Eye Excess Energy and the Rapid Intensification of Hurricane Lili (2002) (original) (raw)
1. Introduction
Occasionally a tropical cyclone (TC) in the Atlantic Ocean basin was sampled over several days by the National Oceanic and Atmospheric Administration (NOAA) WP-3Ds and U.S. Air Force (USAF) C-130 aircraft. These extended investigations may have included the regular deployment of the global positioning system dropwindsondes (GPS sondes) into the eye. As an example, Hurricane Lili (2002) was repeatedly visited over 4.5 days, during which time Lili evolved from a tropical storm (TS) to a category-4 hurricane. The aircraft-borne in situ sensor observations of the eyewall and 44 GPS sondes deployed in the eye captured both the rapid intensification (RI) and rapid decay (RD) phases of Lili’s life. We use these observations to investigate the thermodynamic evolution of the eye below 700 hPa to ascertain if there is evidence of eye to eyewall transfers that have the potential to impact hurricane intensity.
a. Prior eye studies
Earlier studies utilizing radiosonde and dropwindsonde observations have revealed the thermodynamic structure of the eye to be characterized by warm, dry air in the mid- to upper levels of the troposphere, an inversion layer located from 1- to 3-km altitude, and a cool and moist air layer adjacent to the sea that may contain stratiform cloud, sometimes referred to as a “hub cloud” (Jordan 1952; Malkus 1958; Stear 1965; Hawkins and Imbembo 1976). The air at 300 hPa was usually 10°–15°C warmer than the air located far from the TC center; this warming was attributed to a combination of subsidence-induced adiabatic warming (Malkus 1958; Jordan 1961; Gray and Shea 1973; Willoughby 1998) and mixing of warm air from the eyewall into the eye (Rotunno and Emanuel 1987). Malkus (1958) argued that the subsidence was deep and nearly continuous as air detrained from the eyewall and 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 TC’s inception, resulting in a long residence time, and that the sinking in the eye extended only a few kilometers rather than the entire depth of the troposphere. The saturated or nearly saturated conditions observed below the inversion level were attributed to frictional inflow underneath the eyewall, inward mixing across the eye–eyewall boundary, and evaporation from the ocean by Malkus (1958) and Willoughby (1998).
The thermodynamic structure of the lower eye can change dramatically during TC intensity changes (Jordan 1961; Franklin et al. 1988; Willoughby 1998; Kossin and Eastin 2001). Intensifying TCs frequently have enhanced warming and drying above a descending inversion while weakening TCs have a rising inversion with cooling and moistening occurring from the sea surface to a less prominent inversion layer. Jordan (1961) showed that as Hurricane Grace (1958) filled 15 hPa over 6 h, warm and dry air with an inversion near the sea surface was replaced by a moist-adiabatic and saturated layer with no inversion. Franklin et al. (1988) reported remarkably strong warming and drying far below the typical maximum temperature perturbation level of 300 hPa during an intensification period for Gloria (1995). Hawkins and Imbembo (1976) also noted a large positive temperature perturbation below 500 hPa in Inez (1966) when it had a mean sea level pressure (MSLP) of 927 hPa.
Liu et al. (1999) implemented a high-resolution simulation of the inner-core structure of Hurricane Andrew (1992) that reproduced many of the observed thermodynamic eye structures. Equivalent potential temperature (θe) in the lower eye was found to steadily increase as the TC intensified and to decrease as the TC decayed. Some of the warm θe air in the eye mixed into the eyewall updraft, which reinforced convection.
The transition from warm and dry to cool and moist conditions in the midlevels of the eye also has been witnessed in Hurricanes Diana (1984) and Olivia (1994), although these observed changes were explained through contrasting mechanisms (Kossin and Eastin 2001). The changes in Hurricane Diana were explained through ascension of a well-mixed air mass below the inversion level. In Olivia, episodic horizontal mixing between the eye and eyewall via mesovortices was believed to be responsible for the thermodynamic transition. Kossin and Eastin (2001) identified two regimes to describe the radial thermodynamic gradients between the eye and eyewall above the inversion. During the first regime the eye was typically warm and dry with elevated θe in the eyewall and lower values in the eye. The second regime occurred after maximum intensity had been established and was characterized by a θe maximum in the eye with a monotonic decrease radially outward.
