1. Introduction
Tropical cyclones generally exist in environments with some degree of vertical wind shear. Although vertical wind shear tends to hinder intensification (DeMaria 1996; Gallina and Velden 2002; Tang and Emanuel 2012), a small-to-moderate level does not prohibit a weak tropical cyclone from eventually gaining strength. One realistic scenario is for such a tropical cyclone to experience a sharp transition from slow to relatively fast spinup on its way to becoming a hurricane. The present study investigates the changes that must take place within a tropical cyclone for such a transition to occur in cloud-resolving simulations.
Previous studies have suggested that slow intensification is often linked to a shear-induced horizontal separation of the low-level and midlevel vortex centers, which is commonly referred to as a misalignment or tilt of the tropical cyclone. A substantial misalignment generally coincides with a concentration of inner-core convection far downtilt1 from the center of the surface circulation (Stevenson et al. 2014; Nguyen et al. 2017; Fischer et al. 2024), where it is theoretically inefficient in driving spinup (Schecter 2020; cf. Vigh and Schubert 2009; Pendergrass and Willoughby 2009). Factors apparently contributing to the detrimental downtilt localization of convection include a stabilizing warm temperature anomaly and an updraft-limiting depression of relative humidity above an area covering the central and uptilt regions of the boundary layer vortex. A number of earlier papers have illustrated how the warm anomaly and relative humidity deficit can result from the subsidence of incoming middle-tropospheric air (Dolling and Barnes 2012; Zawislak et al. 2016; Schecter 2022; henceforth S22). The literature has further noted that the warm anomaly goes hand in hand with the tilted vortex maintaining a state of approximate nonlinear balance (Jones 1995; DeMaria 1996; S22).
There is a common understanding that tilt-enhanced “ventilation” may either work in concert with the effects of mesoscale subsidence and thermal wind balance to hinder intensification or have a dominant role in suppressing spinup (Tang and Emanuel 2012; Riemer et al. 2010, 2013; Ge et al. 2013; Riemer and Laliberté 2015; Alland et al. 2021a,b; Fischer et al. 2023). To elaborate, a substantial misalignment may facilitate the intrusion of highly unsaturated environmental air above a large section of the surface vortex and create a situation where downdrafts (associated with precipitation) more effectively reduce the moist entropy of boundary layer air that circulates within the inner core. Overall, this can help limit the areal spread of inner-core convection and weaken that which may exist downtilt. A diminishment of downtilt convection would compound the negative effect of its outward displacement on the ability of a tropical cyclone to strengthen.
The preceding discussion suggests that a sufficient reduction of tilt could eliminate the principal impediments to intensification and enable a transition to relatively fast spinup. Accordingly, a number of published studies have identified alignment as a typical precursor to a substantial acceleration of intensification (Zhang and Tao 2013; Munsell et al. 2017; Miyamoto and Nolan 2018; Rios-Berrios et al. 2018; Alvey et al. 2020; S22). One obvious avenue for reducing tilt is reducing the vertical wind shear to a negligible level so as to permit the tropical cyclone to freely align (Reasor and Montgomery 2001; Schecter and Montgomery 2003, 2007; Schecter and Menelaou 2020). However, tropical cyclones often have the capacity to align even if the wind shear persists at moderate strength. Various modeling studies have suggested that alignment amid moderate shear is facilitated by cyclonic precession of the tilt vector to and beyond the point of becoming perpendicular to the shear direction (Rappin and Nolan 2012; Zhang and Tao 2013; Tao and Zhang 2014; Finocchio et al. 2016; Onderlinde and Nolan 2016; Rios-Berrios et al. 2018). Among other considerations, the precession of the tilt vector from a downshear to an upshear orientation coincides with the neutralization and subsequent reversal of shear-related misalignment forcing (Jones 1995; Reasor et al. 2004; Schecter 2016). On the other hand, a major reduction of tilt in moderate shear does not necessarily require precession. For example, a tropical cyclone may align by “core (or center) reformation” even when the tilt vector points directly downshear (Molinari et al. 2004; Molinari and Vollaro 2010; Nguyen and Molinari 2015; Chen et al. 2018; Rogers et al. 2020; Alvey et al. 2022; Stone et al. 2023; Schecter 2023). The process typically entails strong convergence near vigorous downtilt convection causing a subvortex to strengthen underneath the central region of the midlevel vortex to the extent of becoming the new inner core of the low-level circulation. The pathways and time scales of alignment are clearly diverse, and they continue to be studied as part of an ongoing effort to better understand the timing for the onset of fast spinup.
That being said, some modeling and observational studies have suggested that alignment is not a prerequisite for a transition to relatively fast intensification (Chen and Gopalakrishnan 2015; Alvey and Hazelton 2022). The present study will corroborate those just referenced and investigate what apart from the initial tilt magnitude differentiates transitions that occur before and after alignment. Postalignment transitions have been shown to commonly occur after pronounced enhancements of lower-to-middle-tropospheric relative humidity (Chen et al. 2019; Alvey et al. 2020; S22) and lower-tropospheric CAPE (S22) averaged over the inner core of the surface vortex. Moreover, they generally follow appreciable azimuthal spreading of precipitation (Chen et al. 2019, 2021; Alvey et al. 2020; Rios-Berrios et al. 2018) and initiate a quasi-symmetric mode of intensification similar to that which may exist in a shear-free system (Montgomery and Smith 2014). Since the preceding features are coupled to the reduction of the tilt magnitude, they are not expected to be characteristics of transitions that occur before alignment. A number of the distinct thermodynamic and convective features of a prealignment transition and the highly asymmetric—but reasonably efficient—mode of intensification that immediately follows will be illustrated herein.
In short, the central contribution of this paper is the exposition of a binary classification system for transitions from slow to fast spinup that are found within a large and diverse set of tropical cyclone simulations. As explained above, the two classes of transitions are distinguished by the coinciding state of misalignment and the distinct mode of intensification that follows. Both prealignment and postalignment transitions will be seen to occur over a wide range of sea surface temperatures (SSTs) and during times of either weak or moderate environmental vertical wind shear. Similarities and differences between the present tilt-based classification of transitions to fast spinup and other binary conceptualizations of the process contained in earlier studies (Holliday and Thompson 1979; Harnos and Nesbitt 2011, 2016a,b; Judt et al. 2023) will be addressed after details of the former are expounded. Limitations of the binary classification system will also be discussed.
