Loop Current Mixed Layer Energy Response to Hurricane Lili (2002)

400 JOURNAL OF PHYSICAL OCEANOGRAPHY VOLUME 42

Loop Current Mixed Layer Energy Response to Hurricane Lili (2002). Part I: Observations

ERIC W. UHLHORN NOAA/AOML/Hurricane Research Division, Miami, Florida

LYNN K. SHAY Division of Meteorology and Physical Oceanography, Rosenstiel School of Marine and Atmospheric Science, University of Miami, Miami, Florida

(Manuscript received 4 May 2011, in ﬁnal form 3 October 2011)

ABSTRACT

The ocean mixed layer response to a tropical cyclone within and immediately adjacent to the Gulf of Mexico Loop Current is examined. In the ﬁrst of a two-part study, a comprehensive set of temperature, salinity, and current proﬁles acquired from aircraft-deployed expendable probes is utilized to analyze the three-dimensional oceanic energy evolution in response to Hurricane Lili’s (2002) passage. Mixed layer temperature analyses show that the Loop Current cooled ,18C in response to the storm, in contrast to typically observed larger decreases of 38–58C. Correspondingly, vertical current shear associated with mixed layer currents, which is responsible for entrainment mixing of cooler water, was found to be up to 50% weaker, on average, than observed in previous studies within the directly forced region. The Loop Current, which separates the warmer, lighter Caribbean Subtropical Water from the cooler, heavier Gulf Common Water, was found to decrease in intensity by 20.18 6 0.25 m s21 over an approximately 10-day period within the mixed layer. Contrary to previous ocean response studies, which have assumed approximately horizontally homogeneous ocean structure prior to storm passage, a kinetic energy loss of 5.8 6 6.4 kJ m22,or approximately 21 wind stress-scaled energy unit, was observed. By examining near-surface currents derived from satellite altimetry data, the Loop Current is found to vary similarly in magnitude over such time scales, suggesting storm-generated energy is rapidly removed by the preexisting Loop Current. In a future study, the simulated mixed layer evolution to a Hurricane Lili–like storm within an idealized preexisting baroclinic current is analyzed to help understand the complex air–sea interaction and resulting energetic response.

1. Introduction have examined the relationship between the intensity of TCs and the SST. Malkus and Riehl (1960) derived Hurricanes, and more generally tropical cyclones (TCs), a relationship between the decrease in central pressure are among the most intense organized vortical systems and the increase in equivalent potential temperature in observed in the atmosphere. These cyclones derive their the eyewall region (due to imported enthalpy from the energy primarily from the release of latent heat upon ocean). Further studies by Emanuel (1986) and Betts condensation of water vapor (Ooyama 1969). Thus, it is and Simpson (1987) confirmed this relationship to be necessary that a large moisture source be present, such as approximately constant. More recent research has stud- the ocean, and that the sea surface temperature (SST) is ied not only the influence of SST on TC intensity but also sufficiently warm to maintain a moist enthalpy flux from the relationship between intensity and the upper-ocean the sea to the atmospheric boundary layer, as was first thermal energy (Shay et al. 2000). recognized by Palmen (1948). Numerous other studies Because the underlying ocean significantly modulates TC intensity, much attention has been drawn toward gaining a better understanding of the physical interac- Corresponding author address: Dr. Eric W. Uhlhorn, NOAA/ AOML/Hurricane Research Division, 4301 Rickenbacker Cswy., tion between the atmosphere and ocean during these Miami, FL 33149. events. Unfortunately, because of limited observational E-mail: [email protected] data at the air–sea interface in high-wind conditions, the

