Hurricane Sandy's landfall along the New Jersey shoreline at 2330 UTC 29 October 2012 produced a catastrophic storm surge stretching from New Jersey to Rhode Island that contributed to damage in excess of $50 billion—the sixth costliest U.S. tropical cyclone on record since 1900—and directly caused 72 fatalities. Hurricane Sandy's life cycle was marked by two upper-level trough interactions while it moved northward over the western North Atlantic on 26–29 October. During the second trough interaction on 29 October, Sandy turned northwestward and intensified as cold continental air encircled the warm core vortex and Sandy acquired characteristics of a warm seclusion. The aim of this study is to determine the dynamical processes that contributed to Sandy's secondary peak in intensity during its warm seclusion phase using high-resolution numerical simulations. The modeling results show that intensification occurred in response to shallow low-level convergence below 850 hPa that was consistent with the Sawyer–Eliassen solution for the secondary circulation that accompanied the increased baroclinicity in the radial direction. Additionally, cyclonic vertical vorticity generated by tilting of horizontal vorticity along an axis of frontogenesis northwest of Sandy was axisymmetrized. The axis of frontogenesis was anchored to the Gulf Stream in a region of near-surface differential diabatic heating. The unusual northwestward track of Sandy allowed the cyclonic vorticity over the Gulf Stream to form ahead of the main vortex and be readily axisymmetrized. The underlying dynamics driving intensification were nontropical in origin, and supported the reclassification of Sandy as extratropical prior to landfall.
Hurricane Sandy was a late-season tropical cyclone (TC) over the North Atlantic that produced a devastating storm surge along the Northeast U.S. coastline from southern New Jersey to Rhode Island on 29 October 2012. Its landfall on the New Jersey shoreline resulted in 72 deaths,1 and preliminary estimates of U.S. damage are approximately $50 billion (U.S. dollars; Blake et al. 2013). Although Sandy's track and eventual landfall were well forecasted (e.g., Uccellini 2013; Knabb 2013), the fragility of the Northeast U.S. coastal zones, in particular the near-coast urban infrastructure of New York City, was dramatically underscored. Given the impact of Sandy in an increasingly baroclinic environment during the later part of the North Atlantic hurricane season, it is of scientific and societal interest to understand the underlying dynamical processes that governed the structure and intensity of Hurricane Sandy near landfall.
Tropical cyclones that undergo extratropical transition (ET)—defined as the transition of a warm core TC to a cold core extratropical cyclone—can be characterized by strong surface winds and extreme rainfall that result in substantial societal impacts (e.g., Thorncroft and Jones 2000). A detailed review of the ET literature is provided by Jones et al. (2003). Extratropical transition has been documented over the North Atlantic, western North Pacific, southeast Indian Ocean, and western South Pacific, and has been linked to numerous fatalities. For example, flooding associated with the ET of Hurricane Agnes (1972; Bosart and Dean 1991) and Hurricane Hazel (1954; Palmén 1958) resulted in numerous fatalities (Jones et al. 2003). The ET of Hurricane Sandy (2012) was characterized by heavy precipitation located left of track, consistent with the precipitation distribution associated with ET that occurs in conjunction with the approach of a negatively tilted upper-level trough (e.g., Atallah and Bosart 2003; Atallah et al. 2007; Bosart and Carr 1978). Precipitation that occurred over the Appalachians from North Carolina to Pennsylvania in conjunction with the ET of Sandy fell as snow and accumulated to over 90 cm in localized regions (Blake et al. 2013). In addition to heavy precipitation, Sandy's ET was marked by a devastating storm surge from New Jersey to Rhode Island that was driven by the strong pressure gradient on the north side of Sandy, and the long fetch of near-surface easterly flow that extended across the entire North Atlantic basin.
Several studies have examined and classified the structure and evolution of ET (e.g., Klein et al. 2000; Harr and Elsberry 2000; Foley and Hanstrum 1994; Hart 2003). Evans and Hart (2003) note, that for some cases of ET, the lower-tropospheric warm core is retained. Examples of such cases include Hurricane Iris (1995; Thorncroft and Jones 2000) and Hurricane Lili (1996; Browning et al. 1998; Agustí-Panareda et al. 2005). In the case of Hurricane Lili, detailed analysis by Browning et al. (1998) showed how Lili evolved to a structure that resembled a warm core seclusion analogous to the final mature stage of the Shapiro and Keyser (1990) cyclone life cycle model. The difference between the evolution of Hurricane Lili and the classical extratropical cyclone is that the warm seclusion developed from cold air encircling a preexisting warm core vortex, rather than a warm core developing in the cold air along the bent-back warm front in conjunction with low-level cyclonic vorticity generation and enhanced surface sensible and latent heat fluxes (e.g., Neiman and Shapiro 1993; Neiman et al. 1993; Reed et al. 1994). The deepening of cyclones during the warm seclusion phase can occur in response to diabatic heating and interaction with upper-level troughs (e.g., Grønås et al. 1994; Grønås 1995). Cyclones that deepen during the warm seclusion phase have been known to produce damaging low-level winds (e.g., Wernli et al. 2002; Browning 2004). Additionally, numerical experiments by Agustí-Panareda et al. (2005) showed that warm seclusion development of Hurricane Lili (1996) influenced the baroclinic life cycle of the interacting upper-level trough during ET—suggesting that diabatic heating associated with transitioning TCs can impact the mode of extratropical development.
Kitabatake (2008) examined the frontal evolution of ET events over the western North Pacific and stratified all ET cases during 2001–02 into three categories: seclusion–occlusion (SO), open wave, and cold advection (see their Fig. 2). The SO type of ET exhibits a structure similar to the Shapiro and Keyser (1990) warm seclusion during the initial phase of ET and evolves into a cold core occluded cyclone by the end of ET. Of the 23 TCs that underwent ET over the western North Pacific basin, 35% were classified as the SO type. The SO type of cyclone moves on a more northward trajectory and is generally more intense compared to the other types of ET as defined in Kitabatake (2008). Consequently, these ET events have a greater impact on Japan compared to the open wave and cold advection ET events that move rapidly northeastward out to sea.
