Upper oceanic heat content (OHC) in advance of a hurricane is generally superior to prestorm sea surface temperature (SST) for indicating favorable regions for hurricane intensification and maintenance. OHC is important because a hurricane’s surface winds mix the upper ocean and entrain cooler water into the oceanic mixed layer from below, subsequently cooling the sea surface in the region providing heat energy to the storm. For a given initial SST, increased OHC typically decreases the wind-induced sea surface cooling, and a warm ocean eddy (WCR) has a higher OHC than its surroundings, so conditions typically become more favorable for a hurricane to intensify when the storm’s core encounters a WCR. When considering hurricane intensity, however, one often-neglected aspect of a WCR is its anticyclonic circulation. This circulation may impact the location and magnitude of the hurricane-induced sea surface cooling. Using an ocean model, either prescribed hurricane wind stress or wind stress obtained via coupling to a hurricane model is applied to an initial ocean condition in which the SST is homogeneous, but a WCR is embedded in an otherwise horizontally homogeneous subsurface density field. Based on model experiments, when a WCR is located to the right of the storm track (in the Northern Hemisphere), the interaction of the WCR’s circulation with the hurricane-induced cold wake can cause increased sea surface cooling under the storm core and decreased storm intensity relative to the scenario where no WCR is present at all. Therefore, the presence of a WCR in advance of a hurricane sometimes creates a less favorable condition for hurricane intensification.
Evaporation from the sea surface, primarily within a hurricane’s core, provides heat energy required to intensify and maintain the storm (e.g., Cione and Uhlhorn 2003; Emanuel 2003, and references therein). If the sea surface temperature (SST) decreases within the storm core, so does the heat energy available to the storm, thereby limiting the storm’s intensity. Generally, in the deep ocean, SST cooling within the storm core occurs primarily because the storm’s surface winds impose a wind stress on the upper ocean, and the resulting ocean current shear generates turbulent mixing and entrainment of cooler water into the upper oceanic mixed layer (OML) from below (e.g., Ginis 1995, 2002, and references therein). In addition, for slow-moving hurricanes especially, the storm’s cyclonic wind stress generates upper-ocean current divergence and upwelling, which in turn may contribute significantly to storm-core SST cooling (Price 1981; Yablonsky and Ginis 2009, hereafter YG09). Evaporative heat flux to the atmosphere, while vital to the hurricane, contributes far less than mixing/entrainment to storm-core SST cooling in the deep ocean (Price 1981; Shen and Ginis 2003; D’Asaro et al. 2007).
Since the SST in advance of a hurricane cannot account for storm-induced SST cooling, upper oceanic heat content (OHC, also known as tropical cyclone or hurricane heat potential) ahead of the storm has become more widely accepted than prestorm SST as a measure of the ocean energy available to the hurricane for future storm intensification and/or maintenance (e.g., Mainelli et al. 2008; Shay et al. 2000). OHC, originally defined by Leipper and Volgenau (1972), can be calculated as follows:
where d26 is the depth of the 26°C isotherm, ρ is the seawater density, cp is specific heat at constant pressure, T is the ocean temperature, and dz is the change in depth. While certainly a valuable quantity, the utility of OHC as a measure of future heat available within a hurricane’s core may be limited by its inability to account for nonlocal processes, as discussed below.
Another potential mechanism for storm-core SST cooling is horizontal advection of the storm’s cold wake when preexisting ocean currents are oriented in the same direction as the storm track. This situation can occur when a warm ocean eddy, also known as a warm core ring (WCR), is located to the right (left) of the storm track in the Northern (Southern) Hemisphere because a WCR is an anticyclone in approximately geostrophic balance, so it circulates clockwise (counterclockwise) in the Northern (Southern) Hemisphere. For brevity, only the Northern Hemisphere is considered here. Many previous modeling and observational studies have investigated the interaction between a hurricane (or equivalently, a typhoon or cyclone) and a WCR (e.g., Shay et al. 1992, 1998, 2000; Jacob et al. 2000; Hong et al. 2000, 2006; Mao et al. 2000; Chan et al. 2001; Goni and Trinanes 2003; Jacob and Shay 2003; Scharroo et al. 2005, 2006; Lin et al. 2005, 2008, 2011; Ali et al. 2007; Wada and Usui 2007; Wu et al. 2007; Mainelli et al. 2008), yet none of these studies consider a scenario whereby a WCR may be responsible for weakening a hurricane. In fact, Lin et al. (2008) suggest that WCRs can be treated as “boosters,” whereby WCRs are always favorable features for hurricane intensification.
The primary goal of this study is to assess whether advection due to a WCR can play a significant role in storm-core SST cooling; if so, a WCR could have the opposite effect on storm-core SST cooling and subsequent hurricane intensity change than would be predicted by OHC alone. Toward this end, a three-dimensional (3D) ocean model is used to test the impact of a WCR on hurricane-induced sea surface cooling. Also, the feedback of altered storm-core SST cooling on hurricane intensity is investigated with a coupled hurricane–ocean model.
2. Experimental design
a. Ocean model description
The 3D experiments in this study are performed using a version of the Princeton Ocean Model (POM; Blumberg and Mellor 1987; Mellor 2004) that is similar to the version used in the operational National Oceanic and Atmospheric Administration (NOAA) Geophysical Fluid Dynamics Laboratory (GFDL) and Hurricane Weather Research and Forecasting (HWRF) coupled hurricane–ocean models (POM-TC; Bender et al. 2007; Gopalakrishnan et al. 2011), as well as the U.S. Navy’s version of the GFDL model (GFDN), and is nearly identical (except for the initialization) to the version used in YG09. Additionally, one-dimensional (1D) experiments are performed using this same version of POM-TC, except the advection, horizontal diffusion, and pressure gradient terms are removed so that at each grid point, there is no interaction among surrounding grid points in the horizontal, as in YG09.1 This 1D simplification is consistent with the operational GFDL, GFDN, and HWRF models in the ocean basins where 3D ocean coupling has not yet been implemented. For all experiments, the ocean grid spans 108.5°–60°W longitude and 10°–47.5°N latitude. Unlike the operational GFDL, GFDN, and HWRF models, the ocean grid is set on an f plane, where Earth’s rotation rate and the longitudinal grid spacing assume constant latitude of 22.4°N. There are 508 (449) grid points in the x (y) direction, yielding a horizontal grid spacing of 9.8 (9.3) km in the x (y) direction. The entire domain is assumed to be a 2500-m-deep ocean (no land or bathymetry), and the 23 half-sigma levels are placed at the following depths: 2.5, 7.5, 12.5, 17.5, 22.5, 27.5, 32.5, 40, 47.5, 55, 67.5, 87.5, 125, 187.5, 275, 387.5, 550, 775, 1050, 1400, 1800, 2250, and 2500 m.
