Aspects of Moat Formation in Tropical Cyclone Eyewall

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 2001 2002 2005 2006 Time (scale = many, many years) 2007

1 Average Lifespan of a Crow

2 Lifespans of House Sparrows

61 Lifespans of Honey Bees

Aspects of Moat Formation in Tropical Cyclone Eyewall Replacement Cycles Christopher Rozoff 3 April 2007

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 Mc. Noldy, 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.

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

1. Introduction: Eyewall replacement cycles and rapid intensity fluctuations Hurricane Wilma (2005) 10/19 0014 UTC 130 kts/946 h. Pa 10/20 1234 UTC 130 kts/910 h. Pa 10/19 1214 UTC 160 kts/882 h. Pa 10/20 2347 UTC 130 kts/923 h. Pa 10/19 1358 UTC 157 kts/885 h. Pa 10/21 1219 UTC 125 kts/929 h. Pa 10/20 0000 UTC 135 kts/892 h. Pa 10/22 0220 UTC 117 kts/932 h. Pa SSM 85 GHz Composites

1. Introduction: Formation 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 Center of eye r Strong forcing Center of eye r

1. Introduction: Formation of a secondary eyewall 2 D, 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 = 0 hr t = 3 hr y x Stronger vorticity (eyewall) t = 12 hr

1. Introduction: Formation 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). • 3 D 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: 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?

2. Rapid filamentation zones From a materially conserved tracer q in a horizontal, 2 D plane, we can form a tracer gradient equation: where V 2 is the velocity gradient tensor: and where Assuming V 2 is constant, we obtain the Okubo-Weiss criterion (which is the frequency associated with the solution of the tracer gradient equation):

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:

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.

2. Rapid filamentation zones Gaussian vortices Okubo-Weiss tfil Hua-Klein tfil

2. Rapid filamentation zones Pseudo-spectral numerical integration of: Rel Vorticity Hua-Klein tfil < 2. 5 min 2. 5 -7. 5 min 7. 5 - 15 min 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. - n = 20 m 2 s-1 15 - 30 min > 30 min Infinity min

3. Moat observations • • Dropsondes and aircraft data from Frances (2004) and Rita (2005). NOAA P 3 s 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:

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

3. Moat observations vq T Td Atlantic Hurricane Frances on 30 August 2004. NOAA P 3 data collected in this storm. (a) & (b) 1804 – 1822 UTC (c) & (d) 1924 – 1943 UTC (e) & (f) 2108 – 2126 UTC

3. Moat observations Atlantic Hurricane Frances on 30 August 2004. vq Composite profile: - 2 dr = 6 km on a Dr = 250 m grid. - 700 h. Pa flight-level data only (1804 – 1822 UTC; 2108 – 2126 UTC). tfil T Td TOP: Blue (Individual Flight-level Tangential Wind) Red (Filamentation Time (min)) Black Composite) BOTTOM: Red (Temperature) Green (Dew Point) Black (Composites)

3. Moat observations Moat The moat of Frances had eye-like dropsondes in the moat. Low-level instability was marginal. r = 24 km Td T r = 29 km Td T Tparcel Eyewall Dropsonde data points shown to the right. r = 32 km Td T

3. Moat observations Hurricane Rita (2005) Best track data (NHC) Figure taken from Knapp et al. (2005/NHC)

3. Moat observations 216 km Rita 21 September 2005 (N 43) d. BZ 1459 UTC 1510 UTC 1517 UTC 1936 UTC 216 km Rita 22 September 2005 (N 43) 1457 UTC 1612 UTC 1752 UTC 52 50 47 45 42 40 37 35 32 30 27 25 22 20 1911 UTC Radar imagery from HRD/RAINEX

3. Moat observations Rita 21 September 2005 (N 43) vq T 640 h. Pa 1855 – 1956 UTC tfil Td T vq 700 h. Pa tfil 1507 – 1616 UTC Td

