Dependence of Tropical Cyclone Weakening Rate in Response to an Imposed Moderate Environmental Vertical Wind Shear on the Warm‐Core Strength and Height of the Initial Vortex

This study investigated the dependence of the early tropical cyclone (TC) weakening rate in response to an imposed moderate environmental vertical wind shear (VWS) on the warm‐core strength and height of the TC vortex using idealized numerical simulations. Results show that the weakening of the warm core by upper‐level ventilation is the primary factor leading to the early TC weakening in response to an imposed environmental VWS. The upper‐level ventilation is dominated by eddy radial advection of the warm‐core air. The TC weakening rate is roughly proportional to the warm‐core strength and height of the initial TC vortex. The boundary‐layer ventilation shows no relationship with the early weakening rate of the TC in response to an imposed moderate VWS. The findings suggest that some previous diverse results regarding the TC weakening in environmental VWS could be partly due to the different warm‐core strengths and heights of the initial TC vortex.

We conjecture that the uncertainty in the effect of moderate environmental VWS may arise from the dominant role of different ventilation pathways mentioned above.The mid-and upper-level ventilations suggest the "topdown" pathway of TC weakening.Namely, the warm-core structure of the TC weakens from the top down in response to an imposed environmental VWS (Alland et al., 2021b;Frank & Ritchie, 2001;Fu et al., 2019;Gray, 1968;Tang & Emanuel, 2010).The low-level ventilation hypothesis suggests the "bottom-up" weakening of the TC, namely the TC weakening is triggered by the decrease of eyewall entropy in the boundary layer (Alland et al., 2021a;Gu et al., 2015;Riemer et al., 2010).Fu et al. (2019) pointed out that the ventilation of the upperlevel warm core played the most important role in TC weakening in response to an imposed moderate upper-level and lower-level VWS, respectively, during the mature stage of the TC.Their results supported the "top-down" pathway of TC weakening, while results of Riemer et al. (2010) seemed to support the dominant role of the lowlevel ventilation in TC weakening by adding the moderate to strong deep-layer VWS to the TC during its intensifying stage.Therefore, the way by which an imposed moderate environmental VWS affects the TC intensity change, particularly the predominant pathway of initial TC weakening process, has not been fully understood.
The "upper-level ventilation" pathway is closely related to the weakening of the warm core.A question arises as to how the TC weakening rate in response to the imposed moderate environmental VWS depends on the intensity and thus the warm-core strength and height of the initial TC vortex.Previous studies have conducted numerical experiments using either initially weak or strong TCs, and thus with different warm-core strengths and heights (Fu et al., 2019;Gu et al., 2015;Onderlinde & Nolan, 2017;Reasor et al., 2013).Riemer et al. (2010) found in their idealized simulation that for mature storms the moderate to strong VWS might produce persistent vortex-scale downdrafts, flushing the boundary layer and leading to the TC weakening.However, Nguyen et al. (2019) focused on relatively weak TCs and found that enhanced surface enthalpy flux produced by high surface winds of intensifying TCs allowed downdraft-modified boundary layer air to recover effectively and quickly.Riemer and Montgomery (2011) found that stronger TCs are more resilient to radial ventilation.These studies seem to suggest that weak TCs are less resistant to moderate to strong VWS than strong TCs.However, many other studies have shown that weaker TC vortices can intensify rapidly in moderate environmental VWS after a period of adjustment (Molinari et al., 2006;Rios-Berrios, 2020;Rios-Berrios et al., 2016).
Most above studies have focused only on one category of weak or strong sheared TCs.However, few studies have focused on TCs at different intensifying stages under the influence of an imposed moderate environmental VWS.Finocchio and Rios-Berrios (2021) described a set of idealized simulations using the point-downscaling method in which VWS increases from 3 to 15 m s 1 at different stages of an intensifying TC.They found that all experiments exhibited hindered TC intensification, and TCs exposed to increasing shear during or just after rapid intensification tended to weaken the most.However, their study focused on strong environmental VWS, which increases with time to reach 15 m s 1 .As mentioned above, the diverse intensity changes have been reported in previous studies for TCs embedded in moderate environmental VWS.
In a recent study, Gao and Wang (2023) found a strong dependence of TC weakening in response to an imposed moderate VWS on the stage of an intensifying TC.Since the different stages of the intensifying TC correspond to different warm-core strengths and heights of the TC, they hypothesized that the TC intensity change rate in response to an imposed moderate VWS might depend on the warm-core strength and height of the initial TC vortex, which was defined as the maximum potential temperature (θ) anomaly over the TC center relative to the TC environment (Xi et al., 2021).The environmental θ at a certain level was defined as the mean θ of the outermost grids in four directions in the outermost domain.Because Gao and Wang (2023) focused on how the asymmetric structure of the initial TC vortex affects the TC intensity change in response to an imposed moderate VWS, they did not examine the detailed physical processes.This study can be considered as an extension of Gao and Wang (2023) with the focus on the dependence of the initial weakening rate of an intensifying TC on the warm-core strength and height in response to an imposed moderate VWS on an f-plane using idealized numerical experiments performed in Gao and Wang (2023).

