Tropical cyclones (TCs) typically produce intense oceanic upwelling underneath the storm’s center and weaker and broader downwelling outside upwelled regions. However, several cases of predominantly downwelling responses over warm, anticyclonic mesoscale oceanic features were recently reported, where the ensuing upper-ocean warming prevented significant cooling of the sea surface, and TCs rapidly attained and maintained major status. Elucidating downwelling responses is critical to better understanding TC intensification over warm mesoscale oceanic features. Airborne ocean profilers deployed over the Gulf of Mexico’s eddy features during the intensification of tropical storm Isaac into a hurricane measured isothermal downwelling of up to 60 m over a 12-h interval (5 m h−1) or twice the upwelling strength underneath the storm’s center. This displacement occurred over a warm-core eddy that extended underneath Isaac’s left side, where the ensuing upper-ocean warming was ~8 kW m−2; sea surface temperatures >28°C prevailed during Isaac’s intensification. Rather than with just Ekman pumping WE, these observed upwelling–downwelling responses were consistent with a vertical velocity Ws = WE − Rogδ(Uh + UOML); Ws is the TC-driven pumping velocity, derived from the dominant vorticity balance that considers geostrophic flow strength (measured by the eddy Rossby number Rog = ζg/f), geostrophic vorticity ζg, Coriolis frequency f, aspect ratio δ = h/Rmax, oceanic mixed layer thickness h, storm’s radius of maximum winds Rmax, total surface stresses from storm motion Uh, and oceanic mixed layer Ekman drift UOML. These results underscore the need for initializing coupled numerical models with realistic ocean states to correctly resolve the three-dimensional upwelling–downwelling responses and improve TC intensity forecasting.
Tropical cyclones (TCs) obtain their energy from the ocean, and sea surface temperatures (SSTs) have to be sufficiently warm (≥26°C) for TC development and maintenance (Palmén 1948; Malkus and Riehl 1960). As the TC moves over the ocean, the sea surface is cooled off by the combined effects of sensible and latent heat loss to the storm across the air–sea interface, upwelling of cooler thermocline waters underneath the storm’s center that compensates horizontal divergence of wind-driven currents (also named Ekman pumping hereinafter), and turbulent vertical entrainment of cooler thermocline waters across the oceanic mixed layer (OML) base due to wind stirring and vertical shear instability of wind-driven horizontal currents. The cooling of the sea surface results in the reduction of enthalpy fluxes (latent plus sensible heat fluxes) into the TC, leading to a decrease in storm intensity (i.e., negative feedback; Chang and Anthes 1978). When sea surface cooling is strong enough (SSTs typically dropping below the 26°C threshold), the energy source vanishes and the TC decays. Thus, the sea surface cooling response to TC forcing is a key process for storm intensity.
The observed water mass response to category 5 Hurricanes Katrina and Rita (Jaimes and Shay 2009), numerical experiments of the response to TCs in quasigeostrophic oceanic vortices (Jaimes et al. 2011), and large-scale numerical studies of the effects of TCs over the oceans (Zhai et al. 2009; Jullien et al. 2012) indicate that most of the TC-induced turbulent vertical entrainment and associated cooling responses are confined to regions above the thermocline (nearly the upper 200 m). By contrast, cooling associated with wind-driven upwelling can extend throughout the water column (Shay and Elsberry 1987; Shay et al. 1989; Jullien et al. 2012). Vertical advection in upwelling regimes (adiabatic reversible process) brings cooler waters closer to the sea surface during the forced stage (when the storm is overhead), facilitating upper-ocean cooling by wind-driven turbulent vertical entrainment (diabatic irreversible mixing process). Thus, upwelling (or Ekman pumping) is a predominant aspect of the three-dimensional temperature and velocity responses to TC forcing, and the associated SST response during the forced stage impacts enthalpy fluxes into the storm and storm intensity (Yablonsky and Ginis 2009).
The upper-ocean cooling response to TC forcing continues after storm passage (relaxation stage), where horizontal currents over regions that were upwelled during the forced stage undergo a geostrophic adjustment process, and a three-dimensional, baroclinic, near-inertial current response is initiated throughout the water column (Geisler 1970; Gill 1984; Shay et al. 1989). The rotation of these horizontal currents at near-inertial frequencies produces near-inertial pumping (Gill 1984), and vertical shear instability of these currents becomes the dominant cooling mechanism of the upper ocean in the wake of the storm (e.g., Price 1981; Shay et al. 1989, 1992, 2000; Jacob et al. 2000; Jaimes and Shay 2009, 2010; Jaimes et al. 2011). This study is focused on the wind-driven upwelling flow during the forced stage (Ekman pumping), rather than on near-inertial pumping and shear instability in the wake of the storm.
The classical description of upwelling induced by an intense TC considers an energetic upwelling flow confined within a distance of twice the storm’s radius of maximum winds from the center and weak downwelling of the displaced warm water over a broad area outside the upwelled region (O’Brien and Reid 1967; Price 1981; Jullien et al. 2012). The importance of the upwelling flow and ensuing cooling of the sea surface under the storm’s center is well established (O’Brien and Reid 1967; Geisler 1970; Price 1981; Greatbatch 1985; Yablonsky and Ginis 2009). However, little attention has been given to the downwelling flow. Contrary to predominant ideas that the downwelling flow is broad and weak and that the structure in the curl of the wind stress determines horizontal structures in upwelling and downwelling regimes, dominant deepening (warming) of upper-ocean thermal structures over warm anticyclonic mesoscale features was reported for Hurricanes Wilma (Oey et al. 2006) and Rita (Jaimes and Shay 2009) and was reproduced in numerical experiments of the adiabatic ocean response to Hurricane Katrina (Jaimes et al. 2011). In the Katrina and Rita cases, the upwelling response was better explained by the curl of wind-accelerated, prestorm geostrophic currents rather than by just the curl of the wind stress, in agreement with theoretical developments that consider the interaction of a uniform wind stress (with no curl) and a quasigeostrophic oceanic vortex (Stern 1965).
