Hurricane Vortex Dynamics during Atlantic Extratropical Transition

Christopher A. Davis National Center for Atmospheric Research,* Boulder, Colorado

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Sarah C. Jones Universität Karlsruhe, Forschungszentrum Karlsruhe, Karlsruhe, Germany

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Michael Riemer Universität Karlsruhe, Forschungszentrum Karlsruhe, Karlsruhe, Germany

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Abstract

Simulations of six Atlantic hurricanes are diagnosed to understand the behavior of realistic vortices in varying environments during the process of extratropical transition (ET). The simulations were performed in real time using the Advanced Research Weather Research and Forecasting (WRF) model (ARW), using a moving, storm-centered nest of either 4- or 1.33-km grid spacing. The six simulations, ranging from 45 to 96 h in length, provide realistic evolution of asymmetric precipitation structures, implying control by the synoptic scale, primarily through the vertical wind shear.

The authors find that, as expected, the magnitude of the vortex tilt increases with increasing shear, but it is not until the shear approaches 20 m s−1 that the total vortex circulation decreases. Furthermore, the total vertical mass flux is proportional to the shear for shears less than about 20–25 m s−1, and therefore maximizes, not in the tropical phase, but rather during ET. This has important implications for predicting hurricane-induced perturbations of the midlatitude jet and its consequences on downstream predictability.

Hurricane vortices in the sample resist shear by either adjusting their vertical structure through precession (Helene 2006), forming an entirely new center (Irene 2005), or rapidly developing into a baroclinic cyclone in the presence of a favorable upper-tropospheric disturbance (Maria 2005). Vortex resiliency is found to have a substantial diabatic contribution whereby vertical tilt is reduced through reduction of the primary vortex asymmetry induced by the shear. If the shear and tilt are so large that upshear subsidence overwhelms the symmetric vertical circulation of the hurricane, latent heating and precipitation will occur to the left of the tilt vector and slow precession. Such was apparent during Wilma (2005).

+ Current affiliation: Naval Postgraduate School, Monterey, California

Corresponding author address: Christopher A. Davis, National Center for Atmospheric Research, P.O. Box 3000, Boulder, CO 80307. Email: cdavis@ucar.edu

Abstract

Simulations of six Atlantic hurricanes are diagnosed to understand the behavior of realistic vortices in varying environments during the process of extratropical transition (ET). The simulations were performed in real time using the Advanced Research Weather Research and Forecasting (WRF) model (ARW), using a moving, storm-centered nest of either 4- or 1.33-km grid spacing. The six simulations, ranging from 45 to 96 h in length, provide realistic evolution of asymmetric precipitation structures, implying control by the synoptic scale, primarily through the vertical wind shear.

The authors find that, as expected, the magnitude of the vortex tilt increases with increasing shear, but it is not until the shear approaches 20 m s−1 that the total vortex circulation decreases. Furthermore, the total vertical mass flux is proportional to the shear for shears less than about 20–25 m s−1, and therefore maximizes, not in the tropical phase, but rather during ET. This has important implications for predicting hurricane-induced perturbations of the midlatitude jet and its consequences on downstream predictability.

Hurricane vortices in the sample resist shear by either adjusting their vertical structure through precession (Helene 2006), forming an entirely new center (Irene 2005), or rapidly developing into a baroclinic cyclone in the presence of a favorable upper-tropospheric disturbance (Maria 2005). Vortex resiliency is found to have a substantial diabatic contribution whereby vertical tilt is reduced through reduction of the primary vortex asymmetry induced by the shear. If the shear and tilt are so large that upshear subsidence overwhelms the symmetric vertical circulation of the hurricane, latent heating and precipitation will occur to the left of the tilt vector and slow precession. Such was apparent during Wilma (2005).

+ Current affiliation: Naval Postgraduate School, Monterey, California

Corresponding author address: Christopher A. Davis, National Center for Atmospheric Research, P.O. Box 3000, Boulder, CO 80307. Email: cdavis@ucar.edu

1. Introduction

A salient aspect of the extratropical transition (ET) of tropical cyclones is the downstream cyclone development it can induce in the midlatitudes. An important component of the decline in hemispheric predictive skill associated with ET is uncertainty about the interaction of the tropical cyclone with a westerly jet (Jones et al. 2003). One of the key contributors to the uncertainty is the development of the downstream ridge connected with the outflow of the tropical cyclone (Atallah and Bosart 2003). The dynamics of this ridge development, fundamentally involving diabatic heating, depends upon the properties of the jet and of the impinging tropical cyclone as transition occurs.

The cyclone–jet interaction critically depends upon survival of the tropical cyclone as it penetrates deeper into the middle latitudes, generally into an environment of increasing vertical shear. Previous studies (Jones 2000a, b; 2004; Schecter et al. 2002; Reasor et al. 2004) have suggested that adiabatic vortices can realign, if tilted, and can resist vertical shear of a few meters per second imposed across the depth of the vortex. Observations indicate that hurricane vortices remain erect in the presence of vertical shears of at least 10 m s−1 over the vortex depth (DeMaria et al. 1993; Paterson et al. 2005). The ability of a vortex to resist increasing vertical shear is crucial to allow hurricane vortices to approach and perturb midlatitude jets of order 30 m s−1. It is perturbations on strong jets that pose a greater limitation to downstream predictability (Riemer et al. 2008.

A central question is therefore how a real tropical cyclone vortex is maintained as it traverses an environment of increasing vertical shear on its way to the midlatitude tropospheric potential vorticity (PV) gradient. In particular, the warm-core structure is maintained in some cases long after the vortex experiences significant westerly shear. A variety of approaches have been used to examine the behavior of vortices in shear, including analytic studies (Reasor and Montgomery 2001; Schecter et al. 2002; Reasor et al. 2004), idealized modeling (Raymond 1992; Jones 1995; Frank and Ritchie 1999, 2001; Trier et al. 2000; Kimball and Evans 2002; Wong and Chan 2004), and high-resolution, full-physics models of a single, observed case (Rogers et al. 2003; Braun et al. 2006; Zhang and Kieu 2006). The distinction between high and coarse resolution is the ability to resolve the core of the hurricane and the avoidance of a cumulus parameterization scheme to treat deep convection near the core. While the numerous existing studies represent substantial progress toward understanding the dynamics of sheared hurricanes, there still exists a strong need to link theoretical concepts to real-world realizations in the context of ET.

The primary purpose of this paper is to examine the process of ET using simulations of several observed cases and link these results back to idealized simulations and other simulations of observed cases. Fundamental to this endeavor is consideration of moist processes and how vertical shear alters the distribution of latent heating and rainfall, which alters the vortex, further changing the distribution of rainfall, and so on. We utilize fully explicit simulations of six extratropical transitions with the Weather Research and Forecasting (WRF) model, Advanced Research WRF core (Skamarock et al. 2005), focusing on the processes by which these storms acquire extratropical cyclone characteristics. Simulations of six Atlantic tropical cyclones—Irene, Maria, Ophelia, and Wilma from 2005 and Gordon and Helene from 2006—are analyzed. The tracks of these six storms, emphasizing the periods of investigation of the present study, appear in Fig. 1. Detailed summaries of these cases are available from the National Hurricane Center Web site (additional information is available online at http://www.nhc.noaa.gov/pastall.shtml). For brevity, we refer the interested reader to the detailed summaries rather than reproduce any substantial portion of the information herein. Observations of each case will be shown for purposes of model evaluation.