DOI: 10.1175/JPO-D-11-096.1

Ó 2012 American Meteorological Society Unauthenticated | Downloaded 09/29/21 08:47 AM UTC MARCH 2012 U H L H O R N A N D S H A Y 401 understanding of momentum and energy transfer processes has not progressed enough to significantly increase forecast accuracy. The recent Office of Naval Research sponsored Coupled Boundary Layer Air–Sea Transfer (CBLAST) field experiment in 2003–04 (Black et al. 2007) was designed to address questions regarding poorly understood air–sea exchange processes in TCs such as the maturity of the sea state (Donelan et al. 1993), sea spray (Fairall et al. 1994), and boundary layer roll vortices (Foster 2005) and their possible impacts on TC intensity. In sum, the various conclusions generally now agree that the bulk enthalpy and momentum exchange coefficients at high wind speeds are not as large as previously assumed (Drennan et al. 2007; French et al. 2007). Further complicating TC air–sea interactions is the sometimes large variability in the upper ocean typical of FIG. 1. SST (8C) on 4 Oct 2002 from combined Advanced large-scale ocean current systems (e.g., Gulf Stream, Microwave Scanning Radiometer for Earth Observing System Kuroshio) that exist near continental western bound- (AMSR-E)/Tropical Rainfall Measuring Mission Microwave Im- aries where TCs often make landfall. A particularly in- ager (TMI) microwave imagery, 2 days after Hurricane Lili passed teresting region to examine the effects of variable ocean over the southeast GOM. Arrow points to area of significant surface cooling, which is delineated from the LC’s intrusion into the structure on TC intensity is the Gulf of Mexico (GOM). Gulf. Courtesy of Remote Sensing Systems, Inc. Studies of Hurricanes Gilbert (Shay et al. 1992), Opal (Shay et al. 2000), Ivan (Walker et al. 2005), Katrina, and Rita (Shay 2009; Jaimes and Shay 2009, 2010) have air–sea fluxes decrease (Chang and Anthes 1978; Price demonstrated the potential influence GOM upper- 1981; Shay et al. 1992; Schade and Emanuel 1999; ocean variability can have on TC intensity. As revealed Bender and Ginis 2000). These observations demand a by microwave satellite imagery, SST cooling (indicated detailed understanding of the physical mechanisms re- by the arrow in Fig. 1) was associated with Hurricane sponsible for preventing the expected cooling. In this Lili’s (2002) passage through the GOM. However, this first of a two-part study, the analysis of these observa- cooler water is clearly confined to an area outside of the tions in Lili is expanded beyond primarily the thermal GOM Loop Current (LC), which is located in the extreme response previously reported by the authors. Particular southeast portion of the GOM. While Lili traversed the attention is given to analyzed fields of mixed layer cur- GOM, it underwent a period of rapid intensification rents and resulting mechanical energy. In section 2, mass from Saffir–Simpson category 1 to 4, immediately fol- and current field objective analyses are constructed from lowed by a weakening to category-1 intensity, over a 2.5- observations obtained in the GOM Loop Current region day period (Pasch et al. 2004). Particularly relevant to around the time of Lili’s passage. From these data, mixed understanding air–sea energy exchange over the LC, the layer depth and geostrophic current fields are estimated. resulting modulation of SST cooling, and ultimately In section 3, the evolution of mixed layer mechanical feedback to TC intensity is the large horizontal transport energy is computed from the analyses, and section 4 ex- and its impact on shear-induced mixing. Adding to un- amines the variability of the Loop Current system in the certainties in forecasting hurricane intensity in this region southeast GOM to help understand the observational is the often-complex atmospheric environment, which results. A summary of results and conclusions are pre- also exerts an influence on intensity (Bosart et al. 2000). sented in section 5. In a future study, details of the energy During 2002, life cycles of Hurricanes Isidore and Lili interactions are examined with the aid of an idealized in the northwest Caribbean Sea and GOM were exten- numerical model. sively observed (Shay and Uhlhorn 2008), which indicated deep, warm ocean structures cooled relatively little 2. Observed fields and provided a relative positive thermal feedback to these storms. This is in contrast to more typical negative As reported in Shay and Uhlhorn (2008), a large set of feedback on hurricane intensity when shear-induced temperature, salinity, and current vertical profiles was mixing at the ocean mixed layer (OML) base cools and obtained prior to, during, and after passage of Hurricane deepens this layer and causes a cold ocean wake where Lili (2002) across the southeast GOM during a joint

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FIG. 2. Locations of the ocean probes deployed prior to the passage of Hurricane Lili used to estimate the initial temperature conditions. AXBTs (circles), AXCTDs (3’s), and AXCPs (pluses). Lili’s observed ‘‘best track’’ is indicated by the solid line, and marked at 6-h intervals. The storm travels from southeast to northwest. The solid box indicates the analysis region for this study, and the dotted contours identify the 200- and 1000-m isobaths.

National Oceanic and Atmospheric Administration– (AXCP) profile locations over the course of the exper- National Science Foundation (NOAA–NSF) aircraft- iment. The fairly dense horizontal coverage of vertical based field research experiment. These data underwent profiles provided an opportunity to compute optimally an extensive processing and quality-control effort to ana- interpolated objective analyses of three-dimensional lyze details about the upper-ocean evolution in response (3D) synoptic fields for relevant quantities to examine to a Saffir–Simpson category-3 storm. Figures 2–6 show the mass, momentum, and energy evolution over a 10-day aircraft expendable bathythermograph (AXBT) probe, period. Details regarding experimental goals, method- aircraft expendable conductivity–temperature–depth ology, and data processing are provided in the above (AXCTD) probe, and aircraft expendable current probe referenced article.

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FIG. 3. Locations of AXCTDs, which measured salinity profiles FIG. 4. Locations of AXCPs, which measured horizontal current prior to the passage of Hurricane Lili. Symbols are as in Fig. 2. profiles prior to the passage of Hurricane Lili. Symbols are as in Fig. 2. a. Mass distribution found at ;200 m. These gradients gradually become 1) TEMPERATURE AND SALINITY FIELDS weaker at greater depths. Temperature and salinity structures are known to be An SST analysis is shown in Fig. 9a for profiles ob- unique for the Caribbean Subtropical Water (STW) and tained during the storm passage on 2 October. Based on Gulf Common Water (GCW) (e.g., Wu¨ st 1964; Nowlin nearly uniform SSTs found in the prestorm analysis, evi- and Hubertz 1972; Behringer et al. 1977). Prestorm dence of ;28C surface cooling (Fig. 9b) is found in the AXCTD profiles at two locations within the experimental extreme northwest portion of the observation domain at domain separated by ;300 km reveal a distinct differ- the boundary between the LC and GCW and along the ence in measured temperature and salinity and the de- storm track, which is within expected limits of inner-core rived mass density (Fig. 7). Relevant to the upper-ocean SST cooling in TCs (Cione and Uhlhorn 2003). As op- energetics is the LC driven by this density anomaly, posed to the typical situation where larger cooling is ob- which is confined primarily to the upper 200 m. served to the rear of a storm, the cooling occurs forward Based on the observed upper-ocean profiles of tem- of the storm in the GCW while temperatures remain close perature and salinity, objective analyses for these quan- to prestorm values in the LC and STW. tities from the prestorm observations (18–23 September) Several temperature profiles obtained poststorm, are shown for the surface and 100-, 200-, and 300-m mostly from AXCTD and AXBT, show evidence of depths in Fig. 8. Fields are computed at yearday 265.0, near-surface warming and restratification because of corresponding to 0000 UTC 22 September; therefore, strong solar insolation and weak surface winds soon observations obtained later in the prestorm experi- after storm passage, as observed by Hazelworth (1968). mental period (and closer in time to storm passage) are To obtain more realistic poststorm surface temperatures weighted more heavily. Analyses clearly identify the that are representative of the actual thermal response to location of the northern extension of the STW into the the TC, a subjective correction (see example in Fig. 10) southern GOM. This generally warmer and more saline is performed. The mean excess SST for all profiles is core is separated from the GCW by the LC system. found to be 0.31860.198C and occurs over an average Although the surface temperature and salinity show ;10-m layer depth. Assuming an average 270 W m22 relatively little horizontal variability, the subsurface (Price and Morzel 2006) radiative energy flux absorbed fields indicate the marked contrast between water masses. over a 10-m layer for a 48-h duration after storm pas- The strong temperature gradient becomes apparent at sage, a 0.288C temperature increase would result, sug- ;100-m depth, whereas the largest salinity gradient is gesting the observed warming is reasonable.

