Eye Excess Energy and the Rapid Intensification of Hurricane Lili

1446 MONTHLY WEATHER REVIEW VOLUME 138

Eye Excess Energy and the Rapid Intensiﬁcation of Hurricane Lili (2002)

GARY M. BARNES AND PAUL FUENTES University of Hawaii at Manoa, Honolulu, Hawaii

(Manuscript received 14 July 2009, in ﬁnal form 28 October 2009)

ABSTRACT

Over 4.5 days, NOAA and U.S. Air Force personnel in reconnaissance aircraft deployed 44 global positioning system dropwindsondes (GPS sondes) in the eye of Hurricane Lili (2002). The vertical profiles derived from these GPS sondes were used to determine the evolution of the height of the inversion, presence, and height of the hub cloud, the height of the lifted condensation layer, and the depth of the mixed layer. As Lili deepened, underwent rapid intensification (RI), and eventually rapid decay, the lower portion of the eye moistened and the lapse rate became moist adiabatic. The inversion layer rose as Lili intensified and then

quickly fell over 1500 m at the beginning of RI. Comparison of the equivalent potential temperature ue of the eye with that in the eyewall revealed that like many other hurricanes, the eye was a reservoir for the warmest ue. The authors deﬁne a variable called eye excess energy that is a function of the difference in ue between the eye and the eyewall and the depth over which this difference occurs and present evidence that

this quantity became small during RI. The authors hypothesize that the warm ue in the eye served as a boost for convection in the eyewall that may, in turn, initiate RI. However, the small volume of eye excess energy available and the rapidity at which it was transferred to the eyewall demonstrate that eye excess energy cannot sustain RI, which typically continues for many hours. The results are discussed in light of eye–eyewall mixing arguments.

1. Introduction a. Prior eye studies Occasionally a tropical cyclone (TC) in the Atlantic Earlier studies utilizing radiosonde and dropwindsonde Ocean basin was sampled over several days by the Na- observations have revealed the thermodynamic struc- tional Oceanic and Atmospheric Administration (NOAA) ture of the eye to be characterized by warm, dry air in WP-3Ds and U.S. Air Force (USAF) C-130 aircraft. These the mid- to upper levels of the troposphere, an inversion extended investigations may have included the regular layer located from 1- to 3-km altitude, and a cool and moist deployment of the global positioning system drop- air layer adjacent to the sea that may contain stratiform windsondes (GPS sondes) into the eye. As an example, cloud, sometimes referred to as a ‘‘hub cloud’’ (Jordan Hurricane Lili (2002) was repeatedly visited over 4.5 days, 1952; Malkus 1958; Stear 1965; Hawkins and Imbembo during which time Lili evolved from a tropical storm (TS) 1976). The air at 300 hPa was usually 108–158Cwarmer to a category-4 hurricane. The aircraft-borne in situ sensor than the air located far from the TC center; this warming observations of the eyewall and 44 GPS sondes deployed was attributed to a combination of subsidence-induced in the eye captured both the rapid intensiﬁcation (RI) and adiabatic warming (Malkus 1958; Jordan 1961; Gray and rapid decay (RD) phases of Lili’s life. We use these ob- Shea 1973; Willoughby 1998) and mixing of warm air from servations to investigate the thermodynamic evolution of the eyewall into the eye (Rotunno and Emanuel 1987). the eye below 700 hPa to ascertain if there is evidence of Malkus (1958) argued that the subsidence was deep and eye to eyewall transfers that have the potential to impact nearly continuous as air detrained from the eyewall and hurricane intensity. refreshed the eye multiple times throughout the TC’s life. In contrast to this view, Willoughby (1998) believed that the air above the inversion was trapped from the Corresponding author address: Gary M. Barnes, Dept. of Meteorology, University of Hawaii at Manoa, 2525 Correa Rd., TC’s inception, resulting in a long residence time, and Honolulu, HI 96822. that the sinking in the eye extended only a few kilome- E-mail: [email protected] ters rather than the entire depth of the troposphere. The

DOI: 10.1175/2009MWR3145.1

Ó 2010 American Meteorological Society Unauthenticated | Downloaded 09/28/21 11:41 PM UTC APRIL 2010 B A R N E S A N D F U E N T E S 1447 saturated or nearly saturated conditions observed below et al. 2005b; Montgomery et al. 2006, Sitkowski and the inversion level were attributed to frictional inflow Barnes 2009). This air, occupying the lowest 2–3 km, if underneath the eyewall, inward mixing across the eye– mixed into the eyewall updraft, could increase the buoy- eyewall boundary, and evaporation from the ocean by ancy enough to provide a convective boost (Holland Malkus (1958) and Willoughby (1998). 1997; Schubert et al. 1999; Braun 2002; Persing and The thermodynamic structure of the lower eye can Montgomery 2003; Eastin et al. 2005b; Montgomery et al. change dramatically during TC intensity changes (Jordan 2006; Cram et al. 2007). Persing and Montgomery (2003) 1961; Franklin et al. 1988; Willoughby 1998; Kossin and and Montgomery et al. (2006) have argued that a TC may Eastin 2001). Intensifying TCs frequently have enhanced achieve superintensity, a condition where the sustained warming and drying above a descending inversion while wind speeds in the eyewall exceed that estimated from weakening TCs have a rising inversion with cooling and maximum potential intensity theory (MPI; Emanuel moistening occurring from the sea surface to a less prom- 1986, 1988; Holland 1997), if the mass flux of air from the inent inversion layer. Jordan (1961) showed that as eye to the eyewall becomes substantial. Hurricane Grace (1958) filled 15 hPa over 6 h, warm and Warming of the lower portion of the eye usually dry air with an inversion near the sea surface was replaced makes an inconsequential contribution to the hydro- by a moist-adiabatic and saturated layer with no inver- statically induced surface pressure field, but the transfer sion. Franklin et al. (1988) reported remarkably strong of warm ue air from the lower eye into the eyewall could warming and drying far below the typical maximum conceivably reinforce convective elements in the eye- temperature perturbation level of 300 hPa during an wall that could subsequently deepen the TC. We will intensification period for Gloria (1995). Hawkins and explore the thermodynamic changes observed in the eye

