A Cloud-Resolving Simulation of Hurricane Bob
(1991): Storm Structure and Eyewall Buoyancy
Scott A. Braun,
2002: Mon. Wea. Rev.,130, 1573-1592.
2004/08/31
Introduction
• Gray and Shea (1973) remarked that assumption of a relative humidity
of 100% in the eyewall leads to small vertical gradients of equivalent
potential temperature and little diagnosed potential instability.
• Emanuel (1986) suggested that the hurricane eyewall is often close to a
state of moist slantwise neutrality in which the  e and angular
momentum surfaces are nearly parallel. This result implies that
boundary layer air is neutrally buoyant when lifted along surfaces of
constant angular momentum.
• Emanuel (1986) and Zhang et al. (2000) suggest that eyewall updrafts
are generally neutrally or even negatively buoyant. However,
observations of updrafts with in eyewalls show occasionally strong
small-scale updrafts (Jorgensen et al. 1985; Black et al. 1994); Heymsfield et al. 2001).
• This study uses 2-min output from a 1.3-km grid-scale simulation of
Hurricane Bob (1991) to examine the characteristics of the updrafts
and buoyancy field within the eyewall.
Simulation description and
analysis methods
PSU-NCAR MM5 Model
Simulation time: 1991/08/16_0000~1991/08/19_0000 UTC (72 hrs)
Domain designed: 36-km (193×163×27) 0~72 hrs, grid fixed,
12-km (163×178×27) 48~72 hrs, grid fixed,
4-km (163×178×27) 48~72 hrs, grid moved,
1.3-km (163×178×27) 48~72 hrs, grid moved.
Cumulus parameterization scheme:
Betts-Miller cumulus scheme is used on the 12-km grid,
but is not used on 4- and 1.3-km.
Cloud microphysics scheme: Goddard cumulus ensemble scheme.
Boundary layer parameterization: Burk-Thompson scheme.
Cloud radiation scheme: Dudhia (1989) cloud radiation scheme.
4-km grid
low level
upper level
Us, Vs: the zonal and meridional component of the storm motion (averaged the
horizontal wind components within 200 km of storm center).
UE, VE: the vertically integrated environmental steering flow (900 to 150 hPa
of the density-weighted mean following Liu et al., 1999).
Kinematic and reflectivity structure
a. Time-averaged structure
rain mixing ratio(h=42m)
tangential velocity (h=42m)
the direction of storm motion,
the direction of the surface to
8-km wind shear vector.
1.5-km level vertical velocity with
contours drawn at 1( )and 2( )ms-1.
radial velocity (h=42m)
radial velocity (h=1.5km)
inflow
outflow
wavenumber-1
the direction of storm motion,
the direction of the surface to
8-km wind shear vector.
wavenumber-2
the band of wavenumber-0
inflow greater than 20 ms-1.
b. Instantaneous low-level horizontal structure
Simulated radar reflectivity
patterns at 1 km MSL (mean sea
level).
Solid lines in (c) show the
locations of radial cross sections.
At 66 h
inflow
outflow
h = 125 m (WN2)
c. Vertical structure
Vertical velocity & Reflectivity
Radial velocity & Reflectivity
d. Vertical mass flux statistics (at 5.2 km MSL)
The cumulative percentage of the eyewall area occupied
by vertical velocities less than the magnitude given on the
abscissa.
The cumulative percentage of the upward mass flux
coming from updrafts less than the indicated value.
The percentage of the upward mass flux associated with
updrafts falling within 0.5 ms-1 bins centered on the
indicated values of vertical velocity.
+ cumulative percentages of upward mass flux at 4.5 km;
◇ cumulative percentages of upward mass flux at 5.5 km
Thermodynamics structure
a.  e structure
stratiform
 e contour
>345 K
>355 K
reflectivity contours (15, 30, 45dBZ)
66 h
>1 ms-1
>4 ms-1 (vertical velocity)
1 ~ 4 are trajectory locations.
b. Buoyancy in the eyewall
trajectory 3
trajectory 4
 v is virtual potential temperature,
 v 0 is obtained by averaging 1.3-km domain,
 v0,1 WN0 and WN1 of the perturbations from  v 0 .
The total buoyancy (Houze 1993) is defined as
WN2 at 66 h (h = 3.2 km)
κ= 0.286
p is pressure,
q’p is the perturbation hydrometeor mixing ratio
starting at 0.5 K, and 1K interval
>1 ms-1
>3 ms-1 (vertical velocity)
>1 ms-1
>6 ms-1 (vertical velocity)
Following trajectory 3
EL(equilibrium level)
at 11.2 km
LFC(level of free
convection)at 1.4 km
between 8.5 and 10.5 km:
1. the coarser vertical resolution at these levels, which may cause increased errors
in the calculation of the vertical pressure gradient;
2. The fact that the vertical force balance is an instantaneous value while
is
determined over 2-min intervals.
 es (equivalent potential temperature)
absolute angular moment
a hypothetical air parcel trajectory
in the radius-height plane;
the area of the azimuthal mean
eyewall updraft.
Conclusions
• The fact that the majority of the upward mass flux occurs in
small-scale updraft cores (wavenumber-0 and-1) suggests that
buoyancy plays an important role in the eyewall dynamics.
• Calculated eyewall trajectories possess strong vertical
accelerations up to the melting level, above which water loading
significantly dampens the accelerations or reverses them until
precipitation falls out.
• A key source for the eyewall buoyancy is the energy gained near
the surface by fluxes of moisture and heat from the ocean.
• The buoyancy is most often achieved along outward-sloping
paths rather than along purely vertical paths.
• The low-level vertical motions, inflow, outflow and buoyancy
are strongly modulated by a pronounced shaped eyewall.