1. Introduction
Tropical cyclones (TCs) are a priority for innovations in operational forecasting (Gall et al. 2013; Rozoff et al. 2015) and future climate projections (Walsh et al. 2016; Knutson et al. 2020), owing to their wide-reaching hazards, including extreme wind, rainfall, and storm surge. Much of our understanding of TCs has been derived from axisymmetric perspectives, as TCs are generally axisymmetric vortices to first approximation (e.g., Ooyama 1969; Willoughby 1979; Schubert and Hack 1982; Emanuel 1986; Weatherford and Gray 1988; Molinari and Vollaro 1990; Vigh and Schubert 2009; Abarca and Montgomery 2015; Peng et al. 2019). However, asymmetric structures and processes are common in TCs. Higher-order wavenumber modes (wavenumbers 2–3 or higher), such as polygonal eyewalls (e.g., Schubert et al. 1999; Hendricks et al. 2012; Cha et al. 2020), contribute to TC precipitation and potential vorticity (PV) fields (Chen et al. 2006; Reasor et al. 2009; Zhu et al. 2014; Yu et al. 2015; Pei and Jiang 2018). But the most prevalent asymmetry is a wavenumber 1 mode in circulation, convection, and precipitation. One common example is that a TC’s motion (storm-relative flow largely due to environmental steering patterns) can induce asymmetric tangential winds and boundary layer convergence (Shapiro 1983; Frank and Ritchie 1999; Chen et al. 2018). Bender (1997) showed that asymmetries in low-level convergence and precipitation can also be induced by asymmetric planetary vorticity advection.
Among the most prominent examples of TC asymmetry is a wavenumber 1 mode induced by environmental vertical wind shear (VWS) (Corbosiero and Molinari 2003; Houze 2010). VWS has long been considered influential to TCs (Gray 1968; Rios-Berrios et al. 2024), and process-oriented examinations of this interaction expanded as modeling capabilities improved (e.g., Wu and Emanuel 1993; Flatau et al. 1994; DeMaria 1996; Bender 1997; Frank and Ritchie 1999, 2001; Rogers et al. 2003; Wu et al. 2006). TCs can strengthen in sheared environments depending on interactions between moisture, convective-scale processes, and large-scale flow (Rios-Berrios et al. 2016a,b). However, VWS is generally regarded as a negative influence on the TC development and intensity (DeMaria and Kaplan 1994), via the ventilation of dry environmental air into the core (Tang and Emanuel 2012; Alland et al. 2021a,b) and disruption of the warm core aloft (DeMaria 1996; Frank and Ritchie 2001). Using a dry barotropic vortex in unidirectional VWS, Jones (1995) showed that the TC’s initial response is to tilt its vertical column of vorticity in the downshear direction. To maintain balance, an asymmetric vertical circulation develops with ascent downshear and descent upshear. Vertical motion asymmetry adiabatically distorts isentropes, producing cold anomalies downshear and warm anomalies upshear to retain thermal wind balance. These temperature anomalies may then be advected cyclonically (Braun et al. 2006; Reasor and Eastin 2012), establishing an isentropic contribution to vertical motion as parcels rotate around the TC. Meanwhile, the vortex tilt orientation may rotate cyclonically from directly downshear to the left of shear, as upper-level and lower-level PV centers rotate cyclonically about the midlevel center (Jones 1995). While these mechanisms operate concurrently and are often difficult to isolate, they typically result in a structure where inner core convection is most active in the downshear-left quadrant (Northern Hemisphere), and outer rainband convection is most active slightly upwind.
Studies using observations and high-resolution models agree that the TC wind speed and precipitation typically maximize left-of-shear (Marks et al. 1992; Franklin et al. 1993; Black et al. 2002; Eastin et al. 2005; Reasor et al. 2009; Uhlhorn et al. 2014; Fierro and Mansell 2017). Corbosiero and Molinari (2002) used lightning data to show a downshear-left maximum in deep convective updrafts in TC inner cores and a downshear-right maximum in the rainband region resembling the “stationary band complex” described by Willoughby et al. (1984). Aircraft reconnaissance radar observations yield similar results for precipitation (Reasor et al. 2013; DeHart et al. 2014). Further studies asserted that shear-relative asymmetries in precipitation are dominant compared to motion-relative asymmetries for shear ≥ 5 m s−1 (Corbosiero and Molinari 2003; Chen et al. 2006). Using satellite radar, Hence and Houze (2011) found a precipitation life cycle in sheared TC eyewalls, where convective initiation occurs in the downshear-right, followed by maturation in the downshear-left, then decay and transition to stratiform precipitation in the upshear-left. Studies using polarimetric radar observations found that inner core hydrometeors are advected cyclonically after convective initiation to produce a downshear-left rainfall maximum, with lighter stratiform hydrometeors advected farther downwind (Didlake and Kumjian 2017, 2018; Laurencin et al. 2020; Homeyer et al. 2021). These shear-relative microphysical asymmetries are also relevant to secondary eyewall formation through the development of new, persistent updrafts forced by a stratiform-induced mesoscale descending inflow (Didlake et al. 2018; Yu et al. 2021, 2022). Individual sheared TCs may take on structures that deviate from this expected asymmetry (Feng and Bell 2019), which may serve as useful predictors for intensity change (Stevenson et al. 2014).
Modern TC-focused numerical weather prediction models run at convection-permitting resolutions that capture shear-relative asymmetries effectively (Harris et al. 2020; Hazelton et al. 2022). However, global climate models (GCMs), while more capable of reproducing the observed TC climatology in recent years (Camargo and Wing 2016; Roberts et al. 2020; Judt et al. 2021), remain limited to grid spacings ≥ 0.25° and rely heavily on parameterized physics. This presents the challenges for future projections of TC activity (Knutson et al. 2020; Sobel et al. 2021). Recent work has shown that GCMs participating in High Resolution Model Intercomparison Project (HighResMIP) (Haarsma et al. 2016) can better reproduce an axisymmetric TC structure compared to prior generations. However, the simulated TCs remain too broad (Kim et al. 2018), and some high-resolution GCMs still cannot produce TCs with winds above 50 m s−1 (Wing et al. 2019). Many models do not capture subsidence in the centers of the strongest TCs (Moon et al. 2020), and peak rain rates are often overestimated (Moon et al. 2022).
GCMs of similar resolutions depict the TC structure and climatology differently, attributed to differences in the model dynamical core (e.g., Zhao et al. 2012; Reed et al. 2015), physical parameterizations (e.g., Kim et al. 2012; Moon et al. 2020), or time step (Zarzycki 2022). These differences extend to reanalyses, which assimilate conventional and satellite-based observations into a GCM-like model to fill in historical data gaps and produce a multidecadal global analysis. Schenkel and Hart (2012), Murakami (2014), and Hodges et al. (2017) found that reanalyses underrepresent the TC intensity and that some TCs may be missed altogether, particularly if vortex relocation or wind profile assimilation are not utilized. Challenges also exist in properly capturing the life cycle of the TC intensity (Schenkel and Hart 2012). Reanalyses especially struggle with weaker and smaller storms (Schenkel and Hart 2012), with a higher false alarm rate and lower hit rate relative to observations (Zarzycki and Ullrich 2017; Zarzycki et al. 2021), and more sensitivity to the choice of TC tracking algorithm (Bourdin et al. 2022). Jones et al. (2021) showed a wide spread in TC rainfall climatology across reanalyses, relative to the spread in annual mean rainfall. Slocum et al. (2022) identified biases in the reanalysis representation of the TC environment relative to dropsonde observations, particularly in thermodynamic fields and the vertical variation of low-level winds. However, they also concluded that VWS compares well with observations in the reanalysis they considered. In addition, Schenkel et al. (2017) and Bian et al. (2021) found that reanalyses can resolve the outer wind fields of TCs relatively well.
To our knowledge, the only study to directly assess TC shear-relative asymmetries in GCMs or reanalyses is Moon et al. (2022). They found that the HighResMIP ensemble produces a reasonable spatial distribution of rainfall, with substantial intermodel spread in the radius and magnitude of the peak rain rate. Our study expands on such an examination from a process-oriented perspective by focusing on TC kinematic and thermodynamic shear-relative asymmetries in global reanalyses, evaluating these against aircraft reconnaissance radar observations. By beginning with datasets utilizing observational data assimilation, we identify how various aspects of the TC–VWS relationship are captured under the coarse resolution and parameterized convection relevant to GCMs, so that our diagnostics may later be applied to assess how TC asymmetry may change under future warming. We hypothesize that reanalyses will struggle to reliably simulate small-scale processes such as convective rainband precipitation and vortex tilt but better capture large-scale asymmetries.
Section 2 describes the observations, reanalyses, TC tracking algorithm, and VWS calculation used to generate composites. Section 3 highlights shear-relative asymmetries in circulation, precipitation, and thermodynamics. Section 4 attributes asymmetries in vertical motion to specific mechanisms in the inner core and outer rainband regions, addresses the sensitivity of TC precipitation to convective parameterizations, and more thoroughly details the simulated precipitation, cloud, and kinematic asymmetry along the TC circulation. Section 5 summarizes our findings while highlighting future research directions.
2. Data and methods
We diagnose TC structure in two modern reanalyses, whose configuration, dynamical core, physics parameterizations, and data assimilation strategies are outlined in Table 1. We will discuss the different physical parameterizations relevant to precipitation in greater detail in section 4b. The first is ERA5 (Hersbach et al. 2020), which uses 4D-Var data assimilation and model forecasts of the ECMWF Integrated Forecasting System (IFS, fixed version CY41R2) on a grid with nominal 31-km horizontal spacing and 137 levels. Data are output hourly at 0.25° horizontal grid spacing on 37 constant pressure surfaces. We utilize 6-hourly output at 0000, 0600, 1200, and 1800 UTC, largely leveraging fields that are output as “real-time” analyses. Precipitation and surface heat fluxes are instead generated using IFS with the analysis, yielding 18-h forecasts twice-daily initialized at 0600 and 1800 UTC. To match the TC fix times, 6- and 12-h forecasts are used for these fields, lead times where track forecast skill is expected to remain extremely high.
The second reanalysis is the Climate Forecast System Reanalysis (CFSR; Saha et al. 2010), with 3D-Var data assimilation. Specifically, we use the Climate Forecast System, version 2 (Saha et al. 2014), an update extending the original CFSR beyond 2011 with improvements to the cumulus gravity wave drag, radiation, and land surface model parameterizations. CFSR is a coupled atmosphere–ocean–land–sea ice system, with a nominal grid spacing of ∼38 km and 64 vertical levels. Model output is on the same pressure levels as ERA5 but a coarser postprocessed horizontal grid spacing of 0.5°. However, CFSR employs a scheme to relocate a TC vortex based on operational forecast guidance and inserts a synthetic vortex if the analyzed vortex is too weak for the model’s spatial resolution (Liu et al. 2000). This process has been shown to improve CFSR’s depiction of the TC location, intensity, life cycle, and pressure–wind relationships (Schenkel and Hart 2012; Murakami 2014; Zick and Matyas 2015), the latter of which is shown in Fig. 1a, although Schenkel and Hart (2012) also noted that some nonphysical TC structures were also introduced by this algorithm. The differences between these reanalyses allow the assessment of the relative importance of resolution, TC preprocessing, and other model settings for TC asymmetry. Similar to ERA5, surface flux and precipitation fields are generated using short-term forecasts in CFSR.
(a) Wind–pressure relationship and (b),(c) distributions of TC minimum pressure and wind shear magnitude, respectively, for each of the ERA5 (red), CFSR (blue), and TC-RADAR observational (black) samples. (d)–(f) Composite sample sizes for ERA5, CFSR, and TC-RADAR, respectively, binned according to the TC minimum pressure and VWS magnitude. Boundaries for the pressure categories from the Klotzbach et al. (2020) scale are labeled (hPa) in (e).
Citation: Journal of Climate 37, 22; 10.1175/JCLI-D-23-0628.1
TempestExtremes is used to objectively track TCs in the reanalyses (Ullrich and Zarzycki 2017; Zarzycki et al. 2017; Ullrich et al. 2021). It should be emphasized that the algorithm as applied here does not take into account a reference dataset such as IBTrACS (Knapp et al. 2010). This is done to provide a result directly comparable to a free-running model. TempestExtremes first searches for local minima in sea level pressure with a closed contour of at least 2 hPa below the large-scale environmental pressure at a given time. It then searches for a collocated local maximum in 300–500-hPa geopotential thickness to identify a warm core and dismiss extratropical cyclones. Following this candidate detection, trajectories are generated by linking points close in space and time. TCs must persist for at least 2.5 days to be included, and separate trajectories that terminate and begin within 18 h and 8° of one another are merged to eliminate inadvertent double counting of a single track. Refer to Zarzycki and Ullrich (2017) for more information on the parameters chosen for this TempestExtremes configuration. Globally, 881 distinct TC tracks are identified from 2012 to 2021 in ERA5 and 706 in CFSR (Zarzycki et al. 2021). We consider Northern Hemisphere snapshots (extractions of the cyclone-centered field at each 6-hourly time step) equatorward of 30°N to limit extratropical transition events (Hart and Evans 2001), yielding 11 836 total available TC snapshots in ERA5 and 9827 in CFSR.