b. Control experiments with prescribed wind stress
In the control experiments (CTRL), the ocean is initialized with a horizontally homogeneous temperature T and salinity S profile that is representative of Gulf of Mexico Common Water (GCW) during late summer and early autumn; the upper 500 m of the T-GCW and S-GCW profiles are shown in Fig. 1. Once T and S are defined on the POM grid, hurricane wind stress is applied (Figs. 2a,c), with the storm center initially located at (22.4°N, 71.7°W). The wind stress distribution is based on the wind field (Figs. 2b,d) derived from an analytic model of the wind and pressure profiles in hurricanes (Holland 1980), where central pressure pc = 950 hPa, environmental pressure pn = 1013 hPa, maximum wind speed Vm = 55 m s−1, radius of maximum winds (RMW) = 30 km,2 air density ρa = 1.28 kg m−3, exponential decay parameter B = eρa/(pn − pc), and e = 2.718. Asymmetry is included in this otherwise axisymmetric wind field by adding half of the storm translation speed, as in Price (1981). Once the wind field is calculated, the wind stress is calculated using the bulk formula, in which the drag coefficient CD is calculated as an empirical function of the 10-m wind speed, similar to Moon et al. (2007) but modified to decrease CD at high wind speeds to be consistent with observations, as suggested by Tung (2008). This wind stress field translates westward with a constant, prescribed speed of either 1° longitude (16 h)−1 (~2 m s−1; Figs. 2a,b) or 1° longitude (6 h)−1 (~5 m s−1; Figs. 2c,d). Model integration continues first until average SST cooling under the storm core reaches a quasi–steady state, and then it continues further to allow for direct comparison with experiments that include a WCR, as discussed below in section 2c.
c. WCR experiments with prescribed wind stress
In the experiments other than CTRL, an idealized WCR is assimilated into the otherwise horizontally homogeneous ocean of CTRL. This WCR is created using the temperature and salinity within real-world WCRs from the daily Navy Coupled Ocean Data Assimilation (NCODA) product (Cummings 2005), available online in the U.S. Global Ocean Data Assimilation Experiment (GODAE) Data Catalog (http://usgodae.org) as the Fleet Numerical Meteorology and Oceanography Center (FNMOC) high-resolution ocean analysis for GODAE. The primary NCODA WCR used to create the idealized WCR was located in the center of the Gulf of Mexico on 1 October 2009 (Figs. 3a,c,e). Specifically, a radial-vertical cross section from an NCODA grid point near the center of this NCODA WCR to another grid point five points toward the southeast forms the basis for creating an axisymmetric, idealized WCR (Figs. 3b,d,f).
For both temperature and salinity, these six grid points (at all depths) are used directly, except for the following sequential modifications: 1) any temperatures >30°C are set to 30°C (at all applicable depths) and any salinities <36.2 psu are set to 36.2 psu in the upper 75 m only, both of which remove instability; 2) the SST is initially set to 30°C at all six top level points, thereby creating a homogeneous SST field; 3) the temperature (salinity) at the sixth point radially outward (at all depths) is replaced by the temperature (salinity) at the fifth point radially outward plus two-thirds of the difference between the temperature (salinity) at the sixth point radially outward and the fifth point radially outward; and 4) the temperature (salinity) at a hypothetical “seventh” point radially outward is defined by the temperature (salinity) at the fifth point radially outward plus the difference between the temperature (salinity) at the sixth point radially outward and the fifth point radially outward. Next, the radial-vertical temperature (salinity) cross section is converted into an axisymmetric 3D temperature (salinity) field by interpolating it onto a very fine horizontal grid (with 1.67-km grid spacing). The temperature (salinity) at all points (at all depths) on this fine grid with a distance from the WCR center that is greater than the distance of the hypothetical seventh point described earlier (assumed to be GCW) is set equal to the temperature (salinity) at that hypothetical seventh point. Finally, to prevent the OML and upper thermocline in the surrounding GCW from being too shallow (and, hence, resembling the temperature profile in a cold core ring instead of the GCW), the temperature at all grid points and all depths is set equal to 28.862°C if it exceeds 28.862°C; this change resets the SST to be 28.862°C everywhere, allowing it to match the SST used in the development of the initial atmospheric vortex in the coupled hurricane–ocean model experiments, described in section 2d. The temperature and salinity profiles in the GCW after all of the aforementioned modifications (T-GCW and S-GCW, Fig. 1) are consistent with NCODA observations of the GCW around other WCRs in the central Gulf on 1 September 2008 and in the southwestern Gulf on 29 June 2010 (not shown). The T-GCW and S-GCW are also used to initialize all grid points in CTRL, as described in section 2b.