Model and Experimental Design
The three-dimensional, compressible, nonhydrostatic, full-physics Weather Research and Forecasting (WRF) model version 4.2.2 (Skamarock et al., 2008) was used to conduct a series of numerical experiments as in Gao and Wang (2023).All numerical experiments were conducted on an f-plane at 15°N over the ocean with a uniform sea surface temperature of 28.5°C.The initial unperturbed sounding of the model atmosphere was the moist-tropical sounding documented in Dunion (2011).The initial TC vortex in the control experiment was axisymmetric and in gradient and thermal wind balance as in Rotunno and Emanuel (1987) with a maximum tangential wind speed of 18 m s 1 near the surface at a radius of 90 km.The other model settings and experimental design are the same as those described in Gao and Wang (2023) and thus are not repeated here.The vertical profile of the environmental zonal winds is showed in Figure 1a (inset vignette).Only results from four VWS experiments with an initially axisymmetric TC vortex in Gao and Wang (2023) are used in this study.Namely, in these experiments, the moderate environmental VWS was imposed onto an initially axisymmetric vortex after 24 (SHE24_AXI), 48 (SHE48_AXI), 72 (SHE72_AXI), and 96 hr (SHE96_AXI) of the simulation during the TC intensifying period in a quiescent environment experiment (CTRL), respectively.