Over the past two decades, an increasing number of observations and numerical studies have shown that underlying, warm, oceanic mesoscale features prevent significant cooling responses of the sea surface, and TCs often experience rapid intensification and attain major status over these persisting warm regimes (e.g., Emanuel 1999; Shay et al. 2000; Lin et al. 2005, 2009; Wada and Chan 2008; Mainelli et al. 2008; Jaimes and Shay 2009; Jaimes et al. 2015). Thus, elucidating upwelling and downwelling responses in background, geostrophic, oceanic flow is important to better understanding the intensification of TCs over warm oceanic features. Of particular interest are the following questions: How fast is the upwelling response in geostrophic flow? What is the dominant vorticity balance during the direct ocean eddy–TC interaction? What is the role of geostrophic vorticity (structure and strength) in upwelling and downwelling responses? What is the role of the translation speed of the storm in upwelling and downwelling responses over eddy-rich ocean regimes?
As part of the National Oceanographic and Atmospheric Administration (NOAA) Intensity Forecasting Experiment (IFEX), a new case of predominant downwelling responses to TC forcing was observed over the Gulf of Mexico’s (GoM) mesoscale eddy features during the intensification of TC Isaac (2012) from tropical storm (TS) to a category 1 hurricane (H1). In this paper, these observed downwelling responses are analyzed in the context of upwelling theories that ignore or consider the contribution from background geostrophic oceanic flow. Field experiment, measurements, and methods are described in section 2. Isaac’s characteristics and development, theoretical predictions (air–sea parameters) of the ocean response in an initially quiescent ocean, and observed upper-ocean thermal responses are discussed in section 3. Based on water mass analysis, observed upwelling and downwelling regimes are isolated from the full, upper-ocean temperature response, and their structures at the thermocline are described in section 4. The influence of the background geostrophic flow on upwelling and downwelling responses is discussed in section 5 in the context of Stern’s (1965) theory, and a TC-driven pumping velocity in geostrophic flow is derived from the dominant, time-dependent vorticity balance. A discussion and concluding remarks are presented in section 6.
The objectives of this paper are to show that upwelling and downwelling responses can be very fast over geostrophic oceanic features, that structure and strength in the geostrophic vorticity field play a key role in the dominant vorticity balance in these upwelling and downwelling regimes, and that the surface stress from storm motion contributes to the dominant vorticity balance during upwelling and downwelling responses over geostrophic flow.
2. Methodology and data resources
a. Airborne experiment and measurements
Upper-ocean three-dimensional thermal, salinity, and current structures were measured with airborne expendable bathythermographs (AXBT), conductivity–temperature–depth sensors (AXCTD), and current profilers (AXCP) deployed from six NOAA research aircraft flights that were conducted before, during, and after the passage of Isaac over the eastern GoM. In addition to ocean probes, global positioning system dropsondes (or dropwindsondes; Hock and Franklin 1999) were launched to measure atmospheric properties such as wind speed and direction, air temperature, and relative humidity. In total, 376 airborne profilers were deployed, specifically 121 AXBT, 56 AXCTD, 41 AXCP, and 158 atmospheric dropwindsondes (Table 1). During the 16H1 and 28H1 flights (see Table 1 for nomenclature), failures rates for the AXCP were unusually high. These failures were associated with hardware problems, including radio frequency (RF) transmission where the transmitters did not turn on (no RF quieting), low RF signals, and profilers hanging up in the airborne canisters (e.g., floaters). Some of these problems were resolved during the experiment. For example, note that the failure rate was 25% during the 30H1 flight. After detailed investigation of these failures in collaboration with the AXCP manufacturer, success rates of about 90% were recently obtained for AXCPs deployed in Hurricane Edouard in September 2014.
Research flights in Isaac on the NOAA aircraft had durations of 8 to 10 h. During pre- and poststorm flights, the aircraft flew at ~1700 m at an indicated airspeed between 90 and 95 m s−1. During in-storm flights, the aircraft flew at ~3000-m altitude at an airspeed of ~110 m s−1. A key objective of these flights was to measure the hurricane heat potential (Leipper and Volgenau 1972) or ocean heat content (OHC) relative to the 26°C isotherm depth h26, given by
where ρ0 = 1025 kg m−3 is the reference seawater density; cp is the specific heat at constant pressure (4.2 kJ kg−1 K−1); T(z) is the upper-ocean temperature structure measured by the expendable profilers; and H is the sea surface. The 26°C isotherm is used because it is the temperature assumed for tropical cyclogenesis (Palmén 1948). OHC is a useful parameter to estimate upper-ocean thermal energy available for TC development and maintenance.
OHC structures measured during these research flights are presented in Fig. 1 (only the geographic points of quality-controlled ocean profiles obtained from this experiment are shown). Without knowing the genesis of Isaac, the prestorm flight (16 August) was designed to sample both the warm-core eddy (WCE) that had recently separated from the Loop Current (LC) and the cyclonic eddy that developed between the WCE and LC during this shedding event (Fig. 1a). Because GoM hurricanes often experience rapid intensification over WCEs and the LC bulge (i.e., Shay et al. 2000; Jaimes and Shay 2009), there was interest in sampling this WCE in anticipation of potential interaction with a TC. The four in-storm flights (26 to 28 August) were designed to sample Isaac’s structure and underlying ocean features over the storm’s track (Figs. 1b–e). The poststorm flight (30 August) was designed to measure the ocean response on the right side of the storm’s track (where the more energetic response is usually observed), including the DeSoto Canyon and the east side of the WCE (Fig. 1f).
These flights sampled to as deep as 1500 m, to provide the evolving oceanic variability during Isaac. Specifically, AXBT data were acquired to ~400-m depth, compared to 1000 and 1500 m for AXTCD and AXCP data, respectively. Expendable profilers decelerate with depth (Johnson 1995) and shallow probes typically have depth errors ranging from 2% to 5% (Boyd 1987). These depth errors were always better than the ±5% required by Navy standards (Bane and Sessions 1984). Despite differing fall rates, thermal structures measured by different expendable ocean probes are consistent (Shay et al. 2011). The accuracy of the thermistor is ±0.12°C for AXCTDs (Johnson 1995) and ±0.2°C for AXBTs and AXCPs (Boyd 1987). The AXCTD salinity accuracy is 0.03 mS cm−1 or 0.05 practical salinity units (psu) (Shay et al. 2011). Regression analyses between shipboard and aircraft CTD measurements conducted during the Eastern Pacific Investigation of Climate experiment revealed mean temperature and salinity differences of 0.2°C and 0.05 psu, respectively (Shay and Brewster 2010). Thus, the accuracy and resolution of the AXCTDs is sufficient to determine the salinity structure and resolve the differing water masses in the GoM (Jaimes and Shay 2009). AXCP root-mean-square velocity errors are about 1–2 cm s−1 over 3-m vertical intervals in nonstorm deployments (Sanford et al. 1987). These velocity errors are well below upper-ocean current signals of more than 1 m s−1 in the LC domain and WCEs. Temperature (AXBT, AXCP, and AXCTD), salinity (AXCTD), and current (AXCP) profiles were smoothed to form 2-m vertical resolution profiles. Details on the NOAA P-3 data acquisition system, and the quality control of airborne oceanographic data, are discussed in Shay et al. (2011).
