Aspects of Moat Formation in Tropical Cyclone Eyewall Replacement Cycles

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Aspects of Moat Formation in Tropical Cyclone
Eyewall Replacement Cycles

• Christopher Rozoff
• 3 April 2005 2006 2007

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Timeline of world history during Chris Rozoffs
time at CSU
A bunch of bad stuff happens
The Clinton era ends
2000
2005
2006
2007
2002
2001
Time (scale many, many years)
3
1 Average Lifespan of a Crow
4
2 Lifespans of House Sparrows
5
61 Lifespans of Honey Bees
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Aspects of Moat Formation in Tropical Cyclone
Eyewall Replacement Cycles

• Christopher Rozoff
• 3 April 2007

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Acknowledgements

• My advisor Prof. Wayne Schubert / My committee
  Profs. William Cotton, Richard Johnson, Iuliana
  Oprea (CSU mathematics)
• Prof. Michael Montgomery (Naval Postgraduate
  School)
• Other Collaborators Paul Ciesielski, Prof.
  Scott Fulton (Clarkson U.), Dr. Jim Kossin
  (UW-Wisc), Brian McNoldy, Rick Taft, Wes Terwey,
  and Jonathan Vigh
• Drs. Will Cheng, Louie Grasso, Sue van den
  Heever, and Mel Nicholls (U. Colorado) for help
  with RAMS throughout my CSU tenure.
• Drs. Michael Black (HRD), Neal Dorst (HRD), and
  Hugh Willoughby (FIU), and Michael Bell (NCAR)
  and Kevin Mallen for help with real hurricane
  data.
• Prof. Matthew Parker (NCSU) and Russ Schumacher
  for useful discussion on dynamic pressure
  perturbation analysis.
• Gail Cordova and department staff for making life
  easy for research and learning.
• Schubert group members and many others for an
  invigorating learning environment at CSU.
• Your tax dollars
• My family for dedicated support and for attending
  my defense.
• My wife Jill for unearthly patience, support, and
  encouragement.

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Outline

• 1. Introduction
• 2. Rapid filamentation zones
• 3. Observations
• 4. Idealized cloud model results
• 5. Concluding Remarks

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1. IntroductionEyewall replacement cycles and
rapid intensity fluctuations
Hurricane Wilma (2005)
10/19 0014 UTC 130 kts/946 hPa
10/19 1358 UTC 157 kts/885 hPa
10/20 0000 UTC 135 kts/892 hPa
10/19 1214 UTC 160 kts/882 hPa
10/20 1234 UTC 130 kts/910 hPa
10/20 2347 UTC 130 kts/923 hPa
10/21 1219 UTC 125 kts/929 hPa
10/22 0220 UTC 117 kts/932 hPa
SSM 85 GHz Composites
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1. IntroductionFormation of a secondary eyewall

• Axisymmetric (circularly symmetric) hurricane
  models
• Forcing mechanism needed to initiate secondary
  eyewall
• Symmetric instability (Willoughby et al.,1984
  Zeng, 1996)
• Other sources of low-level convergence (Hausman,
  2001 Nong and Emanuel, 2003)
• To sustain, wind-induced surface heat exchange
  (WISHE) (Willoughby et al., 1984 Nong and
  Emanuel, 2003)

Later
Earlier
Subsidence Inversion
Strong forcing
r
r
Center of eye
Center of eye
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1. IntroductionFormation of a secondary eyewall

• 2D, nondivergent barotropic models
• Multiple vortex interactions (e.g., Kuo et al.,
  2004) in a horizontal plane. (Asymmetric
  processes are important here!)