Figures 1a and 1b
show the time evolutions of the TC intensity in terms of the central sea level pressure and the maximum azimuthally averaged total wind speed at the lowest model level (30 m above sea level) in CTRL (black) and four VWS experiments initialized with the axisymmetric TC vortices after 24, 48, 72, and 96 hr of the simulation in CTRL (colored), respectively.We can see that the TC experienced a reduced intensification rate in the early intensifying stage (SHE24_AXI and SHE48_AXI), while the TC experienced obvious weakening when the moderate VWS was imposed onto the TC vortices at the later intensifying stage (SHE72_AXI and SHE96_AXI).The TC weakening rate increases roughly with the increasing initial TC intensity at the time when the VWS is added (Figures 1c and 1d).
The initial vortices at the time when the moderate environmental VWS was introduced correspond to different warm-core strengths and heights at different intensifying stages of the TC (Figures 2a-2d).The initial TC vortex in SHE24_AXI had a very weak and lower upper-level warm core (Figure 2a), with a weak θ anomaly maximized near 8 km altitude.The warm core intensified with positive θ tendency (Figure 2e) even after the VWS was introduced, indicating that the VWS had little effect on the TC intensification at the early stage of an intensifying TC.The initial TC vortex in SHE48_AXI had a weak warm core centered at the height of 8 km (Figure 2b).The warm core weakened slightly after the VWS was introduced (Figure 2f), which is consistent with the slowed intensification followed by a slight weakening of the TC during the first 36 hr in SHE48_AXI.However, the initial TC vortices in SHE72_AXI and SHE96_AXI had stronger and higher (near the height of 15-16 km) upperlevel warm cores (Figures 2c and 2d).The strong and high warm core weakened significantly in response to the imposed moderate VWS.The θ tendency showed negative values from top down as the TC weakened (Figures 2g  and 2h).This strongly suggests that the weakening of the warm core is the important factor reflecting to the early weakening rate of the TC.As we can see from Figure 2i, which shows the θ tendency averaged between 10 and 16 km heights during 0-24 hr and the warm core strength in each VWS experiment, the θ tendency is almost linearly proportional to the warm-core strength of the initial TC vortex.
To understand the warm-core weakening processes of the simulated TCs in the shear experiments, we performed a budget analysis for the azimuthal mean potential temperature (θ) during the warm-core weakening stage in SHE72_AXI as an example.The budget equation can be given below (Stern & Zhang, 2013): (2) where u and w are the radial and vertical velocities, respectively, r and z are radius and height.In Equation 2, the overbar denotes the azimuthal mean, and the prime denotes the deviation from the corresponding azimuthal mean.The variables u, w, and θ are also output at 6-min intervals.The vortex center at the lowest model level was used to calculate the azimuthal mean.
Figure 3 shows the θ budget results for the 12-hr period from 6 to 18 hr of the simulation in SHE72_AXI during which the TC was in its early weakening stage (Figure 1).The actual θ change is mostly positive below 6 km height and negative above (Figure 3a).The large negative change in the layer between 14 and 16 km heights indicates the ventilation of θ in the upper troposphere, suggesting a top-down weakening of the warm core of the simulated TC in response to the imposed VWS.The budgeted θ change is generally consistent with the actual θ change (Figure 3b).Although some unavoidable discrepancies between the actual and the budgeted θ changes exist mainly due to the ignored HDIF, the decomposition and interpolation from the Cartesian coordinates to the cylindrical coordinates, the discrepancies are generally small.The large negative θ change inside a radius of 30 km in the upper troposphere was mainly contributed by advection terms (Figures 3e-3h).Since the mean vertical advection (Figure 3f) is nearly balanced by the contribution of diabatic heating (Figure 3d) in the eyewall region, the azimuthal mean and eddy radial advections dominated the negative θ change in the upper troposphere (Figures 3e and 3g) and thus the warm-core ventilation.The mean radial advection is smaller than the eddy horizontal advection, suggesting that the radial eddy advection was key to the upper-level warm-core ventilation.This is consistent with the result of Frank and Ritchie (2001).Note that the low-level ventilation in the boundary layer will be explained in detail later.
To understand how the high θ air within the upper-level warm core is transported outward, leading to the weakening of the warm core, we tracked the air particles using an advection correction trajectory algorithm following Dai et al. (2023), X. H. Liu et al. (2022), andMiller andZhang (2019).Since the warm core in SHE72_AXI was centered at about 15-16 km height, we chose 16 and 13 km as examples to show how the warmcore particles were transported outward and the surrounding particles were transported inward during the early TC weakening (Figures 4a,4b,4e,and 4f).We also calculated the change of θ e in the warm core during this stage.We selected 375 particles within the radius of 50 km from the TC center at the initial heights of 16 and 13 km and at the time of 6 hr (14 hr) after the VWS was introduced as the initial tracking warm-core particles and tracked them forward (backward) for 8 hr.We calculated the averaged θ e of the particles at the time of 6-hr based on the forward trajectory, which were transported outward from the region within the 50-km radius, which corresponded to air particles of the warm core.We also calculated the averaged θ e of the particles at the time of 14 hr based on the backward trajectory, which was transported inward from outside the 50-km radius and replaced the air in the original warm core from the outer core and weakened the warm core during this period.Combining the results of backward and forward trajectories, we found that the θ e decreased by 7.28 K during the 8 hr at the 16-km height and by 1.5 K at the 13-km height due to the radial export of warm parcels in SHE72_AXI.Since the warm core centered at around the 8-km height in SHE24_AXI, we also conducted the same trajectory analysis for SHE24_AXI to make a comparison with SHE72_AXI but at the heights of 10 and 8 km (Figures 4c,4d,4g,and 4h).Results show that θ e increased by 0.82 K during the 8 hr at the 10-km height and by 0.83 K at the 8-km height instead of weakening like in SHE72_AXI, which is consistent with the intensification of the TC during this period.To further illustrate the VWS effect, we also show the corresponding results with no-shear environment in CTRL in Figures S1 and S2 in Supporting Information S1.We can see that there are much less particles that are transported outward from the warm core and the θ e in the warm core increased, especially at the height of 16 km in SHE72_AXI, during the 8 hr.Therefore, the comparisons between these results clearly demonstrate that the VWS substantially enhanced the radial ventilation in the upper levels compared to the no-shear environment.
As we can see from Figure 4, the stronger environmental flow at higher levels led to stronger eddy outflow, which transported more warm particles outward, leading to the stronger upper-level ventilation for the TC with a stronger and higher warm core (Figures 2a-2d) and thus weakening of the TC as inferred from the hydrostatic relationship (Durden, 2013;Ohno et al., 2016;Shi & Chen, 2021).The stronger initial TCs (SHE72_AXI and SHE96_AXI) with higher-level warm core are subject to stronger outflow induced by the imposed VWS and thus larger weakening rate of the warm core and the TC (Figure 3 and Figure S5 in Supporting Information S1), while the weaker initial TCs (SHE24_AXI and SHE48_AXI) with weaker and lower warm core are subject to relatively weaker eddy outflow and thus weaker ventilation of the warm core and less weakening of the TC (Figures S3 and S4 in Supporting Information S1).In the very early intensifying stage (SHE24_AXI), the warm core of the TC is too weak and too low to be ventilated, and thus the TC is little affected by the imposed moderate VWS (Figure S3 in Supporting Information S1).The TC in SHE96_AXI weakened slightly more rapidly than that in SHE72_AXI mainly because the upper-level warm core and thus the upper-level ventilation is stronger in the former than in the latter (Figure S5 in Supporting Information S1).Therefore, the stronger the initial vortex with a stronger and higher warm core, the more the initial weakening of the TC in response to an imposed moderate VWS.
The above discussion focuses mainly on the weakening due to the upper-level ventilation associated with the warm-core structure.Since previous studies have also demonstrated the importance of boundary layer ventilation to the TC weakening in environmental VWS (e.g., Gu et al., 2015;Riemer et al., 2010), it is of interest to further examine the boundary-layer ventilation during the early weakening stage of the TC when the upper-level ventilation obviously occurred.We calculated the low-level ventilation, which is the sum of the radial and downdraft ventilations averaged in the boundary layer.The radial ventilation is defined as ρu′θ ′ e (u′ < 0) and the downdraft ventilation is defined as ρw′θ ′ e (w′ < 0), where ρ is density, u′ and w′ are asymmetric radial and vertical velocities, and θ ′ e is the perturbation equivalent potential temperature from its azimuthal mean.The positive radial ventilation represents the radial eddy flux of anomalously low θ e air into the inner core, as defined in Tang and Emanuel (2010), and the positive downdraft ventilation represents the downward transport of anomalously low θ e air into the boundary layer, as discussed in Riemer et al. (2010).
Figures 5a-5d show the horizontal distribution of the low-level ventilation averaged within the boundary layer and in the first 24 hr after shear was imposed.To quantify these values, we calculated the averaged values within the inner core (3 times the radius of the maximum wind) and found that the averaged low-level ventilations in four shear experiments were 10. 03, 12.13, 12.06, 11.42 kg K m 2 s 1 , respectively, which showed no clear relationship with the early TC intensity change rate.Figure 5e shows the time evolution of low-level ventilation averaged in the inner core during the first 30 hr of shear experiments, which does not show any clear relationship with the TC weakening rate.Therefore, we can conclude that the different early TC intensity change rates among the four shear experiments resulted mainly from the upper-level ventilation with little contributions by the lowlevel ventilation.