3. Moat observations Rita 21 September 2005 Composite Dropsondes Eyewall Composite profile: - 2 dp = 10 h. Pa on a D p = 0. 5 h. Pa grid. - N 43/NRL drops - (a) 25 km < r < 55 km - (b) 55 km < r < 85 km - Std Dev ~ 0. 9 o. C Td T Tparcel

3. Moat observations Rita 22 September 2005 Flight-level Composites vq T 700 h. Pa 1437 – 2057 UTC tfil vq 2. 1 km 1705 – 1735 UTC tfil vq Td T 1. 5 km tfil 1754 – 2213 UTC Td

3. Moat observations Moat Eyewall Composite profile: - 2 dp = 10 h. Pa on a D p = 0. 5 h. Pa grid. - N 43/N 42/NRL drops - 25 km < r < 40 km 16 – 19 UTC Td T Tparcel 19 - 22 UTC Eye-like soundings consistent with Houze et al. (2007; Science) Td T

3. Moat observations: Balanced 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: Q 1 Q 2 r 1 r 2 r 3 r 4 r

3. Moat observations: Balanced vortex suggestions Assume the following: Results: w (analytical) vq d. T/dt (analytical) T obs. Td obs.

3. Moat observations: Balanced vortex suggestions • A look at mass subsidence in the moat during an idealized eyewall replacement cycle r 3 r 4 Frances

4. Idealized cloud model results • RAMS – 3 D, compressible, nonhydrostatic, onemoment 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.

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. •

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

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

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

4. Idealized cloud model results tl (h) hmax (km) wmax wmin v 00 h 0 1. 8 14. 9 37. 8 -9. 2 v 00 h 2 0. 9 12. 9 30. 8 -9. 1 v 00 h 4 1. 0 10. 9 22. 6 -6. 2 v 00 h 6 0. 2 8. 4 12. 3 -4. 0 • Practical rapid filamentation occurs for vx = -6 x 10 -4 s-1 (exp. v 00 h 6)

z = 1. 25 km at 0. 6 h Exp. v 00 h 6 Vertical Motion (m s-1) 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 = 0. 08 km at 0. 6 h Pert. Relative Vorticity (x 10 -4 s-1) 3 m s-1

4. Idealized cloud model results Exp. v 00 h 4 x 10 -4 s-1 x 10 -2 m s-2 z=1. 25 km First column w: Vertical velocity (contoured) z: Pert. vorticity (shaded) Second column – Dynamic perturbation pressure gradient Third column – Sum of buoyancy and buoyant perturbation gradient o

4. Idealized cloud model results vz = 20 m s-1 (15 km)-1 vx = -2 x 10 -4 s-1

4. Idealized cloud model results Exp. v 20 h 4 Exp. v 20 h 2 x 10 -4 s-1 x 10 -2 m s-2 z=1. 25 km x 10 -2 m s-2

4. Idealized cloud model results Summary of cloud dynamics Vertical Shear Horizontal Shear z z v - L- + + +L - y x Convergence of za>0 y Convergence of za>0 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.

4. Idealized cloud model results Sensitivity Experiments “Unstable” – “Control” “Moist” – “Control” tl (h) hmax (km) wmax wmin v 00 h 0 + 0. 3 + 1. 0 + 3. 5 - 7. 4 v 00 h 0 - 1. 3 + 0. 5 + 5. 9 - 4. 4 v 00 h 6 + 0. 8 + 4. 0 + 13. 3 - 2. 6 v 00 h 6 + 0. 6 + 4. 0 + 13. 3 - 3. 1 v 20 h 0 + 0. 2 - 2. 5 + 7. 2 - 4. 9 v 20 h 0 + 0. 4 + 0. 5 - 1. 2 v 20 h 6 + 1. 0 + 2. 5 + 10. 4 - 5. 7 v 20 h 6 + 0. 6 + 3. 0 + 13. 4 - 3. 3

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.

5. 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 thermo has profound impacts on sheared convection. A refined definition of rapid filamentation should include the instability.

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