Our first finding is that the Advanced Research WRF (ARW) is able to realistically replicate many aspects of the structural changes observed as each hurricane moves into the extratropics. Second, regarding mechanisms of structural change, there is considerable resistance of each vortex to vertical shear, as has been suggested by recent work (e.g., Jones 2004; Reasor et al. 2004), but that (i) the resistance depends critically upon diabatic processes and (ii) resistance can be achieved by either altering the vortex structure (i.e., resilience), forming a new vortex center, or enlisting baroclinic cyclogenesis. In each scenario, diabatic processes systematically offset the effects of shear, consistent with results from Zhang and Kieu (2006). Third, we find that the vertical mass flux is larger during ET than during the mature hurricane phase. This has important implications for the ability of transitioning storms to perturb the westerly jet as they move poleward, and therefore has implications for midlatitude predictability.

Rather than conduct six individual case studies, we first examine all cases together to understand how storms respond to different environments, rooted either in case-to-case variation or time dependence of environmental conditions (section 3). We then examine individual cases, but mostly by contrasting pairs of cases with some similar characteristics (section 4). Conclusions appear in section 5.

2. Model configuration

All simulations in this paper were forecasts integrated in real time. The forecasts therefore fulfill two purposes: demonstrating the ability of high-resolution forecast models to predict storm structure and providing a dataset for dynamically based process studies. A more comprehensive summary of results obtained from real-time hurricane forecasts with the ARW model during 2005 is presented in Davis et al. (2008).

The simulations of cases during 2005 used a two-way nested configuration featuring an outer domain with a 12-km grid spacing containing a movable nest of 4-km grid spacing centered on the minimum 500-hPa geopotential height. Nest repositioning was calculated every 15 simulation minutes, with the additional constraint that the domain could not move farther than 36 km (corresponding to an effective speed of 40 m s−1). The outer domain had dimensions of 460 × 351 (east–west by north–south on a Mercator projection) and was repositioned prior to each forecast depending on the location of the storm. The inner domain had dimensions of 310 × 316. Thirty-five terrain-following coordinate levels were used with the lowest level at about 35 m. The spacing between levels stretched from ∼70 m at the bottom to ∼500 m in the middle and upper troposphere to ∼1 km in the lower stratosphere. The model top was prescribed at 50 hPa.

On the outer 12-km domain we used the Kain–Fritsch cumulus parameterization (Kain 2004), but the inner domain had no parameterization. Both domains used the WRF single-moment 3-class (WSM3) microphysics scheme (Hong et al. 2004) that predicted only one cloud variable (water for T > 0°C and ice for T < 0°C) and one hydrometeor variable, either rainwater or snow (again thresholded on 0°C). Both domains also used the Yonsei University (YSU) scheme for the planetary boundary layer (Noh et al. 2001).

The forecasts were initialized using the Geophysical Fluid Dynamics Laboratory (GFDL) analyses, with data on a ⅙° latitude–longitude grid. Lateral boundary conditions were also taken from the GFDL model. These data were obtained from the National Centers for Environmental Prediction (NCEP) Environmental Modeling Center (EMC) FTP site. Wind, temperature, and humidity data were stored on constant pressure surfaces at an interval of 50 hPa beginning at 1000 hPa. Data at 10 hPa were also included. These data were interpolated bilinearly in the horizontal and linearly in ln(p) in the vertical, where p is the pressure. The GFDL data contained a bogus of the tropical cyclone following the bogusing method of Kurihara et al. (1993). In all cases considered herein, the storms were initialized when they were tropical storms or hurricanes and, in most cases, the initial rainfall distribution around the vortices was much more symmetric than at later times. Simulations extended for varying lengths owing to simultaneous constraints of maintaining a reasonably accurate forecast trajectory, maintaining the moving nest within the coarse domain, and sampling the evolution of each storm as it entered the midlatitudes. Most storms were initialized in the subtropics (Fig. 1), past their time of maximum intensity.

There were several changes to the model in 2006, building from ARW version 2.1 used for the 2005 storms. In 2006, version 2.1.2 was used and another nest was added (domain 3) with 1.33-km grid spacing and centered within the moving 4-km grid. All results from 2006 will be examined on the 4-km grid. The size of the coarse domain, with 12-km grid spacing, was still 460 × 351, while domain 2 contained 202 points on a side and domain 3 contained 241 points on a side. In 2005, the Charnock (1955) specification of surface drag and the Carlson and Boland (1978) formulation of heat and moisture fluxes were used. However, there was an error in the specification of the surface frictional velocity, resulting in friction that was too weak over water.1 In 2006, this and other minor coding errors were fixed. We also implemented a surface drag formulation following Donelan et al. (2004) and the Large and Pond (1981) scheme for the surface enthalpy flux. In the Donelan formulation, the drag was held constant beyond a wind speed of 30 m s−1. In the Large and Pond formulation, the enthalpy flux was invariant with wind speed. The ratio of drag to enthalpy exchange coefficients at wind speeds above 30 m s−1 was approximately 0.7.

In subsequent sections of this article, verification of the general precipitation patterns will be conducted. Here we present comparisons of the prediction of maximum wind speed at 10-m MSL with the best-track data from the National Hurricane Center (NHC). It should be noted that there is considerable uncertainty in some cases where the hurricane is not sampled by reconnaissance aircraft owing to its distance from shore. The only cases wherein the best-track data were aided by reconnaissance information were Wilma and Ophelia, and in these cases, the intensity prediction was highly accurate (Fig. 2). Most cases were in their weakening stage during the forecast, but Maria intensified after 48 h. No direct observations were available to confirm this intensification. Irene, Helene, and Gordon approximately maintained their intensity in the forecast, where there were greater intensity changes (negative for Irene and Helene, positive for Gordon) in the best-track data. Wilma’s brief decay near 48 h (1200 UTC 24 October 2005) corresponded to its landfall over and traversal of south Florida.

3. Diagnostics of six cases

Herein we view statistics of all six cases together to gain a perspective of how each storm behaved in a changing environment. The diagnostic variables include vortex size, vortex intensity, vortex tilt, environmental shear, and vertical mass flux. The area-integrated mass flux is proportional to the area-integrated diabatic heating, divergence in the upper troposphere, and to the total precipitation. The divergent wind within the hurricane outflow has been shown by Riemer et al. (2008) to be the first attribute of the hurricane to interact with the midlatitude jet in idealized simulations. Spatial variations of the mass flux are also important for understanding how diabatic heating relates to, and modifies, the hurricane vortex.

Although the storm-following nest was nearly centered on the hurricane at all times, we elected to compute the location of the center as the grid point in the middle of a square with the maximum area-integrated PV at level 29 (about 1 km MSL). The size of the square was fixed for each case but varied from 120 km for Irene, Maria, Ophelia, and Gordon to 200 km for Wilma and Helene. The varying box size accounted crudely for the variation in storm size in the sample.

Once the center location was determined, a more definitive vortex size was computed from the radial extent of the azimuthally averaged PV on the 310-K isentropic surface exceeding 2 PV units (PVU, where 1 PVU = 10−6 m2 s−1 K kg−1). The 310-K surface is relatively flat outside the inner core and is typically located about 1–1.5 km MSL. In addition, we used the symmetric PV integrated over the area bounded by PV = 2 PVU as a measure of the strength of the vortex. Also, because adiabatic motion does not change the integrated PV on an isentropic surface within an area bounded by a PV contour, the total PV time series gives an estimate of the contribution of diabatic heating to changes in vortex circulation.

An important environmental variable is the vertical wind shear, which we computed from the difference in horizontal wind between layers 17 and 29 in the model, corresponding to a vertical span from about 7 km down to 1 km above mean sea level. Vertical cross sections of potential vorticity revealed that vortices spanned this layer in all cases and sometimes extended to a depth of 12 km. The shear vector was averaged over an area that varied roughly with the size of the hurricane. For Irene, Maria, Ophelia, and Gordon—hurricanes of modest size (Table 1)—we used a region 360 km × 360 km centered on the 4-km nested domain. Recall that the nest moved with the hurricane. For Wilma and Helene— larger storms—the shear was computed over an area 600 km × 600 km.

