Loop Current Response to Hurricanes Isidore and Lili

Transcription

3248
MONTHLY WEATHER REVIEW
VOLUME 136
Loop Current Response to Hurricanes Isidore and Lili
LYNN K. SHAY
Division of Meteorology and Physical Oceanography, Rosenstiel School of Marine and Atmospheric Science, University of Miami,
Miami, Florida
ERIC W. UHLHORN
Hurricane Research Division, NOAA/Atlantic Oceanographic and Meteorological Laboratory, Miami, Florida
(Manuscript received 8 February 2007, in final form 17 December 2007)
ABSTRACT
Recent hurricane activity over the Gulf of Mexico basin has underscored the importance of the Loop
Current (LC) and its deep, warm thermal structure on hurricane intensity. During Hurricanes Isidore and
Lili in 2002, research flights were conducted from both National Oceanic and Atmospheric Administration
(NOAA) WP-3D aircraft to observe pre-, in- and poststorm ocean conditions using airborne expendable
ocean profilers to measure temperature, salinity, and current structure. Atmospheric thermodynamic and
wind profiles and remotely sensed surface winds were concurrently acquired as each storm moved over
the LC.
Observed upper-ocean cooling was about 1°C as Isidore moved across the Yucatan Straits at a speed of
4 m s⫺1. Given prestorm ocean heat content (OHC) levels exceeding 100 kJ cm⫺2 in the LC (current
velocities ⬎1 m s⫺1), significant cooling and deepening of the ocean mixed layer (OML) did not occur in the
straits. Estimated surface enthalpy flux at Isidore’s eyewall was 1.8 kW m⫺2, where the maximum observed
wind was 49 m s⫺1. Spatially integrating these surface enthalpy fluxes suggested a maximum surface heat
loss of 9.5 kJ cm⫺2 at the eyewall. Over the Yucatan Shelf, observed ocean cooling of 4.5°C was caused by
upwelling processes induced by wind stress and an offshore wind-driven transport. During Hurricane Lili,
ocean cooling in the LC was ⬃1°C but more than 2°C in the Gulf Common Water, where the maximum
estimated surface enthalpy flux was 1.4 kW m⫺2, associated with peak surface winds of 51 m s⫺1. Because
of Lili’s asymmetric structure and rapid translational speed of 7 m s⫺1, the maximum surface heat loss
resulting from the surface enthalpy flux was less than 5 kJ cm⫺2.
In both hurricanes, the weak ocean thermal response in the LC was primarily due to the lack of energetic
near-inertial current shears that develop across the thin OML observed in quiescent regimes. Bulk Richardson numbers remained well above criticality because of the strength of the upper-ocean horizontal
pressure gradient that forces northward current and thermal advection of warm water distributed over deep
layers. As these oceanic regimes are resistive to shear-induced mixing, hurricanes experience a more
sustained surface enthalpy flux compared to storms moving over shallow quiescent mixed layers. Because
ocean cooling levels induced by hurricane force winds depend on the underlying oceanic regimes, features
must be accurately initialized in coupled forecast models.
1. Introduction
Coupled models that predict hurricane intensity and
structure change are being used to issue forecasts to the
public, who will increasingly rely on the most advanced
Corresponding author address: Lynn K. Shay, Division of Meteorology and Physical Oceanography, Rosenstiel School of Marine and Atmospheric Science, University of Miami, 4600 Rickenbacker Causeway, Miami, FL 33149.
E-mail: nshay@rsmas.miami.edu
DOI: 10.1175/2007MWR2169.1
© 2008 American Meteorological Society
weather forecasting systems to prepare for landfalling
systems (Marks and Shay 1998; Bender and Ginis
2000). For such models, it has become increasingly clear
over the past decade that the oceanic component will
have to include realistic initial conditions to simulate
not only the oceanic response to hurricane forcing
(Price 1981; Sanford et al. 1987; Shay et al. 1992; Price
et al. 1994; D’Asaro 2003) but also the atmospheric
response to oceanic forcing (Shay et al. 2000; Hong et
al. 2000; Lin et al. 2005; Walker et al. 2005; Wu et al.
2007; Shay 2008).
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SHAY AND UHLHORN
An important example of this latter effect was observed during Hurricane Opal’s passage in 1995, when
atmospheric conditions were conducive for Opal’s
rapid deepening over 14 h over the Gulf of Mexico
(GOM; Bosart et al. 2000). During this deepening process, Opal passed over a warm core ring (WCR) shed
earlier by the Loop Current (LC) as detected by radar
altimeter measurements of the surface height anomaly
(SHA) fields from the National Aeronautics and Space
Administration’s (NASA’s) Ocean Topography Experiment (TOPEX)/Poseidon mission (Shay et al.
2000). Although satellite-derived images revealed that
sea surface temperatures (SSTs) were 29.5° to 30°C,
there was little evidence of this warm ocean feature’s
signature compared to the surrounding Gulf Common
Water (GCW). Using a coupled model, Hong et al.
(2000) performed a series of sensitivity tests with and
without this observed WCR. They found that Opal
deepened an additional 14 mb over the WCR compared
to numerical experiments without it. Walker et al.
(2005) found that cold core rings located on the periphery of the larger WCR helped to weaken Hurricane
Ivan (2004) just prior to landfall. More recently, Shay
(2008) showed that the LC and WCR did not significantly cool during the passage of Hurricanes Katrina
and Rita when these hurricanes rapidly deepened to
Category 5 status. These studies emphasize the importance of initializing models with realistic ocean features
to couple to hurricane forecasting models (Jacob and
Shay 2003; Falkovich et al. 2005; Halliwell et al. 2008).
The upper ocean’s transport from the northwest Caribbean Sea and through the Yucatan Straits significantly influences the GOM circulation patterns. These
transports, ⬃24 Sv (1 Sv ⬅ 106 m3 s⫺1) through the
straits, force LC variability and modulate WCR shedding events (Maul 1977; Sturges and Leben 2000; Leben
2005). The LC transports warm subtropical water with
a markedly different temperature and salinity structure
into the GOM compared to the GCW (Shay et al.
1998). As the LC intrudes north of 25°N, WCRs with
diameters of 100–200 km separate from the LC at an
average interval of 6–11 months, based on radar altimeter-derived SHA fields (Sturges and Leben 2000). In
contrast, when the LC retracts south of 25°N, the time
envelope for WCR shedding events increases to an average of more than 17 months (Leben 2005). Regardless of the northward LC penetration, these anticyclonically rotating WCRs propagate westward at speeds of
3–5 km day⫺1 (Elliot 1982). Note that both the LC and
WCR features contain upper-ocean currents of up to
1.7 m s⫺1 (Forristall et al. 1992; Oey et al. 2005). At any
given time, the GOM may have two or three WCRs
embedded within its circulation pattern, with smallerscale cold core rings located along their periphery. The
anticyclonic circulation around the LC exits the GOM
through the Florida Straits between the United States
and Cuba to form the Florida Current and, eventually,
the Gulf Stream. These ribbons of deeper and warmer
ocean current features transport heat poleward, representing an integral part of the gyre circulation (Gill
1982).
Investigating a central question about upper-ocean
heat, Leipper and Volgenau (1972) developed a relationship to estimate the hurricane heat potential or
ocean heat content (OHC), namely,
Q ⫽ cp
冕
␩
␳ 共z兲关T 共z兲 ⫺ 26兴 dz,
共1兲
h26
where cp is specific heat at constant pressure (4.2 kJ
kg⫺1 K⫺1), ␳(z) is the density structure, the observed
temperature is T(z), and integration limits stretch from
the depth of the 26°C isotherm (h26) to the surface (␩).
In subtropical regimes such as the LC, OHC values
exceed 100 kJ cm⫺2 (Leipper and Volgenau 1972). That
is, the 20° and 26°C isotherm depths are located at
⬃300- and 150-m depths in this subtropical water mass,
compared with ⬃100- and 50-m depths, respectively, in
the GCW.
To improve our understanding of the LC response to
the passage of a mature hurricane, a series of experiments was conducted from National Oceanic and Atmospheric Administration (NOAA) WP-3D research
flights (N42RF, N43RF) and the NOAA GulfstreamIV (N49RF) aircraft during the passage of Hurricanes
Isidore and Lili. The experimental sampling strategy
was designed to deploy global positioning system
(GPS) sondes (Hock and Franklin 1999), airborne expendable current profilers (AXCPs), airborne expendable conductivity, temperature, and depth profilers
(AXCTDs), and airborne expendable bathythermographs (AXBTs) prior to, during, and subsequent to
hurricane passage. This experimental effort in Hurricanes Isidore and Lili improved upon a previous Hurricane Gilbert experiment (Shay et al. 1992) by measuring prestorm, in-storm, and poststorm currents,
temperatures, and salinities along with detailed atmospheric temperature, humidity, and wind soundings
(Table 1). The objective of this paper is to document
the evolving thermal and momentum ocean response to
the heat, moisture, and momentum fluxes across the
air–sea interface based on the combination of GPS
sonde profiler data (Hock and Franklin 1999) and remotely sensed surface winds from the Stepped Frequency Microwave Radiometer (SFMR; Uhlhorn et al.
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VOLUME 136
TABLE 1. Deployed probes (RF failures in parentheses) for Isidore and Lili research flights from NOAA/NESDIS ocean winds (OW),
NSF, and landfall (LF) flights. Note that the 19 and 23 Sep flights represent pre-Lili conditions in the Gulf of Mexico (based on RF
signals, success rates ⬎85%). All dates are in 2002.
Isidore
Date
18
19
19
21
21
22
22
23
Sep
Sep
Sep
Sep
Sep
Sep
Sep
Sep
Lili
Flight
GPS
BTs
CPs
CTDs
Date
Flight
GPS
BTs
CPs
CTDs
NSF
OW
NSF
OW
NSF
OW
LF
NSF
11
25
11
53
22
15
10
12
20(4)
20
19(2)
18
19(1)
10
19
21(2)
16(1)
0
18(2)
0
30(7)
0
0
27(4)
23(2)
0
21(1)
0
14(0)
0
0
16(1)
25 Sep
29 Sep
30 Sep
30 Sep
2 Oct
2 Oct
3 Oct
4 Oct
Total
OW
NSF
NSF
OW
OW
NSF
LF
NSF
16
17
23
18
14
47
43
20
16
347
10
35(2)
31(3)
10
20
19(4)
1
10(1)
282(19)
0
0
6(2)
0
0
26(4)
0
35(4)
158(24)
0
0
0
0
0
18(4)
0
18(0)
110(8)
2007). To accomplish this objective, this paper is organized as follows: a description of the profiler data, including chronologies of Hurricanes Isidore and Lili, is
in section 2; the experimental approach, including the
surface wind forcing and air–sea parameters, is described in section 3; the observational analysis and air–
sea fluxes are discussed in section 4; section 5 describes
the forced LC response with respect to ocean cooling
and mixing; and the results are summarized, together
with concluding remarks, in section 6.