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FIG. 5. Locations of (a) temperature, (b) salinity, and (c) currents from ocean proﬁlers deployed during the in-storm research ﬂight pattern in Hurricane Lili on 2 Oct 2002. Symbols are as in Fig. 2.

Poststorm temperature and salinity analyses shown 2) DENSITY FIELDS in Fig. 11 are generated from profiles acquired on 4 October, about 60 h (;2 inertial periods) after the pas- The 3D mass density distribution r(x, y, z) is re- sage of Lili. Poststorm adjusted surface cooling of sponsible for driving the LC flow under geostrophic ;2.58–38C was found in the GCW to the right of the balance constraints. The prestorm and poststorm den- storm track (Shay and Uhlhorn 2008), slightly less than sity field analyses shown in Fig. 12 are computed from the 38–58C cooling typically observed in TC cold wakes the objectively analyzed temperature T and salinity S (Black 1983). Otherwise, over most of the domain there using the Fofonoff and Millard (1983) seawater equation is relatively little evidence of significant surface cooling. of state r 5 r(S, T, p). The density distribution is ex- The subsurface horizontal temperature gradient appears pectedly (anti-) correlated with the temperature fields, to be generally weaker than observed in the prestorm with warm/light water in the southeast part of the do- fields, especially at 200- and 300-m depths (cf. Figs. 11c,d main and cold/heavy water to the northwest. However, with Figs. 8c,d). In addition, both the temperature and the density gradient becomes weaker at greater depths salinity fields have shifted to the east of their initial po- (Figs. 12d,h), a result of the higher salinity in the STW, sitions, because the axis of the STW extension is now which compensates to homogenize the density field at oriented north–south. It does not appear likely that this depths below 200 m. Poststorm density fields shows an large pattern change was a direct result of the storm. increase of ;0.6 kg m23 associated with the observed

FIG. 6. Locations of (a) temperature, (b) salinity, and (c) currents from ocean proﬁlers deployed during the poststorm research ﬂight on 4 Oct 2002. Symbols are as in Fig. 2.

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FIG. 7. (a) Temperature, (b) salinity, and (c) density anomaly profiles obtained on the 19 Sep flight plotted as the difference profile 1714 minus profile 2104.

2.58C cooling found in the northwest and right of storm current vector V is estimated for each AXCP. The pres- track, and the poststorm ridge axis shifts from its prestorm, near-surface analyzed velocity field (Fig. 13) clearly torm position, as was found in the T and S fields. reveals the LC location relative to Lili’s track and indicates peak current speeds of ;1.1 m s21,althougha b. Currents few individual profiles show peak speeds as high as ;1.6 m s21. 1) OBSERVED CURRENTS Based on observed prestorm currents, the LC is de- 21 Critical to fully understanding LC response to TC forc- fined here to be confined $e jVmaxj analysis isotachs in ing, it was an experimental goal to observe the preex- Fig. 13. This definition limits the LC to the geographic isting mesoscale current field using AXCPs, which might location in which prestorm OML current speed exceeds be responsible for modulating the upper-ocean energy 0.38 m s21. Observations and analysis grid points lying budget. As described in Shay and Uhlhorn (2008), sur- to the warm side of the LC fall into the Caribbean STW; face wave orbital velocity-induced currents are initially accordingly, data on the cold side are assumed to lie removed from the AXCP-measured current profiles. within the GCW. This procedure (Sanford et al. 1987) also estimates the 2) GEOSTROPHIC CURRENTS mean OML current velocity and the current shear directly below the OML for each profile, which are of The strongest observed currents are found to be well primary interest for analyzing the evolving current in correlated with large horizontal density gradient in- response to the storm. Based on these three-layer sta- dicating the LC is primarily driven by the mass-field tistical model fits to current profiles, the mean OML anomaly. The three-dimensional geostrophic velocity

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FIG. 8. Prestorm (a)–(d) temperature (8C) and (e)–(h) salinity (ppt) for 18–23 Sep at (a),(e) the surface and (b),(f) 100-, (c),(g) 200-, and (d),(h) 300-m depths objectively analyzed from observed proﬁles. Contour intervals are 18C and 0.2 ppt, respectively. Storm track is shown with marks every 6 h.

Vg is computed by vertically integrating the Boussinesq- boundary condition Vg(z0) 5 0, where z0 is the smaller approximated thermal wind equations, of 750 m (Jacob et al. 2000) and the actual depth. The ð density fields derived from the T and S analyses are used z ›Vg g to calculate the three-dimensional V field for prestorm 52 [k 3 $r(x, y, z)] dz9, (1) g ›z f r (z) (19–23 September) conditions (Fig. 14). z0 0 0 A vertical cross section in the along-track (cross where g is the gravity acceleration and f0 is the Coriolis stream) direction (Fig. 15) clearly identifies LC struc- parameter. The integration is carried out subject to the ture. As determined by horizontal density gradients, the

FIG. 9. (a) In-storm SST (8C) and (b) SST change from prestorm values on 2 Oct.