An important clarification is necessary before proceeding to discussions of methodologies and results. The concept of fast intensification employed for this study is broader than conventional definitions of rapid intensification (Kaplan et al. 2010; Li et al. 2022) in having no explicit minimum rate. Instead, fast intensification need only occur at a greater rate than a specified multiple of the preceding slow intensification rate (see section 2b). The probability of fast intensification considered in this relative sense under given environmental conditions may thus differ considerably from that of conventional rapid intensification (Kaplan and DeMaria 2003; Hendricks et al. 2010).
The remainder of this paper is organized as follows. Section 2 describes the essential features of the tropical cyclone simulations and explains the method used to identify transitions from slow to fast spinup. Section 3 demonstrates that the transitions generally fall into one of two well-separated categories chiefly distinguished by the coinciding state of vertical alignment. The kinematic and moist-thermodynamic features coinciding with the distinct tilt magnitudes of tropical cyclones during each type of transition are described, and the relevance of these features to enabling fast spinup is discussed. Section 4 qualitatively compares the results of section 3 to observed transitions to fast spinup in natural tropical cyclones. Section 5 summarizes all of the main findings of this study.
2. Methodology
a. Computational dataset
The tropical cyclones considered herein are from a heterogeneous set of roughly one hundred simulations conducted with Cloud Model 1 (CM1; Bryan and Fritsch 2002), for a variety of purposes including the present study. Heterogeneity of the computational dataset is considered beneficial by reducing (but not eliminating) methodological bias in the search for different types of transitions from slow to fast spinup.
While diverse, the simulations do have a number of basic features in common. To begin with, all simulations are conducted on a doubly periodic oceanic f plane at 20°N, with the Coriolis parameter f equaling 5 × 10−5 s−1. The SST is generally held constant in space and time. The initial environmental vertical temperature and relative humidity distributions above the sea surface are taken from the Dunion (2011) moist tropical sounding for hurricane season over the Caribbean Sea.
The physics parameterizations are fairly conventional. Each simulation incorporates a variant of the two-moment Morrison cloud-microphysics module (Morrison et al. 2005, 2009), having graupel as the large icy-hydrometeor category and a constant cloud-droplet concentration of 100 cm−3. Radiative transfer is accounted for by the NASA Goddard parameterization scheme (Chou and Suarez 1999; Chou et al. 2001). The influence of subgrid turbulence above the surface is accounted for by an anisotropic Smagorinsky-type closure analogous to that described by Bryan and Rotunno (2009). The horizontal mixing length lh in each simulation increases linearly from 100 to 700 m as the surface pressure decreases from 1015 to 900 hPa. The asymptotic vertical mixing length lυ is 50 m in most simulations but 70 m in a few. Surface fluxes are parameterized with bulk aerodynamic formulas. The momentum exchange coefficient Cd increases from a minimum of 10−3 to a maximum of 0.0024 as the surface (10 m) wind speed increases from 5 to 25 m s−1 (compare with Fairall et al. 2003; Donelan et al. 2004). The enthalpy exchange coefficient is given by Ce = 0.0012 roughly based on the findings of Drennan et al. (2007). Heating associated with frictional dissipation is activated. Rayleigh damping is imposed above an altitude of z = 25 km.
The equations of motion are discretized on a stretched rectangular grid that spans 2660 km in each horizontal dimension and 29.2 km in the vertical dimension. The 800 × 800 km2 central region of the horizontal mesh that contains the broader core of the tropical cyclone has uniform increments of 2.5 km; at the four corners of the mesh, the increments are 27.5 km. The vertical grid has 40 or 50 levels spaced 100 or 50 m apart near the surface, but farther apart aloft. When the number of levels Nz is 40 (50), the vertical grid spacing gradually grows to 0.7 and 1.4 km (0.6 and 1.1 km) as the height above sea level z increases to 8 and 29 km.
The vast majority of simulations are initialized with the nominal predepression (PD) vortex depicted in Fig. 1 of Schecter and Menelaou (2020). The azimuthal velocity υ of the PD vortex has a maximum value of 6.1 m s−1 located 3 km above the sea surface, at a radius r of 140 km from the central axis of rotation. The maximum of υ on the lowest model level is 4.1 m s−1. Moving outward (upward) from its peak, υ gradually decays until reaching zero at r = 750 (z = 10.5) km. The relative humidity in the core of the PD vortex is moderately enhanced relative to the environment. A small number of simulations are initialized with a modified Rankine (MR) vortex, corresponding to “iinit = 7” in the CM1 (release 21.0) configuration file. For these cases, υ has a maximum value of 15 m s−1 at r = 75 km on the lowest model level. Moving outward (upward) from its peak, υ gradually decays until reaching zero at r = 500 (z = 15) km. Both the PD and MR vortices are introduced in balanced axisymmetric states. While many (but not all) of the vortices are slightly perturbed with quasi-random noise in the lower potential temperature and water vapor fields, none are initially perturbed with coherent mesoscale asymmetries (cf. Nolan et al. 2024).
The principal differences between the simulations are in their SSTs and environmental shear flows. The SSTs range from 26° to 32°C. In general, the environmental shear flows are horizontally uniform and strictly zonal. Their diversity comes from variations of intensity, primary shear-layer characteristics, and time dependence.
Figure 1 illustrates the environmental shear flows described above and used herein. While these shear flows are essentially within the spectrum of those employed in earlier modeling studies of tropical cyclone intensification, one might imagine an infinite number of realistic alternatives. The literature suggests that the timing of fast spinup and details of the viable pathways to its onset could differ with the use of alternative shear flows in which us has an additional constant that reverses the surface velocity (Rappin and Nolan 2012), δzα is appreciably shortened (Finocchio et al. 2016), zα is shifted to a substantially different altitude (ibid.; Ryglicki et al. 2018a,b), or the wind direction rotates with height (Onderlinde and Nolan 2016; Gu et al. 2019).
(a) Vertical profiles of the environmental shear flow [us/ϒ given by Eq. (1)] with two slightly different parameterizations of the primary shear layer used for the simulations at hand. (b) Time dependence of the shear flow [ϒ given by Eq. (2)] with various ramp-down coefficients (ε↓) as indicated on each line.
Citation: Journal of the Atmospheric Sciences 81, 9; 10.1175/JAS-D-23-0223.1
The reader may consult appendix A for a more detailed account of the simulations examined for this study. Table A1 contained therein conveniently summarizes the variation of shear flow parameters considered at each SST, for both PD-type and MR-type initial vortex conditions. Computational nuances pertinent to certain simulation groups—and possibly relevant to reproducibility—are also addressed.
b. Identification of substantial transitions from slow to fast spinup
Let
A substantial transition from slow to fast spinup is said to occur at the time
Of further note, the forthcoming analysis only considers transitions that occur after a depression has formed and before the azimuthal-mean surface vortex achieves minimal hurricane intensity, marked by when Vm = 32.5 m s−1. Not all simulated tropical cyclones in the dataset used for this study were found to exhibit substantial transitions from slow to fast spinup during this developmental time frame (see Table A1).