2. Hurricane chronology
a. Hurricane Isidore
The tropical wave from which Isidore developed
originated over Cape Verde, where several periods of
fluctuating storm intensity occurred until this wave
crossed the 50°W meridian (Pasch et al. 2004). However, only when the tropical depression moved into the
western Caribbean Sea was it named Tropical Storm
Isidore on 17 September 2002. Isidore then moved
slowly along a northwest track, and at 1800 UTC 19
September, Isidore was upgraded to a hurricane with a
central pressure of 983 mb. Isidore’s winds exceeded 40
m s⫺1 on 20 September as it approached the Isle of
Youth and made landfall along the tip of western Cuba.
The storm remained over Cuba for about 12 h, reemerging over the Yucatan Straits midday on 21 September. This slow-moving hurricane (⬃4 m s⫺1) traveled westward (Fig. 2), intensifying to a Category 3
storm just north of the Yucatan Straits over the LC (see
Fig. 1). Isidore moved over the Yucatan Shelf on 22
September and made landfall on the Yucatan Peninsula
for the next 36 h, weakening to a minimal tropical storm
(TS) embedded within a broad atmospheric circulation
pattern. Isidore subsequently moved northward and
created a cool wake of 28.5°C SSTs across the central
GOM (Fig. 1b), making landfall on 26 September just
west of Grande Isle, Louisiana.
b. Hurricane Lili
Lili was also a tropical wave of Cape Verdean origin,
starting on 16 September 2002 (Pasch et al. 2004). This
wave became a tropical depression on 21 September,
and as the system moved just west of north at ⬇10
m s⫺1, initial intensification to TS status occurred on 23
September. The TS subsequently weakened to an open
tropical wave on 26 September, but as the wave slowed
it redeveloped into a TS late on 27 September, with a
minimum central pressure of 994 mb. Lili intensified to
hurricane status at 1200 UTC 30 September while passing over the Cayman Islands. As Lili tracked along a
north-northwest trajectory after emerging off the Cuban coast (Fig. 2), the hurricane intensified to Category
3 status (⬃51 m s⫺1) over the LC and to a Category 4
storm (61 m s⫺1) in the south-central GOM just north
of the boundary between the LC and the GCW. During
this period, Lili’s radius of maximum winds (Rmax) decreased from 25 km over the LC to 18 km along the
northern boundary between the LC and the GCW
when the storm system was moving at 7 m s⫺1. Lili
rapidly weakened to Category 1 status owing to a combination of enhanced atmospheric shear, the intrusion
of dry air along the western edge (Pasch et al. 2004),
and interactions with the shelf water cooled by Isidore.
Hurricane Lili made landfall at 1300 UTC 3 October
near Intracoastal City, Louisiana.
3. Experimental approach
During the 2002 NOAA Hurricane Research Division’s (HRD’s) hurricane field program, a joint National Science Foundation (NSF) and NOAA experiment measured both the kinematic and thermodynamic
upper-ocean response to a propagating mature tropical
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FIG. 1. (a) LC (red contour) position relative to the best tracks of Isidore (black track,
originating in bottom center) and Lili (black track, originating in bottom-right corner) in
September–October 2002 with intensities (see legend) and the location of NDBC 42001 (blue
dot). (b) Observed SSTs (°C) at NDBC 42001 with gray shading indicating lifetimes of Isidore
and Lili.
cyclone over the LC. Motivated by the Hurricane Opal
case, the experimental objective was to measure the
levels of upper-ocean cooling and shear-induced mixing
in the LC circulation system. To achieve this objective,
the experiment used 16 research flights, each deploying
oceanic and atmospheric expendable probes in the
same location before, during, and after the passage of
Hurricanes Isidore and Lili (Table 1). A set of prestorm
flights was conducted during 18–23 September 2002;
in-storm flights occurred on 21 September and 2 October; and poststorm surveys were acquired on 22 and 23
September and 4 October. In addition, there were also
two landfall experiments on 22 September and 3 Octo-
ber off the Yucatan Peninsula and along the Louisiana
Coast for Isidore and Lili, respectively. Success rates
for the oceanic profilers, defined here as receiving radio
frequency (RF) signals on the aircraft, were greater
than 85%. GPS sondes were also concurrently deployed from the aircraft, including the G-IV used to
map the regional-scale atmospheric structure over the
GOM from flight level to the surface in the storm and
the surrounding environment.
The comprehensive set of measurements included
both in situ and remotely sensed data. The data acquired included current and temperature profiles
from AXCPs, temperature and salinity profiles from
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FIG. 2. HRD H*Wind surface wind analysis of Hurricanes (a) Isidore at 2130 UTC 21 Sep
2002 and (b) Lili at 0700 UTC 02 Oct 2002. Isotachs are contoured every 5 m s⫺1. Data used
to generate this analysis include observations from the SFMR, GPS dropwindsondes, QuikSCAT scatterometer, and available hourly buoy reports. The storm track is indicated by the
solid line; the dark box shows the ocean data analysis region considered for this research.
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SHAY AND UHLHORN
AXCTDs, temperature profiles from AXBTs, and surface directional wave spectra from the NASA scanning
radar altimeter (Wright et al. 2001). Note that although
the AXCPs, AXCTDs, and AXBTs all measure temperature, the temperature measurements only penetrate to 350 m for the AXBTs compared to 1000 and
1500 m for AXCTDs and AXCPs, respectively. A second difference is that temperatures from AXBTs and
AXCPs are measured with a thermistor with an accuracy of 0.2°C; an AXCTD’s thermistor accuracy is
0.12°C. In this study, SSTs from all expendable profilers
are defined to be near-surface temperatures within the
first few meters of the sea surface. Also, deeper profiles
allow estimates of geostrophically balanced currents
relative to 750 m for assessing initialization schemes
used in ocean models (Halliwell et al. 2008). Finally, the
surface wind field was measured from observations by
GPS sondes (Hock and Franklin 1999) and SFMR
(Uhlhorn et al. 2007). These in situ data are cast within
a regional-scale context using SHA fields measured
from radar altimetry (Cheney et al. 1994; Sturges and
Leben 2000). TOPEX and Geosat Follow-On Mission
SHA data (in Fig. 3) were objectively analyzed at
0.5° using the method of Mariano and Brown (1992)
based on parameters used with the Hurricane Gilbert
dataset.
a. Isidore
Given uncertainties in Isidore’s track, two grids of
prestorm ocean profilers were deployed from research
aircraft in the northwest Caribbean Sea and in the
south-central part of the GOM on 18 and 19 September
2002 (Figs. 3a,b). Success rates in acquiring profiles
were ⬇75% from oceanic probes. In some cases, the
compound surrounding the thermistor was compromised below 100 m because of pressure effects that
caused bad temperature profiles from AXCPs. A few
AXCTDs also had incorrect calibration coefficients and
were not used in the analyses below. On each of the
prestorm flights, there were eight probes with no RF
signals. During the dual-aircraft Isidore flight on 21
September (Fig. 3c), there were eight failures out of 63
deployed profilers, and 19 additional AXBTs deployed
from N42RF with 5 RF failures. Several AXCPs malfunctioned along the western boundary of the Yucatan
Straits, where large currents and current shears caused
the thin wire connecting the probe to the surface unit to
break. Given the dual-aircraft mission, this still produced unprecedented coverage of the upper ocean as a
hurricane intensified to Category 3 status. On 22 September, there were 29 additional AXBTs deployed
over the same regime where the in-storm flights de-
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ployed profilers, including over the Yucatan Shelf. During the poststorm experiment on 23 September (⬃2
days later), 64 probes were deployed along transects
similar to those of the prestorm and in-storm flights.
Seven of these profilers did not transmit data back to
the aircraft.
b. Lili
One week later, on 28 September 2002, TS Lili
moved to the northwest toward the Yucatan Straits following a track similar to Isidore. During this time, a
prestorm flight was conducted in front of the projected
TS Lili (and potential hurricane) track on 29 September
(not shown) by deploying AXBTs. On 30 September,
additional profilers were deployed from an in-storm
flight centered on Lili at 20°N, 81°W, including six
AXCPs with four probes providing profiler data (not
shown). As Lili continued along this northwest trajectory, moving over the western tip of Cuba as a Category
1 storm, the in-storm flight on 2 October (Fig. 3f) was
centered fortuitously on the pre-Isidore grid of 19 September (Fig. 3b). On this research flight, 63 profilers
were deployed, with 12 of them not providing any RF
signals to the aircraft. It was during this early flight on
N43RF and the later N42RF flight on 2 October [in
support of a NOAA/National Environmental Satellite,
Data, and Information Service (NESDIS) ocean winds
experiment deploying AXBTs] that Lili deepened to a
Category 4 storm just northwest of the boundary between the LC and the GCW in the central GOM basin.
A post-Lili experiment was then conducted on 4 October by deploying the same number of profilers, with
only five RF failures. Thus, these oceanic and atmospheric measurements were acquired when two hurricanes, separated by 10 days, were intensifying over the
same oceanographic regime.
c. Air–sea parameters
Air–sea parameters and scaling arguments, defined
in Table 2, are used to place the observations into a
nondimensional framework based on Price (1983). The
wavelength of the oceanic response induced by a moving tropical cyclone is proportional to the product of
the storm translation speed Uh and the local inertial
period (IP; Geisler 1970). Based on a 4 m s⫺1 translation speed and an IP of 1.3 days (⬇31 h), the predicted
wavelength ⌳ for Isidore is 450 km (Table 2). For Lili,
this wavelength is ⬃770 km because of faster translation speeds of ⬃7 m s⫺1 and IPs ranging from 1.3 days
(31 h) to 1.16 days (28 h) over the LC and GCW, respectively. The Rmax for these storms over the LC
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FIG. 3. SHA field (colors indicate heights in cm) from radar altimetry and oceanic profile
deployments for (a) pre-Isidore in the northwest Caribbean Sea, (b) pre-Isidore in the south
central GOM, (c) Isidore in-storm across the Yucatan Straits, (d) post-Isidore (1 day), (e)
post-Isidore (2 days), (f) Lili in-storm over the grid in (b), and (g) post-Lili on 4 October
relative to the Isidore and Lili tracks with hurricane category levels as in Fig. 1. AXBT data
are indicated by triangles; AXCP, by boxes; AXCTD, by circles. Black symbols indicate good
data; white symbols indicate probe failure.
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SHAY AND UHLHORN
TABLE 2. Air–sea parameters, nondimensional numbers and scales in Isidore and Lili (LC and GCW) based on Price’s (1983)
scaling arguments. Maximum wind stress is estimated from SFMR data.