Imbembo (1976) also noted a large positive temperature of Lili to see if there are variations of ue that are corre- perturbation below 500 hPa in Inez (1966) when it had a lated with notable intensity variations. mean sea level pressure (MSLP) of 927 hPa. b. Goals Liu et al. (1999) implemented a high-resolution simulation of the inner-core structure of Hurricane Andrew We will use the aircraft in situ sensors and the GPS (1992) that reproduced many of the observed thermo- sondes to address the following specific questions: dynamic eye structures. Equivalent potential tempera- 1) How do characteristics in the lower eye such as inver- ture (u ) in the lower eye was found to steadily increase e sion height, lifted condensation level (LCL), mixed as the TC intensified and to decrease as the TC decayed. layer depth, and hub cloud presence vary during the Some of the warm u air in the eye mixed into the eye- e intensifying, steady, and weakening phases? wall updraft, which reinforced convection. 2) How does u in the lower eye evolve in Lili? The transition from warm and dry to cool and moist e 3) Is there evidence of eye to eyewall mixing, when does conditions in the midlevels of the eye also has been it occur, and is there ensuing intensification? witnessed in Hurricanes Diana (1984) and Olivia (1994), 4) Can surface fluxes within the eye explain why u although these observed changes were explained through e observed there is usually higher than the eyewall? contrasting mechanisms (Kossin and Eastin 2001). The changes in Hurricane Diana were explained through as- 2. Data, methodology, and Lili (2002) cension of a well-mixed air mass below the inversion level. In Olivia, episodic horizontal mixing between the eye a. GPS sonde and eyewall via mesovortices was believed to be respon- 1) SAMPLING sible for the thermodynamic transition. Kossin and Eastin (2001) identified two regimes to describe the radial NOAA WP-3D and USAF C-130 aircraft deployed thermodynamic gradients between the eye and eyewall 44 GPS sondes in Hurricane Lili (2002) from altitudes above the inversion. During the first regime the eye was between 850 and 700 hPa. Figure 1 shows the temporal typically warm and dry with elevated ue in the eyewall and distribution of the sondes, from 0000 UTC 29 September lower values in the eye. The second regime occurred to 1200 UTC 3 October, along with the NOAA/Tropical after maximum intensity had been established and was Prediction Center/National Hurricane Center (TPC/NHC) characterized by a ue maximum in the eye with a mono- best-track MSLP. Successive sondes were deployed ev- tonic decrease radially outward. ery 2 h during individual flights with larger gaps of 5–7 h The lowest few kilometers of the eye often has been between flights. Forty-two of the 44 sondes released in shown to harbor some of the highest values of ue found the eye were within 4 km of the circulation center (Fig. 2), in a TC (e.g., Hawkins and Imbembo 1976; Jorgensen which was estimated by the aircraft using the center- 1984; Willoughby 1998; Schneider and Barnes 2005; Eastin finding techniques of Willoughby and Chelmow (1982).

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FIG. 1. Best-track pressure (hPa) as a function of time (thin solid line) with diamonds depicting when each GPS sonde was deployed. Periods when Lili was a tropical storm (TS) and when it was un- dergoing rapid intensiﬁcation (RI, lighter shading) or rapid decay (RD, darker shading) are delineated. Numbers denote the chronological positions of a few key sondes.