The lowest few kilometers of the eye often has been shown to harbor some of the highest values of θe found in a TC (e.g., Hawkins and Imbembo 1976; Jorgensen 1984; Willoughby 1998; Schneider and Barnes 2005; Eastin et al. 2005b; Montgomery et al. 2006, Sitkowski and Barnes 2009). This air, occupying the lowest 2–3 km, if mixed into the eyewall updraft, could increase the buoyancy enough to provide a convective boost (Holland 1997; Schubert et al. 1999; Braun 2002; Persing and Montgomery 2003; Eastin et al. 2005b; Montgomery et al. 2006; Cram et al. 2007). Persing and Montgomery (2003) and Montgomery et al. (2006) have argued that a TC may achieve superintensity, a condition where the sustained wind speeds in the eyewall exceed that estimated from maximum potential intensity theory (MPI; Emanuel 1986, 1988; Holland 1997), if the mass flux of air from the eye to the eyewall becomes substantial.
Warming of the lower portion of the eye usually makes an inconsequential contribution to the hydrostatically induced surface pressure field, but the transfer of warm _θ_e air from the lower eye into the eyewall could conceivably reinforce convective elements in the eyewall that could subsequently deepen the TC. We will explore the thermodynamic changes observed in the eye of Lili to see if there are variations of θe that are correlated with notable intensity variations.
b. Goals
We will use the aircraft in situ sensors and the GPS sondes to address the following specific questions:
- How do characteristics in the lower eye such as inversion height, lifted condensation level (LCL), mixed layer depth, and hub cloud presence vary during the intensifying, steady, and weakening phases?
- How does θe in the lower eye evolve in Lili?
- Is there evidence of eye to eyewall mixing, when does it occur, and is there ensuing intensification?
- Can surface fluxes within the eye explain why θe observed there is usually higher than the eyewall?
2. Data, methodology, and Lili (2002)
a. GPS sonde
1) Sampling
NOAA WP-3D and USAF C-130 aircraft deployed 44 GPS sondes in Hurricane Lili (2002) from altitudes between 850 and 700 hPa. Figure 1 shows the temporal distribution of the sondes, from 0000 UTC 29 September to 1200 UTC 3 October, along with the NOAA/Tropical Prediction Center/National Hurricane Center (TPC/NHC) best-track MSLP. Successive sondes were deployed every 2 h during individual flights with larger gaps of 5–7 h between flights. Forty-two of the 44 sondes released in the eye were within 4 km of the circulation center (Fig. 2), which was estimated by the aircraft using the center-finding techniques of Willoughby and Chelmow (1982).
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 Franklin (1999). In the lower troposphere, ∼7 m vertical resolution is the norm. Typical errors for the pressure, temperature (T), and relative humidity (RH) are 0.5 hPa, 0.2°C, and <5%, respectively (Hock and Franklin 1999). The sonde thermodynamic measurements have been used to diagnose hurricane inflow energetics (Wroe and Barnes 2003), create the first horizontal maps of the low-level thermodynamic fields of a TC (Schneider and Barnes 2005), show evidence for eye to eyewall transport (Eastin et al. 2005b; Aberson et al. 2006; Montgomery et al. 2006), and identify atypical thermodynamic structures in the lower troposphere of TCs (Barnes 2008).
The Atmospheric Sounding Processing Environment (ASPEN) program developed at the National Center for Atmospheric Research (NCAR) was used to process the raw sonde data in the form of Airborne Vertical Atmosphere Profiling System (AVAPS) files. Lili’s sondes were processed using ASPEN version the 2.7.1. (25 September 2006). Details of these quality control algorithms can be found online (http://www.eol.ucar.edu/rtf/facilities/software/aspen/Aspen%20Manual.pdf).
Postprocessed ASPEN data were still subject to questionable values and were examined further to correct for additional errors identified by Barnes (2008). A frequent problem was the failure of the relative humidity sensor to dry out after passage through thick cloud or rain. Corrections follow the scheme developed by Bogner et al. (2000).
3) ASPEN and Editsonde software comparison
An alternative processing of the raw GPS sonde data was done with the use of the Editsonde software package developed at the NOAA/Atlantic Oceanographic and Meteorological Laboratory/Hurricane Research Division (NOAA/AOML/HRD); however, processing can only be done in house at HRD. Editsonde postprocessed data from Hurricane Lili were kindly provided by S. Aberson of HRD, which allowed for an evaluation of ASPEN and Editsonde output.
Comparisons between ASPEN and Editsonde for the 44 sondes revealed only minor differences in temperature that were within the uncertainty of the instrument (Fuentes 2007). Height assignments for the data were determined based on the splash point as the zero-height level. An incorrectly determined splash point can lead to large offsets in the temperature profile. The agreement in the temperature data between ASPEN and Editsonde gave us confidence that we have correct splash points and ensuing height assignments. The relative humidity data have only minor variations with only two of the sondes showing differences slightly greater than 5%. The cause of this discrepancy between the two quality control programs could not be determined with certainty as the changes were dependent on the operator using Editsonde, although the difference may be related to a dry-bias correction applied in Editsonde that was not available in ASPEN. This dry bias can have a magnitude of 5%–20% and is a result of molecular contamination of the RH sensor by airborne particulates (Wang 2005). The higher humidity seen in the Editsonde processing was not applied to the ASPEN output due to the few sondes affected, and the small difference in the relative humidity values. In these situations we ignored those suspicious drops when assembling our analyses. The maximum difference in RH of 5% seen in the two software packages can lead to a θe difference of 3–4 K.