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the 750-m motionless-level assumption is incorrect. Another potential reason for a low bias exists in the balance assumption itself. The LC’s large anticyclonic curvature (i.e., small radius of curvature) suggests gradient balance may be more appropriate for describing ﬂow. In fact, for an anticyclone with radius of curvature

R 52100 km at 248 latitude, jVgj is approximately 20% less than the gradient current (Holton 1992, chapter 3).

3) AGEOSTROPHIC CURRENTS The LC response is quantiﬁed in terms of observed

currents V, geostrophic currents Vg, and ageostrophic current Va 5 V 2 Vg. The estimated OML mean Vg at the AXCP location is estimated by bilinear interpolation. The ageostrophic current in the OML serves as a proxy FIG. 10. Example temperature profile from AXCTD, showing for the forced, near-inertial motion, which scales directly near-surface warming confined to a shallow later. The shaded area with the storm’s intensity when the ocean is initially in represents an estimate of poststorm warming: in this example, a state of rest. The analyzed prestorm and poststorm 10.428C. OML mean observed, geostrophic, and ageostrophic LC is mostly confined to the upper 300 m. Maximum currents and their respective changes are shown in surface geostrophic currents speeds are found in the LC Fig. 16. Observed currents (Figs. 16a–c) generally show a to be ;0.75 m s21, and speeds $0.4 m s21 (;1 e folding slight decrease in intensity within the LC and little change from the peak observed value) are confined to a cross- intheSTW.AsmallincreaseisfoundintheGCW. stream width of ;100 km. Peak geostrophic currents are Geostrophic currents (Figs. 16d–f) show weakening ;0.3 m s21 weaker than the observed maximum in situ of ;0.4 m s21 in the LC, especially at the inflow from currents, for which there are multiple possible reasons. the south. Overall, the ageostrophic current response

The surface Vg is computed relative to 750-m depth; is somewhat mixed and confused with possibly large however, observed currents at large depths are generally errors, because of subtracting two quantities of similar found to ﬂow counter to the surface direction at speeds magnitude, especially in the LC. Clearly, a classic near- of ;0.2 m s21 (Maul 1977; Ochoa et al. 2001), which inertial current wake, as described by linear theory would explain a surface jVgj underestimate and suggests (Geisler 1970), is not evident in these observations.

FIG. 11. As in Fig. 8, but for poststorm proﬁles obtained on 4 Oct.

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23 FIG. 12. Mass density (kg m ) at (a),(e) the surface and (b),(f) 100-, (c),(g) 200-, and (d),(h) 300-m depths for (a)–(d) prestorm and (e)–(h) poststorm. Contour interval is 0.2 kg m23.

Based on measurements of OML V from AXCP clear than for the individual profiles. Analysis field current profiles (Shay and Uhlhorn 2008), statistics for statistics corroborate the results from individual pro- magnitudes are calculated in each of the three physical files, highlighting the general decrease in current regions for prestorm and poststorm profiles, and addi- magnitude within the LC. Contrasting the weak cur- tionally changes are also computed (Table 1). Because rent response found for Lili, Shay et al. (1998) found of the fairly small number of profiles individually for each region, all profiles are included in the statistics re- gardless of radial distance from the storm track. All values in the Caribbean STW show only small average change between prestorm and poststorm con- 21 ditions. An average increase in jVaj of 0.10 6 0.16 m s may be compared with the wind-driven current scale value of 0.20 m s21, which assumes the ocean is initially at rest. The GCW shows a somewhat unexpectedly weak response in jVaj near the storm track, with an average increase of ,0.1 m s21. However, this is consistent with the fairly weak poststorm shear as compared with previous observational results (Shay and Uhlhorn 2008). Because Lili was a rather small, fast-moving storm, it is not surprising that a strong response was not found. Of particular interest is the overall observed decrease in the LC speed from prestorm to poststorm, which is found for both the observed and geostrophic currents. This result contradicts most previous studies of upper-ocean current response to TCs, which have often observed strong 21 near-inertial currents after storm passage. FIG. 13. Prestorm OML mean current velocity V1 (m s ), ob- OML current statistics are computed for a cross- tained from AXCP fits. Observed currents are plotted as red ar- rows, and the analyzed field is plotted in black. Analyzed vectors storm-track swath from 22to14R from the ana- max are plotted at 1/3 the resolution of the computed fields for clarity. lyzed fields (Table 2). Because the objective analyses Contour interval for current speed is 0.1 m s21, and speeds , tend to filter high-frequency variability, results are more 0.4 m s21 are not contoured.