2) GPS SONDE TRAITS AND QUALITY CONTROL The development of the GPS sonde, its sensor accuracy, and its vertical resolution was presented by Hock and FIG. 2. The location of the GPS sonde drops relative to the circulation Franklin (1999). In the lower troposphere, ;7 m vertical center with 5- and 10-km range rings drawn. resolution is the norm. Typical errors for the pressure, temperature (T), and relative humidity (RH) are 0.5 hPa, 0.28C, and ,5%, respectively (Hock and Franklin 1999). and Meteorological Laboratory/Hurricane Research Divi- The sonde thermodynamic measurements have been used sion (NOAA/AOML/HRD); however, processing can to diagnose hurricane inflow energetics (Wroe and Barnes only be done in house at HRD. Editsonde postprocessed 2003), create the first horizontal maps of the low-level data from Hurricane Lili were kindly provided by thermodynamic fields of a TC (Schneider and Barnes S. Aberson of HRD, which allowed for an evaluation of 2005), show evidence for eye to eyewall transport (Eastin ASPEN and Editsonde output. et al. 2005b; Aberson et al. 2006; Montgomery et al. Comparisons between ASPEN and Editsonde for the 2006), and identify atypical thermodynamic structures in 44 sondes revealed only minor differences in tempera- the lower troposphere of TCs (Barnes 2008). ture that were within the uncertainty of the instrument The Atmospheric Sounding Processing Environment (Fuentes 2007). Height assignments for the data were (ASPEN) program developed at the National Center for determined based on the splash point as the zero-height Atmospheric Research (NCAR) was used to process the level. An incorrectly determined splash point can lead to raw sonde data in the form of Airborne Vertical At- large offsets in the temperature profile. The agreement mosphere Profiling System (AVAPS) files. Lili’s sondes in the temperature data between ASPEN and Editsonde were processed using ASPEN version the 2.7.1. (25 gave us confidence that we have correct splash points September 2006). Details of these quality control algo- and ensuing height assignments. The relative humidity rithms can be found online (http://www.eol.ucar.edu/rtf/ data have only minor variations with only two of the facilities/software/aspen/Aspen%20Manual.pdf). sondes showing differences slightly greater than 5%. Postprocessed ASPEN data were still subject to ques- The cause of this discrepancy between the two quality tionable values and were examined further to correct for control programs could not be determined with cer- additional errors identified by Barnes (2008). A frequent tainty as the changes were dependent on the operator problem was the failure of the relative humidity sensor to using Editsonde, although the difference may be related dry out after passage through thick cloud or rain. Correc- to a dry-bias correction applied in Editsonde that was tions follow the scheme developed by Bogner et al. (2000). not available in ASPEN. This dry bias can have a magnitude of 5%–20% and is a result of molecular con- 3) ASPEN AND EDITSONDE SOFTWARE tamination of the RH sensor by airborne particulates COMPARISON (Wang 2005). The higher humidity seen in the Editsonde An alternative processing of the raw GPS sonde data processing was not applied to the ASPEN output due to was done with the use of the Editsonde software pack- the few sondes affected, and the small difference in the age developed at the NOAA/Atlantic Oceanographic relative humidity values. In these situations we ignored

Unauthenticated | Downloaded 09/28/21 11:41 PM UTC APRIL 2010 B A R N E S A N D F U E N T E S 1449 those suspicious drops when assembling our analyses. resulting in dewpoints that are erroneously high. A rudi- The maximum difference in RH of 5% seen in the two mentary correction for instrument wetting recommended software packages can lead to a ue difference of 3–4 K. by Zipser et al. (1981) was applied to supersaturated Td periods: when the Td exceeds T measurements, saturated b. Aircraft observations conditions were assumed and the measurements were 1) SAMPLING adjusted halfway between the observed Td and T.The USAF C-130s did not have a radiometer, so the correc- NOAA and USAF aircraft completed 38 radial pen- tion scheme discussed by Jorgensen and LeMone (1989) etrations through the eye, resulting in 76 eyewall tra- and Eastin et al. (2002) is not viable for our dataset. verses. During a typical mission the eye was sampled Evaluation of both USAF and NOAA flight-level three to four times and all the quadrants of the TC data revealed that these periods of supersaturation only tended to be sampled. Nine penetrations during the occurred in the NOAA data. We suspect that the USAF early stages of Lili’s life were not utilized in determining may have applied a correction during such periods by the eye radius and eyewall thermodynamic variables due simply assigning the Td to be equal to the observed T; to our low confidence in determining a clear radius of this could result in an erroneously low value if the sensor maximum winds (RMW) or loss of aircraft data. The in was compromised by liquid water. Approximately 35% situ measurements were used to examine thermodynamic of the eyewall traverses for the USAF aircraft contained variables and determine the eye–eyewall interface from sections where the temperature dropped by 0.58–2.08C 0000 UTC 29 September through 1200 UTC 3 October. rapidly and are believed to be erroneously low. These Flights were flown at 850 hPa during tropical storm and periods where it was suspected that the USAF corrected lower-category intensities; later flights were flown at supersaturated conditions by simply setting Td equal to ;700 hPa as Lili achieved higher TC categories. T were replaced with a linear extrapolation between 2) IN SITU SENSOR TRAITS AND QUALITY points from just before to just after the suspected region CONTROL and assuming saturated conditions. This increased the ue for these corrected sections by 2–5 K. Flight-level data were available at 10-s resolution for the USAF C-130s. A 1-s resolution option was available c. Diagnosed eye–eyewall interface and maximum for the NOAA flights, but 10-s resolution was selected eyewall ue for consistency with the C-130 data. Both aircraft were If radar data were available from the NOAA WP-3Ds, equipped with a Rosemount sensor, which directly mea- the eye–eyewall interface was assumed to be coincident sures T through thermal relaxation of a platinum resistance with the 10-dBZ contour. Such information was available wire. Both aircraft utilized chilled-mirror hygrometers for only seven penetrations. In the absence of reflectivity (NOAA, General Eastern; USAF, Edgetech 137-C31) data the interface was assumed to be where T and Td first to directly measure dewpoint temperature (dewpoint, Td) become equal as the radial distance increases from the through the controlled stabilization of temperature in a circulation center, and finally, when no such regions exist, chilled mirror at the point when condensation begins. a distance inward from the RMW was chosen based on These dewpoint sensors have a 1-Hz sampling rate re- a relationship between the RMW and the inner edge of sulting in 120–140-m spatial resolution but it is prudent the eyewall as a function of wind speed (Shea and Gray to interpret this sensor for longer time scales (;5 s). A 1973). list of NOAA aircraft instrumentation options and ac- Estimates of u in the main updraft within the eyewall curacies are mentioned by Aberson et al. (2006). e were determined by selecting the maximum value be- Flight-level state variable instruments are subject to tween the inner edge of the eyewall and the RMW. errors as a result of sensor wetting (LeMone 1980; Values of u in this portion of the eyewall were assumed Zipser et al. 1981; Eastin et al. 2002). The T sensor may e to originate in the boundary layer and are considered to read erroneously low because of the evaporation of be the least impacted by entrainment. The correction water in the thin boundary layer around the sensor we made for the USAF’s spuriously cool segments did where the air undergoes compressional warming. The not alter the maximum value of u ; it simply made the Td sensor may also be compromised by liquid collecting e u time series appear to be a smoother, less erratic re- on the mirrors. During such a period, the hygrometer e cord. A composite cross section of u in the inner core of will heat the cooled mirror to evaporate excess moisture, e Hurricane Inez (1966) showed well-mixed conditions in the eyewall (Hawkins and Imbembo 1976). Small (1–2 K) 1 Errors for the Edgetech 137-C3 hygrometer are 60.58C (dew- or no variations in ue inside the RMW from 3 km to the point) and 618C (frost point). Not listed in Jorgensen (1984). surface were also evident in the composite vertical ue