Conclusions
In this study, idealized numerical experiments were conducted to investigate the dependence of TC intensity change rate in response to an imposed environmental moderate deep-layer VWS on the initial warm-core strength and height during the TC intensifying period on an f-plane.Results show that the weakening of the upper-level warm core is the primary factor to the early TC weakening in response to an imposed moderate environmental VWS.The stronger and higher the warm core of the initial TC vortex is, the stronger the upper-level ventilation and thus the larger weakening rate of the upper-level warm core and the TC in response to the imposed moderate VWS.At the early intensifying stage with a weak and lower warm core, the TC intensification is little affected by the imposed moderate VWS because there is almost no significant warm-core ventilation.However, at the later Geophysical Research Letters 10.1029/2023GL107779 intensifying stage when the warm core becomes stronger and higher, the upper-level warm-core implies relatively strong ventilation, resulting in a great weakening of the upper-level warm core and thus the TC.
Results from the azimuthal mean potential temperature (θ) budget reveal that the weakening of the upper-level warm core was largely contributed by the eddy radial advection.Namely, the stronger and higher asymmetric outflow transports the inner-core high θ air outward downshear and downshear-left, as demonstrated by the trajectory analysis, leading to the weakening of the upper-level warm core and thus the TC.In addition, we also show that the magnitudes of the low-level ventilation do not exhibit any clear differences among all shear experiments, suggesting that the different rates of TC intensity change among different shear experiments resulted primarily from the upper-level ventilation in the early response of the TC to the imposed environmental VWS.
Our findings are supported by recent case studies by Rogers et al. (2020) and Stone et al. (2023), who showed that Hurricane Hermine (2016) and Hurricane Sally (2020) experienced intensification in their early weak stage (with weak warm core) in the presence of moderate VWS.Our results also support the result of Finocchio and Rios-Berrios (2021) and Fu et al. (2019) who found that the environmental VWS caused the more significant TC weakening at the later intensification stage of the TC in moderate VWS.Although Riemer et al. (2010) found the importance of the low-level ventilation to TC weakening in environmental VWS, their results might be applicable to the environment with VWS over 15 m s 1 and a relatively dry mid-troposphere.The findings from this study can help understand why some TCs can develop under the influence of the moderate environmental VWS while some others cannot.The key to the rate of TC intensity change in response to an imposed environmental VWS could be the different warm-core strengths and heights of the initial TC vortices.In addition, we would mention that the upper-level ventilation may be sensitive to the inner-core (warm-core) size of a TC.Namely, a larger TC with a large-sized warm core could have a stronger resilience to an imposed moderate environmental VWS.This can explain why larger TCs weaken less in environmental VWS as found in previous studies (e.g., Bi et al., 2023;Wong & Chan, 2004).