Another diagnostic computed was the vortex tilt, using the relation
i1520-0469-65-3-714-e1
in which q denotes the Rossby − Ertel PV, and the difference spans layers 17–29, approximately 7 km down to 1 km MSL. The averaged PV-weighted position vector is computed over the same region A used to compute the vertical shear. This method for computing tilt results in a relatively smooth time series of tilt vectors for a given storm and is more representative of the overall structure of the vortex than is, say, the PV maximum at a particular level (Jones 2004). Convenient measures of the tilt are the magnitude of the vector and its orientation relative to the shear vector, expressed as the angle of the tilt minus the angle of the shear so that a counterclockwise rotation of the tilt relative to the shear yields a positive angle.

A vortex in shear will tilt and, for strong vortices in modest shear, it may precess (Jones 1995, 2004; Schecter et al. 2002; Reasor et al. 2004). Reasor et al. point out that an optimal state for a vortex with an extended radial vorticity gradient is a tilt directed to the left of the shear vector. From the right-hand column of Fig. 3, it is clear that the vortices tilt to the left of the shear vector nearly all the time (tilt angle between 0 and π). Further, this tilt configuration is often steady, and vortices tend to return to this configuration when perturbed. A supporting item for this last point is the time series for Helene, which shows a trend for increasing tilt as the shear increases, but then a leveling off as the tilt rotates to just over 90° to the left of the shear. The oscillations in tilt angle during Helene, representing vortex precession, will be discussed in section 4.

The tilt angle shows some sensitivity to the averaging area used to compute shear and tilt. As has been pointed out (Jones 2004; Davis and Bosart 2006), a tilted vortex induces its own vertical shear across the center directed to the right of the tilt direction. Hence, a storm tilting directly downshear, as measured from shear averaged over a large domain, will be tilted to the left of the shear evaluated using a smaller averaging domain. Because of synoptic-scale variability in real cases, we cannot average the shear over arbitrarily large domains. Hence, in cases where the tilt is large, the angle between the tilt and “environmental” shear would be somewhat less than shown in Fig. 3. For cases with small tilt (Gordon), this effect is not noticeable.

A third diagnostic quantity was the vertical mass flux, computed as the integral of ρw, where ρ is density and w vertical velocity, over a circle of radius equal to twice the size of the vortex (defined from PV above) and evaluated at level 21 of the model (about 4 km MSL). The area-integrated, azimuthal-mean mass flux F, expressed in kilograms per second, provides a measure of the total net upward transport of mass.

We also integrated the azimuthal-mean vertical mass flux over rings of width Δr = 4 km, denoted the symmetric mass flux, Fk = Σ Fi,j, rk ≤ (x2i,j + y2i,j)1/2 < rk + Δr for k = [0, 75], where (xi,j, yi,j) is the Cartesian coordinate relative to the storm center (r = 0) on the model grid. The effect of vertical shear led to large azimuthal asymmetries of vertical mass flux in most of the cases examined. Therefore, a measure of the magnitude of the mass-flux asymmetry compared to the symmetric value was desirable. Within each radial ring of width 4 km, we computed a set of mass-flux summations over semicircles moving in discrete jumps of 10° around the ring, k,l = Σ Fi,j, rk ≤ (x2i,j + y2i,j)1/2 < rk + Δr; ϕlπ/2 ≤ ϕ < ϕl + π/2, with ϕ the azimuthal angle, and ϕl = (π/18, 2π/18, 3π/18, · · · , 2π). From the 36 resulting values of k,l around a ring, let the maximum mass flux be kmax and the minimum value be kmin. We defined the asymmetric mass flux parameter k = (kmaxkmin)/2. In the limit of a purely symmetric vortex, the asymmetric mass flux is zero. More generally, however, there are many wavenumbers that contribute to the azimuthal spectrum of mass flux since isolated updrafts project onto many wavelengths. The parameter k is relatively insensitive to small-scale structures while still retaining the gravest mode of the asymmetry. To obtain an area-integrated value of the asymmetric mass flux analogous to F, we computed the sum of k within a distance of twice the vortex radius, as was done for the area-integrated mass flux F. The asymmetric-flux parameter is therefore not a measure of whether the eyewall is closed; rather, it considers the larger-scale structure of the storm.

Time series of the diagnostic parameters defined above appear in Figs. 3 and 4 for each case. For Irene, Maria, Wilma, and Helene, the vertical shear increased throughout most of the simulation, whereas in Gordon it was nearly constant and in Ophelia it varied by more than a factor of 2 during the simulation. To first order, the area-integrated symmetric vertical mass flux F varied with the shear, provided the shear did not exceed 20 m s−1 or more over the depth of the vortex. In Wilma, the shear reached 30 m s−1 by the end of the simulation, and F fell steadily during the final 18 h while the area-averaged asymmetric mass flux continued to grow. As the storms in our sample approached the midlatitudes and experienced greater vertical shear, F increased and typically attained values greater than in the mature tropical cyclone phase. The increase in mass flux was more rapid in cases such as Maria and Helene. There was a suggestion of an optimum shear of about 15 m s−1 that elicited the greatest symmetric mass flux response for a given storm.

The mass-flux dependency on shear suggests that the upward mass transport will become larger, at least for a while, as a storm approaches a midlatitude jet. Riemer et al. (2008) found that the midlatitude jet is first perturbed by the outflow of the poleward-moving tropical cyclone. Our result implies that the hurricane–jet interaction may grow rapidly with time owing to the approach of the tropical cyclone toward the jet and the increase of its outflow strength. Because the details of the mass flux response to increasing shear may be difficult to treat properly in global models, this process is perhaps an important source of forecast sensitivity. It may partly explain the erratic forecast skill during ET. Errors in the forecast shear can have large consequences for the mass flux in the transitioning cyclone. Furthermore, even knowing the shear, the mass-flux response may depend strongly on the parameterization of deep convection in models. Thus, prediction of the outflow that perturbs the midlatitude jet is likely to be highly uncertain. Relatively large forecast uncertainty on the synoptic scale stemming from mesoscale convection in baroclinic environments has also been demonstrated in some extratropical cyclones (Zhang et al. 2003) and nontransitioning tropical cyclones (e.g., Atallah et al. 2007).

Perhaps the simplest explanation for the positive correlation of mass flux with shear arises from quasigeostrophic theory, wherein the right-hand side of the omega equation is dominated by the so-called Sutcliffe term, advection of vorticity by the thermal wind, that is, by the vertical shear (Sutcliffe 1947). Synoptic-scale vertical motion is stronger when the shear is stronger for a given vorticity. Here, the shear is the total shear, not simply that which might be imposed at the start of an idealized simulation.

Reasor et al. (2000) decomposed the divergence of the Q vector into a piece aligned with an imposed, environmental shear and a piece orthogonal to the vortex tilt, with ascent rotated 90° clockwise from the tilt vector [their Eq. (8)]. The latter term is proportional to both the strength of the vortex (the Rossby number) and the tilt, and is directly analogous to the vorticity advection by the thermal wind (vertical shear) arising from a tilted vortex. Stronger environmental shear will tend to produce a greater tilt. A stronger, tilted vortex will produce a greater perturbation shear, directed 90° to the right of the tilt (Davis and Bosart 2006). The sum of the two shear components yields an even greater total shear, and in Reasor et al. (2000) both effects are multiplied by Ro, the strength of the vortex. It is clear by this adiabatic reasoning that a stronger vortex and stronger shear will result in a proportionally greater response in vertical motion on the scale of the vortex.