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The estimate of a maximum ue was at times a challenging exercise because of the aforementioned problems with the ue and Td sensors. d. Hurricane Lili (2002) A full discussion of the history of Lili (2002) may be found in the Atlantic hurricane season review by Pasch et al. (2004). The TC formed within an easterly wave, at times was weakened by strong vertical shear of the horizontal winds, and passed over the Isle of Youth. Over the Gulf of Mexico Lili began RI at 0000 UTC on 2 October with an increase in winds of 18 m s21 in 24 h (Fig. 1). This intensification was followed by a weakening from category 4 to category 1 with maximum sustained winds decreasing by 23 m s21 in the 13 h before making landfall near Intracoastal City, Louisiana, at 1300 UTC on 3 October. When compared with a data- base of 769 other hurricanes, Frederick (2003) showed that Lili’s intensification rate ranks in the 11th percentile; however, its decay rate over water ranks Lili in the first percentile for Atlantic TCs. Hurricane Lili was unique in that it was the only Atlantic hurricane to decay at a greater rate than it intensified while over water. Babin (2004) showed evidence for dry air being entrained into the circulation and the loss of an outflow channel. SSTs also were about 1.58C cooler near the coast, but Lili had been traveling over cooler water without any weakening for many hours prior to RD.

3. Results a. Long-term trends in eye radius, inversion height, FIG. 3. (a) MSLP (hPa), (b) radius of the inner edge of the eye hub cloud, LCL, and the mixed layer (km), (c) inversion height (m),(d) hub cloud top (m),(e) LCL (m), and (f) mixed layer height (ML, m) as a function of time. Twenty-nine pairs of eyewall traverses at 850 and 700 hPa were used to estimate the radial distance from the circulation center to the inner eyewall edge using RI and when Lili achieved its lowest MSLP. During RD the technique described in section 2c. The mean eye ra- the inversion slowly rose to over 2000 m by the termi- dius at 700 hPa was 12 km with a standard deviation of nation of the sampling period. 1.5 km (Fig. 3b). The eye radius ﬂuctuated from 14 km The moisture sensor often continued to record satu- at 0019 UTC 1 October to its smallest value of 8 km near rated conditions after exiting the cloud base because the time when Lili reached its lowest MSLP at 2139 UTC water had collected on the relative humidity sensor 2 October. The trend in eye radius approximately mimics resulting in questionable cloud-base estimates. In con- that of the MSLP curve, reproduced in Fig. 3a for ease of trast, the top of a cloud layer was easily deﬁned (Fig. 3d). comparison. The top of the hub cloud, inferred to be where RH ’ Initially, the inversion base (Fig. 3c) was between 500 100%, existed for nearly two-thirds of the soundings. and 1000 m during the tropical storm and category 1 The hub cloud top was as high as 1700 m and as low as stage. Near 0000 UTC on 1 October the base rose to 200 m, with a mean of 750 m. The hub cloud top was over 1500 m and occasionally was above 2500 m and was always below the inversion, as expected, but it was only therefore undetectable by the sonde. There was a rapid within 200 m of the inversion base about 20% percent of and large decrease in inversion height near the start of the time. This suggests that for much of the time the 2 October with some heights as low as 700 m over the convergence in the inner 5-km radius of the eye was not next 20 h. These low inversion heights occurred during strong enough to force the air up to the layer that would