3. Results
The present section of this paper examines the characteristics of substantial transitions from slow to fast spinup in the tropical cyclone simulations at hand. Discussion of how the results relate to observed tropical cyclone dynamics is mostly deferred to section 4.
a. Bimodal distribution of tropical cyclone asymmetry at the transition time
Transitional values of the precipitation asymmetry
Citation: Journal of the Atmospheric Sciences 81, 9; 10.1175/JAS-D-23-0223.1
The scatterplot shows that during the transition from slow to fast spinup, the projections of the tropical cyclone state vectors onto the μ–Pasym plane fall largely into one of two clusters, representing relatively symmetric (S) and asymmetric (A) conditions. Tropical cyclones in the S cluster (color-filled symbols) are characterized by
b. Illustrations of selected type S and type A transitions
Figure 3 illustrates the evolution of a tropical cyclone that begins a type S transition from slow to fast spinup at
Snapshots of the evolution of a tropical cyclone that undergoes a type S transition to relatively fast spinup. (a) Streamlines of the horizontal velocity fields in the approximate 1-km-deep boundary layer (white) and 1-km-deep middle-tropospheric layer centered 8 km above sea level (black with white trim) superimposed over the base-10 logarithm of the 2-h precipitation rate P normalized to P0 = 0.375 cm h−1 (color), 20 h before the transition time
Citation: Journal of the Atmospheric Sciences 81, 9; 10.1175/JAS-D-23-0223.1
Figure 4 shows selected snapshots of the evolution of a tropical cyclone that begins a type A transition at
Snapshots of the evolution of a tropical cyclone that undergoes a type A transition to relatively fast spinup. All panels are similar to those of Fig. 3, but the snapshots are taken at (a),(d)
Citation: Journal of the Atmospheric Sciences 81, 9; 10.1175/JAS-D-23-0223.1
c. Intensity and IR differences between systems that experience type S and type A transitions
Time series of (a) the maximum 10-m azimuthal velocity Vm normalized to the maximum potential intensity and (b) the IR normalized to the MPIR for systems that experience type S (red) and type A (blue) transitions to relatively fast spinup. Time is measured from
Citation: Journal of the Atmospheric Sciences 81, 9; 10.1175/JAS-D-23-0223.1
Figure 5a shows that the normalized tropical cyclone intensities during type S transitions (
For good measure, Table 1 shows the environmental variation of the dimensional values of
Environmental variation of tropical cyclone intensity and IR statistics for type S and type A transitions, each expressed as the mean ± one standard deviation for a given simulation group.
Given that substantial surface-vortex asymmetries can exist during early tropical cyclone development and generally extend beyond type A transitions, one might wonder whether the intensification curves in Fig. 5a would radically change upon replacing Vm with the absolute maximum grid value of the 10-m wind speed within the storm system. The latter metric is arguably somewhat closer to an observational standard, but it does not explicitly filter out wind gusts. Appendix C shows that switching to the absolute maximum 10-m wind speed reduces intensification differences preceding type S and type A transitions, but essentially maintains the 1-day posttransitional disparity.
d. Tilt magnitude and radius of maximum wind speed
Figure 6a shows how the tilt magnitude normalized to rm [μ defined by Eq. (4)] evolves during the time frame surrounding a transition to fast spinup. As before, separate time series are shown for systems experiencing type S and type A transitions. The disparity in the average value of μ during type S and type A transitions (Fig. 2) can be seen to extend to periods well before and well after
Time series of (a) the normalized tilt magnitude μ, (b) the dimensional tilt magnitude |xcu − xcl|, and (c) the low-level radius of maximum wind speed rm. Plotting conventions are as in Fig. 5.
Citation: Journal of the Atmospheric Sciences 81, 9; 10.1175/JAS-D-23-0223.1
In addition to having substantially larger values of μ, tropical cyclones evolving through type A transitions generally have larger dimensional tilt magnitudes (Fig. 6b) and values of rm (Fig. 6c) than tropical cyclones evolving through type S transitions. Previous studies have explicitly shown that both the tilt magnitude (Schecter and Menelaou 2020; Rios-Berrios 2020; Fischer et al. 2024) and rm (Carrasco et al. 2014; Xu and Wang 2015, 2018) tend to be anticorrelated to the IR of a tropical cyclone. One might therefore reasonably assume that the larger tilt and rm of a tropical cyclone evolving through a type A transition contribute to its smaller IRs on both sides of
Of further note, the average trends of the tilt magnitude and rm (Figs. 6b,c) differ between systems heading toward transitions of type S or A. Shortly before type S transitions, the group mean of the tilt magnitude sharply drops, while that of rm varies little. Before type A transitions, the group mean of the tilt magnitude modestly decays, while that of rm distinctly grows. The latter result hints that core expansion may sometimes appreciably contribute to the reduction of μ toward unity prior to the onset of fast spinup in relatively asymmetric tropical cyclones.
e. The tilt angle
Figure 7 shows the evolution of the angle φtilt between the tilt vector and the unit vector pointing downshear (
Time series of the tilt angle; plotting conventions are as in Fig. 5.
Citation: Journal of the Atmospheric Sciences 81, 9; 10.1175/JAS-D-23-0223.1
f. Tropical cyclone convection
Thus far, the analysis has focused on differences in vortex parameters during the time frames surrounding type S and type A transitions. The following examines additional differences in various parameters associated with convection.
