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VOLUME 141
Observed Tropical Cyclone Eye Thermal Anomaly Profiles Extending above 300 hPa
STEPHEN L. DURDEN
Jet Propulsion Laboratory, California Institute of Technology, Pasadena, California
(Manuscript received 16 January 2013, in final form 24 July 2013)
ABSTRACT
As recently pointed out by Stern and Nolan, much of our knowledge of the warm core structure of the
tropical cyclone eye has come from composites of in situ data taken from multiple aircraft studies of three
storms in the late 1950s and 1960s. Further observational confirmation of eye thermal structure has been
lacking, since much of the dropsonde data analyzed to date have been limited to pressure levels of 500 hPa or
lower. However, there exist a number of dropsonde eye profiles extending to near 250 hPa; these profiles were
acquired from NASA aircraft during various field campaigns. Here, the author uses these data to calculate eye
temperature anomaly profiles. These data are supplemented by several surface-based radiosonde releases in
tropical cyclone eyes over the period 1944–2003. The author finds that the pressure altitude of the maximum
anomaly varies between 760 and 250 hPa. The author also finds positive correlations between the maximum
anomaly level and storm intensity, size, upper-level divergence, and environmental instability.
1. Introduction
One of the characteristic features of tropical cyclones
is the existence of a warm core, noted at least as far back
as Haurwitz (1935). As recently pointed out by Stern
and Nolan (2012, hereafter SN12), much of our knowledge of the warm core structure of the eye above 500 hPa
comes from composites of in situ data taken from multilevel aircraft studies of three storms in the late 1950s
and 1960s (La Seur and Hawkins 1963; Hawkins and
Rubsam 1968; Hawkins and Imbembo 1976). In light of
the small sample size and coarse vertical resolution of
these data, SN12 suggest, based on their modeling studies, that the maximum temperature anomaly may not
usually be at upper levels. While observational confirmation of eye thermal structure is highly desirable,
much of the dropsonde data analyzed to date have been
limited to altitudes of 500 hPa or lower. However, there
exist a number of dropsonde profiles extending to near
250 hPa; these profiles were acquired from National
Aeronautics and Space Administration (NASA) aircraft
during various field campaigns since 1990. Although
a number of papers in the literature have presented
temperature profiles from some of these datasets (e.g.,
Corresponding author address: Stephen L. Durden, Jet Propulsion Laboratory, 4800 Oak Grove Dr., Pasadena, CA 91109.
E-mail: [email protected]
DOI: 10.1175/MWR-D-13-00021.1
Ó 2013 American Meteorological Society
Willoughby 1998; Simpson et al. 1998; Heymsfield et al.
2001; Zhu et al. 2004; Cram et al. 2007; Dolling and
Barnes 2012a,b; Smith and Montgomery 2013), temperature anomalies based on most of these data have not
been previously published. An exception is the study of
Halverson et al. (2006), discussed by SN12.
In this article, these NASA aircraft dropsonde data
are analyzed and are supplemented by surface-based
(radiosonde or rawinsonde) soundings in tropical cyclone eyes, allowing the thermal anomaly profile up to
relatively high altitudes (above the 300-hPa level) to be
investigated. After describing the data used, this article
presents the anomaly computation method, followed by
results for all the soundings available. Correlations between anomaly characteristics and various storm parameters are presented, followed by discussion of results
here in light of previous studies.
2. Data description
The primary source of the data used in this analysis
is dropsonde data from NASA aircraft for tropical cyclones with reasonably well-defined eyes. The Tropical Cyclone Motion (TCM) 1990 experiment used the
NASA DC-8 aircraft based in Okinawa, Japan, to make
measurements of typhoons in the northwest Pacific
Ocean (Elsberry 1990). While data from this experiment
are no longer readily accessible, a sounding of the eye of
DECEMBER 2013
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DURDEN
TABLE 1. Aircraft tropical cyclone eye soundings used in this study.
Date
Time (UTC)
Storm
Lat/lon
17 Sep 1990
6 Feb 1993
8 Feb 1993
23 Aug 1998
24 Aug 1998
26 Aug 1998
30 Aug 1998
21 Sep 1998
10 Sep 2001
23 Sep 2001
24 Sep 2001
29 Aug 2010
30 Aug 2010
30 Aug 2010
1 Sep 2010
1 Sep 2010
2 Sep 2010
16 Sep 2010
0452
2051
2056
2126
2146
1320
2043
1823
1928
2207
2258
2143
2041
2210
2146
2224
1955
1950
Flo
Oliver
Oliver
Bonnie
Bonnie
Bonnie
Danielle
Georges
Erin
Humberto
Humberto
Earl
Earl
Earl
Earl
Earl
Earl
Karl
25.68N/128.98E
16.28S/152.48E
18.88S/152.28E
24.88N/71.88W
26.38N/72.78W
32.88N/77.88W
27.98N/74.28W
17.88N/65.18W
35.88N/65.48W
32.58N/67.18W
36.48N/64.38W
17.78N/59.58W
19.28N/64.78W
19.48N/64.98W
26.48N/73.18W
26.78N/73.28W
32.18N/75.18W
19.78N/93.58W
Super Typhoon Flo was used by Willoughby (1998).
The data from his Figure 4 were digitized and included
in this analysis. The NASA DC-8 aircraft also participated in the Tropical Ocean Global Atmosphere Coupled Ocean Atmosphere Response Experiment (TOGA
COARE) in 1993 (Yuter et al. 1995), making soundings
and other measurements of South Pacific Tropical Cyclone Oliver (Simpson et al. 1998). The Convection and
Moisture Experiments (CAMEX) 3 and 4 in 1998 and
2001, respectively, were focused on tropical cyclones
(Kakar et al. 2006). These experiments yielded eye
soundings of Hurricanes Bonnie, Danielle, Georges,
Erin, and Humberto from the DC-8 and/or the ER-2
aircraft. In 2010 the DC-8 participated in the Genesis
and Rapid Intensification Experiment (GRIP), acquiring eye soundings in Hurricanes Earl and Karl (Braun
et al. 2013). Tropical cyclone eye sounding cases from the
above experiments are listed in Table 1. The data typically extend to 250 hPa.