b. Aircraft observations
1) Sampling
NOAA and USAF aircraft completed 38 radial penetrations through the eye, resulting in 76 eyewall traverses. During a typical mission the eye was sampled three to four times and all the quadrants of the TC tended to be sampled. Nine penetrations during the early stages of Lili’s life were not utilized in determining the eye radius and eyewall thermodynamic variables due to our low confidence in determining a clear radius of maximum winds (RMW) or loss of aircraft data. The in situ measurements were used to examine thermodynamic variables and determine the eye–eyewall interface from 0000 UTC 29 September through 1200 UTC 3 October. Flights were flown at 850 hPa during tropical storm and lower-category intensities; later flights were flown at ∼700 hPa as Lili achieved higher TC categories.
2) In situ sensor traits and quality control
Flight-level data were available at 10-s resolution for the USAF C-130s. A 1-s resolution option was available for the NOAA flights, but 10-s resolution was selected for consistency with the C-130 data. Both aircraft were equipped with a Rosemount sensor, which directly measures T through thermal relaxation of a platinum resistance wire. Both aircraft utilized chilled-mirror hygrometers (NOAA, General Eastern; USAF, Edgetech 137-C31) to directly measure dewpoint temperature (dewpoint, Td) through the controlled stabilization of temperature in a chilled mirror at the point when condensation begins. These dewpoint sensors have a 1-Hz sampling rate resulting in 120–140-m spatial resolution but it is prudent to interpret this sensor for longer time scales (∼5 s). A list of NOAA aircraft instrumentation options and accuracies are mentioned by Aberson et al. (2006).
Flight-level state variable instruments are subject to errors as a result of sensor wetting (LeMone 1980; Zipser et al. 1981; Eastin et al. 2002). The T sensor may read erroneously low because of the evaporation of water in the thin boundary layer around the sensor where the air undergoes compressional warming. The Td sensor may also be compromised by liquid collecting on the mirrors. During such a period, the hygrometer will heat the cooled mirror to evaporate excess moisture, resulting in dewpoints that are erroneously high. A rudimentary correction for instrument wetting recommended by Zipser et al. (1981) was applied to supersaturated Td periods: when the Td exceeds T measurements, saturated conditions were assumed and the measurements were adjusted halfway between the observed Td and T. The USAF C-130s did not have a radiometer, so the correction scheme discussed by Jorgensen and LeMone (1989) and Eastin et al. (2002) is not viable for our dataset.
Evaluation of both USAF and NOAA flight-level data revealed that these periods of supersaturation only occurred in the NOAA data. We suspect that the USAF may have applied a correction during such periods by simply assigning the Td to be equal to the observed T; this could result in an erroneously low value if the sensor was compromised by liquid water. Approximately 35% of the eyewall traverses for the USAF aircraft contained sections where the temperature dropped by 0.5°–2.0°C rapidly and are believed to be erroneously low. These periods where it was suspected that the USAF corrected supersaturated conditions by simply setting Td equal to T were replaced with a linear extrapolation between points from just before to just after the suspected region and assuming saturated conditions. This increased the θe for these corrected sections by 2–5 K.
c. Diagnosed eye–eyewall interface and maximum eyewall θe
If radar data were available from the NOAA WP-3Ds, the eye–eyewall interface was assumed to be coincident with the 10-dB_Z_ contour. Such information was available for only seven penetrations. In the absence of reflectivity data the interface was assumed to be where T and Td first become equal as the radial distance increases from the circulation center, and finally, when no such regions exist, a distance inward from the RMW was chosen based on a relationship between the RMW and the inner edge of the eyewall as a function of wind speed (Shea and Gray 1973).
Estimates of θe in the main updraft within the eyewall were determined by selecting the maximum value between the inner edge of the eyewall and the RMW. Values of θe in this portion of the eyewall were assumed to originate in the boundary layer and are considered to be the least impacted by entrainment. The correction we made for the USAF’s spuriously cool segments did not alter the maximum value of θe; it simply made the θe time series appear to be a smoother, less erratic record. A composite cross section of θe in the inner core of Hurricane Inez (1966) showed well-mixed conditions in the eyewall (Hawkins and Imbembo 1976). Small (1–2 K) or no variations in θe inside the RMW from 3 km to the surface were also evident in the composite vertical θe analysis from Hurricane Allen (1980) (Jorgensen 1984). The estimate of a maximum θe was at times a challenging exercise because of the aforementioned problems with the θe 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 s−1 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 s−1 in the 13 h before making landfall near Intracoastal City, Louisiana, at 1300 UTC on 3 October. When compared with a database 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 1.5°C 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, hub cloud, LCL, and the mixed layer
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 the technique described in section 2c. The mean eye radius at 700 hPa was 12 km with a standard deviation of 1.5 km (Fig. 3b). The eye radius fluctuated from 14 km at 0019 UTC 1 October to its smallest value of 8 km near the time when Lili reached its lowest MSLP at 2139 UTC 2 October. The trend in eye radius approximately mimics that of the MSLP curve, reproduced in Fig. 3a for ease of comparison.
