Dependence of the relationship between the tropical cyclone track and western Pacific subtropical high intensity on initial storm size: A numerical investigation

3.1 Storm Size

In an operational setting, storm size is described by the area of the outermost closed isobar (ACI) in the surface level. For both Songda and Megi in this study, the value of the outermost closed isobar is about 1000 hPa. Figure 1 shows the temporal evolutions of ACI in the cases of Songda (2004) and Megi (2010). It clearly shows that in both Songda and Megi cases, the ACI is highly sensitive to the initial vortex size determined by the TC Bogus scheme and increases significantly as the initial vortex size increases, especially as the initial vortex size increases from small size in the ES to medium size in the EM. This is consistent with the idealized model results of Xu and Wang [2010], which indicated that a storm with a large initial size usually has strong outer winds and large surface entropy fluxes outside the eyewall. They are accompanied by active spiral rainbands, leading to fast increase in the inner core size. In addition, the ACI in the EL decreases significantly after 2000 UTC 04 September 2004 for Songda case. This is probably caused by the landfall of the storm in the EL, since the time of the decrease in ACI is basically consistent with the landfall time of the storm simulated in the EL (see Figure 3). To further provide a picture of typical precipitation associated with the simulated TC, Figure 2 presents two snapshots of the model-simulated radar reflectivity at 0000 UTC 3 September 2004 for the case of Songda (2004) and 0000 UTC 18 October 2010 for the case of Megi (2010). Compared with that in the ES run, a wider and broader eyewall is evident in the EM and EL runs, along with larger area of precipitation in the outer spiral rainbands in both Songda and Megi cases. This is consistent with our hypothesis and further indicates that the size of the simulated TCs is highly dependent on the initial vortex size, i.e., the larger the initial vortexes, the larger the storms will be later.

3.2 Storm Track

Previous studies have indicated that the storm size affects its motion not only by changing the large-scale environmental flow but also by influencing the BEP [Holland, 1983; Fiorino and Elsberry, 1989; Carr and Elsberry, 1997; Bu et al., 2014; Sun et al., 2014a, 2015a]. Figure 3 compares the storm track simulated in the sensitivity experiments with the JTWC best track of Songda. It indicates that the simulated storm track is highly sensitive to the initial size of the storm and large differences between the results of the three experiments occur about 2 days after the model integration starts. The simulated storm in the EM and EL turns northward earlier than observation and makes landfall in Japan at about 1200 UTC 06 September 2004 and 1800 UTC 05 September 2004, respectively, whereas the simulated storm in the ES continues to move westward and turns northward later than observation and did not make landfall before 0600 UTC 07 September 2004.

Figure 4 compares the storm track simulated in the three experiments with the JTWC best track of Megi. The model with the small initial storm size can well reproduce the track of Megi, but it performs not so well in the experiments with the medium and large initial size. All experiments realistically simulate the northwestward movement of Megi before 0000 UTC 17 October 2010, and the west-southwestward movement along the southern periphery of the WPSH until the storm crossed the Luzon Island. Large differences between results of the three experiments occur after 1800 UTC 18 October 2010. Similar to the results in Songda case, the simulated storm in the EM and EL turns northward earlier than observation, whereas in ES it continues to move westward and turns northward over South China Sea at about 1800 UTC 19 October 2010. Apparently, the simulated storm track is sensitive to the initial size of the storm. It is worth noting that a TC with a larger initial size turns northward earlier in both Megi and Songda cases.

Feedback and interaction between the TC and WPSH are interwoven in these simulations, making it a challenging issue to address what is the root cause of the large biases in both the WPSH and TC simulations. Note that the unrealistic withdrawal and extension of the simulated WPSH is responsible for the failure in RCM simulations of TC motions. The erratic departure of the simulated TC track from its observed position contributes greatly to the RCM's failure in simulating the WPSH [Zhong, 2006]. Thereby, the TC track simulation is a key factor that affects the WPSH simulation. In the following section, we will discuss in detail the possible reasons for the difference in TC track simulation between these experiments.