Besides the dropsonde data listed in Table 1, a number of surface-based soundings have also been taken in
tropical cyclones. The data used here, listed in Table 2,
are the unnamed hurricane described in Riehl (1948),
the unnamed hurricane described in Simpson (1947),
Hurricane Arlene (Stear 1965), Hurricane Inez (Sugg
1967), Typhoon Shirley of 1968 using a sounding from
the Hong Kong Observatory, Hurricane Francelia
(Simpson et al. 1970), Hurricane Gloria (Franklin et al.
1988), Typhoon Rusa (Mashiko 2006), and Typhoon
Etau (Teshiba et al. 2005). For all cases except Rusa
and Etau, soundings were digitized from plots. For Rusa
and Etau, soundings were obtained from the University
of Wyoming sounding archive. Another storm considered
TABLE 2. Ground-based tropical cyclone eye sounding data used in
this study.
Date
Time (UTC)
Storm
Location
19 Oct 1944
8 Oct 1946
9 Aug 1963
5 Oct 1966
21 Aug 1968
1 Sep 1969
27 Sep 1985
29 Aug 2002
7 Aug 2003
1030
0700
1600
0200
1015
2100
0600
1200
1200
—
—
Arlene
Inez
Shirley
Francelia
Gloria
Rusa
Etau
Tampa, FL
Tampa, FL
Bermuda
Boca Chica, FL
Hong Kong
Swan Island
Cape Hatteras, NC
Naze, Japan
Naze, Japan
was Typhoon Kitty, described by Arakawa (1950). However, it is likely that the sounding was not in the eye; all of
the cases in Table 2 appear to have been made in the eye.
Data acquired using the global positioning system
(GPS) dropsondes (Hock and Franklin 1999) should
provide the most accurate pressure, wind, and thermodynamic data. These dropsondes were used in GRIP and
CAMEX-3/4. The data were processed via the standard
National Center for Atmospheric Research (NCAR)
software and quality control. Young et al. (2011) discuss
the quality of the GRIP data; in addition to a number of
soundings with temporary signal losses, they found that
28% of the soundings contained significant noise because of a specific hardware problem with some of the
GRIP dropsondes. The data points affected by noise
were removed by NCAR in reprocessing. Figure 1 shows
an example of missing samples in a sounding for Hurricane
Earl. While some gaps also occur in the CAMEX-3/4
soundings, they are infrequent and much smaller (e.g.,
a few hectopascals). The sounding for Hurricane Bonnie
FIG. 1. Examples of raw dropsonde data from Hurricanes Bonnie
(1998) and Earl (2010). The Earl data have been shifted by 5 K to
the right for plotting clarity.
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FIG. 2. Aircraft temperature soundings of tropical cyclone eyes
(Table 1).
FIG. 3. Aircraft temperature soundings of tropical cyclone eyes
(Table 1).
in Fig. 1 is representative. Apart from missing data,
soundings in 2010 and those in 1998 and 2001 should
have the typical GPS dropsonde measurement errors of
1 hPa and 0.2 K (Hock and Franklin 1999). Dolling and
Barnes (2012a,b) discuss the DC-8 GPS dropsonde data
in Humberto.
The soundings in Oliver used NCAR Omega dropsondes; the position data in these soundings does not
use GPS and is likely of lower accuracy. The temperature and pressure accuracy are also somewhat worse
than the GPS dropsondes. Franklin et al. (1988) report
a pressure accuracy of 2 hPa and a temperature accuracy of 0.5 K. The type of dropsonde used for the Flo
sounding is likely the same as used for Oliver. However,
the Flo data used here are expected to have larger errors
since they were read from a plot. Figures 2 and 3 show
temperature profiles from each of the storms in Table 1.
Accuracies in the surface-based soundings in Table 2
are not known; errors in such data have been generally discussed by Sherwood et al. (2005) and references
therein. Lenhard (1959) reports a temperature accuracy
of 1 K and pressure accuracy of 3 hPa for the instruments
of the late 1950s. The combination of data transcription
error (for data read from plots) and instrumental error
are likely to result in errors of perhaps several kelvins
for the older data. The accuracy of the soundings for
Rusa and Etau, in contrast, are likely to be significantly
more accurate because of digital format and improved
instrumentation. Figure 4 shows soundings for the storms
in Table 2.
The soundings used here have a variety of sample
spacings. The finest is from the GPS dropsondes in
GRIP, with pressure spacing between samples of about
0.5 hPa, but with missing data as shown in Fig. 1. The
Omega dropsonde data from Oliver have 5-hPa spacing.
Digital surface-based soundings have variable spacing,
ranging from 10 to more than 50 hPa. The soundings
estimated from published plots have sample spacing of
50–100 hPa, depending on the quality and labeling of the
plots. To handle all these data in the same manner, the
Matlab cubic spline function was used to interpolate to
2 hPa vertical spacing for the anomaly calculations. For
the digital dropsonde data with no missing samples, the
spacing is fine enough that interpolation is not really
needed. However, since missing samples are fairly frequent, it is simplest to use the same algorithm on all
soundings, including the soundings outside the storm,
described in the next section.
3. Definition of temperature anomaly
The temperature anomaly is defined as the difference
between the observed temperature in the tropical cyclone eye and a reference temperature representative of
the conditions either outside or in the absence of the
FIG. 4. Ground-based temperature soundings of tropical cyclone
eyes (Table 2).
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FIG. 5. Temperature anomalies computed at the same pressure
level for Hurricane Bonnie on 23 Aug and for Hurricane Georges.
The reference in both cases is the climatological (moist tropical)
profile of Dunion (2011).
tropical cyclone. Prior to defining what the reference
sounding should be, let us consider the question of
whether the difference should be taken between temperatures at the same altitude or the same pressure level.
Constant pressure has been used for observations. Calculations using model output can be performed at constant pressure or constant height, with the latter being
possibly more physically intuitive (e.g., SN12), although
Kurihara and Bender (1982) and Liu et al. (1997) computed the anomaly from model output on pressure surfaces. Figures 5 and 6 show the results of computing
anomaly profiles at the same pressure or altitude using
as reference sounding the moist tropical profile of
Dunion (2011). Shapes are fairly similar, but the anomaly
tends to be somewhat larger when differencing at the
same pressure; this same result was noted with other cases
not shown in Figs. 5 and 6. The larger anomaly using
pressure is to be expected since the reference temperature at the same pressure should occur at a higher altitude than in the eye (pressure surfaces are depressed
within the inner core, especially the eye). Hence, the
anomaly is increased by the lapse rate times the altitude
difference, which could result in the addition of several
kelvins to the temperature anomalies at constant pressure. An advantage of using pressure for analyzing observations is that it is a direct measurement whereas
altitude is derived from the hydrostatic equation (Hock
and Franklin 1999).