We utilize the Tropical Cyclone Radar Archive of Doppler Analyses with Recentering (TC-RADAR; Fischer et al. 2022) as an observational reference for much of the reanalysis TC structure. Aircraft reconnaissance radar data are not assimilated into reanalyses, providing a useful independent dataset for verification. TC-RADAR synthesizes observations from the X-band tail Doppler radar (TDR) onboard the NOAA P3 aircraft. Refer to Fischer et al. (2022) for more information on the TDR system and data synthesis process. Specifically, we use the “merged” analyses, which combine and average individual flight legs (“swaths”) for a given mission. Data are available relative to the analyzed TC center (at 2-km altitude) with 2-km horizontal grid spacing and 0.5-km vertical grid spacing from 0.5- to 18-km altitude. We consider the tangential, radial, and vertical velocity after TC motion is removed, as well as radar reflectivity and vortex tilt. Most TCs sampled in TC-RADAR occurred in the North Atlantic basin, although some missions were also conducted over the eastern and central North Pacific (Fischer et al. 2022), which we neglect. We consider all merged analyses equatorward of 30°N from 1997 to 2022. Vertical velocity observations before 2010 are considered unreliable and are not used. Figure 1b shows that a wide range of TC intensities are captured in these 304 distinct missions.
Several approaches exist to compute VWS, differing in area, vertical depth, and handling of the vortex flow (DeMaria and Kaplan 1999; DeMaria et al. 2005). It is challenging to isolate the vertically varying environmental flow from the vortex itself, and it is likely that an optimal strategy depends on the individual TC size, intensity, and vortex depth. We utilize one of the standard operational methods—the deep-layer (850–200 hPa) shear vector using winds averaged in a 200–800-km radial annulus from the TC center (point of minimum surface pressure). Slocum et al. (2022) found that ERA5-derived VWS using this method compares well to observations. The resulting distributions of the VWS magnitude are shown in Fig. 1c. We computed VWS using several approaches, which did not significantly affect our results. For example, we considered shear over shallower layers of 850–500 hPa and 500–200 hPa, as the vertical distribution of shear has been shown to affect the TC’s potential to resist the shear and intensify (Finocchio and Majumdar 2017). We also tried the vortex removal strategy of Davis et al. (2008), subtracting irrotational and nondivergent winds at 850 and 200 hPa before averaging winds in a 0–500-km annulus.
To generate composites, TC-centered fields are rotated to be commonly aligned relative to the VWS vector direction at each reanalysis snapshot (or observational mission) and then averaged over all snapshots falling into a particular bin. TCs are first binned by the VWS magnitude: low (<5 m s−1), moderate (5–10 m s−1), and high (>10 m s−1). Our moderate VWS bin generally aligns with the most frequently occurring VWS magnitudes in our TC-RADAR sample (Fig. 1c) and with the center of the global distribution found by Rios-Berrios and Torn (2017), where the 25th–75th percentiles of VWS fell between 4.5 and 11.0 m s−1. Further binning is done by TC intensity according to the minimum pressure by the Klotzbach et al. (2020) scale (labeled in Fig. 1e), as prior work has shown pressure to be more skillfully simulated in reanalyses (Schenkel and Hart 2012; Hodges et al. 2017; Zarzycki et al. 2021). Figures 1d–f show that the reanalyses, while skewed toward weaker storms, both capture TCs up to C3 intensity (945–960 hPa), although these are likely associated with underresolved C5 observed TCs, and in general, a given TC in the reanalysis is likely weaker than in reality.
3. Overview of structural asymmetry
We present composite shear-relative TC structures in this section, before discussing specific processes relevant to the precipitation and vertical motion asymmetry in section 4. Reanalysis composites are shown for C1 TCs (minimum pressure between 975 and 990 hPa) under moderate shear (5–10 m s−1), unless otherwise stated. To broaden the observational sample, we include C0–C2 TCs for corresponding TC-RADAR composites. We will show an example of how TC structure depends on intensity under VWS in the reanalyses but otherwise focus on the C1 intensity bin, as other bins show similar qualitative results.
a. Circulation
Enhanced ascent and low-level inflow are expected downshear and vice versa upshear. Asymmetries in tangential wind may be driven by the alignment of vortex flow with mean low-level steering flow (Chen et al. 2018) or asymmetric angular momentum convergence by the radial flow (Smith et al. 2009; Ahern et al. 2021). Figure 2 shows the composite mean 900-hPa tangential wind and 850-hPa vertical velocity across the three shear bins for C1 TCs. Shear-relative quadrants are labeled in Fig. 2a: downshear-right (DR), downshear-left (DL), upshear-left (UL), and upshear-right (UR). Tangential wind is the strongest left-of-shear as in Zhang et al. (2013), and asymmetry amplifies as VWS strengthens in both the reanalyses and observations (left–right). Winds in CFSR (Figs. 2d–f) are stronger than in ERA5 (Figs. 2a–c) and the observational composite at 1 km (Figs. 2g–i) despite the coarser resolution, likely owing to the CFSR’s TC preprocessing procedure. Boundary layer parameterizations may also influence this difference, but we find similar patterns at 950 and 850 hPa (not shown).
Composite mean tangential and vertical velocities, relative to the VWS vector (black), for C1 TCs in (a)–(c) ERA5 and (d)–(f) CFSR, and for C0–C2 TCs in (g)–(i) TC-RADAR. Shaded tangential winds are at 900 hPa in reanalyses and 1 km in TC-RADAR, while contoured vertical velocities are at 850 hPa and 1.5 km, respectively. (left) The low shear composite (<5 m s−1), (middle) moderate shear (5–10 m s−1), and (right) high shear (>10 m s−1). Contours are in 0.05 m s−1 intervals in (a)–(f), and only the 0.25 m s−1 contour is shown in (g)–(i). Shear-relative quadrants are labeled in (a). Note that TC-RADAR has a smaller areal coverage.
Citation: Journal of Climate 37, 22; 10.1175/JCLI-D-23-0628.1
Black contours throughout Figs. 2 and 3 show ascent at 850 hPa (1.5 km in observations). Even under low shear (<5 m s−1, left), ascent is maximized downshear in the reanalyses. As shear strengthens (left–right), ascent occurs over a larger area downshear and a lesser area upshear (Figs. 3a–f). At far radii, ascent is the most pronounced DR, suggesting increased rainband activity there (e.g., Fig. 3c), all consistent with observations (e.g., Corbosiero and Molinari 2002; Hence and Houze 2012). In the innermost 2°, the magnitude of peak vertical motion strengthens with shear, occurring DL. Asymmetry in the near-surface radial wind field is well aligned with the vertical motion in the reanalyses. The peak ascent is located just radially inward of the peak inflow, indicating strong convergent forcing for convection. Like vertical motion, inflow strengthens with shear and focuses downshear, particularly DL (Zhang et al. 2013; DeHart et al. 2014). The peak tangential winds in Fig. 2 are located slightly downwind of the peak inflow, suggesting that enhanced angular momentum import helps to generate stronger tangential winds downwind. While the vertical motion observational composite is noisy (due to limited sampling and finer resolution), wavenumber 1 asymmetry emerges in the 1-km radial flow with increasing VWS (Figs. 3g–i).
As in Fig. 2, but with shading representing radial wind.
Citation: Journal of Climate 37, 22; 10.1175/JCLI-D-23-0628.1
Figure 4 presents the radial profiles of 900-hPa level (1-km altitude in observations) tangential and radial winds in the four shear-relative quadrants. In this 975–990-hPa intensity range, the average radius of maximum tangential wind is near 100 km in the reanalyses (Figs. 4a–f). This is much broader than the corresponding value in the observational composite of 30–50 km (Figs. 4g–i), consistent with prior studies evaluating GCMs (Moon et al. 2020) and reanalyses (Schenkel et al. 2017; Bian et al. 2021). We test for statistically significant differences between pairs of shear-relative quadrants (e.g., comparing the distributions of radial wind in the DL and UL) using a Kolmogorov–Smirnov test. Horizontal lines in Figs. 4a–f (and later, Figs. 6 and 8) indicate that a particular quadrant’s wind distribution across the composite is significantly different from that of at least two other quadrants. Figure 4 shows the increasing asymmetry with VWS in both reanalyses and observations, with preferential inflow downshear (yellow and orange squares), and peak tangential wind left-of-shear (yellow and blue triangles). Under high shear, the azimuthal variability in the radial wind is near 10 m s−1 radially outward of 100 km, and the tangential wind varies by roughly 5–8 m s−1. These differences are statistically significant for both reanalyses in all shear bins from the radius of maximum wind outward. These findings are largely consistent with prior studies, although some subtle differences exist. For example, ERA5 exhibits outflow (or its weakest inflow) UL, while observational (Zhang et al. 2013) and idealized modeling (Gu et al. 2016) work suggests that this should occur UR, although their sampled TCs were more intense.
Radial profiles of tangential (triangles) and radial (squares) wind, averaged in the four shear-relative quadrants for C1 TCs in (a)–(c) ERA5 and (d)–(f) CFSR, and for C0–C2 TCs in (g)–(i) TC-RADAR. (left) Low shear, (middle) moderate shear, and (right) high shear. Statistically significant differences in (top) the mean tangential and (bottom) radial wind between pairs of quadrants are plotted as horizontal lines. The presence of a line indicates that a quadrant’s wind distribution is significantly different from at least two other quadrants, based on a Kolmogorov–Smirnov test. This is limited to 200-km radius in TC-RADAR due to sampling limitations.
Citation: Journal of Climate 37, 22; 10.1175/JCLI-D-23-0628.1
We consider the vertical tilt of the TC next, which is both a response to VWS and a key factor affecting a TC’s resulting structure. As Jones (1995) first demonstrated, the initial response of a vertically aligned vortex to VWS is to tilt downshear, causing asymmetric vertical motion and thermal fields. Tilt is associated with a horizontal offset between PV maxima at different vertical levels, so their vertical reflections induce the cyclonic rotation of the low-level and upper-level centers about one another. Because of this, a DL mean tilt direction is expected. More intense TCs have greater inertial stability and resistance to the tilting effect of the shear, and thus less tilt on average, while weaker storms with little tilt are also more likely to intensify (Fischer et al. 2024).
Figure 5 plots the location of the vortex center at 100-hPa intervals from 900 to 500 hPa in reanalyses and at 1-km intervals from 2 to 6 km in observations. This is done for C0–C3 TCs as a function of VWS. The center is identified at each level as the centroid of unsmoothed cyclonic relative vorticity, using the surface pressure minimum as a first guess, adapted from the strategies of Reasor and Montgomery (2001) and Jones (2004). This single-variable algorithm is intended for simple future applicability in GCMs. Figure 5 shows that the mean vortex tilt using this method is substantially overestimated in the coarse reanalyses (Figs. 5a–f) compared to when the same method is applied to the observations (Figs. 5g–i). There is also substantial variability in the location of the midlevel vortex center relative to the low-level center within an individual composite (Figs. S1 and S2 in the online supplemental material). However, several aspects of the mean vortex tilt structure are more reasonable. The average tilt direction is DL, the tilt magnitude increases with VWS (left–right), and stronger TCs are more resistant to shear with less tilt (lighter to darker lines). We used a Kolmogorov–Smirnov test to identify significant differences between composites in their distributions of along-shear and across-shear tilt, finding significant differences between all intensity and shear groups (Figs. S3 and S4). The tilt magnitude is slightly lower in CFSR than ERA5 despite coarser grid spacing, likely due to the stronger winds for a given pressure category attributed to the TC preprocessing. The tilt orientation also becomes more left-of-shear as TCs strengthen in most cases. This implies more cyclonic tilt precession in more intense storms, as stronger PV anomalies at different levels more strongly influence one another (Jones 1995).
Vortex tilt in (a)–(c) ERA5, (d)–(f) CFSR, and (g)–(i) TC-RADAR composited by TC minimum pressure category (line colors) and VWS magnitude (left–right). The vortex center is defined as the centroid of cyclonic relative vorticity at each level. In reanalyses, this is plotted in 100-hPa intervals from 900 to 500 hPa. For observations, this is plotted in 1-km intervals from 2 to 6 km. Shear-relative quadrants are labeled in (g). Note that (g)–(i) cover a smaller area than (a)–(f).