4.1 Potential Vorticity Tendency Diagnosis

Previous studies suggested that the environmental flow and the TC structure are two key factors determining the TC motion over the WNP [e.g., Chan and Gray, 1982; Holland, 1983; Fiorino and Elsberry, 1989; Wu and Wang, 2000; Wu et al., 2005; Zhong, 2006]. Theoretically, the storm size can influence the TC motion in two ways. First, the storm size can modulate the large-scale environmental flow near the TC and thus affect TC motion by influencing the withdrawal and extension of the WPSH. Second, the storm size can affect the TC motion by modifying the thermodynamic and dynamic structures of the TC. As suggested by Carr and Elsberry [1990] and Holland [1993], the large-scale environmental flow is defined as the layer-mean (850–300 hPa) flow averaged over a 5°–7° latitude band of the TC center. In the following paragraph, we will discuss which factor is dominant in the differences between the simulated TC motions of the three sensitivity experiments.

To estimate contributions of the TC structure and environmental flow to TC motion, the potential vorticity tendency (PVT) diagnosis technique is applied in this study [Chan, 1984; Wu and Wang, 2000, hereafter WW00]. Simulations of an ideal TC in WW00 indicated that a baroclinic TC moves toward the region where the azimuthal wave number 1 of the maximum PVT is located. WW00 suggested that the PVT results from horizontal PV advection (HA), vertical PV transportation (VT), and diabatic heating (DH), while the contribution of individual physical process to the TC motion is equivalent to its contribution to the wave number 1 component of the PVT. Equation 1 directly links the TC motion with PVT, and equation 2 estimates the contribution of individual physical process to the PV in the pressure coordinates.

(1)

(2)

where P represents the PV, P_S is the symmetric PV component of PV, V is the horizontal wind speed, V_PV is the velocity of vortex motion estimated from the wave number 1 component of the PVT, p is the pressure, q is the three-dimensional absolute vorticity vector, ∇₃ is the three-dimensional gradient, Λ₁ denotes an operator to obtain the wave number one component, g is the gravitational acceleration, ω is the vertical velocity in the pressure coordinates, θ is potential temperature, and F and denote friction and diabatic heating rate, respectively. As suggested by WW00, in the derivation of equation 1, we have assumed that the wave number 1 component of the PVT is negligibly small compared with the symmetric component of the PVT. We apply equation 1 to each grid point (denoted by subscript i) and compute the gradient of P_S,

(3)

From equation 3 the zonal (c_x) and meridional (c_y) components of the vortex moving speed at each level can be determined. Considering a specific region that is within a radius of 360 km from the TC center, we use the least squares method to calculate c_x and c_y by minimizing

(4)

Where N denotes the number of total grid points in the specified region. The effects of the large-scale steering flow and the BEP are all included in HA (first term on the right-hand side of equation 2), while the effects of the thermodynamic and dynamic structures of TC determine VT (the second term) and DH (the third term). V_PV-HA, V_PV-VT, and V_PV-DH denote the individual contributions of HA, VT, and DH to the vortex moving speed, respectively.

For the convenience to interpret the results, we compare PVT between the EM and EL simulations. Note that for Megi case, the assumption of equation 1 is no longer valid in ES due to the reduced intensity of the symmetric TC circulation and the enhanced asymmetric circulations. A large bias in the estimated speed (i.e., V_PV) occurs in the ES before 1200 UTC 18 October 2010 (see Figure S1). Thereby, we compare the results of PVT between the EM and EL in both Megi and Songda cases.

Figure 5 depicts the temporal evolution of the vertically averaged TC moving speed calculated from the PVT equations as well as the individual contributions of HA, VT, and DH calculated in the EM and EL for the case of Songda (2004). The calculation covers the time period from 1 September to 5 September 2004, corresponding to the period before and after the time when the difference in TC position between the EM and EL becomes significant. The mean moving speed of the TC is averaged between 850 hPa and 400 hPa because of the various vertical extents of the positive PV anomalies in the EM and EL (figure omitted). As is shown, the mean moving speed of TC calculated from the wave number 1 component of the PVT (V_PV) is consistent with that calculated from the TC center position (V_C). A similar result can be found in previous studies [WW00; Sun et al., 2015a]. Thereby, the PVT diagnosis approach has been proved to be an effective method to estimate the TC moving speed for real TC cases.