It will be shown that the evolution of Hurricane Sandy appears to follow the SO type of ET event over the western North Pacific described by Kitabatake (2008) and that Sandy maintains its warm core during ET similarly to North Atlantic TCs Iris (1995; Thorncroft and Jones 2000) and Lili (1996; Browning et al. 1998), suggesting that the occurrence of transitioning TCs like Hurricane Sandy—from a dynamic and thermodynamic perspective—is not unprecedented from a global perspective, although rare over the western North Atlantic. Additionally, Hurricane Sandy reached a secondary peak in intensity during the warm seclusion stage of ET. This study aims to extend previous work that has linked ET and the Shapiro and Keyser (1990) warm seclusion by dynamically diagnosing the intensification of Sandy during the warm seclusion phase. This study will utilize high-resolution explicit numerical simulations from the Advanced Hurricane Weather Research and Forecasting Model (AHW; Skamarock et al. 2008; Davis et al. 2010).
This paper is organized as follows. Section 2 provides a life cycle overview of Hurricane Sandy. Section 3 describes the configuration of the AHW simulations and methods for dynamically diagnosing the intensification of Hurricane Sandy from the axisymmetric balanced framework using the Sawyer–Eliassen (SE) balance equation and from the vorticity framework using a circulation budget. Section 4 presents an analysis of the AHW forecasts of Hurricane Sandy. Section 5 describes how Sandy's warm core vortex evolved and interacted with its environment, and section 6 diagnoses Sandy's warm core vortex intensification during the warm seclusion phase. Section 7 provides the conclusions.
2. Case overview
Hurricane Sandy developed from an easterly wave that moved westward across the tropical North Atlantic during mid- to late October. It was first identified as a tropical depression in the Hurricane Best Track database (HURDAT; Landsea et al. 2004) over the southwest Caribbean on 1800 UTC 21 October 2012 (Fig. 1). Sandy intensified into a category-3 (Simpson 1974) hurricane with winds near 50 m s−1 and a minimum sea level pressure of 954 hPa, as it tracked northward and made landfall over eastern Cuba at 0525 UTC 25 October. Sandy weakened after crossing Cuba, reaching tropical storm status by 0000 UTC 27 October as the convection became asymmetric (Fig. 1). The asymmetric convection was concentrated in a region of enhanced baroclinicity on the northwest side of Sandy that developed in conjunction with an upper-level trough on the subtropical PV waveguide (“Ts”; Fig. 2a). A region of ascent is collocated with the axis of organized convection on the northwest side of Sandy (cf. Figs. 1 and 2a). The upper-level divergent outflow associated with organized convection contributed to negative PV advection by the divergent wind along the eastern flank of Ts, which likely acted to impede the eastward progression of Ts and to further amplify the cyclonic wave breaking of the tropopause PV wave (e.g., Thorncroft et al. 1993). Enhancement of cyclonic wave breaking by midtropospheric diabatic heating and attendant upper-level outflow has been discussed in previous studies, such as Wernli (1997), Bosart (1999), Posselt and Martin (2004), Archambault (2011), and Cordeira and Bosart (2011). We hypothesize that the importance of cyclonic wave breaking enhancement is that it allowed Hurricane Sandy to retain its northward trajectory, rather than track east-northeastward out to sea, by reducing the westerly component of the deep-layer steering flow. Sensitivity experiments are needed, however, to fully address the impact of cyclonic wave breaking enhancement on the track of Hurricane Sandy.
As Sandy traveled northeastward, convection remained focused on its northwestern flank in a region of enhanced baroclinicity despite the maintenance of a well-defined warm core through 0000 UTC 28 October (Figs. 1 and 2b). By 0000 UTC 29 October, a second upper-level trough on the polar PV waveguide (“Tp”) reinforced the baroclinicity on the northwest side of Sandy (Fig. 2c). While a small region of deep convection redeveloped near Sandy's warm core, the large region of convection northwest of Sandy contributed to 15–20 m s−1 east-northeasterly divergent flow that acted to enhance the cyclonic wave break of Tp. During 0000 UTC 29–30 October, the cyclonic wave break of Tp encircled Sandy and steered it northwestward toward the New Jersey shoreline (Fig. 2d). Additionally, cold continental air associated with Tp cyclonically encircled Sandy's warm core prior to landfall, marking the beginning of Sandy's ET, producing a structure similar to the extratropical warm seclusion originally described in Shapiro and Keyser (1990) (Fig. 2d). During the warm seclusion phase, Sandy intensified from a weak category-1 hurricane with winds near 35.0 m s−1 at 1800 UTC 27 October to a category-2 hurricane with winds near 42.5 m s−1 at 1200 UTC 29 October (Fig. 1). The intensification was accompanied by a 20-hPa decrease in sea level pressure to 940 hPa in the 48-h period ending 1800 UTC 29 October, which is equivalent to a ~0.2-m rise in sea level on top of the already devastating storm surge driven by the strong pressure gradient on the north side of Sandy and an easterly fetch that reached across the entire North Atlantic (Fig. 3).