For all WCR experiments (and CTRL), the 3D T and S fields are interpolated horizontally onto the POM grid and then vertically onto the POM half-sigma levels. Next, the 3D POM is integrated for 96 h without wind stress in the vicinity of the WCR, thereby allowing the density and current fields in the WCR to geostrophically adjust.3 The resulting radial-vertical temperature cross section and south–north current magnitudes are shown in Fig. 4a, and the 87.5-m temperature and sea surface current vector field are shown in Fig. 4b, where the maximum sea surface current velocity in the geostrophically adjusted WCR is ~1.2 m s−1; the resulting T and S profiles in the center of the WCR and the surrounding GCW (equivalent to the CTRL experiment) are shown in Fig. 1. This ocean field is then used to initialize both the 1D and 3D experiments, except the currents associated with the geostrophically adjusted WCR are removed for the 1D experiments. Finally, the hurricane wind stress field (described in section 2b) translates westward toward and then past a WCR centered at 85.7°W (allowing enough time for the average SST cooling under the storm core to first reach a quasi–steady state, as in CTRL). Experiments are performed with the WCR located in the center of the storm track (WCRC), to the south (i.e., left) of the storm track (WCRL), and to the north (i.e., right) of the storm track (WCRR) (Fig. 5a). Table 1 summarizes the important parameters for all experiments.
d. Coupled hurricane–ocean model description
In addition to the 3D experiments with prescribed wind stress described previously in sections 2b and 2c, similar 3D experiments are done with a coupled hurricane–ocean model. The clear advantage of coupled model experiments is that the impact of the WCR’s circulation on hurricane intensity can be directly evaluated instead of inferring the intensity change based on storm-core SST cooling; the disadvantage, however, is that the experimental design is less constrained because the surface wind stress field changes as the hurricane size and intensity changes, and the storm track and translation speed cannot be prescribed a priori.
The coupled hurricane–ocean model experiments are performed using a version of the GFDL model that is similar to the version used operationally by NOAA and the U.S. Navy (Bender et al. 2007). The atmospheric model component employs the hydrostatic approximation and solves the primitive equations on a longitude–latitude grid with a sigma vertical coordinate. The atmospheric model domain consists of a triply nested grid configuration, in which two inner grids are moveable and two-way interactive. The stationary outermost grid spans 75° by 75° from 110° to 35°W longitude and from 10°S to 65°N latitude, with ½° grid spacing. The middle grid spans 11° by 11° with ⅙° grid spacing. The innermost grid spans 5° by 5° with ° grid spacing. In the vertical, there are 42 sigma levels. The atmospheric model physics includes a simplified Arakawa and Schubert (1974) scheme for cumulus parameterization (Grell 1993), a Ferrier (2005) cloud microphysics package for large-scale condensation, the Smagorinsky (1963) nonlinear viscosity scheme for horizontal diffusion, the Troen and Mahrt (1986) nonlocal scheme diffusion for vertical diffusion, the Monin–Obukhov scheme for surface flux calculations with an improved air–sea momentum flux parameterization in strong wind conditions (Kurihara and Tuleya 1974; Moon et al. 2007), the Schwarzkopf and Fels (1991) scheme for infrared radiation, and the Lacis and Hansen (1974) scheme for solar radiation. The ocean component of the model is the 3D version of POM-TC, as described in section 2a.
Air–sea coupling between the atmospheric and oceanic components of the GFDL model occurs by passing key variables between the two components during time integration. Since the ocean time step is longer than the atmospheric time step, the SST is held constant in the atmospheric model in between ocean time steps. At each ocean time step, the surface wind stress, heat, moisture, and radiative fluxes from the atmospheric component are passed into the ocean component, and the SST from the ocean component (calculated using the atmospheric fluxes from the previous ocean time step) is passed into the atmospheric component to be used until the next ocean time step.
e. Coupled hurricane–ocean model initialization
The atmosphere is initialized using an idealized, axisymmetric vortex, which is subsequently embedded in a uniform, background environmental wind. The initial vertical profiles of temperature and relative humidity in both the vortex and the environment are specified based on the Global Atlantic Tropical Experiment III conditions, as described in Shen et al. (2002). To create the vortex, an uncoupled, axisymmetric version of the atmospheric component of the GFDL model is integrated for 60 h, where the initial vortex is specified and then continuously nudged toward a central pressure, outermost closed isobar, maximum wind speed, RMW, and radius of outermost closed isobar of 975 hPa, 1010 hPa, 36 m s−1, 55 km, and 375 km, respectively. After the 60-h axisymmetric model integration, the vortex is placed at (19.5°N, 68.0°W) and embedded in an environment with no wind prior to the coupled GFDL model forecast. Since the atmospheric model (unlike the ocean model) is not set on an f plane, beta drift then induces a northwestward storm translation speed of ~(1–2) m s−1 (Smith 1993).
The ocean is initialized similar to the experiments with prescribed wind stress (sections 2b and 2c), except the WCR is strategically placed based on the northwestward motion of the evolving storm so that coupled experiments can be performed with the WCR located near the center of the storm track (CWCRC), to the left of the storm track (CWCRL), and to the right of the storm track (CWCRR), with the center of the storm passing in closest proximity to the center of the WCR ~96 h into the coupled model integration (Fig. 5b). CCTRL designates the coupled model experiments without a WCR.
f. Averaging within the storm core
Since the goal of this study is to quantify the magnitude of SST cooling only within the region providing most of the heat energy to the storm, the average SST cooling is calculated within a 60-km radius around the storm center and within a 200-km radius around the storm center while the storm-induced cooling is being influenced by the WCR (when present). Also, to understand the utility and potential shortcomings of preexisting OHC for predicting the average SST cooling, the area-averaged initial OHC along the storm track but prior to the storm’s arrival is calculated for the experiments with prescribed wind stress (Figs. 6a,c).
The exact radius over which ocean heat flux significantly impacts storm intensity is not well known and likely varies depending on storm size, but 60 km includes what may be considered the storm “inner core” because it is 2 times larger than the RMW in the prescribed wind stress experiments, ~(1–2) times the RMW during the coupled model experiments, and consistent with the inner-core definition of Cione and Uhlhorn (2003). Using a 200-km radius captures what Cione and Uhlhorn (2003) define as the “inner-core wake,” and idealized model sensitivity experiments performed by Shen et al. (2002) suggest that ocean heat flux may be important for storm intensity even at this large radius from the storm center. More recently, Miyamoto and Takemi (2010) performed experiments showing that ocean heat flux is important for storm intensity out to a radius of ~(7–8) times the RMW, but their experiments all assumed a small RMW of 13.6 km, so it is not immediately clear how the results would change for a larger storm. Finally, it should be noted that area averaging effectively considers only the axisymmetric component of SST change around the storm center; Wu et al. (2005) argue that this axisymmetric SST change dominates the asymmetric SST change in terms of subsequent impact on storm intensity.