While the quasigeostrophic (QG) framework clearly fails quantitatively in the present context of hurricanes, the spatial pattern of quasi-balanced lifting at large Rossby number still resembles qualitatively the pattern predicted by quasigeostrophic dynamics (Raymond 1992; Trier et al. 2000). Even in primitive equation simulations of adiabatic, hurricane-like vortices (Jones 1995; Frank and Ritchie 1999), the lifting maximizes to the right of the downtilt direction, as predicted by QG, although QG vertical velocities are an order of magnitude less. A systematic examination of vertical motion response to vortices of increasing strength in shear, perhaps utilizing the balance-equation framework of Shapiro and Montgomery (1993), is needed to fully substantiate the qualitative link that we have made between QG dynamics and the correlation of vertical shear with total mass flux. Such an analysis is not attempted here.

Adiabatic, mesoscale vertical motion will only attain values of order 10 cm s−1 in strong vortices (e.g., Trier et al. 2000). Therefore, mesoscale vertical velocities of more nearly 1 m s−1 that occur (see section 4 and Fig. 10) must arise from a diabatic response to the mesoscale lifting. Quasi-balanced lifting still determines the location of diabatic heating, however, whether the flow is conditionally stable or unstable. In the stable case, condensation heating can be modeled with a locally reduced static stability (Emanuel et al. 1987). In the unstable case, balanced motions determine the rate of thermodynamic destabilization. With the quasi-equilibrium assumption (Emanuel 1994), this rate determines the convective mass flux. Either way, one expects a correlation between the balanced lifting, represented approximately by the QG equations, and the convective mass flux. This heuristic argument supports our interpretation of the mass-flux dependency on shear, as well as conclusions from other studies of the diabatic heating effects in sheared tropical cyclones (Atallah et al. 2007). However, this interpretation does not include the additional potential for thermodynamic destabilization from surface fluxes of heat and moisture from the ocean. Such destabilization would be larger for vortices with stronger surface winds, given the same sea surface temperature and thermodynamic conditions far from the storm. However, most of the six storms traversed paths with decreasing SST and exhibited heat and moisture fluxes that were nearly zero during transition.

The increased diabatic heating represented by an enhanced mass flux will also affect the PV and, hence, storm structure and intensity. From Fig. 4, a sustained mass flux apparently results in a slowly increasing average PV in the vortex as well as an increase in the size of the vortex. A temporal increase of vortex size in sheared flows was also noted by Kimball and Evans (2002) in idealized simulations of hurricanes interacting with troughs. The response appears proportional to the size of the vortex, with large storms (Wilma and Helene) experiencing a relatively greater increase in PV and size for a given shear. Overall, the mass flux, vortex size, and integrated PV (the average PV times the vortex area) tended to increase with shear, even if the intensity as measured by the maximum wind decreased. These transitioning storms, perhaps with the exception of Ophelia, were not decaying in any integrated sense as they experience greater shear.

To investigate the reasons for the systematic change in scale of the vortices, it is instructive to examine time–radius diagrams of the symmetric vertical mass flux Fk (Fig. 5). In all cases the maximum mass flux is found roughly near the same radius as the PV = 2 contour of the symmetric PV (hereafter defining the radial scale of the vortex). This radius lies just outside the radius of maximum azimuthal tangential mean wind (Fig. 5). The asymmetric mass flux k maximizes at approximately the same radius as the symmetric mass flux (not shown). Because the mass flux and diabatic heating have a large asymmetric component near the edge of the vortex, lower-tropospheric cyclonic PV asymmetries will also so be enhanced at these greater radii. Axisymmetrization (e.g., Montgomery and Enagonio 1998) will redistribute the resulting PV anomalies.

Although it has been clearly shown in idealized models that asymmetric PV anomalies can give up their energy to the symmetric circulation (e.g., Montgomery and Enagonio 1998), it is primarily with weak, broad vortices that the process is important for both spinup and contraction of the tangential wind field. The role of diabatic heating on the periphery of contracted, intense vortices is less studied. We note that the migration of the maximum mass flux beyond the edge of the vortex is favored as the vortex tilt increases. This is consistent with subsidence above the tilted vortex suppressing convection near the circulation center and forcing convection to increasingly greater radii as the tilt increases (Raymond 1992; DeMaria 1996). We hypothesize that convection at increasingly greater radii will add PV at greater radii and move the maximum winds outward. Because the mass flux retains a significant symmetric component, this process will also promote subsidence at inner radii, tending to weaken the convection there (Shapiro and Willoughby 1982). On a cautionary note, Nolan and Grasso (2003) and Möller and Shapiro (2005) found that adjustments to asymmetries that are not balanced, a priori, are complicated and do not necessarily increase tangential winds. A deeper analysis than can be presented herein appears to be required to fully understand the broadening of sheared hurricane vortices.

The expansion of vortices was not necessarily monotonic with time. For instance, examine Irene between 24 and 36 h, Maria between 48 and 60 h, and Helene at two times (48–60 h and 72–90 h) in Fig. 5. In each case, there appeared an inward-moving region of enhanced mass flux, which indicated the approach of the hurricane to an initially distinct region of precipitation. In each case, this region was collocated with a surface front or trough. When the secondary mass-flux maximum intersected the edge of the vortex, the total mass flux locally increased and the vortex ceased its expansion temporarily. In the case of Helene, the maximum upward mass flux actually moved inward of the 2-PVU contour. In Irene, as will be discussed in the next section, the contraction was associated with a new circulation center.

4. Case studies and comparisons

a. Irene and Ophelia

Irene and Ophelia offer two examples of one way in which a tropical cyclone vortex attempts to resist vertical shear by forming, or attempting to form, a new center located approximately downshear from the original vortex. As it turns out, Irene was successful in this regard, and Ophelia was not. While the two storms had several differences that could have played a role in their differing evolution, we will show that, at one point in their evolution, the two were remarkably similar and proceeded along radically different paths subsequently.

A comparison of simulated rainwater mixing ratio and imagery from the Special Sensor Microwave Imager (SSM/I) 85-GHz channel (Fig. 6) reveals that the WRF simulation of Irene captured much of the structural change with time. Early in the simulation, Irene was influenced by westerly shear and was steadily weakening, slightly more rapidly in the observations (Fig. 2). At approximately 2200 UTC 17 August (22 h forecast), the convection was displaced to the east-northeast of the storm center with almost no remnant of the eyewall apparent (Figs. 6a and 6b). The simulated PV at 1 km MSL showed weak gradients around a poorly defined center (Fig. 6b). By 1000 UTC 18 August, both the model and observations indicated an approaching frontal precipitation region elongated from southwest to northeast, and an invigoration of the rainfall immediately to the north of the storm center (Figs. 6c and 6d). There was also an arc of convection cells to the east of the center in the model and observations. The elongated strip of PV in Fig. 6d was the remnant PV from the original center of Irene that had been subjected to strong deformation to the south of the new center, represented by the intense PV core.

Ophelia was a minimal hurricane by the time of model initialization at 0000 UTC 15 September 2005, just after its closest approach to land. After this time, the storm weakened steadily in both simulation and observations (Fig. 2). The positions of Ophelia in the forecast agreed to within 100 km of the observed position at both times (Figs. 7b and 7d). A comparison of SSM/I images at 2300 UTC 15 September and 2300 UTC 16 September indicates that the general asymmetry in the precipitation field was well represented in the ARW forecast, but the scale of the region of precipitation was greater in the observations at both times. The simulated core PV anomaly was elongated at both times. The northern periphery of the central cyclonic PV anomaly was locally enhanced within the precipitation shield late on 16 September (Fig. 7d).