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FIG. 15. Prestorm geostrophic current speed jVgj vertical cross section from southeast to northwest (left to right) at the location FIG. 14. Prestorm surface geostrophic velocity V relative to g shown by the red line in Fig. 14. Flow direction is out of the plot and 750 m. Red arrow shows location of vertical cross section plotted in the storm track is left to right as indicated by the arrow. Density Fig. 15. Contour interval is 0.2 m s21, and speeds , 0.4 m s21 are contour interval is 0.5 kg m23. not contoured. wind-forced, near-inertial currents within the GCW in STW to 40 m in the GCW. This method produces av- Hurricane Gilbert . 1ms21. erage DT values as defined above, of 1.8860.68C, which appear to be far too large. c. OML depth Based on the observed current profiles, a subjective Numerous criteria to estimate the OML depth h from estimate of the well-mixed layer depth was made for profiles have been established in the literature, sug- AXCP profiles (Z1 values tabulated in Shay and Uhlhorn gesting a general lack of agreement on a single defini- 2008). For each of the poststorm current profiles, where tion. Thresholds in both temperature decrease and the top of the shear layer was most clearly identified, density increase from surface values have been applied. DT 5 SST 2 T(Z1)iscalculated.AmeanDT 5 0.786 Temperature-based criteria vary from DT 5 0.18C 0.48C is found for 22 profiles. This value compares (Martin 1985) to DT 5 1.08C (Hastenrath and Merle reasonably well with results reported in Kara et al. 1987), where DT 5 SST 2 T(h). A common density (2000), which suggest that a DT 5 0.88C criterion best 3 23 definition in terms of st 5 (r 2 10 )kgm is Dst 5 represents the depth of turbulence penetration into the 20.125 kg m23 (Levitus 1982). Still, other authors have thermocline or the bottom of the entrainment zone applied vertical temperature gradient thresholds (e.g., below the OML. This DT 5 0.88C threshold is applied Lukas and Lindstrom 1991; Shay et al. 1992). to the objectively analyzed temperature fields to esti- Within this definitive range, h can vary several tens of mate the OML depth. meters (Fig. 17). In their analysis of GOM temperature Prestorm and poststorm OML depths (Fig. 18) closely profiles in Hurricane Gilbert, Shay et al. (1992) used a resemble the subsurface distribution of temperature and gradient criterion of dT/dz 5 0.18Cm21. Based on Lili mass in the LC vicinity, ranging from .90 m in the LC to prestorm temperature analyses, mixed layer depths could ,40 m in the GCW. Based on temperature analysis er- not be computed in the STW using this method, because rors, typical OML depth errors are approximately 5–7 m of the very weak stratification, where lapse rates never for both prestorm and poststorm fields over most of the exceeded 0.088Cm21 anywhere in the profile. Depths in experimental domain, except for 15–20-m errors in the the GCW, however, were found to be 30–40 m using this extreme S corner in the poststorm analysis due to locally threshold, in agreement with OML depth estimates in poor data coverage. Because the rate of change of OML Hurricane Gilbert (Shay et al. 1992). Lukas and Lindstrom temperature is inversely proportional to the OML depth (1991) used a dT/dz 5 0.058Cm21 definition in their (e.g., Pollard et al. 1973), greater surface cooling is ex- analysis of western equatorial Pacific depths, which when pectedly found in the northwest portion of the obser- applied here give OML depths ranging from 150 m in the vational domain, as depicted previously in Fig. 9.

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FIG. 16. Analyzed OML currents (a),(d),(g) prestorm; (b),(e),(h) poststorm; and (c),(f),(i) changes (a)–(c) V, (d)–(f) Vg, and (g)–(i) Va. In (c),(f),(i), red (blue) contours are positive (negative) change. Contour intervals are 0.2 m s21.

3. Energy response (Table 5). Because of large variation across the experimental domain, we expect a highly complex response, a. Air–sea parameters and scaling and parameters are developed separately for each of the Parameters that describe the expected energy response three dynamic regions. Considering the signiﬁcant pre- are developed, as proposed by Price (1981). Shay and existing current at least as large the expected wind-driven Uhlhorn (2008) estimated storm-forcing scales (Table 3) current, isolating the near-inertial response from the based on observations in Hurricane Lili, and important highly variable geostrophic background using previous scales from the prestorm upper-ocean ﬁelds are restated methods (e.g., Shay et al. 1998; Jacob et al. 2000) becomes in Table 4. From these parameters, a set of dimensional less practical, as was found in the observation analyses of response scales is estimated to describe OML energetics ageostrophic currents in the previous section.

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TABLE 1. Summary statistics for observed currents obtained di- TABLE 2. Summary statistics for changes in OML currents ob- rectly from AXCP profiles. The pre and post columns are mean and tained from analyzed fields. Bold values indicate significance at the standard deviations, n is number of observations, and d.f. is degrees 95% confidence level. of freedom for the sample differences. Change (D) column is mean difference (post minus pre) and 95% confidence limit. Bold values D indicate statistical significance from zero mean difference. STW jVj 20.02 jV j 10.00 Locations Variable Pre Post D g jVaj 20.01 n 5 6 n 5 8 d.f. 5 12 LC jVj 20.09 STW jVj 0.35 6 0.23 0.40 6 0.16 10.04 jVgj 20.14 jVgj 0.43 6 0.20 0.43 6 0.19 20.01 jVaj 10.08 jVaj 0.27 6 0.14 0.37 6 0.18 10.10 GCW jVj 10.06 n 5 13 n 5 13 d.f. 5 24 jVgj 20.10 LC jVj 0.90 6 0.40 0.78 6 0.32 20.12 jVaj 10.02 jVgj 0.55 6 0.23 0.40 6 0.21 20.16 jVaj 0.63 6 0.43 0.57 6 0.34 20.06 n 5 11 n 5 8 d.f. 5 17 An approximate form of the mechanical energy equa- GCW jVj 0.34 6 0.31 0.37 6 0.17 10.03 tion for the OML is derived by scalar multiplying jV j 0.32 6 0.18 0.17 6 0.10 20.15 g Eq. (2) by V and vertically integrating over the OML jVaj 0.26 6 0.15 0.33 6 0.15 10.07 depth, b. OML mechanical energy d(K 1 P) 52V $ p92p9w 1 V t, (3) The rotating Cartesian, hydrostatic, and Boussinesq dt H equations of motion are given by where K and P are the kinetic and potential energy, dV ›t respectively, with dimensions of energy per unit area of r 52r f k 3 V 2 $p92r g9k 1 . (2) 0 dt 0 0 0 ›z OML given by

FIG. 17. Example (left) density, (middle) temperature, and (right) salinity proﬁles illustrating OML depth estimate variability under a number of cited criteria.

