Abstract

Tropical cyclone–relative environmental helicity (TCREH) is a measure of how the wind vector changes direction with height, and it has been shown to modulate the rate at which tropical cyclones (TCs) develop both in idealized simulations and in reanalysis data. The channels through which this modulation occurs remain less clear. This study aims to identify the mechanisms that lead to the observed variations in intensification rate. Results suggest that the difference in intensification rate between TCs embedded in positive versus negative TCREH primarily results from the position of convection and associated latent heat fluxes relative to the wind shear vector. When TCREH is positive, convection is more readily advected upshear and air parcels that experience larger fluxes are more frequently ingested into the TC core. Trajectories computed from high-resolution simulations demonstrate the recovery of equivalent potential temperature downwind of convection, latent heat flux near the TC core, and parcel routes through updrafts in convection. Differences in trajectory characteristics between TCs embedded in positive versus negative TCREH are presented. Contoured frequency-by-altitude diagrams (CFADs) show that convection is distributed differently around TCs embedded in environments characterized by positive versus negative TCREH. They also show that the nature of the most intense convection differs only slightly between cases of positive and negative TCREH. The results of this study emphasize the fact that significant variability in TC-intensification rate results from vertical variations in the environmental wind direction, even when the 850–200-hPa wind shear vector remains unchanged.

1. Introduction

The location of convection associated with tropical cyclones (TCs) relative to the TC center is modulated by the ambient vertical wind shear. Numerous studies (e.g., Frank and Ritchie 2001; Wang et al. 2004; Riemer et al. 2010; Reasor and Eastin 2012) have demonstrated the importance of deep layer (850–200 hPa) wind shear with regard to modulating the development, intensity, and structure of tropical cyclones. The studies listed above investigated how both vertical wind shear magnitude and duration affect TCs. Observational research supports the general finding that vertical wind shear typically inhibits TC intensification (Gray 1968; Merrill 1988; DeMaria 1996) though there are notable exceptions (e.g., Molinari et al. 2004, 2006; Chen and Gopalakrishnan 2015). This weakening (or lack of intensification) may result directly from shear effects (decoupling of the low- and upper-level portions of the TC) or indirectly through alterations to the convection within the TC. Modeling studies have shown that the general response of the TC to vertical wind shear is to develop a wavenumber 1 asymmetry in the eyewall structure (e.g., Jones 1995; Bender 1997; Frank and Ritchie 1999). Observational studies are in agreement and show that deep convection in vertically sheared TCs is maximized in the downshear-left quadrant (Corbosiero and Molinari 2002; Marks et al. 1992; Molinari et al. 2006; Franklin et al. 1993; Reasor et al. 2013).

While vertical wind shear generally limits the intensification of TCs, the specifics of the vertical shear profile can modify the intensification rate. Rappin and Nolan (2012) used numerical simulations to show that vertical wind shear profiles with equal shear magnitudes but opposite direction relative to TC motion can lead to a different rate of TC development. Nolan and McGauley (2012) expanded upon this result demonstrating that westerly shear was more favorable for genesis than easterly shear due to the differences in surface flux positioning around the TC that arise between the two shear environments. Other studies have noted the dependence of TC-intensification rate on the translation rate of the TC or the specific layer under consideration when computing vertical wind shear. For example, Zeng et al. (2010) found that the intensification rate of fast-moving TCs (≥6 m s−1) was more correlated with wind shear in the 600–200-hPa layer than in the more typically used 850–200-hPa layer, suggesting that TCs are strongly affected by shear in the middle to upper troposphere when they are moving quickly.

Onderlinde and Nolan (2014, hereafter ON14) found that the shape of the vertical wind profile can have a significant impact on TC development rates even when the 850–200-hPa wind shear vector is held constant. They showed that positive values of tropical cyclone–relative environmental helicity (TCREH) promoted faster rates of intensification using both numerical simulations and reanalysis data. TCREH is a measure of how the wind vector changes with height and is defined as the vector product of the TC motion-relative environmental wind and horizontal vorticity vectors:

 
formula

where h is the depth over which TCREH is computed, v is the horizontal component of the wind field, c is the motion vector of the TC, k is the unit vector in the vertical direction, and z is the vertical coordinate. It is important to distinguish TCREH (radius approximately >500 km; magnitudes typically <100 m2 s−2) from TC-scale helicity (radius approximately <500 km; magnitudes often >300 m2 s−2). ON14 presented two hypotheses for the reasons why TCREH modulates TC-intensification rate. First, the characteristics of convection in the TC likely are affected by the TC response to the environmental helicity. They suggested that positive TCREH leads to larger magnitudes of TC-scale helicity, thus allowing more organized and vigorous convection. Second, they proposed that positive TC-scale helicity and the location of maximum convection (in downshear quadrants) were more collocated when TCREH is positive. In this paper, these ideas are more rigorously tested and an alternative explanation is presented in which the azimuthal position of convection and surface latent heat flux is more conducive to TC intensification when TCREH is positive.

Recent studies have related the azimuthal position of convection to the timing of TC formation because this position influences the feedback between diabatic heating and the TC primary circulation (Tao and Zhang 2014). Additional studies have discussed how the precession of the mid- or upper-level circulation around the low-level TC center affects the timing to genesis or rate of intensification (Reasor and Montgomery 2001; Rappin and Nolan 2012; Zhang and Tao 2013). Zhang and Tao (2013), Stevenson et al. (2014), and Chen and Gopalakrishnan (2015) noted that intensification ensued soon after the upper-level center of the vortex precessed beyond 90° to the left of the vertical wind shear vector. In this study, we will show that environments characterized by positive TCREH favor a faster precession of convection and associated surface fluxes into the upshear quadrants.