Figure 8a shows time series of Pasym, which measures the azimuthal asymmetry of the inner-core precipitation field as explained in section 3a. The precipitation asymmetry well before a type S transition [
Time series of parameters characterizing the spatial distributions of precipitation and low-level convergence. (a) The precipitation asymmetry Pasym. (b) The precipitation radius rp (thick dark curves, light shading) compared to the mean of rm (thin dark curves). (c) The distance
Citation: Journal of the Atmospheric Sciences 81, 9; 10.1175/JAS-D-23-0223.1
Figure 8b shows the time series of the nominal precipitation radius rp defined as follows: Let
Of additional interest are the properties of the initially asymmetric low-level convergence field σl ≡ −∇ ⋅ ul that is often enhanced in the vicinity of downtilt convection and plays an important role in local vertical vorticity production through the forcing term ηlσl. Here, ul and ηl are the horizontal velocity field and absolute vertical vorticity in the 1-km-deep boundary layer adjacent to the sea surface. Figure 8c illustrates the evolution of two parameters characterizing the spatial distribution of σl. The first parameter
Before a transition to relatively fast spinup,
Figure 8d further reveals that typical type A transitions are preceded by rapid contraction of the distance between the low-level convergence center and the midlevel vortex center, given by
Having breached the topic of convective intensity, it is now fitting to examine whether precipitation rates and vertical mass fluxes differ during transitions of type S and type A. Figures 9a–c show the evolution of the normalized 2-h surface precipitation rate P averaged within a radius R of 200, 100, or 35 km from xσ (in panels a, b, and c, respectively). To limit the variability associated with the amplification of precipitation as the ocean temperature warms in the model (cf. Lin et al. 2015), P is multiplied by a scaling factor ξ that increases from a base value of 1 as the SST decreases from 32°C (see appendix B). For R = 200 km, there is minimal difference in the steady growth of P leading up to transitions of type S or A. Upon reducing R to 100 km, a secondary oscillation becomes more noticeable, with a distinct plateau or peak (marked by an arrow for each time series in Fig. 9b) occurring shortly before or during the onset of a symmetrization trend (cf. Fig. 8a) and a trough occurring afterward. Whereas a type S transition coincides with the trough of the P oscillation, a type A transition coincides with the peak. Upon reducing R to 35 km, so as to focus on the small end of meso-β-scale convective activity centered on xσ, the nominal oscillation becomes a major feature of the time series. Moreover, the magnitude of P during a type A transition (near
Time series of parameters associated with the strength of convection. (a)–(c) The 2-h precipitation rate P and (d)–(f) the lower-middle-tropospheric vertical mass flux M averaged within (a),(d) 200 km, (b),(e) 100 km, and (c),(f) 35 km of the low-level convergence center xσ. The precipitation rates in (a)–(c) are adjusted to compensate for increasing precipitation at higher SSTs as explained in section 3f and appendix B. The arrows in (b) point to the initial plateau or peak phase of the secondary oscillations mentioned in the main text for the S (red) and A (blue) simulation groups. All other plotting conventions are as in Fig. 5.
Citation: Journal of the Atmospheric Sciences 81, 9; 10.1175/JAS-D-23-0223.1
Figures 9d–f show complementary time series of the vertical mass flux M located 5.2–5.4 km above sea level, averaged as before within a radius R of 200, 100, or 35 km from xσ (in panels d, e, and f, respectively). The composite-mean time series at other altitudes examined for z between 3 and 11 km are virtually proportional to those shown, but (for R < 200 km) generally decrease in magnitude from the middle to upper troposphere. Moreover, the plotted time series of M are qualitatively similar to those of P, especially when R is 100 or 35 km. Such similarity provides reasonable grounds for assuming that the aforementioned peaks and troughs of P in the vicinity of the convergence zone coincide with relatively high and low degrees of moderate-to-deep convective activity. A more detailed analysis of how P divides into contributions from various types of cumuliform and stratiform clouds is deferred to future study.
The mean drops of P and M in the vicinity of the convergence zone shortly preceding a type S transition suggest that the coinciding quasi-symmetrization is here more relevant for the switch to fast spinup than the strengthening of localized convection (cf. Schecter 2022). By contrast, the pronounced peaks of P and M found in the neighborhood of the convergence zone during a type A transition suggest that exceptionally strong convection therein may be required to initiate relatively fast intensification of Vm when the tilt magnitude, rm, and
g. Moist-thermodynamic structure of the tropical cyclone
1) Illustrative examples
Distributions of (a),(d) LCAPE, (b),(e) lower-to-middle-tropospheric RH, and (c),(f) boundary layer equivalent potential temperature θel in a tropical cyclone (top) 20 h before a type S transition begins [
Citation: Journal of the Atmospheric Sciences 81, 9; 10.1175/JAS-D-23-0223.1
Well before the type S transition, the moist-thermodynamic structure of the tropical cyclone seems qualitatively consistent with expectations from past observational studies of tilted tropical storms (such as Dolling and Barnes 2012). To begin with, low and negative values of LCAPE pervade the inner core of the surface vortex, except within a downtilt sector that extends moderately upwind (Fig. 10a). Precipitation-cooled downdrafts bringing low-entropy air into the boundary layer presumably contribute substantially to the peripheral depression of LCAPE that extends appreciably downwind from the downtilt convection zone (located near the ×). However, the depression of LCAPE in the immediate and uptilt neighborhood of the low-level vortex center xcl (marked by the +) may be mostly linked to a positive temperature anomaly in the lower free troposphere5 that is required to maintain approximate nonlinear balance in a tilted tropical cyclone. Otherwise, the depression would seem inconsistent with the presence of relatively high values of θel near xcl (see Fig. 10c). Of equal importance, the lower-to-middle-tropospheric RH fails to exceed 70% in the uptilt semicircle of the inner core and is lower than 60% near xcl (Fig. 10b). Whether the foregoing convection-limiting RH deficiency results more from the influx of dry environmental air (midlevel ventilation) or the subsidence of middle-tropospheric air originating from the more humid downtilt sector of the tropical cyclone (S22) has not been determined for this particular system.
Once the transition to faster spinup officially begins upon a substantial reduction of the tilt magnitude, LCAPE and RH can be seen to have grown throughout previously deficient regions of the inner core (Figs. 10d,e). Figure 10f suggests that a boost of moist entropy in the boundary layer contributes to the growth of LCAPE. A fuller account of how the enhancements of both LCAPE and RH arise will be given shortly in a broader context. One might reasonably hypothesize that these enhancements facilitate a more symmetric distribution of convection that can readily move inward. In other words, the spread of favorable conditions for convection throughout the central disk of radius rm would seem to enable the initiation of the ensuing quasi-symmetric mode of intensification that entails early contraction of the inner core.
Figure 11 shows 2-h averages of LCAPE, lower-to-middle-tropospheric RH, and θel centered 27 h before and 1 h after the start time
Distributions of (a),(d) LCAPE, (b),(e) lower-to-middle-tropospheric RH, and (c),(f) boundary layer equivalent potential temperature θel in a tropical cyclone (top) 27 h before a type A transition begins [
Citation: Journal of the Atmospheric Sciences 81, 9; 10.1175/JAS-D-23-0223.1
2) Group comparison
The following presents composite analyses of selected moist-thermodynamic fields in tropical cyclones that experience type S or A transitions to fast spinup. A discussion of field averages within the xcl-centered inner core of the tropical cyclone is followed by a discussion of field averages in the vicinity of the low-level convergence center xσ.