A more direct comparison of the two cases appears in Fig. 8, wherein wind, PV, and potential temperature are shown at 1 km MSL. Figures 8a and 8b show Irene and Ophelia with notably similar overall structures. The original core PV, traceable from time animations, became elongated to the south of a new PV maximum that developed over the southwestern portion of heavy rainfall. Note that in the case of Irene, however, the PV maximum to the north (the new center) was associated with a stronger circulation, featuring a maximum wind of about 50 m s−1 immediately to the east of the center and a lateral shear across the center of about 70 m s−1. During the ensuing 3 h, the new center in Irene overwhelmed the previous circulation center, causing filamentation of the old center. The failed new center in Ophelia was not as intense and merely coexisted with the remnants of the original core. These contrasting behaviors resonate with previous modeling studies of interacting vortices that demonstrate the greatly differing evolutions possible as the intensity of a small vortex increases relative to a larger vortex nearby (Melander et al. 1987; Guinn and Schubert 1993; Enagonio and Montgomery 2001). Extension of quantitative results of such studies to the simulations of real cases with a full-physics model is difficult, however. Perhaps more important is the question of how a separate, intense circulation was able to initiate in Irene.

From Fig. 8, it is apparent that the lower-tropospheric temperature variations were dominated by the hurricane itself, with weak gradients away from the storm. In particular, although Irene was noted to approach a baroclinic zone as it transitioned (e.g., Fig. 6), the formation of the new center appeared isolated from a direct influence of that baroclinity. The character of the wind field differs in the two cases, with Irene embedded in a well-defined large-scale trough in the lower troposphere. This trough clearly contributed to an enhancement of ground-relative winds on the east side of the storm. However, because surface heat and moisture fluxes were nearly zero to the east of the center by 18 August, the stronger winds likely provided no direct thermodynamic contribution to the formation of a new center.

From Fig. 5 it is evident that the vertical mass flux was larger in Irene through most of its evolution. This is consistent with the greater vertical shear and overall vortex strength, measured by the integrated PV within the PV = 2 contour (Figs. 4a and 4c), and thus echoes the balanced lifting mechanism outlined in section 3. To make the comparison clearer, we have computed the ratio of the shear in Irene to that in Ophelia (Fig. 9), relative to the times shown in Figs. 8a and 8b, namely 0700 UTC 18 August (Irene) and 2300 UTC 16 September (Ophelia). These times are used as a reference because they represent the time in Irene’s evolution when the new circulation center was first clearly evident and the time in Ophelia’s evolution when the secondary PV maximum was most prominent. The largest signal is that of greater vertical shear in Irene, with the overall vortex strength somewhat larger as well. Thus, while it might seem that Irene should have weakened more rapidly than Ophelia due to stronger shear, the opposite was true. The formation of a new circulation center represents an example of resistance to shear that is possible only through diabatic heating.

b. Wilma and Helene

Hurricanes Wilma and Helene were easily the largest hurricanes in the sample of six storms, with Wilma being the most intense storm of all. As was obvious from Figs. 3d and 3f, the vertical shear in Helene was less than half as strong as in Wilma. Hence, this section will be concerned with understanding how two large storms evolve in differing shears.

Wilma was the only storm, of the six which were studied, that made landfall during a simulation. Of note in Figs. 3d and 4d is that, while the maximum wind speed decreased during the period when the center was over land, the integrated PV on the 315-K surface did not decrease until the center had nearly reached the east coast of Florida. Furthermore, the vertical tilt of Wilma abruptly increased during landfall, while decreasing both before and after landfall. Wilma was also unique in the sample in that its tilt was generally in the direction of the shear vector, not to the left as in other cases. Wilma was subjected to the strongest shear of any case, at least after landfall, and its vertical tilt was the largest as well.

Helene evolved in weaker shear relative to Wilma, and its vertical structure evolved significantly. From Fig. 3f, it is evident that the tilt angle became established roughly 90° to the left of the shear vector, then underwent a rapid adjustment to a nearly zero tilt angle, then evolved through a left-of-shear configuration again late in the simulation before another rapid adjustment at the end. The tilt magnitude appeared to oscillate with a small trend superposed. The magnitude of the tilt varied with the shear magnitude more synchronously than in any other case.

A comparison of the evolutions of Wilma in strong shear, and Helene in weak shear, appears in Fig. 10, wherein we have computed the average vertical motion and rainwater mixing ratio in sectors of 10° azimuthal width and radial extent ranging from 0.5 to 1.5 times the vortex size (defined by the extent of the symmetric 2-PVU contour; Fig. 4). For Helene, the maximum upward vertical motion and rainwater mixing ratio were nearly aligned with the tilt vector, although the ascent region as a whole was rotated slightly to the right (clockwise) from the rainwater field. This is to be expected since the ascent determines where hydrometeors form, to a first approximation, and the near-surface rain field includes the effect of advection in the tangential flow (Frank and Ritchie 1999).

Between 30 and 66 h in the simulation, one can estimate the precession frequency of the vortex by the slope of the tilt line in the time–azimuth plot. This turns out to be approximately 10−5 s−1. During this time, the vertical shear averages about 4 m s−1 (Fig. 3f), so, given a vortex radius L = 100 km (Fig. 4f), this corresponds to a shearing inverse time scale (ΔU/2L) of 2 × 10−5 s−1. For precession to dominate the behavior, Reasor et al. (2004) state that the precession frequency should exceed the inverse time scale associated with shearing, but we find the precession frequency is somewhat smaller. Nonetheless, the vortex clearly undergoes a precession of some type, as noted in the tilt, rainwater, and vertical velocity field. Furthermore, the precession is extremely rapid between hours 66 and 72, a frequency almost 10 times greater than the frequency determined between hours 30 and 66. Thus, averaged over an entire precession cycle, the precession frequency is about 2 × 10−5 s−1—very close to the shear time scale.

The evolution of Helene in the real atmosphere is summarized in Fig. 11, wherein it is shown to be broadly consistent with the simulated behavior. At 1449 UTC 20 September (Fig. 11a) the precipitation was highly asymmetric and rotated into the northwest quadrant of the hurricane’s circulation. Slightly more than one day later (1713 UTC 21 September), the outer portion of the precipitation had rotated counterclockwise to the southern side of the circulation, but a maximum in rainfall remained near the center on its north side. This corresponded well with the simulation around 66 h (1800 UTC 21 September; Fig. 11b) when there were two maxima in rainfall, one rotating rapidly through 270° (i.e., directed to the south of the vortex) and the other north-northwest of the vortex center. Only 1200 h later (0518 UTC 22 September; Fig. 11c), the outer precipitation band had rotated further to the east side of the vortex (corresponding to an angle of zero in Fig. 10a). About 11 h later (Fig. 11d), the precipitation maximum was back to the north-northwest quadrant, and the rainfall maxima near the center and farther away had merged into a single large area of precipitation. Both the simulation and the TRMM data indicated that precipitation at this time was the most intense and widespread of any time in the 72-h period analyzed. Recall from Fig. 3f that the integrated symmetric and asymmetric vertical mass flux were also greatest at this time. Thus, there appears to be considerable agreement between the simulated and observed evolution of rainfall in Helene.

We can understand some of the differences in vortex and precipitation structure in terms of the adiabatic vertical motion and associated diabatic response. Because the two vortices possessed similar intensity, the stronger shear in Wilma would lead to stronger adiabatic vertical motion, at least outside the eyewall where the atmosphere was subsaturated. The dipole of vertical motion (Reasor et al. 2000; Trier et al. 2000) would destabilize one-half of the circulation and stabilize the other. The exact quadrant of stabilization and destabilization depends on the total shear (i.e., environmental conditions and vortex tilt and intensity). The rainfall would be enhanced azimuthally downstream from the lifting, and the subsided air in the opposing quadrant would be important for eroding the eyewall on the opposite side, perhaps though entrainment of dry air. In the strong shear that Wilma experienced, shear-induced subsidence created a stronger warm anomaly outside the core than in the center (Fig. 12a). This would seem to define the point at which shear effects overwhelmed the symmetric circulation.