2. Methods

a. Azimuthal positioning of surface fluxes and convection

A total of 32 simulations using 2-km grid spacing were performed in which 850–200-hPa TCREH and wind shear were held fixed but various constant background flows were added to the wind field. The Weather Research and Forecasting (WRF) Model, version 3.4.1, was used with point downscaling (Nolan 2011) and analysis nudging (Stauffer and Seaman 1990; Stauffer et al. 1991). The combination of point downscaling and nudging acts to keep the environmental wind field approximately in the prescribed state such that variations are small relative to the mean state. Analysis nudging is applied only on domain 1 in order to reduce deviations from the prescribed environment while not affecting computations within the TC itself. The model configuration, TC initial intensity, radius of maximum winds (RMW), sea surface temperature (SST), and other characteristics exactly follow the configuration described in ON14. Specifically, all TCs in this study were initialized as modified Rankine vortices with initial maximum tangential velocity of 20 m s−1 on an f plane at 20°N with an SST of 29°C. These simulations were used to test whether certain background flows promoted faster advancement of convection and enhanced surface fluxes into upshear quadrants.

In addition, two very high-resolution (667 m) simulations were performed to analyze the importance of the azimuthal position of features such as surface fluxes, diabatic heating rates, and convection. The 667-m simulations follow the ON14 configuration except with the addition of a 240 km × 240 km fourth nest (360 × 360 grid points), centered on the TC, embedded within the 2-km nest. The environmental 850–200-hPa wind profiles are shown in a hodograph diagram in Fig. 1 and are characterized by a westerly shear of 10 m s−1. It is proposed that when air characterized by larger fluxes, increased moisture, and larger diabatic heating rates is advected into upshear quadrants near the RMW, then more of this air is ingested into the TC core, which leads to faster intensification. Three methodologies were used to test this idea. The first method used time-averaged, TC-center-relative composites of surface fluxes, simulated reflectivity, and diabatic heating rates. Results from these composites are discussed in section 3a. The other methodologies are described in sections 2b,c.

Fig. 1.

Hodographs for the 667-m simulations with positive (red) and negative (blue) TCREH.

Fig. 1.

Hodographs for the 667-m simulations with positive (red) and negative (blue) TCREH.

b. Trajectories

The second analysis method was to compute trajectories (backward and forward) to see the paths traveled by parcels near the TC core and in regions of large fluxes or diabatic heating. To compute accurate trajectories it was required that very high resolution be used in both space and time. Output from the innermost domain of the 667-m simulations was saved every 1 min. The methods used for the trajectory computation followed a predictor–corrector technique. An example for the case of forward trajectories follows. First, wind components are interpolated to the initial parcel location. These components then are used to make a prediction for where the parcel will be advected over the next 30 s. This location serves as the predicted midpoint. Wind components then are interpolated spatially and temporally to this predicted midpoint. These interpolated wind components then are used to advect the parcel for the full 1-min time step. This example describes just one predictor–corrector step per model output interval. Alternatively, each 1-min interval can be broken into numerous predictor–corrector steps. For the trajectories shown in section 3b, each 1-min interval is broken up into thirty 2-s predictor–corrector steps. This 2-s time stepping was chosen because additional time resolution did not substantially improve trajectory accuracy (i.e., trajectories were nearly identical when using a 1-s predictor–corrector step instead of a 2-s step). Airmass properties such as diabatic heating rate, water vapor mixing ratio, equivalent potential temperature θe, etc. were stored at 1-min intervals along the computed trajectories. Trajectories were seeded in locations such as maxima in surface fluxes, within thunderstorms, or near the surface downwind of convection to compare how air in these locations arrives to or proceeds from these locations. Comparisons were typically made during periods just prior to when TC intensity diverged between the positive- and negative-TCREH simulations. Zhang et al. (2013) showed that boundary layer θe recovery rates are related to the distribution of convection around TCs. To determine if boundary layer recovery occurs more rapidly when TCREH is positive, θe recovery rates in the boundary layer downwind of convection were examined.

c. Contoured frequency-by-altitude diagrams

The third method used to analyze the spatial characteristics of fields like simulated reflectivity, diabatic heating rate, and vertical velocity was to compute contoured frequency-by-altitude diagrams (CFADs; Yuter and Houze 1995). CFADs were generated to determine if the frequency at which convection reached large altitudes differed between simulations with positive or negative TCREH. CFADs can also highlight differences in the convection at a specific altitude. The CFAD results described in section 3c were computed over two spatial areas. The first area was a 75 km × 75 km box centered on the region of maximum 700-hPa simulated reflectivity. To determine this location, the simulated reflectivity at the 700-hPa level was processed 500 times through a 9-point smoother and the centroid of the smoothed reflectivity was identified. The second spatial location chosen for CFAD computation was in an annulus centered on the TC and with radial range between 25 and 225 km. This radial range was chosen such that the areas of relatively strong convection were encompassed. For both spatial methods, CFADs are shown for simulated reflectivity and vertical velocity.