3. Results and discussion
a. Storm-core sea surface temperature along the storm track under prescribed wind stress
Figure 6b (Fig. 6d) shows the average SST anomaly within 60 km (200 km) of the storm center for the WCRC prescribed wind experiments, where the anomaly is calculated as WCRC − CTRL. Consistent with the purely thermodynamic view of a WCR, whereby the deeper mixed layer within the WCR restricts the ability of the storm to entrain a significant quantity of cooler water into the upper oceanic mixed layer via shear-induced vertical mixing, the SST anomaly within the storm core increases relative to the CTRL experiments while the storm is passing directly over the center of the WCR from right to left (i.e., from ~300 km east of the WCR to ~300 west of the WCR). Indeed, the SST anomaly within the storm core (Figs. 6b,d) is similar to the initial OHC within the storm core (Figs. 6a,c), although the SST anomaly is shifted ~100 km west of the initial OHC when considering the full 200-km radius (Figs. 6c,d). The WCRC − CTRL SST anomaly is largest (up to ~3.5°C when considering only the 60-km radius) in the slow-moving experiment with full 3D dynamics (T2–3D) because the presence of the WCR restricts the SST cooling due to both vertical mixing and upwelling. For the slow-moving experiment with only 1D dynamics (T2–1D), the anomaly is smaller because the 1D dynamics do not include upwelling (YG09). For the faster-moving experiments (T5–3D and T5–1D), the anomaly is even smaller because vertical mixing is reduced compared to the slow-moving experiments. Also, the impact of upwelling in the faster-moving experiments is small enough to generate little difference between T5–3D and T5–1D, especially when considering the SST anomaly within only the 60-km radius (Fig. 6b), consistent with the findings of YG09 for idealized experiments with no WCR.
Figures 7a–d (Figs. 7e–h) shows the average SST anomaly within 60 km (200 km) of the storm center for the WCRL and WCRR prescribed wind experiments, where the anomalies are calculated as WCRL − CTRL and WCRR − CTRL, respectively. Considering first the 1D experiments (Figs. 7a,c,e,g), the results are qualitatively similar to the WCRC experiments (Figs. 6b,d) in that the storm-core SST anomaly increases while the storm is passing the WCR’s longitude. The magnitude of the SST anomaly is smaller in the WCRL and WCRR–1D experiments than in the WCRC–1D experiments because a smaller percentage of the storm core is over the WCR in the former experiments than in the latter experiment. Also, the magnitude of the SST anomaly is larger in the WCRR–1D experiments than in the WCRL–1D experiments because WCRR is located closer to the core of the cold wake, which is shifted to the right of the storm track, as discussed in section 3b.
Considering now the 3D experiments (Figs. 7b,d,f,h), the most significant result is the negative SST anomaly of up to ~0.7°C that exists within a 60-km radius of the storm center in the slower-moving WCRR experiment (T2–3D, Fig. 7b). This negative SST anomaly is caused by the WCR’s anticyclonic circulation, which advects the storm’s cold wake horizontally in the direction of the storm track, thereby increasing the SST cooling underneath the storm core relative to the CTRL experiment. Similarly, although less dramatically, the positive SST anomaly of up to ~0.7°C that exists within a 60-km radius of the storm center in the slower-moving WCRL–3D experiment (T2–3D, Fig. 7b) is more than double the ~0.3°C positive SST anomaly in the analogous WCRL–1D experiment (T2–1D, Fig. 7a), suggesting that the WCR’s circulation advects the storm’s cold wake farther behind the storm, thereby decreasing the SST cooling underneath the storm core relative to the CTRL experiment. For the faster-moving storm (T5–3D, Fig. 7d), the translation speed of the storm is too fast relative to the preexisting WCR current velocities to create an appreciable negative SST anomaly in the WCRR–3D experiment or an appreciable positive SST anomaly enhancement in the WCRL experiment. These cold wake advection processes associated with the presence of WCRs will be discussed in greater detail in sections 3b–e.
Finally, it is instructive to briefly consider the SST anomaly within a 200-km radius of the storm center for the 3D experiments (Figs. 7f,h), primarily to examine if and how the 200-km radius SST anomaly differs from the 60-km radius SST anomaly as the storm traverses the WCR. One result is a westward shift in the 200-km SST anomaly relative to the 60-km SST anomaly, especially for the slow-moving experiments (T2, Fig. 7f). Perhaps more interesting, however, is that the 200-km anomaly in the WCRR experiments is positive when the storm is ~0–100 km past (i.e., west of) the WCR’s center longitude (Figs. 7f,h). In section 3b, it is shown that the reversal of the sign of the 200-km SST anomaly relative to the 60-km SST anomaly in the WCRR − (T2–3D) experiments (Figs. 7b,f) is due to cancellation during spatial averaging of positive and negative SST anomalies within the 200-km radius circle.
