NASA Technical Reports Server (NTRS) 20010108171: Warm-Core Intensification Through Horizontal Eddy Heat Transports into the Eye

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by  NASA Technical Reports Server (NTRS)

11.2 WARM-CORE INTENSIFICATION THROUGH HORIZONTAL EDDY
HEAT TRANSPORTS INTO THE EYE
Scott A. Braun
NASA, Goddard Space Hight Center
Greenbelt, Maryland
Michael T. Montgomery, John Fulton, and David S.Nolan
Department of Atmospheric Science
Colorado State University
Fort Collins, Colorado
1, Introduction including all components of the heat budget, are saved
every 2 min so that the processes contributing to eye
The mechanism for the formation and intensifica-
warming are well resolved in both space and time.
tion of the hurricane warm core is not well understood.
Physicsoptions for the 1.3-km gridinclude theGoddard
The generally accepted explanation is that the warm
Cumulus Ensemble Model (GCE) cloud microphysics
core forms as a resultof gentle subsidence of air within
scheme, the Burk-Thompson boundary layer
the eye that warms as a result of adiabatic
parameterization, and the Dudhia (1989) cloud radiation
compression. Malkus (1958) suggested that thissubsid- scheme.
ence is part of a deep circulation in which air begins
The stormcenter isdetermined atevery model out-
descent at high levels in the eye, acquires cyclonic
put time using the horizontal distribution of pressure at
angular momentum as itdescends to lower levels, and the lowest model level (42 m) to determine an approxi-
then diverges at low levels, where it is entrained back
mate geometric center of the pressure field. No attempt
into the eyewall. Inward mixing from the eyewall is
is made to determine different centers at higher levels.
hypothesized to force the subsidence and maintain the
Storm motion is computed from the identified near-
moisture and momentum budgets of the subsiding air. surface center locations.
Willoughby (1998) suggested that air withinthe eye has
remained so since it was first enclosed during the for- 3. Results
mation ofthe eyewall andthat it subsides at mostonly a
Conventionally, heat budgets are expressed in
few kilometers rather than through the depth of the
terms of an apparent heat source Q1(Johnson, 1984;
troposphere. He relates the subsidence tothe low-level
divergence and entrainment into the eyewall noted by Houze 1982; Gallus and Johnson 1991; Braun and
Malkus (1958), but suggests that shrinkage of theeye's Houze 1996). Since our interest here is in the local
volume is morethan adequate toaccount for the airlost warming that occurs within the eye, the heat budget is
to the eyewall or converted to cloudy air by turbulent instead expressed in terms of the local tendency of
mixing across the eye boundary. Smith (1980) offered potentialtemperature,
an alternative view of the subsidence forcing, suggest-
aO
ing that vertical motion in a mature hurricane eye is = HADV+VADV+Qhr+Qpu+Qr • (1)
generated largely by imbalances between the down-
ward vertical pressure gradient force and the upward
HADV and VADV are the horizontal and vertical
buoyancy force. The vertical pressure gradient force is
associated with the decay and/or radial spread of the advection, respectively, Qthrthe latent heating associat-
tangential windfield withheightatthose levels were the ed with cloud microphysics, Qpb_the boundary layer
winds are in approximate gradient wind balance. The heating, and Qrthe radiative heating. The budget isfor-
rate of subsidence isjust that required to warm the air mulated ina reference frame moving withthe storm so
sufficiently such that the buoyancy remains in close that the storm motion is included in the horizontal
hydrostatic balance withan increasing vertical pressure advectionterm.
gradient force. Since the eye of the hurricane is dry (with the
In this study, a very high-resolution simulation of exception of the boundary layer, an upper cloud ice
Hurricane Bob (1991) usinga cloud-resolving gridscale layer, and right along the eyewall), latent heating does
of 1.3 km isused to examine the heat budget withinthe notplay a direct role inwarming theeye. Horizontal and
storm with particular emphasis on the mechanisms for vertical advection and radiative heating are the main
warming ofthe eye. terms contributing to temperature changes within the
2. Numerical Model eye. Some evaporative coolingcancels a portion of the
adiabatic warming along the eyewall. InFig. la, the azi-
The model used in this study is the Pennsylvania muthal and time averaged sum of VADV and Qlhr is
State University--National Center for Atmospheric used to show the net subsidence warming in the eye
Research nonhydrostatic mesoscale model MM5 using contour levels that accentuate the patterns inthe
(Dudhia 1993; Grell et al. 1995). A detailed description eye. Figure la clearly shows the adiabatic warming
of the model setup is provided inBraun and Tao (2000) along the inner edge of the eyewall associated with
and Braun (2001). The analysis presented here is moderate downdrafts there and to a lesser extent near
obtained from a 6-h simulation on a 1.3-km nest
thecenter. Weak adiabatic cooling occursabove 12 km
between hours 62-68 of a 72-h forecast. Model fields,
K h"
18
b)
VADV+QIh,
0 i
+HADV+Q r
0 _Rad_ (kin)50 75 _12
Figure 1. Azimuthal and time averaged (a) vertical advection ._
plus latent heating and (b) horizontal advection usingcontours .-t:L'°
values of :1:0.2,0.4, 0.8, 1.6, 3.2, and 6.4 K h"1.The irregular _:_ 6
contour interval is used to highlightvalues withinthe eye. The
thick grey line delineates the boundary between the eye and
eyewall where average subsidence warming transitions to adia-
batic cooling.