Extensive weaker vorticity (e.g., Convective
rainbands)
t 3 hr
t 12 hr
t 0 hr
y
x
Stronger vorticity (eyewall)
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1. IntroductionFormation of a secondary eyewall

• Other perhaps crucial asymmetric processes
• Vortex Rossby waves and wave-mean flow
  interactions accelerate mean flow at a radius
  determined by the mean vortex structure (e.g.,
  Montgomery and Kallenbach, 1997)
• Convective rainbands generate potential vorticity
  (PV).
• 3D modeling with sufficiently small grid spacing
  (Houze et al., 2007 Terwey and Montgomery, 2006
  Wang, 2006 Yau et al., 2006 Zhang et al., 2005)
  produces concentric eyewalls in intense
  hurricanes.
• Where are secondary eyewalls unlikely to form?

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1. Introduction
The moat

• Formation of a moat
• Region of subsidence as a secondary eyewall
  matures (Dodge et al., 1999 Houze et al., 2007)
• Region of intense horizontal strain before and
  after secondary eyewall formation (Shapiro and
  Montgomery, 1993 Kossin et al., 2000 R. et al.,
  2006)
• Which processes dominate in the moat region
  before and after secondary eyewall formation?

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2. Rapid filamentation zones
From a materially conserved tracer q in a
horizontal, 2D plane, we can form a tracer
gradient equation
where V2 is the velocity gradient tensor
and where
Assuming V2 is constant, we obtain the
Okubo-Weiss criterion (which is the frequency
associated with the solution of the tracer
gradient equation)
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2. Rapid filamentation zones
Rather than assuming a constant velocity gradient
tensor, we obtain a second order equation
describing tracer gradient growth, which yields
more accurate solutions (Hua and Klein, 1998)
Which has the following eigenvalues
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2. Rapid filamentation zones
Okubo-Weiss and Hua-Klein eigenvalues are
frequencies associated with either oscillatory
or exponential decay/growth. An e-folding type
timescale can be defined the filamentation
time for the real part li (i.e., where there
is exponential growth rates)
Given typical convective overturning timescales
of about 30 min, we define a rapid filamentation
zone as a region where
We hypothesize that deep convection is strongly
deformed and susceptible to enhanced entrainment
and subsequent suppression in such regions.
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2. Rapid filamentation zones
Gaussian vortices
Hua-Klein tfil
Okubo-Weiss tfil
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2. Rapid filamentation zones
Hua-Klein tfil
Rel Vorticity
Pseudo-spectral numerical integration of
lt 2.5 min
2.5 -7.5 min
7.5 - 15 min
Initial Conditions
15 - 30 min

• Random vorticity elements
• between 20 40 km.
• Random vorticity has 1/10
• magnitude of central vortex.
• Positive bias to random
• vorticity field.

gt 30 min
Infinity min
Model config

• 600 x 600 km
• 1024 x 1024 collocation
• points gt 1.76 km res.
• - n 20 m2 s-1

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3. Moat observations

• Dropsondes and aircraft data from Frances (2004)
  and Rita (2005).
• NOAA P3s give 1 s T, Td, p, u, v.
• T, Td corrected for instrument wetting (Zipser et
  al., 1981).
• GPS dropsondes p, T, R.H., u, and v at 5 m
  intervals (2 Hz.) (QCd on ASPEN or Editsonde
  (HRD)).
• Data tranformed into cylindrical coordinates
  Willoughby and Chelmow (1982) center-finding
  technique (3 km error).
• Data composites defined as

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3. Moat observations
Hurricane Frances (2004)
Best track data (NHC)
Figure taken from Beven (2004/NHC)
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3. Moat observations