Patra (2004) interpreted the effect of shear on moist, TC-like vortices in terms of the magnitude of the asymmetric vertical circulation compared to the symmetric vertical circulation. Latent heating was represented as proportional to vertical motion (Durran and Klemp 1982; Emanuel et al. 1987). Two scenarios were considered. First, the shear-induced asymmetric vertical circulation was assumed to be weaker than the symmetric vertical circulation so that the whole inner core was saturated. If the magnitude of the heating was chosen to represent moist stable ascent, then the vortex behavior was analogous to the adiabatic case but for weaker stability. Thus, the ascent and heating maximized between the tilt and environmental shear vectors (here, environmental shear was unambiguous). If moist neutrality was assumed, the ascent maximum was predominantly, although not exclusively, left of the shear direction. In both cases there was no net heating and no intensification of the vortex from asymmetries. In the second scenario the asymmetric circulation was assumed to be stronger than the symmetric circulation, resulting in saturated ascent and heating on one side of the vortex and unsaturated descent with no heating on the other. By extension of results from Möller and Montgomery (2000), this asymmetric heating would maintain vortex intensity even in strong shear. We speculate that Helene behaved more like the moist, stable case and Wilma was perhaps better described by the case where asymmetric heating dominated the TC secondary circulation.

A heuristic description of the effect of latent heating on the vertical structure of a vortex appears in Fig. 13. It is convenient to view a vortex tilted by vertical shear as an upper-tropospheric and lower-tropospheric pair of discrete cyclonic PV anomalies. Precession of this pair occurs as the circulation associated with the lower member advects the upper vortex to the left of the initial tilt direction, while the opposite advection occurs in the lower troposphere. This reorients the tilt to the left of its original direction and to the left of the background shear vector, if we assume that tilt and background shear were originally parallel.

Now suppose that diabatic heating is occurring with a maximum updraft to the left of the tilt vector. The primary influence on the PV is to place a negative PV tendency in the upper troposphere and positive PV tendency in the lower troposphere to the left of the tilt vector. This dipole in the vertical acts to cancel, at least partially, the PV tendencies associated with precession (middle column of Fig. 13). If the maximum updraft is directly downtilt, there is no anticipated effect on precession because the diabatic and advective tendencies are out of phase (rightmost column in Fig. 13). Note that this orientation of the diabatic heating would tend to reduce the tilt itself, as discussed in DeMaria (1996), and this could eventually inhibit precession by reducing the mutual advection of upper and lower portions of the vortex.

The nearly continuous alignment of vertical tilt and upward mass flux in Helene suggests that precession would not have been inhibited directly by diabatic processes. Occurrence of the updraft to the left of the tilt in Wilma may have slowed the vortex precession in that case, allowing the shear and tilt to be parallel for a longer time.

c. Maria

The simulation of hurricane Maria, initialized at 0000 UTC 5 September 2005, evolved the storm into a strong, warm-core seclusion within 60 h (Fig. 14). During the simulated intensification, the structure of Maria changed substantially from an asymmetric hurricane with a north–south band of convection extending southward on the east side of the storm to a frontal cyclone with maximum precipitation on the northwest side and an arced line of convection to the southeast of the center (Fig. 14c). The rainwater field from the model agreed well with SSM/I 85-GHz images in this regard. Such agreement might imply that the general character of the evolution was driven by synoptic-scale conditions. Although the intensification in the forecast beyond 24 h (0600 UTC 6 September) appeared erroneous (Fig. 2), it should be noted that all observed intensity estimates were derived from satellite data as the storm acquired a baroclinic structure. Satellite-based estimates of maximum wind speed become increasingly uncertain for more baroclinic storms because techniques based on geostationary satellite data, for instance, are more applicable for storms with complete, or nearly complete, eyewalls (e.g., Velden et al. 1998).

From Fig. 14 it is evident that the warm core, denoted by the small circle of 306-K virtual potential temperature near the center of each simulation panel, was relatively invariant despite changes in other structural aspects. Maria was positioned within a northward-extended wedge of warm air (outlined by the 300-K contour) that narrowed with time. The western boundary of this wedge accelerated eastward and acquired characteristics of a cold front. The environment of rainfall to the northwest of the hurricane became increasingly baroclinic (note the close approach of 300-K and 306-K contours there, Fig. 14c). The convective line to the east and southeast of the storm center maintained its position within the narrowing warm wedge of air. By 1000 UTC 7 September, the structure resembled an occluded cyclone, but with a strikingly intense warm core, made more pronounced by the greater differential that arose as the storm environment cooled and the core maintained its warmth.

The upper troposphere was characterized by the advance of an east–west elongated trough, outlined by the 2-PVU contour on the 350-K isentropic surface. The cyclonic PV in the upper troposphere lay over the surface cyclone near the time of maximum intensity. The cyclone weakened as the cyclonic upper PV spread further downstream. The trough was negatively tilted as it approached the hurricane, consistent with conditions favoring intensification of the hurricane during ET derived the composite analysis by Hart et al. (2006).

Maria was the only storm in which a well-defined upper-tropospheric trough overspread the surface cyclone during the simulation. The rapid decrease in vertical tilt beginning at hour 56 (0800 UTC 7 September, Fig. 3c) was the response to a large change in the environmental wind shear as opposed to an adjustment of the vortex to a given shear as in Helene, for example. As the trough approached, the vertical shear increased and changed direction from northwesterly to southwesterly. Convection was invigorated with the approach of the trough around 48 h (0000 UTC 7 September) and Maria intensified in the simulation. Convection rapidly weakened and intensity soon followed after the PV aloft had increased. In this regard, Maria behaved as a baroclinic cyclone even though it had not yet officially become extratropical (Fig. 1). The highly transient nature of the development qualitatively resembles that in theoretical models of cyclogenesis (Farrell 1984; Montgomery and Farrell 1993).

d. Gordon

Gordon was the storm with the smallest temporal variation in structure and environmental conditions among the six in our sample. Figures 3e and 4e demonstrate that a quasi-steady structure in vertical shear was realized, possessing a tilt oriented roughly 90° to the left of the shear, consistent with results of Frank and Ritchie (1999, 2001) and Reasor et al. (2004). Recall that the shear was defined by the average over a box 360 km × 360 km (section 2). The angle between the shear and tilt vectors remained nearly unchanged when we used a larger area for defining the shear (720 km × 720 km).

Both the shear and tilt in this case were small. The tilt of about 20 km (Fig. 3e) was only about 20% of the vortex diameter and the shear over the depth of the vortex averaged only 7–8 m s−1. We performed an identical azimuth time analysis of the vertical velocity as in section 4b, and at all times after hour 36 the tilt and vertical motion maximum were nearly aligned (not shown). In this configuration, latent heating would not affect precession directly, but could ultimately reduce precession by reducing the vertical tilt such that mutual advection of the upper and lower portions of the vortex was also reduced. We surmise that the primary effect of the latent heating was therefore to make the system behave as if the vertical shear were weaker. This could explain why the theoretical tendency toward a stable state with the vortex tilting to the left of the shear (Reasor et al. 2004) is still valid with condensational heating included.

5. Conclusions

We have examined simulations of six Atlantic hurricanes as they progressed into the midlatitudes and encountered generally more baroclinic environments. We used the Advanced Research WRF (ARW) model with an innermost, storm-following nest of 4-km grid spacing in 2005, and 1.33 km in 2006, on which cumulus parameterization was removed. The simulations of Irene, Maria, Ophelia, and Wilma from 2005, and Gordon and Helene from 2006 were initialized using GFDL analyses and integrated varying lengths from 45 to 96 h. Extratropical transition (ET) did not complete in all cases, but our primary purpose was to diagnose the behavior of the hurricane vortex, attendant precipitation patterns, and the relationship between the two, as the hurricane moved poleward and encountered greater shear. A practical forecast issue for ET is the ability of hurricanes to survive increasingly hostile environments in order to more acutely perturb the midlatitude jet. While we did not consider the downstream effects of these storms on predictability, our focus is clearly relevant to that topic.