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FIG. 4. Vertical profiles of (a) potential temperature (K) and (b) equivalent potential temperature (K) for four soundings chronologically numbered 1 (thin line, initial conditions), 25 (thin dashed, beginning of RI), 36 (boldface dashed, end of RI), and 44 (boldface solid, end of RD). See Fig. 1 for times of soundings. serve as the strongest inhibitor to upward motion. The Riehl 1981), rose prior to RI, and then rapidly descended hub cloud occurred most consistently during RD from at the commencement of RI, followed by a recovery to 0600 to 1200 UTC on 3 October with five out of the six higher levels during RD. GPS sondes revealing a cloud layer. The LCL evolution in the eye has been estimated b. Long-term trends in state variables: Profiles using average temperature and moisture conditions in and selected levels the lowest 50 m (Fig. 3e). The LCL averaged 170 m and never exceeded 400 m. The LCL tended to lower Marked in Fig. 1 are the chronological launch num- throughout the 4.5 days of sampling. bers for four sondes that are representative of the ear- The mixed layer depth (Fig. 3f), determined by where liest conditions sampled (1), just prior to RI (25), near the potential temperature (u) ceases to be constant with the lowest MSLP (36), and, during the end of the RD height, remained below 350 m throughout the sampled period, a few hours prior to landfall (44). portion of the TC’s life cycle. When it was present, it The u profiles (Fig. 4a) evolved toward warmer values had a mean depth of 160 m with a standard deviation of with a .5 K increase throughout the lowest 1000 m as 75 m. In the early stages, at 0000 UTC on 29 September Lili deepens. The increase below 1000 m was almost through 2230 UTC on 30 September, mixed layers were entirely due to isothermal expansion. At 1500 m the deeper and occurred more frequently with 13 of the increase in u is about 10 K, and at 2000 and 2500 m it total 20 soundings revealing a mixed layer. There was exceeded that value by a few more degrees Kelvin. no evidence of any mixed layers from 0000 to 1300 UTC These increases were not isothermal as T increases 38, on 1 October. During RI from approximately 0000 to 58, and 78C from 1500 to 2500 m, respectively (Fig. 5). As 1800 UTC on October 2, the shallow mixed layer shrank Lili fills more than 20 hPa (sonde 36 to sonde 44), u or disappeared completely and remained absent as Lili decreased more than 5 K above 1500 m. Below 1000 m entered its RD phase through to landfall. an increase in temperature of 18–28C (Fig. 5) countered Relative to undisturbed tropical conditions (e.g., the reduction in u caused by the filling.

Augstein et al. 1974; Barnes et al. 1980; Kloesel and In contrast to the u evolution, ue in the eye increased Albrecht 1989), the LCL and mixed layer top in the eye throughout the life of Lili (Fig. 4b) with maximum values were a few hundred meters lower, and decreased through- found during the decaying stage (44) after RD. There out the life cycle of Lili. The likelihood of encountering was an increase of ue $ 15 K through most of the proﬁle a hub cloud increased as the TC aged as well. Essen- from the initial sampling to the decay period. Obviously, tially, the eye was becoming moister and the lapse rate the lower portion of the eye was continuing to gain in was becoming more moist adiabatic below 1000 m. The moisture even during its decay process, in contrast to inversion height, in contrast to the LCL and mixed layer what is expected in the eyewall (e.g., Malkus and Riehl top, did not descend throughout the life of Lili. Instead, 1960; Emanuel 1986). The vertical structure of ue can be it appeared to be nearly constant from the early tropical roughly approximated by two mixed layers separated by storm stage to Safﬁr–Simpson category 2 (Simpson and a transition zone of variable thickness and gradient.

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FIG. 5. Temperatures (8C, open triangles) and dewpoint tem- FIG. 6. Equivalent potential temperature (K) for six levels from 2 peratures (8C, closed triangles) for levels from 10 to 2500 m as 10 to 2500 m as a function of time. Linear regression ﬁt and R a function of time. Other delineations follow those in Fig. 1. value are shown for the three lowest levels. Other delineations follow those in Fig. 1.

The trends of T and Td at 10, 500, 1000, 1500, 2000, lower ue inward and homogenize the eye–eyewall re- and 2500 m within the eye (Fig. 5) show the following: 1) gion. The vertical gradient of ue in the eye precluded only slight changes in T and an increase in Td below increasing ue via entrainment from above (see Fig. 4b). 1000 m and 2) warming and drying at and above 1500 m To develop the maximum of ue in the eye, we envision until near the end of the record when there was a rapid the following scenario. First, some of the inﬂow must cooling and a reduction in the dewpoint depression in have passed under the eyewall instead of rising in the the latter half of RD. There were no data at 1500 m or updraft as envisioned by Malkus (1958) and Willoughby above early in the time series as the aircraft was ﬂying (1998). Second, this air must have remained in the just below this level. boundary layer where it received additional sensible and

The long-term increasing trend in ue (Fig. 6) is well latent energy from the ocean. The air in the center of the approximated by a linear regression with a coefficient of lower eye might require a significant residence time to 2 fit (R ) for the lowest three levels averaging 0.7. The have acquired a surfeit of ue given the much lower wind mean increase of ue through 1000-m depth is 17 K. Note speeds and the consequent lower interfacial fluxes ex- that despite the reasonable linear approximation for the pected in the eye core.