3. Data and methods
a. AHW model setup
The numerical simulations for the present study were generated in real time using version 3.3.1 of the AHW with 36 vertical levels up to 20 hPa (Skamarock et al. 2008). Details of the AHW configuration are described in Davis et al. (2010). The configuration of the 2012 real-time version of AHW is summarized in Table 1. The numerical forecasts were made over an outer domain at 36-km horizontal resolution that covers the entire North Atlantic basin, with moving two-way inner nests of 12- (133 × 133 grid points) and 4-km (199 × 199 grid points) centered on Hurricane Sandy (Fig. 3). The movement of the inner nests, at 15-min intervals during the model integration, is determined by the hurricane's motion during the previous 15 min. While the lateral boundary conditions are updated every 6 h from the corresponding 0.5° × 0.5° National Centers for Environmental Prediction (NCEP) Global Forecast System (GFS) forecast, the initial conditions are derived from a 96-member AHW analysis ensemble generated every 6 h on the 36- and 12-km domains2 by cycling an ensemble data assimilation system that runs for the entire North Atlantic hurricane season. Details of the data assimilation setup are provided in Torn (2010) and Torn and Davis (2012). The initial condition for the 126-h AHW deterministic forecast is determined by selecting the individual analysis ensemble member that minimizes a cost function [see Torn and Davis (2012), their Eq. (1)] that measures how close the analysis TC position and minimum sea level pressure are to the ensemble-mean values.
In addition to the real-time AHW forecasts described above, the AHW forecast initialized at 0000 UTC 28 October 2012 (Fig. 1) was run retrospectively (AHW-RERUN) using AHW version 3.4.1, and is subject of the dynamical diagnosis herein. The same model setup was used as for the real-time forecasts, including the initial and lateral boundary conditions, except using unmodified versions of the Tiedtke cumulus parameterization (Zhang et al. 2011) and surface drag formulation.3
The AHW-RERUN forecast was generated in order to output momentum accelerations due to friction from the Yonsei University (YSU) boundary layer scheme (Table 1; Hong et al. 2006) and diffusion scheme, which was needed to conduct the dynamical diagnosis described in sections 3b and 3c. The minor differences in formulation of the cumulus parameterization and surface drag contributed to small differences in track and intensity compared to the real-time forecast, but Sandy's life cycle evolution was unchanged. Unless otherwise noted, the analysis and diagnosis of the AHW-RERUN forecast presented herein are performed on the 4-km domain that is run without cumulus parameterization.
b. Sawyer–Eliassen balance equation
When the evolution of a balanced vortex is driven by momentum and thermodynamic forcings, a compensating secondary circulation is needed in order to restore thermal wind balance (e.g., Eliassen 1951). The quasigeostrophic theory analogy would be the thermally direct (or, indirect) secondary circulation that acts to maintain thermal wind balance in the presence of frontogenesis (e.g., Keyser 1986). The streamfunction of the secondary circulation is obtained by solving the SE balance equation, which provides the basis of a theory for the evolution of rapidly rotating vortices that are experiencing forcing from azimuthal heat and momentum sources (Montgomery and Smith 2012). The SE balance equation has been applied to the hurricane intensification problem in several papers in the literature, from both the observational and numerical simulation perspective (e.g., Shapiro and Willoughby 1982; Pendergrass and Willoughby 2009; Molinari et al. 1993).
To examine the intensification of Hurricane Sandy from a balanced framework, we followed the methodology of Hendricks et al. (2004) for the SE balance equation in pseudoheight coordinates [Hoskins and Bretherton (1972); their Eq. (2.1)] for a Bousinessq fluid (e.g., Shapiro and Willoughby 1982) defined as
The solution for the mean transverse streamfunction is used to determine the mean radial velocity, , and vertical velocity, . The static stability is defined , vortex inertia parameter , azimuthal mean tangential velocity , azimuthal mean absolute vertical vorticity , and radius r. The azimuthal mean thermodynamic and momentum forcing terms that are introduced into the SE balance equation are defined as
The variables have their standard meteorological meanings, with primed variables defined as the perturbation from the azimuthal mean, and overbars representing the azimuthal mean. The relative vertical vorticity is defined as ζ. The friction term represents the momentum tendency from the YSU planetary boundary layer and diffusion schemes. The SE balanced equation is a linear elliptic partial differential equation for the mean transverse streamfunction that is valid provided that the discriminant is positive [Shapiro and Montgomery 1993; see Eq. (12) in Hendricks et al. 2004]. In the AHW-RERUN simulation, negative discriminant values were relaxed to positive values following the methods of Hendricks et al. (2004).
Montgomery and Smith (2012) described a simple method for computing the tendency of the azimuthal mean tangential wind for a balanced vortex using the SE balance equation solution (see also Sundqvist 1970; Schubert and Alworth 1987; Möller and Smith 1994). After computing the velocity components and from the SE balance solution, one can predict the local time tendency in the azimuthal mean tangential wind by substituting the and components into the tangential momentum equation defined as
All symbols have the same meteorological meanings as described previously. Implementing this method quantifies slow evolution of the balanced flow, and may help indicate the relative importance of the balanced evolution to changes in vortex intensity.
c. Circulation budget methodology
The traditional form of the vorticity equation can be rewritten as [Davis and Galarneau (2009), their Eq. (2)]
where ζ is the relative vorticity, η is the absolute vorticity, ω is the vertical velocity in pressure coordinates, and Fr is the frictional force (Haynes and McIntyre 1987). The horizontal vector K is defined as the vorticity flux vector, and divergence is in the horizontal plane. The “flux” form of the vorticity equation has been utilized in several studies to analyze the evolution of vorticity in convective systems of continental and tropical origin (e.g., Davis and Weisman 1994; Raymond et al. 1998). Integration of (5) over a closed region and application of the divergence theorem results in
where C defines the circulation over a closed region. The mean absolute vertical vorticity represents the mean along the edge of the circulation box. The primed variables represent the perturbation from the mean. The mean divergence was computed over the area A of the circulation box. The component of K normal to the boundary of closed region dictates the tendency of circulation over that region. The first term on the right-hand side is defined as the stretching term, the second term as the eddy flux term, third term as the tilting term, and fourth term as friction. Discussion on the interpretation of the terms is described in Davis and Galarneau (2009) in their analysis of two mesoscale convective vortices (MCVs) that occurred during the Bow Echo and Mesoscale Convective Vortex Experiment (BAMEX; Davis et al. 2004). The value of using (6) to analyze the change in vorticity, or circulation, over a closed region is that it provides insight to the underlying dynamics governing the evolution of complex vorticity structures within a convective system in a simplified framework.