Now we consider the more complicated question of
choosing the reference sounding. There have been
a number of definitions used previously, and SN12 discuss the choice of a reference profile in detail in their
appendix B. The early study of Jordan and Jordan
(1954) computed the anomaly by differencing their
4259
FIG. 6. As in Fig. 5, but temperature anomalies are computed at the
same altitude rather than the same pressure level.
mean soundings in hurricanes with the mean tropical
sounding of Schacht (1946). The studies of La Seur and
Hawkins (1963), Hawkins and Rubsam (1968), and
Hawkins and Imbembo (1976) used the mean tropical
sounding of Jordan (1958a). Bell and Kar-sing (1973)
developed a mean sounding for the western North Pacific region and used that for deriving anomalies for typhoons. Halverson et al. (2006) used soundings taken
outside Hurricane Erin. Modeling studies have used the
average initial temperature profile (e.g., Zhang and
Chen 2012) or the domain-averaged temperature during
the simulation (Liu et al. 1997).
SN12 define the reference in their simulations as the
average temperature profile over an annulus from 558 to
648 km radius from the storm’s center. They find that
this profile warms somewhat with time and thus produces a different temperature anomaly profile as compared with using a fixed reference profile (specifically,
the moist tropical climatological sounding of Dunion
2011). This leads them to recommend using an average
taken at least several hundred kilometers from the
storm’s center.
For calculation of the temperature anomalies for the
data in Table 1, I initially used both the moist tropical
sounding of Dunion (2011) and environmental dropsondes released just outside the storms. However, the
environmental soundings were often warmer than the
Dunion sounding at upper levels. This caused the maximum temperature anomaly to be smaller and often
occur at lower altitudes than when using the Dunion
sounding. Figure 7 shows environmental soundings at
various distances from Hurricane Earl on 1 September
2010. The closer soundings are warmer than the more
distant soundings, especially at upper levels. Jordan and
Jordan (1954) and Sheets (1969) also noted upper-level
warming outside the storm center. Hence, based on
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TABLE 3. Environmental sounding data used in this study.
Soundings marked with an asterisk are surface based.
FIG. 7. Environmental soundings at varying distances from
Hurricane Earl on 1 Sep 2010.
these studies and Fig. 7 and following the recommendation of SN12, I looked for soundings that were taken
at least several hundred kilometers from the storm
center. This eliminated many of the DC-8 soundings.
Additional soundings were obtained from the National
Oceanic and Atmospheric Administration (NOAA)
Gulfstream IV aircraft and from surface-based sondes
(radiosondes or rawinsondes). Surface-based soundings
also provided the environment for some of the cases in
Table 2.
Table 3 lists the environmental soundings for storms
in Tables 1 and 2. In picking the soundings, I gave
preference to soundings to the east or west of the storm,
since the atmosphere is more homogeneous in that dimension. For the Atlantic the surface soundings are
from San Juan (Puerto Rico), Grand Cayman Island,
Nassau (Bahamas), Florida, and the Carolinas. Environmental soundings in the Pacific are from Japanese
islands (Ishigakijima, Naze, and Minamidait
ojima),
Taiwan, and Townsville (Australia). In some cases, the
storm track came much closer to the surface location
than the distances shown in Table 3. In these cases,
surface sounding times were chosen to give larger distances. For example, Flo came within 200 km of
Minamidait
ojima; the sounding for comparison with
the Flo eye sounding on 17 September 1990 was acquired on 15 September, when Flo was 756 km away.
This provides a sounding of the environment into which
Flo moved.
Figure 8 shows a plot of Dunion’s moist tropical climatological sounding, along with all of the environmental
profiles used to calculate anomalies. In computing the
anomaly for each case, all the environmental profiles
for that case were averaged. In this process the individual profiles making the average were examined and
bad samples were removed; all environmental profiles
Storm
No. of soundings
Distance from eye
(km)
Flo
Oliver 6
Oliver 8
Bonnie 23
Bonnie 24
Bonnie 26
Danielle
Georges
Erin
Humberto 23
Humberto 24
Earl 29
Earl 30
Earl 01
Earl 02
Karl
Arlene
Francelia
Gloria
Rusa
Etau
2
2
2
3
3
3
3
3
2
2
2
2
2
4
4
4
1
1
2
2
2
756,* 746*
782, 689*
590, 435*
870,* 383, 611
869,* 775, 425
679,* 500,* 481
983, 574, 350*
499,* 723, 818
516,* 509
375,* 380
578, 405
295, 902*
368,* 619
502,* 740, 508, 579
368, 388, 469,* 469*
491,* 767,* 480, 499
388*
353*
800,* 528*
488,* 803*
745,* 508*
used for a given case were reasonably consistent with
each other (i.e., within a few kelvins). Most of the environmental soundings in Fig. 8 are warmer than the
Dunion profile. The storms at higher latitudes (e.g.,
Humberto) generally possessed colder profiles.
Comparison of calculated anomalies using the climatological reference of Dunion (2011) versus the environmental soundings noted in Table 3 indicate that the
choice of the reference can make a difference in the resulting anomaly profile in some cases. Figure 9 shows an
example of using both types of reference for Hurricane
FIG. 8. Plot of environmental reference soundings for all cases
(Table 3). Solid line is the moist tropical profile of Dunion (2011),
shown for comparison.
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DURDEN
FIG. 9. Temperature anomalies for Hurricanes Bonnie (26 Aug)
and Georges computed using the moist tropical sounding of
Dunion (2011) and the environmental soundings listed in Table 3.
Bonnie on 26 August and for Hurricane Georges. For
Bonnie, the maximum anomaly is slightly reduced and
depressed in altitude. For Georges, upper and midlevel
anomaly maxima are evident for both references. However, the size of the anomalies changes by several kelvins.
4. Calculated temperature anomalies
Based on the results of the previous section, anomalies were calculated for each eye profile using the average environmental profile for each storm and using
pressure as the vertical coordinate. Anomaly profiles
using the Dunion (2011) moist tropical sounding were
also calculated. Although not shown for most cases,
significant differences between the two anomaly calculations are noted in the text. The exceptions are the eye
surface soundings prior to 1969; only the Dunion (2011)
sounding was used as the reference for these cases.