b. Altimeter products
Altimeter-based daily maps of surface height anomaly (SHA), OHC, OML, and the 20°C isotherm depth from the Systematically Merged Atlantic Regional Temperature and Salinity (SMARTS) climatology (Meyers et al. 2014) are used to compute surface geostrophic currents needed to evaluate Stern’s (1965) theory and to verify that the warm feature that extended underneath Isaac’s right side in the 28H1 flight was robust (only one quality-controlled ocean profiler was obtained in this feature; Fig. 1d). The computation of these space-based measurements is described in detail in Shay and Brewster (2010) and more recently in Meyers et al. (2014).
The time period for a satellite altimeter to pass again over the same geographic point to measure SHA is 10 days or more depending on the satellite. However, different SHA points in a mesoscale feature can be measured over contiguous ground tracks in subsequent days from different satellites. Because a 10-day temporal scale is impractical for hurricane applications, SMARTS was developed to produce objectively analyzed (in space and time), satellite-based daily images of SHA, OHC, OML, and the 20° and 26°C isotherm depths. The objective analysis (OA) scheme of Mariano and Brown (1992) was used in SMARTS to interpolate unevenly spaced SHA data from multiple altimeters to a common grid; this OA scheme is based on a parameter matrix algorithm that grids nonstationary fields using time-dependent correlation functions. SHA data from 5 days before and 5 days after the date of interest were used to ensure basinwide coverage by at least the 10-day altimeters (only two altimeters, NASA Jason-1 and Jason-2, were active during Isaac). For each data point, the OA used 20 influential data points determined by the correlation model from Mariano and Brown (1992). Feature drift velocities were estimated as a function of latitude; the entire SHA dataset was reanalyzed to make adjustments in feature structure and position using these estimated drift velocities (Meyers et al. 2014). SMARTS values were compared to more than 60 000 thermal profiles from XBT transects, Argo profiling floats, PIRATA moorings, and aircraft expendables (Meyers et al. 2014). Daily products from the real-time version of SMARTS are used operationally at the National Hurricane Center (NHC) and the National Environmental Satellite, Data, and Information Service (NESDIS) (Shay et al. 2012). The reanalyzed version of SMARTS is used in this study.
Based on Stern’s (1965) theory, the role of background geostrophic currents in the dominant OML vorticity balance during the upwelling response to Isaac is evaluated in section 5. Geostrophic vorticity ζg in the OML is a key element in this theory. Because direct measurements of in-storm OML currents obtained in this experiment are insufficient to estimate ζg, the required geostrophic vorticity is estimated from altimeter-based surface geostrophic currents. Daily maps of SHA from SMARTS were obtained for August 2012. Following Jaimes and Shay (2010), the absolute sea surface height H was reproduced for the entire GoM by adding the SHA fields to the Combined Mean Dynamic Topography Rio05 (CMDT Rio05), which represents the mean sea surface height above a geoid computed over a 7-yr period (1993–99) and results from the ocean mean geostrophic currents (Rio and Hernandez 2004). Surface geostrophic current vectors Vg = Ugi +Vgj were calculated from H with Ug = −(g/f)∂H/∂y and Vg = (g/f)∂H/∂x (zonal and meridional velocity components, respectively). The vertical component of surface geostrophic vorticity is ζg = ∂Vg/∂x − ∂Ug/∂y, where g is the acceleration of gravity, and f is the Coriolis frequency.
c. Wind stress
Wind fields used in this investigation are from two NOAA products: Hurricane Research Division H*Wind data and NHC’s 6-h best-track data. H*Wind blends wind measurements in TCs from a variety of observation platforms into high-resolution, OA fields of standard 10-m surface winds (Powell et al. 1996). H*Wind vectors, defined as U10 = U10i +V10j, are used to calculate the wind stress vector τ = τxi + τyj, where U10 and V10 are the 10-m zonal and meridional wind vector components, τx = ρaCDU10|U10| and τy = ρaCDV10|U10| are zonal and meridional wind stress vector components, ρa is the air density, and CD is the drag coefficient; τ is used in calculating the curl of the wind stress and associated Ekman pumping (section 4) as well as in evaluating Stern’s (1965) theory (section 5). In the case of NHC best-track data, the reported 10-m maximum wind speed Umax is used in calculating the maximum wind stress ; τmax is used in characterizing Isaac’s maximum strength over the storm’s track (section 3).
The computation of τ and τmax considers the observed saturation of CD at wind speeds between 25 and 35 m s−1 (Powell et al. 2003; Donelan et al. 2004; Shay and Jacob 2006; French et al. 2007; Sanford et al. 2007; Vickery et al. 2009). In this context, the expression used in this research to compute CD is based on recent results from field experiments in hurricanes (Powell et al. 2003; Black et al. 2007), where CD is given by
where Us is either |U10|(H*Wind data) or Umax(NHC best-track data).