3. Results

a. Azimuthal positioning of surface fluxes and convection

The azimuthal positions as well as the characteristics of surface fluxes, simulated reflectivity, and diabatic heating rates are compared for simulations with positive and negative TCREH. Comparisons are made primarily during periods just prior to when TC intensity diverged between simulations with positive and negative TCREH. The TC intensity diverges for the two simulations beginning at approximately t = 36 h (Fig. 2). This period is chosen in an attempt to relate differences in azimuthal positioning to the differences in subsequent TC-intensification rate. The 667-m simulations show that the location of larger values of latent heat flux advances into upshear quadrants near the RMW more quickly when TCREH is positive. Not only do these flux locations move upshear more quickly, the fluxes in these regions are of larger magnitude when compared to the negative-TCREH simulation. The result of larger latent heat fluxes in the upshear-left quadrant near the RMW is a more efficient ingestion of surface air into the TC core. Figure 3 shows surface latent heat fluxes that are averaged over 4-h subsets of the 12-h period prior to divergence of minimum central pressure between the simulations with positive and negative TCREH. Figures 3a–c show how fluxes of larger magnitude proceed into the upshear quadrants sooner than they do in the case with negative TCREH (Figs. 3d–f). Note that the 850–200-hPa vertical shear vector is identical for both simulations and is directed due eastward with a magnitude of 10 m s−1. Figure 4 shows time-averaged plots of convection, as visualized by 700-hPa simulated reflectivity, which show the faster upshear advection in the positive-TCREH simulation (Figs. 4a–c). While the magnitude of time-mean reflectivity increases with time for the negative TCREH case (Figs. 4d–f), the azimuthal position of the maxima makes essentially no progress toward the upshear quadrants. Time-mean reflectivity for the positive TCREH case (Figs. 4a–c) shows a steady advancement of convection into upshear quadrants. It is this advancement of convection and surface fluxes (shown further in the trajectory analysis in section 3b) that leads to the discrepancy in intensification rate.

Fig. 2.

Evolution of minimum central pressure for the 667-m simulations with positive (red) and negative (blue) TCREH. The green lines encompass the time period during which much of the composite analysis of section 3a occurred. The red (blue) arrow denotes when the midlevel circulation center first advances into the upshear-left quadrant when TCREH is positive (negative).

Fig. 2.

Evolution of minimum central pressure for the 667-m simulations with positive (red) and negative (blue) TCREH. The green lines encompass the time period during which much of the composite analysis of section 3a occurred. The red (blue) arrow denotes when the midlevel circulation center first advances into the upshear-left quadrant when TCREH is positive (negative).

Fig. 3.

Time-averaged surface latent heat flux (W m−2) for a simulation with (a)–(c) positive TCREH equal to 43 m2 s−2 and (d)–(f) negative TCREH equal to −43 m2 s−2. Surface latent heat flux is averaged during (a),(d) 24–28 h; (b),(e) 28–32 h; and (c),(f) 32–36 h. These three 4-h time periods correspond to the 12-h period just prior to the divergence of minimum central pressure between the two simulations.

Fig. 3.

Time-averaged surface latent heat flux (W m−2) for a simulation with (a)–(c) positive TCREH equal to 43 m2 s−2 and (d)–(f) negative TCREH equal to −43 m2 s−2. Surface latent heat flux is averaged during (a),(d) 24–28 h; (b),(e) 28–32 h; and (c),(f) 32–36 h. These three 4-h time periods correspond to the 12-h period just prior to the divergence of minimum central pressure between the two simulations.

Fig. 4.

Time-averaged 700-hPa simulated radar reflectivity (dBZ) for a simulation with (a)–(c) positive TCREH equal to 43 m2 s−2 and (d)–(f) negative TCREH equal to −43 m2 s−2. Reflectivity is averaged during (a),(d) 24–28 h; (b),(e) 28–32 h; and (c),(f) 32–36 h. These three 4-h time periods correspond to the 12-h period just prior to the divergence of minimum central pressure between the two simulations.

Fig. 4.

Time-averaged 700-hPa simulated radar reflectivity (dBZ) for a simulation with (a)–(c) positive TCREH equal to 43 m2 s−2 and (d)–(f) negative TCREH equal to −43 m2 s−2. Reflectivity is averaged during (a),(d) 24–28 h; (b),(e) 28–32 h; and (c),(f) 32–36 h. These three 4-h time periods correspond to the 12-h period just prior to the divergence of minimum central pressure between the two simulations.

The azimuthal location of convection and surface fluxes are related to TC-vortex tilt and the precession of the midlevel vortex around the low-level vortex. Tilt is calculated as the vector difference between the surface and 500-hPa circulation centers. The time at which this vector first points toward the upshear-left quadrant is noted (Fig. 2) since this has been shown to be related to the onset of rapid intensification (Rappin and Nolan 2012; Tao and Zhang 2014). By comparing the precession of the circulation center to the azimuthal location of convection and fluxes, inferences can be made about the relative importance of both factors. Figure 5a shows time series of the storm-relative azimuth angle from the TC surface center to the location of maximum 700-hPa convection for the 667-m simulations with positive (red) and negative (blue) TCREH. Azimuth angles for the midlevel circulation center also were computed (not shown) and were generally correlated with the position of the maximum 700-hPa convection. Figure 5b shows the radial distance from the TC surface center to the location of maximum 700-hPa convection (positive TCREH: red, negative TCREH: blue). The time series demonstrate that convection precesses faster and reaches smaller radii sooner when TCREH is positive. Interestingly, in both the positive- and negative-TCREH simulations, the advancement of convection and surface fluxes occurs at the same time or slightly before the precession of the midlevel circulation center. This suggests that surface fluxes and ensuing deep convection may play an important role in determining how easily the midlevel vortex can precess cyclonically around the low-level TC center (perhaps by preconditioning the environment in the upshear quadrants), or instead that convection is relocating the center by generating vorticity. This result stands somewhat in contrast to the results of Davis et al. (2008) who showed that convection to the left of the vortex tilt vector can inhibit the precession rate by reducing the cyclonic advection of the low-level center by the upper-level potential vorticity maximum.

Fig. 5.

Time series of (a) storm-relative azimuth angle of location of maximum convection and (b) radial distance (km) from the TC center to the location of maximum convection for the 667-m simulations with positive (red) and negative (blue) TCREH. Here, 0° is defined as parallel to and in the same direction as TC motion such that angles between 0° and 180° denote a convective maximum to the right of TC motion.

Fig. 5.

Time series of (a) storm-relative azimuth angle of location of maximum convection and (b) radial distance (km) from the TC center to the location of maximum convection for the 667-m simulations with positive (red) and negative (blue) TCREH. Here, 0° is defined as parallel to and in the same direction as TC motion such that angles between 0° and 180° denote a convective maximum to the right of TC motion.