Initially, the inversion base (Fig. 3c) was between 500 and 1000 m during the tropical storm and category 1 stage. Near 0000 UTC on 1 October the base rose to over 1500 m and occasionally was above 2500 m and was therefore undetectable by the sonde. There was a rapid and large decrease in inversion height near the start of 2 October with some heights as low as 700 m over the next 20 h. These low inversion heights occurred during RI and when Lili achieved its lowest MSLP. During RD the inversion slowly rose to over 2000 m by the termination of the sampling period.
The moisture sensor often continued to record saturated conditions after exiting the cloud base because water had collected on the relative humidity sensor resulting in questionable cloud-base estimates. In contrast, the top of a cloud layer was easily defined (Fig. 3d). The top of the hub cloud, inferred to be where RH ≈ 100%, existed for nearly two-thirds of the soundings. The hub cloud top was as high as 1700 m and as low as 200 m, with a mean of 750 m. The hub cloud top was always below the inversion, as expected, but it was only within 200 m of the inversion base about 20% percent of the time. This suggests that for much of the time the convergence in the inner 5-km radius of the eye was not strong enough to force the air up to the layer that would serve as the strongest inhibitor to upward motion. The hub cloud occurred most consistently during RD from 0600 to 1200 UTC on 3 October with five out of the six GPS sondes revealing a cloud layer.
The LCL evolution in the eye has been estimated using average temperature and moisture conditions in the lowest 50 m (Fig. 3e). The LCL averaged 170 m and never exceeded 400 m. The LCL tended to lower throughout the 4.5 days of sampling.
The mixed layer depth (Fig. 3f), determined by where the potential temperature (θ) ceases to be constant with height, remained below 350 m throughout the sampled portion of the TC’s life cycle. When it was present, it had a mean depth of 160 m with a standard deviation of 75 m. In the early stages, at 0000 UTC on 29 September through 2230 UTC on 30 September, mixed layers were deeper and occurred more frequently with 13 of the total 20 soundings revealing a mixed layer. There was no evidence of any mixed layers from 0000 to 1300 UTC on 1 October. During RI from approximately 0000 to 1800 UTC on October 2, the shallow mixed layer shrank or disappeared completely and remained absent as Lili entered its RD phase through to landfall.
Relative to undisturbed tropical conditions (e.g., Augstein et al. 1974; Barnes et al. 1980; Kloesel and Albrecht 1989), the LCL and mixed layer top in the eye were a few hundred meters lower, and decreased throughout the life cycle of Lili. The likelihood of encountering a hub cloud increased as the TC aged as well. Essentially, the eye was becoming moister and the lapse rate was becoming more moist adiabatic below 1000 m. The inversion height, in contrast to the LCL and mixed layer top, did not descend throughout the life of Lili. Instead, it appeared to be nearly constant from the early tropical storm stage to Saffir–Simpson category 2 (Simpson and Riehl 1981), rose prior to RI, and then rapidly descended at the commencement of RI, followed by a recovery to higher levels during RD.
b. Long-term trends in state variables: Profiles and selected levels
Marked in Fig. 1 are the chronological launch numbers for four sondes that are representative of the earliest conditions sampled (1), just prior to RI (25), near the lowest MSLP (36), and, during the end of the RD period, a few hours prior to landfall (44).
The θ profiles (Fig. 4a) evolved toward warmer values with a >5 K increase throughout the lowest 1000 m as Lili deepens. The increase below 1000 m was almost entirely due to isothermal expansion. At 1500 m the increase in θ is about 10 K, and at 2000 and 2500 m it exceeded that value by a few more degrees Kelvin. These increases were not isothermal as T increases 3°, 5°, and 7°C from 1500 to 2500 m, respectively (Fig. 5). As Lili fills more than 20 hPa (sonde 36 to sonde 44), θ decreased more than 5 K above 1500 m. Below 1000 m an increase in temperature of 1°–2°C (Fig. 5) countered the reduction in θ caused by the filling.