One result was that the total vertical mass flux (in the middle troposphere) was roughly proportional to the vertical shear, and typically maximized during ET rather than during the mature hurricane phase. When the vertical shear exceeded roughly 20 m s−1, the mass flux decreased. Hence, a shear of roughly 15 m s−1 seems optimal for the total mass flux. This result implies that the precipitation and upper-tropospheric divergence will generally increase until the cyclones are well into the midlatitudes.

Further, we noted three distinct mechanisms by which hurricanes can resist shear. First, vortex precession was diagnosed. In five of six cases the vortex tilt was directed by more than 45° to the left of the shear vector. In Gordon, this configuration was especially steady, persisting nearly unchanged for more than 2 days. In Helene, precession of the vortex for two periods was noted. The precession rate varied with time, however, with the vortex spending a longer time in a configuration with the tilt directed roughly 90° to the left of the shear.

A second mechanism by which a vortex can resist vertical shear was diabatic heating that cancelled the effect of tilting. The manifestation of this heating was evident in two ways. One was exemplified by Irene, wherein an entirely new circulation center formed within the precipitation shield slightly left of the downshear direction. Deformation associated with this new center quickly eradicated the original PV center through filamentation. Ophelia was a weaker, but rather similar, storm overall to Irene. A new center was nearly formed, but the convection was not strong enough to complete formation. The key differences between the two storms seemed to be the greater circulation and vertical shear in Irene. The basic explanation was traced to the Sutcliffe form of the quasigeostrophic omega equation. Similar formation of new circulation centers in sheared tropical cyclones has also been noted (Molinari et al. 2004, 2006). These recent observational studies linked the formation of a new center with the asymmetric intensification concepts, wherein PV anomalies generated by convection downshear were strong enough to overcome the primary vortex (Melander et al. 1987; Guinn and Schubert 1993; Enagonio and Montgomery 2001).

The third mechanism, found in Maria, was essentially transient baroclinic development that occurred when an upper-tropospheric PV anomaly was positioned upshear from the hurricane vortex. As the upper-tropospheric trough approached, convection was invigorated on the northwest side of the hurricane center, producing a transient intensification of the storm. The passage of the upper-level trough resulted in decay of the surface cyclone.

Wilma was the one case that did not feature a systematic tilt to the left of the shear vector. It was also the most intense hurricane and was embedded in the strongest shear. While some evidence of precession was found late in the life cycle, the extreme shear tilted the storm to the extent that the subsidence-induced warming on the upshear flank exceeded the warm anomaly in the core. Further, the southern side of the storm was fully eroded by the subsidence. The need for parcels to resaturate as they spiraled around the storm placed the maximum vertical motion and heating substantially to the left of the tilt vector, which we inferred would slow precession. The primary balance in this case was between the shear and strong latent heating, but, with the heating not fully aligned with the tilt, the shear ultimately dominated. However, it is remarkable how vertically aligned Wilma remained in such a strongly sheared environment (Fig. 15).

A vivid contrast between the scales of Irene and Wilma is evident in Fig. 15. Irene was able to form a new center, but clearly the shear was still tearing apart the upper-level cyclonic PV anomaly at this time, based on the raggedness of the PV downshear. Wilma, having a much larger PV core, was able to withstand shear that was three times larger than in Irene. While not forming a new center as in Irene, the basic mechanism was still the near balance of vortex shearing and latent heating.

In conclusion, we have shown how hurricane vortices can resist shear in multiple ways and thus penetrate far into the midlatitudes as strong storms with intense diabatic heating. While we have not examined directly the consequences of vortex resiliency on midlatitude predictability, the apparently crucial role of diabatic heating in vortex resiliency points to a well-known difficulty in global models, namely, the parameterization of deep convection in baroclinic flows. It is in these flows where upscale growth of errors has been shown to be rapid (e.g., Zhang et al. 2003). Furthermore, it has been documented that global models do not accurately simulate the structural changes of transitioning storms (Evans et al. 2006). Therefore, we surmise that a key element of the apparently large sensitivity of downstream error growth to the region of ET is related to errors in diabatic heating and their manifestation in cyclone structure. The improvement of convection representation in baroclinic environments characteristic of transitioning storms therefore remains a critical issue, whether the goal is short-term deterministic prediction of the transitioning storm or longer-range probabilistic prediction of its downstream influence.

Acknowledgments

The authors wish to thank Dr. Kristen Corbosiero of NCAR, three anonymous reviewers for their helpful comments on the manuscript, and Dr. Wei Wang of NCAR for performing the real-time simulations analyzed herein.

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Fig. 1.
Fig. 1.

Tracks (from the NHC best-track database) of the six storms investigated in the present study. Heavy lines delineate the portion of the track spanned by the respective WRF-model simulation. Gray line segments and labels refer to 2006 storms. Black dots denote time at which storm became extratropical according to NHC.

Citation: Journal of the Atmospheric Sciences 65, 3; 10.1175/2007JAS2488.1

Fig. 2.
Fig. 2.

Maximum 10-m sustained winds (m s−1) from ARW (solid) and NHC best-track data (dashed).

Citation: Journal of the Atmospheric Sciences 65, 3; 10.1175/2007JAS2488.1

Fig. 3.
Fig. 3.

(left) Time series of vertical shear, represented as the magnitude of the velocity difference between approximately 1 and 7 km MSL (orange, m s−1), area-integrated vertical mass flux F (black, × 108 kg s−1), and area-integrated asymmetric mass flux (cyan, × 108 kg s−1; see text for details). (right) Time series of vortex tilt (black, km) and angle of the tilt relative to the shear, defined as positive for tilt to the left of the shear (orange, deg). Vertical gray bar in right side of (d) denotes the period that the center of Wilma was over Florida.

Citation: Journal of the Atmospheric Sciences 65, 3; 10.1175/2007JAS2488.1

Fig. 4.
Fig. 4.

Time series of vertical shear (orange, as in Fig. 2), radius of 2-PVU contour of the symmetric vortex (black, km) and average PV within the 2-PVU contour (cyan, PVU) for (a) Irene, (b) Maria, (c) Ophelia, (d) Wilma, (e) Gordon, and (f) Helene. Gray bar in (d) denotes the period that the center of Wilma was over Florida.

Citation: Journal of the Atmospheric Sciences 65, 3; 10.1175/2007JAS2488.1

Fig. 5.
Fig. 5.

Symmetric vertical mass flux Fk at approximately 4 km MSL displayed in time–radius plots from hourly data binned in radial increments of 4 km, units: 106 kg s−1. Heavy black solid line denotes radius of the 2-PVU contour of symmetric PV at level 29 (about 1 km MSL); thin black solid contour denotes radius of maximum azimuthal-mean tangential wind at the same level.

Citation: Journal of the Atmospheric Sciences 65, 3; 10.1175/2007JAS2488.1

Fig. 6.
Fig. 6.

Observed and forecast precipitation patterns of Irene: 85-GHz images from SSM/I for (a) 2200 UTC 17 Aug and (c) 1000 UTC 18 Aug 2005; (b), (d) ARW rainwater mixing ratio (g kg−1) at 10 m MSL and PV at level 29 (1 km MSL) contoured at 2, 4, 8, 18, and 32 PVU for times corresponding to (a) and (c), respectively. Black × symbols in (b) and (d) and white × in (a) and (c) denote the observed location of the center of Irene obtained from the best-track data. Latitude and longitude lines are spaced at 2° intervals in (a) and (c); tick marks in (b) and (d) are spaced 40 km apart. SSM/I images obtained courtesy of the Naval Research Laboratory.