b. Spatial structure of sea surface temperature under prescribed wind stress
Having examined the average SST anomaly within 60 and 200 km of the storm center along the storm track for the WCRL and WCRR experiments (Fig. 7), the next step is to examine the spatial structure of the SST anomaly at specific times of interest for the experiments that yielded the most significant results to obtain more evidence for the physical mechanism(s) that explain these results. Toward this end, Fig. 8 shows the SST and surface current vector anomaly fields for the WCRR experiments (i.e., WCRR − CTRL) when the storm center is ~50 km (Figs. 8a–d) and ~200 km (Figs. 8e–h) past the WCR’s center longitude. In the 1D experiments (Figs. 8a,c,e,g), the SST anomaly is positive within the WCR because of reduced shear-induced mixing and entrainment due to the existence of a deeper mixed layer within the WCR relative to the surrounding Gulf Common Water (Figs. 1 and 4). In the 3D experiments (Figs. 8b,d,f,h), however, the situation is more complex. When the storm center is ~50 km past the WCR’s center longitude (Figs. 8b,d), the WCRR–3D SST anomaly is positive from the WCR’s center toward its eastern periphery, but the WCRR–3D SST anomaly is negative on the southern periphery of the WCR (i.e., near the storm center), particularly in the slower-moving experiment (T2, Fig. 8b). This sign change in the WCRR-T2–3D SST anomaly northeast of the storm center (when the storm center is ~50 km past the WCR’s center longitude) reveals why the average SST anomaly within a 200-km radius of the storm center is positive (Fig. 7f), while the average SST anomaly within a 60-km radius of the storm center is negative (Fig. 7b). The negative SST anomaly near the storm center (Figs. 8b,d), especially in WCRR-T2–3D (Fig. 8b), is caused by advection of the storm’s cold wake westward along the storm track by the WCR’s anticyclonic circulation, as indicated by the surface current vector anomaly field. Similarly, the WCR’s circulation creates a positive SST anomaly east of the WCR’s center by advecting the cold wake southward toward the storm track (Figs. 8b,d). When the storm center is ~200 km past the WCR’s center longitude (Figs. 8f,h), the WCRR–3D SST anomaly is negative on the southern and western peripheries of the WCR, especially in WCRR-T2–3D (Fig. 8f), where the cold wake continues to be advected around the WCR. Indeed, this negative SST anomaly in WCRR-T2–3D is large enough and strong enough to yield a net negative SST anomaly within a 200-km radius of the storm center at this time (Fig. 7f).
Figure 9 shows the SST and surface current vector anomaly fields for the WCRL experiments (i.e., WCRL − CTRL) when the storm center is ~50 (Figs. 9a–d) and ~200 km (Figs. 9e–h) past the WCR’s center longitude. In the 1D experiments (Figs. 9a,c,e,g), the SST anomaly is positive within the WCR because of reduced shear-induced mixing and entrainment, similar to the 1D WCRR experiments (Figs. 8a,c,e,g). In the 3D experiments (Figs. 9b,d,f,h), however, the situation is again more complex. When the storm center is ~50 km past the WCR’s center longitude (Figs. 9b,d), the WCRL–3D SST anomaly is positive from the WCR’s center toward its northern periphery, but the WCRL–3D SST anomaly is negative on the eastern periphery of the WCR (i.e., ~200 km southeast of the storm center), particularly in the slower-moving experiment (T2, Fig. 9b). The enhanced positive SST anomaly near the storm center (Figs. 9b,d), especially in WCRL-T2–3D (Fig. 9b), is caused by advection of the unmodified prestorm SST eastward along the storm track by the WCR’s anticyclonic circulation, as indicated by the surface current vector anomaly field. Similarly, the WCR’s circulation creates a negative SST anomaly east of the WCR’s center by advecting the cold wake southward across and then away from the storm track (Figs. 9b,d). When the storm center is ~200 km past the WCR’s center longitude (Figs. 9f,h), the WCRL–3D SST anomaly is negative on the eastern and southern peripheries, especially in WCRL-T2–3D (Fig. 9f), where the cold wake continues to be advected around the WCR. Since this negative SST anomaly in WCRR-T2–3D is well behind the storm center, however, it is entirely absent from the average storm-core SST anomalies at this time (Figs. 7b,d).
While the anomaly fields discussed above highlight the most significant results (Figs. 8 and 9), it is instructive to examine the actual SST and surface current fields in one set of experiments (i.e., the T2 experiments) when the storm center is ~50 km past the WCR’s center longitude (Fig. 10). Focusing first on CTRL (Figs. 10g,h), the most notable feature is the cold wake, which along with the surface current vectors is generally maximized to the right of the storm track. As discussed by Price (1981), the rightward bias in the surface current field is caused by the superposition of the wind stress vector’s rotation due to the storm’s forward motion, inertial rotation due to the Coriolis force, and to a lesser extent, the asymmetry in the wind stress magnitude; the rightward bias in the SST cooling is a result of the rightward bias in the shear-induced turbulent mixing in the water column. The cold wake in CTRL-T2–3D (Fig. 10h) is colder than in CTRL-T2–1D (Fig. 10g); this difference is due to the inclusion of upwelling in the former but not the latter (e.g., Price 1981; YG09). Significant SST differences between CTRL-1D and CTRL–3D within the storm core are limited to the T2 experiments, however (Figs. 10g,h); in the CTRL-T5 experiments (not shown), upwelling is much weaker and occurs too far behind the storm center to significantly impact the storm-core SST (as in YG09).
In the 1D experiments with a WCR (Figs. 10a,c,e), the shape and position of the cold wake are identical to the CTRL experiments (Fig. 10g), except where the deeper mixed layer and higher OHC within the WCR (Figs. 1, 4, and 6) restrict the SST cooling, consistent with the purely thermodynamic view of a WCR. By examining the 3D experiments with a WCR (Figs. 10b,d,f), however, the impact of advection becomes clear. In WCRC-T2–3D, WCRL-T2–3D, and WCRR-T2–3D, the cold wake is shifted (relative to CTRL) toward the south, east, and west, respectively, due to the anticyclonic circulation around the WCR. This cold wake shift has little impact within the storm core in WCRC-T2–3D (Fig. 10b), but in WCRL-T2–3D, the cold wake is advected backward (i.e., out of the storm core; Fig. 10d), while in WCRR-T2–3D, the cold wake is advected forward (i.e., into the storm core; Fig. 10f), consistent with the SST anomaly fields discussed earlier. Also, while qualitatively similar, the relative impact of advection into or out of the storm core is greater for the T2 experiments (Fig. 10) than for the T5 experiments (not shown) because 2 m s−1 is closer than 5 m s−1 to the WCR’s maximum circulation velocity.