4. Results of the AHW simulations
The AHW storm-track forecasts for Hurricane Sandy, initialized at 0000 UTC 23–29 October 2012, are shown in Fig. 4. The AHW forecasts initialized early in Sandy's life cycle prior to 0000 UTC 27 October are characterized by significant left-of-track error, as Sandy tracked northward over Cuba. Track forecasts improved during and after the interaction with the upper-level tropopause PV wave, Ts, on 26–27 October as Sandy moved northeastward. All AHW real-time forecasts (except for the 0000 UTC 24 October initialization) and the AHW-RERUN forecast initialized at 0000 UTC 28 October were able to capture Sandy's interaction with the second upper-level tropopause PV wave, Tp, and attendant northwestward turn toward New Jersey (Fig. 4).
The AHW intensity forecasts for Hurricane Sandy captured the initial peak in intensity as it made landfall over Cuba and the secondary peak in intensity after 0000 UTC 27 October (Fig. 5a). In general, the AHW forecasts for the period 0000 UTC 26–29 October were too intense, with 10-m winds generally 5–10 m s−1 too strong and minimum sea level pressure 10–20 hPa too low (Figs. 5a,c). The timing of the secondary peak in intensity that was observed varied in the AHW forecasts, with the early initializations intensifying Sandy 12–24 h too early. The secondary peak in intensity was captured particularly well by the real-time and AHW-RERUN forecasts initialized at 0000 UTC 28 October (Fig. 5a). In both forecasts, the intensity increased by 10–15 m s−1 and the sea level pressure decreased by 20 hPa in the 36-h period ending 1200 UTC 29 October (Figs. 5a,c). The intensification of Sandy on 28–29 October was accompanied by a reduction in the radius of maximum tangential wind in all AHW forecasts (most notably in the real-time and AHW-RERUN 0000 UTC 28 October initialization), suggesting that the vortex contracted while it intensified (Fig. 5b). The observed change in radius of maximum wind was less dramatic, but also suggested that the vortex contracted during intensification.
A comparison of the vertical profile of wind speed between the AHW-RERUN (hereafter, AHW) forecast and observed dropsondes during the intensification period of 0000–2000 UTC 29 October is shown in Fig. 6. Recall that the most robust intensification occurred during 0000–1200 UTC 29 October, but the longer intensification period is used here to facilitate comparison with reconnaissance flights. Note that for AHW, the azimuthal mean wind speed in the 100–200-km radial band increased below 550 hPa between 0000 and 2000 UTC 29 October. An increase in wind speed of 5–10 m s−1 occurred near 800 hPa in AHW, suggesting that vortex intensification occurred primarily at low levels. The observed dropsondes show a similar evolution. The mean wind speed of all dropsondes in a 100–200-km radial band show a ~5.0 m s−1 increase between 0000 and 2000 UTC 29 October, also suggesting that the intensification of the observed vortex occurred primarily at low levels, although not below 900 hPa. Since the evolution of Hurricane Sandy in the AHW forecast initialized at 0000 UTC 28 October compared reasonably well with observations, the next two sections will use this AHW forecast to analyze and dynamically diagnose Sandy's intensification on 28–29 October.
5. Vortex interaction with its environment
As Hurricane Sandy tracked north and northwestward on 28–29 October it moved into an increasingly baroclinic lower-tropospheric environment, evolved into a warm seclusion, and underwent ET. Figure 7 shows 850-hPa potential temperature and wind for the period 0000–2000 UTC 29 October. Note that while Sandy's warm core remained intact, the surrounding environment became cooler as relatively cold air on the western flank of the Gulf Stream began to cyclonically encircle the vortex after 0000 UTC 29 October. The strong cold advection associated with this encirclement occurred in conjunction with the development of >50 m s−1 westerly low-level jet on Sandy's southwest side (Figs. 7a,b). The low-level jet formed in a region of surface pressure falls on the northwest side of Sandy over the Gulf Stream, represented by the development of an inverted trough on the northwest side of Sandy (Fig. 8c). During the period 1800 UTC 28 October–0200 UTC 29 October, an axis of 700-hPa Petterssen frontogenesis [cf. Schultz and Sienkiewicz (2013), their Eq. (2)] was anchored over the western flank of the Gulf Stream as Sandy approached from the southeast (Fig. 8a). Persistent convection occurred in conjunction with frontogenesis along the Gulf Stream (Figs. 8d and 9b) and acted to generate low-level cyclonic PV (Fig. 9a).
At 0000 UTC 29 October, the axis of frontogenesis was aligned along the Gulf Stream in a locally enhanced sea level pressure gradient (Figs. 8a, 9b, and 10a). The frontogenesis was maximized at the surface in response to differential diabatic heating associated with surface latent heat fluxes that approached 1600 W m−2 over the Gulf Stream (Figs. 8b and 10b,c). The vertical cross sections [formatted as in Schultz and Sienkiewicz (2013), their Fig. 4] show that frontogenesis extended upward through 500 hPa while tilting toward the cold air (Fig. 10b). The cyclonic flow associated with the axis of frontogenesis, superposed on the larger-scale cyclonic circulation of Sandy, resulted in the intense low-level jet on the southwest side of Sandy, which marked the beginning of Sandy's intensification.
