1. Introduction
In 2002, a joint National Oceanic and Atmospheric Administration (NOAA)–National Science Foundation (NSF) aircraft-based experiment was executed to quantify upper-ocean response, and potential thermal feedback, to hurricanes in the northwest Caribbean Sea and Gulf of Mexico (Shay and Uhlhorn 2008). Results were clear that within the Loop Current (LC), ocean mixed layer (OML) cooling was highly limited (<1°C) when forced by Saffir–Simpson category-3 hurricanes Isidore and Lili. In Part I (Uhlhorn and Shay 2012, hereafter Part I) of a two-part study, further analysis revealed a negative kinetic energy (KE) response to direct forcing by Hurricane Lili (2002). Considering the observational errors, at a minimum, no significant change in OML mechanical energy was detected within the LC near the storm track at two inertial periods (IP) after storm passage. This result directly contradicts many previous observational (e.g., Black et al. 1988; Shay et al. 1989, 1990; Price et al. 1994; Jacob et al. 2000; D’Asaro et al. 2007), analytical (e.g., Geisler 1970; Lighthill 1978; Gill 1984) and numerical (e.g., Price 1981, 1983; Price et al. 1994; Jacob and Shay 2003) studies of upper-ocean response to TC, which concluded that a significant increase in currents and KE could be found several IPs after a storm had passed. However, these studies were based on weak or quiescent background ocean conditions compared to an energetic flow regime like the LC.
Given the observed intense surface-wind forcing (maximum wind stress τmax ≃ 7 N m−2) from Lili, a significant positive response still cannot be ruled out. Although poststorm mechanical energy analysis snapshots reveal little classical storm signature, it is not clear how the OML evolved from the time of direct forcing (i.e., 0 IP) until the ocean was sampled after Lili’s passage. Thus, it is presumed that a strong initial OML response could have occurred, but that the presence of the LC somehow prevented the expected poststorm, near-inertial response from being readily observable. To test this, a set of model experiments is conducted to help understand the interactions between the preexisting geostrophic current, directly forced wind current, and the near-inertial current response. With similar spatial scales and magnitudes (and therefore, time scales) of these dynamically distinct flows, strong nonlinear interactions could be expected, therefore advection of mass and momentum must be considered.
Most modeling studies of TC ocean response have focused on the ocean’s temperature change, as moist enthalpy flux is the primary energy source for a TC. Methodologies have ranged from simple 1D slab mixed layer models (e.g., Emanuel et al. 2004; Lin et al. 2005) through 3D baroclinic, reduced-gravity systems (e.g., O’Brien and Reid 1967; Elsberry et al. 1976; Chang and Anthes 1978; Price 1981, 1983; Schade and Emanuel 1999) to fully nonlinear 3D primitive equation systems (e.g., Bender and Ginis 2000; Jacob et al. 2000; Halliwell et al. 2011). Here the interest is to examine the mechanical response within an idealized preexisting baroclinic current, without explicit regard for the temperature’s effect on the mass distribution. Thus, a model system is chosen in which the upper ocean is approximated by a reduced-gravity formulation.
Previous applications of a reduced-gravity layered model to TC response studies have usually assumed initially horizontally homogeneous structure, therefore minimal 1.5-layer systems (e.g., Chang and Anthes 1978; Chan et al. 2001), in which a single active layer overlies an inactive and infinitely deep ocean, have been shown to be adequate for simulating near-inertial current response and resulting isopycnal deflection. Physically, this particular approximation is acceptable since the geostrophic current in response to a TC is typically weak compared to the wind-driven, near-inertial current. In contrast, the scenario examined here requires far greater resolution of the mass distribution to support the relatively large geostrophic currents associated with a Loop Current–like frontal zone.
To clarify the interaction of a TC with the ocean mixed layer embedded in an energetic preexisting current, a numerical model is developed as described in section 2, including subgrid-scale parameterizations and initialization procedures. In section 3, experiments are performed to compare and contrast the ocean response under certain approximations. Mechanical energy budget analysis is carried out in section 4 to understand the roles of individual physical processes in the response. The model-derived budget, along with observations, are used to construct a conceptual model of Loop Current response to a TC. Sensitivity experiments in a nondimensional framework are performed in section 5, with a summary and concluding remarks presented in section 6.
2. Model description
In the scenario examined herein, the initial geostrophically balanced current’s magnitude is comparable to the expected near-inertial current response [O(1 m s−1)], indicating the presence of large preexisting internal pressure gradients that support strong meso- and synoptic-scale current systems (LC, Gulf Stream, etc). To generate a balanced current under a realistic horizontal pressure gradient, the upper ocean must be discretized into several layers. The model developed here is similar in several aspects to that of Price (1981), as isopycnic layers are separated by discrete density jumps across these interfaces. The upper layer absorbs wind energy from a TC-like storm, and exchanges this energy with lower layers through both turbulent entrainment mixing and pumping by divergence of the near-inertial current.
a. Turbulent flux parameterizations
b. Model storm
The surface forcing is approximated by a translating TC-like vortex whose near-surface wind structure is based on observations of stepped frequency microwave radiometer (SFMR) surface winds (Uhlhorn et al. 2007). The radial distribution of surface wind speed |U10(r)| is estimated using a double-exponential parametric model (Willoughby et al. 2006) fit to the azimuthal mean wind speed observed by SFMR. This method has been shown to represent tangential wind structure better than the traditional Holland (1980) model, by incorporating a number of additional parameters, including inner- and outer-core radial decay rates, transition zone width, and if necessary, multiple wind maxima.
Observed SFMR surface winds are first placed into 1-km radial bins, and averages are computed. Since all quadrants of Lili were sampled (Shay and Uhlhorn 2008), an azimuthal average can be well approximated. As shown in Fig. 1, the fitted radial profile represents the wind speed radial structure well. For comparison, the Holland (1980) parametric model is also fit to the data by constraining |U10max| and Rmax. Next, the two-dimensional wind vector field is computed by decomposing the wind speed into tangential and radial components with respect to storm center. The radial component is estimated assuming a constant 23° inflow angle (Zhang and Uhlhorn 2012) radially outward of Rmax, although significant variability in this value (up to 100%) as a function of storm motion speed and azimuth could be expected. Finally, a storm motion–induced asymmetry is applied to produce the total earth-relative wind field U10(x, y). The storm translates at a speed Vs = 7 m s−1 in the along-track (+y) direction, along the center grid column of the cross-track (x) dimension.