Citation: Journal of Climate 37, 22; 10.1175/JCLI-D-23-0628.1
As discussed previously, reanalyses have well-documented deficiencies in simulating the TC circulation, particularly for intense TCs. Despite these limitations, including biases in vortex tilt magnitude, several aspects of shear-relative asymmetry are found in ERA5 and CFSR that are broadly consistent with theory, observations, and high-resolution modeling. While observational data assimilation likely plays a role in forcing the resulting structure toward a more realistic state, these findings provide optimism for the ability of high-resolution GCMs to capture TC asymmetry with reasonable fidelity.
b. Precipitation
Rainfall is critical to model effectively, as it is among the most significant TC hazards (Rogers et al. 2009). The challenges that reanalyses have in depicting precipitation have been documented globally by Bosilovich et al. (2008) and for TCs by Jones et al. (2021). Moon et al. (2022) recently demonstrated that shear-relative TC precipitation asymmetries exist in HighResMIP, motivating a comprehensive process-level examination of precipitation asymmetry. Reanalyses are a useful starting point, as data assimilation somewhat constrains precipitation.
Figures 6a and 6c show that for the C1, moderate shear composite, the DL quadrant produces the heaviest rain inside of 300 km, followed by DR, UL, and UR. This broadly resembles the radial profile of radar reflectivity in observations (Fig. 6e). At outer radii, there is a very slight preference for the heaviest rain DR, similar to prior work (Chen et al. 2006; Wingo and Cecil 2010). While the coarser CFSR produces more rain than ERA5 at outer radii (Figs. 6a,c), their maximum rain rates inside of 150 km are comparable. Statistically significant differences exist between downshear and upshear quadrants throughout the 0–500-km radial range in the reanalyses (horizontal lines in Figs. 6a,c). The maximum rainfall in both reanalyses is approximately collocated with the maximum midlevel ascent, inside 150-km radius in the DL (Figs. 6b,d). While this is less pronounced in the TC-RADAR composite, a wavenumber 1 asymmetry is still clear with amplified reflectivity and ascent downshear (Fig. 6f). In observational studies, a slight offset is typically seen in the inner core between the area of peak ascent and the area of peak precipitation (Reasor et al. 2013), as moisture and hydrometeors are advected cyclonically (e.g., Didlake and Kumjian 2017). While such an offset between the midlevel ascent (black contours) and the rain rate is not obvious in Figs. 6b and 6d, it will become more apparent when rainfall is separated into contributions from the convective parameterization and large-scale cloud scheme (section 4a). This is also hinted at by the stark contrast in rain rates between the DR and DL (and UR and UL) quadrants at inner radii, despite comparable vertical velocities (Figs. 6a,c).
Precipitation and midlevel vertical velocity in (a),(b) ERA5, (c),(d) CFSR, and (e),(f) TC-RADAR, for C1 TCs (C0–C2 in TC-RADAR) under moderate shear. (left) Quadrant radial profiles, where total rain rate and 600-hPa pressure velocity are plotted for reanalyses, and 2-km reflectivity and 5-km vertical velocity are plotted for TC-RADAR. (right) Spatial maps of these fields, where contours in (b) and (d) represent pressure velocity values of −0.2, −0.5, −1.0, −1.5, and −2.0 Pa s−1, and the 0.25 m s−1 contour is shown in (f). Statistical significance is shown on left panels, similar to Fig. 4. Quadrants are labeled in (d).
Citation: Journal of Climate 37, 22; 10.1175/JCLI-D-23-0628.1
c. Thermodynamics
As discussed in section 1, dry dynamics predict a cold anomaly downshear, as ascent develops in response to the initial vortex tilt and vice versa upshear. These anomalies would then be advected cyclonically, with isentropic ascent as parcels flow from the warm to the cold sector. While moist physics complicates this interaction, expected thermal perturbations include anomalous warmth right-of-shear. Given the asymmetries of the circulation and precipitation fields in Figs. 2–6, asymmetries are expected in other fields such as humidity and surface heat fluxes.
Figures 7a and 7b assess 925-hPa humidity and equivalent potential temperature θe as anomalies from the azimuthal mean. The CFSR composite has slightly more low-level moisture and higher raw θe than ERA5 (not shown). Low-level thermodynamic asymmetry is mostly oriented across the shear vector, with moist, high-θe air right-of-shear (Figs. 7a,b), as in observations (Zhang et al. 2013). Asymmetry exists at all radii but is most prominent at outer radii, where anomalous warmth and moisture extend particularly into the UR. In idealized convection-permitting simulations, Riemer and Montgomery (2011) and Riemer (2016) found this same pattern where the low-level moist envelope is preferentially distorted right-of-shear. They postulated that when the TC circulation interacts with nonzero environmental low-level flow, a stagnation point, in the streamlines, occurs at far radii right-of-shear. This allows for inner core moisture to drift farther from the TC center at these azimuths. The low-level thermodynamic asymmetry in Figs. 7a and 7b may also suggest that the UR is a region of boundary layer entropy recovery following enhanced evaporation and low-θe air intrusion by rain fallout in the UL, as seen in observations (Zhang et al. 2013) and simulations (Ahern et al. 2021). This is supported by the amplified surface latent heat fluxes left-of-shear (Figs. 7c,d), collocated with the maximum tangential wind (Figs. 2a–f) and minimum low-level θe (Figs. 7a,b). We acknowledge that there is sensitivity in boundary layer processes such as surface fluxes to model physics (e.g., Nardi et al. 2022), which may contribute to the higher raw latent heat fluxes in CFSR along with the stronger low-level winds. However, this asymmetry in surface fluxes is consistent with observations and idealized simulations (Chen et al. 2018, 2019).
Composite mean (a),(b) 925-hPa specific humidity anomaly from the azimuthal mean, (c),(d) surface latent heat flux, and (e),(f) 700–500-hPa relative humidity in (left) ERA5 and (right) CFSR. Contours in (a) and (b) show the azimuthal anomalies of 925-hPa θe in intervals of 0.5 K (positive in red, negative in blue). In (c) and (d), these contours represent the azimuthal anomalies in latent heat flux in intervals of 10 W m−2. In (e) and (f), these contours represent the azimuthal anomalies in 600-hPa θ in intervals of 0.2 K. Black contours in (e) and (f) show the 600-hPa ascent in 0.5 Pa s−1 intervals. Shear-relative quadrants are labeled in (c).
Citation: Journal of Climate 37, 22; 10.1175/JCLI-D-23-0628.1
Midlevel relative humidity and θ distributions (shading and red/blue contours in Figs. 7e,f, respectively) are aligned approximately along the tilt vector in Fig. 5, with warm and dry air UR. The alignment between 600-hPa ascent (black contours in Figs. 7e,f) and θ is largely as expected, as wider-reaching DR ascent occurs as air flows from the warm to the cold sector. Like low-level θe, midlevel θ asymmetry is most pronounced at outer radii. This distribution indicates that the DR quadrant is the focal point for warm air advection and isentropic ascent (Jones 1995; Frank and Ritchie 1999; Boehm and Bell 2021), particularly at outer radii where the DR and DL quadrants produce comparable precipitation (Figs. 6a,b). While convective-scale thermal gradients and individual rainbands do not emerge in the composite and are likely poorly resolved (if at all), thermodynamic processes such as buoyancy advection may be important to ascent and precipitation in the DR rainband region. This hypothesis will be examined in the next section by introducing several advanced process-oriented diagnostics.
4. Process-oriented perspectives
After presenting composite TC structural asymmetries in section 3, we now introduce a series of diagnostics to analyze specific processes contributing to the asymmetries in precipitation and vertical motion. These can be used to break down parameterized rainfall, examine the shear-relative three-dimensional circulation and simulated cloud properties, and attribute vertical motion to processes such as vorticity advection, buoyancy advection, and diabatic effects. We acknowledge that detailed conclusions of each require detailed knowledge of model parameterization suites that is outside the scope of our study. Here, we speculate on aspects of the reanalysis TCs that compare well to observed shear-relative behavior and state the fields and frequency of output data required to fully apply these diagnostics in GCMs.
a. Precipitation processes
TC inner core and outer rainband regions undergo precipitation regime changes azimuthally. These are marked in observations by changes in the reflectivity structure (e.g., Hence and Houze 2011, 2012; Reasor et al. 2013), updraft behavior (e.g., DeHart et al. 2014; Barron et al. 2022), and thermodynamic and microphysical properties (e.g., Didlake and Kumjian 2017; Feng and Bell 2019; Laurencin et al. 2020; Boehm and Bell 2021). In the inner core, the DR is most often where convective growth begins. We expect a mature convective precipitation regime in the DL inner core, given that this is the quadrant which the vortex most often tilts into. Moving downwind into the UL, precipitation becomes more stratiform in nature, marked by reductions in cloud ice column counts and shape diversity (Didlake and Kumjian 2017; Homeyer et al. 2021). In the outer rainbands, convective initiation occurs most frequently right-of-shear (Hence and Houze 2012). In the DR, enhanced buoyancy has been shown to contribute to convective growth and maturation (Molinari et al. 2012; Li and Fang 2019). In the DL, precipitation becomes more stratiform in nature, marked by the broadening and increased homogeneity of the precipitation shield and the development of a “mesoscale descending inflow” (MDI) via latent cooling (Didlake and Houze 2013; Didlake et al. 2018; Yu and Didlake 2019; Yu et al. 2021). Following this convective-to-stratiform transition, rainfall is generally lowest in the UR, consistent with our Fig. 6.
Both CFSR and ERA5 partition rain rate into components from the convective parameterization (“convective”) at subgrid scales, and the large-scale cloud scheme at and beyond the gridscale (“large scale”). We note that large scale is occasionally referred to as “resolved” scale in other literature studies, and it does not explicitly mean “stratiform,” as the gridscale implies little about microphysical properties. Each reanalysis uses a mass flux-based convection scheme. ERA5 employs an update of the Tiedtke (1989) bulk mass flux scheme with modifications by Dee et al. (2011) and Bechtold et al. (2014). Its closure is based on an assumption of quasi-equilibrium in the free troposphere (Arakawa and Schubert 1974), subject to boundary layer forcings including surface heat fluxes. It is designed such that convective available potential energy (CAPE) is fully available for consumption only at the conclusion of lower-tropospheric entropy buildup (Bechtold et al. 2014). CFSR uses a modified Arakawa–Schubert deep convection scheme (Moorthi et al. 2001) with shallow convection handled by a Tiedtke (1983)-like parameterization. Its convective trigger function is based on a combination of surface heterogeneities, boundary layer and free tropospheric turbulence, and resolved-scale vertical motion (Rogers and Fritsch 1996). This trigger has been found to activate more readily in a moist subcloud layer (Hong and Pan 1998). For the large-scale cloud schemes, ERA5 uses a modified Tiedtke (1993) scheme which separates cloud liquid and ice (Tompkins et al. 2007), while CFSR uses a simpler parameterization with prognostic cloud condensate (Xu and Randall 1996; Zhao and Carr 1997). A thorough summary of these parameterizations is presented by Fujiwara et al. (2017).
The convective and large-scale rain rates are shown in Fig. 8. The dominant contributor inside of 250 km is the large-scale rain in the DL (yellow squares in Figs. 8a,b). This indicates that the majority of inner core rain is forced by resolved low-level convergence, which may be underestimated given the coarse resolution of the reanalyses. Beyond 250 km, the convective rain in the DR (orange triangles) becomes the leading contributor, particularly in CFSR. This represents the increased prevalence of the subgrid scale, instability-driven convective cells in the outer rainbands. The distribution of convective precipitation is broad and diffuse in the coarser CFSR with a substantially lower maximum value (2.2 mm h−1 at r = 175 km in CFSR, compared to 3.7 mm h−1 at r = 100 km in ERA5 in the DR quadrant, Figs. 8a–d). This also reflects sensitivity in rain rate magnitudes to the parameterizations (Jones et al. 2021). Therefore, our remaining discussion of rainfall focuses less on magnitude and more on its spatial collocation with fields such as instability, convergence, and cloud properties.
Composite mean shear-relative rain rate attributed to the convective parameterization and large-scale cloud scheme. (a),(b) Quadrant radial profiles for ERA5 and CFSR, respectively, using similar statistical significance criteria and labeling as in Figs. 4 and 6. (c),(d) Convective parameterization rain rate. (e),(f) Large-scale rain rate. Red contours in (c)–(f) show the positive CAPE anomalies from the azimuthal mean in 50 J kg−1 intervals, and black contours show the 900-hPa convergence in 2 × 10−5 s−1 intervals.