In contrast to the θ evolution, θe in the eye increased throughout the life of Lili (Fig. 4b) with maximum values found during the decaying stage (44) after RD. There was an increase of θe ≥ 15 K through most of the profile from the initial sampling to the decay period. Obviously, the lower portion of the eye was continuing to gain in moisture even during its decay process, in contrast to what is expected in the eyewall (e.g., Malkus and Riehl 1960; Emanuel 1986). The vertical structure of θe can be roughly approximated by two mixed layers separated by a transition zone of variable thickness and gradient.
The trends of T and Td at 10, 500, 1000, 1500, 2000, and 2500 m within the eye (Fig. 5) show the following: 1) only slight changes in T and an increase in Td below 1000 m and 2) warming and drying at and above 1500 m until near the end of the record when there was a rapid cooling and a reduction in the dewpoint depression in the latter half of RD. There were no data at 1500 m or above early in the time series as the aircraft was flying just below this level.
The long-term increasing trend in θe (Fig. 6) is well approximated by a linear regression with a coefficient of fit (_R_2) for the lowest three levels averaging 0.7. The mean increase of θe through 1000-m depth is 17 K. Note that despite the reasonable linear approximation for the 4.5 days there were shorter periods where θe quickly decreased or increased. Example periods were from 0300 to 1200 UTC on 1 October and from 0000 to 0600 UTC on 2 October.
c. Eye excess energy and its evolution
The warmest θe within the entire TC in the lower troposphere was found in the eye; therefore, transfers of air from the lower cloud and subcloud layers of the eyewall to the eye could only have served to transport lower θe inward and homogenize the eye–eyewall region. The vertical gradient of θe in the eye precluded increasing θe via entrainment from above (see Fig. 4b).
To develop the maximum of θe in the eye, we envision the following scenario. First, some of the inflow must have passed under the eyewall instead of rising in the updraft as envisioned by Malkus (1958) and Willoughby (1998). Second, this air must have remained in the boundary layer where it received additional sensible and latent energy from the ocean. The air in the center of the lower eye might require a significant residence time to have acquired a surfeit of θe given the much lower wind speeds and the consequent lower interfacial fluxes expected in the eye core.
As noted earlier, the eye underwent an increase of ∼17 K throughout the 4.5 days of sampling. This is an increase above the background environmental conditions, not the eyewall; so much of this increase could have been realized during a parcel’s inward journey from a distant radius to the RMW where there were high winds and correspondingly high fluxes. Most of the increase has been shown to occur close to the eyewall in other TCs (e.g., Hawkins and Imbembo 1976; Jorgensen 1984; Wroe and Barnes 2003). The difference that concerns us is the increase in _θ_e beyond that found in and under the eyewall. To determine this difference, we must estimate the maximum θe that feeds the eyewall updrafts, found between the RMW and the eyewall inner edge.
There are several points to be made about this estimate. First, the maximum values sensed by the aircraft in the midtroposphere can vary by several degrees kelvin from one side of the eyewall to the other, associated with the asymmetries in convection in the eyewall. Sometimes there was no saturated section between the RMW and the inner edge for one side of the eyewall. The variations in the convective scale features in the eyewall may be due to a variety of causes that include 1) the presence of the vertical shear of the horizontal wind (e.g., Black et al. 2002; Eastin et al. 2005b), 2) variable boundary layer convergence due to the TC motion (e.g., Shapiro 1983), and 3) if the aircraft passed through an updraft, downdraft, or quiescent air (e.g., Eastin et al. 2005a).
With these issues in mind, we have identified the maximum θe found for any penetration of the eye, the highest value from either of the two-eyewall traverses included in a given penetration. We then assume that this portion of the eyewall was well mixed from the sampling level (850 or 700 hPa) to the surface. This is a common assumption used to derive cross sections based on observation (e.g., Hawkins and Rubsam 1968; Hawkins and Imbembo 1976; Jorgensen 1984) and appears in axisymmetric simulations as well (Rotunno and Emanuel 1987). It also has a theoretical basis as the moist isentropes have been argued to be parallel to the angular momentum surfaces that are nearly vertical in the lower eyewall (Emanuel 1986). We compare the θe of this well-mixed eyewall with the θe measured near the circulation center from the GPS sonde that was deployed during the same transect. The difference between the eyewall maximum θe and the eye θe, integrated through the depth from the sea to the height where the two values are equal, may be viewed as the excess energy found within the eye compared to the eyewall. We label it the eye excess energy:
with ρ the density, Cp the specific heat at constant pressure, and ∂z the depth from the sea surface to the level where the θe in the eye and eyewall become equal. It is the differential in moist static energy between a column in the eye and one in the lower part of the eyewall (units of J m−2). Because of the various assumptions and sensor errors (e.g., LeMone 1980; Eastin et al. 2002), we feel that the eyewall θe would tend to be an underestimate resulting in an eye energy excess that would be inclined toward the maximum possible.