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FIG. 18. (a) Prestorm and (b) poststorm OML depth (m), estimated from objectively analyzed temperature ﬁelds. Contour interval is 10 m.

V V and OML deepening from wind forcing. The remain- K 5 r h and (4) 0 2 ing source/sink flux terms are examined in simulations in a future study, because they are particularly diffi- h2 P 5 r g9 . (5) cult to directly compute from the observations obtained 0 2 herein. From observed current and mass–density analyses, The first and second terms on the right-hand side of OML mechanical energy is computed from the prestorm Eq. (3) are the work done by current against the pressure and poststorm fields, as shown in Fig. 19. LC prestorm gradient, and the third term is net surface energy flux to kinetic energy (Fig. 19a) is approximately 20–25 kJ m22, the OML (wind stress minus shear stress). Initially, nearly decreasing to less than 5 kJ m22 outside. In accord with all wind energy input will go toward increasing the me- the observed decrease in current magnitude in the LC chanical energy, and it will take several inertial periods from prestorm to poststorm conditions, K curiously also before significant energy is transferred to the thermo- weakens to approximately 10–15 kJ m22 (Fig. 19b). A cline by the wave-energy flux (Gill 1984). Furthermore, small increase in K is found in the GCW, as the expected with a preestablished OML, most of the energy is ex- response to the storm. The potential energy fields gener- pected to go to increasing kinetic energy of the current ally reflect the analyzed OML depth distribution. Based (Pollard et al. 1973). on scaling arguments, a slight increase in P would be ex- In an approximate one-dimensional system, internal pected; however, observational analyses suggest much wave fluxes cannot be supported and correspond to more complex modification, possibly due to mesoscale purely inertial motion. Although the Loop Current or any oceanic variability independent of the storm. highly variable oceanic regime can hardly be accurately The energy distribution in the LC and surrounding modeled by such a system, comparisons of observations STW and GCW is further quantified as a function of here can be made with previous studies, which have often normalized cross-storm-track distance (x/Rmax), as shown assumed approximately horizontally homogeneous ini- in Figs. 20 and 21. Error statistics are computed by a tial conditions, primarily aimed at understanding mixing Monte Carlo method based on analyzed field errors, as

TABLE 3. Storm scaling parameters based on observations in Hurricane Lili. TABLE 4. Upper-ocean scaling parameters based on prestorm observations. Parameter Value Parameter STW LC GCW Radius of max stress Rmax 20 km 23 Max stress tmax 7.0 Pa OML reference density r0 (kg m ) 1023 1023 1023 21 Storm speed Vs 7.0 m s OML depth h0 (m) 90 60 40 21 Inertial period 2p/f0 29.4 h at 248N Geostrophic current jVgj (m s ) 0.2 0.7 0.1 2 22 Inertial wavelength Vs/f0 740 km Thermocline stratiﬁcation g9 (310 ms ) 1.0 1.5 2.5

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TABLE 5. Dependent variable scales of the upper-ocean response.

Parameter Scale STW LC GCW

21 Wind-driven current dU 5 tmaxRmax/r0h0Vs (m s ) 0.22 0.33 0.49 1/2 OML deepening dh 5 (tmax/r0) dU/g9 (m) 1.8 1.8 1.6 2 22 Kinetic energy increase r0h0dU (kJ m ) 4.3 6.5 9.8 2 22 Potential energy increase r0g9dh (kJ m ) 0.03 0.05 0.07 described in Shay and Uhlhorn (2008). In Fig. 20c, the although because of relatively large uncertainty in OML LC shows an overall decrease in K of 5–10 kJ m22, depth, P errors are expectedly highly magniﬁed. which appears fairly signiﬁcant considering the error Summary statistics for prestorm, poststorm, and bars on the mean change. The GCW shows a slight in- changes in observed K and P are presented in Tables 6 crease in K but no clear indication of strong response and 7, respectively. Between 22 and 14Rmax, the OML 22 close to the peak forcing location at Rmax. Large changes mean K is found to decrease an average 5.8 6 6.4 kJ m in P, especially in the STW, are found (Fig. 21c), in response to the storm, corresponding to the observed

FIG. 19. (a),(c) Prestorm and (b),(d) poststorm OML (a),(b) kinetic energy and (c),(d) potential energy ﬁelds. Values are in units of kJ m22.

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TABLE 6. Summary statistics (means and standard deviations) for 22 K (kJ m ) between 22 and 14Rmax.

Location Pre Post D STW 7.2 6 3.6 5.8 6 2.3 21.5 6 3.5 LC 18.7 6 8.4 12.9 6 3.3 25.8 6 6.4 GCW 3.2 6 3.5 4.6 6 2.5 11.4 6 2.2

for capturing these other processes to properly estimate the energy budget of the OML response in a region of large horizontal variability. Furthermore, a large-scale current system such as the LC is also highly variable in space in time, independent of strong surface forcing events. These energy ﬂuctuations in the LC and sur-