3. Storm characteristics and upper-ocean response
a. Hurricane Isaac
Isaac originated from a tropical wave that moved off the coast of Africa on 16 August, becoming a TS at 1800 UTC 21 August to the east of the Lesser Antilles (Berg 2013). After 5 days of westward and northwestward motion over the Caribbean, Isaac moved over the Florida Straits on 26 August, entering the southeastern GoM on 27 August as a TS (Figs. 1b,c). Isaac gradually strengthened while it was slowly moving northwesterly over the GoM, becoming a hurricane around 1200 UTC 28 August. Note that Isaac attained H1 status over a region where the storm’s center was flanked by warm ocean features, where OHC levels were between 80 and 120 kJ cm−2 (Fig. 1d). A midlevel blocking ridge caused the considerable reduction in Isaac’s translation speed Uh as it approached the coast of Louisiana (Berg 2013). During this slowing down stage (Uh was between 3 and 4.5 m s−1), Isaac became stronger and larger, attaining values in radius of maximum winds Rmax between 60 and 95 km (Fig. 2). Isaac made landfall as H1 on the mouth of the Mississippi River around 0000 UTC 29 August with maximum sustained winds of ~36 m s−1 (Berg 2013).
b. Parameters of the ocean response
A theoretical framework for the observed ocean response is defined by assuming an ocean initially at rest (i.e., no background geostrophic flow) and by estimating key air–sea parameters of the ocean response to a hurricane moving at speed Uh; Price (1983) derived these parameters by scaling the equations of motion and continuity. The parameters of interest are vertical advection velocity or upwelling velocity (WE = τmax/ρ0Uh; also referred to hereinafter as the undisturbed Ekman pumping); vertical displacement of isopycnals (η = −τmax/ρ0fUh); OML horizontal velocity response to the wind stress or undisturbed Ekman drift velocity (UOML = τmaxRmax/ρ0hUh, where h is the OML thickness); Froude number (Fr = Uh/c1; c1 is the phase speed of the first baroclinic mode at the thermocline); and frictional Rossby number (Rob = UOML/fRmax).
Estimated scaling values for upwelling velocity and isopycnal displacements are between −3.3 and −4 m h−1 and −13.5 and −16 m (the convention here is that negative values are for upwelling regimes), respectively (Figs. 3a,b). The estimated maximum horizontal OML velocity response is 1.8 m s−1 (Fig. 3c). Note that UOML, Fr, and Rob are resolved only over the storm’s track segment, where ocean measurements were available from in-storm flights 27H2 and 28H1. Values of Fr ≥ 2 (Fig. 3d) indicate that the storm moved faster than the phase speed of the first baroclinic mode at the thermocline; thus, a baroclinic near-inertial response is expected in the wake of the storm (Geisler 1970). The average value of Rob ~ 0.23 for the observational time period (Fig. 3e) indicates that the velocity response was dominated by rotational effects rather than by frictional horizontal advective processes.
c. Upper-ocean thermal response
A striking aspect of the observed ocean response is the increase in OHC underneath Isaac’s flanks during its intensification to H1 (cf. Figs. 1c and 1d). Considering the time difference Δt of about 12 h between flights 27H2 and 28H1 (Table 2), the rate of increase in OHC over regions beyond a distance of 2Rmax from the storm’s center was between 2 and 6 kW m−2 underneath the storm’s right side and between 2 and 8 kW m−2 over the WCE that extended below its left side (Fig. 4). By contrast, the rate of decrease in OHC beneath the storm’s inner-core region (within a distance of an Rmax from the storm’s center) was between −2 and −5 kW m−2 or 2 to 5 times the magnitude of sea surface heat losses by enthalpy fluxes of O(−1) kW m−2 observed in intense TCs (Shay et al. 2000; Oey et al. 2006; Shay and Uhlhorn 2008; Lin et al. 2009; Jaimes et al. 2015). Assuming a sea surface heat loss by enthalpy fluxes of O(−1) kW m−2, the cooling regime underneath the storm’s center was more likely caused by upwelling of cooler thermocline waters and wind-driven vertical mixing of these waters with OML waters, as found elsewhere (e.g., Price 1981; Jacob et al. 2000; Jacob and Shay 2003; Shay and Uhlhorn 2008; Jaimes and Shay 2009, 2010; Jaimes et al. 2011; Uhlhorn and Shay 2012).
Because the combined effect of enthalpy fluxes into the storm across the air–sea interface and vertical entrainment across the OML base typically produces a net upper-ocean cooling, the hypothesis here is that the predominant warming tendency observed over the flanks of the storm’s track was more likely caused by enhanced wind-driven downwelling flows in underlying anticyclonic features. This hypothesis is explored in detail in section 4 in terms of directly observed isotherm fluctuations. Notice that this warming response (OHC increase) was between 40% and 80% more intense than the cooling response that occurred under the storms’ center (Fig. 4). Deepening of upper-ocean thermal structures over oceanic anticyclonic features during TC passages was reported for Hurricanes Wilma (Oey et al. 2006) and Rita (Jaimes and Shay 2009) and was reproduced in realistic numerical experiments of the adiabatic ocean response to Hurricane Katrina (Jaimes et al. 2011).
The development of the in-storm warm anomaly below Isaac’s right side over a 12-h interval is remarkable (Figs. 1c,d). Because only one quality-controlled in situ measurement was obtained at the core of this feature (Fig. 1d), satellite-based OHC measurements are used to gain further insight on this warming response. The latter measurements indicate that before the passage of Isaac (20 to 26 August), the region over which the warm anomaly developed was occupied by a smaller WCE (Figs. 5a–c). As this smaller WCE started to interact with Isaac on 27 August, its OHC levels were reduced in relation to prestorm conditions (Figs. 5c,d). Similar to the in situ observations, the satellite-based OCH levels over the right side of the storm’s track were increased from 27 to 28 August (Figs. 5d–f). Thus, the in-storm warm anomaly below Isaac’s right side presumably developed over the smaller WCE because of the combined effects of enhanced downwelling and eddy intensification (vortex stretching) by the curl of the wind stress (sections 4 and 5). Note that the distinctive aspects of the warming responses from in situ and satellite-based observations are consistent (Figs. 4, 5f). However, the response from the latter product is weaker. The coarse resolution of raw altimeter data, as well as the limited temporal resolution of the OA SMARTS products (24 h), presumably missed the intense and fast observed in situ OHC response. Investigating the differences between SMARTS and in situ data is beyond the scope of this research (see Meyers et al. 2014).