Citation: Journal of Climate 37, 22; 10.1175/JCLI-D-23-0628.1
Figures 8c–f show the convective and large-scale rain rates spatially, with 950-hPa convergence (black contours), and positive azimuthal CAPE anomaly (red) overlaid. Each reanalysis outputs a different type of CAPE, so we use the analyzed thermodynamic fields to compute CAPE, lifting a parcel from a 0–1-km mixed layer (Craven et al. 2002). There is strong collocation of the low-level convergence with the vertical velocity shown in Figs. 2, 3, 6, and 7. CAPE anomaly maximizes right-of-shear (particularly UR) and is the greatest at radii outside of 200 km, aligned with the low-level moist, high-θe air in Figs. 7a and 7b. The CAPE maximum we identify differs from prior observational studies (e.g., Molinari et al. 2012; Schenkel et al. 2020), where CAPE maximizes DR or directly downshear. Possible causes for this difference include the coarse resolution of the reanalyses, potential boundary layer thermodynamic biases (Slocum et al. 2022), and how CAPE is consumed in the convective parameterization. For example, the convective rain rate increases sharply from the UR to DR (Figs. 8c,d), implying that the convective parameterization is preferentially triggered at this stage, likely due to sufficient CAPE buildup and increasing convergence. We speculate that ERA5’s lower raw CAPE values (not shown), coupled with concentrated convergence downshear, lead to a more focused distribution of convective rainfall downshear and DR (Fig. 8c) as CAPE is gradually consumed from its right-of-shear maximum. In other words, ERA5’s convective rainfall distribution is potentially more focused because the kinematic and thermodynamic forcings triggering the convective parameterization occur over a smaller area. Meanwhile, the more diffuse distribution of convective rainfall in CFSR is potentially due to higher raw CAPE, broadly distributed convergence, and the tendency for the parameterization to activate in a moist environment (Hong and Pan 1998). The dynamically forced nature of the large-scale rain is more apparent in Figs. 8e and 8f, where the maximum convergence and rainfall occur at similar radii. ERA5’s large-scale rainfall maximum is slightly downwind of the peak convergence and vertical motion (Fig. 8e), as prognostic rainwater is advected cyclonically from the updraft location. CFSR features diagnostic rainwater, which falls out of the column at the same time step it is generated at, so this offset is less pronounced (Fig. 8f).
Decreasing instability through the downshear semicircle in Fig. 8, along with weakening ascent from the DL to the UL, suggests that a precipitation regime transition occurs left-of-shear. While it is challenging to isolate convective versus stratiform modes at these resolutions, information on such a regime change can be gathered by considering vertically resolved cloud, kinematic, and thermodynamic properties. Figure 9 shows the cloud water and ice content, and the TC overturning circulation for each quadrant in radius–pressure space. We focus our discussion on ERA5 (Figs. 9a–d) as CFSR only outputs a unified cloud liquid and ice variable (Figs. 9e–h), although we acknowledge that CFSR’s shear-relative overturning circulation behaves similarly to ERA5’s and that the total cloud water aloft is generally higher in CFSR, potentially due to the differences in the convective and microphysics parameterizations. The freezing level (pink contour) is near 550 hPa in the outer environment and lifts to near 500 hPa at the center. This 50-hPa difference is broadly consistent with observations (Homeyer et al. 2021). Strong ascent and high cloud water concentrations are apparent through a deep-layer downshear, and the overturning circulation features strong low-level inflow as in Zhang et al. (2013) with upper-level outflow (Figs. 9a,b). The low-level convergence layer is the deepest and widest DR, where midlevel ascent extends to 400-km radius (Fig. 9b). The profiles of ascent and divergence at inner radii in the DL largely resemble a convective growth regime, where Brauer et al. (2024) identified dominance of collision–coalescence precipitation in observations. Along with the strongest updrafts and precipitation, the DL also features the greatest cloud ice aloft and supercooled liquid above the freezing level (Fig. 9a).
Shear-relative profiles of the cloud water and ice content in (top) ERA5 and (bottom) CFSR. (a),(e) DL; (b),(f) DR; (c),(g) UL; (d),(h) UR. For ERA5, cloud liquid is shaded in gray, and cloud ice is contoured in black in intervals of 0.03 g kg−1. For CFSR, the sum of cloud liquid and ice is shaded. (red) Ascent in intervals of 0.2 Pa s−1. (vectors) Radial and vertical winds. (pink) Freezing level.
Citation: Journal of Climate 37, 22; 10.1175/JCLI-D-23-0628.1
Convective growth also appears to take place DR, given its robust “in-up-out” circulation compared to the UR (Figs. 9b,d). Black et al. (2002) found a similar pattern of preferential convective development downshear. The DL shows the signs of some convective decay at outer radii, marked by slightly weaker updrafts and low-level inflow, and inflow from 550 to 400 hPa at r = 150–250 km (Fig. 9a). Weaker updrafts at far radii of the DL are especially apparent at lower levels, suggesting “bottom-up” updraft decay, which may reflect environments favorable for downdrafts (Barron et al. 2022). Convective decay is most apparent from the DL to UL (Figs. 9a,c). In the UL, updrafts at all radii and heights are weakened, low-level inflow is limited to the lowest 100 hPa, and there is a lower concentration of cloud water. Inflow emerges aloft from the freezing level to 250 hPa, as well as outflow from 900 to 650 hPa. This UL upper-level convergence feature is located at a higher altitude than a typical MDI jet associated with latent cooling of stratiform precipitation in rainbands (Didlake et al. 2018). It resembles the “forced downdraft” found in idealized simulations by Dai et al. (2021), where the environmental storm-relative flow due to VWS undercuts the TC’s divergent outflow. Updrafts are the weakest at inner radii UR (Fig. 9d), and the cloud ice concentration is the lowest, but the region of ascent shown by the red contours expands slightly radially outward compared to the UL (i.e., near r = 200 km). This aligns with increasing moisture and instability right-of-shear (Figs. 7 and 8). While it is difficult to isolate stratiform processes given the lack of information about precipitation microphysics, the reanalyses produce the patterns of rainfall types, kinematic structure, and cloud vertical structure that are broadly consistent with theory and observations.
b. Vertical motion processes
Figure 10 presents the vertical profiles of the terms in Eq. (1) in the inner core, which we define as the innermost 150 km (Figs. 4a–f). We note that in future work, a dynamic radial range may be used that scales with TC size for each snapshot. A logarithmic transform is applied to the terms in Figs. 10 and 11 for visualization, and we omit the small terms related to differential vertical advection of vorticity and differential vorticity tilting. By assuming L(ω) ∝ −ω, terms shaded in warm colors in Fig. 10 are expected to contribute to ascent and those shaded in cool colors are expected to contribute to descent. This assumption is imperfect, as evidenced by the strong descent implied by a strongly negative L(ω) term upshear (Figs. 10c,d,g,h), where there is still mean (albeit weaker) ascent. Numerical instabilities complicated efforts to numerically solve for ω as in Yu and Didlake (2019), which would be the ideal method to implement this diagnostic. However, several features in our calculations are consistent with the reanalysis vertical velocity to suggest a quantitative comparison of forcing terms is feasible. First, L(ω) maximizes downshear, although it is notably stronger in CFSR despite a similar ω field to ERA5’s (Figs. 10a,b,e,f). Second, the shapes of the ω profiles are captured by L(ω), as there are a minimum in ω upshear between 700 and 400 hPa, and a maximum downshear at these levels. Third, the thermal advection aloft appears to be captured, with the buoyancy advection term maximizing right-of-shear (particularly DR, Figs. 10b,f), in phase with the thermal asymmetry in Fig. 7.
Vertical profiles of terms in the generalized ω equation for (a)–(d) ERA5 and (e)–(h) CFSR. Positive values are shown in warm colors and are expected to contribute to ascent. Terms are averaged in shear-relative quadrants as in Fig. 9, from 0- to 150-km radius to capture inner core processes.
Citation: Journal of Climate 37, 22; 10.1175/JCLI-D-23-0628.1
As in Fig. 10, but with terms averaged over 150–300-km radius to assess contributors to vertical motion in the rainband region.
Citation: Journal of Climate 37, 22; 10.1175/JCLI-D-23-0628.1
Differential vorticity advection is positive at all vertical levels in the DR, up to 600 hPa in the DL, and only in the boundary layer and upper-troposphere upshear (second column in Fig. 10). We hypothesize that the weakening contribution with height in the DL (the direction of mean vortex tilt) is related to the weakening vortex with height. The differential vorticity advection term is the dominant positive contributor to ω in all quadrants below 900 hPa in ERA5 and below 800 hPa in CFSR. This finding differs from Yu and Didlake (2019), who found that buoyancy advection dominates low-level vertical motion in both the inner core and rainbands. However, their model used a free-slip surface boundary condition, so it is possible that our result is an axisymmetric boundary layer effect where vorticity advection by the inflow along the radial gradient of storm-scale vorticity weakens with height. It is also possible that the coarser resolution of the reanalyses is relevant to this difference. The DR is where buoyancy advection appears to be most important to inner core convective growth, as this is where the maximum warm air advection is taking place based on the thermal asymmetry in Fig. 7 (third column in Figs. 10b,f). This term is also positive through most of the troposphere in the UR in ERA5 and the DL in CFSR (Figs. 10d,e). The magnitudes of the buoyancy advection and vorticity advection terms are comparable between ERA5 and CFSR, although we note that there are subtle azimuthal differences. For example, positive contributions of the buoyancy advection term are mostly confined to the right-of-shear semicircle in ERA5 (Figs. 10b,d), while noteworthy positive contributions exist at varying levels in CFSR in the DL, DR, and UR (Figs. 10e,f,h).
We have computed the differential vorticity advection and buoyancy advection terms explicitly. Next, we speculate on possible diabatic processes taking place under the residual term in Fig. 10, again acknowledging that these are prone to substantial uncertainty in the absence of explicit diabatic heating output. The residual term is strongly negative throughout the troposphere upshear, resembling the vertical structure of L(ω) (Figs. 10c,d,g,h), which may imply that evaporative rain cooling produces negative buoyancy there. Notably, regions of a positive residual are either collocated with or immediately downwind of positive buoyancy advection. For example, in ERA5, positive buoyancy advection right-of-shear is followed by a maximum in the residual aloft in the DL (Figs. 10a,b,d). If this indeed reflects a diabatic effect, then the overall dynamical forcing for shear-relative inner core vertical motion in the reanalyses can be described as follows: Differential vorticity advection lifts air from the boundary layer in all quadrants. Right-of-shear (particularly DR), enhanced buoyancy advection triggers deep convective growth, assisted by preferential differential vorticity advection aloft downshear. This leads to intense latent heating DL that augments deep convection, before buoyancy reduces left-of-shear and upshear as rain fallout occurs.
Figure 11 presents the same analysis for the rainband region, defined as the 150–300-km radius range, where forcing terms are mostly weaker than in the inner core. Differential vorticity advection again helps force ascent out of the boundary layer and is positive throughout most of the troposphere downshear (Figs. 11a,b,e,f). While weaker than the inner core, the buoyancy advection term is again positive through most of the troposphere in the DR (Figs. 11b,f). Interestingly, this term is also positive in the low- and midlevels left-of-shear in ERA5 (Figs. 11a,c). Below 700 hPa, this is maximized in the UL (Fig. 11c), immediately downwind of and beneath a strong negative residual term in the DL between 750 and 450 hPa (fourth column of Fig. 11a). A possible physical process that this could highlight is a sinking cold pool (diabatic cooling) coupled with high-θe boundary layer air in the DL, creating a buoyant airmass that is advected into the UL (positive buoyancy advection) (Didlake et al. 2018). This buoyancy advection signal is not as clear in CFSR, possibly due to its coarser resolution or the broader circulation coupled with our static boundaries. The vertical structure of the residual strongly resembles that of L(ω) in all quadrants (fourth column of Fig. 11). This is most often negative, although an exception is a strong positive signal above 600-hPa DL in CFSR (Fig. 10e). This resembles the heating profile of a stratiform precipitation regime, with diabatic heating above 600 hPa and cooling below. However, this signal is much weaker and more confined to the upper levels in ERA5 (Fig. 11a). In general, we find several similarities in the controls on vertical motion between the rainbands and inner core. Namely, we identify the importance of differential vorticity advection and buoyancy advection downshear, though leading to weaker vertical motions in the rainbands compared to the inner core, as expected. However, the increased prevalence of stratiform precipitation and associated patterns of diabatic heating in the rainbands may affect the shear-relative distribution of buoyancy at outer radii. This diagnostic tool suggests that moist physics parameterizations may have a substantial influence on the simulated vertical motion of TCs in reanalyses, and we will optimize its use in future studies diagnosing vertical motion in high-resolution GCMs.