4.5 days there were shorter periods where ue quickly de- As noted earlier, the eye underwent an increase of creased or increased. Example periods were from 0300 ;17 K throughout the 4.5 days of sampling. This is an to 1200 UTC on 1 October and from 0000 to 0600 UTC increase above the background environmental condi- on 2 October. tions, not the eyewall; so much of this increase could have been realized during a parcel’s inward journey from c. Eye excess energy and its evolution a distant radius to the RMW where there were high winds

The warmest ue within the entire TC in the lower and correspondingly high ﬂuxes. Most of the increase has troposphere was found in the eye; therefore, transfers of been shown to occur close to the eyewall in other TCs air from the lower cloud and subcloud layers of the (e.g., Hawkins and Imbembo 1976; Jorgensen 1984; Wroe eyewall to the eye could only have served to transport and Barnes 2003). The difference that concerns us is the

Unauthenticated | Downloaded 09/28/21 11:41 PM UTC APRIL 2010 B A R N E S A N D F U E N T E S 1453 increase in ue beyond that found in and under the eye- resulting in an eye energy excess that would be inclined wall. To determine this difference, we must estimate the toward the maximum possible. maximum ue that feeds the eyewall updrafts, found be- Figure 7 shows the profiles of ue for two sondes dropped tween the RMW and the eyewall inner edge. in the eye, 21 and 29 (chronological order). The boldface There are several points to be made about this esti- vertical line that appears in each sounding is the estimate mate. First, the maximum values sensed by the aircraft in of the maximum ue in the eyewall updraft. The difference the midtroposphere can vary by several degrees kelvin between the boldface , perfectly mixed line and the eye from one side of the eyewall to the other, associated with sounding defines an area that is EEeye. Note that there the asymmetries in convection in the eyewall. Sometimes was a dramatic reduction in the energy content from there was no saturated section between the RMW and sonde 21 to sonde 29. the inner edge for one side of the eyewall. The variations The best-track MSLP, ue for the eyewall and eye at in the convective scale features in the eyewall may be due 500 m, and EEeye as a function of time for Lili are shown to a variety of causes that include 1) the presence of the in Fig. 8. Initially, in the early hours of 29 September, the vertical shear of the horizontal wind (e.g., Black et al. eyewall had warmer ue than the eye. In this early stage 2002; Eastin et al. 2005b), 2) variable boundary layer we expect the residence time of the air in the developing convergence due to the TC motion (e.g., Shapiro 1983), eye to be too short to result in a maximum. By late 29 and 3) if the aircraft passed through an updraft, down- September, the situation reversed and the eye ue was draft, or quiescent air (e.g., Eastin et al. 2005a). warmer than the eyewall by about 4 K, on average. On 2 With these issues in mind, we have identified the October, corresponding to the commencement of RI, maximum ue found for any penetration of the eye, the the ue in the eye decreased and the eyewall ue increased highest value from either of the two-eyewall traverses (shaded region in Fig. 8b between the two trend lines). included in a given penetration. We then assume that this After midday on 2 October the eye again had the warmer portion of the eyewall was well mixed from the sampling ue, which continued to the end of the sampling. level (850 or 700 hPa) to the surface. This is a common The EEeye (Fig. 8c) was near zero at the beginning of assumption used to derive cross sections based on ob- the record and then slowly built before rapidly decreasing servation (e.g., Hawkins and Rubsam 1968; Hawkins and to near-zero values in the early hours of 2 October. This Imbembo 1976; Jorgensen 1984) and appears in axisym- rapid decrease was correlated with the start of the RI metric simulations as well (Rotunno and Emanuel 1987). period. Later, as the TC decayed, the EEeye increased It also has a theoretical basis as the moist isentropes till the end of the record. The behavior of EEeye was have been argued to be parallel to the angular mo- somewhat similar to the behavior of the inversion height mentum surfaces that are nearly vertical in the lower (Fig. 3c). Note that ue in the eyewall (Fig. 8b) was greater eyewall (Emanuel 1986). We compare the ue of this well- than that in the eye for two periods but that does not mixed eyewall with the ue measured near the circulation result in a negative or zero estimate for EEeye. This is center from the GPS sonde that was deployed during because we have plotted the value at 500 m; below this the same transect. The difference between the eyewall level, ue was usually warmer in the eye than the eyewall maximum ue and the eye ue, integrated through the depth resulting in an EEeye that remained positive. from the sea to the height where the two values are d. Can interfacial fluxes within the eye core be equal, may be viewed as the excess energy found within responsible for EE ? the eye compared to the eyewall. We label it the eye eye excess energy: From 0000 UTC 29 September to 0000 UTC 2 Octo- ber, EE increased from near 0 to 13.4 3 106 Jm22. ð eye This is based on a linear regression during that time with 2 eye excess energy 5 EEeye 5 rCp(ue,eye À ue,eyewall)›z, a coefficient of fit (R ) of 0.77. The slope of the line, of course, defines the combined sensible and latent heat fluxes needed for balance (i.e., 52 W m22). Are there such with r the density, Cp the specific heat at constant fluxes in the eye core? pressure, and ›z the depth from the sea surface to the The GPS sondes provide wind speed, T, and mixing level where the ue in the eye and eyewall become equal. ratio estimates at ;10 m; combined with satellite esti- It is the differential in moist static energy between a mates of the sea surface temperature (SST), we can es- column in the eye and one in the lower part of the eyewall timate the fluxes at the sea surface for Lili. This simple (units of J m22). Because of the various assumptions and calculation assumes no energy loss out of the top of the sensor errors (e.g., LeMone 1980; Eastin et al. 2002), we column and is applicable from the circulation center feel that the eyewall ue would tend to be an underestimate to about 5-km radius. We apply the bulk aerodynamic