c. Vertical structure of upper-ocean temperature under prescribed wind stress
The spatial SST anomaly structure clearly shows the impact of horizontal advection at the sea surface (Figs. 8 and 9), but it is worthwhile to look beneath the ocean surface by examining vertical along-track upper ocean temperature anomaly cross sections when the storm center is ~50 km past the WCR’s center longitude for the experiments that yielded the most significant results (i.e., WCRL-T2–3D and WCRR-T2–3D). Considering first the WCRL-T2–3D temperature anomaly (Fig. 11a), it is evident that the strong warm anomaly observed in the storm core at the sea surface (Fig. 9b) only extends to a depth of ~50 m. This warm anomaly is collocated with a strong eastward current anomaly (Fig. 11a), suggesting that uncooled water ahead of the storm center is being advected toward and behind the storm center by WCRL, thereby suppressing the magnitude of the cooling within the storm core relative to CTRL. Considering now the WCRR-T2–3D temperature anomaly (Fig. 11b), the strong cold anomaly observed in the storm core at the sea surface (Fig. 8b) only extends to a depth of ~50 m. This cold anomaly is collocated with only a weak westward current anomaly (Fig. 11b), but the north–south component of the current anomaly plays a larger advective role here than the south–north component does in WCRL-T2–3D (not shown), as evidenced by the direction of the surface current vector anomalies in Fig. 8b relative to Fig. 9b. Also, the maximum WCRR-T2–3D westward current anomaly occurs ~55 km north of the storm track, as discussed in section 3d. Below ~50-m depth, in a narrow swath centered ~100 km behind the WCR’s center longitude, a warm WCRR-T2–3D anomaly exists that could be caused by reduced upwelling (Fig. 11b). Finally, note that the turbulent kinetic energy (TKE; a proxy for mixing) anomaly at the WCR’s center longitude is strongly negative at ~50–80-m depth in both WCRL (Fig. 11a) and WCRR (Fig. 11b) because of the deeper OML in WCRL and WCRR relative to CTRL.
While the vertical along-track upper ocean temperature anomaly cross sections discussed above highlight the role of horizontal advection (Fig. 11), it is also important to examine the actual temperature, current, and mixing patterns below the surface in one set of experiments (i.e., the T2 experiments) when the storm center is ~50 km past the WCR’s center longitude (Fig. 12). Focusing first on CTRL in the along-track direction (Fig. 12g), the most notable features are the near-inertial waves behind and below the storm center, associated with the upwelling–downwelling cycle that lags the regions of maximum along-track upper-ocean current divergence/convergence. Also notable is the region of maximum TKE, located ~(50–60) km behind the storm center at ~(50–80-m) depth. Considering now CTRL in the across-track direction ~50-km behind the storm center (Fig. 12h), the mixing is nearly symmetrical about the storm track, and the west–east (i.e., along track) components of the currents are generally oriented in the same direction as the wind stress (Fig. 2a), except above ~50-m depth where the currents have begun to geostrophically adjust to the right-of-track-biased cold wake. Focusing now on WCRC (Fig. 12a), WCRL (Fig. 12c), and WCRR (Fig. 12e) in the along-track direction, the temperature, current, and mixing patterns below the surface are generally similar to CTRL (Fig. 12g), except for 1) the drastic suppression of the magnitude of the WCRC upper-ocean cooling relative to CTRL near and immediately behind the storm center, where the much thicker warm layer in WCRC inhibits upper-ocean cooling due to either mixing and upwelling; and 2) the more subtle differences in WCRL and WCRR relative to CTRL, as discussed earlier and shown in Fig. 11. Finally, considering WCRC (Fig. 12b), WCRL (Fig. 12d), and WCRR (Fig. 12f) in the across-track direction, it is important to notice that the primary circulation of the WCR remains intact, even under strong wind forcing from a slow-moving hurricane; therefore, WCR-based advection is still possible under strong wind forcing.
d. Hodograph of ocean surface current vectors over time under prescribed wind stress
The next step toward isolating the role of horizontal advection on relocation of the cold wake in the presence of a WCR is to examine hodographs of ocean surface current vectors over time in the T2–3D experiments at a location that is near both the core of the cold wake and the maximum WCRR circulation velocity (i.e., ~55 km north of the storm track at the WCR’s center longitude, when present; Fig. 13h). (For reference, this hodograph point location, indicated by an ○ marker, is also included in Figs. 8, 9, 10, 15, and 16.) Returning to Fig. 13, it is first instructive to examine CTRL-T2–3D (Fig. 13g). As the storm approaches the hodograph point’s longitude from the east, a westward surface current (with a slight southward component) nearly in line with the wind stress is generated, reaching a maximum value of ~1.5 m s−1 with a slight northward component when the storm is at the hodograph point’s longitude. As the storm passes the hodograph point’s longitude, wind stress forcing begins to diminish relative to the inertial oscillation, which causes the surface current vector to rotate anticyclonically. Since the T2 storm is moving slowly, however, the time scale of geostrophic adjustment in the developing cold wake is short enough relative to the storm translation speed to prevent the surface current at the hodograph point from ever having an eastward component. Such an adjustment is of course only possible in the CTRL-T2–3D experiment (Fig. 10h) and not in the CTRL-T2–1D experiment (Fig. 10g). Nonetheless, the surface current magnitude at the hodograph point is only ~0.5 m s−1 toward the north-northwest by the time the storm is ~100 km west of the hodograph point’s longitude (Fig. 13g).
Figure 13a shows the ocean surface current hodograph in WCRC-T2–3D, and Fig. 13b shows the hodograph anomaly for WCRC-T2–3D − CTRL-T2–3D. The preexisting anticyclonic circulation in WCRC creates an eastward current velocity of ~0.75 m s−1 at the hodograph location prior to the storm’s arrival (Fig. 13a), but as the storm approaches and then passes the hodograph location, the rotation of the current vector follows a rather similar pattern to CTRL-T2–3D (Fig. 13g). Certainly, interesting differences emerge if examining the evolution of the anomaly over time (Fig. 13b), but those details are not discussed further here because the WCRC-T2–3D case is not responsible for a significant storm-core SST anomaly due specifically to advection. Also, the WCRL-T2–3D hodograph (Fig. 13c) and hodograph anomaly (Fig. 13d) require little discussion because the hodograph location is far enough north of the WCRL circulation to yield almost no difference between the WCRL-T2–3D hodograph (Fig. 13c) and the CTRL-T2–3D hodograph (Fig. 13g).