Figure 10 shows the temperature anomaly from the
eye of Super Typhoon Flo in 1990, by far the most intense case in this study, with minimum surface pressure
of 891 hPa. There is significant warming at all levels, with
especially large values from 700 to 300 hPa and a maximum of approximately 17 K near the 400-hPa level.
When using Dunion’s profile as the reference, the maximum anomaly is increased to 20 K but still occurs at just
above the 400-hPa level.
Figure 10 also shows the anomalies for Oliver on two
different days. There is a single maximum on 6 February
1993 near the 470-hPa level; using Dunion’s profile, the
maximum anomaly magnitude is increased by about 2 K
but remains at the same level. On 8 February there is
also a maximum near 470 hPa, but there are two additional maxima at about 550 and 350 hPa. Similar multiple maxima are found using Dunion’s profile, but again,
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FIG. 10. Temperature anomalies computed using environmental
soundings for Flo and for Oliver on both days.
the magnitude is somewhat larger (2 K). Schwartz et al.
(1996) show a temperature anomaly profile for Oliver
taken on 7 February near 1800 UTC (their Fig. 8); this
time is roughly halfway between the times of the two
soundings used here on 6 and 8 February. Their sounding is based on an aircraft microwave radiometer, which
should not have the spatial resolution issues of spaceborne radiometers noted by SN12. The reference appears to be a second radiometer sounding outside the
storm. Their profile shows the maximum anomaly at
500 hPa but with a secondary maximum of almost equal
magnitude just above the 300-hPa level. It seems that
there was a transition of the anomaly structure from one
maximum on 6 February to two on 7 February and three
on 8 February. However, in both Schwartz et al. (1996)
and in Fig. 10, the maxima are rather small compared to
the overall anomaly.
Figure 11 shows anomaly profiles for Bonnie for three
days. On 23 August 1998, Bonnie had maximums at 450,
350, and 250 hPa. However, these maxima are not very
FIG. 11. Temperature anomalies computed using environmental
soundings for Bonnie on all three days.
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FIG. 12. Temperature anomalies computed using environmental
soundings for Danielle, Georges, and Erin.
FIG. 13. Temperature anomalies computed using environmental
soundings for Humberto on both days and for Karl.
distinct; the anomaly that day is perhaps better thought
of as having a single, broad maximum extending from
about 575 hPa up to at least the 250-hPa level. When
using Dunion’s profile, the anomaly tilts more toward
larger values at upper levels, with a maximum anomaly
of about 13 K at 250 hPa. There are two notable maxima
on 24 August (near 550 and 250 hPa) and a single
maximum on 26 August (near 350 hPa) in Fig. 11. With
Dunion’s profile as reference, a single maximum at
250 hPa occurs on these days. Danielle’s anomaly profile
is shown in Fig. 12. It has both midlevel and upper-level
maxima with similar magnitudes. Georges also has two
anomaly maxima at 380 and 630 hPa; in contrast to
Danielle’s anomaly maxima, they are both quite distinct.
The minimum between them at 500 hPa is about 4 K less
than the anomaly maxima. Figure 12 also shows the
anomaly profile for Erin. Its maximum occurs just above
500 hPa, in agreement with the finding of Halverson
et al. (2006) for this same case. Interestingly, they also
constructed the anomaly in a vertical cross section using
dropsondes through the storm, not just the eye. Their
Figure 6 shows a sharp increase in the maximum anomaly
height to the southwest of the eye, suggesting that the
thermal structure just outside the eye may not always
represent the anomaly in the eye. As noted in section 2,
the soundings in Tables 1 and 2 appear to be in the eye,
based on location and winds; however, errors due to
structures like that documented by Halverson et al.
(2006) cannot be completely ruled out.
Figure 13 shows results for Hurricane Humberto on
both days. The shape on both days is similar, having
a prominent low-level (700 hPa) maximum, although the
magnitude is smaller on 24 September 2001 as the storm
had filled. A low-level maximum anomaly was also observed from DC-8 soundings on 22 September, when
Humberto was still a tropical storm (Dolling and Barnes
2012b, their Figure 8, showing the anomaly from surface
to 5000 m). The anomaly for Karl, also in Fig. 13, has
a slight maximum at lower levels but extends from about
700 to above 300 hPa.
Figures 14 and 15 show the anomalies computed from
drops on four different days in Hurricane Earl of 2010.
On 29 August, Earl was beginning a period of deepening that was completed during the measurements on
30 August. On 1 September it was deepening again, to its
lifetime minimum surface pressure, after filling slightly
on 31 August. On 2 September it was filling as it moved
north of 308 latitude. Upper- and midlevel maxima are
visible on 29 and 30 August, while a strong upper-level
maximum is seen on 1 September. On 2 September
there are maxima at both mid- and upper levels. Using
Dunion’s profile as reference on each of the four days,
maxima are enhanced at upper levels and reduced or
even disappear at lower levels. This illustrates the
FIG. 14. Temperature anomalies computed using environmental
soundings for Earl, showing one eye profile on 29 Aug and two eye
profiles on 30 Aug.
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4263
FIG. 15. Temperature anomalies computed using environmental
soundings for Earl, showing two eye profiles on 1 Sep and one eye
profile on 2 Sep.
FIG. 16. Temperature anomalies computed using environmental
soundings for Arlene, Francelia, Gloria, Rusa, and Etau. All
soundings are ground based.
frequently warmer environment of tropical cyclones relative to climatology, as discussed in the previous section.
Figure 16 shows the anomalies for those cases in Table
2 with environmental soundings. The most intense storm
in this set, Etau, also has the largest anomaly, about 15 K
at 360–290 hPa. The weaker maximum near 540 hPa
disappears when using the Dunion profile. Gloria, also
fairly intense, has an upper-level anomaly of about 13 K
from 430 to 250 hPa, becoming more concentrated near
the 250-hPa level if the Dunion reference is used. Rusa
has a primary maximum at about 460 hPa. Arlene has
maxima at 700 and 560 hPa. Francelia’s upper-level
maximum becomes larger than the lower maximum if
Dunion’s sounding is used as the reference.