Figures 12a and 12b respectively show the time series of the lower-to-middle-tropospheric RH (defined as in Figs. 10 and 11) and LCAPE averaged within a radius rm of the low-level vortex center xcl for systems that experience type S (red) and type A (blue) transitions to fast spinup. As in previous plots, solid dark curves represent group means and the semitransparent background shading extends from the 20th to 80th percentile of the plotted variable. Averages over the entire inner core such as those considered here will be denoted by the subscript “ic” from this point forward.
(a),(b) Time series of lower-to-middle-tropospheric RH in (a) and LCAPE in (b) averaged over the entire inner-core region of the low-level vortex. Plotting conventions are as in Fig. 5. (c),(d) Time series of lower-to-middle-tropospheric RH in (c) and LCAPE in (d) averaged within each inner-core octant [oct ∈ {0, 1, …, 7}] for systems that undergo type S transitions. Each curve represents the mean for all such systems. The octants are shown in Fig. 13. (e),(f) As in (c) and (d), but for systems that undergo type A transitions.
Citation: Journal of the Atmospheric Sciences 81, 9; 10.1175/JAS-D-23-0223.1
In agreement with the first example considered above (Fig. 10), the two figures at hand (Figs. 12a,b) show that type S transitions generally coincide with peaks of RHic and LCAPEic that follow pronounced troughs. By contrast, type A transitions are seen to typically begin while RHic and LCAPEic are depressed (as in Fig. 11). Although LCAPEic does not appreciably grow after a type A transition, RHic generally exhibits a prominent posttransitional peak. Such mean humidification of the inner core is apparently a common feature of (as opposed to a trigger for) the fast intensification mechanism that involves progressive vertical alignment of the tropical cyclone and contraction of rm (Figs. 4 and 6).
Figures 12c and 12d respectively show composite time series of octant-averaged inner-core values of lower-to-middle-tropospheric RH and LCAPE in systems that experience type S transitions. Figures 12e and 12f are similar, but for systems that experience type A transitions. Figure 13 diagrammatically defines the octants; the octant number increases in the counterclockwise direction from 0, which corresponds to the octant centered directly downtilt. Figures 12c and 12d verify that the enhancements of RHic and LCAPEic immediately preceding type S transitions largely result from enhancements of RH and LCAPE in the octants completely or partly within the uptilt semicircle (2–6). Figure 12e suggests that while the octants with large azimuthal displacements from the tilt vector (2–6) continually lose RH leading up to type A transitions, the octants along the tilt vector and immediately upwind (0 and 7) start gaining RH prior to
Division of the inner core of the low-level vortex into octants labeled 0–7. Each octant extends to a radius rm from the vortex center (+). Notably, octant 0 is centered directly downtilt at 0°, whereas octant 4 is centered directly uptilt at 180°. The arrows on the thin central circle convey the approximate direction of the cyclonic surface winds.
Citation: Journal of the Atmospheric Sciences 81, 9; 10.1175/JAS-D-23-0223.1
While informative, Fig. 12 does not reveal how the pretransitional and transitional moist-thermodynamic conditions of the inner core might vary with the environment of the tropical cyclone. Table 2 shows the environmental variations of RHic and LCAPEic during type S and A transitions to fast spinup. Also shown are the changes in both variables leading up to the transitions. Such changes are defined by
Environmental variation of inner-core thermodynamic statistics associated with type S and type A transitions, each expressed as the mean ± one standard deviation for a given simulation group. The third column from the left gives the sample sizes for the transitional values (
Figure 14 shows the changes in the vertical profiles of the absolute temperature (ΔT), the water vapor mixing ratio (Δqυ), and the relative humidity (ΔRH) prior to type S transitions at a moderate SST (28°C) and a warm SST (32°C). The results shown correspond to averages within a radius r of 25 km from the low-level vortex center xcl and within the annulus defined by 25 ≤ r ≤ 50 km. These fixed areas generally cover much of the inner core of a tropical cyclone during the time of fast spinup after a type S transition when rm contracts (on average) from a radius just outside to well inside the annulus (Fig. 6c). The results at 28°C (32°C) are qualitatively similar to those for any cool-to-moderate (warm) SST. In both cases, the day preceding
(a),(b) Changes in absolute temperature ΔT (green) and the water vapor mixing ratio Δqυ (purple) during the day leading up to a type S transition at an SST of 28°C, averaged over a circular disk of radius r = 25 km from the low-level vortex center xcl in (a) and over the annulus defined by 25 ≤ r ≤ 50 km in (b). The dark solid or dashed curve represents the z-dependent mean of the plotted variable for all pertinent simulations, whereas the color-matched semitransparent shading extends horizontally from the z-dependent 20th to 80th percentile. (c) Corresponding group-mean changes in RH averaged over the disk of panel (a) (solid curve) and annulus of panel (b) (dashed curve). The inset shows the group-mean change in LCAPEic (circle); the error bars extend from the 20th to 80th percentile. (d)–(f) As in (a)–(c), but for simulations with an SST of 32°C.
Citation: Journal of the Atmospheric Sciences 81, 9; 10.1175/JAS-D-23-0223.1
The preceding discussion focused on the moist-thermodynamic conditions of the inner core of the tropical cyclone over a relatively short time frame surrounding a transition to fast spinup. Before moving on, it is worthwhile to comment on some additional aspects of the broader time series of RHic (Fig. 12a) and LCAPEic (Fig. 12b). To begin with, both variables decay following alignment at or after
The next issue to be addressed is whether there exists a consistent change in the moist-thermodynamic conditions of the convergence zone that could trigger a type A transition. Figures 15a and 15b respectively show the time series of the lower-to-middle-tropospheric RH and LCAPE averaged within 35 km of the convergence center xσ. The foregoing average will be denoted by the subscript “cz.” Here, the group mean of RHcz is fairly high (91%–96%) before and during transitions of either type S or type A. The previously seen “major” enhancement of RH above the moving convergence zone leading up to a type A transition [section 3g(1)] does not appear to be universal. Although a small change could theoretically cause an instability, the author would be surprised if a modest rise of RHcz starting from 91% (or so) is necessary for enabling the fast spinup of an asymmetric tropical cyclone.7 The mean values of LCAPEcz are also seen to be relatively high before and during transitions of either type S or type A. The slightly negative trend seen before a type A transition (also seen before a type S transition) would seem to disprove any notion that a local boost of LCAPE enables the amplification of convection in the convergence zone during that transition (Figs. 9c,f). In summary, the values of RHcz and LCAPEcz on average seem to be suitable for the onset of fast spinup any time before a type A (or S) transition actually occurs.