Based on equation 2, the contribution of each individual physical process (i.e., HA, VT, and DH) to the difference in TC motion between the EM and EL can be estimated. In the following analysis, we will focus on the period before 1200 UTC 03 September, when the difference in TC position between the EL and EM is not significant for Songda case. This period is selected to ensure the background circulation is the same or similar for the EM and EL experiments. Once the difference in TC position becomes evident, the effects of individual physical process in equation 2 will be susceptible to differences in the background environment and thus cannot be used for comparison.

Due to the strong large-scale forcing of the WPSH in the EM, the contribution of HA (i.e., V_PV-HA) is notably stronger than that in EL, resulting in a large difference in the zonal TC moving speed especially after 0000 UTC 02 September 2004 (Figures 5b and 5e). Similar to the zonal wind impact on TC motion, the meridional wind also contributes greatly to the TC motion along the meridional direction (Figures 5c and 5f). More importantly, the magnitude of zonal V_PV-HA in the EL is notably smaller than that in EM by up to −3 m s⁻¹, but the magnitude of meridional V_PV-HA in the EL is much larger than that in the EM by up to 4 m s⁻¹. This suggests that V_PV-HA plays an important role in reducing the westward moving speed of TC and accelerating its northward moving speed in the EL. This is consistent with the results of Bi et al. [2015], which also emphasized the important impact of horizontal vorticity advection on TC motion. Similar to the results in Sun et al. [2015a], V_PV-VT makes little contribution to the TC moving speed and thus causes almost no difference in TC motion between the two experiments. Previous studies suggested that there is a fast adjustment between the asymmetric diabatic heating (DH) and relatively asymmetric flow (HA) [Peng et al., 1999; WW00]. This is why the temporal evolutions of V_PV-DH and V_PV-HA are anticorrelated in meridional direction. Although V_PV-DH contributes greatly to the difference in meridional TC motion, it is not the direct and major reason for the difference in meridional TC moving since it is of opposite phase to the meridional TC moving and it is smaller than V_PV-HA (Figure 5i). Therefore, it is the contribution of HA (V_PV-HA) that is responsible for the difference in TC motion, especially the early northward turning of TC in the EL. Comparing the results in ES with that in EM, we can reach similar conclusions (see Figure S2).

Figure 6 illustrates the temporal variations of the vertically averaged TC speed calculated from the PVT equations as well as each individual contributions of HA, VT, and DH in the EM and EL for the case of Megi (2010). The time period is from 17 October to 21 October 2010, which corresponds to the period before and after the time when the difference in TC position between the EM and EL becomes significant. Similar to studies for Songda case, the mean moving speed of TC is also averaged between 850 hPa and 400 hPa. The results indicate that V_PV is almost identical to V_C in all the three experiments of ES, EM, and EL, implying that the PVT diagnosis approach is also effective in estimating the motion of TC for Megi case.

In the following analysis for the case of Megi, we focus on the period before 0000 UTC 19 October 2010 when the difference in TC position between the EM and EL is not significant. Similar to the results in Songda case, differences in the contribution of HA (V_PV-HA) to the TC motion is primarily responsible for the difference in the simulated TC motion between the EM and EL (Figures 6h and 6i). V_PV-HA contributes greatly to early northward turning of the TC in the EL experiment (Figure 6i).