Because TC motion is slightly different in the positive and negative TCREH cases described above, it was proposed that the position of surface fluxes and convection relative to the TC motion vector may play an important role in determining how efficiently buoyant surface parcels are ingested into the TC core. To investigate this issue, simulations similar to the 667-m cases described above were performed at coarser grid spacing (finest domain uses 2 km rather than 667 m) and with the addition of spatially constant background flow. The background flow is of constant magnitude at all altitudes such that the shape of the environmental hodograph does not change; however, its position on the diagram moves around depending on the direction of the background flow. Figure 6 shows an example of how the environmental hodograph is shifted by the addition of southwesterly background flow of 4 m s−1. Four simulations are performed for each background wind direction in 45° increments (i.e., northerly, northeasterly, easterly, southeasterly, southerly, southwesterly, westerly, and northwesterly). For each direction, two simulations with negative TCREH and the addition of background flow are performed: one with magnitude 4 m s−1 and one with 8 m s−1. Two simulations with additional background flow of 4 and 8 m s−1 but with positive TCREH also are performed for each direction. Significant differences in the timing of intensification result simply from varying the direction of the background flow.

Fig. 6.

Hodographs for (a) a simulation with no additional background flow added and (b) a simulation with southwesterly background flow of 4 m s−1 added. The black arrow in (b) denotes the additional southwesterly flow and the green arrows denote the resultant storm motion for both simulations.

Fig. 6.

Hodographs for (a) a simulation with no additional background flow added and (b) a simulation with southwesterly background flow of 4 m s−1 added. The black arrow in (b) denotes the additional southwesterly flow and the green arrows denote the resultant storm motion for both simulations.

To demonstrate that the differences in intensification rate between the westerly and easterly background flow cases are larger than random fluctuations, Fig. 7 shows minimum central pressure evolution from a mini-ensemble containing six positive-TCREH simulations (three with westerly and three with easterly background flow). This mini-ensemble is generated by introducing small random perturbations (<0.5 m s−1) to the initial TC-vortex wind field. TCREH and vertical wind shear remain positive and approximately constant for all six simulations in which a uniform background flow with magnitude 8 m s−1 is added to the three-dimensional wind field. The main differences between the westerly and easterly experiments are the direction from which this background flow is imposed and the resultant increased (decreased) storm-relative shear in the easterly (westerly) case. Storm-relative shear has been shown to relate to the distribution of convection in TCs (e.g., Rogers et al. 2003) and is defined as the difference between the wind shear and storm motion vectors. There is a fairly large range of intensification rate when only the direction of the background flow is varied. For example, a difference of approximately 22 hPa exists at t = 60 h between the westerly background flow cases (Fig. 7, blue lines) and the easterly background flow cases (Fig. 7, red lines). The different intensification rate is smaller (~10 hPa) but consistent in terms of easterly flow being more favorable when a 4 m s−1 background flow is added. The simulations also demonstrate a steady increase in development rate as the additional background flow transitions from westerly to easterly (not shown; from westerly to southwesterly, to southerly, to southeasterly, and to easterly). To determine what causes the different rate of development, time-mean plots of 700-hPa simulated radar reflectivity and surface latent heat flux from one westerly and one easterly additional background flow case are analyzed during the 12-h period just prior to when TC intensity diverges. Figure 8 shows how stronger convection remains near and just upshear of the TC core when the additional background flow is easterly (Figs. 8a–c) versus westerly (Figs. 8d–f). The convection also progresses more rapidly around the TC center when the additional background flow is easterly. By t = 24–28 h, a more symmetric appearance is noted in the easterly background flow case when compared to the westerly case (Fig. 8c vs Fig. 8f). Corresponding to the more organized convection in the easterly background flow case, a broad area of relatively large surface latent heat fluxes persists near the RMW in the upshear-left quadrant. Contours of horizontal divergence on the lowest model level (Figs. 8g–l) show that there is much more overlap of larger surface latent heat flux and convergence when the background flow is easterly. The overlap of surface latent heat flux and convergence occurs despite the fact that storm-relative shear is increased when the background flow is easterly. Storm-relative shear is reduced when the background flow is westerly; however, decreased overlap between convection and low-level convergence disallows a faster TC-intensification rate. The combination of increased convection and fluxes collocated with low-level convergence in upshear quadrants most likely is why the case with easterly additional background flow develops more rapidly than the westerly case.

Fig. 7.

Mini-ensemble showing minimum central pressure evolution for six positive-TCREH simulations with the addition of a vertically constant background flow with magnitude equal to 8 m s−1. The direction of the additional background flow is westerly (blue lines) and easterly (red lines). The 850–200-hPa vertical wind shear vector and TCREH magnitude are identical for all six cases. Small perturbations to the initial vortex wind field create the differences for the mini-ensemble. The green lines encompass the time period during which the composite analysis occurred for the additional background flow discussion.

Fig. 7.

Mini-ensemble showing minimum central pressure evolution for six positive-TCREH simulations with the addition of a vertically constant background flow with magnitude equal to 8 m s−1. The direction of the additional background flow is westerly (blue lines) and easterly (red lines). The 850–200-hPa vertical wind shear vector and TCREH magnitude are identical for all six cases. Small perturbations to the initial vortex wind field create the differences for the mini-ensemble. The green lines encompass the time period during which the composite analysis occurred for the additional background flow discussion.

Fig. 8.

Time-averaged (a)–(f) 700-hPa simulated reflectivity (dBZ) and (g)–(l) surface latent heat flux (W m−2) for two simulations with positive TCREH and additional background flow of 8 m s−1: (a)–(c),(g)–(i) one with easterly background flow and (d)–(f),(j)–(l) one with westerly background flow. Values are averaged (left) from t = 16 to 20 h, (middle) from t = 20 to 24 h, and (right) from t = 24 to 28 h. The vectors in the lower-left corner of (a) and (d) represent mean storm motion during the period t = 16–28 h (red) and 850–200-hPa environmental wind shear (10 m s−1; blue).