Figure 17 shows the remaining cases from Table 2; in
these cases Dunion’s moist tropical profile is used as the
reference, so the results should be viewed with more
caution. The stronger storms, the 1944 hurricane described by Riehl and Typhoon Shirley, have upper-level
anomaly maxima. The other cases were minimal hurricanes at best and have maxima at various levels (700–
350 hPa). Bell and Kar-sing (1973) present temperature
anomalies from a number of these same storms in their
Figure 5 (1944 and 1946 hurricanes, Arlene, Inez, and
Shirley). In particular, they show an upper-level maximum for Shirley and the 1944 hurricane (200 hPa),
a maximum at 400 hPa for Inez, and the maximum
anomaly for Arlene occurring near 700 hPa. Although
using different references, their anomaly profiles for the
cases common to this work appear similar.
in Figs. 10–17, are summarized in Table 4. In cases with
multiple maxima, each maximum and the corresponding
pressure level are shown. As can be seen, there is a large
variation in the vertical location of the maximum
anomaly (760–250 hPa). Also shown in Table 4 are
best-track minimum sea level pressure (MSLP) and
parameters from development data for the Statistical
Hurricane Intensity Prediction Scheme (SHIPS; DeMaria
et al. 2005). These data go back to 1982 in the Atlantic and
to 2000 in the northwest Pacific and so are not available
for a number of cases. The three parameters shown are
the average 200-hPa divergence D200 (averaged over the
0–1000-km radius), the average equivalent potential
temperature difference Due between a parcel lifted from
the surface to 200 hPa and its environment (over the
200–800-km radius), and the 500-hPa tangential wind
azimuthally averaged at radius 500 km (V500).
5. Relationship to other storm parameters
The calculated anomaly profiles from all of these eye
soundings, described in the previous section and shown
FIG. 17. Temperature anomalies computed for cases with no
environmental sounding by using Dunion’s climatological mean
sounding for the moist tropical atmosphere.
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TABLE 4. Summary of anomaly profile results for all cases. MSLP is near time of sounding.
Storm
MSLP (hPa)
Flo
Oliver 6
Oliver 8
Bonnie 23
Bonnie 24
Bonnie 26
Danielle
Georges
Erin
Humberto 23
Humberto 24
Earl 29
Earl 30
Earl 01
Earl 02
Karl
Unnamed 1944
Unnamed 1946
Arlene
Inez
Shirley
Francelia
Gloria
Rusa
Etau
891
955
965
955
963
964
983
970
970
983
991
978
940
935
948
976
967
987
976
987
965
992
942
963
933
Due (K)
D200 (1027 s21)
V500 (m s21)
17
15
14
14
18
7
13
9
15
15
13
10
7
41
53
64
53
5
20
16
217
22
42
60
26
20
7
9
12
4
6
4
3
0
8
10
11
11
6
6
10
12
100
41
105
10
17
18
As would be expected, the larger eye temperature
anomalies generally correspond to more intense storms.
Figure 18 plots the MSLP versus both the maximum
temperature anomaly and the temperature anomaly
DT(p) averaged over pressure p from 900 to 250 hPa
[integral of DT(p)d ln(p), with normalization by integral
of d ln(p)]. The MSLP is well correlated with both the
maximum and the average anomaly; correlation is significant at the 0.5% level based on statistical hypothesis
testing. This correlation is expected from simple hydrostatic considerations; indeed, the differential change
in surface pressure is proportional to the average anomaly, as noted in SN12 [their Eq. (4.1), from Hirschberg
and Fritsch 1993] and McIlveen (2010, p. 552). The proportionality constant relating the average temperature
anomaly in kelvins to the pressure drop in hectopascals
is roughly five, depending on the exact choice of surface
pressure and mean column temperature.
The maximum anomaly and the average anomaly are
also highly correlated with each other (not shown),
suggesting that in stronger storms both the maximum
anomaly and the vertical extent of the anomaly tend to
be larger than in weaker storms. This can be seen, for
example, in Figs. 10 and 14; the anomalies for Flo and for
Earl on 1 September have both large maxima and large
vertical extent (from 700 to at least 250 hPa). If the entire temperature anomaly profile were concentrated into
Max anomaly (K)
Anomaly level (hPa)
17
9
9/9/8
10/10/10
10/9/8
11
9/8
11/10
13
10/10
7
7/6
13/12
15/13/10
12/12/12
6
14
5
10/9
8
12
6
13
10
15/8
380
475
355/470/550
250/345/455
270/405/550
340
600/260
380/630
480
630/550
670
350/540
350/560
260/460/590
640/350/250
680
350
650
705/560
400
275
760
350
450
290/540
a uniform layer with the same maximum anomaly, the
pressure level at the top of the layer would need to be
about half that of the bottom to give an average anomaly
that is two-thirds of the maximum anomaly, a typical
ratio from inspection of Fig. 18. Since the anomaly is not
actually constant with height, we can expect the layer
containing the main part of the anomaly to have a larger
extent than expected using the uniform anomaly. In fact,
FIG. 18. Maximum and average temperature anomalies vs MSLP
for the cases in Tables 1 and 2. Also shown are the linear regression
lines for each case (solid lines).
DECEMBER 2013
DURDEN
an examination of Figs. 10–17 indicates that the vertical
extent of the anomaly (from increase at low levels to
drop off at higher levels or 250 hPa) is typically more
than a 50% drop in pressure. A 50% reduction in pressure is about the minimum seen in these data, with the
maximum vertical extent being 800–250 hPa (pressure at
the top of the anomaly is 31% of the pressure at the
bottom). To better define the vertical extent, data extending above 250 hPa would need to be examined.
From Fig. 18 it seems that an average anomaly of at
least 4 K is needed for even the weakest storms. Using
the proportionality of pressure drop to average anomaly
(roughly a factor of 5), an average temperature anomaly
of 4 K would correspond to a 20-hPa pressure drop,
which would not be unreasonable for a strong tropical
storm or minimal hurricane. For Super Typhoon Flo,
the average anomaly of 13.6 K gives a pressure drop of
68 hPa, which underestimates the true pressure drop.
The linear relation between the pressure and temperature drop is most accurate when both are small, which is
not the case with Flo.
Possible correlations between the level of the maximum anomaly and storm parameters were also investigated. For storms with multiple peaks, the level of the
largest and generally broadest anomaly was used. The
correlation between the level of the maximum anomaly
and the MSLP is statistically significant near the 0.5%
level; more intense storms (lower MSLP) tend to have
a higher maximum anomaly level (higher altitude, lower
pressure), as shown in Fig. 19. The maximum anomaly
height is positively correlated with V500 and the 200-hPa
divergence, both at the 5% significance level. The potential temperature difference is positively correlated
with the anomaly height at the 10% significance level.