Following the approach in WW00 (a case study of ideal TC), we have considered the vortex as a symmetric PV anomaly in equation 1. However, this assumption may not hold strictly because significant asymmetric PV anomalies might exist in real TC cases, which contributes to the notable difference between V_PV-SUM in Figure 6f (Figure 6c) and V_PV in Figure 6d (Figure 6a). Nevertheless, this difference does not affect the reliability of our main conclusions. Due to the significant asymmetry of TC in the Megi case (Figures 2d–2f), V_PV-SUM in Figure 6f (Figure 6c) are underestimated. However, the difference in V_PV-SUM between the EL and EM (Figure 6i) is basically consistent with the difference in V_PV between the EL and EM (Figure 6g). We make conclusions based on the difference between EL and EM simulations rather than on the individual result of EM or EL. Together with the difference in V_PV-HA between EL and EM (Figure 6i), all the different results between EL and EM clearly indicate that it is the contribution of HA (V_PV-HA) that is responsible for the difference in TC motion between the EL and EM. As suggested in WW00, V_PV-HA not only includes the contribution of BEP but also includes the contribution of the environmental flow. Thus, the storm size affects TC motion by changing the BEP and the environmental flow near the TC. Next, we will discuss which one is primarily responsible for the large difference in TC motion between the sensitivity experiments.

4.2 Contribution of BEP on the Northward Turning of TC

To further investigate the contribution of BEP to the meridional TC motion and thus the northward turning of the TC, we calculate the meridional BEP speed based on the relationship between the mean relative angular momentum (MRAM) of the cyclonic circulation and the meridional BEP speed [Wang and Li, 1992]. The MRAM is defined by

(5)

where r denotes the radial distance from the vortex center, v_λ(r) is the tangential wind of the vortex, A is the horizontal area occupied by the vortex flow at level p, and p₁ and p₀ are the upper and lower boundaries of the vortex circulation, respectively.

The relationship between the MRAM (in units of 10⁶ m² s⁻¹) and the meridional beta drift speed (m s⁻¹) is essentially nonlinear. As suggested by Wang and Li [1992], the northward drift speed is approximated by

(6)

where the coefficients a and b are 1.01 and −0.11, respectively, for cyclones. They also suggested that the westward drift speed exhibits a weak linear correlation with the absolute value of MRAM (see their Figure 3b).

Figure 7 shows the vertically mean meridional TC motion speed calculated from the contribution of HA (V_PV-HA) and the meridional BEP speed (V_BEP) in the cases of Songda and Megi. While V_PV-HA displays significant changes over time, V_BEP tends to be almost stable with an insignificant change and remains at roughly 2 m s⁻¹ in all these sensitivity experiments (Figures 7a, 7b, 7d, and 7e). The results of Songda and Megi cases all show that V_BEP in the EL is slightly larger than that in the EM due to the larger storm size in EL. However, as the difference in V_BEP is much smaller than the difference in V_PV-HA in most of the time, the difference in V_BEP contributes little to the difference in V_PV-HA and thus has little impact on TC motion between the EL and EM (Figures 5i and 6i). This indicates that it is not the BEP that is responsible for the large difference in TC motion between the EL and EM, especially the early northward turning of the TC in both Songda and Megi cases. As mentioned previously, V_PV-HA not only includes the contribution of BEP but also includes the contribution of environmental flow. If the contribution of BEP is excluded, then the large-scale environmental flow plays a critical role in determining TC motion in the EM and EL. Figure 8 shows the meridional steering flow, the meridional TC moving speed, and their difference, in the ES, EM, and EL simulations for the cases of Songda and Megi. Following Carr and Elsberry [1990] and Holland [1993], we use the layer-mean (850–300 hPa) flow averaged over a 5–7° latitude band of the TC center to estimate the large-scale environmental steering flow in this study. Comparing the meridional steering flow with the meridional TC moving speed, we find that in Songda case, the meridional TC moving speed is basically consistent with the meridional steering flow and increases significantly when the initial storm size increases. However, in Megi case, although the time evolution trend of the meridional TC moving speed is similar to that of the meridional steering flow, the magnitude of the meridional TC moving speed is different from that of the meridional steering flow. More importantly, compared to the effects of the other factors, the large-scale environmental flow plays a much more important role in determining the TC moving speed in both Songda and Megi cases. To further address this issue, the residual term obtained by subtracting the steering flow from the TC moving speed is depicted in Figures 8c and 8f. As is shown, compared with the role of the steering flow, the residual term plays a secondary role in determining the TC motion. The difference in the residual term can be considered as one of the reasons for the difference in TC moving speed between the ES and EM, but it cannot explain the difference in TC moving between the EM and EL. Therefore, it is the large-scale environmental flow that plays a critical role in determining the TC motion. In the following section, we will investigate how the storm size affects the large-scale environmental flow near the TC and finally leads to changes in TC motion.