Time series of (a) lower-to-middle-tropospheric RH and (b) LCAPE averaged within 35 km of the convergence center xσ for type S (red) and A (blue) transitions. Plotting conventions are as in Fig. 5.
Citation: Journal of the Atmospheric Sciences 81, 9; 10.1175/JAS-D-23-0223.1
h. Core reformation
One of the most dramatic transformational events in a tropical cyclone that can be linked to the onset of fast spinup is core (or center) reformation. As noted in section 1, the process typically involves the rapid emergence of a strong subvortex in the downtilt convection zone that within a few hours dominates the broader parent cyclone and takes over as the inner core. The question at hand is how transitions via core reformation fit into the quasi-binary classification scheme proposed herein. The main issue is whether core reformation occurs before, after, or during the transition period. If core reformation were to occur appreciably before
Clear-cut permanent core reformation events are not very common in the simulations under consideration, but occasionally take place. One particular event occurring in a system with an SST of 32°C and a 0–12-km shear magnitude of 10.5 m s−1 will be considered for illustrative purposes. Figure 16a shows the time series of Vm. A prominent spike occurs within the short (6 h) period after
Special type A transition involving core reformation. (a) Time series of Vm; the spacing between dots (3 min for
Citation: Journal of the Atmospheric Sciences 81, 9; 10.1175/JAS-D-23-0223.1
4. Discussion
The following discusses how the preceding results relate to earlier observations of transitions to rapid intensification in natural tropical cyclones. One original objective of this modeling study was to search a broad region of parameter space for novel transition types that might have been overlooked owing to observational limitations. In the end, this study may have served more to corroborate earlier observations and to further elucidate the role of tilt in differentiating transition dynamics.
To begin with, there are numerous observations of tropical cyclones experiencing transitions that seem to resemble those of type S. Comprehensive surveys of satellite data have suggested that substantial azimuthal spreading of inner-core precipitation akin to that which occurs upon a type S transition commonly transpires by the initial phase of rapid intensification (e.g., Harnos and Nesbitt 2011, 2016c; Kieper and Jiang 2012; Tao and Jiang 2015; Tao et al. 2017; Fischer et al. 2018). There are also observations qualitatively consistent with the characteristic stagnation or decline of the precipitation rate within 100 km of the convergence center prior to a type S transition. Specifically, Tao et al. (2017) report that inner-core “rainfall intensity and total volumetric rain (typically) do not increase much until several hours after” the onset of rapid intensification.
Of particular relevance to this study, Harnos and Nesbitt (2011) previously presented empirical evidence for (at least) two modes of rapid intensification. The introduction of their 2016b paper concisely summarizes their observational finding as follows:
-
Harnos and Nesbitt (2011) used 20+ years of passive microwave ice scattering signals to suggest two shear-delineated structures associated with (tropical cyclones) undergoing (rapid intensification): widespread modest convection with a relatively symmetric ring-like presence under low wind shear and asymmetric intense convection preferentially downshear and downshear-left under high shear.
The relatively “asymmetric intense convection” of the nominal high-shear mode of rapid intensification seems akin to the relatively high levels of vertical mass flux and precipitation that are usually found in close proximity to the convergence center during and shortly after a type A transition to fast spinup. A “downshear and downshear-left” preference for convection in the high-shear mode also seems consistent with intensification initiated by a type A transition, at which time the position of the convergence center (xσ − xcl) has a polar angle of 67° ± 23° measured cyclonically from the shear vector.8 On the other hand, we have seen (Fig. 4c) that the most prominent region of convection can readily migrate into the upshear semicircle (x − xcl < 0) during the asymmetric intensification process that follows a type A transition. Perhaps a more important difference between the asymmetric modes of fast spinup considered here and those described by Harnos and Nesbitt above could be the extent to which the coinciding environmental wind shear determines the precipitation asymmetry at and shortly after
Of course, Harnos and Nesbitt are neither the first nor the most recent researchers to have presented a binary conceptualization of transitions to fast spinup based completely or partly on observations. Long ago, Holliday and Thompson (1979) suggested that transitions to rapid deepening of the central pressure naturally divide into those preceded by either moderate or slow deepening. The extent to which the observed changes from moderate to rapid deepening correspond to transitions of the intensification rate sharp enough for inclusion in the present study is unclear. Nevertheless, the tilt-based classification scheme expounded herein appears to be marginally consistent with that of Holliday and Thompson in that the 24-h intensification rates (for Vm) preceding transitions of type S tend to be larger than those preceding transitions of type A (Table 1; cf. appendix C).
In connection to both global convection-permitting simulations and supportive observational data, Judt et al. (2023) discussed a binary perspective in which transitions lead to either marathon or sprint modes of rapid intensification. Fundamentally, the marathon mode is “characterized by a moderately paced and long-lived intensification period,” whereas the sprint mode is “characterized by explosive and short-lived intensification bursts.” The marathon mode is described as symmetric in nature, whereas the sprint mode is described as asymmetric. The archetypal transition to a sprint mode illustrated by Judt et al. entails core reformation similar to that observed (for instance) by Molinari and Vollaro (2010). As currently seen by the author, the foregoing binary perspective differs from that of the present study. Both composite and individual time series of tropical cyclone intensity (Figs. 5, C1 and C2) suggest that transitions of either type S or type A commonly initiate long-lived periods of fast spinup similar to those characterizing marathon modes of rapid intensification. Furthermore, core reformation is not essential to type A (or S) transitions.
One might reasonably contend that any binary classification scheme including that proposed herein will paint an incomplete picture of transitions to fast spinup. The clustering of the vast majority of data points into two well-separated groups (Fig. 2) was a convenient result of the present study with questionable relevance to the distribution of natural transitions. The existence of some (type G) transitions outside of the two main clusters hints at a fuzzier reality. Even within a single (type A) cluster, we have seen mechanical differences in the transitions [those involving and (normally) not involving core reformation] that encourage the introduction of subcategories. There are also observationally based reasons to believe that additional categories may be needed to adequately classify transitions to fast spinup in systems beyond those (considered herein) with unidirectional environmental vertical wind shear maximized in the middle troposphere. Ryglicki et al. (2018a), for example, suggest that there may exist unique aspects to the precursors and manifestations of rapid intensification in tropical cyclones exposed to shallow upper-tropospheric shear layers.