Isidore
Parameter
Radius of maximum winds (km)
Maximum wind (m s⫺l)
Maximum wind stress (N m⫺2)
Speed of the hurricane (m s⫺1)
Wavelength (km)
First mode phase speed (m s⫺1)
First mode deformation radius (km)
Time scale (IP)
Inertial period (days)
Reduced gravity (m s⫺2 ⫻ 10⫺2)
Mixed layer depth (m)
Rmax
Wmax
␶max
Uh
⌳
c1
␣⫺1
n
t1
IP
g⬘
h
Froude number Fr
Nondimensional storm speed S
Mixed-layer Burger number M
Thermocline Burger number T
Nondimensional forcing Fo
Non-dimensional numbers
Uh /c1
Uh /(2Rmax f )
(1 ⫹ S⫺2)g⬘h/(2Rmax f )2
bh⫺1M
2Rmax/␣1
Wind-driven velocity Vml (m s⫺1)
Thermocline velocity Vth (m s⫺1)
Isopycnal displacements ␩s (m)
Geostrophic velocity Vgs (cm s⫺1)
Frequency shift ⑀
Scales
␶maxRmax/(␳␱hUh)
hb⫺1 Vml
␶max/( fUh)
g⬘␩s/( fRmax)
M/2
ranged from 23 to 25 km; however, as Lili moved northwestward over the GCW, Rmax decreased to 18 km during a deepening cycle to a Category 4 storm. In this
context, along- and cross-track directions are nondimensionalized in terms of ⌳ and Rmax to examine the
forced ocean response relative to the observed storm
structure (Shay et al. 1998).
The first baroclinic mode wave phase speed in the LC
is approximately 1.5 m s⫺1; in the GCW, this phase
speed increases to 2.8 m s⫺1 because of stronger stratification at the base of the mixed layer. Reduced gravities (g⬘) ranged from ⬃1 ⫻ 10⫺2 m s⫺2 in the LC to
2.5 ⫻ 10⫺2 m s⫺2 within the GCW (e.g., Shay et al.
2000). The Caribbean subtropical water (STW) stratification is weaker, with large ocean mixed layers
(OMLs) of O(100 m) compared to the GCW stratification, where the initial OML depth lies between 35
and 40 m. The Froude number, defined as the ratio
of the translation speed to the first baroclinic mode
wave phase speed Uh c⫺1
1 , exceeds 2.5 in both cases,
implying a predominant baroclinic ocean response
(Geisler 1970). The baroclinic radius of deformation
(␣⫺1
1 ) was 28 km in the LC, compared with 46 km in the
GCW. When the length scale of the wind stress forcing
(2Rmax ⬇ 50 km) is greater than the deformation radius
Lili
LC
LC
GCW
23
50
7.1
4
449
1.5
28
1.2
1.3
1
110
25
50
7.1
6.9
771
1.5
26
1.7
1.3
1
110
18
61
10.
7.7
775
2.8
46
0.3
1.16
2.5
35
2.6
0.54
0.08
0.072
1.64
0.38
0.42
10.9
2.9
0.04
2.5
0.8
0.04
0.036
1.92
2.8
1.15
0.035
0.2
0.78
0.24
0.26
6.1
1.4
0.02
0.68
0.12
7.3
5.3
0.018
associated with the first baroclinic mode (Gill 1984),
the baroclinic time scale required for a phase difference
of ␲/2 to develop between the first baroclinic mode and
the other baroclinic modes is given by
t1 ⫽
␲f
k2c21
,
共2兲
where k represents the horizontal wavenumber of the
wind stress, f is the local Coriolis parameter, and c1 is
the first baroclinic mode phase speed. The relevant
time scales are 1.2–1.7 IPs in the LC regime compared,
with 0.3 IPs in the GCW. This more rapid time scale is
due to a decrease in Rmax coupled with a faster phase
speed when Lili moved over the GCW. Note that this
time scale was O(2 IPs) during Gilbert due to an Rmax
that was 3 times larger than that observed in either
Isidore or Lili (Shay et al. 1992).
Isotherm displacements (␩) scale as ␶max/(␳ofUh),
about 11 m (6 m) in the expected Isidore (Lili) ocean
response. The geostrophic velocity response Vgs, proportional to g⬘␩/(fRmax), is predicted to be weak,
with values of 1 to 3 cm s⫺1 in the LC compared with
5 cm s⫺1 in the GCW, consistent with the Gilbert
dataset (Shay et al. 1992). Wind-driven ocean veloc-
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ity Vml scales as ␶maxRmax/(␳ohUh) representing a velocity of 24–38 cm s⫺1, with similar values in the thermocline based on the expression Vmlh/b (where h is the
initial OML depth and b is the thermocline thickness).
Weak upper-ocean stratification distributed over
deeper layers will cause the LC response to be weaker
than in the more stratified GCW (Price 1981; Shay and
Elsberry 1987; Shay et al. 1992). In the GCW, however,
the predicted wind-forced thermocline current is 12
cm s⫺1 because of stronger stratification and shallower
OML depths. The magnitude of the ocean response
depends not only on the characteristics of the hurricane forcing but also, crucially, on the background
initial ocean conditions based on these scaling arguments. Price (1983) defined a mixed-layer Burger number as
M⫽
共1 ⫹ S⫺2兲g⬘h
共2Rmax f 兲2
,
共3兲
where S is the nondimensional storm speed
Uh/(2Rmax f ) and h is the OML depth. For the LC, M
ranged between 0.04 and 0.08 because of large values of
S for Lili (0.8) and for Isidore (0.54). Over the GCW,
Lili’s acceleration toward the northwest coupled with a
smaller Rmax caused S to increase to 1.15. The thermocline Burger numbers T ⫽ b/hM are nearly equal to
M in the LC because the ratio of thermocline and OML
thicknesses is O(1), as noted above. In the GCW, however, T is 0.2 (i.e., a magnitude larger than in the LC),
representing more dynamical coupling between the
OML and thermocline layer. The resultant blue shift in
the mixed-layer inertial frequency is proportional to
M/2 (Table 2), equating to frequencies shifted above f
by 2% to 4%, consistent with previous results (Shay et
al. 1998).
4. Analysis approach
a. Orbital velocities
To examine the current and shear measurements
from the AXCPs, the surface wave–induced orbital velocity signals must be removed from the current profiles
observed from the in-storm flights. When averaged
over a cycle, the resolved low-frequency surface waves
do not contribute significantly to the mean current
(with the exception of a small Stokes drift due to nonlinear wave structure). Observed current profiles are fit
to the Sanford et al. (1987) three-layer model with an
assumed monochromatic, linear, deep-water surface
gravity wave superimposed; thus,
VOLUME 136
冋冉冊
冋冉
u共z兲 ⫽ C cos
冉冊册
冊册
␻z
␻z
⫹ S sin
W
W
⫹ Szi z ⫺
Zi⫺1 ⫺ Zi
2
ekz ⫹ Ui
, for 共i ⫽ 1, 3兲,
共4兲
where u(z) is the modeled east–west current profile [a
similar expression holds for the north–south component ␷(z)], C and S are the amplitudes of the orbital
velocities associated with surface waves, ␻ ⫽ 公kg is
the wave frequency for wavenumber k following from
linear theory, W ⫽ ⫺4.5 m s⫺1 is the AXCP fall rate,
and Ui and Szi are the mean current and shear in layer
i, respectively. Observed current profiles are fit to (4)
using a standard Levenberg–Marquardt nonlinear least
squares regression (Marquardt 1963) by minimizing the
error over a range of trial wave periods T ⫽ 7–14 s
(␻ ⫽ 2␲/T ). An additional constraint is that the current
profiles are continuous across layer interfaces, thereby
reducing the number of free parameters from eight to
six.
Model fits to the Isidore (21, 23 September) and Lili
(2 October) current profiles are listed in Tables 3, 4,
and 5, respectively. In-storm orbital velocity amplitudes
were typically 1 m s⫺1, in accord with previous experimental efforts (Sanford et al. 1987). As shown in Fig. 4,
the RMS residual currents, estimated by calculating differences between the model (4) and the observed profile to a depth where kz ⫽ ⫺2 (i.e., where wave amplitudes are reduced to about 13% of their surface velocity amplitudes based on the fits), were generally less
than 10 cm s⫺1, indicative of a reasonably good fit for
strongly forced mixed layer conditions. However, there
were a few exceptions with relatively large residuals.
Vertical shears of the horizontal velocity components in
the upper two layers (Z1, Z2) were O(10⫺2 s⫺1),
whereas the shears in the lower layer (Z3) decreased by
an order of magnitude. The orbital velocity amplitudes
have been removed from the observed current profiles
to examine the observed upper-ocean response (Shay
et al. 1992; Price et al. 1994).
b. Objective analyses
Objectively analyzed fields of observed variables are
produced using a statistical interpolation methodology.
The analysis procedure used here is the OAX5 package
(developed at Canada Bedford Institute of Oceanography), which is based on the algorithm presented in
Bretherton et al. (1976). This approach uses a linear
optimal interpolation technique to estimate values at
SEPTEMBER 2008
3257
SHAY AND UHLHORN
TABLE 3. Coefficients from fits with the Sanford et al. (1987) model and the Isidore storm AXCP profiles in the upper 200 m where
Z0 is the start depth of the good data used in the fit; T is the period of the surface wave with coefficients of C and S; Z1,2,3, V1,2,3 and
S1,2,3 ⫻ 10⫺2 represent layer depth, layer–averaged currents, and current gradients in each layer, respectively; and R is the residual
current not explained by the model to a depth of e⫺2.