•
-0.6 '-013 0 0.3 0.6
in the eye as a result of weak upward motion ina diffuse K h"t
cloud ice layer. In the eyewall, adiabatic cooling gener-
ally exceeds latent heating except near the inner edge Figure 2. (a) Vertical profiles of the area and time averaged
of the eyewall where the opposite is true. Horizontal vertical advection and latent heating (solid line), horizontal
advection (Fig. lb) produces cooling along the inner advection (short-dashed line), and radiative heating (tong-
edge of the eyewall, strongest in the region of maximum dashed line). (b)As in(a), but forallterms combined.
subsidence warming, and warming through much of the
rest of the eye, with maximum values generally close to summed (Fig. 2b), the net heating profile shows aver-
the center. Outside of the eye, HADV largely balances age warming of 0.4-0.5 K h-I peaking near 8.5 km,
the sum of VADV and O=,,so that the net tendencies are approximately the height of the warm anomaly (not
weak. Therefore, inthe eye, both VADV and HADV con- shown). Thus, only by including the effects of horizontal
tribute to warming. advection can one account for the development of the
To determine the relative contributions from advec- warm core inthis case.
tive and radiative processes, these terms are averaged Since the warming from horizontal advection con-
over the area of the eye, taking into account the increas- tributes to a significant portion of the warming in the
ing radius with height (thick, gray line in Fig. 1), and eye, it is instructive to decompose it into contributions
over the 6-h simulation time. The boundary of the aver- from azimuthal mean and eddy terms as follows:
aging area was determined from the VADV term and
marks the transition from eye warming to eyewall
u a° v_eo - eB ,ao' v_,ao'
cooling. Figure 2a shows vertical profiles of area- and - r_-7"a"_ =-Ur'_7-Ur-_ r e2 (2)
time-averaged heating rates. The profile for VADV+qh r
shows warming between 1-11 km with a peak of 0.55 K
h"Inear 4 km. Adiabatic cooling at upper levels is gener- where ris radius, 2 azimuth, urand vathe storm-relative
ally offset by warming from Iongwave radiative process- radial and tangential velocities, respectively, e potential
es in the diffuse cloud layer. Warming from HADV is temperature, overbars indicate azimuthal averages, and
concentrated in the middle to upper troposphere with a the prime symbol denotes perturbations from the azi-
magnitude of ~0.3 K h1. Since the hydrostatic surface muthal mean. The azimuthal mean component of the
pressure is most sensitive to warming at upper levels tangential advection is zero, but the eddy component
(Jeanne Simpson, personal communication), warming can be nonzero. The terms in (2), referred to (from left
from HADV appears to play a significant role inlowering to right) as the mean horizontal advection, the mean
of the surface pressure. When the three terms are radial advection, the eddy radial advection, and the
eddy tangential advection, are computed at each 2-min perature anomalies and wind vectors at 10.4 km, which
output time and averaged over the 6-h simulation are representative of the layer between 5-11 km. The
period. potential temperatures are generally warmer on the
A radius-height cross section of the azimuthal western side of the storm, cooler on the eastern side,
mean horizontal advection [left side of (2)] is shown in with the maximum anomalies in the eyewall. The orien-
Fig. 3a. The warming associated with the mean radial tation of the peak temperature anomalies inthe eyewall
advection [first term on right in (2), Fig. 3b] accounts for are rotated somewhat counterclockwise relative to the
the low-level cooling inthe inflow and the warming with- anomalies just outside the eyewall and within the eye.