4. Upwelling and downwelling responses
a. Vertical structure in cooling and warming responses
The 12-h temperature responses over the left, central, and right regions of the storm are presented in Fig. 6. Moderate OML cooling (difference in temperature profiles) of less than 0.5°C occurred over the left and central regions, where SSTs of more than 29°C prevailed during Isaac’s passage (Figs. 6a,b). By contrast, OML deepening of about 80 m produced a layer thickness of nearly 125 m in the small anticyclonic feature that developed underneath the storm’s right side (Fig. 6c); despite this large OML deepening, indicative of vertical mixing, OML cooling was of O(0.5)°C, and the layer temperature remained above 28°C to as deep as 125 m. These weak, upper-ocean cooling responses extended to as deep as 120, 130, and 40 m underneath the left, central, and right regions of the storm, respectively. Warming responses were developed below these depth levels. Because this subsurface warming occurred away from the OML base and was more intense than OML cooling, it was not necessarily associated with the subsurface warming that usually develops below OML bases when shear-induced vertical mixing entrains warm OML waters into the thermocline. These warming responses were presumably associated with downwelling regimes that developed over a predominantly anticyclonic background eddy field.
b. Isolating upwelling and downwelling regimes
Data from AXCTD probes deployed at about the same radial distance of probes from Fig. 6 are used in characterizing the water mass response (Fig. 7). In the WCE (left side of the storm, red profile), the temperature–salinity (T–S) distribution during Isaac was essentially the same as that observed in these features in the absence of wind forcing (i.e., climatological conditions, green profile); differences in the T–S structure occurred principally in surface waters (above h26), where temperature was cooler and salinity higher during Isaac’s passage. Beneath the storm’s center (black profile), the GCW was fresher during Isaac, presumably by vertical entrainment of freshwater from precipitation. This freshwater anomaly was larger over surface waters where the difference in salinity was about −0.5 psu in relation to climatological conditions (yellow profile). Underneath the storm’s right side, the water mass response was similar to that observed under the storm’s center. However, the surface freshwater anomaly was twice as large, reaching values of about −1 psu (blue profile). Independent of the storm’s region, the water mass change was confined to waters above the 20°C isotherm depth h20, which is the approximate thermocline depth in the GoM (Shay et al. 1998; Jaimes and Shay 2009). Thus, warming below the thermocline (or below h20) was not associated with wind-driven vertical mixing.
Considering the water mass analysis, the temperature response can be separated into a diabatic surface regime and an adiabatic interior regime. The rate of change in these regimes over a 12-h interval is presented in Fig. 8 for the selected geographic points of Fig. 6. Under the combined cooling effects of sea-to-air fluxes of enthalpy, wind-driven vertical mixing, and upwelling, isotherms above h20 shallowed in the region underneath the storm’s center at a rate of −0.5 to −1 m h−1 (black line) or between 14% and 29% of the estimated upwelling velocity of about −3.5 m h−1 for an eddy-free ocean (cf. Figs. 3a and 8). In the WCE (red line), a diabatic cooling regime was developed above h26, where the thermal structure shallowed at a rate of about −1 m h−1. In the two anticyclonic features (red and blue lines), the predominant downwelling of isotherms masked the diabatic cooling response above h20. In the adiabatic regimes (below h20), isotherms downwelled at 1 to 3.5, 3 to 4, and 5 to 7.5 m h−1 under the storm’s center, WCE, and small anticyclone, respectively. In the latter feature, the vertical isotherm displacements were nearly twice the estimated upwelling velocity for quiescent ocean conditions. These intense downwelling velocities explain the rapid increase in OHC along the storm’s periphery (Fig. 4).
c. Structure in upwelling and downwelling regimes
Pure upwelling and downwelling regimes (assumed adiabatic) are described in terms of the rate of change in h20 during Isaac’s intensification to H1 (Fig. 9a). The observed upwelling flows were confined within a distance of an Rmax from the storm’s center, reaching maximum vertical displacements of about −30 m in a 12-h interval (2.5 m h−1) or more than twice the theoretical estimate of about −14 m for quiescent ocean conditions (see Fig. 3b and Table 3). By contrast, maximum observed vertical displacements of about 60 m in 12 h (5 m h−1), or twice the maximum vertical displacements in upwelled regions, occurred over the downwelling regime within the WCE. The background mesoscale eddy field presumably defined these contrasting responses because they cannot be explained by the structure of just the wind stress curl that predicted a weak upwelling response (Ekman pumping) over regions of observed maximum downwelling responses (Figs. 9a,b).
The vertical structure of the thermal response is presented in Fig. 10. With the exception of the large WCE, initial thermal structures were essentially flat above h20 during the 27H2 flight (Figs. 10.1a–c). Rather than being associated with the storm-generated upwelling, the subsurface cool anomaly that extended below h20 during this flight was presumably related to a frontal cyclone that was developing along the WCE’s edge (following the recent shedding of the WCE from the LC). Isotherms became substantially sloped during the 28H1 flight (Figs. 10.2a–c), strengthening the frontal cyclone, WCE, and smaller anticyclone (a similar intensification of the LC eddy field was observed during Hurricane Rita; see Jaimes and Shay 2009). With the exception of near-surface waters at transect b (Fig. 10.3b), the maximum upwelling responses did not necessarily occur directly underneath the storm’s center, as waters mostly upwelled over the storm’s left side (from approximately Rmax = −1.5 to 0; Figs. 10.3a–c) or over the frontal region between the WCE and the developing cyclone (where horizontal and vertical temperature gradients tightened). These upwelled waters produced maximum adiabatic cooling of −1° to −2°C below the initial h20 (Figs. 10.3a–c). By contrast, downwelling produced maximum adiabatic warming between 2° and 3°C below h20 and beyond a distance of 2Rmax from the storm’s center.
Overall, Isaac induced a predominantly downwelling regime over the oceanic eddy field during its intensification to H1 (12-h interval). This enhanced downwelling response, in combination with the initial warm and deep thermal structure (high OHC levels of more than 80 kJ cm−2), maintained SSTs above 28°C over most of the storm’s central region during Isaac’s intensification (Figs. 10.2a–c). These observations are inconsistent with O’Brien and Reid’s (1967) results, where stronger upwelling under the storm’s center and weaker and broad downwelling outside the storm’s center are predicted over an ocean initially at rest (i.e., no background ocean eddy features).