Time
T
UTC
Variable
s
1824
u
␷
u
␷
u
␷
u
␷
u
␷
u
␷
u
␷
u
␷
u
␷
u
␷
u
␷
u
␷
u
␷
u
␷
u
␷
u
␷
u
␷
u
␷
u
␷
u
␷
10.5
9.5
7.5
10.0
8.0
7.0
7.0
6.0
10.5
9.5
10.0
7.0
11.5
12.0
12.0
8.0
8.5
7.0
10.5
8.0
7.0
7.0
8.0
7.0
12.0
8.0
9.5
9.5
12.0
10.0
8.5
11.0
9.0
10.0
10.5
9.0
8.5
9.0
9.5
8.0
1835
1850
1926
1936
1957
2007
2030
2036
2100
2110
2120
2145
2148
2159
2210
2320
2331
0007
0016
C
cm s
S
⫺1
⫺7
13
⫺77
92
8
23
⫺28
45
6
⫺8
⫺11
23
5
⫺3
41
⫺12
⫺288
174
⫺36
7
291
⫺491
37
4
⫺64
⫺83
⫺44
⫺50
26
⫺102
10
62
⫺19
2
0
⫺35
⫺35
19
⫺108
⫺46
cm s
Z0
⫺1
13
⫺21
9
132
⫺2
9
⫺19
⫺79
⫺16
⫺18
18
⫺57
⫺0
10
⫺74
⫺76
⫺85
372
⫺48
⫺63
⫺1155
⫺268
72
13
⫺48
⫺132
0
⫺68
⫺9
9
⫺43
23
22
⫺72
⫺7
⫺3
241
⫺396
28
⫺202
m
⫺10
⫺10
⫺18
⫺18
⫺10
⫺10
⫺8
⫺8
⫺10
⫺10
⫺15
⫺15
⫺5
⫺5
⫺8
⫺8
⫺15
⫺15
⫺8
⫺8
⫺20
⫺20
⫺10
⫺10
⫺10
⫺10
⫺10
⫺10
⫺10
⫺10
⫺10
⫺10
⫺8
⫺8
⫺7
⫺7
⫺8
⫺8
⫺8
⫺8
V1
cm s
⫺1
⫺18
32
⫺15
70
⫺39
15
11
23
49
40
⫺13
53
10
24
31
126
⫺30
166
⫺4
27
⫺45
12
⫺24
⫺28
90
87
57
33
6
⫺71
32
⫺71
30
⫺19
75
⫺13
⫺63
119
⫺11
⫺24
S1
s
⫺1
0.11
0.14
⫺0.48
3.29
0.10
⫺0.78
⫺0.02
1.80
0.72
⫺1.22
⫺0.42
⫺1.07
⫺0.05
0.04
1.52
⫺0.13
⫺2.14
2.36
1.16
1.35
⫺8.63
⫺1.64
⫺3.78
⫺0.05
⫺0.17
0.05
⫺2.93
⫺0.87
0.56
0.27
0.00
0.65
0.65
1.18
⫺0.11
1.02
⫺6.94
16.39
0.11
3.15
grid points based on observations at the nearest neighbors. A covariance model of the form (Freeland and
Gould 1976)
冉
␳共r兲 ⫽ e⫺r 1 ⫹ r ⫹
r2
3
冊
共5兲
is used, where r is the weighted nondimensional distance between an observation and a grid point. In the
absence of detailed climatological information avail-
Z1
m
⫺60
⫺60
⫺50
⫺50
⫺50
⫺50
⫺30
⫺30
⫺50
⫺50
⫺50
⫺50
⫺50
⫺50
⫺50
⫺50
⫺60
⫺60
⫺30
⫺30
⫺40
⫺40
⫺40
⫺40
⫺70
⫺70
⫺40
⫺40
⫺120
⫺120
⫺60
⫺60
⫺30
⫺30
⫺60
⫺60
⫺30
⫺30
⫺30
⫺30
V2
cm s
⫺1
⫺33
⫺5
⫺31
10
⫺5
57
4
28
30
58
7
79
11
27
20
124
7
65
⫺2
10
40
0
13
⫺10
69
77
76
43
⫺23
⫺60
14
⫺52
21
⫺9
70
⫺67
9
⫺38
⫺18
⫺61
S2
s
⫺1
0.58
1.66
1.19
0.32
⫺3.60
⫺2.64
0.36
⫺1.23
0.11
0.15
⫺0.65
⫺0.37
0.01
⫺0.14
⫺2.09
0.45
0.51
2.39
⫺2.96
0.55
0.28
5.70
1.29
⫺1.17
1.30
0.45
1.24
0.13
⫺0.10
⫺1.64
1.83
⫺3.52
0.14
⫺1.54
0.81
2.64
0.41
⫺2.36
1.18
0.57
Z2
m
⫺100
⫺100
⫺90
⫺90
⫺70
⫺70
⫺70
⫺70
⫺140
⫺140
⫺90
⫺90
⫺100
⫺100
⫺70
⫺70
⫺100
⫺100
⫺40
⫺40
⫺50
⫺50
⫺70
⫺70
⫺110
⫺110
⫺80
⫺80
⫺150
⫺150
⫺80
⫺80
⫺60
⫺60
⫺80
⫺80
⫺50
⫺50
⫺40
⫺40
V3
⫺1
cm s
⫺42
⫺14
⫺40
8
17
59
⫺2
22
17
25
21
53
2
25
23
103
⫺1
19
9
⫺24
34
⫺30
1
14
20
44
18
39
⫺6
⫺10
⫺6
⫺10
11
11
56
⫺48
6
⫺4
⫺32
⫺44
S3
Z3
R
⫺1
m
cm s⫺1
⫺200
⫺200
⫺200
⫺200
⫺200
⫺200
⫺200
⫺200
⫺180
⫺180
⫺200
⫺200
⫺200
⫺200
⫺90
⫺90
⫺200
⫺200
⫺50
⫺50
⫺60
⫺60
⫺140
⫺140
⫺200
⫺200
⫺120
⫺120
⫺200
⫺200
⫺200
⫺200
⫺120
⫺120
⫺200
⫺200
⫺200
⫺200
⫺50
⫺50
4.4
5.9
7.7
7.8
3.4
12.0
5.2
11.0
4.1
8.5
8.7
16.3
2.9
2.9
5.0
3.4
6.1
9.7
5.4
7.0
2.6
15.5
4.2
4.9
9.8
6.0
6.8
5.7
4.3
7.1
4.2
6.7
3.0
5.8
5.1
11.5
2.8
9.5
5.9
15.2
s
⫺0.05
⫺0.49
⫺0.26
⫺0.06
0.21
0.37
⫺0.02
0.47
0.39
1.29
⫺0.02
0.61
0.16
0.10
1.82
1.61
⫺0.03
⫺0.03
0.82
6.28
0.89
0.25
⫺0.19
⫺0.20
0.52
0.53
1.67
0.07
⫺0.62
⫺1.05
0.03
⫺0.12
0.26
0.10
0.11
⫺0.76
⫺0.02
⫺0.14
1.71
⫺4.00
able about LC structural and temporal variability over
the scales of interest exposed to severe forcing, a quantitative development of the optimal parameter scales is
difficult (e.g., Baker et al. 1987). Therefore, scales are
chosen through trial and error to adequately resolve the
mesoscale ocean structure. Because the largest variability is observed near the surface during hurricane passage, spatial scales here are smaller, and they increase
with depth (Table 6). The horizontal covariance model
␳(r) is plotted for each layer as a function of dimen-
3258
VOLUME 136
TABLE 4. Same as Table 3, but for Lili storm AXCP profiles in the upper 200 m.
Time
T
C
S
Z0
V1
S1
Z1
V2
S2
Z2
V3
S3
Z3
R
UTC
Variable
s
cm s⫺1
cm s⫺1
m
cm s⫺1
s⫺1
m
cm s⫺1
s⫺1
m
cm s⫺1
s⫺1
m
cm s⫺1
0240
u
␷
u
␷
u
␷
u
␷
u
␷
u
␷
u
␷
u
␷
u
␷
u
␷
u
␷
u
␷
u
␷
u
␷
u
␷
u
␷
u
␷
u
␷
u
␷
u
␷
13.5
8.5
11.5
7.0
10.0
14.0
14.5
10.5
10.5
8.5
11.0
9.0
8.0
11.5
10.5
11.5
8.0
11.0
9.5
10.
7.5
8.5
8.0
10.0
9.0
9.0
11.0
7.0
11.5
11.5
11.0
12.0
13.0
8.0
12.5
14.0
8.0
12.0
12.0
8.0
⫺21
64
⫺56
⫺176
85
⫺47
⫺19
23
⫺39
73
⫺8
13
34
5
51
1
⫺76
⫺4
8
28
178
15
⫺178
⫺111
25
57
⫺28
55
9
⫺5
0
3
⫺13
⫺34
⫺2
3
⫺54
27
⫺21
⫺11
25
⫺93
⫺145
57
⫺52
⫺17
101
44
6
⫺47
7
⫺6
⫺48
⫺27
⫺53
46
⫺27
⫺49
14
30
⫺104
58
⫺165
0
44
⫺42
22
⫺81
⫺10
⫺25
⫺39
⫺28
⫺11
6
⫺10
18
⫺83
⫺9
⫺6
⫺29
⫺10
⫺10
⫺10
⫺10
⫺12
⫺12
⫺12
⫺12
⫺8
⫺8
⫺10
⫺10
⫺8
⫺8
⫺8
⫺8
⫺10
⫺10
⫺10
⫺10
⫺8
⫺8
⫺17
⫺17
⫺10
⫺10
⫺10
⫺10
⫺10
⫺10
⫺12
⫺12
⫺8
⫺8
⫺10
⫺10
⫺10
⫺10
⫺8
⫺8
⫺4
4
26
51
⫺3
16
⫺28
⫺6
⫺5
⫺2
⫺28
⫺12
⫺7
⫺8
⫺5
⫺19
14
19
⫺6
9
38
⫺17
⫺12
⫺22
14
105
12
106
22
42
16
39
⫺14
8
86
⫺3
26
92
11
152
⫺0.61
5.13
⫺0.27
0.03
0.86
0.65
⫺2.20
0.57
⫺0.71
⫺0.53
⫺0.38
1.20
0.37
0.45
1.71
⫺0.87
0.07
1.96
⫺0.08
0.14
0.32
⫺1.52
⫺2.97
⫺1.90
0.01
⫺0.15
0.05
0.67
0.47
0.08
⫺0.06
0.28
⫺0.08
0.22
⫺0.23
0.45
0.27
0.47
0.64
1.23
⫺30
⫺30
⫺60
⫺60
⫺50
⫺50
⫺50
⫺50
⫺50
⫺50
⫺50
⫺50
⫺30
⫺30
⫺40
⫺40
⫺35
⫺35
⫺50
⫺50
⫺40
⫺40
⫺55
⫺55
⫺65
⫺65
⫺50
⫺50
⫺70
⫺70
⫺80
⫺80
⫺80
⫺80
⫺80
⫺80
⫺100
⫺100
⫺65
⫺65
5
⫺22
32
51
⫺10
⫺13
0
⫺5
⫺4
12
⫺16
⫺19
⫺6
⫺4
⫺13
⫺15
12
7
6
11
24
21
52
21
17
104
22
57
16
41
3
10
⫺21
⫺44
79
⫺32
12
44
⫺1
86
⫺0.35
⫺3.34
⫺0.01
⫺0.07
⫺0.37
0.67
0.55
⫺0.43
0.52
⫺0.08
⫺0.27
⫺1.12
⫺0.34
⫺0.58
⫺1.97
1.06
0.11
⫺1.04
⫺0.71
⫺0.30
1.21
⫺1.74
⫺0.30
⫺0.25
⫺0.08
0.13
⫺0.74
2.36
⫺0.30
⫺0.06
0.51
0.65
0.92
4.48
0.75
0.63
0.08
1.33
⫺0.78
4.10
⫺45
⫺45
⫺80
⫺80
⫺100
⫺100
⫺100
⫺100
⫺100
⫺100
⫺80
⫺80
⫺60
⫺60
⫺60
⫺60
⫺60
⫺60
⫺80
⫺80
⫺55
⫺55
⫺110
⫺110
⫺150
⫺150
⫺80
⫺80
⫺120
⫺120
⫺140
⫺140
⫺100
⫺100
⫺120
⫺120
⫺140
⫺140
⫺80
⫺80
1
⫺4
31
41
⫺1
⫺9
0
14
⫺12
14
⫺15
1
7
6
9
⫺22
11
20
9
9
20
21
38
21
⫺6
58
8
12
16
39
⫺4
⫺15
⫺15
⫺41
51
⫺34
2
10
⫺5
44
0.12
0.14
0.02
0.17
⫺0.00
⫺0.43
⫺0.27
⫺0.17
⫺0.10
⫺0.01
0.04
⫺0.06
⫺0.11
⫺0.03
⫺0.03
⫺0.06
⫺0.01
⫺0.00
0.13
0.11
⫺0.08
0.18
0.51
0.15
1.03
1.64
0.49
0.18
0.17
0.08
⫺0.28
0.16
⫺0.29
⫺0.97
0.34
⫺0.26
0.27
0.27
0.16
0.20
⫺150
⫺150
⫺200
⫺200
⫺200
⫺200
⫺200
⫺200
⫺200
⫺200
⫺200
⫺200
⫺200
⫺200
⫺200
⫺200
⫺200
⫺200
⫺200
⫺200
⫺200
⫺200
⫺200
⫺200
⫺200
⫺200
⫺180
⫺180
⫺200
⫺200
⫺200
⫺200
⫺200
⫺200
⫺200
⫺200
⫺200
⫺200
⫺200
⫺200
2.2
7.9
8.7
10.4
4.3
6.1
4.9
6.2
8.4
12.2
3.0
5.3
2.4
6.5
2.5
2.8
4.4
6.0
2.1
4.6
8.7
4.3
9.9
4.2
12.6
11.7
8.4
8.5
10.1
8.6
9.7
14.7
5.1
11.4
2.8
6.1
9.6
9.9
4.3
9.7
0312
0336
0342
0440
0527
0538
0545
0614
0625
0635
0648
0711
0740
0749
0759
0809
0853
0905
0918
sional distance rL (Fig. 5). For the observed profiles,
the grid structure used for all Lili (Isidore) analyses is
31 ⫻ 31 (41 ⫻ 41) nodes in the horizontal plane, encompassing a 3° ⫻ 3° (4° ⫻ 4°) domain in latitude and
longitude, respectively. The vertical grid contains 151
points at 5-m depth intervals from the surface to 750 m.