(Positive correlation indicates that larger values of these
parameters correspond to anomaly at greater height).
Other SHIPS parameters tested were the 12-h change in
maximum wind speed, the vertical shear of the horizontal wind between 850 and 200 hPa, and the relative
humidity at lower, middle, and upper levels. No correlation was found between these parameters and the
maximum anomaly height at even the 40% significance
level. Stern and Zhang (2013b) also found no systematic
dependence of the anomaly height on wind shear in their
simulations.
6. Discussion
This section examines the results of section 4 and
section 5 in light of previous work. While the cases in
Tables 1 and 2 represent most of the known eye soundings extending to upper levels, there have been many
previous studies dealing with the warm core of tropical
4265
FIG. 19. Pressure height of the maximum temperature anomaly vs
MSLP. Solid line is the linear regression fit to the data.
cyclones (close to but not in the eye). Palm
en (1948),
Arakawa (1950), Kasahara (1953), Schacht (1946),
Jordan and Jordan (1954), Sheets (1969), Bell and Karsing (1973), Frank (1977), and Keenan and Templeton
(1983) provide either case or statistical studies of surface
soundings outside the eye. The reference is usually a
mean sounding, and the results tend to show the maximum warm core anomaly at mostly upper levels [e.g.,
250 hPa in Frank (1977), but as low as 400 hPa in
Kasahara (1953)]. However, as noted in section 4, the
warm core anomaly near the eye may not always be
the same as the anomaly that would be found if eye
soundings had been available in these studies, based
on the two-dimensional anomaly structure shown in
Figure 6 of Halverson et al. (2006). The study of Bell and
Kar-sing (1973) looked at the correlation between the
storm intensity and the warm core temperature at
a number of heights in the storm. They found the
largest correlation between intensity and the 200-hPa
temperature for typhoons. They also show the same
quantity for hurricanes (Sheets 1969), with the best
correlation occurring near the 400-hPa level, dropping
slightly as 200 hPa is approached.
Additional studies have used flight data at multiple
levels; these have provided data at mid- and upper levels
in the eye but have very coarse vertical resolution. Jordan
(1958b) reports an anomaly at 240 hPa that is likely 3–6 K
warmer than the anomaly at 597 hPa for flights in one
storm. Shea and Gray (1973) performed compositing of
flight-level data from a number of storms and five flight
levels. The pressure level with the largest temperature
anomaly in the eye (referenced to temperature at a radius of 70 km) appears to be 525 hPa. Improving on the
coarse vertical resolution of these studies, Brown et al.
(2007) retrieved the thermal structure of two hurricanes
from airborne radiometer data, finding a primary anomaly
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MONTHLY WEATHER REVIEW
at 200 hPa and secondary at 500 hPa in one case and
a single maximum at about 480 hPa in another case.
They used an environmental sounding as reference (the
distance to the reference is not specified).
The studies of LaSeur and Hawkins (1963), Hawkins
and Rubsam (1968), and Hawkins and Imbembo (1976)
used flight-level data from three hurricanes of varying
intensity. The last of these studies found a lower, secondary anomaly at 600 hPa, in addition to an upper-level
maximum. There is also some evidence of an increase
in height of the primary anomaly, as the intensity increased. The primary anomaly was at 300 hPa on the first
day and 250 hPa on the second flight, when the storm
was near peak intensity, although the vertical resolution
of the measurements was very coarse. Simpson et al.
(1998) showed budget-based estimates of warming in
Hurricane Daisy of 1958 (their Figure 4), peaking at
about 500 hPa on the first flight and 400 hPa on the
second flight, two days later as the storm matured.
Viltard and Roux (1998) performed a thermodynamic
retrieval from dual-Doppler radar measurements of
a hurricane. Their maximum anomaly was around 8 km
(350 hPa) and rose in height somewhat as the storm intensified. In summary, these studies, dating back over
several decades, found a variety of maximum anomaly
heights and allow the possibility of some dependence of
the height on intensity.
The increasing height of the anomaly maximum
with increasing upper-level divergence, increasing
Due , and increasing V500 do not appear to have been
directly examined in previous studies. The large-scale
divergence provides a measure of synoptic-scale forcing with larger divergence being associated with intensification; its role in the intensification of one case
is described by Jones and Cecil (2007). The Due provides a measure of environmental instability, again
with larger values being correlated with intensification
(Jones and Cecil 2007). V500 is a measure of the
storm’s size. It is not clear whether any of these parameters has a direct impact on the height of the maximum anomaly. Since they may be related to intensity,
the correlations noted may simply reflect the stronger
correlation between anomaly height and intensity, as
measured by MSLP.
There have also been a number of modeling and
theoretical studies that have examined the eye thermal
anomaly. SN12 and follow-on work reported in Stern
and Zhang (2013a,b) use the Weather Research and
Forecasting Model (WRF) and find the main anomaly
occurring between 4 and 8 km (roughly 600–350 hPa).
Zhang and Chen (2012) also use WRF but find the
center of warming to be above 12 km. Liu et al. (1997)
find the maximum temperature anomaly at about 450 hPa
VOLUME 141
in their simulation, while Kurihara and Bender (1982)
find the maximum at about 300 hPa. Studies that include theoretical work on the tropical cyclone eye thermal characteristics are Malkus (1958), Smith (1980),
Emanuel (1986, 1997), Willoughby (1998), and Schubert
et al. (2007). Of these, Emanuel (1986) presents a calculated temperature anomaly (his Figure 11), which
peaks just above 12 km (roughly 200 hPa).
7. Conclusions
This work has examined a set of tropical cyclone eye
soundings that extend above 300 hPa. Calculated temperature anomaly profiles were found to peak at varying
pressure levels (760–250 hPa), suggesting that numerical
models should also exhibit similar variability. Of particular interest are correlations between the maximum
anomaly level and storm intensity, upper-level divergence, environmental instability, and storm size (as measured by the wind speed at 500-km radius). Perhaps the
main limitation of this work is the small number of
soundings extending to upper levels in tropical cyclone
eyes. While future dropsonde and radiometer soundings
from unmanned aircraft may provide significantly more
soundings (extending well above 250 hPa), short-term
work should also include searching for additional surfacebased soundings, such as those for Typhoons Rusa and
Etau, which were found somewhat serendipitously.