5. Conclusions
Proper representation of the TC asymmetric structure in models is important for weather and climate prediction. This is particularly true for state-of-the-art climate models, which still struggle to capture the aspects of the axisymmetric structure (Camargo and Wing 2016; Kim et al. 2018; Wing et al. 2019; Moon et al. 2020). The dominant asymmetry often seen in TCs is a wavenumber 1 mode induced by environmental VWS. We are only aware of one study that directly assessed shear-relative TC asymmetry in GCMs (Moon et al. 2022). This motivates our comprehensive process-oriented analysis of shear-relative asymmetry in reanalyses (ERA5 and CFSR), a useful first step to assess how the TC-VWS interaction is captured in a setting with GCM-like resolution (≥0.25°) and parameterized convection. There are documented shortcomings of TCs in reanalyses, including low intensity biases, intermodel precipitation spread, occasional nonphysical structure, inability to simulate the TC intensity life cycle, and poor skill scores of observed TC detection (Schenkel and Hart 2012; Murakami 2014; Zick and Matyas 2015; Hodges et al. 2017; Zarzycki et al. 2021; Jones et al. 2021; Dirkes et al. 2023). Despite these shortcomings, we find that many aspects of shear-relative asymmetric structure are captured reasonably. We have substantiated this argument by directly comparing the reanalysis circulation and precipitation fields to airborne radar observations. Particular structural characteristics in the reanalyses that compare favorably to prior theoretical, observational, and high-resolution modeling work are listed below:
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Circulation: Inner core inflow and ascent are most prominent in the DL, aligned with vortex tilt. While the magnitude of vortex tilt is significantly overestimated compared to radar observations, the simulated tilt increases for weaker intensity and stronger VWS. The strongest tangential winds are found left-of-shear, slightly downwind of the maximum near-surface inflow. At outer radii, ascent and convergence are more prominent DR, conditions favoring rainband occurrence.
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Precipitation: The heaviest rainfall is in the DL inner core, with less rain upshear. The large-scale (dynamically forced) rainfall maximizes in the DL inner core, near or slightly downwind of the peak low-level convergence and ascent. At outer radii, the heaviest precipitation occurs in the DR, mostly attributed to the convective parameterization (instability-driven).
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Thermodynamics: While CAPE seemingly maximizes in different locations between reanalyses and observations, we find moist, high-θe low-level air is right-of-shear, particularly UR, downwind of enhanced surface enthalpy fluxes. This is especially prevalent at outer radii, where the interaction of the TC circulation with low-level environmental flow may cause inner core moisture to drift outward (e.g., Riemer 2016). Aloft, anomalously warm air is located in the UR, and thermal perturbations are approximately aligned with the vortex tilt.
It is difficult to diagnose convective and stratiform precipitation regimes in reanalyses, but we identify kinematic and thermodynamic features resembling a realistic shear-relative precipitation process. The downshear quadrants suggest a predominantly convective precipitation regime, where convective initiation and maturation are marked by strong and wide-reaching updrafts, high concentrations of cloud ice and supercooled liquid, and an “in-up-out” overturning circulation. Robust inner core convection occurs DL, while appreciable updrafts and low-level convergence extend to farther radii DR. Downwind in the UL, updrafts weaken while upper-level convergence and low-level divergence emerge near the center. The UL is a region of convective decay and rain fallout, while the UR serves as a “recharge” region, where the thermodynamic environment becomes primed for convective growth downwind.
As a proof-of-concept analysis, we also sought an explanation for vertical motion asymmetry using a generalized ω equation. In the inner core, differential vorticity advection (dynamic forcing) helps to lift air out of the boundary layer in all quadrants. Buoyancy advection generates lift above the boundary layer, particularly in the DR as high-θe air is advected from the UR. This yields convective growth downshear, where latent heating and ascent maximize DL. We speculate that diabatic effects are impactful through most of the TC environment, such as evaporative cooling in the rain fallout region left-of-shear and upshear. It is possible that the effect of buoyancy advection in the outer rainbands is underestimated, particularly right-of-shear, as localized updrafts are often dependent on subgrid scale thermal gradients. Such processes make proper representation of rainband convection imperative in parameterizations. We will aim to optimize the use of the ω equation diagnostic in future work, including reducing uncertainty in the diabatic heating term.
Some differences also emerge between the two reanalyses. CFSR employs TC preprocessing that relocates a vortex and synthetically adjusts its wind field, while ERA5 does not. Because of this, CFSR produces stronger tangential winds for a given minimum pressure, despite its coarser resolution. Each of these fields also has some sensitivity to the specifications of the boundary layer parameterization. For TCs with a similar minimum pressure, CFSR tends to feature higher baseline CAPE and low-level moisture, despite a similar distribution of shear-relative azimuthal anomalies to ERA5. This seems to affect the distribution of precipitation attributed to the convective parameterization. Also, ERA5 features prognostic rainwater, which is directly advected by the TC circulation, while CFSR’s rainwater immediately falls out of the column it is generated in. This causes an azimuthal offset in where the large-scale rain rate maximizes, where ERA5’s maximum is slightly downwind of the peak inner core ascent and low-level convergence. We again caution that some of our results may be influenced by coarse grid spacing, conservative physics parameterizations, and data assimilation used in the reanalyses. Nonetheless, our findings present optimism for the ability of GCM-like datasets to capture at least the large-scale aspects of TC asymmetry reliably.
Future directions center around a core question: What happens when the “training wheels” of observations are removed by considering free-running GCMs? For example, this process-oriented analysis of shear-relative asymmetry could be applied to a model such as the Community Atmosphere Model (CAM; e.g., Neale et al. 2012; Zarzycki et al. 2014). CAM’s flexibility presents a powerful opportunity to assess numerous model sensitivities in a relatively controlled setting, including how the shear-relative TC structure depends on resolution, convective parameterizations, microphysics, and dynamical core in historical and warming simulations. Such an analysis can be extended to consider TCs at various stages, including genesis and periods of intensity change. We speculate that this work has great potential to inform future model development. While substantial progress has been made in simulating the TC structure in GCMs, simulating the asymmetric TC structure presents a new avenue for progress, paramount to improving TC prediction on climatic time scales.
Acknowledgments.
We acknowledge computing support from the Roar and Roar Collab Supercomputers, maintained by the Penn State Institute for Computational and Data Sciences. Additional computing was performed on Cheyenne (https://doi.org/10.5065/D6RX99HX), provided by NCAR’s Computational and Information Systems Laboratory, sponsored by the National Science Foundation. Reanalyses were downloaded from the NCAR Research Data Archive. JDC is supported by the Penn State College of Earth and Mineral Sciences, Dean’s Fund for Postdoc-Facilitated Innovation. C. M. Z. acknowledges the support from the U.S. Department of Energy, Office of Science, Office of Biological and Environmental Research program under Award DE-SC0016605 “A framework for improving analysis and modeling of Earth system and intersectoral dynamics at regional scales.” Finally, we thank three anonymous reviewers for their thorough, constructive comments.
Data availability statement.
ERA5 is available from the Copernicus Climate Change Service Climate Data Store at https://cds.climate.copernicus.eu/#!/search?text=ERA5&type=dataset. CFSv2 is available from the NOAA National Centers for Environmental Information at https://www.ncei.noaa.gov/access/metadata/landing-page/bin/iso?id=gov.noaa.ncdc:C00877, while the original CFSR (1979-2011) is available at https://www.ncei.noaa.gov/access/metadata/landing-page/bin/iso?id=gov.noaa.ncdc:C00765. TempestExtremes is available from GitHub at https://github.com/ClimateGlobalChange/tempestextremes. TC-centered data snapshots, TC tracks, wind shear information, and MATLAB code to produce generalized versions of the figures in this manuscript, are accessible from GitHub at https://github.com/jdcarstens17/tc-asymmetry and the Penn State Data Commons at https://doi.org/10.26208/EYZR-XD37 (Carstens et al. 2023).
REFERENCES
Abarca, S. F., and M. T. Montgomery, 2015: Are eyewall replacement cycles governed largely by axisymmetric balance dynamics? J. Atmos. Sci., 72, 82–87, https://doi.org/10.1175/JAS-D-14-0151.1.
Ahern, K., R. E. Hart, and M. A. Bourassa, 2021: Asymmetric hurricane boundary layer structure during storm decay. Part I: Formation of descending inflow. Mon. Wea. Rev., 149, 3851–3874, https://doi.org/10.1175/MWR-D-21-0030.1.
Alland, J. J., B. H. Tang, K. L. Corbosiero, and G. H. Bryan, 2021a: Combined effects of midlevel dry air and vertical wind shear on tropical cyclone development. Part I: Downdraft ventilation. J. Atmos. Sci., 78, 763–782, https://doi.org/10.1175/JAS-D-20-0054.1.
Alland, J. J., B. H. Tang, K. L. Corbosiero, and G. H. Bryan, 2021b: Combined effects of midlevel dry air and vertical wind shear on tropical cyclone development. Part II: Radial ventilation. J. Atmos. Sci., 78, 783–796, https://doi.org/10.1175/JAS-D-20-0055.1.
Arakawa, A., and W. H. Schubert, 1974: Interaction of a cumulus cloud ensemble with the large-scale environment, part I. J. Atmos. Sci., 31, 674–701, https://doi.org/10.1175/1520-0469(1974)031<0674:IOACCE>2.0.CO;2.
Barron, N. R., A. C. Didlake Jr., and P. D. Reasor, 2022: Statistical analysis of convective updrafts in tropical cyclone rainbands observed by airborne Doppler radar. J. Geophys. Res. Atmos., 127, e2021JD035718, https://doi.org/10.1029/2021JD035718.
Bechtold, P., N. Semane, P. Lopez, J.-P. Chaboureau, A. Beljaars, and N. Bormann, 2014: Representing equilibrium and non-equilibrium convection in large-scale models. J. Atmos. Sci., 71, 734–753, https://doi.org/10.1175/JAS-D-13-0163.1.
Bender, M. A., 1997: The effect of relative flow on the asymmetric structure of the interior of hurricanes. J. Atmos. Sci., 54, 703–724, https://doi.org/10.1175/1520-0469(1997)054<0703:TEORFO>2.0.CO;2.
Berrisford, P., P. Kallberg, S. Kobayashi, D. Dee, S. Uppala, A. J. Simmons, P. Poli, and H. Sato, 2011: Atmospheric conservation properties in ERA-interim. Quart. J. Roy. Meteor. Soc., 137, 1381–1399, https://doi.org/10.1002/qj.864.
Bian, G.-F., G.-Z. Nie, and X. Qiu, 2021: How well is outer tropical cyclone size represented in the ERA5 reanalysis dataset? Atmos. Res., 249, 105339, https://doi.org/10.1016/j.atmosres.2020.105339.
Black, M. L., J. F. Gamache, F. D. Marks Jr., C. E. Samsury, and H. E. Willoughby, 2002: Eastern Pacific Hurricanes Jimena of 1991 and Olivia of 1994: The effect of vertical shear on structure and intensity. Mon. Wea. Rev., 130, 2291–2312, https://doi.org/10.1175/1520-0493(2002)130<2291:EPHJOA>2.0.CO;2.
Boehm, A. M., and M. M. Bell, 2021: Retrieved thermodynamic structure of Hurricane Rita (2005) from airborne multi–Doppler radar data. J. Atmos. Sci., 78, 1583–1605, https://doi.org/10.1175/JAS-D-20-0195.1.
Bosilovich, M. G., J. Chen, F. R. Robertson, and R. F. Adler, 2008: Evaluation of global precipitation in reanalyses. J. Appl. Meteor. Climatol., 47, 2279–2299, https://doi.org/10.1175/2008JAMC1921.1.
Bourdin, S., S. Fromang, W. Dulac, J. Cattiaux, and F. Chauvin, 2022: Intercomparison of four algorithms for detecting tropical cyclones using ERA5. Geosci. Model Dev., 15, 6759–6786, https://doi.org/10.5194/gmd-15-6759-2022.
Brauer, N. S., P. E. Kirstetter, J. B. Basara, S. Hristova-Veleva, S. Tanelli, and F. J. Turk, 2024: Precipitation microphysics in tropical cyclones: A global perspective using the NASA global precipitation measurement mission dual-frequency precipitation radar. J. Geophys. Res. Atmos., 129, e2023JD038709, https://doi.org/10.1029/2023JD038709.
Braun, S. A., M. T. Montgomery, and Z. Pu, 2006: High-resolution simulation of Hurricane Bonnie (1998). Part I: The organization of eyewall vertical motion. J. Atmos. Sci., 63, 19–42, https://doi.org/10.1175/JAS3598.1.
Camargo, S. J., and A. A. Wing, 2016: Tropical cyclones in climate models. Wiley Interdiscip. Rev.: Climate Change, 7, 211–237, https://doi.org/10.1002/wcc.373.
Carstens, J. D., A. C. Didlake Jr., and C. M. Zarzycki, 2023: Tropical cyclone structure snapshots in global reanalysis datasets. Penn State Data Commons, accessed 11 October 2023, https://doi.org/10.26208/EYZR-XD37.