• Atlantic Hurricane Frances on
• 30 August 2004.
• NOAA P3 data collected in
• this storm.
• (b) 1804 1822 UTC
• (c) (d) 1924 1943 UTC
• (e) (f) 2108 2126 UTC

vq
T
Td
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3. Moat observations
Atlantic Hurricane Frances on 30 August
2004. Composite profile - 2 dr 6 km on a
Dr 250 m grid. - 700 hPa flight-level
data only (1804 1822 UTC 2108
2126 UTC). TOP Blue (Individual Flight-level
Tangential Wind) Red (Filamentation Time
(min)) Black Composite) BOTTOM Red
(Temperature) Green (Dew Point) Black (Composites)
vq
tfil
T
Td
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3. Moat observations
Moat
Dropsonde data points shown to the right. The
moat of Frances had eye-like dropsondes in the
moat. Low-level instability was marginal.
Eyewall
Eyewall
r 24 km
r 29 km
r 32 km
Td
T
T
Td
Tparcel
Td
T
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3. Moat observations
Hurricane Rita (2005)
Best track data (NHC)
Figure taken from Knapp et al. (2005/NHC)
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3. Moat observations
Rita 21 September 2005 (N43)
dBZ
216 km
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50
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45
42
40
1459 UTC
1936 UTC
1517 UTC
1510 UTC
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Rita 22 September 2005 (N43)
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30
27
25
22
216 km
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1752 UTC
1612 UTC
1457 UTC
1911 UTC
Radar imagery from HRD/RAINEX
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3. Moat observations
Rita 21 September 2005 (N43)
T
vq
640 hPa 1855 1956 UTC
Td
tfil
T
vq
700 hPa 1507 1616 UTC
Td
tfil
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3. Moat observations
Rita 21 September 2005 Composite Dropsondes
Composite profile - 2 dp 10 hPa on a
D p 0.5 hPa grid. - N43/NRL drops - (a)
25 km lt r lt 55 km - (b) 55 km lt r lt 85 km -
Std Dev 0.9oC
Eyewall
T
Td
Tparcel
T
Td
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3. Moat observations
Rita 22 September 2005 Flight-level Composites
vq
T
700 hPa 1437 2057 UTC
Td
tfil
vq
T
2.1 km 1705 1735 UTC
Td
tfil
vq
T
1.5 km 1754 2213 UTC
Td
tfil
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3. Moat observations
Composite profile - 2 dp 10 hPa on a
D p 0.5 hPa grid. - N43/N42/NRL drops -
25 km lt r lt 40 km
Moat
Eyewall
Eyewall
16 19 UTC
19 - 22 UTC
Eye-like soundings consistent with Houze et al.
(2007 Science)
Td
T
Td
T
Tparcel
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3. Moat observationsBalanced vortex suggestions

• 5-region approximation to the Sawyer-Eliassen
  equation (Similar approaches are used in Schubert
  et al., 2007 Shapiro and Willoughby, 1982
  Schubert and Hack, 1982). This model diagnoses
  the secondary circulation for a given tangential
  wind profile and prescribed diabatic heating.
• Consider axisymmetric, quasi-static, stratified,
  compressible, and inviscid motions on an f-plane.
• Assume a barotropic vortex.

Vorticity
Heating
Q1
Q2
r1
r3
r4
r
r1
r3
r4
r
r2
r2
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3. Moat observationsBalanced vortex suggestions
Results
Assume the following
dT/dt (analytical)
T obs.
Td obs.
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3. Moat observationsBalanced vortex suggestions

• A look at mass subsidence in the moat during an
  idealized eyewall replacement cycle

r4
r3
Frances
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4. Idealized cloud model results

• RAMS 3D, compressible, nonhydrostatic,
  one-moment microphysics.
• f-plane, Dx Dy 500 m over 125 x 125 km.
  Dz 160 m near surface, stretching to a maximum
  spacing of 500 m aloft. 25 km depth.
• Radiation neglected
• Lower boundary is free slip.
• Rayleigh friction layer at rigid lid and
  Klemp-Wilhelmson (1978) lateral boundary
  conditions.
• Smagorinsky (1963) diffusion.
• Convection initiated with a 2 K bubble.

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4. Idealized cloud model results

• Sounding constructed using several outer-core
  dropsondes from Hurricane Isabel (2003) and
  carefully blended with a proximity sounding (13
  Sep 2003) (courtesy W. Terwey and M. Bell)
• CAPE 2067 J/kg and CIN 1 J/kg.