Meanwhile, Stern and Zhang (2013a,b) have made
progress in understanding the warming in the eye of a
tropical cyclone model simulation by performing a potential temperature budget analysis and a trajectory
analysis of parcels within the eye.
Acknowledgments. The author would like to thank
Dr. Daniel Stern for reviewing and providing very
helpful comments on an early version of this manuscript.
The author is also grateful to Dr. Jonathan Vigh and two
anonymous reviewers for their detailed and extensive
comments and questions on the submitted manuscript;
their suggestions led to significant improvements in the
quality of the paper. The author thanks the University
of Wyoming for making its sounding archive publicly
available and NOAA/RAMMB for making the SHIPS
development data available. Dropsonde data processing
was provided by NCAR/EOL under sponsorship of the
National Science Foundation. The research described in
this paper was carried out at the Jet Propulsion Laboratory,
California Institute of Technology, under contract with the
National Aeronautics and Space Administration. Funding
from Dr. Ramesh Kakar at NASA headquarters under
NASA Research Announcement NNH09ZDA001NHSRP is gratefully acknowledged.
DECEMBER 2013
DURDEN
REFERENCES
Arakawa, H., 1950: Vertical structure of a mature typhoon. Mon.
Wea. Rev., 78, 197–200.
Bell, G. J., and T. Kar-sing, 1973: Some typhoon soundings and
their comparison with soundings in hurricanes. J. Appl. Meteor., 12, 74–93.
Braun, S. A., and Coauthors, 2013: NASA’s Genesis and Rapid
Intensification Processes (GRIP) field experiment. Bull.
Amer. Meteor. Soc., 94, 345–363.
Brown, S., B. Lambrigtsen, A. Tanner, J. Oswald, D. Dawson, and
R. Denning, 2007: Observations of tropical cyclones with a 60,
118, and 183 GHz microwave sounder. Preprints, Proc. IEEE
Geoscience and Remote Sensing Symp., Barcelona, Spain,
IEEE, 3317–3320.
Cram, T. A., J. Persing, M. T. Montgomery, and S. A. Braun, 2007:
A Lagrangian trajectory view on transport and mixing processes between the eye, eyewall, and environment using a
high-resolution simulation of Hurricane Bonnie (1998). J. Atmos. Sci., 64, 1835–1856.
DeMaria, M., M. Mainelli, L. K. Shay, J. A. Knaff, and J. Kaplan,
2005: Further improvements to the Statistical Hurricane Intensity Prediction Scheme (SHIPS). Wea. Forecasting, 20,
531–543.
Dolling, K. P., and G. M. Barnes, 2012a: The creation of a high
equivalent potential temperature reservoir in Tropical Storm
Humberto (2001) and its possible role in storm deepening.
Mon. Wea. Rev., 140, 492–505.
——, and ——, 2012b: Warm-core formation in Tropical Storm
Humberto (2001). Mon. Wea. Rev., 140, 1177–1190.
Dunion, J. P., 2011: Rewriting the climatology of the tropical North
Atlantic and Caribbean Sea atmosphere. J. Climate, 24, 893–
908.
Elsberry, R. L., 1990: International experiments to study tropical
cyclones in the western North Pacific. Bull. Amer. Meteor.
Soc., 71, 1305–1316.
Emanuel, K., 1986: An air–sea interaction theory for tropical cyclones. Part I: Steady-state maintenance. J. Atmos. Sci., 43,
585–604.
——, 1997: Some aspects of hurricane-core dynamics and energetics. J. Atmos. Sci., 54, 1014–1026.
Frank, W. M., 1977: The structure and energetics of the tropical
cyclone: I. Storm structure. Mon. Wea. Rev., 105, 1119–1135.
Franklin, J. L., S. J. Lord, and F. D. Marks Jr., 1988: Dropwindsonde and radar observations of the eye of Hurricane Gloria
(1985). Mon. Wea. Rev., 116, 1237–1244.
Halverson, J. B., J. Simpson, G. Heymsfield, H. Pierce, T. Hock,
and L. Ritchie, 2006: Warm core structure of Hurricane Erin
diagnosed from high altitude dropsondes during CAMEX-4.
J. Atmos. Sci., 63, 309–324.
Haurwitz, B., 1935: The height of tropical cyclones and of the ‘‘eye’’
of the storm. Mon. Wea. Rev., 63, 45–49.
Hawkins, H. F., and D. T. Rubsam, 1968: Hurricane Hilda, 1964. II:
Structure and budgets of the hurricane on October 1, 1964.
Mon. Wea. Rev., 96, 617–636.
——, and S. M. Imbembo, 1976: The structure of a small, intense
hurricane—Inez 1966. Mon. Wea. Rev., 104, 418–442.
Heymsfield, G. M., J. B. Halverson, L. Tian, and T. P. Bui, 2001:
ER-2 Doppler radar investigations of the eyewall of Hurricane
Bonnie during the Convection and Moisture Experiment-3.
J. Appl. Meteor., 40, 1310–1330.
Hirschberg, P. A., and J. M. Fritsch, 1993: On understanding height
tendency. Mon. Wea. Rev., 121, 2646–2661.
4267
Hock, T. F., and J. L. Franklin, 1999: The NCAR GPS dropwindsonde. Bull. Amer. Meteor. Soc., 80, 407–420.
Jones, T. A., and D. J. Cecil, 2007: SHIPS-MI forecast analysis of
Hurricanes Claudette (2003), Isabel (2003), and Dora (1999).
Wea. Forecasting, 22, 689–707.
Jordan, C. L., 1958a: Mean soundings for the West Indies area.
J. Meteor., 15, 91–97.
——, 1958b: The thermal structure of the core of tropical cyclones.
Geophysica, 6, 281–297.
——, and E. S. Jordan, 1954: On the mean thermal structure of
tropical cyclones. J. Meteor., 11, 440–448.
Kakar, R., M. Goodman, R. Hood, and A. Guillory, 2006: Overview of the Convection and Moisture Experiment (CAMEX).
J. Atmos. Sci., 63, 5–18.
Kasahara, A., 1953: A note on the vertical structure of the pressure and
temperature fields in a typhoon. J. Meteor. Soc. Japan, 31, 22–35.