Fig. 8.

Time-averaged (a)–(f) 700-hPa simulated reflectivity (dBZ) and (g)–(l) surface latent heat flux (W m−2) for two simulations with positive TCREH and additional background flow of 8 m s−1: (a)–(c),(g)–(i) one with easterly background flow and (d)–(f),(j)–(l) one with westerly background flow. Values are averaged (left) from t = 16 to 20 h, (middle) from t = 20 to 24 h, and (right) from t = 24 to 28 h. The vectors in the lower-left corner of (a) and (d) represent mean storm motion during the period t = 16–28 h (red) and 850–200-hPa environmental wind shear (10 m s−1; blue).

We propose that the reason for the differences between these cases has to do with the TC-scale advection of air experiencing large fluxes relative to TC storm motion. For both the easterly and westerly cases, convection is initially maximized north (left of shear) of the TC center. In the easterly background flow case (Figs. 8a–c and 8g–i), the path from the surface flux maximum to the storm motion vector (which is directed toward approximately 280°) is much shorter than the same path in the westerly case. In addition to the shorter path, near-surface easterly winds to the north of the TC in regions of convection are stronger when the additional background flow is easterly due to the projection of TC motion onto the vortex winds. These stronger surface winds lead to larger fluxes over a broader region in the upshear-left quadrant. Surface latent heat flux averaged over a 360 km × 360 km box centered on the storm are 376 W m−2 when the background flow is easterly (Figs. 8g–i) compared to 331 W m−2 when the background flow is westerly (Figs. 8j–l). This difference increases when considering a 180 km × 180 km box in the upshear-left quadrant where average surface latent heat fluxes are 497 versus 370 W m−2. Another way to conceptualize the difference is by comparing the motion vector of the near-surface air north of the TC (and its associated fluxes) to the TC motion vector. In the easterly case these vectors are approximately 10° apart while in the westerly case they are nearly 180° apart. This difference and the resultant slower rate of TC development in the westerly case implies that the ingestion of surface air experiencing large fluxes into the TC core becomes less efficient when this angle is larger. This idea is more rigorously tested in the following section.

Because varying the additional background flow appears to lead to large differences in intensity (~22-hPa difference at t = 60 h between easterly and westerly background flow cases), the results from the simulations with positive TCREH and background flow (Fig. 7) were compared to simulations with background flow and negative TCREH. Figure 9 shows four simulations with additional background flow of 8 m s−1. The solid lines show westerly (blue) versus easterly (red) background flow for simulations with positive TCREH. The dashed lines show westerly (blue) versus easterly (red) background flow for simulations with negative TCREH. What is apparent from Fig. 9 is that both the direction of the background flow and the sign of TCREH are important in dictating intensification rate. For example, the intensity at t = 48 h is approximately 972 hPa for the simulation with easterly flow and positive TCREH compared to 992 hPa for the simulation with easterly flow and negative TCREH. The difference here is of equal magnitude to that when varying just the background flow. However, this difference increases to 28 hPa when TCREH is negative and the background flow is westerly. This result indicates that both TCREH and the orientation of the background flow are important in dictating intensification rate.

Fig. 9.

Minimum central pressure (hPa) vs time (h) for four simulations with additional background flow of 8 m s−1. The four simulations are denoted: positive TCREH and westerly flow (solid blue), positive TCREH and easterly flow (solid red), negative TCREH and westerly flow (dashed blue), and negative TCREH and easterly flow (dashed red).

Fig. 9.

Minimum central pressure (hPa) vs time (h) for four simulations with additional background flow of 8 m s−1. The four simulations are denoted: positive TCREH and westerly flow (solid blue), positive TCREH and easterly flow (solid red), negative TCREH and westerly flow (dashed blue), and negative TCREH and easterly flow (dashed red).

b. Trajectory analysis

Results from forward trajectories suggest that near-surface parcels experiencing large latent heat flux are advected around the TC center and lofted into new convection more efficiently when TCREH is positive. Figure 10 shows 6-h forward trajectories for the 667-m positive-TCREH simulation from t = 30 to 36 h and Fig. 11 shows forward trajectories for the 667-m negative-TCREH simulation for the same time period. In both cases, the trajectories originate from the lowest model level in regions of large surface latent heat flux. It is apparent when comparing Figs. 10a to 11a that parcels wrap around the TC core more efficiently when TCREH is positive. It is also apparent is that parcels tend to be lofted more frequently in the positive-TCREH simulation (Figs. 10b vs 11b). Parcel θe remains larger and parcels experience more diabatic heating during the 6-h period for the positive-TCREH simulation than in the negative simulation (Figs. 10c,d vs 11c,d). All of these factors contribute the faster rate of TC development observed in the positive-TCREH simulation.

Fig. 10.

(a) The 6-h forward trajectories for parcels originating on the lowest model level in a region of large latent heat flux overlaid on 6-h time-averaged surface latent heat flux (W m−2) from t = 30 to 36 h. (b) Parcel altitude (m) vs time. (c) Parcel θe (K) vs time. (d) Parcel diabatic heating rate (K h−1) vs time. These trajectories are from the 667-m grid spacing simulation with positive TCREH. The green boxes denote the beginning of the forward trajectories.

Fig. 10.

(a) The 6-h forward trajectories for parcels originating on the lowest model level in a region of large latent heat flux overlaid on 6-h time-averaged surface latent heat flux (W m−2) from t = 30 to 36 h. (b) Parcel altitude (m) vs time. (c) Parcel θe (K) vs time. (d) Parcel diabatic heating rate (K h−1) vs time. These trajectories are from the 667-m grid spacing simulation with positive TCREH. The green boxes denote the beginning of the forward trajectories.