The Isidore (Lili) grids are rotated 270° (292°) clockwise from north to align with the storm track direction.
Isidore’s (Lili’s) storm track is aligned with the 21st
(5th) grid column from the south (southwest) side of
the domain, and the peak surface wind travels along
approximately the 23rd (8th) column. Each analysis
uses an e-folding time scale of 2.9 days, consistent with
previously observed response time scales (Shay et al.
1992).
Assuming properly chosen scales for the interpolation, uncertainty estimates for each gridded field are
available based upon the input measurement noise. For
nominal measurement errors of surface temperatures,
maximum mapping errors are 0.4°C in the northwest
part of the pre-Lili grid because of data sparsity in that
region compared to temperature mapping errors of
0.2°C (not shown) over the remainder of the domain.
Similarly, mapping errors for 26°C isotherm depths
range from 1 to 3 m, whereas those associated with
OHC values have a maximum of 12 kJ cm⫺2. Finally,
SEPTEMBER 2008
3259
SHAY AND UHLHORN
TABLE 5. Same as Table 3, but for Lili post-storm AXCP profiles.
Time
T
C
S
Z0
V1
S1
Z1
V2
S2
Z2
V3
S3
Z3
R
UTC
Variable
s
cm s⫺1
cm s⫺1
m
cm s⫺1
s⫺1
m
cm s⫺1
s⫺1
m
cm s⫺1
s⫺1
m
cm s⫺1
1755
u
␷
u
␷
u
␷
u
␷
u
␷
u
␷
u
␷
u
␷
u
␷
u
␷
u
␷
u
␷
u
␷
u
␷
u
␷
u
␷
u
␷
u
␷
u
␷
8.0
8.5
11.0
9.0
13.0
7.0
8.5
11.0
9.0
7.5
8.0
7.0
13.0
10.0
9.0
13.0
8.5
9.0
10.0
9.0
10.0
12.0
9.0
8.0
8.0
10.0
11.0
10.0
8.0
7.0
15.0
9.0
8.0
8.0
9.0
9.0
8.5
8.0
211
64
18
⫺39
18
⫺10
⫺23
⫺2
19
37
14
4
⫺17
⫺1
⫺20
50
32
3
6
⫺56
⫺9
223
0
21
⫺92
58
12
3
18
⫺72
⫺25
⫺26
⫺37
48
30
⫺7
⫺48
⫺8
⫺44
⫺41
4
6
⫺1
⫺55
⫺31
19
⫺27
⫺143
⫺17
2
5
46
⫺19
66
6
3
⫺27
18
⫺6
⫺42
8
17
36
⫺17
0
15
64
⫺65
5
84
⫺13
8
10
1
20
6
⫺9
⫺9
⫺8
⫺8
⫺8
⫺8
⫺15
⫺15
⫺10
⫺10
⫺10
⫺10
⫺10
⫺10
⫺15
⫺15
⫺15
⫺15
⫺15
⫺15
⫺22
⫺22
⫺8
⫺8
⫺10
⫺10
⫺12
⫺12
⫺10
⫺10
⫺10
⫺10
⫺10
⫺10
⫺8
⫺8
⫺10
⫺10
22
⫺6
114
⫺28
68
13
⫺6
⫺15
⫺6
53
29
92
⫺20
⫺79
34
35
65
67
⫺5
15
1
36
⫺22
14
⫺42
87
47
⫺21
⫺23
60
⫺48
⫺51
⫺12
⫺38
⫺52
79
⫺3
5
1.46
0.91
⫺0.02
0.48
0.01
0.39
⫺1.51
1.09
0.74
3.01
⫺0.13
⫺0.09
⫺0.23
0.20
0.02
1.11
0.50
0.62
5.02
⫺1.94
⫺0.10
6.45
0.23
⫺1.14
⫺1.65
0.15
0.24
0.35
1.10
⫺0.40
1.45
0.30
⫺0.68
2.06
⫺0.20
0.18
⫺0.27
0.35
⫺35
⫺35
⫺60
⫺60
⫺95
⫺95
⫺50
⫺50
⫺25
⫺25
⫺70
⫺70
⫺80
⫺80
⫺70
⫺70
⫺70
⫺70
⫺25
⫺25
⫺50
⫺50
⫺45
⫺45
⫺60
⫺60
⫺80
⫺80
⫺60
⫺60
⫺25
⫺25
⫺40
⫺40
⫺40
⫺40
⫺100
⫺100
7
⫺13
79
⫺16
44
⫺7
11
⫺22
⫺17
14
22
78
⫺6
⫺40
24
15
48
33
⫺25
6
0
⫺24
⫺10
33
⫺4
89
30
⫺29
⫺21
75
⫺37
⫺25
5
⫺35
⫺22
60
14
7
⫺0.16
⫺0.17
1.17
⫺0.83
3.10
0.41
0.27
⫺0.37
0.39
1.28
0.72
1.10
⫺0.33
⫺2.31
0.26
⫺0.30
0.17
1.11
⫺0.38
1.44
0.10
⫺1.02
⫺0.92
0.12
0.19
⫺0.30
0.44
⫺0.23
⫺1.48
⫺0.28
⫺0.59
⫺0.75
⫺0.60
⫺3.29
⫺1.35
0.82
⫺0.28
⫺1.18
⫺90
⫺90
⫺120
⫺120
⫺110
⫺110
⫺120
⫺120
⫺50
⫺50
⫺100
⫺100
⫺120
⫺120
⫺140
⫺140
⫺100
⫺100
⫺50
⫺50
⫺110
⫺110
⫺80
⫺80
⫺100
⫺100
⫺120
⫺120
⫺100
⫺100
⫺100
⫺100
⫺60
⫺60
⫺80
⫺80
⫺130
⫺130
10
⫺7
40
1
22
3
⫺4
⫺5
⫺17
⫺1
8
46
10
4
15
25
34
6
⫺22
⫺18
⫺4
13
⫺5
16
0
62
22
⫺38
0
46
30
⫺3
6
⫺7
⫺5
37
17
3
0.02
⫺0.03
0.09
0.20
⫺0.04
⫺0.30
0.14
⫺0.09
⫺0.09
⫺0.03
0.06
0.30
⫺0.21
0.06
0.00
0.01
0.37
0.36
0.19
0.87
0.02
⫺0.14
0.19
0.26
⫺0.15
0.67
⫺0.03
0.35
0.17
0.71
⫺0.89
0.14
0.07
0.06
0.16
0.12
0.02
0.62
⫺200
⫺200
⫺200
⫺200
⫺200
⫺200
⫺200
⫺200
⫺140
⫺140
⫺200
⫺200
⫺200
⫺200
⫺200
⫺200
⫺160
⫺160
⫺65
⫺65
⫺200
⫺200
⫺200
⫺200
⫺200
⫺200
⫺200
⫺200
⫺200
⫺200
⫺200
⫺200
⫺200
⫺200
⫺200
⫺200
⫺200
⫺200
7.6
3.2
3.2
9.2
3.5
8.7
3.5
5.7
2.1
7.2
5.7
4.7
3.5
7.8
2.3
4.7
2.5
2.6
2.2
1.2
5.1
11.1
10.2
23.7
4.9
10.9
3.5
3.3
5.9
6.7
8.7
5.4
3.4
4.3
5.5
9.1
4.8
5.1
1807
1820
1846
1929
1946
2003
2047
2055
2108
2117
2125
2135
2233
2318
2333
2353
0007
0020
current mapping errors are typically in the realm of
0.1–0.2 m s⫺1, with the larger values located in the
northwest corner of the pre-Lili domain. In all of the
mapped fields, these mapping errors are much less than
those in the observed oceanic signals (e.g., high signalto-noise ratios).
c. Air–sea fluxes
Sea surface forcing is described by the fluxes of momentum, heat, and moisture. These fluxes are estimated from bulk formulas utilizing near-surface (10 m)
atmospheric thermodynamic and wind measurements
and upper-ocean thermal data. Atmospheric data are
measured from the large number of GPS sondes de-
ployed within the storm from both aircraft (Table 1),
including sondes deployed from Air Force Reserve reconnaissance and NOAA G-IV synoptic flights. Surface winds are estimated from SFMR measurements by
sensing brightness temperatures at multiple frequencies, as thoroughly described in Uhlhorn et al. (2007).