Keenan, T. D., and J. I. Templeton, 1983: A comparison of tropical
cyclone, hurricane, and typhoon mass and moisture structure.
Mon. Wea. Rev., 111, 320–327.
Kurihara, Y., and M. A. Bender, 1982: Structure and analysis of
the eye of a numerically simulated tropical cyclone. J. Meteor.
Soc. Japan, 60, 381–395.
La Seur, N. E., and H. F. Hawkins, 1963: An analysis of Hurricane
Cleo (1958) based on data from research reconnaissance aircraft. Mon. Wea. Rev., 91, 694–709.
Lenhard, R. W., 1959: Meteorological accuracies in missile testing.
J. Meteor., 16, 447–453.
Liu, Y., D.-L. Zhang, and M. K. Yau, 1997: A multiscale numerical
study of Hurricane Andrew (1992). Part I: Explicit simulation
and verification. Mon. Wea. Rev., 125, 3073–3093.
Malkus, J. S., 1958: On the structure and maintenance of the mature hurricane eye. J. Meteor., 15, 337–349.
Mashiko, W., 2006: A cloud-resolving simulation of Typhoon
Rusa (2002): Polygonal eyewall and mesovortices structure.
Preprints, 27th Conf. on Hurricanes and Tropical Meteorology, Monterey, CA, Amer. Meteor. Soc., P4.16. [Available
online at https://ams.confex.com/ams/pdfpapers/108166.pdf.]
McIlveen, R., 2010: Fundamentals of Weather and Climate. 2nd ed.
Oxford University Press, 632 pp.
Palmen, E., 1948: On the formation and structure of tropical hurricanes. Geophysica, 3, 26–38.
Riehl, H., 1948: A radiosonde observation in the eye of a hurricane.
Quart. J. Roy. Meteor. Soc., 74, 194–196.
Schacht, E. J., 1946: A mean hurricane sounding for the Caribbean
area. Bull. Amer. Meteor. Soc., 27, 324–327.
Schubert, W. H., C. M. Rozoff, J. L. Vigh, B. D. McNoldy, and J. P.
Kossin, 2007: On the distribution of subsidence in the hurricane eye. Quart. J. Roy. Meteor. Soc., 133, 1–20.
Schwartz, M. J., J. W. Barrett, P. W. Fieguth, P. W. Rosenkranz,
M. S. Spina, and D. H. Staelin, 1996: Observations of thermal
and precipitation structure in a tropical cyclone by means of
passive microwave imagery near 118 GHz. J. Appl. Meteor.,
35, 671–678.
Shea, D. J., and W. M. Gray, 1973: The hurricane’s inner core region. I. Symmetric and asymmetric structure. J. Atmos. Sci.,
30, 1544–1564.
Sheets, R. C., 1969: Some mean hurricane soundings. J. Appl.
Meteor., 8, 134–146.
Sherwood, S. C., J. R. Lanzante, and C. L. Meyer, 2005: Radiosonde daytime biases and late-20th century warming. Science,
309, 1556–1559.
Simpson, J., and Coauthors, 1998: On the role of ‘‘hot towers’’ in
tropical cyclone formation. Meteor. Atmos. Phys., 67, 15–35.
4268
MONTHLY WEATHER REVIEW
Simpson, R. H., 1947: A note on the movement and structure of
the Florida hurricane of October 1946. Mon. Wea. Rev., 75,
53–58.
——, A. L. Sugg, G. B. Clark, N. L. Frank, J. R. Hope, P. J. Hebert,
R. H. Kraft, and J. M. Pelissier, 1970: The Atlantic hurricane
season of 1969. Mon. Wea. Rev., 98, 293–306.
Smith, R. K., 1980: Tropical cyclone eye dynamics. J. Atmos. Sci.,
37, 1227–1232.
——, and M. T. Montgomery, 2013: How important is the isothermal expansion effect in elevating equivalent potential
temperature in the hurricane inner core? Quart. J. Roy. Meteor. Soc., 139, 70–74.
Stear, J. R., 1965: Sounding in the eye of Hurricane Arlene to
108,760 feet. Mon. Wea. Rev., 93, 380–382.
Stern, D. P., and D. S. Nolan, 2012: On the height of the warm core
in tropical cyclones. J. Atmos. Sci., 69, 1657–1680.
——, and F. Zhang, 2013a: How does the eye warm? Part I: A
potential temperature budget analysis of an idealized tropical
cyclone. J. Atmos. Sci., 70, 73–90.
——, and ——, 2013b: How does the eye warm? Part II: Sensitivity
to vertical wind shear, and a trajectory analysis. J. Atmos. Sci.,
70, 1849–1873.
Sugg, A. L., 1967: The hurricane season of 1966. Mon. Wea. Rev.,
95, 131–142.
VOLUME 141
Teshiba, M., H. Fujita, H. Hashiguchi, Y. Shibagaki, M. D.
Yamanaka, and S. Fukao, 2005: Detailed structure within
a tropical cyclone ‘‘eye.’’ Geophys. Res. Lett., 32, L24805,
doi:10.1029/2005GL023242.
Viltard, N., and F. Roux, 1998: Structure and evolution of Hurricane Claudette on 7 September 1991 from airborne Doppler
radar observations. Part II: Thermodynamics. Mon. Wea. Rev.,
126, 281–302.
Willoughby, H. E., 1998: Tropical cyclone eye thermodynamics.
Mon. Wea. Rev., 126, 3053–3067.
Young, K., J. Wang, T. Hock, and D. Lauritsen, cited 2011: Genesis
and Rapid Intensification Processes (GRIP) 2010 quality controlled dropsonde data set. [Available at http://data.eol.ucar.
edu/master_list/?project5PREDICT.]
Yuter, S. E., R. A. Houze, S. R. Brodzik, B. F. Smull, J. R.
Daugherty, and F. D. Marks, 1995: TOGA COARE aircraft
mission summary images: an electronic atlas. Bull. Amer.
Meteor. Soc., 76, 319–328.
Zhang, D.-L., and H. Chen, 2012: Importance of the upper-level
warm core in the rapid intensification of a tropical cyclone.
Geophys. Res. Lett., 39, L02806, doi:10.1029/2011GL050578.
Zhu, T., D.-L. Zhang, and F. Weng, 2004: Numerical simulation of
Hurricane Bonnie (1998). Part I: Eyewall evolution and intensity changes. Mon. Wea. Rev., 132, 225–241.