Figure 13e shows the ocean surface current hodograph in WCRR-T2–3D and Fig. 13f shows the hodograph anomaly for WCRR-T2–3D − CTRL-T2–3D. The preexisting anticyclonic circulation in WCRR creates a westward current velocity of ~1.2 m s−1 at the hodograph location prior to the storm’s arrival (Fig. 13a), but as the storm approaches and then passes the hodograph location, the rotation of the current vector follows a rather similar pattern to CTRL-T2–3D (Fig. 13g). Here, however, important differences emerge when analyzing the evolution of the anomaly over time (Fig. 13f). Specifically, the anticyclonic rotation of the current vector at the hodograph location from westward to northwestward as the storm passes the WCR’s longitude is suppressed when WCRR is present, yielding a southward anomaly of up to 0.5 m s−1 (Fig. 13f). This continuously westward current of 1.2–2.2 m s−1 at the hodograph location in WCRR-T2–3D (Fig. 13e) yields westward advection of the cold wake farther underneath the storm core (Figs. 8b and 10f).
e. Budget of contributions to sea surface cooling under prescribed wind stress
The final analysis technique toward isolating the role of advection in the 3D prescribed wind experiments is to examine the SST budget, separating the temperature tendency due to advection from the temperature tendency due to mixing. These SST budget terms are calculated directly from the discretized temperature equation solved by subroutines “advt” and “proft” in POM (Mellor 2004). At the topmost half-sigma model level, treated here as the sea surface even though it is technically at 2.5-m depth, the vertical velocity is small. Therefore, SST advection is almost entirely horizontal and is composed of both the hurricane-driven currents and the WCR’s primary circulation (when a WCR is present). Also, recall that horizontal diffusion is negligible, so mixing is almost entirely vertical, and no heat or moisture is exchanged with the atmosphere.
Figure 14 shows the average SST cooling rate (hereafter dSST) due to either advection (Figs. 14a,c) or mixing (Figs. 14b,d) within 60 km of the storm center for the WCRL, WCRR, and CTRL 3D prescribed wind experiments. Considering first the CTRL experiments, advection contributes about half as much to dSST as mixing does in the T2 experiment (Figs. 14a,b), and advection contributes less than half as much to dSST as mixing does in the T5 experiment (Figs. 14c,d). Mixing-induced dSST in the WCRL and WCRR experiments generally varies by ±0.02°C h−1 or less from CTRL (Figs. 14b,d), but the magnitude of advection-induced dSST decreases (increases) by ~0.05°C h−1 in the T2 WCRL (WCRR) experiment relative to CTRL as the storm passes the WCR’s center longitude (Fig. 14a). These variations of advection-induced dSST (Fig. 14a) closely follow the variations of the SST anomalies (Fig. 7b) within 60 km of the storm center. So for slower-moving storms, advection is primarily responsible for the differences in the SST anomalies when a WCR is located to the left or right of the storm track compared to the situation with no WCR. Considering now faster moving storms, WCRL-T5–3D dSST is similar to CTRL-T5–3D dSST, but the magnitude of dSST in WCRR-T5–3D is ~0.03°C h−1 greater than CTRL-T5–3D dSST as the storm passes the WCR’s center longitude (Fig. 14c).
Having examined the budget of the average SST cooling rate (dSST) within 60 km of the storm center along the storm track for the WCRL, WCRR, and CTRL 3D experiments (Fig. 14), the next step is to examine the spatial structure of the dSST anomaly budget at a specific time of interest. Figure 15 shows the dSST anomaly budget fields for the WCRR–3D experiments (i.e., WCRR − CTRL) (Figs. 15a–d) and the WCRL–3D experiments (i.e., WCRL − CTRL) (Figs. 15e–h) when the storm center is ~50 km past the WCR’s center longitude. Considering advection first (Figs. 15a,c,e,g), it is clear that a primarily negative dSST anomaly exists near the storm center in the WCRR–3D experiments (Figs. 15a,c), while a primarily positive dSST anomaly exists near the storm center in the WCRL 3D experiments (Figs. 15e,g), consistent with the 60-km radial average advection-induced dSST (Figs. 14a,c) and with the fact that the cold wake is being advected toward (away from) the storm core in the WCRR (WCRL)–3D experiments. This advection-induced dSST anomaly is maximized in the T2–3D experiments (Figs. 15a,e) relative to the T5–3D experiments (Figs. 15c,g). Farther toward the northeast, behind and to the right of the storm in the WCRR 3D experiments (Figs. 15a,c), a positive advection-induced dSST anomaly exists where the WCRR circulation is replacing the cold wake water with warmer water from undisturbed water on the northern side of WCRR (Figs. 8b,d and 10f). Now considering mixing (Figs. 15b,d,f,h), weakly positive and negative mixing-induced dSST anomalies near the storm center in both the WCRR and WCRL–3D experiments generally offset each other if spatially averaging, explaining the small differences between 60-km radial average mixing-induced dSST in the WCRL–, WCRR–, and CTRL–3D experiments (Figs. 14b,d).