Moving beyond classification issues, it is worth remarking that a variety of observational studies have suggested a connection between substantial intensification and relatively strong contributions to moist convection (latent heat release) at or inside the radius of maximum wind speed (Stevenson et al. 2014; Susca-Lopata et al. 2015; Rogers et al. 2013, 2015, 2016). The analysis of idealized simulations in section 3f did not explicitly examine the distribution of heating relative to the maximum wind speed of the primary circulation at any particular altitude, but did show that the composite mean of
5. Conclusions
Transitions from slow to fast spinup during tropical cyclone intensification in cloud-resolving simulations have been examined over wide ranges of SSTs and environmental vertical wind shears. The transitions have been classified into two types depending on whether they occur when the tropical cyclone is relatively untilted and symmetric (S) or tilted and asymmetric (A). The probability for either type of transition in a given environment has not been determined for a sufficiently broad spectrum of initial conditions, but both appear to be physically possible at any SST between 26° and 32°C combined with either weak or moderate vertical wind shear (see Figs. 2 and C3).
The composite analysis presented herein suggests the following scenario surrounding a type S transition. An ordinary type S transition is preceded by gradual declines of the tilt magnitude and the radius of maximum wind speed rm in the boundary layer. The decay of the tilt magnitude begins to accelerate at about the time t⊥ when the cyclonically rotating tilt vector becomes perpendicular to the direction of the environmental vertical wind shear. Between then and the transition period, the tilt magnitude reduces to less than one-half of rm. The alignment coincides with the pronounced growth of LCAPE and lower-to-middle-tropospheric RH in the central and uptilt regions of the inner core of the surface vortex. Such moist-thermodynamic changes may enable the azimuthal spreading of inner-core convection seen during the transition period and the onset of a quasi-symmetric mode of fast spinup that initially entails a rapid contraction of rm.
Tropical cyclones that eventually experience type A transitions tend to acquire larger tilts during their initial developments. The mean transitional values of the tilt magnitude and rm substantially exceed those found during type S transitions. Moreover, the mean transitional ratio μ of the tilt magnitude to rm is approximately 1 as opposed to 0.4. Consistent with such major misalignment, type A transitions characteristically occur while convection is still concentrated far downtilt and while the inner-core averages of LCAPE and lower-to-middle-tropospheric RH are depressed. Of further note, the azimuthally averaged cyclonic surface winds are generally weaker during transitions of type A than during those of type S.
A composite analysis has shown that the lead-up to a type A transition commonly entails gradual amplifications of the meso-β-scale surface precipitation rate P and lower-middle-tropospheric vertical mass flux M around the principal low-level convergence center xσ. Similar amplifications are seen before a type S transition, but the type S and A growth trends for either P or M averaged within 100 km or less of xσ noticeably diverge shortly before the transition time
That being said, the present study seems to have provided a fairly clear picture of various kinematic changes to the structure of a tropical cyclone that commonly precede type A transitions to fast spinup. To begin with, type A transitions occur on average at the time t⊥ when the tilt vector crosses into the upshear semicircle. The coinciding nullification of misalignment forcing may well facilitate rapid decay of the tilt magnitude, which in concert with quick contractions of rm and the characteristic precipitation radius rp appears to be an integral part of the initially asymmetric fast spinup mechanism. Furthermore, type A transitions are commonly preceded by substantial declines of μ to values near 1. Along with the reduction of μ to unity, the center of the convergence zone initially located outside the maximal surface winds becomes situated roughly at rm. Such a change, which also precedes type S transitions, has the potential to appreciably increase the IR (e.g., Schecter 2020). Another notable kinematic precursor to a type A transition is a reduction of the distance between the convergence center and midlevel vortex center to a magnitude that on average approximately equals the midlevel radius of maximum wind speed. The significance of this change to the vigor of local convection and surface wind speed intensification could be a worthwhile topic of future study.
Section 4 discussed existing observations of transitions to fast spinup in tropical cyclones with either quasi-symmetric or asymmetric distributions of inner-core precipitation. As explained therein, the present study has corroborated many of the observations while providing some additional details on how each type of transition transpires (in the simulations at hand). One distinctive feature of this study has been to expound the central role of tilt—which is not necessarily commensurate with the coinciding environmental vertical wind shear—in differentiating the transition types. This study has also underscored that the initiation of fast spinup in a strongly tilted tropical cyclone with highly asymmetric convection (a type A transition) need not and often does not entail an archetypal core reformation event.
“Downtilt” refers to a displacement in the general direction of the tilt vector, whereas “uptilt” refers to a displacement in the opposite direction. The “tilt vector” is the horizontal position vector of the midlevel vortex center measured from the low-level center. See Fig. 3d of section 3b.
In nature, the second term on the right-hand side of Eq. (3) would be associated with a meridional potential temperature gradient. Such a gradient is neglected herein to permit periodic boundary conditions, as in many previous studies. The reader may consult Nolan (2011) for an evaluation of this approach to simulating tropical cyclones.
The distribution of
The author has verified the existence of such a positive temperature anomaly above the central and uptilt regions of the surface vortex of the pretransitional tropical cyclone. Similar anomalies are illustrated in S22.
For most cases, these values are strongly linked to the state of the tropical cyclone prior to introducing shear at τ↑. For the complete set of systems that experience type S or A transitions, the 20th and 80th percentiles of
A similarly modest rise from roughly 91% to 94% is seen when the RH is averaged over a thinner layer with a lower boundary (1 ≤ z ≤ 3 km).
This angle is appreciably smaller than the corresponding tilt angle
Two transitions (one of type A followed by another of type S) occurred in one particular simulation with an SST of 26°C,
All but one of these simulations were from the supplemental set.
Acknowledgments.
The author would like to express his gratitude to three anonymous reviewers for their constructive feedback on the original version of this paper and to Dr. George Bryan of the National Center for Atmospheric Research (NCAR) for developing and maintaining the atmospheric model used for this study (CM1). The author also thanks student project participants Ian Mansfield and Brittany Lazzaro Freeman for conducting the supplemental simulations (see appendix A) that were incorporated into the composite analyses presented herein. Most of the simulations in the dataset used for this study were made possible with resources provided by NCAR’s Computational and Information Systems Laboratory (https://doi.org/10.5065/D6RX99HX). This work was supported by the National Science Foundation under Grant AGS-2208205.
Data availability statement.
Namelist files and initial conditions in the form of netCDF CM1-restart files for selected simulations are available at https://doi.org/10.5281/zenodo.10951675. Archived simulation output files too large and numerous for public repositories are available to researchers upon request sent to schecter@nwra.com. Modifications to CM1 version 19.5 used to add time-dependent environmental shear flows (section 2a) and peripheral Rayleigh damping with a circular inner boundary (appendix A) are available at https://doi.org/10.5281/zenodo.7637579.
