aspects of moat formation in tropical cyclone eyewall replacement cycles
DESCRIPTION
Aspects of Moat Formation in Tropical Cyclone Eyewall Replacement Cycles. Christopher Rozoff 3 April 2005 2006 2007. Timeline of world history during Chris Rozoff’s time at CSU. A bunch of bad stuff happens. The Clinton era ends. 2000. 2005. 2006. 2007. 2001. 2002. - PowerPoint PPT PresentationTRANSCRIPT
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Aspects of Moat Formation Aspects of Moat Formation in Tropical Cyclone Eyewall in Tropical Cyclone Eyewall
Replacement CyclesReplacement Cycles
Christopher Rozoff 3 April 2005 2006 2007
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Timeline of world history during Chris Rozoff’s time at CSU
Time (scale = many, many years)
2000 20022001 2005 2006 2007
The Clinton era endsThe Clinton era ends
A bunch of bad stuff happensA bunch of bad stuff happens
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1 Average Lifespan of a Crow
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2 Lifespans of House Sparrows
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61 Lifespans of Honey Bees
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Aspects of Moat Formation Aspects of Moat Formation in Tropical Cyclone Eyewall in Tropical Cyclone Eyewall
Replacement CyclesReplacement Cycles
Christopher Rozoff3 April 2007
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AcknowledgementsAcknowledgements• 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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OutlineOutline
1. Introduction
2. Rapid filamentation zones
3. Observations
4. Idealized cloud model results
5. Concluding Remarks
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1. Introduction:1. Introduction:Eyewall replacement cycles and rapid intensity fluctuationsEyewall replacement cycles and rapid intensity fluctuations
10/19 0014 UTC130 kts/946 hPa
10/19 1214 UTC160 kts/882 hPa
10/19 1358 UTC157 kts/885 hPa
10/20 0000 UTC135 kts/892 hPa
10/20 1234 UTC130 kts/910 hPa
10/20 2347 UTC130 kts/923 hPa
10/21 1219 UTC125 kts/929 hPa
10/22 0220 UTC117 kts/932 hPa
Hurricane Wilma (2005)
SSM 85 GHz Composites
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1. Introduction:1. Introduction:Formation of a secondary eyewallFormation 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)
z
rCenter of eye
z
rCenter of eye
Earlier Later
Subsidence Inversion Strong forcing
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1. Introduction:1. Introduction:Formation of a secondary eyewallFormation 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!)
y
x
Extensive weaker vorticity (e.g., Convective rainbands)
Stronger vorticity (eyewall)
t = 0 hr t = 3 hr t = 12 hr
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• 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?
1. Introduction:1. Introduction:Formation of a secondary eyewallFormation of a secondary eyewall
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• 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?
1. Introduction:1. Introduction:
The “moat”
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2. Rapid filamentation zones2. Rapid filamentation zones
( ) 022 =∇•+∂≡ q
Dt
qDt u
⎟⎟⎠
⎞⎜⎜⎝
⎛−+−
=ns
sn
SS
SS
ζ
ζ
2
12V
uv yx ∂−∂=ζvuS yxn ∂−∂=uvS yxs ∂+∂=
022 =⎟
⎟⎠
⎞⎜⎜⎝
⎛
∂∂
+⎟⎟⎠
⎞⎜⎜⎝
⎛
∂∂
DtD
y
xT
y
xV
222
2
1 ζλ −+±= sno SS
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 thefrequency associated with the solution of the tracer gradient equation):
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2. Rapid filamentation zones2. Rapid filamentation zones
022 =⎟
⎟⎠
⎞⎜⎜⎝
⎛
∂∂
+⎟⎟⎠
⎞⎜⎜⎝
⎛
∂∂
DtD
y
xT
y
xV 02222
2
22 =⎟⎟⎠
⎞⎜⎜⎝
⎛∂∂
⎟⎟⎠
⎞⎜⎜⎝
⎛−+⎟⎟
⎠
⎞⎜⎜⎝
⎛∂∂
Dt
Dqq
Dt
D
y
xTTT
y
x VVV
( ) 2/1222222
2 22
1⎥⎦⎤
⎢⎣⎡ −+±−+±= ζζλ &&&
snsn SSSS
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 zones2. Rapid filamentation zones
}max{/1fil iλτ =
min30convfil =<ττ
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 λi
(i.e., where there is exponential growth rates):
Given typical convective overturning timescales of about 30 min, we definea 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 zones2. Rapid filamentation zones
Hua-Klein τfilOkubo-Weiss τfil
Gaussian vortices
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2. Rapid filamentation zones2. Rapid filamentation zones
ζυζψζ 2
),(
),(∇=
∂
∂+
∂
∂
yxt < 2.5 min
2.5 -7.5 min
7.5 - 15 min
15 - 30 min
> 30 min
Infinity min
Hua-Klein τfilRel Vorticity
ψζ 2∇=
Pseudo-spectral numerical integration of:
Initial Conditions:-Random vorticity elements between 20 – 40 km.-Random vorticity has 1/10 magnitude of central vortex.-Positive bias to random vorticity field.