By 1000 UTC 29 October, Sandy reached its secondary intensity peak as the low-level jet along the southern flank of Sandy increased to over 55 m s−1 (Fig. 7b). A strip of cyclonic PV associated with the low-level jet was located within Sandy's closed circulation as shown by the storm-relative streamlines, and wrapped cyclonically into the center of the vortex (Fig. 9c)—suggesting that axisymmetrization of low-level cyclonic PV was important for the intensification of the vortex. Circulation budget diagnostics shown in section 6b show that the eddy flux was an important contributor to intensification through 1000 UTC, which is further evidence of the importance of axisymmetrization in intensification. The axis of frontogenesis and attendant convection moved radially inward between 0000 and 1000 UTC 29 October, contributing to an increase in the radial thermal gradient and a shift of diabatic heating (inferred from model reflectivity fields and ascent) closer to the vortex center (Figs. 9d and 10d,e,f). The vertical cross sections show the presence of a deep warm core structure that extends above 500 hPa, with axes of frontogenesis that extend into the cooler air on the edges of the warm core (Fig. 10e). The intense low-level jet on the south side of the warm core vortex is embedded in a region of frontolysis and descent in the cold air beneath the axis of frontogenesis aloft (Figs. 10e,f). Although the intense low-level jet and its collocation with frontolysis suggests that it has characteristics of the “sting jet” (Browning 2004), it appears that the intense low-level winds are not a result of the advection of higher momentum air downward from aloft (Schultz and Sienkiewicz 2013). Rather, the low-level jet is embedded in the cold air beneath the tilting frontal zone on the south side of Sandy's warm core, and may be more analogous to the cold conveyor belt (e.g., Schultz 2001, and references within). By 2000 UTC 29 October, Sandy's warm core vortex became completely encircled by cooler continental air (Fig. 7c). The vortex horizontally contracted to a compact cyclonic PV anomaly as sea level pressure continued to decrease to 940 hPa, and diabatic heating tied to the axis of frontogenesis moved radially inward to near the vortex center (Figs. 9e,f).
In summary, Hurricane Sandy's secondary peak in intensity occurred as it moved northwestward and interacted with an increasingly baroclinic environment. From a thermodynamic perspective, the evolution of Sandy's structure and intensity progressed in two stages. The initial stage occurred during 0000–1000 UTC 29 October where Sandy reached its secondary peak in intensity as cold continental air began to wrap cyclonically around Sandy's warm core. The surge of cold air was associated with a low-level westerly jet that developed along an axis of frontogenesis originally tied to the western flank of the Gulf Stream. The second stage occurred during 1000–2000 UTC 29 October as the warm core vortex contracted and the axis of frontogenesis and diabatic heating maximum shifted radially inward, resulting in a compact intense cyclonic PV anomaly that resembled the warm seclusion described by Shapiro and Keyser (1990). From the PV perspective, persistent convection over the Gulf Stream produced low-level cyclonic PV anomalies within the closed circulation, as shown by the storm-relative streamlines, that axisymmetrized in the main vortex and contributed to intensification. A key aspect of Sandy's intensification appears to be the northwestward storm track, which allowed for generation of low-level cyclonic PV along the Gulf Stream ahead of Sandy, facilitating axisymmetrization of the cyclonic PV. For the more usual northeastward storm track, cyclonic PV generation along the Gulf Stream occurs to the west of and behind the TC, likely making it more difficult to axisymmetrize the low-level PV. The thermodynamic and PV perspectives motivate the use of the SE balance equation and a circulation budget, respectively, to elucidate the underlying dynamics that led to Sandy's intensification during warm core seclusion.
6. Intensification during warm core seclusion
a. Sawyer–Eliassen balance perspective
We now present a SE balance diagnosis of Hurricane Sandy's intensification from a balanced vortex perspective. The primary focus is to investigate how the vortex intensified from a quasi-balanced perspective; namely, how the warm seclusion process that enhanced the radial gradient of potential temperature contributed to an increase in the azimuthal mean tangential wind. The time–radius diagram of azimuthal mean tangential wind4 at 1600 m for 1200 UTC 28 October–0000 UTC 31 October 2012 (12–72-h AHW forecast) shows how the radius of maximum tangential wind was located near 300–350 km prior to 0000 UTC 29 October (Fig. 11a). During the initial phase of intensification, the radius of maximum tangential wind contracted to 180 km and intensified to over 40 m s−1 by 1200 UTC 29 October in conjunction with an increase in the radial gradient of potential temperature (Fig. 11b). During the second phase of intensification, the radius of maximum tangential wind continued to decrease to near 80 km, the maximum tangential wind speed remained above 32 m s−1, and the maximum in tangential wind tendency was collocated with an increase in the radial gradient of potential temperature through landfall at 2100 UTC 29 October.
The vertical profile of azimuthal mean tangential wind and temperature gradient shows how Hurricane Sandy evolved from a TC with a deep upright warm core—marked by a quasi-upright radial temperature gradient signature—at 0000 UTC 29 October, to a shallow baroclinic warm seclusion structure with a sloping radial temperature gradient signature at 2000 UTC 29 October (Fig. 12c). In all, the intensification and contraction of Sandy occurred in a frontogenetical environment as cool air was ingested into the circulation at a large radius, while the warm core was maintained. To summarize this evolution, we show in Fig. 13 the change in angular momentum () from the base state (defined as 0000 UTC 29 October) and the equivalent potential temperature θe near the top of the boundary layer at 1600 m. The largest increase in angular momentum occurred just outside the location of the largest radial gradient of θe at 1000, 1500, and 2000 UTC 29 October. There was an initial increase of M at larger radii at 1000 UTC 29 October, which coincided with the development of a strong westerly low-level jet south of the vortex, and well-defined easterly flow along the warm front on the north side of the vortex (e.g., Fig. 7b). At 1500 and 2000 UTC, M at radii ≥250 km was slightly stronger than the base state (Fig. 13a). The increase in M at 2000 UTC 29 October shifted radially inward as the vortex contracted during its second phase of evolution. Note that the inward shift of M change and tangential wind occurred in conjunction with frontogenesis—a signature of the development of a warm seclusion—as θe cooled by 20–25 K at larger radii while the inner warm core fluctuated by 1–2 K (Fig. 13b). Although the θe gradient increased with vortex contraction during 1000–2000 UTC 29 October, the maximum wind speed did not continue to increase. The lack of intensification during the contraction phase may be due to the decrease in mean θe, which corresponds to a decrease in moist entropy and condensational heating.
