. The other ascending maximum emerges in the upper troposphere, which may be partly related to the secondary circulation induced by the upper-level front. In contrast, the frontal zone is distributed at mid- and upper-levels in the NOTC run, while the lower-levelθ_e contours appear to be thin (Fig. 8c). In addition, because of the disappearance of easterly flow ahead of the midlatitude front, the lifting of warm, moist air associated with the TC disappears. The major ascending motion, coincident with the region of the secondary maximum ascent shown in Fig. 8a, is likely attributed to the joint contributions from lower-level convective instability and secondary circulation related to the midlatitude front. As the two systems approach each other, the frontal zone is strengthened, and upward motion expands spatially throughout the deep troposphere (Fig. 8b). In contrast, the θ_e surfaces appear to be flat, and no evident ascent can be detected in the NOTC run (Fig. 8d).

Similarly, relative vorticity and simulated reflectivity, which are in good agreement with upward motion, also indicate the differences between the two runs (not shown). Initially, positive vorticity is weak and distributed at lower levels, while anticyclonic circulation is dominant in the middle to upper troposphere. As the reflectivity zone expands during the ET stage, cyclonic vorticity is strengthened and extends vertically such that negative vorticity is elevated to the upper troposphere. This increased reflectivity and ascending motion imply that a large amount of latent heat of condensation is released, leading to the enhancement of lower-level convergent and cyclonic circulation and upper-level divergent and anticyclonic circulation. As discussed by [Hoskins et al., 1985], a heating source in the free atmosphere can generate a positive PV anomaly below the area of maximum heating and a negative PV anomaly above the area of maximum heating. This effect can partly account for the westward bulge in the northern part of the upper-level trough and the distortion of the jet streak as demonstrated in Fig. 7b. In comparison, the upper-level trough is relatively weak and is shifted further eastward in the NOTC run because of the absence of interaction with TC Haima (2004).

The interaction between the TC and the baroclinic midlatitude environment is often accompanied by frontal development. The vector frontogenesis function can be used to quantify individual contributions to frontogenesis. Following the formula of Kitakatake (2008), frontogenesis can be defined in vector form as

F=d▽θ_e/dt=F_nn+F_sS (1)

This function is resolved into natural coordinates (n,s) defined by the local orientation of θ_e contours on the isobaric surface, where n=-|▽θ|^-1▽θ_e and s=n×k. Thus, the components of the vector frontogenesis in Eq. (1) are given as follows:

scalar frontogenesis (F_n) acts to change the magnitude of theθ_e gradient, while rotational frontogenesis (F_n) acts to rotate the θ_e gradient. The first, second and third terms summed in Eq. (2) represent the contributions to scalar frontogenesis caused by horizontal divergence (F_n,Div), shear deformation (F_n,Def) and the tilting effect (F_n,Title), respectively. The contributions from the first, second and third terms summed in Eq. (3) to rotational frontogenesis are referred to as relative vorticity (F_s,var), stretching deformation (F_s,Def) and the tilting effect (F_s,Title), respectively. Negative (positive) F_n corresponds to the traditional frontogenesis (frontolysis), whereas positive (negative) F_s corresponds to the cyclonic (anticyclonic) rotational frontogenesis.

Figures 9a-c describe the individual contribution of each term in Eq. 2 to scalar frontogenesis on 0000 UTC 14 September. Along the dense θ_e zone, high values of the F_n,Div term are found to the northwest of the TC. These high F_n,Div values primarily contribute to cold frontogenesis to the west of the TC and warm frontogenesis to the north of the TC (Fig. 9a). On the one hand, the region north of the TC is characterized by easterly flow that can give rise to significant convergence ahead of the midlatitude trough. On the other hand, there exists a strong θ_e gradient along the cold (warm) front to the west (north) of the TC circulation. Therefore, the F_n,Div term that is related to enhanced convergence and to the θ_e gradient plays a primary role in the contribution to frontogenesis near the frontal zone. In comparison, the deformation term appears to be quite small (Fig. 9b), and the tilting term has a secondary contribution to scalar frontogenesis in the vicinity of ascending motion (Fig. 9c). Based on the individual components, the outer circulation of the TC and the thermal contrast between the two systems can play a crucial role in strengthening scalar frontogenesis.

Figure 9.  The distribution of equivalent potential temperature (contour, units: K) and different components of scalar frontogenesis -F_n at 700 hPa at 0000 UTC 14 September (shaded, units: 1.0×10^-9 K m^-1), associated with (a) horizontal divergence, (b) shear deformation, (c) the tilting effect and (d) the total contribution. For clarity, the fields are nine-point smoothed.

