Aspects of Moat Formation in Tropical Cyclone Eyewall Replacement Cycles

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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

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

1 Average Lifespan of a Crow

2 Lifespans of House Sparrows

61 Lifespans of Honey Bees

Aspects of Moat Formation Aspects of Moat Formation in Tropical Cyclone Eyewall in Tropical Cyclone Eyewall

Replacement CyclesReplacement Cycles

Christopher Rozoff3 April 2007

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.

OutlineOutline

1. Introduction

2. Rapid filamentation zones

3. Observations

4. Idealized cloud model results

5. Concluding Remarks

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

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)

rCenter of eye

Earlier Later

Subsidence Inversion Strong forcing

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)

Stronger vorticity (eyewall)

t = 0 hr t = 3 hr t = 12 hr

• 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?

• 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”

2. Rapid filamentation zones2. Rapid filamentation zones

( ) 022 =∇•+∂≡ q

⎟⎟⎠

⎞⎜⎜⎝

⎛−+−

uv yx ∂−∂=ζvuS yxn ∂−∂=uvS yxs ∂+∂=

022 =⎟

⎟⎠

⎞⎜⎜⎝

∂∂

+⎟⎟⎠

⎞⎜⎜⎝

∂∂

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):

022 =⎟

⎟⎠

⎞⎜⎜⎝

∂∂

+⎟⎟⎠

⎞⎜⎜⎝

∂∂

xV 02222

22 =⎟⎟⎠

⎞⎜⎜⎝

⎛∂∂

⎟⎟⎠

⎞⎜⎜⎝

⎛−+⎟⎟

⎞⎜⎜⎝

⎛∂∂

( ) 2/1222222

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:

}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.

Hua-Klein τfilOkubo-Weiss τfil

Gaussian vortices

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

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

xxxxxK

δδδδ

+≥+<≤<≤−

⎪⎪⎩

⎪⎪⎨

+−+−

if if if

0/)(/)(

Hurricane Frances (2004)

Figure taken from Beven (2004/NHC)

Best track data (NHC)

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

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)

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.

T Td Td TTparcel

Hurricane Rita (2005)

Figure taken from Knapp et al. (2005/NHC)

Best track data (NHC)

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

403735

323027

252220

Rita 21 September 2005 (N43)

640 hPa1855 – 1956 UTC

700 hPa1507 – 1616 UTC

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 Tparcel

700 hPa1437 – 2057 UTC

2.1 km1705 – 1735 UTC

1.5 km1754 – 2213 UTC

Rita 22 September 2005 Flight-level Composites

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)

Td TdT TTparcel

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

Vorticity:

221 km) 50(dayK 125))(/())(/( =−+− rrcQrrcQ pp

1-5 s 10 x 5 −=f

T obs.

Td obs.

dT/dt (analytical)

w (analytical)

-12 s 10 x 1 −=N

Assume the following: Results:

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

221 km) 50(dayK 125))(/())(/( =−+− rrcQrrcQ pp

Frances

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.

• 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 ++=),,,(

vz = 20 m s-1 (15 km)-1

vx = 0 x 10-4 s-1

vz = 0 m s-1 (15 km)-1

vx = -4 x 10-4 s-1

vz = 0 m s-1 (15 km)-1

vx = -6 x 10-4 s-1

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

rtilt∂∂

∂∂

−∂∂

∂∂

=∂∂ 'ζ

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

3 m s-1

Vertical Motion (m s-1)

Pert.RelativeVorticity(x 10-4 s-1)

Exp. v00h6

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

vz = 20 m s-1 (15 km)-1

vx = -2 x 10-4 s-1

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

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.

Convergence of ζa>0

4. Idealized cloud model results4. Idealized cloud model results Sensitivity ExperimentsSensitivity Experiments

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

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”

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.

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.

Questions?Questions?

16 September 2006Montrose, SDRemnants of Ioke?

Aspects of Moat Formation in Tropical Cyclone Eyewall Replacement Cycles

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