5. Influence of the background flow
a. Theoretical framework
The impact of the background oceanic eddy field (Fig. 11a, assumed in an initial geostrophic balance) on the upwelling response is evaluated based on Stern’s (1965) theory. The total fluid flow is separated into two components: the wind-driven component (hereinafter named the frictional component and denoted by subscript b) and the background geostrophic component (hereinafter denoted by subscript g). More specifically, the total horizontal velocity vector is V = Vg + Vb, where Vg = Ugi + Vgj and Vb = Ubi + Vbj; and the total vertical velocity (upwelling or pumping velocity) is w = wg + wb. In this context, and are the geostrophic and the frictional vorticity, respectively, and k is the unit vector in the vertical direction.
b. Vorticity balance of the frictional flow component in the OML
The vorticity balance of the frictional component in the OML during the interaction of the wind stress and a quasigeostrophic oceanic vortex is given by (Stern 1965)
where θ is the turbulent stress vector (at the sea surface, θ is merely the wind stress vector; see below). The terms Ti in (2) are
By using a scale of (Table 4),1 it follows that |ζg| ~ 0.18f and . Thus, by neglecting the term in (2), and ignoring the terms Ti based on the scaling analysis from Table 5, the dominant vorticity balance of the frictional flow component in the OML is assumed to be
For the case of a uniform wind stress (Stern 1965), the first term on the right-hand side of (3) vanishes as . However, in the case of TCs, this term must be retained because . The term on the left-hand side of (3) is vortex stretching, and the first and second terms on the right-hand side represent turbulent stresses and horizontal advection of geostrophic vorticity by the frictional velocity, respectively. From a physical perspective, the vertical shear in Vb will cause the Ekman flow to advect ζg more rapidly at the sea surface than at the bottom of the OML, tending to tilt the vortex away from the vertical in an amount proportional to the shear in Vb. However, for low Rog (strong constrain of rotation), the vortex in the OML will tend to maintain vertical rigidity by developing vertical velocities that balance the horizontal advection of ζg by the frictional velocity Vb (Stern 1965). That is, vortex stretching will compensate the Ekman drift in an amount proportional to the horizontal gradient in ζg.
The frictional vorticity scale used in the scaling analysis that yielded (3) is valid for cases where (Stern 1965). Here, Rob ~ 0.03 ≪ 1 (Table 4).2 With regards to the size of the error in (3), note that the two largest omitted terms are and T1; their respective magnitudes are O(Rog) and O(Rob). Thus, ignoring these terms in (3) introduces a combined error O(Rog + Rob) in estimates based on this equation. Considering the values of Rog and Rob from the cases of Isaac, as well as Katrina and Rita (see the appendix), the estimated error is between 10% and 25%. More cases need to be analyzed in the future to more accurately evaluate the size of this error. Note that most of the Ti terms (with exception of T4) and the frictional vorticity scale consider the effect of the background flow through Rog or Vg. Because the horizontal scale Rmax appears in both the numerator and denominator of the ratios , changing the horizontal scale does not impact the scaling analysis (Tables 4 and 5). In the case of the interaction between a uniform wind stress and a quasigeostrophic vortex, Stern (1965) used the criterions Rog ≪ 1 and Rob ≪ 1 to eliminate the terms Ti in (2).
c. Frictional pumping velocity
Now integrate (3) from z = −h (bottom of the OML) to z = 0 (sea surface)
By using the undisturbed Ekman relation
in (4), as well as the boundary conditions , , (where τ is the surface wind stress vector), and , the frictional pumping velocity at the free surface is given by
The velocity is not just associated with the curl of the wind stress [i.e., undisturbed Ekman pumping, first term on the right-hand side of (5)], but also with the curl of background geostrophic currents accelerated by the Ekman drift [“nonlinear” Ekman pumping, second term on the right-hand side of (5)]. Note that the undisturbed Ekman pumping alone cannot reproduce the observed upwelling structure in Isaac (Fig. 9b). In an investigation of the Ekman divergence in an oceanic geostrophic jet, Niiler (1969) derived an expression similar to (5) by taking the divergence of the Ekman velocity equation as modified by geostrophic relative vorticity.
d. Vorticity balance of the geostrophic flow component in the OML
In this Eulerian description of the flow, the term represents transport of ζg by the total horizontal velocity across the lateral boundaries of an Eulerian control volume. Because the interest is evaluating the effects of the local surface wind stress on the local geostrophic flow, the exchange of geostrophic vorticity with the environment is ignored in the present treatment. Thus, by making , and by vertically averaging (6) over the OML, we get
Considering the frictional and geostrophic vertical velocity components, the requirement is that at the sea surface. That is, (Stern 1965). Thus, using as the boundary condition at the free surface and as the boundary condition at the bottom of the OML in (7), the time-dependent vorticity balance of the geostrophic flow in the OML is given by
According to (7), the change in ζg over the OML is driven by an active boundary condition at the free surface, , and a passive boundary condition at the bottom of the layer, . Thus, the coupling between the geostrophic and frictional vertical velocity components at the free surface, (Stern 1965), drives the change in ζg over the OML. The time scale over which this coupling occurs is or the time interval for a storm moving at speed Uh to cover a distance Rmax over the ocean eddy. That is, the frictional boundary condition acting at the free surface causes the change in ζg over the OML during the time interval that the storm is overhead; the passive boundary condition determines the ensuing forcing onto the thermocline. The interaction of the Ekman drift with the horizontal gradients in ζg significantly reduces the time scale of in (5) for this coupling to be possible.
e. TC-driven pumping velocity in geostrophic flow
At a fixed point in the ocean (Eulerian framework) under the influence of a storm moving in the y direction (along-track motion in a storm coordinated system), the local rate of change can be approximated as (Price 1983). Noting that −dh/dt is the vertical velocity at the bottom of the OML (−dh/dt = 0 for a rigid mixed layer), the pumping velocity at the top of the thermocline is defined as . Using these definitions in (8), the TC-driven pumping velocity is given by
For quiescent ocean conditions (ζg = 0), the term in parentheses is zero, and (9) becomes the classical unperturbed Ekman pumping velocity. By contrast, in the case of a uniform wind stress (), (9) predicts a vertical velocity driven by the horizontal transport of ζg by the Ekman drift (cf. Stern 1965; Morel and Thomas 2009). In this context, intense TC-driven pumping velocities can be expected even over regions where vanishes (away from the storm’s eyewall), as long as the background geostrophic vorticity field is energetic enough. Note that the operator assumes a constant translation speed of the storm Uh and accounts for time evolution in (9).