Radial distribution of observed azimuthal-mean surface wind speed (m s−1). Best fits from the Willoughby et al. (2006) model (WDR) and the Holland (1980) are shown.
Citation: Journal of Physical Oceanography 43, 6; 10.1175/JPO-D-12-0203.1
Radial distribution of observed azimuthal-mean surface wind speed (m s−1). Best fits from the Willoughby et al. (2006) model (WDR) and the Holland (1980) are shown.
Citation: Journal of Physical Oceanography 43, 6; 10.1175/JPO-D-12-0203.1
Radial distribution of observed azimuthal-mean surface wind speed (m s−1). Best fits from the Willoughby et al. (2006) model (WDR) and the Holland (1980) are shown.
Citation: Journal of Physical Oceanography 43, 6; 10.1175/JPO-D-12-0203.1
c. Numerics
The model equations are discretized using finite difference approximations, and are integrated numerically on a staggered “C” grid (Messinger and Arakawa 1976). All spatial derivatives are center-differenced to fourth-order accuracy in the model domain interior. Coriolis terms are averaged on the staggered grid to conserve energy as suggested by Dobricic (2006). A conditionally stable, second-order leapfrog–time integration scheme with a modified antidiffusive Robert–Asselin time filter (Williams 2009) is applied to control decoupling of solutions at adjacent time steps. The model domain extends 1000 km in the cross-storm track direction, 1500 km in the along-track direction, with a constant horizontal grid spacing of Δ(x, y) = 10 km. The upper ocean is discretized into 9 active layers of variable resolution in the vertical, depending upon the stratification. The time step is set to 1/10 of the time for the storm to travel one grid length (Δt = 0.1Δx/Vs ≃ 143 s), which is far less than the Courant–Friedrichs–Lewy (CFL) limit for simulating near-inertial wave propagation and transport by the preexisting baroclinic current.
d. Lateral boundary condition
Because of the stationary baroclinic jet, specification of lateral boundary conditions becomes slightly more complicated than in previous model applications. Previous limited-domain, numerical hurricane response studies have typically used either zero gradient (Neumann) (e.g., Chang and Anthes 1978) or radiative (e.g., Price 1983) lateral boundary conditions for the prognostic variables. In this study, internal wave energy should be allowed to freely propagate out of the domain, while simultaneously maintaining the structural integrity of the background current system, at least in the far-field region.
e. Upper-ocean structure initialization
Observations in the SE Gulf of Mexico (GOM) traversed by Lili indicate an abrupt transition from a warmer, lighter, and weakly stratified ocean equatorward to relatively cooler and more strongly stratified fluid poleward. Separating these regimes is a baroclinic current jet, which is largely confined to the upper 300 m with maximum velocity near the sea surface, as observed and reported in Part I. For the experiments in which the near-inertial current response interacts with a preexisting baroclinc current, the upper-ocean mass and momentum fields are initialized as follows.
Currents are initialized through a geostrophic adjustment process by integrating a linearized version of the model in which the advection terms are neglected, hk is held constant in the mass-flux divergence term of the continuity equation, and the surface stress forcing is eliminated (τnet = 0). The spinup integration runs for one year allowing internal gravity wave energy to disperse, until an approximate steady-state is reached. Figures 2 and 3 show the initialized model mass and momentum distributions in the horizontal and vertical, respectively; these fields are used as initial conditions for the experiments with a preexisting current.
(left) Initial model top (mixed) layer thickness and (right) geostrophic current. Boxes represent approximate dimensions of the Hurricane Lili experimental domain. Left panel axes are normalized cross-track (r/Rmax) and along-track (y/Λ) distances, where Rmax = 20 km is the radius of maximum winds and Λ = 740 km is the Geisler (inertial) wavelength. Simulated storm travels from bottom to top along x = 0 r/Rmax, and current vectors are plotted at ⅕ resolution for clarity.
Citation: Journal of Physical Oceanography 43, 6; 10.1175/JPO-D-12-0203.1
(left) Initial model top (mixed) layer thickness and (right) geostrophic current. Boxes represent approximate dimensions of the Hurricane Lili experimental domain. Left panel axes are normalized cross-track (r/Rmax) and along-track (y/Λ) distances, where Rmax = 20 km is the radius of maximum winds and Λ = 740 km is the Geisler (inertial) wavelength. Simulated storm travels from bottom to top along x = 0 r/Rmax, and current vectors are plotted at ⅕ resolution for clarity.
Citation: Journal of Physical Oceanography 43, 6; 10.1175/JPO-D-12-0203.1
(left) Initial model top (mixed) layer thickness and (right) geostrophic current. Boxes represent approximate dimensions of the Hurricane Lili experimental domain. Left panel axes are normalized cross-track (r/Rmax) and along-track (y/Λ) distances, where Rmax = 20 km is the radius of maximum winds and Λ = 740 km is the Geisler (inertial) wavelength. Simulated storm travels from bottom to top along x = 0 r/Rmax, and current vectors are plotted at ⅕ resolution for clarity.
Citation: Journal of Physical Oceanography 43, 6; 10.1175/JPO-D-12-0203.1
Initial density (kg m−3) and geostrophic current (m s−1) vertical cross section in the along-storm track/cross-stream direction. Top panel extends over full domain, and bottom panel is zoomed on approximate bounds of the Hurricane Lili observation domain to aid in comparison with observational cross-section analysis in Fig. 15 of Uhlhorn and Shay (2012). Simulated storm travels from left to right, indicated by the arrow, and the view is upstream.
Citation: Journal of Physical Oceanography 43, 6; 10.1175/JPO-D-12-0203.1
Initial density (kg m−3) and geostrophic current (m s−1) vertical cross section in the along-storm track/cross-stream direction. Top panel extends over full domain, and bottom panel is zoomed on approximate bounds of the Hurricane Lili observation domain to aid in comparison with observational cross-section analysis in Fig. 15 of Uhlhorn and Shay (2012). Simulated storm travels from left to right, indicated by the arrow, and the view is upstream.
Citation: Journal of Physical Oceanography 43, 6; 10.1175/JPO-D-12-0203.1
Initial density (kg m−3) and geostrophic current (m s−1) vertical cross section in the along-storm track/cross-stream direction. Top panel extends over full domain, and bottom panel is zoomed on approximate bounds of the Hurricane Lili observation domain to aid in comparison with observational cross-section analysis in Fig. 15 of Uhlhorn and Shay (2012). Simulated storm travels from left to right, indicated by the arrow, and the view is upstream.