Since frontogenesis appears to play an important role in the intensification of Hurricane Sandy, we use the SE balance equation to diagnose the evolution of the secondary circulation.5 In Fig. 14, we compare the azimuthal mean secondary circulation from the AHW forecast to the mean secondary circulation from the SE balance equation. The SE mean secondary circulation compares well with the AHW mean secondary circulation. The AHW mean secondary circulation shows strong inflow below 2000 m with weaker outflow above 3000 m at large radii at 0000 UTC 29 October (Fig. 14a). There are two regions of well-defined azimuthal mean ascent, one located within 100 km of the storm center and is associated with dissipating eyewall convection (cf. with Fig. 9b). The second region of ascent is located near 300-km radius, and is associated with convection forced by frontogenesis along the Gulf Stream (cf. Figs. 8a,d;,9b; and 10a,c). The SE secondary circulation agrees well with the AHW secondary circulation at 0000 UTC 29 October, except the low-level inflow was too weak by ~1.0 m s−1 (Fig. 14d). The region of ascent shifts radially inward and the low-level inflow increases in response to low-level frontogenesis by 1000 UTC 29 October, an evolution that is also captured by the SE solution, although it does not appear to capture the low-level outflow and strong ascent near 1500–3000 m in the region of convection (Figs. 14b,e).
By 2000 UTC 29 October, the deep ascent shifts radially inward in conjunction with frontogenesis, an evolution that is also seen in the SE solution (Figs. 14c,f). Note that the SE solution does not capture the axis of strong low-level outflow just above the boundary layer near 1500–3000 m (cf. Figs. 14c,f), suggesting that the evolution of the vortex is not in quasi balance. This result is consistent with analytical solutions for rotating flows of TCs in axisymmetric numerical models. Bryan and Rotunno (2009a; their Fig. 10) show that a trajectory that passes through the maximum tangential wind oscillates between subgradient and supergradient with overshoot of the low-level inflow and unbalanced outflow at the top of the boundary layer. The inertial oscillation decays with height as it approaches the outflow layer in the upper troposphere. The SE balanced solution does not account for this inertial oscillation, which serves as a possible explanation for the inability of the SE solution to capture the strong low-level outflow at the top of the boundary layer. In Fig. 15, we show the streamfunction solution from the SE balance equation and the azimuthal mean diabatic heating. Note that the secondary circulation intensifies and moves radially inward concurrently with the most intense azimuthal mean diabatic heating. The region of diabatic heating is tied to the axis of frontogenesis and begins along the western side of the vortex then subsequently moves cyclonically around the southern side of the vortex and radially inward through 2000 UTC 29 October.
Using and derived from the SE balance solution, we predict the tangential wind tendency from the evolution of the balanced vortex using (4) (Fig. 16). The mean 1600-m AHW tangential wind tendency for 0700–1100 UTC 29 October—which coincides with the spin up of the vortex at ~200-km radius (Fig. 11a)—shows a positive tendency near 200-km radius and a negative tendency within a 140-km radius (consistent with increasing cyclonic vorticity in the 100–200-km radial band). The predicted tendency from the SE solution shows a similar radial profile of tangential wind tendency, except overpredicted by 1.0–1.5 m s−1 h−1 within (outside) the 120-km (200 km) radius. During 1600–2000 UTC 29 October, the positive tangential wind tendency shifted radially inward to near 100 km, consistent with contraction of the vortex and growth of cyclonic vorticity within a 100-km radius. Again, the predicted tangential wind tendency from the SE solution shows a similar pattern as the AHW tangential wind tendency, but is markedly overpredicted by nearly 2.5 m s−1 h−1 near an 80-km radius (Fig. 16). The overprediction of the mean tangential wind tendency by the SE solution is related to the inability of the SE solution to capture the intense low-level outflow just above the top of the boundary layer (at ~1500–3000 m; cf. Figs. 14b,e and 14c,f). Recall the mean tangential momentum balance in (4). The mean radial vorticity flux () acts to produce a negative tangential wind tendency in regions of positive vorticity and outflow. The SE solution overpredicts the mean tangential wind tendency because the decreased magnitude of the low-level outflow above the boundary layer reduces the negative impact of the mean radial vorticity flux term on the tangential wind tendency. This overprediction of the tangential wind tendency from the SE solution was systematic in this case because the outflow just above the boundary layer was likely an unbalanced response (Bryan and Rotunno 2009a).
b. Circulation budget
The terms in (6) were computed from hourly AHW output files for two periods in Sandy's intensification: 0000–1100 and 1100–2000 UTC 29 October. The former period marks the spinup of the vortex as the warm seclusion process began, and the latter period marks the horizontal contraction of the vortex. The scale of the circulation box over which the terms in (6) were computed was chosen as 360 km × 360 km for the 0000–1100 UTC period and 160 km × 160 km for the 1100–2000 UTC period, centered on the vortex. The size of the circulation box for the two periods was chosen so the edge of the box approximately coincided with the radius of maximum tangential wind (cf. Fig. 11a). The translational velocity was subtracted from the ground-relative winds prior to computing the vorticity budget diagnostics. Since the edge of the box intercepted regions of active convection and vorticity generation, we followed the budget ensemble approach of Davis and Galarneau (2009) to improve the balance of the budget. The box was perturbed from its central location by ±40 km in 8-km increments in the x and y directions, creating a 121-member budget ensemble at each time. We then interpreted the results from the budget ensemble mean.