From each GPS dropwindsonde (Hock and Franklin
1999), 10-m values of temperature and specific humidity were acquired and objectively analyzed using the
Bretherton et al. (1976) OI method projected onto a
storm-relative grid aligned with the direction of storm
motion. SFMR wind observations are objectively analyzed using HRD’s H*Wind system (Powell and Houston 1996) and then interpolated bilinearly to a storm-
3260
VOLUME 136
FIG. 4. Examples of model fits (solid) using a three-layer approach of Sanford et al. (1987) compared to observed profiles (dots) for
(a)–(c) Isidore and (d)–(f) Lili for the (a), (d) u and (b), (e) ␷ components (m s⫺1). (c), (f) Differences between observed and model
profiles for both velocity components normalized by the surface wave amplitudes (from Tables 3 and 4). Note that the RMS differences
are smaller in Lili, but because the surface wave is less energetic, the (c) normalized differences for Lili are larger than (f) for the Isidore
profiles.
relative grid as for the GPS atmospheric thermodynamic variables (See Fig. 2). Finally, sea surface
temperature observations are also optimally interpolated to the same storm-relative grid (as noted above),
resulting in a set of variables at a common location
from which the spatial distribution of the bulk surface
momentum, sensible, and latent heat fluxes are estimated; that is,
TABLE 6. Horizontal and vertical correlation scales used in the
objective analyses.
Depth
range (m)
0–50
50–100
100–150
150–200
200–400
400–600
600–750
Horizontal
scale L (°)
Vertical
scale (m)
0.5
1.5
2.0
2.5
3.0
4.0
5.0
20
40
60
80
100
150
200
| ␶ | ⫽ ␳aCd | U10 |2,
Qs ⫽ ␳acpCh | U10 | ⌬T,
Ql ⫽ ␳aL␷Cq | U10 | ⌬q,
共6兲
and
共7兲
共8兲
where ␳a is the atmospheric density; Cd, Ch, and Cq are
exchange coefficients of momentum, sensible and latent heat, respectively; U10 is the 10-m wind speed; cp is
specific heat of air at constant pressure; L␷ is the latent
heat of vaporization; and ⌬T (Ts ⫺ Ta) is the difference
between SST and 10-m air temperature. SSTs are defined to be near-surface temperatures within the first
few meters of the sea surface from the expendables,1
1
The temperature of a bulk OML, defined as the depth where
the temperature decreases by more than 0.2°C, is given by a vertical average from near-surface to this depth. During periods of
strong wind forcing, the upper ocean is well mixed in temperature,
which represents a bulk OML temperature as observed during
hurricanes (Sanford et al. 1987; Shay et al. 1992, 2000).
SEPTEMBER 2008
SHAY AND UHLHORN
FIG. 5. Covariance model weighting function ␳(r) as a function
of dimensional distance r ⫻ L (°) applied to observations
for the objective analyses as per Table 6 for differing length scales L.
and ⌬q (qs ⫺ qa) is the difference between the saturated
specific humidity at the SST and unsaturated 10-m atmospheric specific humidity. The surface drag coefficient Cd is computed from the Large and Pond (1981)
relationship but is capped at a maximum value of 2.5 ⫻
10⫺3, based on recent results indicating a threshold or
saturation value of Cd at 28–33 m s⫺1 wind speeds
(Powell et al. 2003; Donelan et al. 2004; Shay and Jacob
2006; Jarosz et al. 2007). Heat exchange coefficients
(Ch, Cq) are set equal to Cd, which is conservative compared to the theory proposed by Emanuel (1995) (i.e.,
Emanuel’s theoretical results suggest that this enthalpy
and drag coefficient ratio lies between 1.2 and 1.5 in
severe hurricanes). An additional ocean forcing mechanism results from the surface precipitation flux (rain
rate). Freshwater input by rain can alter the ocean’s
response both by direct cooling (caused by rain at a
lower temperature than the SST) and by reducing the
3261
salinity, which stabilizes the OML and reduces the rate
of vertical mixing (Jacob and Kolinsky 2007). Tropical
Rainfall Measuring Mission (TRMM) Microwave Imager (TMI)-derived rain rates (Fig. 6) were used to
estimate surface precipitation fluxes for Isidore and Lili
(with maximum rain rates of 35 and 20 mm hr⫺1, respectively).
Surface flux distributions during the Isidore in-storm
flight (21 September) are shown in Fig. 7. Peak enthalpy flux is found in the right rear quadrant of the storm
to be ⬇1.8 kW m⫺2 as a result of high SSTs that show
negligible decrease from prestorm conditions. The
maximum momentum flux (⬃7 N m⫺2) is located in the
right front quadrant and is associated with a highly symmetric storm because of its fairly slow 4 m s⫺1 translational speed. Similarly, the estimated surface fluxes in
Lili are shown in Fig. 8. Lili’s surface wind field (2
October) indicates marked asymmetry resulting from
the more rapid storm motion toward the NW (⬃7
m s⫺1), and correspondingly, surface fluxes are enhanced on the right side of the track. Compared to
Isidore, the maximum surface enthalpy flux in Lili is
weaker (1.4 kW m⫺2) despite peak surface winds of 51
m s⫺1. This lower flux results primarily from SSTs observed in the LC regime that are approximately 1°C
lower than those during Isidore. This is an important
point that highlights how modest surface temperatures
differences can effectively alter surface heat fluxes under hurricane wind conditions (Cione and Uhlhorn
2003).
To improve our understanding of how these estimated fluxes relate to sea–air heat exchange, enthalpy
(heat and moisture) fluxes are integrated in the alongtrack direction to obtain a cross-track (radial) distribution of the ocean heat loss through the sea surface. An
along-track spatial coordinate is used to convert to
FIG. 6. Rain rates (mm h⫺1) based on TRMM data during (a) Isidore and (b) Lili.
3262
VOLUME 136
FIG. 7. Air–sea heat, moisture, and momentum fluxes derived from GPS sondes and SFMR from Isidore on 21 Sept 2002 for (a)
sensible heat (W m⫺2), (b) latent heat (W m⫺2), (c) momentum or wind stress (N m⫺2), and (d) enthalpy (i.e., sensible plus latent heat)
(W m⫺2) in a storm-coordinate system normalized by Rmax.
time, assuming a steadily moving storm based on the
observed storm speed (Table 2). Estimated surface heat
losses (kJ cm⫺2) for Isidore and Lili are shown in Fig. 9.
At the eyewall, surface heat loss in Isidore is 9.5 kJ
cm⫺2, compared to 4.5 kJ cm⫺2 during Lili. These differences result from higher enthalpy fluxes (1.8 versus
1.4 kW m⫺2) and slower storm speeds (4 versus 7 m s⫺1)
in Hurricane Isidore.
Based on the TRMM data (see Fig. 6), net freshwater
input (precipitation minus evaporation, hereafter P ⫺
E rate) is estimated for both storms by integrating these
data in the along-track direction (Fig. 9b). As suggested
by the fluxes, the P ⫺ E rate in Isidore was three times
larger than in Lili (between ⫾4Rmax). At levels of 300
mm within Isidore’s core, rain impacted the OML balance through the P ⫺ E rate. In contrast, the P ⫺ E rate
in Lili’s core was 115 mm because of a faster translation
speed. Such rain events induce changes in the OML
salinity balance of 0.2 to 0.4 practical salinity units
(psu), as documented by conductivity, temperature,
and depth (CTD) measurements acquired in typhoon
wakes in the western Pacific Ocean (Pudov and Petrichenko 2000). Thus, the OML salinity balance and the
surface buoyancy flux must be accounted for in ocean
response models for light and strong winds (Price et al.
1986; Jacob and Koblinsky 2007).
d. Temperature and velocity profiles
Current and temperature profiles from the B⬘–B
transect (see Fig. 3g) along 1.5 to 2 Rmax to the right of
the track are shown in Fig. 10, 2 IPs (⬃63 h) following
Lili’s passage over the domain. Current profiles along
the northern part of transect (B⬘) in the GCW indicated
an anticyclonic rotation with depth suggestive of verti-
SEPTEMBER 2008
SHAY AND UHLHORN
3263
FIG. 8. Same as Fig. 7, but for Lili on 2 Oct 2002.
cal energy propagation out of the wind-forced OML
(Leaman 1976). During Gilbert’s passage, this observed
anticyclonic rotation with depth was found to 4 times
more energetic than the cyclonically rotating component (Shay and Jacob 2006). This current vector rotation forced strong current shears beneath the OML,
inducing cooling by entrainment mixing processes. This
effect lowers Richardson numbers to below criticality
for a deepening and cooling OML (Pollard et al. 1973;
Price 1981; Jacob et al. 2000). In the center of the B⬘–B
transect, OML currents approach 1 m s⫺1 flowing toward the east. Notice that the warmer thermal structure
approaches 100 m depth where the currents remain
relatively constant with depth in the LC. This baroclinic
current structure tends to be in geostrophic balance
with a current reversal at 500 m and with weaker currents extending to a depth of 1000 m. By contrast, the
current structure at point B is shallower, with maximum
OML currents of 0.35 m s⫺1.
In the GCW, located in the northwest corner of the
analysis domain, OML cooling and deepening are typical signatures of a stronger ocean response that often
provide a negative feedback during hurricane passage
(Chang and Anthes 1978; Bender and Ginis 2000).
However, in the LC, this negative feedback to the atmosphere is minimized compared to that observed over
the GCW. Because the assumption of horizontal homogeneity is violated in the LC and WCR regimes, Halliwell et al. (2008) stress the importance of initializing
three-dimensional oceanic models to accurately predict
intensity from coupled forecasting models. In fact,
Falkovich et al. (2005) introduced a numerical approach for feature-based ocean modeling that involves
cross-frontal sharpening of the background temperature and salinity and, hence, the density fields. These
studies underscore the need for three-dimensional experimental data to improve oceanic model initialization
schemes.
3264
VOLUME 136
than 170 m in the eastern part of the Yucatan Straits
because of downwelling of the isotherms.
As shown in Fig. 12, mean cross-track variability in
the along-track direction prior and subsequent to Lili’s
passage revealed similar features except that the currents and horizontal temperature (density) gradients
were not impacted quite as much by the steep bottom
terrain. Maximum upper-ocean currents were directed
toward the north at speeds of more than 0.5 m s⫺1.
There was cooling in the northern part of the domain
where the 26°C isotherm depth was located at 50-m
depth before Lili; the isotherm depth then decreased by
about 10 m on 4 October, due in part to upwelling along
the track. Spatially averaged baroclinic currents increased to 0.7 m s⫺1 in response to Lili. As in the oceanic response to Isidore, there was little evidence of
significant upper-ocean cooling between snapshots. Although the time envelope between the pre- and postLili measurements was nearly two weeks, there was not
much evidence that this Category 3 hurricane impacted
the LC even just 2 days following passage. By contrast,
forced near-inertial current shears deepened and
cooled the OML by about 4°C in the GCW during
Hurricane Gilbert’s passage (Shay et al. 1992).