FIG. 20. (a) Prestorm, (b) poststorm, and (c) change in OML rounding ocean at short (weekly) time scales may be far kinetic energy (kJ m22) for three analyzed regions as a function of greater than changes induced by TCs, suggesting accu- cross-storm-track distance. rate and frequent reinitialization of upper-ocean structure in similar regimes is necessary for coupled numerical weakened OML current. Furthermore, large changes in models. P are found, which do not appear to be in direct response to the storm forcing. By adding the results for changes in 4. Background Loop Current variability K and P, a general increase in OML mechanical energy is found; however, kinetic energy response should far In light of the somewhat unexpected result that the exceed potential energy for wind-induced upper-ocean OML LC energy is observed to decrease after storm mixing (at least 3 times greater; Pollard et al. 1973). passage, it appears necessary to perform an analysis of Referring to the energy scales developed based on the LC variability independent of TC forcing. With little known forcing, the overall loss of K near the storm track existing sustained and continuous in situ data about LC is around 0.9 input units (1 unit 5 6.5 kJ m22). How- variability (Sturges 1992) and most certainly not at the ever, in terms of total mechanical energy (K 1 P), an time scales of interest here (days to weeks), satellite increase of around 0.6 units is found in the LC, sug- radar altimetry data become the most viable option to gesting that around 20.4 units are gained through ad- address this uncertainty. An obvious limitation of alti- vective transport and wave flux. Although the error metric data is the absence of vertical structure infor- estimates are rather large and therefore energy changes mation; the sea surface elevation and associated balanced are not statistically significant, results point to the need current merely respond to the vertically integrated mass distribution. Particular attention here is given to LC energetic variability through the Hurricane Lili experimental domain and not to the overall structure as it periodically penetrates, retreats, and sheds eddies throughout the GOM (e.g., Sturges and Leben 2000). a. Altimetric analysis The sea surface elevation, as measured by a radar altimeter, responds to the mass–density distribution within the ocean and below the ocean floor. After subtracting the solid-earth-induced topography (the geoid),

TABLE 7. Summary statistics (means and standard deviations) for 22 P (kJ m ) between 22 and 14Rmax.

Location Pre Post D STW 23.0 6 8.6 35.6 6 17.0 112.5 6 24.6 FIG. 21. (a) Prestorm, (b) poststorm, and (c) change in OML LC 12.4 6 4.8 21.9 6 9.8 19.5 6 11.0 potential energy (kJ m22) for three analyzed regions as a function GCW 8.9 6 2.6 15.6 6 6.9 16.7 6 6.9 of cross-storm-track distance.

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FIG. 22. (a) Rio-05 7-yr combined MDT, (b) 10-day mean SHA centered at yearday 265 in 2002, and (c) dynamic topography [(a) 1 (b)]. Values are in meters, and the contour interval is 0.2 m. The box represents Lili observational domain. the sea surface dynamic topography, which is related to g Vg(x, y) 52 $Hh (x, y). (6) surface currents via mass–momentum balance, can be f0 measured. The 0.58-resolution Rio-05 mean dynamic topography (MDT) product (Rio and Hernandez 2004) To analyze the time series of currents within the LC serves as a reference topography and is developed flowing through the Lili domain, the LC is defined here by averaging over 7 yr of multisensor altimeter data as containing current magnitudes $(1/e)jV j, as for gmax (Fig. 22a). The mean LC position is clearly identified in the in situ data, where jV j is the peak current speed gmax this field, and, because the product averages multiple found in the domain and must be at least 0.5 m s21 to modes of extension into the GOM, the LC appears to be consider the LC as flowing through the experimental stretched in the northwest–southeast direction relative to domain. Because this domain lies nearly due north of the its instantaneous and typically much narrower channel. Yucatan Straits, some portion of the LC is always found To estimate the total instantaneous (10-day mean) to intersect this area of interest. The LC location, as surface elevation field, sea height anomaly (SHA) fields depicted in Fig. 23, appears well correlated with that are added to the MDT. Altimeter SHA ground tracks determined by the in situ analysis (Fig. 13). In addition, are obtained from Naval Research Laboratory (NRL)/ currents estimated from geostrophic balance indicate Naval Oceanographic Office (NAVOCEANO) for all marked consistency with measured near-surface cur- available satellite altimeters operating during 1997–2006 rents, with peak values of ;0.9 m s21 and similar LC [Ocean Topography Experiment (TOPEX)/Poseidon, channel width, indicating the height gradient is fairly European Remote Sensing Satellite-1 (ERS-1), ERS-2, well resolved. Jason, and Geosat Follow-On (GFO)]. Because of rel- Mean current speed and variability (1s) are computed atively infrequent revisit periods, available SHA tracks at grid points simultaneously falling within the Lili do- are placed into 10-day bins, and the global mean SHA main and within the LC, as defined, every 10 days for the over the 10-day period is removed separately for each entire 10-yr record (Fig. 24, top). Over the entire record, satellite to eliminate possible cross-platform bias. Finally, the mean current speed is 0.72 6 0.12 m s21, although optimal interpolation is used to produce a 0.258 grid of significant local excursions clearly exist. Given this ob- SHAs (Fig. 22b) and is added to the MDT (interpolated served variability, changes in currents over the time to 0.258) to produce dynamic height h(x, y) fields every period that the in situ measurements were acquired 10 days. The sea height in Fig. 22c is a 10-day average seems quite plausible, as indicated in the 1-yr time series field centered around yearday 265 in 2002, or near the centered on the time Lili passed (Fig. 24, bottom). To time of Lili’s passage. examine this, the autocorrelation of the derived current time series is shown in Fig. 25 for lags from zero to 2 yr. b. Derived currents and spectra Evidently, there is a fairly rapid decorrelation of the Currents driven by the mass distribution as inferred from current speed such that less than 50% of the variance is the h(x, y) field are estimated from geostrophic balance, retained after around 20 days. No significant correlation