• Background wind
• vz 0, 5, 10, and 20 m s-1 per 15 km and vx 0,
  -2, -4, and -6 x 10-4 s-1. All cases are
  initialized in geostrophic and hydrostatic
  balance.
• The initial absolute vorticity, vx f, is always
  equal to 1 x 10-4 s-1.

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4. Idealized cloud model results
vz 20 m s-1 (15 km)-1 vx 0 x 10-4 s-1
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4. Idealized cloud model results
vz 0 m s-1 (15 km)-1 vx -4 x 10-4 s-1
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4. Idealized cloud model results
vz 0 m s-1 (15 km)-1 vx -6 x 10-4 s-1
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4. Idealized cloud model results

• Practical rapid filamentation occurs for vx -6
  x 10-4 s-1 (exp. v00h6)

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Exp. v00h6
z 1.25 km at 0.6 h
Vertical Motion (m s-1)
z 1.25 km at 0.6 h
z 1.25 km at 0.6 h
z 1.25 km at 0.6 h
Pert. Relative Vorticity (x 10-4 s-1)
z 1.25 km at 0.6 h
z 1.25 km at 0.6 h
z 0.08 km at 0.6 h
Pert. Relative Vorticity (x 10-4 s-1)
z 1.25 km at 0.6 h
z 1.25 km at 0.6 h
3 m s-1
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4. Idealized cloud model results
Exp. v00h4
x 10-4 s-1
x 10-2 m s-2
x 10-2 m s-2
z1.25 km
First column - w Vertical velocity
(contoured) z Pert. vert. vorticity
(shaded) Second column Dynamic perturbation
pressure gradient Third column Sum of
buoyancy and buoyant perturbation gradient
o
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4. Idealized cloud model results
vz 20 m s-1 (15 km)-1 vx -2 x 10-4 s-1
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4. Idealized cloud model results
Exp. v20h2
Exp. v20h4
x 10-4 s-1
x 10-2 m s-2
x 10-2 m s-2
x 10-4 s-1
x 10-2 m s-2
x 10-2 m s-2
z1.25 km
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4. Idealized cloud model resultsSummary of cloud
dynamics
Vertical Shear
Horizontal Shear
z
z

-
v
-

L
L
-

y
y
Convergence of zagt0
Convergence of zagt0
x
x
v
Dynamic pressure perturbations/ buoyant forcing
important in forcing primary updrafts.
Dynamic pressure perturbations also force an
upright updraft.
Buoyant forcing along edges of cold pool are
important in forcing primary updrafts.
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4. Idealized cloud model results Sensitivity
Experiments
Unstable Control
Moist Control
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5. Conclusions

• Rapid filamentation zones (RFZs), defined from
  local kinematics, are regions where the
  filamentation time is smaller than the typical
  timescale of convective overturning.
• Observations suggest moats coincide with RFZs.
  Moats contain marginal thermodynamic conditions
  for the existence of deep, moist convection.
• As a moat forms, balanced theory suggests
  eye-like downward mass fluxes can take place in
  the moat early in an eyewall replacement cycle.
• Rapid filamentation is most likely relevant prior
  to mature moat formation.

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5. Conclusions

• Cloud simulations suggest that, in relatively
  marginal thermodynamic conditions, adverse
  filamentation occurs for sufficiently strong
  horizontal shear.
• Weve uncovered new dynamics of horizontally
  sheared convection. Future work should include
  low-level inflow.
• PV wakes left behind sheared convection could be
  important in the genesis of secondary eyewalls
  (e.g., Franklin et al., 2006).
• Slight changes in the thermo has profound impacts
  on sheared convection. A refined definition of
  rapid filamentation should include the
  instability.

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Questions?
16 September 2006 Montrose, SD Remnants of Ioke?