4.3 Contribution of Environmental Flow on the Northward Turning of the TC

The above analysis has shown that the storm size affects TC motion by changing the environmental flow near the TC (e.g., HA in PVT), which is closely related to the intensity and extent of the WPSH. This indicates that TCs are steered primarily by the large-scale environmental flow, and the characteristics of the TC tracks over the WNP are modulated by the extension and withdrawal of the WPSH. Figure 9 shows the geopotential height at 500 hPa from NCEP reanalysis data and from simulations at 0000 UTC 3 September 2004 and 0000 UTC 18 October 2010, corresponding to the cases of Songda and Megi, respectively. In order to clearly represent the difference in the simulated WPSH between the ES, EM, and EL, the geopotential height contour of 5900 m (5880 m) is used to indicate the intensity of WPSH for Songda (Megi) case in this study. Results of the experiments for both Songda and Megi cases indicate that the strength of the simulated WPSH decreases significantly as the initial storm size increases. Comparing the simulations with the NCEP reanalysis, it is found that larger TCs have more capability to weaken the WPSH and thus are more prone to turn northward, which is consistent with the results of observational analysis in Lee et al. [2010] and the conceptual model results in Carr et al. [2001]. A comparison of Figures 3, 4, and 9 suggests that the time and location of the northward turning of the storm is closely related to the degree of the weakening of WPSH due to the strong influence of the steering flow in the southern edge of the WPSH. Actually, the unrealistic early northward turning of the TC simulated in sensitivity experiments (e.g., EM and EL) can be attributed to the unrealistic split of the WPSH. Note that the unrealistic break of the WPSH simulated in these experiments is not caused by the strong storm intensity, since the simulated TC intensity does not increase with the size of the initial storm in these experiments. The simulated TC intensity in EM is even stronger than that in EL for both Songda and Megi cases (see Figure S3 and S4).

To understand the impact of storm size on the intensity of WPSH, we provide a Hovmöller diagram of the azimuthal-averaged geopotential height at 500 hPa in the TC outer region before the northward turning of the TC in Songda and Megi cases (Figure 10). We only show the radial profiles in TC outer region within a radius of 400–1200 km from TC center. As is shown, there is a semidiurnal cycling in the geopotential height at 500 hPa in both Songda and Megi cases, which may be attributed to the semidiurnal atmospheric tide. More importantly, in both Songda and Megi cases, the simulated geopotential height in the TC outer region decreases significantly as the initial storm size increases, and the contour of the low-value geopotential height (e.g., 5880 m in Songda case and 5860 m in Megi case) extends outward notably following the increase of the initial storm size. This implies that the simulated intensity of the WPSH on its fringe on the TC side decreases notably with the increase of the initial storm size, which eventually causes the WPSH break in the EM and EL and leads to large differences in TC track simulation.