Figure 7 shows the profiles of θe for two sondes dropped in the eye, 21 and 29 (chronological order). The boldface vertical line that appears in each sounding is the estimate of the maximum θe in the eyewall updraft. The difference between the boldface, perfectly mixed line and the eye sounding defines an area that is EEeye. Note that there was a dramatic reduction in the energy content from sonde 21 to sonde 29.
The best-track MSLP, θe for the eyewall and eye at 500 m, and EEeye as a function of time for Lili are shown in Fig. 8. Initially, in the early hours of 29 September, the eyewall had warmer θe than the eye. In this early stage we expect the residence time of the air in the developing eye to be too short to result in a maximum. By late 29 September, the situation reversed and the eye θe was warmer than the eyewall by about 4 K, on average. On 2 October, corresponding to the commencement of RI, the θe in the eye decreased and the eyewall θe increased (shaded region in Fig. 8b between the two trend lines). After midday on 2 October the eye again had the warmer θe, which continued to the end of the sampling.
The EEeye (Fig. 8c) was near zero at the beginning of the record and then slowly built before rapidly decreasing to near-zero values in the early hours of 2 October. This rapid decrease was correlated with the start of the RI period. Later, as the TC decayed, the EEeye increased till the end of the record. The behavior of EEeye was somewhat similar to the behavior of the inversion height (Fig. 3c). Note that θe in the eyewall (Fig. 8b) was greater than that in the eye for two periods but that does not result in a negative or zero estimate for EEeye. This is because we have plotted the value at 500 m; below this level, θe was usually warmer in the eye than the eyewall resulting in an EEeye that remained positive.
d. Can interfacial fluxes within the eye core be responsible for EEeye?
From 0000 UTC 29 September to 0000 UTC 2 October, EEeye increased from near 0 to 13.4 × 106 J m−2. This is based on a linear regression during that time with a coefficient of fit (_R_2) 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 m−2). Are there such fluxes in the eye core?
The GPS sondes provide wind speed, T, and mixing ratio estimates at ∼10 m; combined with satellite estimates of the sea surface temperature (SST), we can estimate the fluxes at the sea surface for Lili. This simple calculation assumes no energy loss out of the top of the column and is applicable from the circulation center to about 5-km radius. We apply the bulk aerodynamic equations and follow the recommendation of 1.15 × 10−3 for the latent heat flux transfer coefficient and 1.2 × 10−3 for the sensible heat flux transfer coefficient (Fairall et al. 2003). The wind speeds in the eye core are 3–6 m s−2, 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 28.4°C is chosen that is about 0.7°C 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 m−2.
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 on 3 October, EEeye increased from about 3.0 × 106 J m−2 to 9.7 × 106 J m−2. These values are based again on a linear regression. The surface fluxes needed to account for this increase would be 100–110 W m−2, which is about 25% higher than what we estimate for this time. Subtle increases in wind speed, and the moisture and temperature gradients at 10 m, could account for this. However, if one pushes the exercise for shorter periods (∼3 h), then there are times where it is impossible for the surface fluxes within 5 km of the circulation center to supply the necessary energy for balance. This may be partly due to errors in the estimate of EEeye, which is why we have deemphasized relying on any one estimate in favor of the linear trend over a longer period.
Our observations cannot resolve the gradients in any variable from the circulation center to the inner edge of the eyewall. In this annulus, the wind speed would increase in a fashion similar to that expected from solid-body rotation. Wind speeds would approach eyewall values and the fluxes could increase by an order of magnitude or more. Transport of this air into the inner core could result in much swifter increases of EEeye than what we have estimated for the quiescent core alone.
One of the reviewers of this manuscript mentioned that the interaction of the sea surface with the boundary layer not only adds heat and moisture, but also extracts angular momentum. This would cause convergence toward the center, upward motion and the development of the hub cloud, and eventually transport air near the inversion base into the eyewall. The surface friction and this forced outflow will tend to make the radial profile inside the eye U-shaped, whereas lateral mixing brought on by barotropic or another unidentified instability will push it back toward solid rotation. A U-shaped wind profile would create a larger, low-vorticity quiescent core and could increase the residence time to stoke up EEeye while solid-body rotation could reduce the residence time to achieve a given EEeye by many hours. Our dataset does not allow us to discern which scenario existed in Lili.