Citation: Journal of Physical Oceanography 43, 6; 10.1175/JPO-D-12-0203.1
3. Model experiments
A series of numerical experiments is conducted to simulate the upper-ocean response to a translating tropical cyclone. Each experiment is run with selected forcing terms enabled or disabled in the governing equations [Eqs. (1) and (2)]. Table 2 provides a summary of experiments.
Summary of experiments in terms of enabled forcing mechanisms in model equations.
a. Homogeneous test cases (H-1D, H-3DL, H-3DNL)
To understand and verify basic model performance, the first experiment is a “test” case, in which the model domain is initialized as a horizontally homogeneous ocean [setting α = 0 in Eq. (7)], and the vertical structure corresponds closely to the mean density profile observed prior to Hurricane Lili’s passage (Fig. 4). As the thermodynamic observations captured both cold and warm structure on either side of the LC front, this mean profile corresponds approximately to the observed vertical structure in the LC. In the absence of a horizontal pressure gradient, the current is initially zero everywhere. The prescribed upper-ocean structure consists of an initial OML depth of 50 m and reduced gravity below the OML of g′ = 2 × 10−2 m s−2, which leads to a first baroclinic mode phase speed of approximately 1.5 m s−1. The model ocean responds to the Lili-like wind field as described in section 2b, where the peak earth-relative momentum flux is |τmax| = 7 N m−2, corresponding to |U10max| = 50 m s−1.
Initial ocean density (kg m−3) vertical structure for the homogeneous test case in which the ocean is at rest. Observed horizontally averaged density profile is plotted as the solid line, and the fitted model initial condition, based on Eqs. (7) and (8) with α = 0, is indicated by points at layer middepths.
Citation: Journal of Physical Oceanography 43, 6; 10.1175/JPO-D-12-0203.1
Initial ocean density (kg m−3) vertical structure for the homogeneous test case in which the ocean is at rest. Observed horizontally averaged density profile is plotted as the solid line, and the fitted model initial condition, based on Eqs. (7) and (8) with α = 0, is indicated by points at layer middepths.
Citation: Journal of Physical Oceanography 43, 6; 10.1175/JPO-D-12-0203.1
Initial ocean density (kg m−3) vertical structure for the homogeneous test case in which the ocean is at rest. Observed horizontally averaged density profile is plotted as the solid line, and the fitted model initial condition, based on Eqs. (7) and (8) with α = 0, is indicated by points at layer middepths.
Citation: Journal of Physical Oceanography 43, 6; 10.1175/JPO-D-12-0203.1
The model is run three times under identical initial conditions and with the same forcing, denoted as follows: H-1D, H-3DL, and H-3DNL. In the one-dimensional case (H-1D), ocean vertical columns are uncoupled in the horizontal and the only forcing terms are the wind stress, mixing, and Coriolis rotation. Therefore, no internal wave can develop to disperse energy and poststorm response cannot be accurately simulated, although prestorm evolution that is dominated by mixing can be approximated. For the H-3DL case, advective forcing is switched off, and hk is held constant as for the initialization procedure, but the pressure gradient force is now activated. Finally, in the H-3DNL case the advection terms are enabled, and hk is allowed to evolve in the continuity equation mass-flux divergence term.
As an example, horizontal and vertical cross sections of simulated currents and OML depth are shown in Fig. 5 for the H-3DNL case. As these snapshots are taken only shortly after storm passage (+0.7 IP), very little energy has begun to escape the mixed layer, and the near-inertial current oscillation within the OML is clearly evident. The simulations here reproduce the expected strong rightward response bias, due primarily to resonant coupling between the clockwise-rotating stress and mixed layer current vectors.
Simulated fields for H-3DNL test case at 0.7 IP after storm passes midpoint of domain (y = 0). Fields are as follows: (a) surface wind stress (τwind, Pa), (b) mixed layer currents (V1, m s−1), (c) mixed layer depth (h1, m); along-track vertical sections of (d) cross-track current (u, m s−1), (e) along-track current (υ, m s−1), and (f) current magnitude (|V|, m s−1).
Citation: Journal of Physical Oceanography 43, 6; 10.1175/JPO-D-12-0203.1
Simulated fields for H-3DNL test case at 0.7 IP after storm passes midpoint of domain (y = 0). Fields are as follows: (a) surface wind stress (τwind, Pa), (b) mixed layer currents (V1, m s−1), (c) mixed layer depth (h1, m); along-track vertical sections of (d) cross-track current (u, m s−1), (e) along-track current (υ, m s−1), and (f) current magnitude (|V|, m s−1).
Citation: Journal of Physical Oceanography 43, 6; 10.1175/JPO-D-12-0203.1
Simulated fields for H-3DNL test case at 0.7 IP after storm passes midpoint of domain (y = 0). Fields are as follows: (a) surface wind stress (τwind, Pa), (b) mixed layer currents (V1, m s−1), (c) mixed layer depth (h1, m); along-track vertical sections of (d) cross-track current (u, m s−1), (e) along-track current (υ, m s−1), and (f) current magnitude (|V|, m s−1).
Citation: Journal of Physical Oceanography 43, 6; 10.1175/JPO-D-12-0203.1
1) OML currents and depth
The OML (layer k = 1) current and depth response time series for the three cases are analyzed at the along-track domain center (y = 0), and averaged between x = 0 and +2Rmax in the cross-track direction (Fig. 6). The large difference in response between H-1D and H-3DL cases after approximately +0.5 IP is clearly evident. The H-1D model is incapable of dispersing energy, as internal waves cannot develop, and currents remain trapped in the OML near the storm track for all time. Overall, including the advective terms (H-3DNL) slightly weakens the response over the quasi-linear simulation (H-3DL) for both currents and mixed layer depth. Mixing is apparently the dominant process prior to storm passage, as all cases indicate similar OML current acceleration and deepening for times <0 IP, consistent with the conclusions of Jacob et al. (2000).
Cross-track (u) and along-track (υ) current vector components, current speed (|V|), and mixed layer depth (h) responses for three test cases. Currents are in units of meters per second and depth is in meters.
Citation: Journal of Physical Oceanography 43, 6; 10.1175/JPO-D-12-0203.1
Cross-track (u) and along-track (υ) current vector components, current speed (|V|), and mixed layer depth (h) responses for three test cases. Currents are in units of meters per second and depth is in meters.