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FIG. 7. Vertical profiles of equivalent potential temperature (K) from the GPS sondes in the eye (solid line) and for the estimated eyewall derived from the aircraft (solid vertical line) for soundings (a) 21 and (b) 29. equations and follow the recommendation of 1.15 3 1023 temperature gradients at 10 m, could account for this. for the latent heat flux transfer coefficient and 1.2 3 1023 However, if one pushes the exercise for shorter periods for the sensible heat flux transfer coefficient (Fairall et al. (;3 h), then there are times where it is impossible for 2003). The wind speeds in the eye core are 3–6 m s22, the surface fluxes within 5 km of the circulation center so we are not in a regime where the bulk aerodynamic approximation is being unduly pushed, save perhaps for the influence of the sea state. An SST of 28.48C is chosen that is about 0.78C less than the estimates of SST from airborne expendable bathythermographs and airborne expendable current probes deployed ahead of Lili during research flights by NOAA. We have lowered the SST assuming that the winds have produced some overturning and reduce the value under the eye in concordance with Cione and Uhlhorn (2003), who demonstrated that a TC modifies SST not only in the wake but also in the inner core. The 10-m T, specific humidity q, and wind speed data from the GPS sondes yield a total enthalpy flux of 65–75 W m22. It appears possible that the fluxes derived from the bulk aerodynamic equations can explain the long-term trends that we observe for EEeye prior to RI. They are less successful for estimating the recovery of EEeye during RD. From about 2100 UTC on 2 October to about 1200 UTC 6 22 on 3 October, EEeye increased from about 3.0 3 10 Jm to 9.7 3 106 Jm22. These values are based again on FIG. 8. (a) Best-track MSLP, (b) equivalent potential temper- a linear regression. The surface fluxes needed to account ature (K) for the eyewall (EW) from the aircraft (open circles, 22 boldface solid line) and the eye (E) at 500 m from the GPS sonde for this increase would be 100–110 W m , which is (closed triangles, thin solid line), and (c) eye excess energy about 25% higher than what we estimate for this time. (3 106 Jm22, solid diamonds). Shaded regions in (b) mark where Subtle increases in wind speed, and the moisture and the ue of the eyewall is warmer than that found in the eye.

Unauthenticated | Downloaded 09/28/21 11:41 PM UTC APRIL 2010 B A R N E S A N D F U E N T E S 1455 to supply the necessary energy for balance. This may be 1984; Barnes et al. 1991), then the reservoir of high ue partly due to errors in the estimate of EEeye, which is would be exhausted in about 15 min. This is assuming why we have deemphasized relying on any one estimate that half of the eyewall flux that varied between 11.7 and in favor of the linear trend over a longer period. 16.6 3 108 m3 s21 originates in the eye. Our observations cannot resolve the gradients in any Based on these estimates, a few broad points can be variable from the circulation center to the inner edge of offered. First, TCs with a small eye such as Lili can supply the eyewall. In this annulus, the wind speed would in- only a momentary boost to the convection in the eye- crease in a fashion similar to that expected from solid-body wall before the excess energy of the eye is exhausted. rotation. Wind speeds would approach eyewall values Draining the eye would take as little as 15–30 min, de- and the fluxes could increase by an order of magnitude pending on the mass flux in the eyewall. If the eyewall or more. Transport of this air into the inner core could contained two or three active Cbs that drew half their result in much swifter increases of EEeye than what we updraft volume from the eye, the reservoir would be have estimated for the quiescent core alone. exhausted in a little over just 1 h. Rapid intensification One of the reviewers of this manuscript mentioned usually is observed over much longer periods, at least that the interaction of the sea surface with the boundary 12–24 h (e.g., Willoughby et al. 1982; Kaplan and DeMaria layer not only adds heat and moisture, but also extracts 2003; Sitkowski and Barnes 2009), so it is difficult to angular momentum. This would cause convergence to- imagine that the eye to eyewall transfer of warmer ue ward the center, upward motion and the development of could be entirely responsible for the deepening. the hub cloud, and eventually transport air near the in- Second, if the fluxes within the eye are solely respon- version base into the eyewall. The surface friction and sible for the warmer ue in the lower eye, then the resi- this forced outflow will tend to make the radial profile dence time necessary to build up EEeye is many hours. If inside the eye U-shaped, whereas lateral mixing brought we assume that Lili has a 5-K surplus over a mean depth on by barotropic or another unidentified instability will of 1350 m, then the column needs to acquire 6.89 3 push it back toward solid rotation. A U-shaped wind pro- 106 Jm22. If the fluxes are 70 W m22, then a residence file would create a larger, low-vorticity quiescent core and time of ;27hisrequired.Thisassumesnolossthrough could increase the residence time to stoke up EEeye while the top of the layer. solid-body rotation could reduce the residence time to Combining the rapid transfer rate and the much lon- achieve a given EEeye by many hours. Our dataset does ger restoration time scale, one can arrive at a third point. not allow us to discern which scenario existed in Lili. The ratio of the time to drain the EEeye over the time the surface fluxes need to restore EE is quite small, on the e. Limits on the importance of EE eye eye order of 0.02–0.05. This means that the boost using most