APPENDIX A
Simulation Details
Table A1 summarizes the simulations that are used for the present study. The simulations are separated into groups with a specified SST (first column from the left) and into subgroups (second and third columns) determined by the initial vortex structure (PD or MR) and the τ couplet specifying when the environmental shear flow is ramped up (τ↑) and down (τ↓). The fourth column lists the kinds of shear layers found in each subgroup, with L1 corresponding to (zα, δzα) = (5.0, 2.5) km and L2 corresponding to (zα, δzα) = (5.5, 3.5) km. The fifth column shows the range of the shear strength parameter
Summary of the computational dataset excluding the zero-shear simulations used to estimate the maximum potential intensities of the tropical cyclones (appendix B).
The simulations with τ↑ > 0 in Table A1 were originally conducted for the present study, whereas those with τ↑ = 0 were pulled in from a separate study to moderately increase the amount of data. Hereafter, the former (latter) will be called the main (supplemental) simulations. The main simulations were run with version 19.5 of CM1 tailored to include time-dependent environmental shear flows and Rayleigh damping near the periphery of the horizontal domain. The aforementioned Rayleigh damping entails adding a term of the form
The supplemental simulations were conducted with version 21.0 of CM1, modified slightly to handle PD vortex initializations. No supplemental simulation includes peripheral Rayleigh damping. All supplemental simulations incorporate their time-independent shear flows through a standard CM1 configuration procedure. The supplemental simulations also differ from the main simulations in having 50 as opposed to 40 vertical levels.
A small number of simulations failed to complete before the edge of the core of the tropical cyclone neared the edge of the central square (with 2.5-km resolution) of the computational grid.10 In these cases, the simulations were paused and then resumed with all 2D and 3D fields in the CM1 restart file horizontally shifted so as to allow the tropical cyclone to continue its evolution without a loss of inner resolution.
APPENDIX B
Analysis Details
a. Vortex and convergence centers
For the present study, the vortex center in a given layer of the tropical cyclone is computed as in Schecter (2023). Let uκ denote the vertical average of the horizontal velocity field over the depth of layer κ. Let
The variable xcl appearing throughout the main text is the vortex center in a roughly 1-km-deep boundary layer adjacent to the sea surface. The variable xcu is the vortex center in a roughly 1-km-deep atmospheric layer with a mean height of approximately 8 km. The calculation of the broad cyclone center
In analogy to the vortex center, the convergence center xσ appearing in the main text corresponds to the origin of the particular polar coordinate system that maximizes
b. Ad hoc objective algorithm for identifying substantial transitions
The identification of a substantial transition to relatively fast spinup is a multistep process. Step 1 involves converting dVm/dt into a 7-h running average IRa and finding all local maxima of the resulting time series. Local maxima with values less than a modest threshold (
c. Maximum potential intensity estimates
The present study employs a very basic method to estimate the maximum potential intensity Vmax of a simulated tropical cyclone. Among other simplifications, the method implicitly neglects shear-related differences in the temporal evolution (over 10 days or less) of certain environmental parameters (besides the SST) that theoretically influence Vmax, such as the tropopause temperature and near-surface relative humidity (Emanuel 1986; cf. Emanuel and Rotunno 2011). To begin with, 2–3 tropical cyclone simulations initialized with either PD or MR vortices are run without environmental shear flows at each SST. In each case, the simulation lasts well beyond the time tγ of maximum tropical cyclone intensity. Let Vma denote the average of Vm (defined in section 2b) during the 24 h immediately after tγ. Let
Estimates of Vmax and related parameters.
d. Precipitation rate scaling factor
The scaling factor for the 2-h surface precipitation rate P in Fig. 9 is given by the following formula:
APPENDIX C
Supplemental Findings
a. Precipitation versus updraft asymmetry
Alternatively, one might consider the updraft asymmetry UDasym given by the right-hand side of Eq. (C2) with d as before and G → ρwH(ρw − Mo) evaluated at a specific height z. Here, ρ is density, w is vertical velocity, and Mo is a selected value of ρw above (below) which the Heaviside step function H is 1 (0). Letting z = 3.6 km and Mo = 1 kg m−2 s−1 for illustrative purposes, the mean updraft asymmetry ± one standard deviation is given by
b. Vm versus the absolute maximum surface wind speed
The definition of tropical cyclone spinup adopted for this study is the amplification of Vm, which represents the maximum value of the azimuthally averaged tangential velocity 10 m above sea level in a coordinate system centered on xcl. All conclusions regarding spinup should be viewed in this context. That being said, one might reasonably ask how the picture of intensification changes upon replacing Vm with the absolute maximum surface wind speed within a tropical cyclone.
Figure C1 shows time series of the instantaneous maximum magnitude of the 10-m ground-relative velocity field |u10|m normalized to Vmax for tropical cyclones that experience type S and type A transitions. The S-A intensity difference near
Time series of the absolute maximum 10-m horizontal wind speed (normalized to Vmax) in tropical cyclones that experience type S and type A transitions to fast spinup. Plotting conventions are as in Fig. 5.
Citation: Journal of the Atmospheric Sciences 81, 9; 10.1175/JAS-D-23-0223.1
Figure C2 complements the composite time series (Figs. 5a and C1) by showing Vm and |u10|m for six selected tropical cyclones that transition to both symmetric and (initially) asymmetric modes of fast spinup. The |u10|m curves expectedly have positive displacements and larger fluctuations. For two of the tropical cyclones that experience type A transitions (Figs. C2d,f), |u10|m appears to begin relatively fast intensification modestly ahead of Vm. On the other hand, |u10|m generally follows the smoother and long-lasting posttransitional intensification trend of Vm.
(a)–(c) Time series of the absolute maximum 10-m horizontal wind speed (solid) and Vm (dashed) in three selected tropical cyclones that experience type S transitions to fast spinup at
Citation: Journal of the Atmospheric Sciences 81, 9; 10.1175/JAS-D-23-0223.1
c. Relationship between the transitional asymmetry of a tropical cyclone and the coinciding vertical wind shear
Section 4 asserted that for the simulations at hand, the precipitation asymmetry is better correlated to the normalized tilt magnitude
Figure C3 shows how type S, type A, and a small number of type G transitions are distributed over
Locations of type S (color filled), type A (empty), and type G (gray filled) transitions to fast spinup in the environmental parameter space defined by
Citation: Journal of the Atmospheric Sciences 81, 9; 10.1175/JAS-D-23-0223.1
It is worth noting that there are no simulations in which the shear magnitude changes to
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