Citation: Journal of Physical Oceanography 43, 6; 10.1175/JPO-D-12-0203.1
Cross-track (u) and along-track (υ) current vector components, current speed (|V|), and mixed layer depth (h) responses for three test cases. Currents are in units of meters per second and depth is in meters.
Citation: Journal of Physical Oceanography 43, 6; 10.1175/JPO-D-12-0203.1
2) Mechanical energy
(left) OML kinetic energy and (right) potential energy responses for test cases.
Citation: Journal of Physical Oceanography 43, 6; 10.1175/JPO-D-12-0203.1
(left) OML kinetic energy and (right) potential energy responses for test cases.
Citation: Journal of Physical Oceanography 43, 6; 10.1175/JPO-D-12-0203.1
(left) OML kinetic energy and (right) potential energy responses for test cases.
Citation: Journal of Physical Oceanography 43, 6; 10.1175/JPO-D-12-0203.1
3) Shear and Richardson number
Shear-induced entrainment mixing from the thermocline is mostly responsible for cooling the OML near the storm’s inner-core, and the underlying stratification alters the cooling rate. Shear and bulk Richardson number are computed in the vertical mixing parameterization previously described and are shown for the three test cases in Fig. 8.
(left) OML current shear magnitude and (right) bulk Richardson number responses for three test cases.
Citation: Journal of Physical Oceanography 43, 6; 10.1175/JPO-D-12-0203.1
(left) OML current shear magnitude and (right) bulk Richardson number responses for three test cases.
Citation: Journal of Physical Oceanography 43, 6; 10.1175/JPO-D-12-0203.1
(left) OML current shear magnitude and (right) bulk Richardson number responses for three test cases.
Citation: Journal of Physical Oceanography 43, 6; 10.1175/JPO-D-12-0203.1
Initially, the shear tracks almost identically for each case up to the storm’s arrival at 0 IP. Maximum shear values are found to be 2 × 10−2 s−1 near the center of the storm, consistent with values observed outside of the LC region (Shay and Uhlhorn 2008). After storm passage, shear continues to increase until around +0.5 IP for the H-3DNL and H-3DL cases, in contrast to the OML currents that were found to have weakened by this point. However, RiB remains fairly constant over this period, because of the increased stratification from the strong upwelling to the rear of the storm (Fig. 6). It should be noted again that, in this model, the OML mass density does not change in response to cooling or surface evaporation/precipitation flux, so stability effects should be viewed with some caution. If the OML were allowed to cool, and thus increase convection, RiB could be expected to remain subcritical (i.e., ≤1) for a longer period of time than shown here.
b. Horizontally variable case (C-3DNL)
The model is subsequently run with the same storm forcing but the ocean structure is perturbed as described in section 2e. The model results are examined at the same grid location as for the homogeneous case, which is at the center of the prescribed baroclinic current system (y = 0) and averaged between x = 0 to +2Rmax in the cross-track dimension. This preexisting current case, denoted C-3DNL, is run in 3D nonlinear mode, and is compared with the H-3DNL solution corresponding to the initially homogeneous case. Again, the vertical structure at the location where the response is diagnosed is initially identical for both cases (Fig. 4).
OML current and depth solutions for the C-3DNL case are shown in Fig. 9 for comparison with the H-3DNL case previously shown in Fig. 5. Vertical cross sections face upstream of the preexisting flow (Figs. 9d–f). Note that the current response is significantly stronger to the cooler side of the jet, where peak currents are 1.4 m s−1, as the initial OML depth is realistically shallower than on the warmer side, where peak currents are 0.9 m s−1.
As in Fig. 5, but for the preexisting current case (C-3DNL).
Citation: Journal of Physical Oceanography 43, 6; 10.1175/JPO-D-12-0203.1
As in Fig. 5, but for the preexisting current case (C-3DNL).
Citation: Journal of Physical Oceanography 43, 6; 10.1175/JPO-D-12-0203.1
As in Fig. 5, but for the preexisting current case (C-3DNL).
Citation: Journal of Physical Oceanography 43, 6; 10.1175/JPO-D-12-0203.1
1) OML currents and depth
The OML current and depth time series for the C-3DNL case are shown in Fig. 10. Also shown are solutions for the H-3DNL test case for comparison. As compared to the initially homogeneous case, the preexisting current has a profound impact on the storm-generated current and OML depth responses near the storm track. Near-inertial current oscillations are highly damped soon after storm passage (+2 IP). This is most evident in the along-track component (v), since there is no initial geostrophic current in the along-track direction. Current speeds (|V|) increase from 0 to ~1.2 m s−1 in the H-3DNL case, but only increase from 0.8 to a peak of ~1.4 m s−1 in the C-3DNL case, or a 50 less increase from the initial state. By +2 IP, the current speed has essentially returned to its background level in the preexisting current case, while it is still ~0.5 m s−1 (absolute and relative) in an initially homogeneous situation. The OML current (|V| = 0.78 ± 0.23 m s−1) observed within the LC near the storm track at approximately +2 IP was found to be approximately 0.1 m s−1 weaker than measured before the storm. Considering observational uncertainty, this result suggests that the numerical experiments that indicate that no significant storm-generated momentum remains near the track after +2 IP are reasonable.
As in Fig. 6, but for initially horizontally variable C-3DNL case and the initially quiescent H-3DNL test case. Also plotted is observed average OML current speed in the LC based on AXCPs deployed in the poststorm experiment.
Citation: Journal of Physical Oceanography 43, 6; 10.1175/JPO-D-12-0203.1
As in Fig. 6, but for initially horizontally variable C-3DNL case and the initially quiescent H-3DNL test case. Also plotted is observed average OML current speed in the LC based on AXCPs deployed in the poststorm experiment.
Citation: Journal of Physical Oceanography 43, 6; 10.1175/JPO-D-12-0203.1
As in Fig. 6, but for initially horizontally variable C-3DNL case and the initially quiescent H-3DNL test case. Also plotted is observed average OML current speed in the LC based on AXCPs deployed in the poststorm experiment.
Citation: Journal of Physical Oceanography 43, 6; 10.1175/JPO-D-12-0203.1
2) Mechanical energy
As for the OML currents, there are clear differences in the K and P responses, particularly after storm passage (Fig. 11). Here, the energy is analyzed relative to its initial condition for each case, since initial energy levels differ among cases. Prior to the storm’s arrival, OML K decreases in the C-3DNL case because of the oppositely directed wind stress and current vectors. At 0 IP, the wind stress vector is rapidly rotating clockwise to align with the surface current that injects additional energy over the H-3DNL case. However, K is quickly attenuated to near nominal levels <2 IP after storm passage (Fig. 11, left), presumably from advection of KE away from the storm track by the pre-existing current. Note that although the relative increase in current is smaller for the C-3DNL case (Fig. 10), the relative increase in KE is larger for the C-3DNL case because of the quadratic dependence of K on |V|.