Citation: Journal of the Atmospheric Sciences 65, 3; 10.1175/2007JAS2488.1

Fig. 7.
Fig. 7.

Observed and forecast precipitation patterns of Ophelia: 85-GHz images from SSM/I for (a) 2300 UTC 15 and (c) 2300 UTC 16 Sep 2005; (b), (d) ARW rainwater mixing ratio (g kg−1) at 100 m MSL and PV at level 29 (about 1 km MSL) contoured at 2, 4, 8, 18, and 32 PVU for times corresponding to (a) and (c), respectively. The × in (d) denotes the observed center of Ophelia. Position of the simulated storm in (b) is indistinguishable from the observed location. White × in (a) and (c) also indicate the position of the center of Ophelia. Latitude and longitude lines are spaced at 2° intervals in (a) and (c); tick marks in (b) and (d) are spaced 40 km apart. SSM/I images obtained courtesy of the Naval Research Laboratory.

Citation: Journal of the Atmospheric Sciences 65, 3; 10.1175/2007JAS2488.1

Fig. 8.
Fig. 8.

Potential vorticity at level 29 (about 1 km MSL; light gray: >2 PVU, dark gray: >8 PVU), virtual potential temperature (interval is 2 K, ≤304 K in thin lines, ≥306 K in heavy lines) and wind barbs (every 15th shown, long barb: 5 m s−1) at the same level. The PV and virtual potential temperature have been smoothed 5 times with a 2Δx smoother to remove short-wavelength variations. Domain shown is 100 grid points (400 km) east–west and 120 grid points (480 km) north–south. Irene is shown at (a) 0700 and (c) 1000 UTC 18 Aug and Ophelia at (b) 2300 UTC 16 Sep and (d) 0200 UTC 17 Sep. Tick marks are 40 km apart.

Citation: Journal of the Atmospheric Sciences 65, 3; 10.1175/2007JAS2488.1

Fig. 9.
Fig. 9.

Time series of ratios, Irene to Ophelia, of vertical shear (dashed) and integrated PV (solid), computed from shifted time series so that 2300 UTC 16 Sep (Ophelia) aligns with 0700 UTC 18 Aug (Irene) at time 0. Shear and integrated PV are computed as for Fig. 2.

Citation: Journal of the Atmospheric Sciences 65, 3; 10.1175/2007JAS2488.1

Fig. 10.
Fig. 10.

Time–azimuth diagrams of (a), (c) rainwater mixing ratio (g kg−1) at 10 m MSL and (b), (d) vertical velocity (m s−1) at model level 17 (roughly 600 hPa). Azimuthal resolution is 10°. Within each azimuthal bin, quantities are averaged in radius from 0.5 to 1.5 times the radius of the 2-PVU contour of symmetric PV. This is approximately from 50 to 150 km radius for (a), (b) Helene and (c), (d) Wilma. Display begins at hour 24 of each simulation, 0000 UTC 20 Sep 2006 for Helene and 1200 UTC 23 Oct 2005 for Wilma. Horizontal gray lines in (b), labeled [1]–[4], correspond to times shown in Figs. 11a–d, respectively.

Citation: Journal of the Atmospheric Sciences 65, 3; 10.1175/2007JAS2488.1

Fig. 11.
Fig. 11.

Tropical Rainfall Measuring Mission (TRMM) 85-GHz images of Helene at (a) 1445 UTC 20, (b) 1713 UTC 21, (c) 0518 UTC 22, and (d) 1614 UTC 22 Sep. Latitude–longitude lines are spaced at 2°. Images obtained courtesy of the Naval Research Laboratory.

Citation: Journal of the Atmospheric Sciences 65, 3; 10.1175/2007JAS2488.1

Fig. 12.
Fig. 12.

Potential vorticity at 1 km MSL (PV > 2 PVU in light gray, PV > 8 PVU in dark gray), virtual potential temperature (interval is 2 K; ≤304 K in thin lines, ≥306 K in heavy lines), and wind barbs (every 15th shown; long barb: 5 m s−1) at 1 km MSL. PV, virtual potential temperature, and rainwater have been smoothed 5 times with a 2Δx smoother to remove short-wavelength variations. Domain shown is 100 grid points (400 km) east–west and 120 grid points (480 km) north–south; (a) Wilma at 0900 UTC 25 Aug (69-h forecast); and (b) Helene at 1800 UTC 22 Sep (90-h forecast). Tick marks are 40 km apart.

Citation: Journal of the Atmospheric Sciences 65, 3; 10.1175/2007JAS2488.1

Fig. 13.
Fig. 13.

Schema showing effects of condensational heating and PV anomaly generation on precession. The top row shows vertical cross section in which a vortex is tilted by a shear flow. Circulations associated with the lower vortex are denoted by gray lines, with black lines denoting the circulation due to the upper vortex. Dashed lines indicate the sense of advection from the opposite vortex. The bottom two rows show plan views with the tilt oriented to the right. PV tendencies from advection by the opposite vortex indicated with +/− symbols within circles. Diabatic PV tendencies are indicated by +/− symbols within black squares. The first (second) row depicts upper (lower) tropospheric PV tendencies. The middle column shows case where heating is left of the tilt vector and precession is reduced; the right column shows heating in the downtilt direction, which does nothing directly to the precession, but reduces the tilt.

Citation: Journal of the Atmospheric Sciences 65, 3; 10.1175/2007JAS2488.1

Fig. 14.
Fig. 14.

Comparison of Maria from (left column) SSM/I 85-GHz images to (right column) ARW rainwater mixing ratio at 100 m MSL, plus the 2-PVU contour on the 350-K isentropic surface (black), winds on the 350-K surface, and virtual potential temperature at level 29 (about 1 km MSL, magenta), with only 300- and 306-K contours shown. The 306-K contour delineates the warm core near the center of the domain in each plot from the ARW. Times shown are (a) 2200 UTC 5 (22-h forecast), (b) 2100 UTC 6 (45-h forecast), (c) 1000 UTC 7 (58-h forecast), and (d) 2200 UTC 7 (70-h forecast) Sep.

Citation: Journal of the Atmospheric Sciences 65, 3; 10.1175/2007JAS2488.1

Fig. 15.
Fig. 15.

Potential vorticity at 7 km for (a) Irene at 0700 UTC 18 Aug and (b) Wilma at 0900 UTC 25 Oct (light gray for PV > 2 PVU, dark gray for PV > 8 PVU) and PV at level 29 (about 1 km MSL) (2- and 8-PVU contours) along with 1–7-km vector wind difference (long barb = 5 m s−1). Winds have been averaged over a 600 km × 600 km area surrounding each point. Wind symbols are displayed every 20th grid point (80 km apart). Tick marks are 40 km apart.

Citation: Journal of the Atmospheric Sciences 65, 3; 10.1175/2007JAS2488.1

Table 1.

List of tropical cyclones, simulation initialization times (h, UTC), simulation durations, and vortex radii (km). Vortex radius is defined as the radial extent of the 2-PVU value of symmetric PV, herein averaged over the first 24 h displayed for each storm in Fig. 4.

Table 1.

* The National Center for Atmospheric Research is sponsored by the National Science Foundation.

1

We reran both Wilma and Maria, the strongest two ETs from 2005, using the latest version of WRF ARW (2.2) with the surface fluxes corrected (and other minor changes implemented). While surface winds were reduced by approximately 10%–15% in the new simulations, the storm structure, vertical shear, vortex tilt, and vortex size were in remarkable agreement with the results presented herein from the real-time forecasts. Thus, none of our conclusions is affected by the error in surface drag that occurred during the 2005 season.

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