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FIG. 24. (a) 10-yr time series of LC current (mean and standard deviation) through the Lili observation region, and (b) 1-yr record FIG. 23. Estimated near-surface geostrophic current derived centered at time of Lili’s passage. Prestorm and poststorm jVj from sea height field (Fig. 22c) for 2002 yearday 265. Current within the LC estimated from the objectively analyzed fields are magnitude, as it defines the LC here, is contoured, and the interval plotted for comparison. is 0.1 m s21. Notice the weaker current at the location of rapidly turning LC (;258N), where the geostrophic approximation is un- derestimating the current. should be temporally resolved on at least a monthly cycle for accurate coupled atmosphere–ocean tropical is found beyond around 6 months, although there is cyclone forecasts. apparently a small return associated with a relatively weak annual cycle. 5. Summary and conclusions The OML mechanical energy cannot be directly computed from the altimeter data because there is no For the first time, the Gulf of Mexico Loop Current direct estimate of the OML depth. However, the in situ response to a major hurricane has been directly ob- observations of OML depth and associated errors can be served with a comprehensive set of in situ profilers. The combined with the altimeter data to estimate the vari- combination of current, temperature, and salinity three- ability of K in the LC over the relatively long-period dimensional synopses before, during, and after Hurricane record examined here. Using the estimate for the mean geostrophic surface current derived from the h fields and a mean OML depth of 60 6 10 m based on the observed profiles, the mean OML LC kinetic energy is 16.5 6 6.1 kJ m22, which compares quite well with the values presented in Table 6, determined from observations obtained only around 10 days apart. Finally, energy spectra for the LC are computed from the 10-yr record, specifically to examine intraannual variability. First, the record is broken into ten 64 data point records, each with 50% overlap. Each individual record is detrended and multiplied by a Hanning data window before computing the Fourier transform. The 10 resulting energy spectra are then averaged to yield spec- tral estimates with approximately 40 degrees of freedom (Fig. 26). Energy peaks are found centered at 0.0109 and 0.0281 cycles per day (cpd), which correspond to periods of approximately 90 and 35 days, respectively. Of par- FIG. 25. Autocorrelation function for lags from zero to 2 yr ticular interest here is the higher-frequency, shorter- computed from the time series shown in Fig. 24. The 95% confi- period energy peak, which suggests that LC structure dence interval for the sample is indicated by the dashed lines.

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data. Derived current speeds in the LC were found to vary 60.12 m s21 (1s) over 10-day periods. OML mean currents estimated from in situ profiles indicated a decrease of 0.12 m s21 from prestorm to poststorm in the LC. Thus, it appears plausible that the experimental measurements merely revealed background LC variability and that any response to Hurricane Lili was ei- ther mitigated in or quickly removed from the LC region by the time poststorm observations were made around two local inertial periods after storm passage. Particularly relevant to the motivating research goal of improving TC intensity forecasts is more accurately specifying the total (mechanical and thermal) energy exchange across the air–sea interface. The two most important quantities representing these processes are the wind stress and the enthalpy flux. Unfortunately, FIG. 26. Variance-preserving energy spectrum of LC current these quantities represent turbulent processes and, for magnitude within Lili observational domain. Dashed lines are the practical purposes, must be parameterized in terms of 95% confidence interval based on a x2 test. mean variables in numerical weather forecast models. The enthalpy flux from the ocean to the atmospheric Lili’s passage in 2002 provided an adequate description boundary requires specifying the SST within the TC’s of upper-ocean mechanical and thermal energy evolu- inner core, which is not generally equal to prestorm tion. Contrary to most previous poststorm ocean tem- values. Associated with the storm’s wind stress is the perature response studies, which generally showed excitation of mixed layer currents and shear (jdVjh21), 38–58C SST cooling, in situ and satellite observations which in a bulk OML model locally act to cool the OML indicated SST cooling of ,18Cat12 IP after Lili’s via entrainment at a rate, passage over the LC. This limited surface cooling may have allowed a large ocean-to-atmosphere enthalpy ›T dTjdVj 52 1 , (7) flux to be maintained, possibly positively contributing ›t bh to Lili undergoing rapid intensification in the southeast Gulf of Mexico. where dT is the discrete temperature jump between the Although Lili was nearly a Saffir–Simpson category-3 OML and the seasonal thermocline below and b is a hurricane at the time of observation with maximum nondimensional number proportional to the bulk Ri- 21 surface winds of 50 m s , its small size (Rmax 5 20 km) chardson number. Under approximately horizontally 21 and rapid translation speed (Vs 5 7ms ) might have homogeneous initial conditions, this process is typically somewhat limited the energetic response. However, the the dominant OML cooling mechanism. As the ocean- observational analyses revealed an initially unexpected to-atmosphere enthalpy flux in a TC is highly sensitive to result that the LC lost kinetic energy in the region tra- the SST (or, more precisely, the air–sea enthalpy dif- versed by Lili. Previous studies of TC ocean response ference), variability in subsurface structure, such as have generally found strong near-inertial currents after observed here, may have a profound effect on a TC’s storm passage, and scaling arguments suggested a 16.5 intensity. kJ m22 energy response within the LC, based on storm These results shed light on the possibility that the LC, parameters and the initial observed OML depth. In con- or any other large current system for that matter, simply trast, LC mixed layer mean kinetic energy was observed does not respond significantly to TC forcing (at least for 22 to weaken by 5.8 kJ m between 22 and 14Rmax.As storms of Lili-like structure). Although the time scales ageostrophic currents within the LC were found to in- over which the altimetry-based current variations are crease slightly, much of this kinetic loss appears to cor- found to be somewhat longer than the prestorm to relate with a decrease in OML geostrophic current, poststorm in situ synopses, it is apparent that structural suggesting a change in kinetic energy independent of changes on the order of weeks, at a minimum, must be storm forcing. taken into account in further studies. It is rather fortu- To place the observations within the context of back- nate the LC was found to weaken over this particular ground LC variability, upper-ocean currents were de- experiment’s time period, as a strengthening LC could rived from satellite altimetry sea surface topography very well have occurred, leading to a different and possibly

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