As in Fig. 7, but for initially homogeneous (H-3DNL) and perturbed (C-3DNL) simulations. For comparison, observed changes found for the in situ observations within the LC are plotted at +2 IP.
Citation: Journal of Physical Oceanography 43, 6; 10.1175/JPO-D-12-0203.1
As in Fig. 7, but for initially homogeneous (H-3DNL) and perturbed (C-3DNL) simulations. For comparison, observed changes found for the in situ observations within the LC are plotted at +2 IP.
Citation: Journal of Physical Oceanography 43, 6; 10.1175/JPO-D-12-0203.1
As in Fig. 7, but for initially homogeneous (H-3DNL) and perturbed (C-3DNL) simulations. For comparison, observed changes found for the in situ observations within the LC are plotted at +2 IP.
Citation: Journal of Physical Oceanography 43, 6; 10.1175/JPO-D-12-0203.1
Plan view and vertical cross section Hovmöller plots of mechanical energy (K and P) are shown in Fig. 12. The simulated response is plotted as a function of time relative to storm passage at the along-track midpoint of the domain (y = 0), in the core of the current jet. These views provide some insight into the energy flux away from the storm track. As compared to the initially homogeneous case (H-3DNL) shown in the left column, the storm-generated OML energy is transported away from the point of peak forcing by the geostrophic current (case C-3DNL, right column). Additionally, it appears in Fig. 12d that within the preexisting current, a significant amount of wave energy propagates downward into the thermocline, very soon after storm passage. This result is suggestive of a wave-trapping mechanism described by Kunze (1985), and further analyzed by Jaimes and Shay (2010), in which near-inertial wave energy impinging on geostrophic flows of sufficient shear vorticity are not allowed free horizontal propagation, resulting in strong downward energy flux.
OML kinetic energy (colored contours) and potential energy (white contours) at the model domain center for (a),(c) H-3DNL case and (b),(d) C-3DNL case. Cross-track plan views vs time are shown in (a),(b) and depth vs time in (c),(d). Simulated storm travels right-to-left, as indicated by the arrow, and the dashed black line is the location of maximum wind stress. Fields are changes from intial conditions. Potential energy contour interval is 5 kJ m−2, and negative changes are white dashed lines.
Citation: Journal of Physical Oceanography 43, 6; 10.1175/JPO-D-12-0203.1
OML kinetic energy (colored contours) and potential energy (white contours) at the model domain center for (a),(c) H-3DNL case and (b),(d) C-3DNL case. Cross-track plan views vs time are shown in (a),(b) and depth vs time in (c),(d). Simulated storm travels right-to-left, as indicated by the arrow, and the dashed black line is the location of maximum wind stress. Fields are changes from intial conditions. Potential energy contour interval is 5 kJ m−2, and negative changes are white dashed lines.
Citation: Journal of Physical Oceanography 43, 6; 10.1175/JPO-D-12-0203.1
OML kinetic energy (colored contours) and potential energy (white contours) at the model domain center for (a),(c) H-3DNL case and (b),(d) C-3DNL case. Cross-track plan views vs time are shown in (a),(b) and depth vs time in (c),(d). Simulated storm travels right-to-left, as indicated by the arrow, and the dashed black line is the location of maximum wind stress. Fields are changes from intial conditions. Potential energy contour interval is 5 kJ m−2, and negative changes are white dashed lines.
Citation: Journal of Physical Oceanography 43, 6; 10.1175/JPO-D-12-0203.1
3) Shear and Richardson number
Within a baroclinic jet (case C-3DNL), a persistent weak shear may be found (Fig. 13), but in its initial state of rest, this shear is far too weak to overcome stratification and initiate vertical mixing. In the H-3DNL case, the shear quickly increases to nearly 2 × 10−2 s−1 during storm passage, as compared to ~1.5 × 10−2 s−1 for the C-3DNL case. However, ~1 IP after passage the shear in the C-3DNL case is reduced to near-nominal levels, while for the H-3DNL case, shear remains elevated and readily observable well after TC passage. Associated with the weaker current shear found for the C-3DNL case, RiB never reaches criticality, when averaged between 0 and 2Rmax, suggestive of particularly weak shear-induced mixing. However, turbulent mixing at the base of the OML does in fact occur because of highly localized reduction of RiB to a critical level.
(left) Shear across OML base and (right) bulk Richardson number for homogeneous and perturbed simulations.
Citation: Journal of Physical Oceanography 43, 6; 10.1175/JPO-D-12-0203.1
(left) Shear across OML base and (right) bulk Richardson number for homogeneous and perturbed simulations.
Citation: Journal of Physical Oceanography 43, 6; 10.1175/JPO-D-12-0203.1
(left) Shear across OML base and (right) bulk Richardson number for homogeneous and perturbed simulations.
Citation: Journal of Physical Oceanography 43, 6; 10.1175/JPO-D-12-0203.1
It has been shown previously that OML cooling can be limited in preexisting current systems as a result of warm-water advection (Jacob et al. 2000). The simulation results here suggest that, in addition to this previously documented heat source, entrainment cooling may be limited by relatively weaker current shear in the presence of a strong preexisting current. These model results are consistent with observations in the real LC (Shay and Uhlhorn 2008), which indicate both cooling and current shear are weaker than observed in previous studies in which the ocean was initially at rest.
4. OML budget
Clearly, the energetic processes are far different because of the presence of the current (Fig. 14). In the standard case with no preexisting current (H-3DNL, Fig. 14a), there initially is a large increase of mean OML KE to around 40 kJ m−2 as a result of wind energy input (SFF peak ~65 kJ m−2). Around one-third of the wind energy input to the OML is lost to turbulent mixing (ENF), and most of the remaining energy is gradually dispersed horizontally away from the track by the near-inertial wave wake (PWH). As expected, a relatively small increase in potential energy (averaged over a wave cycle) because of the OML deepening is realized, since a significant mixed layer has been already established prior to the storm’s arrival. Energy advection is comparatively insignificant.