Model config:
- 600 x 600 km - 1024 x 1024 collocation points => 1.76 km res.- = 20 m2 s-1
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3. Moat observations3. 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.)
(QC’d on ASPEN or Editsonde (HRD)).• Data tranformed into cylindrical coordinates – Willoughby and
Chelmow (1982) center-finding technique (~3 km error).• Data composites defined as:
∫
∫+
−
+
−= xx
xx
xx
xxo o
o
o
o
dxxK
dxxKx
x δ
δ
δ
δ
η
η
)(
)()(
)(
xxx
xxxx
xxxx
xxx
xxxx
xxxxxK
o
oo
oo
o
o
o
δδ
δδ
δδδδ
+≥+<≤<≤−
−<
⎪⎪⎩
⎪⎪⎨
⎧
+−+−
=
if
if if if
0/)(/)(
0
)(
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3. Moat observations3. Moat observations
Hurricane Frances (2004)
Figure taken from Beven (2004/NHC)
Best track data (NHC)
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3. Moat observations3. Moat observations
Atlantic Hurricane Frances on30 August 2004.
NOAA P3 data collected inthis storm.
(a) & (b) 1804 – 1822 UTC(c) & (d) 1924 – 1943 UTC(e) & (f) 2108 – 2126 UTC
v
T
Td
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3. Moat observations3. Moat observationsAtlantic Hurricane Frances on30 August 2004.
Composite profile: - 2 δr = 6 km on a r = 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)
T
Td
v
τfil
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3. Moat observations3. Moat observations
Moat
r = 24 km r = 29 km r = 32 km
Dropsonde data points shown tothe right.
The moat of Frances had eye-like dropsondes in the moat.Low-level instability was marginal.
TTd
Eye
wall
Eye
wall
T Td Td TTparcel
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3. Moat observations3. Moat observations
Hurricane Rita (2005)
Figure taken from Knapp et al. (2005/NHC)
Best track data (NHC)
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3. Moat observations3. Moat observationsRita 21 September 2005 (N43)
Rita 22 September 2005 (N43)
Radar imagery from HRD/RAINEX
1459 UTC
1752 UTC1612 UTC1457 UTC
1936 UTC1517 UTC1510 UTC
1911 UTC
525047
4542
dBZ
403735
323027
252220
216
km21
6 km
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3. Moat observations3. Moat observations
Rita 21 September 2005 (N43)
640 hPa1855 – 1956 UTC
700 hPa1507 – 1616 UTC
T
Td
T
Td
v
v
τfil
τfil
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3. Moat observations3. Moat observationsRita 21 September 2005 Composite Dropsondes
Composite profile: - 2 δp = 10 hPa on a p = 0.5 hPa grid. - N43/NRL drops - (a) 25 km < r < 55 km - (b) 55 km < r < 85 km - Std Dev ~ 0.9oC
TTd
Eye
wall
TTd Tparcel
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3. Moat observations3. Moat observations
700 hPa1437 – 2057 UTC
2.1 km1705 – 1735 UTC
1.5 km1754 – 2213 UTC
Rita 22 September 2005 Flight-level Composites
v
v
v
τfil
τfil
τfil
T
T
T
Td
Td
Td
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3. Moat observations3. Moat observations
Composite profile: - 2 δp = 10 hPa on a p = 0.5 hPa grid. - N43/N42/NRL drops - 25 km < r < 40 km
16 – 19 UTC 19 - 22 UTC
Eye-like soundingsconsistent with Houze et al. (2007;Science)
Eye
wall
Eye
wall
Moat
Td TdT TTparcel
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3. Moat observations:3. Moat observations:Balanced vortex suggestionsBalanced 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.
)(ˆ rQ Heating:
rr1 r2 r3 r4
Q1 Q2
rr1 r2 r3 r4
Vorticity:
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3. Moat observations:3. Moat observations:Balanced vortex suggestionsBalanced vortex suggestions
2-123
243
21
221 km) 50(dayK 125))(/())(/( =−+− rrcQrrcQ pp
1-5 s 10 x 5 −=f
T obs.