The major contribution to rotational frontogenesis is associated with the vorticity term shown in Fig. 10a. As expected, one maximum center is situated near the core region of the TC because of the cyclonic circulation of the TC. The other positive center can be identified near theθ_e ridge region to the northwest of the outer circulation of the TC, which is a joint between the cold front west of the TC and the warm front north of the TC. In addition to its contribution to the inner core of the TC, the horizontal deformation term also makes a considerable contribution to rotational frontogenesis near this joint region, with a magnitude comparable to the F_s,var term (Fig. 10b). In contrast, the tilting effect is almost negligible (Fig. 10c). Positive rotational frontogenesis acts to rotate the gradient ofθ_e in a cyclonic direction (Keyser et al., 1988). As a result, the effects associated with horizontal vorticity and deformation jointly assist in cyclonically rotating theθ_e gradient, changing the orientation of the midlatitude trough from north-south to northwest-southeast.

Figure 10.  The distribution of equivalent potential temperature (contour, units: K) and different components of rotational frontogenesis F_s at 700 hPa at 0000 UTC 14 September (shaded, units: 1.0×10^-9 K m^-1), associated with (a) relative vorticity, (b) stretching deformation, (c) the tilting effect and (d) the total contribution. For clarity, the fields are nine-point smoothed.

When a midlatitude system and a TC approach each other, the baroclinic system can destroy the original tropical features of the TC, causing ET to occur. Conversely, the TC circulation can also exert significant influence on the characteristics of the midlatitude system in terms of its structure, intensity and displacement. Thus far, the effects of a TC during the ET stage on the evolution of a midlatitude frontal system are not well understood. In this study, a typical case in which TC Haima (2004) interacted with a potent midlatitude front was reasonably reproduced using the WRF model. Two experiments were conducted to examine the role of the TC circulation in modulating the front evolution. In the CTL run, the intensified vortex was extracted from the pre-run simulation with an initialization period of 24 hours and was then inserted into the coarse FNL analysis as an initial condition, such that the modeled TC had an intensity similar to that of the observed TC at the initial time. As verified against the observations, the CTL run reasonably captures the characteristics of TC Haima (2004) and its interaction with the midlatitude front. In the NOTC run, with the removal of the TC circulation, the midlatitude front evolves without the influence of the synoptic pattern associated with the TC.

Comparisons between the two model runs show that the dynamic and thermodynamic fields in association with the TC circulation can substantially impact the intensity, areal extent and structure of the midlatitude front. As the two systems approach each other in the CTL run, the northerly flow to the west of the TC enhances the cold advection, which suppresses convective activity in the southern part of the midlatitude front, leading to a limited meridional extent of the front compared with that in the NOTC run. In contrast, because of the absence of easterly flow related to the TC cyclonic circulation to the east of the front in the NOTC run, the front has a more expansive zonal extent and is displaced further eastward. In the CTL run, TC Haima (2004) progressively undergoes the ET process, during which cold air wraps around the TC cyclonically to the southern side of the TC, producing a large-scale cloud-free region. Furthermore, convective activity in the form of comma-shaped anvil clouds is dominant in the northern part of the TC. In contrast, the midlatitude front spreads more widely and shifts further eastward in the NOTC run, but its intensity becomes weaker.

Another salient difference between these two runs is that warm, moist air from the east is transported westward by the TC cyclonic circulation, and thus, warm advection is enhanced to the northwest of the TC. Because air is lifted along θ_e surfaces, ascending motion is mainly distributed on the eastern side of the midlatitude front. As TC Haima (2004) moves into the northern part of the front and transforms into an ET cyclone, vertical motion increases. As a result, a large amount of diabatic heating is released through condensation in this region because the lifting of moisture generates precipitation. The positive vorticity column extending horizontally and vertically gives rise to anticyclonic and divergent flow at upper levels, which can intensify the jet streak by feeding its momentum flux. Additionally, the reduced PV in association with anticyclonic outflow distorts the upper-level trough in a northwest-southeast orientation. In comparison, the NOTC run shows lower magnitudes of temperature advection and vertical motion, and the mid- and lower-level frontal zones appear to be relatively flat due to the absence of the TC circulation.

Finally, the dynamic and thermodynamic effects of the TC circulation modulating the frontal intensity are investigated by partitioning the vector frontogenesis into scalar and rotational components. In the CTL run, the combined effects of thermal contrast and dynamic convergence associated with the TC identify the primary contribution to scalar frontogenesis as areas near zones with dense θ_e. Concerning rotational frontogenesis, the contribution related to the vorticity term is dominant over the frontal zone, facilitating the cyclonic rotation of the front to form an occlusion pattern. Moreover, intensified frontogenesis can also induce a secondary circulation that contributes to enhancing the ascending motion in the vicinity of the frontal zone.