FIG. 9. Cross-track distribution of the (a) surface heat loss induced by surface fluxes (kJ cm⫺2) and (b) P ⫺ E rain fluxes (mm)
observed during Hurricanes Isidore (solid) and Lili (dashed), with
error bars (1 std dev) based on measurements.
e. Temperature and velocity sections
Background ocean flows are set up by horizontal
pressure gradients resulting from nonzero temperature
and salinity gradients and may play a significant role in
affecting the development of strong wind-driven current shears within the LC and WCR regimes (Fig. 11).
Pre- and post-Isidore measurements across the Yucatan
Straits indicate strong density and pressure gradients
associated with the LC. Pre-Isidore measurements suggest a northward-flowing LC of 1 m s⫺1 skewed toward
the western boundary of the Yucatan Straits. This is the
region where the horizontal density and pressure gradients sharpen because of a strong bottom slope. The
initial 26°C isotherm depth was a maximum of ⬃150-m
depth in the straits but was near the bottom over the
Yucatan Shelf. These spatial variations were sharpened
because Isidore cooled the shelf waters by more than
4.5°C compared to ⬃1°C across the Yucatan Straits.
The LC response was an increase of 0.4 m s⫺1, consistent with the expected current response of 0.38 m s⫺1 as
per scaling arguments in Table 2. On the western side of
the straits, the 26°C isotherm upwelled toward the sea
surface, whereas this isotherm depth increased to more
5. Forced response in the Loop Current
An important question emerging from recent studies
is the upper-ocean cooling levels during hurricane passage. Although early studies focused on the concept of
negative feedback during hurricane passage (i.e.,
Chang and Anthes 1978), observational evidence has
suggested that the STW mass associated with the LC
and WCR does not significantly cool compared to the
GCW. Based on profiler measurements before and after Rita, the oceanic cooling was minimized, suggesting
less negative feedback even though Rita was a Category 5 hurricane over the LC (Shay 2008). Historical
records suggest that once a hurricane enters the GOM
basin it will likely intensify prior to making a landfall
(Marks and Shay 1998). Contrasting the details of the
oceanic response differences of the LC and WCR versus the GCW water masses has implications with respect to negative feedback to the atmosphere. The focus here is on examining the observed oceanic response
to Hurricanes Isidore and Lili.
a. SST
Pre- and post-Isidore and Lili SST fields are shown in
Fig. 13. Pre-Isidore SSTs ranged from 28.5° to 29.5°C
over the experimental domain. During the post-Isidore
experiment on 23 September, SST changes were ob-
SEPTEMBER 2008
SHAY AND UHLHORN
3265
FIG. 10. Section B–B⬘ current vector stick plot (cm s⫺1) and temperature (°C) at 1.5 Rmax from Lili’s track on 4 Oct (poststorm).
Time is scaled in terms of inertial period. Black dots represent the OML depth in the upper panel extending from the surface to 150-m
depth.
FIG. 11. (top) Pre- and (bottom) post-Isidore along-track section of temperature (°C, color)
and geostrophic velocity (m s⫺1, dashed contours) across the Yucatan Straits. The heavy
dashed black line depicts the depth of the 26°C isotherm.
3266
FIG. 12. Same as Fig. 11, but for (top) pre- and (bottom) post-Lili.
FIG. 13. (a) Pre- and (b) post-Isidore SSTs; (c) ⌬SST for Isidore; (d) pre- and (e) post-Lili
SSTs; and (f) ⌬SST for Lili (all in °C) relative to Isidore’s or Lili’s track (black line) across the
Yucatan Straits or the southeast GOM relative to bottom topography (dotted lines) for the
200- and 1000-m-depth contours. Storm motion is indicated by arrows in (a) for Isidore and
⫺1
) dimen(d) for Lili, respectively. Coordinate system (cross-track: xR⫺1
max; along-track: y⌳
sions are relative to the mean storm locations from in-storm flights (for which the Rmax and
⌳ values are given in Table 2).
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SHAY AND UHLHORN
3267
FIG. 14. Same as Fig. 13, but for the 26°C isotherm depth (m).
served along these bottom topographical gradients,
with the largest SST changes of 4.5°C occurring over
the Yucatan Shelf (Fig. 13c). That is, SSTs decreased to
less than 25°C, because along-shelf wind stress driving a
net surface offshore flow resulted in upwelling of a shallow seasonal thermocline. Although significant SST
cooling and upward isotherm displacements occurred
over the shelf just prior to landfall, only small thermal
structure and isotherm depth changes were observed
across the Straits to the western tip of Cuba. Thus, SSTs
remained above 28.5°C in the straits a day after Isidore,
suggestive of less negative feedback to the storm. Given
the 10-day interval between Isidore and Lili, pre-Lili
SSTs were 29° to 29.5°C over most of the experimental
domain. After Lili’s passage, SSTs decreased to only
28.5°C in the LC; however, along the northwest part of
the measurement domain, SSTs cooled to less than
27°C in the GCW. Consistent with the National Data
Buoy Center (NDBC) 42001 measurements (see Fig.
1), this observed SST change equated to more than 2°C
cooling (Fig. 13f) as Lili intensified to a Category 4
storm in the south-central GOM (Pasch et al. 2004).
b. 26°C isotherm depths
Prior to Isidore, a strong horizontal gradient of the
26°C isotherm depth was observed, such that depths
were found to be ranging from more than 150 m in the
Yucatan Straits to less than 30 m over the Yucatan
Shelf (Fig. 14). These horizontal differences were con-
strained by strong cross-stream topographical gradients
separating the Yucatan Straits from the Yucatan Shelf.
Consistent with these large SST changes over the shelf,
isotherm depths decreased along these bottom topographical gradients after Isidore. However, in the center and eastern part of the deeper Yucatan Straits, isotherm depth increased by 20 m (Fig. 14c), which might
be a manifestation of the downwelling cycle. This alternating upwelling cycle along the steep bottom slope and
over the shelf and downwelling cycle in the straits is an
integral part of the oceanic response to hurricane forcing (Geisler 1970). These processes result in a tightening of the isotherm depths (and hence the thermocline)
and their gradients across the abrupt topographical
changes.
The corresponding 26°C isotherm depths for pre-Lili
conditions were located at more than 150-m depth in
the southeast part of the LC (Fig. 14d) and decreased to
50 m along the northwest periphery in the GCW. Compared to a monthly climatology (Teague et al. 1990),
these isotherm depths seem to be anomalously deep,
but they were consistent with satellite-derived isotherm
depths derived from satellite altimetry based on a seasonal climatology (Halliwell et al. 2008). Given Lili’s
rapid translation speed, poststorm isotherm depths
changed little compared to the pre-Lili values in the LC
(Fig. 14e); that is, isotherm depths ranged between 90–
140 m in the LC compared to about 100–150 m before
the storm. The isotherm displacements induced by Lili
were about 10 m, which is consistent with scaling argu-
3268
VOLUME 136
FIG. 15. Same as Fig. 13, but for OHC (kJ cm⫺2) relative to the depth of the 26°C
isotherm in Fig. 14.
ments using both the maximum wind stress and translation speed values in Table 2.
c. OHC variability
Pre- and poststorm OHC distributions (Fig. 15) reflect these SSTs and 26°C isotherm depths. Pre-Isidore
OHC in the northwest Caribbean basin and through the
eastern part of the Yucatan Straits exceeded 160 kJ
cm⫺2, in accord with satellite-derived OHC values derived from radar altimetry (Halliwell et al. 2008). Over
the Yucatan Shelf, pre-Isidore OHC values were about
40 kJ cm⫺2 (Fig. 15a), suggestive of a shallow seasonal
thermocline maintained by the trade winds (Gill 1982).
In the post-Isidore distributions, the OHC values were
less than those observed during prestorm conditions,
although by less than 20 kJ cm⫺2 along the western
parts of the straits; along the eastern part, the OHC
increased by about 20 kJ cm⫺2, consistent with a downwelling signal (i.e., deepening of the 26°C isotherm; Fig.
15c). Over the shelf, however, the OHC losses were
more than 40 kJ cm⫺2 where SSTs cooled by 4.5°C. In
the center of the straits, there was essentially no OHC
change, which was presumably due to northward heat
transport by the LC. Evidently, these large spatial gradients in SSTs and OHC across the Yucatan Straits
impacted the enthalpy fluxes that affected Isidore’s intensification to Category 3 status. Because isotherm
depths decreased by about 20 m in the LC with a 1°C
SST cooling, the LC essentially maintained OHC levels
of more than 100 kJ cm⫺2 prior to Lili (Fig. 15d). Maximum OHC levels from profiler measurements exceeded 140 kJ cm⫺2 compared to satellite-inferred values of ⬃130 kJ cm⫺2 (not shown). By contrast, in the
GCW, OHC values after Lili decreased by more than
35 kJ cm⫺2, compared to less than 15 kJ cm⫺2 in the LC
regime. This larger OHC loss, associated with an SST
decrease of more than 2°C, may have been caused by
enhanced vertical shears because the surface enthalpy
fluxes only accounted for about 4–5 kJ cm⫺2 of heat
loss through the surface. Given that the post-Lili survey
was conducted 1.5 IPs (48 h) after passage (Fig. 15e),
the OHC loss may have been greater than this value
because a major contributor to the oceanic heat budget
is associated with the northward advection of heat by
the LC. Differencing pre- and post-Lili OHC fields indicates that average fluxes were significantly less than
17 kJ cm⫺2 d⫺1 (⬃2.0 kW m⫺2) because of the hurricane passage. Along the northwest part of the Lili domain (i.e., the GCW), thin OMLs cool and deepen
quickly during hurricane passage where the SST decreases typically range from 3 to 6°C (Price 1981; Shay
et al. 1992; Jacob et al. 2000) and induce a negative
feedback (Chang and Anthes 1978; Bender and Ginis
2000). Price et al. (1994) argued that the North Atlantic
subtropical front over which Hurricanes Josephine
(1984) and Gloria (1985) passed is inconsequential to
the simulated ocean response. In the three-dimensional
LC regime, however, the horizontal pressure gradients
SEPTEMBER 2008
3269
SHAY AND UHLHORN
TABLE 7. Observed current shear from AXCP profiles deployed
in TCs. Means and standard deviations.