Because direct OML current measurements obtained in Isaac are limited, ws in (9) is computed following an approach by Jaimes and Shay (2009) that considers τ from the H*Wind product and ζg derived from altimetry-based surface geostrophic currents Vg (section 2b), where Vg is a proxy to OML currents; OML depths h are from SMARTS. One limitation of this approach is that the time scale of 1 day, inherent to these OA satellite-based data, could be missing some aspects of the observed rapidly changing upper-ocean response (e.g., Fig. 9a). A second limitation is that only two altimeters were active during the time period of Isaac (section 2b), which impacted resolving the mesoscale eddy velocity field more accurately. Figure 11a shows the altimetry-based eddy field on 28 August; this daily eddy field is used in estimating ws.
Vertical velocities computed with (9) are presented in Fig. 12. The horizontal structure in ws resembles the salient aspects of the observed upwelling–downwelling response to Isaac (cf. Figs. 9a and 12). Similar to direct measurements, the stronger downwelling response occurs over the anticyclonic features away from the storm’s center, in particular over the large WCE. These results support the hypothesis that (8) represented the dominant time-dependent vorticity balance of the geostrophic flow component in the OML during the upper-ocean response to Isaac.
f. Parametric TC-driven pumping velocity in geostrophic flow
or, by rearranging terms and using the time scale ,
where δ = h/Rmax is the aspect ratio, and WE = Wb and are undisturbed Ekman pumping and drift velocities, respectively (section 3b, Fig. 3, and Table 4). Price (1983) derived the latter two parameters for quiescent ocean conditions. For Rog = 0 (no background geostrophic flow), Ws in (10) is merely the undisturbed Ekman pumping. By contrast, in the case of a uniform wind stress (WE = 0), (10) predicts a vertical velocity that compensates the local frictional horizontal transport of ζg (cf. Stern 1965).
In this context, the TC-driven pumping velocity at the bottom of the OML is expected to increase with the strength of the background flow (measured by Rog), toward the equator (smaller f), and with an increasing OML depth h, as found in previous theoretical developments for less intense wind forcing events (Cushman-Roisin 1994). In addition, Ws is proportional to the strength in the total surface stress (Uh + UOML). This is a key result in the context of Stern’s (1965) theory. That is, to maintain vertical rigidity in the background OML flow (assumed in an initial quasigeostrophic balance), the vertical advection velocity balances frictional horizontal advection of ζg. Notice that the sign of ζg impacts the horizontal structure in Ws (upwelling and downwelling regimes), and the relevant length scale is related to the horizontal gradient in geostrophic vorticity in relation to the scale of the storm. In this context, the horizontal divergence scale in geostrophic flow is proportional to (Ws considers the effect of the background flow through Rog). According to (10), for a slowly moving storm Ws ≈ WE − RogδUOML, and because Uh appears in the denominator of WE and UOML, as , which is consistent with (Geisler 1970).
An evaluation of Ws, (10) is presented in Table 6. Values estimated with this parameter at the core of the large WCE, storm’s central region, and the small anticyclone’s center are consistent with values estimated with (9) (Fig. 12) and with the observed response to Isaac (Fig. 9a). Finally, it is important to emphasize that (9) and (10) are valid in an Eulerian framework, under the assumption that Rob and Rog are sufficiently smaller than 1 for the terms Ti in (2) to have a negligible contribution in the ocean response to TC forcing.
6. Discussion and concluding remarks
Predominantly downwelling and warming responses to TC Isaac were directly measured over GoM’s warm, anticyclonic mesoscale oceanic features that interacted with the storm during its intensification from TS to H1. Observed upwelling and downwelling regimes were compared with the undisturbed Ekman pumping velocity (that only considers the horizontal structure in the wind stress) as well as with a pumping velocity ws derived from the dominant time-dependent vorticity balance in the OML that considers horizontal structures in both wind stress and oceanic geostrophic vorticity.
An upper-ocean cooling response between −2 and −5 kW m−2 over a 12-h interval was directly measured below the storm’s central region or 2 to 5 times the sea-to-air heat loss by enthalpy fluxes of O(−1) kW m−2 observed in intense TCs (Shay et al. 2000; Oey et al. 2006; Shay and Uhlhorn 2008; Lin et al. 2009; Jaimes et al. 2015; Uhlhorn and Shay 2013). Rather than by enthalpy fluxes into the storm, this observed cooling response was more likely caused by vertical entrainment across the OML base, as found elsewhere (e.g., Price 1981; Jacob et al. 2000; Shay and Uhlhorn 2008; Jaimes et al. 2011; Uhlhorn and Shay 2012). By contrast, warming between 4 and 8 kW m−2 was measured away from the storm’s center, over regions that were occupied by warm, anticyclonic mesoscale oceanic features. Wind-driven upper-ocean warming over similar features was reported for Hurricanes Wilma (Oey et al. 2006) and Rita (Jaimes and Shay 2009) and was reproduced in numerical models for different strength in the background eddy field (Jaimes et al. 2011). Overall, the enhanced downwelling response over the oceanic eddy field prevented significant cooling of the sea surface during Isaac’s intensification. The impact of this upper-ocean warming response on ensuing enthalpy fluxes into Isaac will be investigated in a separate study.
OML cooling and subsurface warming by wind-driven vertical mixing were confined to waters above the 20°C isotherm depth (proxy to the thermocline depth in the GoM), similar to direct measurements in major Hurricanes Katrina and Rita (Jaimes and Shay 2009, 2010) and results in numerical experiments (Zhai et al. 2009; Jaimes et al. 2011; Jullien et al. 2012). These vertical mixing processes are irreversible, thus the ensuing subsurface heat “gain” is not available to be subsequently transported by ocean currents, as proposed in previous studies on the contribution of hurricanes to the meridional overturning circulation (Emanuel 2001; Sriver and Huber 2007). Cooling and warming beneath the thermocline were mainly associated with vertical advection of temperature in upwelling and downwelling regimes (reversible adiabatic processes). Observed horizontal structures in OHC (surface response) and vertical velocities at the thermocline (subsurface response) were consistent, indicating that upper-ocean thermal responses consisted of predominantly tridimensional upwelling and downwelling flows that were impacted by background eddy features and were simultaneously cooled off by local irreversible vertical mixing processes. Pure upwelling and downwelling regimes were better depicted at the thermocline, away from regions of intense vertical mixing regimes. Thus, additional research in eddy-rich oceans is needed to delineate three-dimensional structures in these regimes at depth.