In order to further investigate this issue, we take a look at the results for the time when there is no significant difference between the sensitivity experiments with different initial storm size. Figure 11 illustrates the radial profiles of geopotential height at 500 hPa at such a time for Songda and Megi cases. Due to the difference in the initial storm size, the simulated geopotential height in the outer region of the TC varies significantly even after 2–3 days of integration. The result clearly indicates that the geopotential height in the outer region decreases significantly with the increase in the initial storm size. Although the difference in the 500 hPa geopotential height between the different sensitivity experiments tends to decrease with the increase of the radial distance, remarkable differences occur even at the radial distance of 1200 km. The simulated geopotential height in ES is notably larger than that in EL by up to 21 m in Songda case and by up to 10 m in Megi case. Meanwhile, the distance between the TC center and the edge of the WPSH is only about 500–1000 km in terms of the geopotential height contour of 5880 m in both Songda and Megi cases (Figure 9). Furthermore, corresponding to increases in the initial TC size, the 500 hPa geopotential height decreases with a higher decreasing rate in areas to the north of the TC than in other areas (see Figures S5 and S6). In other words, with the increase in initial storm size, the simulated intensity of WPSH over the region to the north of the TC decreases notably in both Songda and Megi cases.

Figure 11 implies that the pressure gradient at 500 hPa in the TC outer region is closely related to the initial storm size and increases following the increase of the initial storm size. The pressure gradient below 500 hPa is basically consistent with that at 500 hPa (see Figure S7). As suggested by Gopalakrishnan et al. [2011] and Sun et al. [2013, 2014b], increases in pressure gradient in the TC outer region could induce increases in inward radial wind speed, and the inflow mass flux (IMF) entering the TC region increases correspondingly. As the TC approaches the WPSH, part of the IMF is transported from the WPSH, contributing to the weakening of the WPSH. To further investigate the possible reasons for the weakening of the WPSH prior to the significant departure of the simulated TC from its realistic location in the EM and EL, we depict the temporal evolution of IMF entering the TC region in the sensitivity experiments for the cases of Songda (2004) and Megi (2010) (Figure 12). It shows clearly that the calculated IMF is sensitive to the initial storm size and increases with the initial storm size, especially during the period prior to the occurrence of significant difference in TC positions between the sensitivity experiments. As the initial storm size increases, more IMF enters the TC region, corresponding to the weakening of the WPSH in the EM and EL (Figures 9 and 12). Thereby, the difference in IMF is one of the reasons for the difference in the WPSH simulation between the sensitivity experiments in Songda and Megi cases. Such a decrease in the WPSH intensity leads to a break of the WPSH in the EM and EL. The simulated TC in the EM and EL are subsequently forced to turn northward toward the break in the subtropical ridge. The northward movement of TC will further weaken the intensity of the WPSH near the TC in the EM and EL. This is a positive feedback between the weakening of the WPSH near the TC and northward motion of the TC. However, this positive feedback cannot be initiated in the ES, since the small storm size cannot effectively reduce the geopotential height in the TC outer region. As a result, the intensity of the WPSH over its fringe region on the TC side cannot weaken. It is important to note that the feedback of the TC on the WPSH intensity is more attributed to the larger IMF that enters the TC region rather than the larger contribution of the BEP for the larger TCs (e.g., the TCs in the EM and EL). This is because TCs affect the WPSH through the inflow mass flux, which is not an instantaneous process. The TC motion changes significantly only when critical change in the WPSH happens (i.e., the break of the WPSH). This also explains why the break of the WPSH is prior to the large departure of the position of the TC center (Figure 9). Additionally, the calculated IMF above 850 hPa is anticorrelated with that below 850 hPa (Figure S8), which offsets the inflow mass fluxes in the lower troposphere due to the large outflow of mass flux in the upper troposphere. There is a net outflow of mass flux according to the calculated IMF below 100 hPa (Figure S9), which contributes to the intensification and expansion of the TC in both Songda and Megi cases.

Note that due to the existence of the WPSH in the north of the TC, the difference in geopotential height in the lower troposphere between the outer and inner regions of TC is notably larger than in areas to the north of the TC than that to the other areas (see Figures S10 and S11). This difference results in a larger inward pressure gradient force to the north of the TC, which further induces a larger inflow mass flux from the TC outer region to the TC inner region (see Figure S12). Due to the larger loss of mass caused by the IMF to the north of the TC, the geopotential height in the north of the TC decreases at a higher rate, which subsequently results in the WPSH break and thus facilitates the northward turning of the TC in EM and EL experiments.