Figure 17 shows vertical profiles of the budget terms in (6), expressed as box-averaged accumulated tendencies over the periods of interest. For both periods, the vorticity budget was nearly balanced, with some minor differences in the vertical structure of the vorticity change (Figs. 17a,c). For the initial period of 0000–1100 UTC 29 October, the vorticity increased below 500 hPa and decreased above. The decrease in vorticity above 500 hPa was driven by the stretching term (friction is negligible at this level), which was consistent with the radial outflow shown by the AHW and SE secondary circulation (Fig. 17b; also cf. Fig. 14). Below 500 hPa the stretching term was compensated by the tilting term. The remaining positive vorticity tendency was driven by the eddy flux term. The 800-hPa vertical vorticity and storm-relative flow at 0400 UTC 29 October shows that cyclonic vorticity aligned along the cyclonic shear side of a westerly low-level jet (see also Figs. 9a,c) “fluxed” into the circulation box on the western side of Sandy (Fig. 18a). The highly rotational flow, and weaker outward directed flow on the eastern side of the box, contributed to an accumulation of vorticity in the box. It appears that the vorticity along the cyclonic shear side of the low-level jet developed, in part, in conjunction with tilting of horizontal vorticity along the baroclinic zone west of the circulation box (Fig. 18b; see also Figs. 10a,c). The eddy flux contribution is a representation of the effect of axisymmetrization of low-level vorticity discussed in section 5. By 1000 UTC 29 October 2012—near the end of the initial period—tilting played a more prominent role in increasing the vorticity in the circulation box as ascent along the baroclinic zone intersected the western edge of the circulation box where horizontal vorticity vectors pointed outward (Fig. 19a). The outward-pointing horizontal vorticity vectors are consistent with what would be expected for a warm core vortex in thermal wind balance (e.g., Kurihara 1975).
During the second vorticity budget period of 1100–2000 UTC 29 October, the vortex contracted as its vorticity below (above) 500 hPa continued to increase (decrease) resulting in an intense and compact vorticity center (Fig. 17c; see also Fig. 9e). The stretching + friction term contributed to a cyclonic vorticity tendency below 875 hPa, and a negative vorticity tendency above (Fig. 17d). The contribution from stretching was consistent with the increased inflow near the top of the boundary layer and outflow above the boundary layer shown by the AHW and SE secondary circulation (Figs. 14c,f and 15c). The low-level convergence and vorticity stretching was also consistent with the horizontal contraction of the vortex and concentration of vorticity (Fig. 9e). There was a positive contribution from tilting primarily in the 850–650-hPa layer that more than compensated for the stretching term (Fig. 17d). The tilting term was prominent on the west and south side of the circulation box, where horizontal vorticity vectors pointed outward in regions of ascent, consistent with the radially inward movement of the baroclinic zone and attendant frontogenesis maximum (Fig. 19b; see also Figs. 7c and 12c). The eddy flux term was small compared to the other terms during 1100–2000 UTC 29 October since much of the vertical vorticity that was generated away from the circulation box along the baroclinic zone on Sandy's west side was not transported into the smaller circulation box during the period of interest.
7. Summary and conclusions
This study addressed the intensification of Hurricane Sandy (2012) during the warm seclusion phase of its extratropical transition (ET). We presented an analysis and diagnosis of Sandy's life cycle during ET using an Advanced Hurricane Weather Research and Forecasting Model (AHW) simulation configured with explicit cloud-permitting convection. Extratropical transition of Sandy commenced on 29 October when Sandy interacted with an upper-level polar trough. Diabatically enhanced upper-level outflow associated with Sandy reinforced the negative tilt and cyclonic wave break of the upper-level trough through negative potential vorticity (PV) advection by the divergent wind on the forward flank of the trough (e.g., Archambault 2011). The enhancement of cyclonic wave breaking and shortening of the downstream half wavelength through diabatic ridge building, and its importance in promoting surface cyclogenesis and intensification by focusing quasigeostrophic forcing for ascent over the surface low center, has been documented in previous studies on the inland reintensification of Hurricane David (1979; Bosart and Lackmann 1995) and development of the March 1993 “Superstorm” (Dickinson et al. 1997; Bosart 1999). Sensitivity experiments are needed, however, to fully address the impact of Sandy's diabatic outflow on the evolution and structure of the upper-level trough and impact on baroclinic life cycles as shown for Hurricane Lili (1996; Agustí-Panareda et al. 2005).
The transition of Hurricane Sandy from a deep warm core vortex to a Shapiro and Keyser (1990, see their Fig. 10.27) warm seclusion represents a nonconventional pathway to warm seclusion development. Hurricane Sandy's ET followed the seclusion-occlusion type (Kitabatake 2008) and began as a low-level jet developed on the cold side of an axis of frontogenesis on the northwest side of Sandy. The low-level jet appeared to develop along an axis of frontogenesis in response to persistent midtropospheric diabatic heating, low-level cyclonic PV generation, and surface pressure falls. The axis of frontogenesis was initially anchored along the western flank of the Gulf Stream through 0200 UTC 29 October likely in response to differential diabatic heating and surface roughness (e.g., Bosart et al. 2008, see their Fig. 4 and attendant discussion of coastal frontogenesis on p. 39) as Hurricane Sandy approached from the southeast. The axis of frontogenesis, which acted to organize persistent convection on the western side of Sandy, subsequently rotated cyclonically inward around the south side of Hurricane Sandy in conjunction with Sandy's highly rotational flow.