While the dSST anomaly budget fields highlight the most significant results (Fig. 15), it is instructive to examine the actual dSST budget fields in one set of experiments (i.e., the T2–3D experiments) when the storm center is ~50 km past the WCR’s center longitude (Fig. 16). Focusing first on CTRL (Figs. 16g,h), the most notable features are the positive advection-induced dSST immediately behind the storm (Fig. 16g), in the same region as the negative mixing-induced dSST (Fig. 16h), and the negative advection-induced dSST in front of and to the right of the storm center (Fig. 16g), which is not counterbalanced by positive mixing-induced dSST (Fig. 16h). Focusing now on WCRC (Figs. 16a,b), the pattern is rather similar to CTRL (Figs. 16g,h), but both the advection-induced (Fig. 16a) and mixing-induced (Fig. 16b) dSST magnitudes are drastically reduced compared to CTRL (Figs. 16g,h). WCRL (Figs. 16c,d) is generally similar in both pattern and magnitude to CTRL (Figs. 16g,h), requiring the dSST anomaly budget fields discussed earlier (Figs. 15e,f) to observe clear differences. In WCRR (Figs. 16e,f), however, the advection-induced dSST (Fig. 16e) clearly shows an area of strongly negative dSST that encompasses more of the storm core than the advection-induced dSST in CTRL does (Fig. 16g), consistent with the advection-induced dSST anomaly field (Fig. 15a).
f. Impact of WCR location on storm intensity from coupled hurricane–ocean model experiments
All results thus far in sections 3a–e have focused on the prescribed wind experiments, which neglected two-way coupling between the atmosphere and the ocean. Here, the impact of WCR location on storm intensity is discussed using the coupled hurricane–ocean model experiments (CWCRC, CWCRL, CWCRR, and CCTRL; Fig. 17). Before analyzing the hurricane intensity, however, it is instructive to first examine the average SST cooling within the storm core in the coupled experiments. The SST cooling within a 60-km radius (200-km radius) of the storm center during the hurricane’s passage by the WCR (hours 48–120) is shown for all experiments in Fig. 17a (Fig. 17b). Unlike the uncoupled ocean model experiments with prescribed wind forcing presented in sections 3a–e and in YG09, the average SST cooling within the storm core varies over time in CCTRL (Figs. 17a,b), particularly because subtle variations in the storm propagation direction and speed (Fig. 17d) may have a significant impact on the location and magnitude of upwelling and the subsequent contribution of upwelling to both the storm-core SST cooling and storm intensity. In addition, storm intensity and structure are changing in the coupled model in response to the SST cooling. Regardless, the CCTRL storm-core SST cooling provides a suitable baseline for measuring the impact of a WCR in each of the non-CCTRL experiments. Consistent with the prescribed wind experiments, passage of the storm over CWCRC decreases the magnitude of the storm-core SST cooling relative to CCTRL, while passage of the storm over the right edge of CWCRL has similar storm-core SST cooling to CCTRL, and passage of the storm over the left edge of CWCRR increases the magnitude of the storm-core SST cooling relative to CCTRL (Figs. 17a,b).
The central pressure (i.e., a measure of storm intensity) during the hurricane’s passage by the WCR (hours 48–120) is shown for all experiments in Fig. 17c. Before hour 72, the intensities are similar for all experiments, reaching ~(940–943) hPa at hour 72. By hour 108, after the storm has passed the WCR, CWCRC intensity increases to ~929 hPa, CWCRL intensity remains similar at ~944 hPa, CWCRR intensity decreases to ~955 hPa, and CCTRL intensity decreases slightly to ~947 hPa. Of particular note is the 5–10-hPa weakening of the CWCRR storm intensity relative to CCTRL, indicating that the presence of a WCR on the right side of the storm track can cause a weaker storm relative to the case where no WCR is present. Indeed, the spatial structure of the SST and surface current vectors at hour 96 of CWCRC (Fig. 17e), CWCRL (Fig. 17f), CWCRR (Fig. 17g), and CCTRL (Fig. 17h) support the main conclusion drawn in the prescribed wind experiments, whereby advection of the cold wake toward the storm core by a WCR’s circulation, when it is located to right of the storm track, can create a less favorable condition for hurricane intensification than would exist if there was no WCR present.
4. Summary and conclusions
A WCR’s anticyclonic circulation is typically neglected as a contributing factor for hurricane intensity change. Here, it is shown that this anticyclonic circulation can have an impact on the location and magnitude of hurricane-induced sea surface cooling. Contrary to the result expected when considering OHC alone, advection of the hurricane-induced cold wake by a WCR’s circulation, when the WCR is located to the right of the storm track, may cause increased sea surface cooling under the storm core relative to the case where no WCR is present, thereby creating a less favorable condition for hurricane intensification.
It is worth mentioning that the magnitude of the results presented here are sensitive to properties of both the hurricane and the WCR. For example, changing the RMW, the inflow angle of the surface winds, or the latitude of the storm center would change the wind stress vector rotation rate relative to the local inertial period; hence, the distance of maximum upwelling from the storm center and the rightward bias and magnitude of the cold wake would change even for the same storm translation speed. A WCR with a faster (slower) circulation velocity would be expected to advect the cold wake more (less) in the same amount of time. Also, a WCR on the right side of the storm track that is larger (smaller), but with the same circulation velocity, could advect the cold wake along the storm track for a longer (shorter) amount of time. Nonetheless, the key conclusion remains the same: a WCR’s circulation can contribute to hurricane intensity change via advection of the cold wake.
For future study, the concepts presented here could be extended to a hurricane propagating along an oceanic front, such as the Gulf Stream, Kuroshio, or one of the branches of the Loop Current. Similarly, experiments could be run with a cyclonically rotating cold core ring (CCR) instead of a WCR to determine if a CCR to the right of the storm track created a more favorable condition for hurricane intensification by advecting the hurricane-induced cold wake farther behind the storm core, thereby decreasing the SST cooling within the storm core.
The authors thank Drs. Biju Thomas (URI/GSO), Carlos Lozano (NOAA/NCEP/EMC/MMAB), George Halliwell (NOAA/OAR/AOML/HRD), and Nick Shay (UM/RSMAS/MPO) for constructive comments. This research was funded by NOAA Grants NOAA4400080656 and NA12NWS4680002, awarded to the University of Rhode Island.
Supplementary experiments with alternative storm sizes (not discussed further) show qualitatively similar results, although the overall magnitude of SST cooling increases (deceases) with increasing (decreasing) storm size.
Note that the WCR does not experience beta drift because the ocean model is set on an f plane.