Fig. 11.

(a) The 6-h forward trajectories for parcels originating on the lowest model level in a region of large latent heat flux overlaid on 6-h time-averaged surface latent heat flux (W m−2) from t = 30 to 36 h. (b) Parcel altitude (m) vs time. (c) Parcel θe (K) vs time. (d) Parcel diabatic heating rate (K h−1) vs time. These trajectories are from the 667-m grid spacing simulation with negative TCREH. The green boxes denote the beginning of the forward trajectories.

Fig. 11.

(a) The 6-h forward trajectories for parcels originating on the lowest model level in a region of large latent heat flux overlaid on 6-h time-averaged surface latent heat flux (W m−2) from t = 30 to 36 h. (b) Parcel altitude (m) vs time. (c) Parcel θe (K) vs time. (d) Parcel diabatic heating rate (K h−1) vs time. These trajectories are from the 667-m grid spacing simulation with negative TCREH. The green boxes denote the beginning of the forward trajectories.

In addition to the 6-h trajectories shown in Figs. 10 and 11, forward trajectories are computed for surface (lowest model level) parcels originating in a 33 km × 33 km box in the upshear-left quadrant for both the positive- and negative-TCREH simulations. This location is chosen because it is just downwind of convection during this time period. Trajectories are spawned from each model grid point in this box so that 2500 trajectories are computed for both simulations. Of the 2500 parcels originating on the lowest model level in this location, 18% are lofted above 2000 m when TCREH is positive versus only 1.5% when TCREH is negative. Figure 12 shows the evolution of parcel altitude versus time. In total 5% (0%) of parcels are lofted above 5000 m and 2.5% (0%) are lofted above 10 000 m when TCREH is positive (negative). This again suggests that the process of advecting θe-rich air and relatively large latent heating rate into the TC circulation is more efficient when the environment outside the TC is characterized by positive TCREH.

Fig. 12.

The 2-h forward trajectories showing altitude (m) vs time (min) for parcels originating on the lowest model level in the upshear-left quadrant downwind of convection for a simulation with (a) positive and (b) negative TCREH. The green boxes denote the beginning of the forward trajectories.

Fig. 12.

The 2-h forward trajectories showing altitude (m) vs time (min) for parcels originating on the lowest model level in the upshear-left quadrant downwind of convection for a simulation with (a) positive and (b) negative TCREH. The green boxes denote the beginning of the forward trajectories.

Another way to consider the impact of TCREH on parcel trajectories is to analyze the parcel paths through convective updrafts. Figures 13 and 14 show parcel trajectories through updrafts located in the upshear-left quadrants in the 667-m simulations with positive (Fig. 13) and negative (Fig. 14) TCREH. In the positive TCREH case, the trajectories shown include 3 h of backward trajectories and 3 h of forward trajectories. For the negative TCREH case, the trajectories include 0.5 h of backward trajectories and 5.5 h of forward trajectories. These intervals for forward and backward trajectories were chosen in the negative TCREH case so that a convective feature in the upshear-left quadrant could be examined. Convection in this quadrant was very rare during this time period in the negative-TCREH simulation. Both Figs. 13 and 14 represent the 6-h period during t = 30–36 h. The first clear difference is that the parcels are lifted higher (Figs. 13b vs 14b) and curve cyclonically about the TC center (Figs. 13a vs 14a) much more when TCREH is positive. It is also clear that θe remains larger for the trajectories in the positive-TCREH simulation (Figs. 13c vs 14c). The θe in parcels originating on the lowest model level drops from approximately 346 to 344 K for trajectories in the positive TCREH case while θe falls from 345 K to approximately 337 K for the trajectories in the negative-TCREH simulation. This drop likely is related to the entrainment of midlevel air characterized by relatively lower θe. Also, as was the case for surface parcels described earlier, diabatic heating (Figs. 13d vs 14d) is larger for the trajectories in the positive-TCREH simulation. An apparent difference between these two sets of trajectories is that the thunderstorm is much deeper in the positive-TCREH simulation. Parcels traveling through this storm reach altitudes approaching 10 000 m whereas parcels traveling through the storm in the negative-TCREH simulation reach altitudes only around 3800 m. This shallower convective feature in the negative TCREH case was selected because it was one of only two storms in the upshear-left quadrant during this time period and it was closer to the RMW. This is consistent with the fact that convection is much more common and more vigorous in the upshear-left quadrant when TCREH is positive.

Fig. 13.

(a) The 6-h trajectories (3 h backward, 3 h forward) for parcels traveling through an upshear-left thunderstorm updraft overlaid on 6-h time-averaged surface latent heat flux (W m−2; shading) and surface pressure (hPa; magenta contours) from t = 30 to 36 h. (b) Parcel altitude (m) vs time. (c) Parcel θe (K) vs time. (d) Parcel diabatic heating rate (K h−1) vs time. These trajectories are from the 667-m grid spacing simulation with positive TCREH. The green boxes denote the beginning of the trajectories and the brown boxes denote the endpoints.

Fig. 13.

(a) The 6-h trajectories (3 h backward, 3 h forward) for parcels traveling through an upshear-left thunderstorm updraft overlaid on 6-h time-averaged surface latent heat flux (W m−2; shading) and surface pressure (hPa; magenta contours) from t = 30 to 36 h. (b) Parcel altitude (m) vs time. (c) Parcel θe (K) vs time. (d) Parcel diabatic heating rate (K h−1) vs time. These trajectories are from the 667-m grid spacing simulation with positive TCREH. The green boxes denote the beginning of the trajectories and the brown boxes denote the endpoints.

Fig. 14.