The evolution of Hurricane Sandy during its warm core seclusion occurred in two phases. The initial phase (0000–1100 UTC 29 October) involved the development of an intense low-level westerly jet on the southwest side of Sandy, warm seclusion development, and vortex intensification. The second phase (1100–2000 UTC 29 October) involved the horizontal contraction of the vortex and concentration of low-level PV. We examined the intensification of Hurricane Sandy during its warm core seclusion from both the Sawyer–Eliassen (SE) balanced framework and circulation budget perspective. In the azimuthal mean balanced vortex perspective, intensification of Hurricane Sandy occurred in response to frontogenesis within the highly vortical flow. As cold air swept cyclonically around the vortex, the radial gradient of potential temperature increased and the maximum tangential wind increased. The SE solution shows an increase in the vigor of the secondary circulation that is consistent with the frontogenesis signature. During the vortex contraction phase of the intensification, the secondary circulation moved radially inward in concert with the frontogenesis maximum. This evolution is analogous to the relationship between the radial gradient of entropy and radial gradient of angular momentum in the eyewall derived by Emanuel (1986). The radial gradients occur near the location of maximum tangential wind because the vortical flow is frontogenetical (e.g., Emanuel 1997; Bryan and Rotunno 2009b). For Hurricane Sandy, however, the frontogenesis occurred as the air outside of the radius of maximum tangential wind cooled dramatically during warm seclusion while the inner warm core remained nearly steady.
From a circulation budget perspective, the growth of cyclonic vorticity and intensification of the low-level vortex for the initial stage of intensification (0000–1100 UTC 29 October) occurred as (i) cyclonic vorticity was generated via tilting along the axis of frontogenesis on the west side of Sandy, and (ii) the intense low-level westerly jet transported the cyclonic vorticity to near the center of the warm core vortex. During the vortex contraction phase of intensification (1100–2000 UTC 29 October), growth of cyclonic vorticity occurred in midlevels in response to tilting along the axis of frontogenesis on the west and south side of Sandy. Growth of vorticity at low levels occurred in response to enhanced convergence and stretching of cyclonic vorticity. The enhanced low-level convergence is consistent with the solution for the SE secondary circulation, and explains the contraction and spinup of the vortex prior to landfall.
That Hurricane Sandy evolved into a warm seclusion structure during ET was important because it dictated the governing dynamics that drove Sandy's intensification, as illustrated by the SE balance solution and circulation budget results. The governing dynamics of intensification were nontropical in origin, and were consistent with previous studies that described mechanisms for the development and intensification of warm core seclusions (e.g., Grønås 1995; Reed et al. 1994; Neiman and Shapiro 1993). A key aspect of Sandy's warm seclusion intensification appears to be the northwestward storm track, which allowed the cyclonic PV that developed over the Gulf Stream (and within Sandy's closed circulation) to be readily axisymmetrized, as shown by the eddy flux contribution in the circulation budget. The importance of cyclonic vorticity generation within Sandy's closed circulation in intensification is analogous to the “marsupial paradigm” for easterly waves discussed by Dunkerton et al. (2009). For the more typical northeastward storm track, cyclonic PV generation along the Gulf Stream would be located on the west side and behind the TC, likely making PV axisymmetrization more difficult. This study of Hurricane Sandy offers a quantitative dynamical diagnosis of the processes that contributed to the warm core seclusion intensification during ET. Future research directions may include conducting similar dynamical diagnoses over a large number of ET cases over the North Atlantic, western North and South Pacific, and south Indian Ocean to determine the range of dynamical mechanisms that contribute to warm core seclusion development and intensification across the spectrum of ET events.
The real-time AHW deterministic and ensemble forecasts were generated by Prof. Ryan Torn (University at Albany) on the NOAA-jet supercomputer as part of 2012 Hurricane Forecast Improvement Program (HFIP) Stream 1.5. The AHW-RERUN forecast was generated by the lead author on the NCAR-Yellowstone supercomputer. The authors thank Rich Rotunno (NCAR) for his valuable comments on the manuscript. This study benefitted from discussions with Greg Holland, George Bryan, Dan Stern (all NCAR), and Lance Bosart (University at Albany). Comments from Dave Schultz (University of Manchester) and three anonymous reviewers helped to improve the manuscript. The Air Force reconnaissance flight dropsonde data were obtained from the NOAA/Hurricane Research Division of AOML. The HURDAT (Landsea et al. 2004) was obtained from the NOAA/NWS/National Hurricane Center. The NCEP GFS analysis data were downloaded from NOAA's NOMADS data server. The 4-km remapped color enhanced infrared satellite imagery was obtained from the CIRA/RAMMB Tropical Cyclone Image Archive.
The National Center for Atmospheric Research is sponsored by the National Science Foundation.
Hurricane Sandy caused 147 deaths total when accounting for its initial landfall over Cuba.
The 12-km moving nest(s) are employed to follow any disturbance identified as an INVEST or tropical cyclone by the National Oceanic and Atmospheric Administration (NOAA)/National Weather Service (NWS)/National Hurricane Center (NHC). The nest is removed in the data assimilation system once NHC stops tracking the disturbance of interest.
The real-time AHW forecasts use a version of the Tiedtke cumulus parameterization that is modified from the standard configuration to reduce the vigor of shallow convection over oceans. Additionally, the surface drag coefficient is increased compared to the standard configuration to reduce the strength of near-surface winds in the 5–20 m s−1 range (R. D. Torn 2013, personal communication).
For azimuthal mean calculations, SE diagnostic, and circulation budget, the storm center was defined as the minimum in sea level pressure that was smoothed by 10 passes of a 9-point local smoother (provided with the standard distribution of the National Center for Atmospheric Research (NCAR) Command Language version 6.1.1 software package).
The SE solution was computed using the 12-km nest from the AHW forecast. The 12-km nest was used because the relatively larger size of the domain, compared to the 4-km nest, produced a more realistic solution.