Cha, T.-Y., M. M. Bell, W.-C. Lee, and A. J. DesRosiers, 2020: Polygonal eyewall asymmetries during the rapid intensification of Hurricane Michael (2018). Geophys. Res. Lett., 47, e2020GL087919, https://doi.org/10.1029/2020GL087919.
Chen, B.-F., C. A. Davis, and Y.-H. Kuo, 2018: Effects of low-level flow orientation and vertical shear on the structure and intensity of tropical cyclones. Mon. Wea. Rev., 146, 2447–2467, https://doi.org/10.1175/MWR-D-17-0379.1.
Chen, B.-F., C. A. Davis, and Y.-H. Kuo, 2019: An idealized numerical study of shear-relative low-level mean flow on tropical cyclone intensity and size. J. Atmos. Sci., 76, 2309–2334, https://doi.org/10.1175/JAS-D-18-0315.1.
Chen, S. S., J. A. Knaff, and F. D. Marks Jr., 2006: Effects of vertical wind shear and storm motion on tropical cyclone rainfall asymmetries deduced from TRMM. Mon. Wea. Rev., 134, 3190–3208, https://doi.org/10.1175/MWR3245.1.
Corbosiero, K. L., and J. Molinari, 2002: The effects of vertical wind shear on the distribution of convection in tropical cyclones. Mon. Wea. Rev., 130, 2110–2123, https://doi.org/10.1175/1520-0493(2002)130%3C2110:TEOVWS%3E2.0.CO;2.
Corbosiero, K. L., and J. Molinari, 2003: The relationship between storm motion, vertical wind shear, and convective asymmetries in tropical cyclones. J. Atmos. Sci., 60, 366–376, https://doi.org/10.1175/1520-0469(2003)060%3C0366:TRBSMV%3E2.0.CO;2.
Craven, J. P., R. E. Jewell, and H. E. Brooks, 2002: Comparison between observed convective cloud-base heights and lifting condensation level for two different lifted parcels. Wea. Forecasting, 17, 885–890, https://doi.org/10.1175/1520-0434(2002)017<0885:CBOCCB>2.0.CO;2.
Dai, Y., S. J. Majumdar, and D. S. Nolan, 2021: Tropical cyclone resistance to strong environmental shear. J. Atmos. Sci., 78, 1275–1293, https://doi.org/10.1175/JAS-D-20-0231.1.
Davis, C., C. Snyder, and A. C. Didlake Jr., 2008: A vortex-based perspective of eastern Pacific tropical cyclone formation. Mon. Wea. Rev., 136, 2461–2477, https://doi.org/10.1175/2007MWR2317.1.
Dee, D. P., and Coauthors, 2011: The ERA-Interim reanalysis: Configuration and performance of the data assimilation system. Quart. J. Roy. Meteor. Soc., 137, 553–597, https://doi.org/10.1002/qj.828.
DeHart, J. C., R. A. Houze Jr., and R. F. Rogers, 2014: Quadrant distribution of tropical cyclone inner-core kinematics in relation to environmental shear. J. Atmos. Sci., 71, 2713–2732, https://doi.org/10.1175/JAS-D-13-0298.1.
DeMaria, M., 1996: The effect of vertical shear on tropical cyclone intensity change. J. Atmos. Sci., 53, 2076–2088, https://doi.org/10.1175/1520-0469(1996)053<2076:TEOVSO>2.0.CO;2.
Demaria, M., and J. Kaplan, 1994: Sea surface temperature and the maximum intensity of Atlantic tropical cyclones. J. Climate, 7, 1324–1334, https://doi.org/10.1175/1520-0442(1994)007<1324:SSTATM>2.0.CO;2.
DeMaria, M., and J. Kaplan, 1999: An updated Statistical Hurricane Intensity Prediction Scheme (SHIPS) for the Atlantic and eastern North Pacific basins. Wea. Forecasting, 14, 326–337, https://doi.org/10.1175/1520-0434(1999)014%3C0326:AUSHIP%3E2.0.CO;2.
DeMaria, M., M. Mainelli, L. K. Shay, J. A. Knaff, and J. Kaplan, 2005: Further improvements to the Statistical Hurricane Intensity Prediction Scheme (SHIPS). Wea. Forecasting, 20, 531–543, https://doi.org/10.1175/WAF862.1.
Didlake, A. C., Jr., and R. A. Houze Jr., 2013: Dynamics of the stratiform sector of a tropical cyclone rainband. J. Atmos. Sci., 70, 1891–1911, https://doi.org/10.1175/JAS-D-12-0245.1.
Didlake, A. C., Jr., and M. R. Kumjian, 2017: Examining polarimetric radar observations of bulk microphysical structures and their relation to vortex kinematics in Hurricane Arthur (2014). Mon. Wea. Rev., 145, 4521–4541, https://doi.org/10.1175/MWR-D-17-0035.1.
Didlake, A. C., Jr., and M. R. Kumjian, 2018: Examining storm asymmetries in Hurricane Irma (2017) using polarimetric radar observations. Geophys. Res. Lett., 45, 13 513–13 522, https://doi.org/10.1029/2018GL080739.
Didlake, A. C., Jr., P. D. Reasor, R. F. Rogers, and W.-C. Lee, 2018: Dynamics of the transition from spiral rainbands to a secondary eyewall in Hurricane Earl (2010). J. Atmos. Sci., 75, 2909–2929, https://doi.org/10.1175/JAS-D-17-0348.1.
Dirkes, C. A., A. A. Wing, S. J. Camargo, and D. Kim, 2023: Process-oriented diagnosis of tropical cyclones in reanalyses using a moist static energy variance budget. J. Climate, 36, 5293–5317, https://doi.org/10.1175/JCLI-D-22-0384.1.
Eastin, M. D., W. M. Gray, and P. G. Black, 2005: Buoyancy of convective vertical motions in the inner core of intense hurricanes. Part II: Case studies. Mon. Wea. Rev., 133, 209–227, https://doi.org/10.1175/MWR-2849.1.
Emanuel, K. A., 1986: An air-sea interaction theory for tropical cyclones. Part I: Steady-state maintenance. J. Atmos. Sci., 43, 585–605, https://doi.org/10.1175/1520-0469(1986)043<0585:AASITF>2.0.CO;2.
Feng, Y.-C., and M. M. Bell, 2019: Microphysical characteristics of an asymmetric eyewall in major Hurricane Harvey (2017). Geophys. Res. Lett., 46, 461–471, https://doi.org/10.1029/2018GL080770.
Fierro, A. O., and E. R. Mansell, 2017: Electrification and lightning in idealized simulations of a hurricane-like vortex subject to wind shear and sea surface temperature cooling. J. Atmos. Sci., 74, 2023–2041, https://doi.org/10.1175/JAS-D-16-0270.1.
Finocchio, P. M., and S. J. Majumdar, 2017: A statistical perspective on wind profiles and vertical wind shear in tropical cyclone environments in the Northern Hemisphere. Mon. Wea. Rev., 145, 361–378, https://doi.org/10.1175/MWR-D-16-0221.1.
Fischer, M. S., P. D. Reasor, R. F. Rogers, and J. F. Gamache, 2022: An analysis of tropical cyclone vortex and convective characteristics in relation to storm intensity using a novel airborne Doppler radar database. Mon. Wea. Rev., 150, 2255–2278, https://doi.org/10.1175/MWR-D-21-0223.1.
Fischer, M. S., R. F. Rogers, P. D. Reasor, and J. P. Dunion, 2024: An observational analysis of the relationship between tropical cyclone vortex tilt, precipitation structure, and intensity change. Mon. Wea. Rev., 152, 203–225, https://doi.org/10.1175/MWR-D-23-0089.1.
Flatau, M., W. H. Schubert, and D. E. Stevens, 1994: The role of baroclinic processes in tropical cyclone motion: The influence of vertical tilt. J. Atmos. Sci., 51, 2589–2601, https://doi.org/10.1175/1520-0469(1994)051%3C2589:TROBPI%3E2.0.CO;2.
Frank, W. M., and E. A. Ritchie, 1999: Effects of environmental flow upon tropical cyclone structure. Mon. Wea. Rev., 127, 2044–2061, https://doi.org/10.1175/1520-0493(1999)127<2044:EOEFUT>2.0.CO;2.
Frank, W. M., and E. A. Ritchie, 2001: Effects of vertical wind shear on the intensity and structure of numerically simulated hurricanes. Mon. Wea. Rev., 129, 2249–2269, https://doi.org/10.1175/1520-0493(2001)129%3C2249:EOVWSO%3E2.0.CO;2.
Franklin, J. L., S. J. Lord, S. E. Feuer, and F. D. Marks Jr., 1993: The kinematic structure of Hurricane Gloria (1985) determined from nested analyses of dropwindsonde and Doppler radar data. Mon. Wea. Rev., 121, 2433–2451, https://doi.org/10.1175/1520-0493(1993)121<2433:TKSOHG>2.0.CO;2.
Fujiwara, M., and Coauthors, 2017: Introduction to the SPARC Reanalysis Intercomparison Project (S-RIP) and overview of the reanalysis systems. Atmos. Chem. Phys., 17, 1417–1452, https://doi.org/10.5194/acp-17-1417-2017.
Gall, R., J. Franklin, F. Marks, E. N. Rappaport, and F. Toepfer, 2013: The hurricane forecast improvement project. Bull. Amer. Meteor. Soc., 94, 329–343, https://doi.org/10.1175/BAMS-D-12-00071.1.
Gray, W. M., 1968: Global view of the origin of tropical disturbances and storms. Mon. Wea. Rev., 96, 669–700, https://doi.org/10.1175/1520-0493(1968)096<0669:GVOTOO>2.0.CO;2.
Gu, J.-F., Z.-M. Tan, and X. Qiu, 2016: Quadrant-dependent evolution of low-level tangential wind of a tropical cyclone in the shear flow. J. Atmos. Sci., 73, 1159–1177, https://doi.org/10.1175/JAS-D-15-0165.1.
Haarsma, R. J., and Coauthors, 2016: High Resolution Model Intercomparison Project (HighResMIP v1.0) for CMIP6. Geosci. Model Dev., 9, 4185–4208, https://doi.org/10.5194/gmd-9-4185-2016.
Harris, L., and Coauthors, 2020: GFDL SHiELD: A unified system for weather-to-seasonal prediction. J. Adv. Model. Earth Syst., 12, e2020MS002223, https://doi.org/10.1002/essoar.10503567.2.
Hart, R. E., and J. L. Evans, 2001: A climatology of the extratropical transition of Atlantic tropical cyclones. J. Climate, 14, 546–564, https://doi.org/10.1175/1520-0442(2001)014<0546:ACOTET>2.0.CO;2.
Hazelton, A., and Coauthors, 2022: Performance of 2020 real-time Atlantic hurricane forecasts from high-resolution global-nested hurricane models: HAFS-globalnest and GFDL T-SHiELD. Wea. Forecasting, 37, 143–161, https://doi.org/10.1175/WAF-D-21-0102.1.
Hence, D. A., and R. A. Houze Jr., 2011: Vertical structure of hurricane eyewalls as seen by the TRMM precipitation radar. J. Atmos. Sci., 68, 1637–1652, https://doi.org/10.1175/2011JAS3578.1.
Hence, D. A., and R. A. Houze Jr., 2012: Vertical structure of tropical cyclone rainbands as seen by the TRMM precipitation radar. J. Atmos. Sci., 69, 2644–2661, https://doi.org/10.1175/JAS-D-11-0323.1.
Hendricks, E. A., B. D. McNoldy, and W. H. Schubert, 2012: Observed inner-core structural variability in Hurricane Dolly (2008). Mon. Wea. Rev., 140, 4066–4077, https://doi.org/10.1175/MWR-D-12-00018.1.
Hersbach, H., and Coauthors, 2020: The ERA5 global reanalysis. Quart. J. Roy. Meteor. Soc., 146, 1999–2049, https://doi.org/10.1002/qj.3803.
Hodges, K., A. Cobb, and P. L. Vidale, 2017: How well are tropical cyclones represented in reanalysis datasets? J. Climate, 30, 5243–5264, https://doi.org/10.1175/JCLI-D-16-0557.1.
Homeyer, C. R., and Coauthors, 2021: Polarimetric signatures in landfalling tropical cyclones. Mon. Wea. Rev., 149, 131–154, https://doi.org/10.1175/MWR-D-20-0111.1.
Hong, S.-Y., and H.-L. Pan, 1998: Convective trigger function for a mass-flux cumulus parameterization scheme. Mon. Wea. Rev., 126, 2599–2620, https://doi.org/10.1175/1520-0493(1998)126<2599:CTFFAM>2.0.CO;2.