(a) The 6-h trajectories (0.5 h backward, 5.5 h forward) for parcels traveling through an upshear-left thunderstorm updraft overlaid on 6-h time-averaged surface latent heat flux (W m−2; shading) and surface pressure (hPa; magenta contours) from t = 30 to 36 h. (b) Parcel altitude (m) vs time. (c) Parcel θe (K) vs time. (d) Parcel diabatic heating rate (K h−1) vs time. These trajectories are from the 667-m grid spacing simulation with negative TCREH. The green boxes denote the beginning of the trajectories and the brown boxes denote the endpoints.

Fig. 14.

(a) The 6-h trajectories (0.5 h backward, 5.5 h forward) for parcels traveling through an upshear-left thunderstorm updraft overlaid on 6-h time-averaged surface latent heat flux (W m−2; shading) and surface pressure (hPa; magenta contours) from t = 30 to 36 h. (b) Parcel altitude (m) vs time. (c) Parcel θe (K) vs time. (d) Parcel diabatic heating rate (K h−1) vs time. These trajectories are from the 667-m grid spacing simulation with negative TCREH. The green boxes denote the beginning of the trajectories and the brown boxes denote the endpoints.

The final way in which trajectories are analyzed is by considering the boundary layer θe recovery rate downwind of convection. We propose that faster boundary layer recovery rates in upshear quadrants promote fresh convective development and faster deepening of the parent TC. Figures 15 (positive-TCREH simulation) and 16 (negative-TCREH simulation) show 2-h backward trajectories from locations near the surface (lowest model level) downwind of convection. For both experiments the trajectories are released at t = 38 h (t = 120 m in Figs. 15 and 16) and go back to t = 36 h (t = 0 m in Figs. 15 and 16). In both cases, parcels travel through convection at larger radii en route to their locations in the boundary layer downwind of convection at smaller radii. The primary difference between the two cases is the rate at which θe recovers during the final stages of this journey. While the recovery rates shown in Figs. 15c and 16c look similar, the mean rate in the positive TCREH case is 6.4 K h−1 compared to 4.1 K h−1 in the negative-TCREH simulation. These recovery rates are different even though the initial values of θe for both sets of trajectories are quite similar. The faster recovery rate is likely due to the fact that wind speeds and surface fluxes are larger in regions downwind of convection when TCREH is positive (Figs. 10a vs 11a). This faster recovery also allows surface parcels to be lifted into new convection sooner and more easily due to increased buoyancy, as was seen above (18% of parcels rising into convection vs only 1.5% in the negative TCREH case).

Fig. 15.

(a) The 2-h backward trajectories for parcels originating on the lowest model level downwind of convection at t = 38 h overlaid on 700-hPa simulated reflectivity valid at t = 38 h. (b) Parcel altitude (m) vs time. (c) Parcel θe (K) vs time. These trajectories are from the 667-m grid spacing simulation with positive TCREH. The brown boxes denote the ending locations of the backward trajectories.

Fig. 15.

(a) The 2-h backward trajectories for parcels originating on the lowest model level downwind of convection at t = 38 h overlaid on 700-hPa simulated reflectivity valid at t = 38 h. (b) Parcel altitude (m) vs time. (c) Parcel θe (K) vs time. These trajectories are from the 667-m grid spacing simulation with positive TCREH. The brown boxes denote the ending locations of the backward trajectories.

Fig. 16.

(a) The 2-h backward trajectories for parcels originating on the lowest model level downwind of convection at t = 38 h overlaid on 700-hPa simulated reflectivity valid at t = 38 h. (b) Parcel altitude (m) vs time. (c) Parcel θe (K) vs time. These trajectories are from the 667-m grid spacing simulation with negative TCREH. The brown boxes denote the ending locations of the backward trajectories.

Fig. 16.

(a) The 2-h backward trajectories for parcels originating on the lowest model level downwind of convection at t = 38 h overlaid on 700-hPa simulated reflectivity valid at t = 38 h. (b) Parcel altitude (m) vs time. (c) Parcel θe (K) vs time. These trajectories are from the 667-m grid spacing simulation with negative TCREH. The brown boxes denote the ending locations of the backward trajectories.

c. Contoured frequency-by-altitude diagram results

Results from CFADs show that the characteristic differences between convection (and associated vertical velocities and heat fluxes) in the positive- and negative-TCREH simulations are not as distinguishing as expected. The primary difference is where the convection is located azimuthally. Figure 17 shows CFADs of simulated reflectivity (dBZ) versus altitude (km) for t = 30–36 h for the positive-TCREH simulation (Figs. 17a,d) and the negative-TCREH simulation (Figs. 17b,e). The CFADs are computed using a 75 km × 75 km box centered on the region of maximum convection. This region is chosen so that the characteristics of the strongest convection can be directly compared between the two cases. Figure 17c shows the difference in reflectivity frequency versus altitude (positive TCREH case minus negative TCREH case). Figures 17a and 17b show that the overall characteristics of the convection between the two cases are quite similar. The main difference is that stronger convection (reflectivity >35 dBZ) reaches higher altitudes when TCREH is negative. A key result here is that even though the strongest convection may be deeper in the negative-TCREH simulation, the rate at which minimum central pressure falls remains slower than when TCREH is positive. This highlights the importance of the azimuthal position of the convection relative to the storm motion. Because convection was located farther upshear when TCREH is positive, the associated diabatic heating and larger surface fluxes were closer to the path of the TC allowing for a faster rate of intensification. The results from CFADs of vertical velocity (Figs. 17d–f) show that the characteristics of updrafts and downdrafts are similar for the two simulations. Figure 17f shows that, except for small magnitudes of vertical velocity (−3 < w < 3 m s−1), the differences in frequency are less than 1%. Total vertical mass flux in the region of maximum convection (not shown) is larger for the negative TCREH case. However, since this flux occurs at larger radii and downshear right of the TC, it is less effective at reducing the minimum central pressure.

Fig. 17.