Vertical velocities associated with just the curl of the wind stress (undisturbed Ekman pumping) could not explain the observed structure and strength in upwelling and downwelling regimes at the thermocline during Isaac. The main drawback was that downwelling regimes predicted by undisturbed Ekman pumping were 2 to 5 times weaker than those observed because regions of maximum downwelling over underlying anticyclonic features were not resolved. A more realistic representation of the upwelling and downwelling responses was obtained with (9), which was derived from the dominant time-dependent vorticity balance in the OML. A parametric TC-driven pumping velocity scale, Ws = WE − Rogδ(Uh + UOML), was derived by scaling (9) in terms of relevant scales in TCs; this velocity is a function of the undisturbed Ekman pumping WE, the strength in the background geostrophic flow (measured by the eddy Rossby number Rog = ζg/f), the horizontal structure in ζg (its positive and negative values are associated with upwelling and downwelling regimes), the aspect ratio δ, and total surface stresses Uh + UOML.
From a dynamical perspective, Ws is proportional to the horizontal advection of geostrophic vorticity by total surface stresses from storm motion Uh and the undisturbed Ekman drift UOML. This vertical velocity is developed to maintain vertical rigidity in strongly rotating geostrophic flows when a surface-intensified stress is applied at the free surface (Stern 1965). That is, Ws compensates the integral horizontal advection of ζg by Uh and UOML. This vorticity balance is predicted to predominate in the OML when both the eddy and frictional Rossby numbers (Rog and Rob) are sufficiently small, such that rotational effects are dominant at the horizontal scale of both the eddy field and the nonuniform surface wind stress. By ignoring the terms with smaller magnitude, the error in the dominant vorticity balance (8) is O(Rog + Rob) (<25% in the present treatment).
Predominantly downwelling responses to TC wind forcing over warm oceanic features have been recently documented (Oey et al. 2006; Jaimes and Shay 2009; Jaimes et al. 2011; Halliwell et al. 2011). The vorticity analysis conducted in the present study indicates that strength and structure in the oceanic geostrophic flow significantly impacts upwelling and downwelling responses, and these responses can be very fast. Because downwelling responses warm the upper-ocean, preventing significant cooling of the sea surface in TCs, they are expected to create favorable ocean conditions for TC development, maintenance, and rapid intensification. The coupled interaction of the wind stress and oceanic geostrophic flows is a leading-order, tridimensional dynamical process. Thus, incorporating realistic ocean states in coupled numerical hurricane models is a necessary condition to improve intensity forecasting. The results from Halliwell et al. (2011) indicate that a horizontal grid size of 10 km (or smaller) in these models is appropriate to resolve both the dominant storm’s eyewall structure and horizontal gradients in the GoM mesoscale eddy field.
The research team gratefully acknowledges Gulf of Mexico Research Institute–sponsored Deep-C consortium for supporting this research (Grant SA1212GoMRI008). The project continues to be grateful to the NOAA Aircraft Operation Center (Dr. Jim McFadden) that makes it possible to acquire high-quality data during hurricanes through the Hurricane Field Program and strong collaborative ties with NOAA’s Hurricane Research Division directed by Dr. Frank Marks at AOML. Jodi Brewster and Ryan Schuster from the University of Miami provided invaluable support during the aircraft flights in Isaac. Insightful comments and suggestions from three anonymous reviewers helped to clarify and improve this paper. Processed altimeter data are from the U.S. Navy’s Altimetry Data Fusion Center (ADFC) at Stennis Space Center; the derived product suite (and its evaluation) is available online (at either http://www.rsmas.miami.edu/groups/upper-ocean-dynamics/research/ocean-heat-content/ or http://www.ospo.noaa.gov/Products/ocean/ocean_heat.html).
Evaluation of the Vorticity Parameters with Mooring Data
Because data obtained in Isaac is not enough to directly evaluate Rog, ζb, Rob, and T1 (biggest Ti term), these parameters were alternatively calculated using data from a mooring array that was impacted by major Hurricanes Katrina and Rita (Jaimes and Shay 2009, 2010); these storms moved over a similar eddy field than the one encountered by Isaac. In Katrina and Rita, the average measured values of |Rog| at the bottom of the OML were between 0.02 and 0.11; that is, |ζg| was 2% to 11% the value of f, and |Rob| < 0.08 ≪ 1 (Figs. A1a,b). While instruments in the mooring array did not resolve the surface layer, an increase in Rog and Rob larger than one order of magnitude should not be expected at this layer. For instance, if we evaluate Rob = ζb/f by using the frictional vorticity scaling parameter ζb = |Rog|(τmax/ρ0hUh) (Table 4) rather than the observed values of ζb, and assuming a value of |Rog| = 0.2 (2 to 4 times large than the observed values in Figs. A1a,b), values of Rob ≤ 0.08 are obtained for these storms, which are similar to the magnitude of the observed values. In these estimates, ρ0 = 103 kg m−3, τmax = 7.6 (8.7) Pa, h = 74 (70) m, and Uh = 6.3 (4.7) m s−1 for Katrina (Rita).
The mooring data were also used in computing T1, the largest of the Ti terms; its maximum values are at about 3 × 10−10 s−2 (Figs. A1c,d). By considering the magnitude of the leading-order term () for Katrina and Rita (2.5 × 10−9 and 6.7 × 10−9 s−2, respectively), the corresponding ratio of T1 for this leading term is 0.12 and 0.05; these values are smaller than the value of 0.18 estimated for Isaac (Table 5). Thus, T1 can be between one and two orders of magnitude smaller than the leading-order term in GoM hurricanes.
These results support the assumptions followed in deriving (3) based on the scaling analysis for Isaac (Tables 4 and 5). That is, Rog ≪ 1 (not much smaller though); Rob ≪ 1; ; the frictional vorticity scale in geostrophic flow is valid because Rob ≪ 1; and the Ti terms can safely be ignored because they are two to three orders of magnitude smaller than the leading-order term. The error in (3) associated with these assumptions is estimated at O(Rog + Rob) (section 5b).