e. Limits on the importance of EEeye
The correlation between intensity and EEeye in Hurricane Lili makes an intriguing case for the role of the lower eye and is supporting evidence for the arguments put forth by Holland (1997), Braun (2002), Persing and Montgomery (2003), Eastin et al. (2005b) Montgomery et al. (2006), and Cram et al. (2007). However, the frequency that a convective boost can occur and contribute to intensification is unlikely to be often. For Lili the volume of air with warmer θe was small, and the difference between the θe of the eye and the eyewall was also modest (∼5 K). If the volume of air with an excess of θe reaches to the inner edge of the eyewall for Lili (12 km), which is a generous if not extreme assumption, and its height is coincident with the mean inversion base (1350 m), we would have about 61.1 × 1010 m3 of warmer θe to contribute to a convective boost. If one assumes a mix of 50:50 between the eye and eyewall to elevate the θe 2–3 K, a single good-sized Cb with an upward volume flux of 1 × 108 m3 s−1 (Barnes et al. 1991) surviving for 30 min will use about 9 × 1010 m3 of the eye air; seven or so such Cbs would exhaust the supply. If one looks at estimates of upward mass flux for the eyewall (Jorgensen 1984; Barnes et al. 1991), then the reservoir of high θe would be exhausted in about 15 min. This is assuming that half of the eyewall flux that varied between 11.7 and 16.6 × 108 m3 s−1 originates in the eye.
Based on these estimates, a few broad points can be offered. First, TCs with a small eye such as Lili can supply only a momentary boost to the convection in the eyewall before the excess energy of the eye is exhausted. Draining the eye would take as little as 15–30 min, depending on the mass flux in the eyewall. If the eyewall contained two or three active Cbs that drew half their updraft volume from the eye, the reservoir would be exhausted in a little over just 1 h. Rapid intensification usually is observed over much longer periods, at least 12–24 h (e.g., Willoughby et al. 1982; Kaplan and DeMaria 2003; Sitkowski and Barnes 2009), so it is difficult to imagine that the eye to eyewall transfer of warmer θe could be entirely responsible for the deepening.
Second, if the fluxes within the eye are solely responsible for the warmer θe in the lower eye, then the residence time necessary to build up EEeye is many hours. If we assume that Lili has a 5-K surplus over a mean depth of 1350 m, then the column needs to acquire 6.89 × 106 J m−2. If the fluxes are 70 W m−2, then a residence time of ∼27 h is required. This assumes no loss through the top of the layer.
Combining the rapid transfer rate and the much longer restoration time scale, one can arrive at a third point. The ratio of the time to drain the EEeye over the time the surface fluxes need to restore EEeye is quite small, on the order of 0.02–0.05. This means that the boost using most of the inner core is available infrequently. Examining the best-track pressure records for many TCs shows that RI rarely occurs more than once save for those TCs that have eyewall replacement cycles. These concentric TCs have at times very large eyes that could conceivably contain a much larger supply of EEeye than did Lili. Revisiting the recovery times of the boundary layer for the tropical atmosphere reveals a similar ratio with updrafts depleting the mixed layer on the order of a few minutes while the surface fluxes would take many hours to replenish to their background, undisturbed states.
4. Conclusions
Aircraft reconnaissance over 4.5 days provided a view of the thermodynamics below 3 km for the eye of Hurricane Lili (2002). GPS sondes dropped within 5 km of the circulation center revealed that as Lili aged, the lifted condensation level lowered and the mixed layer shrank and eventually disappeared. The eye moistened, the lapse rate became moist adiabatic, and a hub cloud was detected two-thirds of the time. Potential temperature in the eye behaved as expected with a warming during intensification and a cooling as the hurricane filled. In contrast, the long-term trend of equivalent potential temperature (θe) in the eye was for warming throughout the life of Lili. The inversion that separated the cool, moist lower layer from the warm and dry upper layer did not evolve like the LCL or mixed layer. Instead, it appeared to be nearly constant from the early tropical storm stage to category 2, rose prior to rapid intensification (RI), and then rapidly descended more than 1500 m at the commencement of RI, followed by a recovery to higher levels during RD. During this period, θe in the lower eye cooled to values similar to those diagnosed for the eyewall.
Mimicking the inversion height is the eye excess energy (EEeye), which is a function of the difference in θe between the eye and the eyewall updraft, integrated through the depth where θ e,eye – θ e,eyewall ≥ 0. We see that EEeye increased from the early tropical storm stage to just prior to rapid intensification. At the commencement of RI, EEeye decreased to a very small quantity. We interpret this as a substantial transfer of air from the inner eye region to the eyewall updraft. The correlation between the decrease in EEeye and the deepening of the hurricane supports the argument that eye to eyewall transfers can trigger intensification (Holland 1997; Braun 2002; Persing and Montgomery 2003; Eastin et al. 2005b; Montgomery et al. 2006; Cram et al. 2007). The increase of ∼5 K in θe through the eyewall column could conceivably lower pressure more than 16 hPa [_δP_ = −3.3_δθe_; Emanuel (1986)]. A reduction in pressure of similar magnitude was observed in the early stages of RI for Lili. Additionally, when the air in the lower eye is transferred into the eyewall, compensating subsidence in the eye above the inversion could occur that would strengthen the warm core and contribute to intensification.