Storm
Shear (s⫺1 ⫻ 10⫺2)
Norbert (1984)
Gilbert (1988)
Isidore (2002)
Lili (2002)
2.2 ⫾ 1.3
3.5 ⫾ 1.7
2.0 ⫾ 1.4
1.4 ⫾ 1.3
and balanced currents are considerably stronger than in
the North Atlantic Ocean subtropical front. Thus, to
simulate the response, ocean models must be initialized
with these basic state flows (Marks and Shay 1998; Halliwell et al. 2008).
d. Vertical current shear
The most effective process for OML cooling and decreasing SST is by entrainment mixing (downward heat
flux) across the base of the OML associated with vigorous near-inertial current shears (e.g., Price 1981;
Schade and Emanuel 1999). This process is parameterized in numerical models and has been shown to produce widely varying results depending on the chosen
mixing parameterization (Jacob et al. 2000; Jacob and
Shay 2003). The results presented here suggest that
strong prestorm current regimes may limit the development of wind-forced near-inertial currents and their
vertical shears.
Current profiles are used to assess the vertical shear
using profiles with a vertical resolution of 2 m after
removal of the orbital velocities (see section 4a). Based
on (4), current shears at the OML base are estimated
from the model-fitted shear coefficients in layer 2 (Sz2)
from Tables 3, 4, and 5. The means and standard deviations of Sz2 are compared to Norbert and Gilbert
shear measurements in Table 7. Within measurement
error (Gregg et al. 1986), weaker shears were observed
in the current profiles acquired during two severe hurricanes. These estimated shear values in layer 2 are
objectively analyzed for both in- and poststorm fields
only (Fig. 16). Evident in these fields is the weaker
shear observed in the LC regime compared to measured shears in the GCW. Within the LC, for example,
current shears ranged from 0.5–1.5 ⫻ 10⫺2 s⫺1, but outside the LC, the shears were 2.0–5.0 ⫻ 10⫺2 s⫺1, or 2 to
4 times larger. This effect is obvious in the in-storm
Isidore and poststorm Lili current fields (Figs. 16a,d).
The lagged current shear response in Lili may also result from rapid storm motion and its asymmetric wind
stress distribution compared to the symmetric and
slower-moving Isidore. Given these wide-ranging results between two distinct water masses, considerably
more current and shear measurements are needed to
fully assess model parameterizations.
e. Bulk Richardson number
The bulk Richardson number is estimated from the
following expression:
Rib ⫽
gh␣⌬T
␦V2
,
共9兲
where ␣ is the coefficient of thermal expansion (2 ⫻
10⫺4 °C⫺1; Kraus and Businger 1994), h is the OML
depth, ⌬T is the temperature difference between the
bulk OML and averaged temperature in layer 2, and
the magnitude of the bulk current shears ( | ␦V |) are
determined from the model-fitted mean current differences between layers 1 and 2 as per Tables 3, 4, and 5.
Pollard et al. (1973) used a value of unity for the bulk
Richardson number as a condition for the onset of mixing processes at the OML base, whereas Ellison and
Turner (1959) found that more appropriate values
ranged between 0.4 and 0.8 for the initiation of vertical
mixing. Price (1981) used a Rib of 0.8 as the critical
value for mean current shear-induced mixing based on
a scaled entrainment law from experimental laboratory
results.
Small values of Rib indicate regions where shearinduced mixing is likely to overwhelm the damping effect of stratification during the cooling process (Fig.
17). However, in-storm measurements in Isidore indicate Rib ⬎ 1 over most of the domain. These values in
the LC are consistent with the observed 1°C cooling
and the OHC change of 20 kJ cm⫺2. Even where the
maximum SST cooling of 4.5°C was observed, bulk
Richardson numbers were above critical values (Figs.
17a,b) suggesting that upwelling of colder thermocline
water (induced by the wind stress curl) was the dominant mechanism over the shelf. The results for Lili are
similar (Figs. 17c,d), although they are more evident in
the poststorm analysis of current shear measurements.
Both of these cases point to a reduction in shearinduced mixing events in regions of strong background
currents; that is, the presence of deep warm layers
coupled with strong background flows of 1 m s⫺1
(caused by horizontal density and pressure gradients)
precludes the generation of strong shears observed in
the near-inertial wave wake (Shay et al. 1998). These
results point to a physical mechanism that must be well
understood in coupled models that predict hurricane
intensity.
6. Summary and concluding remarks
The goal of the aircraft-based experiment was to
measure the three-dimensional current, temperature,
3270
VOLUME 136
FIG. 16. In-storm and poststorm current shears (⫻10⫺2 s⫺1) in layer 2 based on the Sanford et al. (1987) model
for (a), (b) Isidore and (c), (d) Lili relative to the storm tracks (solid lines) and the bottom topography (dotted
lines) for the (a), (c) 200- and (b), (d) 500-m depth contours.
and salinity responses excited by hurricane passage
with a focus on assessing the responses in and over the
LC. The aircraft-based sampling strategy resulted in
several snapshots of upper-ocean current, temperature,
and salinity structure, required to examine the response
to the passage of two Category 3 hurricanes moving
over the same domain over a 10-day period. Given the
inherent uncertainties of storm-track prediction for the
pre-Isidore flights, this experimental objective was
achieved with a high degree of success for Isidore and
Lili. This is one of only a few datasets in which currents
and shears were directly measured during hurricane
passages (Sanford et al. 1987; Shay et al. 1992; Price et
al. 1994; Sanford et al. 2005). In this case, the GPS
sondes and SFMR data complement these in situ ocean
measurements to improve our understanding of their
mutual response.
The ocean response to the passage of Hurricanes Isidore and Lili was investigated using in situ observations
from oceanic and atmospheric sondes and remotely
sensed ocean surface winds (Uhlhorn et al. 2007).
These hurricanes intensified to major hurricane status
(Category 3 and above) over the LC, and Lili’s deepening cycle continued into the central GOM basin as
the storm reached Category 4 status just northwest of
the LC boundary. Atmospheric conditions were conducive for deepening, as noted by Pasch et al. (2004), over
an ocean where the extent of the cooling was O(1°C)
and the upper-ocean heat loss was less than 20 kJ cm⫺2.
Even after both hurricanes, the upper ocean was still
SEPTEMBER 2008
SHAY AND UHLHORN
3271
FIG. 17. Same as Fig. 16, but for Rib.
warm, with SSTs of 28.5° to 29°C and OHC levels exceeding 100 kJ cm⫺2. These results are similar to observations acquired prior and subsequent to Hurricane
Rita, which followed a track close to Katrina over the
LC and WCR (Shay 2008). Based on these profiler
data, lessons learned from Isidore and Lili included the
following:
1) the three-dimensional LC precludes the development of strong vertical current shears to force mixing and deepening of the OML despite applied wind
stresses of 7 N m⫺2 due to the strength of the current
and the depth of the warm isotherms;
2) cooling of 4.5°C over the Yucatan Shelf to Isidore
was due to wind-forced upwelling, and more than
2°C cooling during Lili was due to shear-induced
mixing events in the GCW; and,
3) maximum surface heat loss from the ocean was less
than 10 kJ cm⫺2 at Rmax, where enthalpy fluxes
ranged from 1.4 to 1.8 kW m⫺2 for Lili and Isidore,
respectively.
The first point is important with regard to initializing
ocean models with realistic background conditions
(Halliwell et al. 2008; Mainelli et al. 2008). Emanuel
(2001) argues that the upper ocean can be treated as a
series of one-dimensional column models for coupled
hurricane forecasting. The results reported, and other
recent studies such as Wu et al. (2007), imply that threedimensional advective tendencies must be accounted
for in such models. Because the ocean response is
weakest in strong frontal regimes, the negative feedback to the atmosphere is much less than over quiescent ocean regimes. The third conclusion has direct rel-
3272
evance to the threshold value for sustaining a hurricane’s intensity. Leipper and Volgenau (1972)
suggested a value of 17 kJ cm⫺2 day⫺1, but this threshold must be revisited to understand how much oceanic
heat loss is related to surface enthalpy fluxes versus
entrainment heat loss to the thermocline. In this context, Cione and Uhlhorn (2003) argue that only innercore SSTs are necessary for intensity forecasting, but
their results are inconclusive because the OHC held
constant even though SSTs were changing. With temperature profiles, OHC changes relative to the 26°C
isotherm can be estimated at finer scales than currently
available from coarse altimeter tracks (Cheney et al.
1994).
The scientific issue is not just the OHC magnitude;
the depth of the 26°C isotherms in the LC and WCR
regime are of equal importance in determining the
value of the OHC as per Eq. (1). The deeper this layer
of warm water, the more turbulent mixing is required to
overturn and cool the OML. Significant internal wave
shears associated with near-inertial motions were not
observed in the LC during Isidore and Lili because of
the strength of the horizontal pressure gradients that
force the background currents. If shear-induced mixing
is arrested, significant OML cooling and deepening will
not occur. In contrast, when current shears are large,
they lower the bulk Richardson numbers to below critical values and cool the SST (a proxy for OML temperatures under high winds) as the OML deepens (Price
1983; Shay et al. 1992). Entrainment heat fluxes into the
thermocline will result in lower surface enthalpy fluxes
that feed the hurricane and impact hurricane intensity
(Chang and Anthes 1978; Schade and Emanuel 1999,
Bender and Ginis 2000). For coupled model forecasting, currents and shears (momentum responses) are as
important as thermal profiles for simulating OML cooling and deepening processes. Given the number of vertical mixing models using bulk and turbulence closure
schemes (Jacob and Shay 2003), exploring parameter
space under differing ocean conditions (water masses)
will require more current (and shear) measurements
than have been previously acquired under hurricane
conditions. Once obtained, these could be integrated
into the NOAA Intensity Forecasting Experiments
(Rogers et al. 2006). The ocean’s momentum response
to hurricane forcing has been used to determine the
behavior of the surface drag coefficient (Shay and Jacob 2006; Jarosz et al. 2007). These data are needed to
test and evaluate innovative forecasting schemes involving both air–sea and vertical mixing parameterizations. This is a crucial test for coupled models designed
for operational hurricane intensity forecasts (Marks
and Shay 1998).
VOLUME 136
Acknowledgments. LKS acknowledges the support of
the National Science Foundation for both the experiment and data analysis through Grants ATM-01-08218
and ATM 04-44525; flight hours were provided by
NOAA’s Hurricane Research Division (HRD) and the
National Hurricane Center. E. Uhlhorn was supported
by both NOAA and ONR-CBLAST under the leadership of Dr. Peter Black. We gratefully acknowledge Dr.
Jim McFadden of the Office of Aircraft Operations
(OAO) and Drs. Hugh Willoughby and Frank Marks
(NOAA HRD) in orchestrating these aircraft experiments. Dr. Paul Chang of NOAA/NESDIS directed the
Ocean Winds flights on N42RF and provided support
for both the Isidore and Lili flights. Mr. Michael Black
(HRD field director) directed all field support for these
flights. We appreciate the extraordinary efforts of the
OAO pilots, engineers, and technicians during these
experimental efforts. Tom Cook and Scott Guhin assisted in the aircraft-based experiments, and Jodi Brewster provided graphical support. Reviews from three
anonymous reviewers significantly improved the manuscript.
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Loop Current Response to Hurricanes Isidore and Lili

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