Hortal, M., 2002: The development and testing of a new two-time-level semi-Lagrangian scheme (SETTLS) in the ECMWF forecast model. Quart. J. Roy. Meteor. Soc., 128, 1671–1687, https://doi.org/10.1002/qj.200212858314.
Houze, R. A., Jr., 2010: Clouds in tropical cyclones. Mon. Wea. Rev., 138, 293–344, https://doi.org/10.1175/2009MWR2989.1.
Janiga, M. A., and C. D. Thorncroft, 2013: Regional differences in the kinematic and thermodynamic structure of African easterly waves. Quart. J. Roy. Meteor. Soc., 139, 1598–1614, https://doi.org/10.1002/qj.2047.
Jiang, X., and Coauthors, 2009: Vertical heating structures associated with the MJO as characterized by TRMM estimates, ECMWF reanalyses, and forecasts: A case study during 1998/99 winter. J. Climate, 22, 6001–6020, https://doi.org/10.1175/2009JCLI3048.1.
Jones, E., A. A. Wing, and R. Parfitt, 2021: A global perspective of tropical cyclone precipitation in reanalyses. J. Climate, 34, 8461–8480, https://doi.org/10.1175/JCLI-D-20-0892.1.
Jones, S. C., 1995: The evolution of vortices in vertical shear. I: Initially barotropic vortices. Quart. J. Roy. Meteor. Soc., 121, 821–851, https://doi.org/10.1002/qj.49712152406.
Jones, S. C., 2004: On the ability of dry tropical-cyclone-like vortices to withstand vertical shear. J. Atmos. Sci., 61, 114–119, https://doi.org/10.1175/1520-0469(2004)061<0114:OTAODT>2.0.CO;2.
Judt, F., and Coauthors, 2021: Tropical cyclones in global storm-resolving models. J. Meteor. Soc. Japan, 99, 579–602, https://doi.org/10.2151/jmsj.2021-029.
Kim, D., A. H. Sobel, A. D. Del Genio, Y. Chen, S. J. Camargo, M. Yao, M. Kelley, and L. Nazarenko, 2012: The tropical subseasonal variability simulated in the NASA GISS general circulation model. J. Climate, 25, 4641–4659, https://doi.org/10.1175/JCLI-D-11-00447.1.
Kim, D., and Coauthors, 2018: Process-oriented diagnosis of tropical cyclones in high-resolution GCMs. J. Climate, 31, 1685–1702, https://doi.org/10.1175/JCLI-D-17-0269.1.
Kiranmayi, L., and E. D. Maloney, 2011: Intraseasonal moist static energy budget in reanalysis data. J. Geophys. Res., 116, D21117, https://doi.org/10.1029/2011JD016031.
Klotzbach, P. J., M. M. Bell, S. G. Bowen, E. J. Gibney, K. R. Knapp, and C. J. Schreck III, 2020: Surface pressure a more skillful predictor of normalized hurricane damage than maximum sustained wind. Bull. Amer. Meteor. Soc., 101, E830–E846, https://doi.org/10.1175/BAMS-D-19-0062.1.
Knapp, K. R., M. C. Kruk, D. H. Levinson, H. J. Diamond, and C. J. Neumann, 2010: The International Best Track Archive for Climate Stewardship (IBTrACS). Bull. Amer. Meteor. Soc., 91, 363–376, https://doi.org/10.1175/2009BAMS2755.1.
Knutson, T. R., and Coauthors, 2020: Tropical cyclones and climate change assessment: Part II: Projected response to anthropogenic warming. Bull. Amer. Meteor. Soc., 101, E303–E322, https://doi.org/10.1175/BAMS-D-18-0194.1.
Krishnamurti, T. N., 1968: A diagnostic balance model for studies of weather systems of low and high latitudes, Rossby number less than 1. Mon. Wea. Rev., 96, 197–207, https://doi.org/10.1175/1520-0493(1968)096%3C0197:ADBMFS%3E2.0.CO;2.
Laurencin, C. N., A. C. Didlake Jr., S. D. Loeffler, M. R. Kumjian, and G. M. Heymsfield, 2020: Hydrometeor size sorting in the asymmetric eyewall of Hurricane Matthew (2016). J. Geophys. Res. Atmos., 125, e2020JD032671, https://doi.org/10.1029/2020JD032671.
Li, Q., and Q. Fang, 2019: Buoyancy of convective-scale updrafts in the outer cores of sheared tropical cyclones. Atmos. Oceanic Sci. Lett., 12, 58–65, https://doi.org/10.1080/16742834.2019.1548883.
Liu, Q., T. Marchok, H.-L. Pan, M. Bender, and S. Lord, 2000: Improvements in hurricane initialization and forecasting at NCEP with global and regional GFDL models. National Weather Service Tech. Procedures Bull. 472, 7 pp.
Marks, F. D., Jr., R. A. Houze Jr., and J. F. Gamache, 1992: Dual-aircraft investigation of the inner core of Hurricane Norbert. Part I: Kinematic structure. J. Atmos. Sci., 49, 919–942, https://doi.org/10.1175/1520-0469(1992)049%3C0919:DAIOTI%3E2.0.CO;2.
Molinari, J., and D. Vollaro, 1990: External influences on hurricane intensity. Part II: Vertical structure and response to the hurricane vortex. J. Atmos. Sci., 47, 1902–1918, https://doi.org/10.1175/1520-0469(1990)047%3C1902:EIOHIP%3E2.0.CO;2.
Molinari, J., D. M. Romps, D. Vollaro, and L. Nguyen, 2012: CAPE in tropical cyclones. J. Atmos. Sci., 69, 2452–2463, https://doi.org/10.1175/JAS-D-11-0254.1.
Moon, Y., and Coauthors, 2020: Azimuthally averaged wind and thermodynamic structures of tropical cyclones in global climate models and their sensitivity to horizontal resolution. J. Climate, 33, 1575–1595, https://doi.org/10.1175/JCLI-D-19-0172.1.
Moon, Y., and Coauthors, 2022: An evaluation of tropical cyclone rainfall structures in the HighResMIP simulations against satellite observations. J. Climate, 35, 7315–7338, https://doi.org/10.1175/JCLI-D-21-0564.1.
Moorthi, S., H.-L. Pan, and P. Caplan, 2001: Changes to the 2001 NCEP operational MRF/AVN global analysis/forecast system. NOAA NWS Tech. Procedures Bull. 484, 14 pp.
Murakami, H., 2014: Tropical cyclones in reanalysis data sets. Geophys. Res. Lett., 41, 2133–2141, https://doi.org/10.1002/2014GL059519.
Nardi, K. M., C. M. Zarzycki, V. E. Larson, and G. H. Bryan, 2022: Assessing the sensitivity of the tropical cyclone boundary layer to the parameterization of momentum flux in the community Earth system model. Mon. Wea. Rev., 150, 883–906, https://doi.org/10.1175/MWR-D-21-0186.1.
Neale, R. B., and Coauthors, 2012: Description of the NCAR Community Atmosphere Model (CAM 5.0). NCAR Tech. Note NCAR/TN-486+STR, 289 pp., www.cesm.ucar.edu/models/cesm1.0/cam/docs/description/cam5_desc.pdf.
Ooyama, K., 1969: Numerical simulation of the life-cycle of tropical cyclones. J. Atmos. Sci., 26, 3–40, https://doi.org/10.1175/1520-0469(1969)026%3C0003:NSOTLC%3E2.0.CO;2.
Parker, W. S., 2016: Reanalyses and observations: What’s the difference? Bull. Amer. Meteor. Soc., 97, 1565–1572, https://doi.org/10.1175/BAMS-D-14-00226.1.
Pei, Y., and H. Jiang, 2018: Quantification of precipitation asymmetries of tropical cyclones using 16-year TRMM observations. J. Geophys. Res. Atmos., 123, 8091–8114, https://doi.org/10.1029/2018JD028545.
Peng, K., R. Rotunno, G. H. Bryan, and J. Fang, 2019: Evolution of an axisymmetric tropical cyclone before reaching slantwise moist neutrality. J. Atmos. Sci., 76, 1865–1884, https://doi.org/10.1175/JAS-D-18-0264.1.
Reasor, P. D., and M. T. Montgomery, 2001: Three-dimensional alignment and corotation of weak, TC-like vortices via linear vortex Rossby waves. J. Atmos. Sci., 58, 2306–2330, https://doi.org/10.1175/1520-0469(2001)058<2306:tdaaco>2.0.co;2.
Reasor, P. D., and M. D. Eastin, 2012: Rapidly intensifying Hurricane Guillermo (1997). Part II: Resilience in shear. Mon. Wea. Rev., 140, 425–444, https://doi.org/10.1175/MWR-D-11-00080.1.
Reasor, P. D., M. D. Eastin, and J. F. Gamache, 2009: Rapidly intensifying Hurricane Guillermo (1997). Part I: Low-wavenumber structure and evolution. Mon. Wea. Rev., 137, 603–631, https://doi.org/10.1175/2008MWR2487.1.
Reasor, P. D., R. F. Rogers, and S. Lorsolo, 2013: Environmental flow impacts on tropical cyclone structure diagnosed from airborne Doppler radar composites. Mon. Wea. Rev., 141, 2949–2969, https://doi.org/10.1175/MWR-D-12-00334.1.
Reed, K. A., J. T. Bacmeister, N. A. Rosenbloom, M. F. Wehner, S. C. Bates, P. H. Lauritzen, J. E. Truesdale, and C. Hannay, 2015: Impact of the dynamical core on the direct simulation of tropical cyclones in a high-resolution global model. Geophys. Res. Lett., 42, 3603–3608, https://doi.org/10.1002/2015GL063974.
Riemer, M., 2016: Meso-β-scale environment for the stationary band complex of vertically sheared tropical cyclones. Quart. J. Roy. Meteor. Soc., 142, 2442–2451, https://doi.org/10.1002/qj.2837.
Riemer, M., and M. T. Montgomery, 2011: Simple kinematic models for the environmental interaction of tropical cyclones in vertical wind shear. Atmos. Chem. Phys., 11, 9395–9414, https://doi.org/10.5194/acp-11-9395-2011.
Rios-Berrios, R., and R. D. Torn, 2017: Climatological analysis of tropical cyclone intensity changes under moderate vertical wind shear. Mon. Wea. Rev., 145, 1717–1738, https://doi.org/10.1175/MWR-D-16-0350.1.
Rios-Berrios, R., R. D. Torn, and C. A. Davis, 2016a: An ensemble approach to investigate tropical cyclone intensification in sheared environments. Part I: Katia (2011). J. Atmos. Sci., 73, 71–93, https://doi.org/10.1175/JAS-D-15-0052.1.
Rios-Berrios, R., R. D. Torn, and C. A. Davis, 2016b: An ensemble approach to investigate tropical cyclone intensification in sheared environments. Part II: Ophelia (2011). J. Atmos. Sci., 73, 1555–1575, https://doi.org/10.1175/JAS-D-15-0245.1.
Rios-Berrios, R., P. M. Finocchio, J. J. Alland, X. Chen, M. S. Fischer, S. N. Stevenson, and D. Tao, 2024: A review of the interactions between tropical cyclones and environmental vertical wind shear. J. Atmos. Sci., 81, 713–741, https://doi.org/10.1175/JAS-D-23-0022.1.
Roberts, M. J., and Coauthors, 2020: Impact of model resolution on tropical cyclone simulation using the HighResMIP–PRIMAVERA multimodel ensemble. J. Climate, 33, 2557–2583, https://doi.org/10.1175/jcli-d-19-0639.1.
Rogers, R., S. Chen, J. Tenerelli, and H. Willoughby, 2003: A numerical study of the impact of vertical shear on the distribution of rainfall in Hurricane Bonnie (1998). Mon. Wea. Rev., 131, 1577–1599, https://doi.org/10.1175//2546.1.
Rogers, R., F. Marks, and T. Marchok, 2009: Tropical cyclone rainfall. Encyclopedia of Hydrological Sciences, 1st ed. M. G. Anderson and J. J. McDonnell, Eds., John Wiley and Sons, https://doi.org/10.1002/0470848944.hsa030.
Rogers, R. F., and J. M. Fritsch, 1996: A general framework for convective trigger functions. Mon. Wea. Rev., 124, 2438–2452, https://doi.org/10.1175/1520-0493(1996)124<2438:AGFFCT>2.0.CO;2.
Rozoff, C. M., C. S. Velden, J. Kaplan, J. P. Kossin, and A. J. Wimmers, 2015: Improvements in the probabilistic prediction of tropical cyclone rapid intensification with passive microwave observations. Wea. Forecasting, 30, 1016–1038, https://doi.org/10.1175/WAF-D-14-00109.1.