Simulated mechanical energy budget for the OML averaged between 0 and +2Rmax for (top) initially homogeneous case (H-3DNL) and (bottom) for preexisting Loop Current-like baroclinic jet (C-3DNL). KE values are relative to initial state to aid in comparison between cases.
Citation: Journal of Physical Oceanography 43, 6; 10.1175/JPO-D-12-0203.1
Simulated mechanical energy budget for the OML averaged between 0 and +2Rmax for (top) initially homogeneous case (H-3DNL) and (bottom) for preexisting Loop Current-like baroclinic jet (C-3DNL). KE values are relative to initial state to aid in comparison between cases.
Citation: Journal of Physical Oceanography 43, 6; 10.1175/JPO-D-12-0203.1
Simulated mechanical energy budget for the OML averaged between 0 and +2Rmax for (top) initially homogeneous case (H-3DNL) and (bottom) for preexisting Loop Current-like baroclinic jet (C-3DNL). KE values are relative to initial state to aid in comparison between cases.
Citation: Journal of Physical Oceanography 43, 6; 10.1175/JPO-D-12-0203.1
In stark contrast to the H-3DNL case, the C-3DNL case is far more complex. Two of the most striking differences are the expectedly large energy sink after storm passage owing to advection, and a less obvious overall net source of energy from horizontal pressure work, which is a reversal from the typical sink found in the H-3DNL case. As the storm approaches, at −0.5 IP, V · τwind < 0 because of the opposing wind stress and geostrophic current vectors, and the wind is initially working to decelerate the current. However, to the right of storm track, a developing inertial current begins flowing down gradient (−V· ∇p′ > 0), and therefore the OML acquires KE. These two processes apparently largely cancel prior to the storm center’s arrival, as only a small net change (decrease) in KE from its initial value prior to the arrival of the storm center is found.
As the storm center passes, the stress vector rapidly rotates clockwise and begins to inject energy since V · τwind is now positive, although because of the initial negative input, the net input is some 10% lower than for case H-3DNL. Even though the net wind input is lower, KE increases to a far greater level over the H-3DNL case (60 kJ m−2, ~50% more) owing to the strong pressure work energy source. Soon after storm center passage at around +0.3 IP, but before the wind forcing has ceased, the current vector has rotated to being up gradient, and a very rapid decrease of OML KE begins. This decrease is compounded by strong energy advection [−(V · ∇)K < 0], and vertical energy flux (−pw < 0) out of the OML, as previously shown in Fig. 12d. By +0.5 IP, all energy input by the storm at the location of peak forcing has been removed. The “final” state at ~2 IP after storm passage indicating essentially no change in KE is remarkably consistent with observations taken in the LC at approximately the same time after the passage of Hurricane Lili (Uhlhorn and Shay 2012). Table 3 summarizes the OML mechanical energy budget for each case at +2 IP (averaged over an inertial period, or approximately one wave cycle) in units relative to the net wind energy input for each case.
Mechanical energy budget for H-3DNL and C-3DNL cases, averaged over 1 IP (along-track) and between 0 and 2Rmax (cross-track), at 2 IP after storm passage. Values for each term are relative to wind energy input for each case (+100 units).
Figure 15 shows a schematic representation of OML energetics within the idealized current in response to a tropical cyclone. This approximate budget is developed from the observations and numerical solutions at 2 IP after storm passage, near and immediately to the right of the peak wind forcing. Values are in units of kJ m−2, and this model assumes no background variability in the geostrophic current and supporting mass structure. Lateral eddy diffusion is also ignored, but could be important in such a regime. As observed, a strong current flows perpendicularly left-to-right across the storm track, in response to a pressure gradient directed up-track.
Schematic diagram of approximate OML energetics within a preexisting baroclinic jet forced by a tropical cyclone. Energy budget term quantities (kJ m−2) are based on observations in Lili and numerical simulation snapshots at ~2 IP after storm passage.
Citation: Journal of Physical Oceanography 43, 6; 10.1175/JPO-D-12-0203.1
Schematic diagram of approximate OML energetics within a preexisting baroclinic jet forced by a tropical cyclone. Energy budget term quantities (kJ m−2) are based on observations in Lili and numerical simulation snapshots at ~2 IP after storm passage.
Citation: Journal of Physical Oceanography 43, 6; 10.1175/JPO-D-12-0203.1
Schematic diagram of approximate OML energetics within a preexisting baroclinic jet forced by a tropical cyclone. Energy budget term quantities (kJ m−2) are based on observations in Lili and numerical simulation snapshots at ~2 IP after storm passage.
Citation: Journal of Physical Oceanography 43, 6; 10.1175/JPO-D-12-0203.1
5. Dynamic similarity and parameter sensitivity
The first nondimensional quantity on the RHS of Eq. (13) represents the storm’s intensity, and it is clear that a more intense and/or slower storm elicits a stronger response (Chang and Anthes 1978; Price 1981; Black 1983; Bender and Ginis 2000). The second and third numbers are both length scale ratios: h0f0/Vs is the aspect ratio of the OML depth to the inertial wavelength (since Λ = Vs/f0), and h0/Rmax is the ratio of OML depth to storm forcing scale. The assumptions of a hydrostatic and baroclinic near-inertial response are satisfied provided h0f0/Vs ≪ 1 and h0/Rmax ≫ h0f0Vs, since this latter condition implies Rmax ≪ Λ. These conditions are readily met for propagating TCs, but typically are not applicable in midlatitude, synoptic-scale cyclones. The final nondimensional number (Ug/Vs) represents the strength of the initial pressure gradient.
Previous studies of ocean response (and TC thermal feedback) have focused on the sensitivity to variations in the first three parameters, that is, the forcing intensity and size, location, OML depth, and thermocline stratification (e.g., Price 1981; Black 1983). Generally, storm-induced OML temperature changes are directly proportional to intensity and stratification, and inversely proportional to OML depth. Here, the analysis is extended to examining how the effect of variations in preexisting ocean structure may modulate the mechanical responses (currents and associated shear) for a known forcing. This is accomplished by repeating the C-3DNL case simulations after modifying Ug and Vs in a series of experiments.
a. Variable current Ug
Experiments are repeated with the first three parameters held fixed, based on the observed surface wind forcing and vertical ocean structure (Table 4). Coefficients defining the initial ocean structure h(x, y, z) are modified for each experiment yielding different values of the Ug scale. The value of α in Eq. (7) is changed, and the geostrophic adjustment initialization procedure is executed to produce balanced current jets of specific strength. Similar to the Lili case, the model storm propagates perpendicular to the jet, from the warmer/lighter to the cooler/heavier side, as would typically be expected for a TC. Experimental values are shown in Table 5.