Td obs.
dT/dt (analytical)
w (analytical)
v
-12 s 10 x 1 −=N
Assume the following: Results:
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3. Moat observations:3. Moat observations:Balanced vortex suggestionsBalanced vortex suggestions
Flux Mass Downward Total
Eye in theFlux Mass Downward=eyeσ
Flux Mass Downward Total
Moat in theFlux Mass Downward=moatσ
• A look at mass subsidence in the moat during an idealized eyewall replacement cycle
r4r3
2-123
243
21
221 km) 50(dayK 125))(/())(/( =−+− rrcQrrcQ pp
Frances
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4. Idealized cloud model results4. Idealized cloud model results
• RAMS – 3D, compressible, nonhydrostatic, one-moment microphysics.
• f-plane, x = y = 500 m over 125 x 125 km. z = 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 results4. 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.
refzx vzvxvtzyxv ++=),,,(
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4. Idealized cloud model results4. 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 results4. 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 results4. 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 results4. Idealized cloud model results
τl (h) hmax (km) wmax wmin
v00h0 1.8 14.9 37.8 -9.2
v00h2 0.9 12.9 30.8 -9.1
v00h4 1.0 10.9 22.6 -6.2
v00h6 0.2 8.4 12.3 -4.0
• Practical rapid filamentation occurs for vx = -6 x 10-4 s-1 (exp. v00h6)⎟
⎟⎠
⎞⎜⎜⎝
⎛−−= )(
,
'
vtotalov
v rrgBθ
θ
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z
v
x
w
z
u
y
w
tr
r
r
rtilt∂∂
∂∂
−∂∂
∂∂
=∂∂ 'ζ
z = 1.25 km at 0.6 h
z = 1.25 km at 0.6 h
z = 0.08 km at 0.6 h
z = 1.25 km at 0.6 h z = 1.25 km at 0.6 h
z = 1.25 km at 0.6 h z = 1.25 km at 0.6 h
z = 1.25 km at 0.6 h z = 1.25 km at 0.6 h
3 m s-1
Vertical Motion (m s-1)
Pert.RelativeVorticity(x 10-4 s-1)
Pert.RelativeVorticity(x 10-4 s-1)
Exp. v00h6
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4. Idealized cloud model results4. Idealized cloud model results
SBzDt
Dwvo ++
∂∂
−='π
Exp. v00h4 x 10-4 s-1 x 10-2 m s-2 x 10-2 m s-2
First column -w: Vertical velocity (contoured)ζ: Pert. vert. vorticity (shaded)
Second column –Dynamic perturbation pressure gradient
Third column –Sum of buoyancy andbuoyant perturbationgradient
z=1.25 km
''''' cbdh πππππ +++=o
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4. Idealized cloud model results4. 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 results4. Idealized cloud model results
x 10-2 m s-2x 10-2 m s-2x 10-4 s-1 x 10-4 s-1 x 10-2 m s-2 x 10-2 m s-2
Exp. v20h2 Exp. v20h4
z=1.25 km
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Convergence of ζa>0
+
4. Idealized cloud model results4. Idealized cloud model resultsSummary of cloud dynamicsSummary of cloud dynamics
Vertical Shear Horizontal Shear
++ -
-
-
Dynamic pressure perturbations/buoyant forcing important in forcing
primary updrafts. Dynamicpressure perturbations also
force an upright updraft.
Buoyant forcing along edges of coldpool are important in forcing
primary updrafts.
x
y
z z
x
y
LL
v
v
Convergence of ζa>0
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4. Idealized cloud model results4. Idealized cloud model results Sensitivity ExperimentsSensitivity Experiments
τl (h) hmax (km) wmax wmin
v00h0 + 0.3 + 1.0 + 3.5 - 7.4
v00h6 + 0.8 + 4.0 + 13.3 - 2.6
v20h0 + 0.2 - 2.5 + 7.2 - 4.9
v20h6 + 1.0 + 2.5 + 10.4 - 5.7
τl (h) hmax (km) wmax wmin
v00h0 - 1.3 + 0.5 + 5.9 - 4.4
v00h6 + 0.6 + 4.0 + 13.3 - 3.1
v20h0 + 0.4 + 0.5 + 0.5 - 1.2
v20h6 + 0.6 + 3.0 + 13.4 - 3.3
“Unstable” – “Control” “Moist” – “Control”
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5. Conclusions5. 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. Conclusions5. Conclusions
• Cloud simulations suggest that, in relatively marginal thermodynamic conditions, adverse filamentation occurs for sufficiently strong horizontal shear.
• We’ve 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?Questions?
16 September 2006Montrose, SDRemnants of Ioke?