Saha, S., and Coauthors, 2010: The NCEP Climate Forecast System Reanalysis. Bull. Amer. Meteor. Soc., 91, 1015–1058, https://doi.org/10.1175/2010BAMS3001.1.
Saha, S., and Coauthors, 2014: The NCEP Climate Forecast System version 2. J. Climate, 27, 2185–2208, https://doi.org/10.1175/JCLI-D-12-00823.1.
Schenkel, B. A., and R. E. Hart, 2012: An examination of tropical cyclone position, intensity, and intensity life cycle within atmospheric reanalysis datasets. J. Climate, 25, 3453–3475, https://doi.org/10.1175/2011JCLI4208.1.
Schenkel, B. A., and R. E. Hart, 2015: An analysis of the environmental moisture impacts of western north Pacific tropical cyclones. J. Climate, 28, 2600–2622, https://doi.org/10.1175/JCLI-D-14-00213.1.
Schenkel, B. A., N. Lin, D. Chavas, M. Oppenheimer, and A. Brammer, 2017: Evaluating outer tropical cyclone size in reanalysis datasets using QuikSCAT data. J. Climate, 30, 8745–8762, https://doi.org/10.1175/JCLI-D-17-0122.1.
Schenkel, B. A., R. Edwards, and M. Coniglio, 2020: A climatological analysis of ambient deep-tropospheric vertical wind shear impacts upon tornadoes in tropical cyclones. Wea. Forecasting, 35, 2033–2059, https://doi.org/10.1175/WAF-D-19-0220.1.
Schubert, W. H., and J. J. Hack, 1982: Inertial stability and tropical cyclone development. J. Atmos. Sci., 39, 1687–1697, https://doi.org/10.1175/1520-0469(1982)039<1687:ISATCD>2.0.CO;2.
Schubert, W. H., M. T. Montgomery, R. K. Taft, T. A. Guinn, S. R. Fulton, J. P. Kossin, and J. P. Edwards, 1999: Polygonal eyewalls, asymmetric eye contraction, and potential vorticity mixing in hurricanes. J. Atmos. Sci., 56, 1197–1223, https://doi.org/10.1175/1520-0469(1999)056<1197:peaeca>2.0.co;2.
Seager, R., and N. Henderson, 2013: Diagnostic computation of moisture budgets in the ERA-interim reanalysis with reference to analysis of CMIP-archived atmospheric model data. J. Climate, 26, 7876–7901, https://doi.org/10.1175/JCLI-D-13-00018.1.
Sela, J. G., 2010: The derivation of the sigma pressure hybrid coordinate semi-Lagrangian model equations for the GFS. NCEP Office Note 462, 31 pp., https://repository.library.noaa.gov/view/noaa/6971.
Shapiro, L. J., 1983: The asymmetric boundary layer flow under a translating hurricane. J. Atmos. Sci., 40, 1984–1998, https://doi.org/10.1175/1520-0469(1983)040<1984:TABLFU>2.0.CO;2.
Slocum, C. J., M. N. Razin, J. A. Knaff, and J. P. Stow, 2022: Does ERA5 mark a new era for resolving the tropical cyclone environment? J. Climate, 35, 7147–7164, https://doi.org/10.1175/JCLI-D-22-0127.1.
Smith, R. K., M. T. Montgomery, and N. Van Sang, 2009: Tropical cyclone spin-up revisited. Quart. J. Roy. Meteor. Soc., 135, 1321–1335, https://doi.org/10.1002/qj.428.
Sobel, A. H., A. A. Wing, S. J. Camargo, C. M. Patricola, G. A. Vecchi, C.-Y. Lee, and M. K. Tippett, 2021: Tropical cyclone frequency. Earth’s Future, 9, e2021EF002275, https://doi.org/10.1029/2021EF002275.
Stevenson, S. N., K. L. Corbosiero, and J. Molinari, 2014: The convective evolution and rapid intensification of Hurricane Earl (2010). Mon. Wea. Rev., 142, 4364–4380, https://doi.org/10.1175/MWR-D-14-00078.1.
Tang, B. H., and K. A. Emanuel, 2012: A ventilation index for tropical cyclones. Bull. Amer. Meteor. Soc., 93, 1901–1912, https://doi.org/10.1175/BAMS-D-11-00165.1.
Tiedtke, M., 1983: The sensitivity of the time-mean large-scale flow to cumulus convection in the ECMWF model. ECMWF Modeling Workshop on Convection in Large-Scale Models, Reading, United Kingdom, ECMWF, 297–316, https://www.ecmwf.int/en/elibrary/76694-sensitivity-time-mean-large-scale-flow-cumulus-convection-ecmwf-model.
Tiedtke, M., 1989: A comprehensive mass flux scheme for cumulus parameterization in large-scale models. Mon. Wea. Rev., 117, 1779–1800, https://doi.org/10.1175/1520-0493(1989)117<1779:ACMFSF>2.0.CO;2.
Tiedtke, M., 1993: Representation of clouds in large-scale models. Mon. Wea. Rev., 121, 3040–3061, https://doi.org/10.1175/1520-0493(1993)121<3040:rocils>2.0.co;2.
Tompkins, A. M., K. Gierens, and G. Radel, 2007: Ice supersaturation in the ECMWF integrated forecast system. Quart. J. Roy. Meteor. Soc., 133, 53–63, https://doi.org/10.1002/qj.14.
Uhlhorn, E. W., B. W. Klotz, T. Vukicevic, P. D. Reasor, and R. F. Rogers, 2014: Observed hurricane wind speed asymmetries and relationships to motion and environmental shear. Mon. Wea. Rev., 142, 1290–1311, https://doi.org/10.1175/MWR-D-13-00249.1.
Ullrich, P. A., and C. M. Zarzycki, 2017: TempestExtremes: A framework for scale-insensitive pointwise feature tracking on unstructured grids. Geosci. Model Dev., 10, 1069–1090, https://doi.org/10.5194/gmd-10-1069-2017.
Ullrich, P. A., C. M. Zarzycki, E. E. McClenny, M. C. Pinheiro, A. M. Stansfield, and K. A. Reed, 2021: TempestExtremes v2.1: A community framework for feature detection, tracking, and analysis in large datasets. Geosci. Model Dev., 14, 5023–5048, https://doi.org/10.5194/gmd-14-5023-2021.
Vigh, J. L., and W. H. Schubert, 2009: Rapid development of the tropical cyclone warm core. J. Atmos. Sci., 66, 3335–3350, https://doi.org/10.1175/2009JAS3092.1.
Walsh, K. J. E., and Coauthors, 2016: Tropical cyclones and climate change. Wiley Interdiscip. Rev.: Climate Change, 7, 65–89, https://doi.org/10.1002/wcc.371.
Weatherford, C. L., and W. M. Gray, 1988: Typhoon structure as revealed by aircraft reconnaissance. Part I: Data analysis and climatology. Mon. Wea. Rev., 116, 1032–1043, https://doi.org/10.1175/1520-0493(1988)116<1032:tsarba>2.0.co;2.
Willoughby, H. E., 1979: Forced secondary circulations in hurricanes. J. Geophys. Res., 84, 3173–3183, https://doi.org/10.1029/JC084iC06p03173.
Willoughby, H. E., F. D. Marks Jr., and R. J. Feinberg, 1984: Stationary and moving convective bands in hurricanes. J. Atmos. Sci., 41, 3189–3211, https://doi.org/10.1175/1520-0469(1984)041<3189:SAMCBI>2.0.CO;2.
Wing, A. A., and Coauthors, 2019: Moist static energy budget analysis of tropical cyclone intensification in high-resolution climate models. J. Climate, 32, 6071–6095, https://doi.org/10.1175/JCLI-D-18-0599.1.
Wingo, M. T., and D. J. Cecil, 2010: Effects of vertical wind shear on tropical cyclone precipitation. Mon. Wea. Rev., 138, 645–662, https://doi.org/10.1175/2009MWR2921.1.
Wu, C.-C., and K. A. Emanuel, 1993: Interaction of a baroclinic vortex with background shear: Application to hurricane movement. J. Atmos. Sci., 50, 62–76, https://doi.org/10.1175/1520-0469(1993)050<0062:IOABVW>2.0.CO;2.
Wu, L., S. A. Braun, J. Halverson, and G. Heymsfield, 2006: A numerical study of Hurricane Erin (2001). Part I: Model verification and storm evolution. J. Atmos. Sci., 63, 65–86, https://doi.org/10.1175/JAS3597.1.
Xu, K.-M., and D. A. Randall, 1996: A semiempirical cloudiness parameterization for use in climate models. J. Atmos. Sci., 53, 3084–3102, https://doi.org/10.1175/1520-0469(1996)053<3084:ASCPFU>2.0.CO;2.
Yu, C.-L., and A. C. Didlake Jr., 2019: Impact of stratiform rainband heating on the tropical cyclone wind field in idealized simulations. J. Atmos. Sci., 76, 2443–2462, https://doi.org/10.1175/JAS-D-18-0335.1.
Yu, C.-L., A. C. Didlake Jr., J. D. Kepert, and F. Zhang, 2021: Investigating axisymmetric and asymmetric signals of secondary eyewall formation using observations-based modeling of the tropical cyclone boundary layer. J. Geophys. Res. Atmos., 126, e2020JD034027, https://doi.org/10.1029/2020JD034027.
Yu, C.-L., A. C. Didlake Jr., and F. Zhang, 2022: Updraft maintenance and axisymmetrization during secondary eyewall formation in a model simulation of Hurricane Matthew (2016). J. Atmos. Sci., 79, 1105–1125, https://doi.org/10.1175/JAS-D-21-0103.1.
Yu, Z., Y. Wang, and H. Xu, 2015: Observed rainfall asymmetry in tropical cyclones making landfall over China. J. Appl. Meteor. Climatol., 54, 117–136, https://doi.org/10.1175/JAMC-D-13-0359.1.
Zarzycki, C. M., 2022: Sowing storms: How model timestep can control tropical cyclone frequency in a GCM. J. Adv. Model. Earth Syst., 14, e2021MS002791, https://doi.org/10.1029/2021MS002791.
Zarzycki, C. M., and P. A. Ullrich, 2017: Assessing sensitivities in algorithmic detection of tropical cyclones in climate data. Geophys. Res. Lett., 44, 1141–1149, https://doi.org/10.1002/2016GL071606.
Zarzycki, C. M., M. N. Levy, C. Jablonowski, J. R. Overfelt, M. A. Taylor, and P. A. Ullrich, 2014: Aquaplanet experiments using CAM’s variable-resolution dynamical core. J. Climate, 27, 5481–5503, https://doi.org/10.1175/JCLI-D-14-00004.1.
Zarzycki, C. M., D. R. Thatcher, and C. Jablonowski, 2017: Objective tropical cyclone extratropical transition detection in high-resolution reanalysis and climate model data. J. Adv. Model. Earth Syst., 9, 130–148, https://doi.org/10.1002/2016MS000775.
Zarzycki, C. M., P. A. Ullrich, and K. A. Reed, 2021: Metrics for evaluating tropical cyclones in climate data. J. Appl. Meteor. Climatol., 60, 643–660, https://doi.org/10.1175/JAMC-D-20-0149.1.
Zhang, F., S. E. Koch, C. A. Davis, and M. L. Kaplan, 2000: A survey of unbalanced flow diagnostics and their application. Adv. Atmos. Sci., 17, 165–183, https://doi.org/10.1007/s00376-000-0001-1.
Zhang, J. A., R. F. Rogers, P. D. Reasor, E. W. Uhlhorn, and F. D. Marks Jr., 2013: Asymmetric hurricane boundary layer structure from dropsonde composites in relation to the environmental vertical wind shear. Mon. Wea. Rev., 141, 3968–3984, https://doi.org/10.1175/MWR-D-12-00335.1.
Zhao, M., I. M. Held, and S.-J. Lin, 2012: Some counterintuitive dependencies of tropical cyclone frequency on parameters in a GCM. J. Atmos. Sci., 69, 2272–2283, https://doi.org/10.1175/JAS-D-11-0238.1.
Zhao, Q., and F. H. Carr, 1997: A prognostic cloud scheme for operational NWP models. Mon. Wea. Rev., 125, 1931–1953, https://doi.org/10.1175/1520-0493(1997)125<1931:APCSFO>2.0.CO;2.
Zhu, P., K. Menelaou, and Z. Zhu, 2014: Impact of subgrid-scale vertical turbulent mixing on eyewall asymmetric structures and mesovortices of hurricanes. Quart. J. Roy. Meteor. Soc., 140, 416–438, https://doi.org/10.1002/qj.2147.
Zick, S. E., and C. J. Matyas, 2015: Tropical cyclones in the North American regional reanalysis: An assessment of spatial biases in location, intensity, and structure. J. Geophys. Res. Atmos., 120, 1651–1669, https://doi.org/10.1002/2014JD022417.