Consideration of the amount of air available in the eye to mix into the eyewall, the rate at which this air would be extracted, and the time it would take for surface fluxes to replenish EEeye leads us to believe that eye–eyewall mixing would intensify a hurricane infrequently. A fairly complete transfer of eye air could occur on the order of once every 25–30 h for a hurricane with an eye as small as Lili’s (mean radius = 12 km). The mass of air in the lower eye can be consumed by the eyewall updrafts in as little as 15 min. Given that rapid intensification usually occurs over far longer periods (12–24 h), the transfer of the excess energy can only serve as an initiator of RI, and it is unlikely that it could be responsible for the entire event. Such short injections of energy may largely be lost in radiating gravity waves instead of intensifying the vortex.
There are several caveats concerning this analysis. First, to estimate EEeye, we must identify θe for both the eye and the eyewall. The latter is especially challenging given the aircraft sensor performance in saturated conditions. Second, the recovery time for EEeye is currently viewed as a function of the conditions found within 5 km of the circulation center. We cannot address the role of the annulus between the inner eyewall edge and the quiescent core with these observations. This annulus could have higher surface wind speeds if the annulus is in solid-body rotation and would allow for a more rapid replenishment of EEeye. Third, the eyewall may extract air from the annulus adjacent to it more regularly, but we cannot detect this entrainment with this dataset.
When θe in the eyewall column is increased, there should be a consequent decrease in mean sea level pressure (e.g., Malkus and Riehl 1960; Emanuel 1986). The question then arises as to how a hurricane can maintain this new more intense state after the eye air is completely, and most likely quickly, exhausted. Guillermo (1997) underwent eye–eyewall exchange (e.g., Eastin et al. 2005b; Reasor et al. 2009) but also established an annulus with warmer _θ_e adjacent but radially outward of the eyewall (Sitkowski and Barnes 2009). Does the boost, however brief, result in a reduction of the radius of maximum winds, an increase in the winds in the inflow, greater fluxes, and a new balanced state that does not rely on eye air?
Acknowledgments
Without the support of National Science Foundation Grant ATM-0735867 and the dedicated field work of NOAA/AOC, NOAA/AOML/HRD, and the USAF hurricane reconnaissance group this work would not have been possible. We thank Sim Aberson of NOAA/AOML/HRD for access to his Editsonde files of the GPS sondes for Lili. We also are indebted to Joe Cione of NOAA/AOML/HRD, who provided the SST data for Lili. The reviews from Hugh Willoughby and another anonymous reviewer are appreciated and led to improvements in this work. Garpee Barleszi’s editorial sniping improved our writing.
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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 undergoing rapid intensification (RI, lighter shading) or rapid decay (RD, darker shading) are delineated. Numbers denote the chronological positions of a few key sondes.
Citation: Monthly Weather Review 138, 4; 10.1175/2009MWR3145.1
Fig. 2.
The location of the GPS sonde drops relative to the circulation center with 5- and 10-km range rings drawn.
Citation: Monthly Weather Review 138, 4; 10.1175/2009MWR3145.1
Fig. 3.
(a) MSLP (hPa), (b) radius of the inner edge of the eye (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.
Citation: Monthly Weather Review 138, 4; 10.1175/2009MWR3145.1
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.
Citation: Monthly Weather Review 138, 4; 10.1175/2009MWR3145.1
Fig. 5.
Temperatures (°C, open triangles) and dewpoint temperatures (°C, closed triangles) for levels from 10 to 2500 m as a function of time. Other delineations follow those in Fig. 1.
Citation: Monthly Weather Review 138, 4; 10.1175/2009MWR3145.1
Fig. 6.
Equivalent potential temperature (K) for six levels from 10 to 2500 m as a function of time. Linear regression fit and _R_2 value are shown for the three lowest levels. Other delineations follow those in Fig. 1.
Citation: Monthly Weather Review 138, 4; 10.1175/2009MWR3145.1
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.
Citation: Monthly Weather Review 138, 4; 10.1175/2009MWR3145.1
Fig. 8.
(a) Best-track MSLP, (b) equivalent potential temperature (K) for the eyewall (EW) from the aircraft (open circles, boldface solid line) and the eye (E) at 500 m from the GPS sonde (closed triangles, thin solid line), and (c) eye excess energy (× 106 J m−2, solid diamonds). Shaded regions in (b) mark where the θe of the eyewall is warmer than that found in the eye.
Citation: Monthly Weather Review 138, 4; 10.1175/2009MWR3145.1