CFADs of (a)–(c) simulated reflectivity (dBZ; x axis) and (d)–(f) vertical velocity (m s−1; x axis) vs altitude (km; y axis) for a simulation with (a),(d) positive TCREH; (b),(e) negative TCREH; and (c),(f) the difference between the two. CFADs are computed for a 75 km × 75 km box centered on the region of maximum convection for t = 30–36 h. In (a),(b),(d), and (e), contours have a logarithmic scale such that a frequency of 100% corresponds with a value of 2. In (c) and (f), the difference between the frequencies for the two cases (positive TCREH case minus negative TCREH case) are shown on a nonlogarithmic scale. The thick black contour in (c) and (f) denotes a 0% difference.

Fig. 17.

CFADs of (a)–(c) simulated reflectivity (dBZ; x axis) and (d)–(f) vertical velocity (m s−1; x axis) vs altitude (km; y axis) for a simulation with (a),(d) positive TCREH; (b),(e) negative TCREH; and (c),(f) the difference between the two. CFADs are computed for a 75 km × 75 km box centered on the region of maximum convection for t = 30–36 h. In (a),(b),(d), and (e), contours have a logarithmic scale such that a frequency of 100% corresponds with a value of 2. In (c) and (f), the difference between the frequencies for the two cases (positive TCREH case minus negative TCREH case) are shown on a nonlogarithmic scale. The thick black contour in (c) and (f) denotes a 0% difference.

A second way to compute CFADs is to choose an annulus with radii that encompass the areas of relatively strong convection. Figure 18 shows this annulus within radii of 25 and 225 km. As before, the period of consideration is t = 30–36 h, which is just prior to when intensities diverge. The primary difference when an annulus is used is that stronger convection is more frequent at all altitudes when TCREH is positive. This highlights the fact that the strongest convection may be slightly stronger in the negative TCREH (Fig. 17c) case, but overall convective coverage is larger when TCREH is positive (Fig. 19c). As was the case when the data were centered on the region of maximum reflectivity, the characteristics of vertical velocity are similar for the two cases outside the range of ±2 m s−1, likely due to the fact that strong updrafts are highly localized. Total convective mass flux (not shown) was similar for the positive and negative TCREH cases for the annular region.

Fig. 18.

Example of the annular area for CFAD computations. The black contour denotes the region in which the CFAD is computed, the magenta contours show smoothed surface pressure, and simulated 700-hPa reflectivity is shaded.

Fig. 18.

Example of the annular area for CFAD computations. The black contour denotes the region in which the CFAD is computed, the magenta contours show smoothed surface pressure, and simulated 700-hPa reflectivity is shaded.

Fig. 19.

CFADs of (a)–(c) simulated reflectivity (dBZ; x axis) and (d)–(f) vertical velocity (m s−1; x axis) vs altitude (km; y axis) for a simulation with (a),(d) positive TCREH; (b),(e) negative TCREH; and (c),(f) the difference between the two. CFADs are computed for an annulus centered on the TC between the radii of 25 and 225 km for t = 30–36 h. In (a),(b),(d), and (e), contours have a logarithmic scale such that a frequency of 100% corresponds with a value of 2. In (c) and (f), the difference between the frequencies for the two cases (positive TCREH case minus negative TCREH case) are shown on a nonlogarithmic scale. The thick black contour in (c) and (f) denotes a 0% difference.

Fig. 19.

CFADs of (a)–(c) simulated reflectivity (dBZ; x axis) and (d)–(f) vertical velocity (m s−1; x axis) vs altitude (km; y axis) for a simulation with (a),(d) positive TCREH; (b),(e) negative TCREH; and (c),(f) the difference between the two. CFADs are computed for an annulus centered on the TC between the radii of 25 and 225 km for t = 30–36 h. In (a),(b),(d), and (e), contours have a logarithmic scale such that a frequency of 100% corresponds with a value of 2. In (c) and (f), the difference between the frequencies for the two cases (positive TCREH case minus negative TCREH case) are shown on a nonlogarithmic scale. The thick black contour in (c) and (f) denotes a 0% difference.

4. Conclusions

The TC-intensification rate is modulated by the shape of the environmental wind profile (i.e., TCREH). Time composites of surface latent heat flux and simulated reflectivity show how the maxima of these features rotate cyclonically into upshear quadrants more rapidly when TCREH is positive. Simulations including the addition of uniform background flow demonstrate that certain storm motions relative to the vertical wind shear vector allow for more rapid intensification. These simulations suggest that intensification is most efficient when the TC is moving toward the regions experiencing larger surface latent heat flux or increased diabatic heating. In these cases, there is considerably more overlap of boundary layer convergence and latent heat flux. Trajectories show that the process of advecting buoyant, θe-enhanced air into the TC is more efficient and a much higher percentage of parcels are lofted into convection in the upshear quadrants near the RMW when TCREH is positive. They also show that boundary layer recovery is faster downwind of convection when TCREH is positive.

CFAD analyses illustrate the fact that differences in characteristics of convection such as depth of reflectivity between TCs embedded in positive versus negative TCREH are small. CFADs computed in an annulus centered on the TC, however, show that total convective coverage is slightly larger when TCREH is positive. Using both simulations and reanalysis data, ON14 showed that positive TCREH favors faster TC intensification. In that study, they suggested that the nature of convection in a TC embedded in positive TCREH was more organized and robust. In the present study, further evaluation of TC structure and intensification in environments characterized by varying TCREH suggests that discrepancies in intensification rate primarily result from the ability of convection and associated surface latent heat fluxes to rotate cyclonically into the upshear quadrants. This precession has been shown in previous studies to relate to the onset of rapid intensification and it occurs more rapidly when TCREH is positive.

Acknowledgments

This work was supported by the National Science Foundation under Grant AGS-1132646. Computational resources and data storage were provided by the University of Miami Center for Computational Sciences.

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