The correlation between intensity and EEeye in Hur- of the inner core is available infrequently. Examining ricane Lili makes an intriguing case for the role of the the best-track pressure records for many TCs shows that lower eye and is supporting evidence for the arguments RI rarely occurs more than once save for those TCs that put forth by Holland (1997), Braun (2002), Persing and have eyewall replacement cycles. These concentric TCs Montgomery (2003), Eastin et al. (2005b) Montgomery have at times very large eyes that could conceivably con- et al. (2006), and Cram et al. (2007). However, the fre- tain a much larger supply of EEeye than did Lili. Re- quency that a convective boost can occur and contribute visiting the recovery times of the boundary layer for the to intensification is unlikely to be often. For Lili the tropical atmosphere reveals a similar ratio with updrafts volume of air with warmer ue was small, and the differ- depleting the mixed layer on the order of a few minutes ence between the ue of the eye and the eyewall was also while the surface fluxes would take many hours to re- modest (;5 K). If the volume of air with an excess of ue plenish to their background, undisturbed states. reaches to the inner edge of the eyewall for Lili (12 km), which is a generous if not extreme assumption, and its 4. Conclusions height is coincident with the mean inversion base (1350 m), 10 3 we would have about 61.1 3 10 m of warmer ue to Aircraft reconnaissance over 4.5 days provided a view contribute to a convective boost. If one assumes a mix of the thermodynamics below 3 km for the eye of Hur- of 50:50 between the eye and eyewall to elevate the ue ricane Lili (2002). GPS sondes dropped within 5 km of 2–3 K, a single good-sized Cb with an upward volume the circulation center revealed that as Lili aged, the lifted flux of 1 3 108 m3 s21 (Barnes et al. 1991) surviving for condensation level lowered and the mixed layer shrank 30 min will use about 9 3 1010 m3 of the eye air; seven or and eventually disappeared. The eye moistened, the lapse so such Cbs would exhaust the supply. If one looks at rate became moist adiabatic, and a hub cloud was detected estimates of upward mass flux for the eyewall (Jorgensen two-thirds of the time. Potential temperature in the eye

Unauthenticated | Downloaded 09/28/21 11:41 PM UTC 1456 MONTHLY WEATHER REVIEW VOLUME 138 behavedasexpectedwithawarmingduringintensifi- eye and the eyewall. The latter is especially challenging cation and a cooling as the hurricane filled. In contrast, given the aircraft sensor performance in saturated con- the long-term trend of equivalent potential temperature ditions. Second, the recovery time for EEeye is currently (ue) in the eye was for warming throughout the life of viewed as a function of the conditions found within 5 km Lili. The inversion that separated the cool, moist lower of the circulation center. We cannot address the role of layer from the warm and dry upper layer did not evolve the annulus between the inner eyewall edge and the like the LCL or mixed layer. Instead, it appeared to be quiescent core with these observations. This annulus nearly constant from the early tropical storm stage to could have higher surface wind speeds if the annulus is in category 2, rose prior to rapid intensification (RI), and solid-body rotation and would allow for a more rapid then rapidly descended more than 1500 m at the com- replenishment of EEeye. Third, the eyewall may extract mencement of RI, followed by a recovery to higher levels air from the annulus adjacent to it more regularly, but during RD. During this period, ue in the lower eye cooled we cannot detect this entrainment with this dataset. to values similar to those diagnosed for the eyewall. When ue in the eyewall column is increased, there Mimicking the inversion height is the eye excess en- should be a consequent decrease in mean sea level pres- ergy (EEeye), which is a function of the difference in ue sure (e.g., Malkus and Riehl 1960; Emanuel 1986). The between the eye and the eyewall updraft, integrated question then arises as to how a hurricane can maintain through the depth where ue,eye – ue,eyewall $ 0. We see this new more intense state after the eye air is completely, that EEeye increased from the early tropical storm stage and most likely quickly, exhausted. Guillermo (1997) un- to just prior to rapid intensification. At the commence- derwent eye–eyewall exchange (e.g., Eastin et al. 2005b; ment of RI, EEeye decreased to a very small quantity. Reasor et al. 2009) but also established an annulus with We interpret this as a substantial transfer of air from the warmer ue adjacent but radially outward of the eyewall inner eye region to the eyewall updraft. The correlation (Sitkowski and Barnes 2009). Does the boost, however between the decrease in EEeye and the deepening of brief, result in a reduction of the radius of maximum the hurricane supports the argument that eye to eyewall winds, an increase in the winds in the inflow, greater transfers can trigger intensification (Holland 1997; Braun fluxes, and a new balanced state that does not rely on 2002; Persing and Montgomery 2003; Eastin et al. 2005b; eye air? Montgomery et al. 2006; Cram et al. 2007). The increase of ;5Kinue through the eyewall column could con- Acknowledgments. Without the support of National ceivably lower pressure more than 16 hPa [dP 523.3due; Science Foundation Grant ATM-0735867 and the dedi- Emanuel (1986)]. A reduction in pressure of similar cated field work of NOAA/AOC, NOAA/AOML/HRD, magnitude was observed in the early stages of RI for Lili. and the USAF hurricane reconnaissance group this work Additionally, when the air in the lower eye is transferred would not have been possible. We thank Sim Aberson of into the eyewall, compensating subsidence in the eye NOAA/AOML/HRD for access to his Editsonde files of above the inversion could occur that would strengthen the GPS sondes for Lili. We also are indebted to Joe the warm core and contribute to intensification. Cione of NOAA/AOML/HRD, who provided the SST Consideration of the amount of air available in the eye data for Lili. The reviews from Hugh Willoughby and to mix into the eyewall, the rate at which this air would another anonymous reviewer are appreciated and led to be extracted, and the time it would take for surface improvements in this work. Garpee Barleszi’s editorial

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