Fixed parameters for response experiments.
Varied parameters for response experiments. For reference, Ug/Vs ≃ 0.12 in Lili.
Simulation results are evaluated in terms of OML currents, both total (V) and ageostrophic (Va), averaged between 0 and +2Rmax as before (Fig. 16). The most striking result is the current response weakening with increasing jet intensity. In the initially homogeneous case (Ug/Vs = 0), the cross-track ageostrophic current ua, peaks at ~1.1 m s−1, and decreases to ~0.5 m s−1 in the strong current jet case (Ug/Vs = 0.2). In addition, the response amplitude generally decays more rapidly for stronger initial currents. Because the initial along-track geostrophic velocity (υg) is zero, the along-track component υ, is similar to υa, indicating the dominant wind-driven current response. However, the rapid decay as a function of increasing jet strength occurs soon after the storm, as for the cross-track (ua) component.
Nondimensional response for five initial current jet intensity cases (Ug/Vs). (top) Total current (u, υ) and (bottom) ageostrophic currents (ua, υa) are shown.
Citation: Journal of Physical Oceanography 43, 6; 10.1175/JPO-D-12-0203.1
Nondimensional response for five initial current jet intensity cases (Ug/Vs). (top) Total current (u, υ) and (bottom) ageostrophic currents (ua, υa) are shown.
Citation: Journal of Physical Oceanography 43, 6; 10.1175/JPO-D-12-0203.1
Nondimensional response for five initial current jet intensity cases (Ug/Vs). (top) Total current (u, υ) and (bottom) ageostrophic currents (ua, υa) are shown.
Citation: Journal of Physical Oceanography 43, 6; 10.1175/JPO-D-12-0203.1
The ocean response to the storm forcing is represented by the OML current; however, to better understand potential thermal feedback to a TC, the current shear across the OML base that is responsible for mixing cooler water from the thermocline is examined. Time series of current shear for each of the five Ug/Vs values is plotted along with observed in– and post-Lili current shear estimates (Fig. 17). A decrease in shear is indicated for increased current jet strength, such that the peak shear is some 25% less for Ug/Vs > 0.1. Based on these results, it appears rather unlikely that a significant shear response could be observed in the LC as little as 1 IP poststorm for storms of Lili’s intensity, size, and speed. These simulations are in reasonably good agreement with observed poststorm shear, which show near nominal background levels as soon as +2 IP (Shay and Uhlhorn 2008). Therefore, a continuous and sustained observation period from 0 to +0.5 IP would be required to clearly document OML response evolution in such a storm versus current configuration.
Current shear response for five initial current jet intensity cases (Ug/Vs).
Citation: Journal of Physical Oceanography 43, 6; 10.1175/JPO-D-12-0203.1
Current shear response for five initial current jet intensity cases (Ug/Vs).
Citation: Journal of Physical Oceanography 43, 6; 10.1175/JPO-D-12-0203.1
Current shear response for five initial current jet intensity cases (Ug/Vs).
Citation: Journal of Physical Oceanography 43, 6; 10.1175/JPO-D-12-0203.1
b. Variable storm speed Vs
Next, the ocean current response to storms of varying motion speed is investigated. Experiments are conducted for the same set of Ug/VS values, but in this case for fixed Ug = 0.68 m s−1 (excluding the Ug/Vs = 0 case corresponding to infinite storm speed). By modifying Vs, two other nondimensional quantities necessarily vary as well (Table 6). Otherwise, the model storm is the same intensity and structure, and the ocean remains unchanged (h0/Rmax = 2.5 × 10−3).
Varied parameters for response experiments in which Vs is varied while holding Ug fixed at 0.68 m s−1.
For the fast storm (Ug/Vs = 0.05) case (Fig. 18), the current response is weakest, with maximum ua ~ 0.7 m s−1, as compared to the slowest storm (Ug/Vs = 0.2) for which a peak ageostrophic near-inertial current of ~1.5 m s−1 results. This contradicts conclusions reached in the simulations of Chang and Anthes (1978), which suggested that maximum current speeds were largely insensitive to Vs in initially horizontally homogeneous regimes. However, the response for the fast storm shows little sign of decay at +2 IP, while for the slow storm, the current is hardly discernible. At +1 IP, higher-frequency oscillations begin to appear for the slower storm speeds (Ug/Vs > 0.1), suggesting enhanced nonlinear interactions between the near-inertial and preexisting currents. This result is consistent with increased Ro for smaller Vs.
Nondimensional response for four storm motion speed cases (Ug/Vs). (top) Total current (u, υ), and (bottom) ageostrophic currents (ua, υa) are shown.
Citation: Journal of Physical Oceanography 43, 6; 10.1175/JPO-D-12-0203.1
Nondimensional response for four storm motion speed cases (Ug/Vs). (top) Total current (u, υ), and (bottom) ageostrophic currents (ua, υa) are shown.
Citation: Journal of Physical Oceanography 43, 6; 10.1175/JPO-D-12-0203.1
Nondimensional response for four storm motion speed cases (Ug/Vs). (top) Total current (u, υ), and (bottom) ageostrophic currents (ua, υa) are shown.
Citation: Journal of Physical Oceanography 43, 6; 10.1175/JPO-D-12-0203.1
Consistent with the simulated currents, the shear response (Fig. 19) suggests stronger peak shear levels for the slowest storms, while progressively becoming weaker as Vs increases and the surface forcing intensity is diminished. The shear remains elevated well above the background near the storm track at +2 IP in these cases, however. Given the initial current jet intensity here of Ug = 0.68 m s−1, which is reasonable comparable to that observed in the LC, storm speeds Vs > ~7 m s−1 cannot generate a significant shear much beyond 1 IP after storm passage. The observed shear levels in Lili, which show weak shear in the poststorm current profiler observations, agree fairly well with these simulated results. Interestingly, the +2 IP response is stronger than the +1 IP level for the slow-storm speed cases, probably a result of amplifying higher-frequency modes.
Current shear response for five initial current jet intensity cases (Ug/Vs).
Citation: Journal of Physical Oceanography 43, 6; 10.1175/JPO-D-12-0203.1
Current shear response for five initial current jet intensity cases (Ug/Vs).