Figure 1 .
Figure 1.Time evolutions of (a) the simulated central sea level pressure (hPa), (b) the maximum near-surface wind speed (m s 1 ) in CTRL (black) and in all easterly vertical wind shear (VWS) experiments (colored), and (c, d) the differences from their corresponding values at the initial time in CTRL.The inset vignette indicates the vertical profile of the environmental zonal wind.The colors represent the VWS experiments as given in each panel.

Figure 2 .
Figure 2. (a-d) Time-height cross section of the θ anomaly (shading; K) and (e-h) the θ tendency (shading; K h 1 ) averaged within a radius of 50 km from the surface tropical cyclone (TC) center obtained from the model output at 6-min intervals during the simulations, along with the time evolution of the central sea level pressure anomaly of the TC in each vertical wind shear (VWS) experiment (black solid, hPa, right axis).(i) The scatter plots (dots) of the warm-core strength (K) versus the θ tendency (K h 1 ) averaged between 10 and 16-km heights during 0-24 hr in VWS experiments, the gray line shows the linear fitting.

Figure 3 .
Figure 3. Radial-height cross sections of θ budget terms (K h 1 ; shading).(a) The actual 12-hr change of θ, (b) the sum of the right-hand side of Equation 1; terms on the right-hand side contributed by (c) PBL; (d) diabatic heating (HEAT); (e) the azimuthal mean radial advection (RADVM); (f) the azimuthal mean vertical advection (VADVM); (g) eddy radial advection (RADVE); (h) eddy vertical advection (VADVE), based on the model output at 6-min intervals from 6 to 18 hr of the simulation in SHE72_AXI.Contours in (e) and (f) are the radial wind speed and vertical motion, respectively (m s 1 , solid is positive and dashed is negative).

Figure 4 .
Figure 4. (a, b, e, f) The horizontal distribution of θ (shading; K) at z = 16 and 13 km heights after the 6-hr simulation with shear, superposed with the following 8-hr horizontal trajectories (gray lines) in SHE72_AXI with red (orange) points (in the lime circle) and green (blue) crosses indicating the beginning and ending points of the forward (backward) trajectories, respectively.The start times for the forward and backward trajectories are 6 and 14 hr of shear simulation, and the start levels are 16 and 13-km heights, respectively.The black arrows indicate the direction of the environmental vertical wind shear (VWS), and the dashed black circles are plotted every 100 km from the tropical cyclone (TC) center.(c, d, g, h) As in (a, b, e, f) but for SHE24_AXI at the 10-km and 8-km heights, respectively.

Figure 5 .
Figure 5. (a-d) Low-level ventilation (kg K m 2 s 1 ) averaged below z = 1.5 km in the 24-hr period after the vertical wind shear (VWS) was imposed.Red shading means radially inward and vertically downward transport of anomalously low θ e air.The area within the black dashed big circle indicates the inner core and the small circle nearly indicates the central location of the eyewall.The gray arrows indicate the direction of the environmental VWS; (e) time evolutions of the low-level ventilation (kg K m 2 s 1 ) averaged in the inner core up to 30 hr in the shear experiments.The red, orange, green and blue colors represent the VWS experiments with tropical cyclone vortices after 24, 48, 72, and 96 hr of the simulation in CTRL, respectively.