Aspects of Moat Formation in Tropical Cyclone Eyewall Replacement Cycles Christopher Rozoff 3 April Timeline of world history during Chris Rozoffs time at CSU Time (scale = many, many years) The Clinton era ends A 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 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 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. 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 10/ UTC 130 kts/946 hPa 10/ UTC 160 kts/882 hPa 10/ UTC 157 kts/885 hPa 10/ UTC 135 kts/892 hPa 10/ UTC 130 kts/910 hPa 10/ UTC 130 kts/923 hPa 10/ UTC 125 kts/929 hPa 10/ UTC 117 kts/932 hPa Hurricane Wilma (2005) 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) r Center of eye r Earlier Later Subsidence Inversion Strong forcing 1. Introduction: Formation 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 hrt = 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? 1. Introduction: Formation of a secondary eyewall 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: The moat 2. Rapid filamentation zones From a materially conserved tracer q in a horizontal, 2D 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 i (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 Hua-Klein fil Okubo-Weiss fil Gaussian vortices 2. Rapid filamentation zones < 2.5 min min min min > 30 min Infinity min Hua-Klein fil Rel Vorticity 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: x 600 km x 1024 collocation points => 1.76 km res. - = 20 m 2 s -1 3. Moat observations Dropsondes and aircraft data from Frances (2004) and Rita (2005). NOAA P3s give 1 s T, T d, p, u, v. T, T d 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: 3. Moat observations Hurricane Frances (2004) Figure taken from Beven (2004/NHC) Best track data (NHC) 3. Moat observations Atlantic Hurricane Frances on 30 August NOAA P3 data collected in this storm. (a)& (b) 1804 1822 UTC (c) & (d) 1924 1943 UTC (e) & (f) 2108 2126 UTC vv T TdTd 3. Moat observations Atlantic Hurricane Frances on 30 August Composite profile: - 2 r = 6 km on a r = 250 m grid 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 TdTd vv fil 3. Moat observations Moat r = 24 kmr = 29 kmr = 32 km Dropsonde data points shown to the right. The moat of Frances had eye-like dropsondes in the moat. Low-level instability was marginal. T TdTd Eyewall T TdTd TdTd T T parcel 3. Moat observations Hurricane Rita (2005) Figure taken from Knapp et al. (2005/NHC) Best track data (NHC) 3. Moat observations Rita 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 dBZ km 3. Moat observations Rita 21 September 2005 (N43) 640 hPa 1855 1956 UTC 700 hPa 1507 1616 UTC T TdTd T TdTd vv vv fil 3. Moat observations Rita 21 September 2005 Composite Dropsondes Composite profile: - 2 p = 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 ~ 0.9 o C TTdTd Eyewall TTdTd T parcel 3. Moat observations 700 hPa 1437 2057 UTC 2.1 km 1705 1735 UTC 1.5 km 1754 2213 UTC Rita 22 September 2005 Flight-level Composites vv vv vv fil T T T TdTd TdTd TdTd 3. Moat observations Composite profile: - 2 p = 10 hPa on a p = 0.5 hPa grid. - N43/N42/NRL drops - 25 km < r < 40 km 16 19 UTC UTC Eye-like soundings consistent with Houze et al. (2007; Science) Eyewall Moat TdTd TdTd T T T parcel 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. Heating: r r1r1 r2r2 r3r3 r4r4 Q1Q1 Q2Q2 rr1r1 r2r2 r3r3 r4r4 Vorticity: 3. Moat observations: Balanced vortex suggestions T obs. T d obs. dT/dt (analytical) w (analytical) vv Assume the following: Results: 3. Moat observations: Balanced vortex suggestions A look at mass subsidence in the moat during an idealized eyewall replacement cycle r4r4 r3r3 Frances 4. 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. 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: v z = 0, 5, 10, and 20 m s -1 per 15 km and v x = 0, -2, -4, and -6 x s -1. All cases are initialized in geostrophic and hydrostatic balance. The initial absolute vorticity, v x + f, is always equal to 1 x s -1. 4. Idealized cloud model results v z = 20 m s -1 (15 km) -1 v x = 0 x s -1 4. Idealized cloud model results v z = 0 m s -1 (15 km) -1 v x = -4 x s -1 4. Idealized cloud model results v z = 0 m s -1 (15 km) -1 v x = -6 x s -1 4. Idealized cloud model results l (h) h max (km)w max w min v00h v00h v00h v00h Practical rapid filamentation occurs for v x = -6 x s -1 (exp. v00h6) z = 1.25 km at 0.6 h z = 0.08 km at 0.6 h z = 1.25 km at 0.6 h 3 m s -1 Vertical Motion (m s -1 ) Pert. Relative Vorticity (x s -1 ) Pert. Relative Vorticity (x s -1 ) Exp. v00h6 4. Idealized cloud model results Exp. v00h4 x s -1 x m s -2 First column - w: Vertical velocity (contoured) : Pert. vert. vorticity (shaded) Second column Dynamic perturbation pressure gradient Third column Sum of buoyancy and buoyant perturbation gradient z=1.25 km o 4. Idealized cloud model results v z = 20 m s -1 (15 km) -1 v x = -2 x s -1 4. Idealized cloud model results x m s -2 x s -1 x m s -2 Exp. v20h2 Exp. v20h4 z=1.25 km Convergence of a > Idealized cloud model results Summary of cloud dynamics Vertical Shear Horizontal Shear 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. x y z z x y LL v v Convergence of a >0 4. Idealized cloud model results Sensitivity Experiments l (h) h max (km)w max w min v00h v00h v20h v20h l (h) h max (km)w max w min v00h v00h v20h v20h Unstable ControlMoist Control 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. 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. Questions? 16 September 2006 Montrose, SD Remnants of Ioke?