Citation: Journal of Physical Oceanography 43, 6; 10.1175/JPO-D-12-0203.1
Current shear response for five initial current jet intensity cases (Ug/Vs).
Citation: Journal of Physical Oceanography 43, 6; 10.1175/JPO-D-12-0203.1
Comparing experimental simulated response results [Ua/Vs = f(Ug/Us)], as shown in Fig. 20, helps to clarify the effect of a preexisting current. In the experiments for fixed Vs, the geostrophic current has only a minor effect on the peak ageostrophic current magnitude, but weakens it nearly 100 by +2 IP in the strongest initial Ug situations (Fig. 20a). In contrast, the effect of a moderately strong geostrophic current on the ageostrophic response can be mitigated in situations for very rapid Vs, at least >10 m s−1 (Fig. 20b). A slow storm yields a very strong maximum current near the storm’s inner core, but enhanced nonlinearity at large Ro yields highly complicated results.
Nondimensional ageostrophic current response Ua/Vs = f(Ug/Vs) for (a) varied initial OML current (Ug) and (b) varied storm speed (Vs). In (a), storm speed is fixed at Vs = 7.0 m s−1, and in (b), current speed is fixed at Ug = 0.68 m s−1.
Citation: Journal of Physical Oceanography 43, 6; 10.1175/JPO-D-12-0203.1
Nondimensional ageostrophic current response Ua/Vs = f(Ug/Vs) for (a) varied initial OML current (Ug) and (b) varied storm speed (Vs). In (a), storm speed is fixed at Vs = 7.0 m s−1, and in (b), current speed is fixed at Ug = 0.68 m s−1.
Citation: Journal of Physical Oceanography 43, 6; 10.1175/JPO-D-12-0203.1
Nondimensional ageostrophic current response Ua/Vs = f(Ug/Vs) for (a) varied initial OML current (Ug) and (b) varied storm speed (Vs). In (a), storm speed is fixed at Vs = 7.0 m s−1, and in (b), current speed is fixed at Ug = 0.68 m s−1.
Citation: Journal of Physical Oceanography 43, 6; 10.1175/JPO-D-12-0203.1
Other factors not directly considered here may influence solutions, including wind stress and mixing parameterizations, modifications to the radial shape of the surface wind, and higher-order wind asymmetries, to name a few. Neglecting these additional uncertainties, it appears based on these simulations that, in general, a rapidly moving storm would provide the best opportunity to measure poststorm ocean response to a TC and directly relate the response to the forcing. This result applies to a wide range of preexisting ocean regimes, including strong geostrophic current systems.
6. Summary and conclusions
Based on observations obtained during a joint NOAA–NSF field experiment of tropical cyclone air–sea interactions (Shay and Uhlhorn 2008; Uhlhorn and Shay 2012), it has been quantitatively demonstrated that within the Gulf of Mexico Loop Current system 1) the upper ocean tends to cool very little when exposed to intense surface wind forcing of a TC, and 2) the signature near-inertial current wake is not readily observable after TC passage. Temperature and mechanical energy transports by the preexisting current are sufficient to eliminate much of the expected response, thus providing a potential “positive feedback” mechanism in which strong surface enthalpy fluxes may be sustained for a longer period of time within the Loop Current and similar oceanic regimes. With regard to the particular storm studied in this experiment (2002 Hurricane Lili), it is noteworthy that the storm experienced a period of rapid intensification as it traversed the study region intersected by the Loop Current and subsequently rapidly weakened as it encountered the northern Gulf of Mexico (Frederick 2003; Pasch et al. 2004), which is more susceptible to significant ocean cooling by hurricanes, as is typical for major hurricanes on approach to this area (Rappaport et al. 2010).
To help better understand details about the significant observational findings, an idealized numerical model is developed to simulate the mechanical energy response of the mixed layer within a preexisting baroclinic current system and the interactions between the wind stress, directly-forced wind current, and near-inertial current response with the preexisting current. These model simulations clearly reveal the rapid attenuation of storm-generated kinetic energy around the directly forced region, consistent with the observational findings (Uhlhorn and Shay 2012). Furthermore, the simulated interaction among several dynamic processes suggests a highly complex energy decay, as opposed to simple transport by the mean current (i.e., energy advection). Strong wave energy fluxes appear to be a result of coupling between near-inertial and background geostrophic currents and trapping of energy because of Doppler-shifting by the background vorticity.
Implicit in the idealized ocean model developed here is the inability to simulate Loop Current variability independent of the storm forcing over similar time scales. In Part I, observations revealed that the OML kinetic energy decreased from its prestorm level, and it was speculated that the Loop Current varies significantly in magnitude (on the order of the expected response) such that changes in its intensity are simply natural excursions from a mean state. Coincidentally, we also find a small decay in energy relative to the initial condition in these simulations, although this could be some numerical artifact and it remains unclear whether the TC is directly responsible for a spin-down of the Loop Current.
Finally, the results of these series of research studies point to the need for better capturing details of TC–ocean interactions for improved intensity predictions. While storm track forecasts have improved significantly over the past couple of decades, forecasting the future intensity of TCs has proven to be far more challenging. These difficulties have been shown to be in part due to inaccurate specification of energy and momentum exchanges at the air–sea interface. Future work will include a detailed, data-assimilative atmosphere–ocean model study using a coupled Advanced Hurricane Weather Research and Forecasting (WRF)-Hybrid Coordinate Ocean Model (HYCOM) system (Winterbottom et al. 2012), to help understand the competing roles of the ocean and atmospheric environment in Hurricane Lili, which led to its observed rapid intensity fluctuations.
Acknowledgments
EWU acknowledges the support provided by the multi-agency Hurricane Forecast Improvement Project (HFIP). LKS acknowledges support from the NSF (AGS-04-44525), NASA Hurricane Science Program (NASA-NNX09AC47G), the Gulf of Mexico Research Institute Deep-C Project at the Florida State University, and the Department of the Interior’s Bureau of Ocean Energy Management Regulation and Enforcement (BOEMRE) Dynamics of the Loop Current Study (MMS Contract M08PC20052). The project continues to be grateful to the pilots, engineers, and technicians at NOAA’s Aircraft Operation Center (Dr. James McFadden, Chief, Programs and Projects) who make it possible to acquire high quality data during hurricanes through the Hurricane Field Program Intensity Forecasting Experiments (IFEX) and HFIP. Finally, we wish to thank Dr. George Halliwell (NOAA/AOML) and two annoymous reviewers for their helpful comments, which improved the quality of the manuscript.
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