inthe eyewall outflow, butdoes not account for the cool- Approximately collocated with the peak temperature
ing along the inner edge of the eyewall or the warming anomalies are counter-rotating vortices with the warm
within the eye, which result from the eddy components. (cold) anomaly associated with an anticyclonic
The radial eddy advection (Figs. 3c) produces the bulk (cyclonic) vortex. Airflow outside of the eyewall is direct-
of the cooling along the inner edge of the eyewall and ed toward the northwest, approximately in the direction
about half of the warming in the eye. The tangential of the mean environmental storm-relative flow. Inside
eddy advection (Figs. 3d) produces warming in the eye the eye, the flow moves in the opposite direction
through most of the troposphere, while along the inner between the two vortices. This flow pattern is nearly
edge of the eyewall, it produces upper level warming identical tothat observed at mid-to-upper levels in Hurri-
and weak low-level cooling. Within and outside of the cane Norbert [1984, Marks etal. (1992)]. Marks et al.
eyewall, the radial eddy component is much stronger (1992) argued that these small-scale gyres were similar
than the tangential eddy component. to gyres associated with a linear barotropic instability of
These eddy components can be further decom- the mean vortex as described by Peng and Williams
posed into contributions from different azimuthal (1990). The study of Nolan and Montgomery (2000)
wavenumbers (not shown). The main contributions to suggests that this flow field is related to a steady
the warming in the eye come from the wavenumber 1 wavenumber 1 neutral mode, or pseudomode, that rep-
components of both the radial and tangential eddy resents a linear displacement of the vortex. A growing
terms. Although wavenumber 2 asymmetries play a sig- normal mode and vortex Rossby waves may also play
nificant role inthe structure and evolution of the eyewall important roles and will be investigated in the future.
(Braun 2001), their contributions to eye warming are These studies suggest that the gyres may be character-
generally small. The impacts of wavenumbers 3 and istic features of mature hurricanes. The airflow within
higher are strong, but are confined to the region close to the eye is oriented roughly 45°with respect to the orien-
the eyewall. tation of the warm anomalies such that the flow trans-
Figure 4 shows the wavenumber 1 potential tem- ports warmer air inand cooler air out of the eye.
18
E 12
v
!-
"_ 6
-r
0
0 25 50 75 25 50 75
Radius (km) Radius (km)
18
_" 12
E
m 6
-1-
0
0 25 50 75 25 50 75
Radius (km) Radius (km)
Figure3. Azimuthal andtime averagedcross sectionsof (a) totalhorizontal advection,(b) meanradial advection,(c) eddyradial
advection,and(d)eddy tangentialadvection.Shadingindicatessimulatedradar reflectivityat valuesof5,20,and35 dBZ Contours
foradvectionfields aredrawn at:1:0,0.1,0.2,0.4,0.8, 1.6,3.2,6.4Kh1. Positive(negative)valuesare indicatedbysolid(dashed)
lines.Thethincontour indicatesvaluesofzero.
5. Conclusions 5ms-1 --,
18o[ .
The calculations indicate an important role of
horizontal eddy heat transports into the eye andsuggest
a new conceptualization of the process by which the
warm core ofthe eye intensifies. This warming by hori-
zontal advection iscounter to heat exchange by mixing
6o X -
across the mean vortex since the mean eyewall air is
typicallycoolerthan that ofthe eye. The warming ofthe "l'f
eye by horizontaleddy heat transports isconsistentwith
idealized model calculations ofasymmetric disturbances
that form on three-dimensional, baroclinic vortices
(Moiler and Montgomery 2000; Nolan and Montgomery
2000). These vortex Rossby waves import not only
momentum (Montgomery and Kallenbach, 1997) but
also heat into the eye (Montgomery and Enagonio,
1998).
The warming from horizontal advection has been
shown to be the result of azimuthal eddies, which
means that asymmetries in the eyewall structure are
contributing to warming of the eye. The mechanism by -180 -120 -60 0 60 120 180
which these asymmetries warm the eye needs to be X (km)
explored further. Since tropical cyclones often undergo Figure4.Time-averaged wavenumber 1potentialtemperature
transitions from asymmetric systems to more symmetric (contours)andwindanomalies (vectors)at10.4km MSL Con-
systems, it is important to develop an understanding of tours are drawn at intervals of 0.3 K. Shadingdenotes time-
how this process varies during transition. Such under- averagedverticalmotionsinexcessof1ms_.
standing can provide the critical linkage between these
eddies and convective blowups in the eyewall Japan, 60, 396-410.
(observable from satellite and aircraft remote sensing) Johnson, R. H., 1984: Partitioning tropical heat and
and their relationship with rapid intensification, which moisture budgets into cumulus and mesoscale
may then lead to improved forecasts of intensity components: Implications for cumulus
change. parameterization. Mon. Wea. Rev., 112, 1590-
1601.
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