Formation of the Hurricane Eye

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Formation of the Hurricane Eye

• Jonathan Vigh
• Colorado State University
• April 24, 2006

Hurricane Emily as viewed from the ISS at 1852
GMT, July 16, 2005.
Image courtesy of the Image Science Analysis
Laboratory, NASA Johnson Space Center.
(ISS011-E-10509)
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Hurricane Wilma, as seen from the International
Space Station 822 AM CDT, 19 October 2005. Wilma
was near peak intensity at this time with a
minimum sea level pressure of 882 hPa and maximum
sustained surface winds of 160 kt. The lower eye
diameter was 2 n mi, a new record for smallest
observed eye. NASA Photo ISS012-E-5241.
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High altitude aerial photograph of Super Typhoon
Ida taken from a U-2 spy plane 25 September
1958. Photo courtesy of Frank Marks
(NOAA/AOML/HRD).
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Philosophical Approach

• Eye formation apparently involves two structural
  trends
• convection begins to form into an annulus
• central subsidence begins over the storm center
• Goal describe transition from a one-cell vortex
  -gt two-cell vortex

From Willoughby (1995) and Palmen and Newton
(1969)
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Formation of Hurricane Michelles (2001) primary
eye, courtesy of Brian McNoldy link
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Photo looking straight up in the eye. Photo by
Scott A. Dommin (Hurricane Hunters)
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Secondary Circulation induced in a balanced vortex
Heat source
Momentum source
From Willoughby (1995)
Heating at RMW
Tangential wind tendency
Momentum at RMW
Heating at 2xRMW
From Shapiro and Willoughby (1982)
Vortex intensity
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Importance of the Boundary Layer

• Eliassen (1971) and Eliassen and Lystad (1977)
• Boundary layer type critically affects the radial
  distribution of upward mass flux out of BL top
• laminar BL produces radially-constant upward mass
  flux near the vortex center
• turbulent BL produces a maximum of upward motion
  out some radial distance from center

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19 Sep 2005 1336 UTC 1136Z recon 997 mb
64 kt flt lvl, N
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19 Sep 2005 1919 UTC 1931Z recon 995 mb
62 kt flt lvl, NE
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19 Sep 2005 2312 UTC 2302Z recon 993 mb
67 kt flt lvl, SW (850 mb)
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19 Sep 2005 2349 UTC 2302Z recon 993 mb
67 kt flt lvl, SW (850 mb)
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20 Sep 2005 0052 UTC 0213Z Recon 992 mb
51 kt flt lvl, SE (700 mb) good banding,
30 eye feature, open SSE-SSW
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20 Sep 2005 0828 UTC 0811Z Recon 988 mb

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20 Sep 2005 1220 UTC 1203Z Recon 985 mb
69 kt flt lvl, E 50 n mi elliptical eye, open
to S
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20 Sep 2005 1323 UTC 1330Z Recon 982 mb
78 kt flt lvl, NW
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20 Sep 2005 1500 UTC 1517Z Recon 980 mb
77 kt flt lvl, NW 40 n mi elliptical eye,
open NW
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20 Sep 2005 1835 UTC 1730Z Recon 976 mb
85 kt flt lvl, W 40 n mi ragged, elliptical
eye
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21 Sep 2005 0154 UTC 0204Z Recon 965 mb
103 kt flt lvl, NE 28 n mi circular eye,
closed wall
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21 Sep 2005 0909 UTC
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21 Sep 2005 1424 UTC 1517Z Recon 934 mb
137 kt flt lvl, E 25 n mi circular eye, closed
wall
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21 Sep 2005 1918 UTC 1936Z Recon 914 mb
(Ext.) 161 kt flt lvl, NE 20 n mi circular
eye, closed wall
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Hurricane Rita, as seen by MODIS at 1920 GMT on
21 September 2005. Best track maximum sustained
winds of 145 kt, minimum central pressure of 914
hPa. Image credit SSEC/Univ. Wisconsin.
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Hurricane Bonnie Hot Tower

• Local strong subsidence can produce a
  prototypical warm core (Simpson et al. 1998)
• An encircling rainband may also induce
  subsidence (Willoughby 1979,1990,1995)
• Stochastic in nature
• But once started, positive feedback process may
  lock in

From Heymsfield et al. (2001), Fig. 12
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Other possible factors

• Vorticity distribution theories
• Chaotic PV mixing at vortex boundaries leads to
  transport barriers in the polar stratospheric
  vortex (Mizuta and Yoden 2001 Shuckburgh and
  Haynes 2003 Nakamura 2004).
• Inertial stability plays a key role in
  determining the nature of the vortex scale
  subsidence (Schubert and Hack 1982).
• Air-sea interaction
• Formation may happen at an air-sea interaction
  threshold where sea spray and drag effects
  radically change transfer coefficients of heat
  and momentum
• Waves
• Vortex Rossby Waves transport angular momentum
  out of core and in towards the center
• Inertia-gravity waves may be absorbed near the
  core, contributing to warm core

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Questions
The eyes of Hurricane Wilma at two different
times during the storms lifecycle. Image
courtesy of Scott Bachmeier (CIMSS/SSEC/Univ.
Wisconsin).
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Future Work

• Observational
• Formulate a useful definition for detecting eye
  formation
• Determine the intensity/size characteristics
• Trace kinematic and thermal structural evolution
• Characterize convective morphology and ecology
• Determine the role of environment in formation
• Diagnose cases of failed eyes in nondeveloping
  systems, contrast to successful eye developments
• Modeling with WRF and HWRF
• Verify historical theories (symmetric subsidence,
  role of BL friction)
• Diagnose local descent from hot towers
• Determine threshold of eye formation
• Examine air-sea interaction
• Theory?

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Observational Goals

• Formulate a useful definition for detecting when
  an eye has formed.
• Determine the intensity/size characteristics of
  the initial eye at the time it is first detected
  and when it reaches a mature state.
• Trace the evolution of the complete wind profile
  during eye formation.
• Determine the observable internal and external
  factors which control initial eye size.
• Characterize the convective morphology
  (rainbands, convective arcs, convective rings,
  isolated cells) and ecology during eye formation
  using microwave imagery and space-, land-, and
  aircraft-based radar.
• Determine the role of the environment during eye
  formation by examining the thermodynamic and
  angular momentum distribution at the inflow
  source radius.
• Diagnose cases of failed eyes in nondeveloping
  systems and contrast these to successful eye
  cases in developing systems.
• Strategy
• Ideally, highly observed case studies are
  available from coordinated aircraft missions
• Synthesize comprehensive case studies from the
  diverse data available
• Do broader studies of the data to answer some of
  the above questions (e.g. intensity threshold at
  time of eye formation)
• Gain understanding to motivate modeling work and
  theory.
• Reanalysis/data assimilation approach.

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Modeling Methodology

• Conduct both idealized and real storm studies of
  eye formation using Advanced Research WRF (ARW)
  and/or HWRF.
• Models are new and relatively untried, so initial
  work will be to find optimal research
  configuration (domain size, lateral boundary
  conditions, underlying boundary conditions,
  physics options, nesting configuration, and
  gridpoint spacing).
• Challenges for idealized experiments how to
  initialize the model and the correct method of
  expressing convective morphology (axisymmetric or
  asymmetric, parameterized vs. explicit, thermal
  vs. wind asymmetries).
• Experiments to determine relationship between eye
  formation and initial vortex intensity and size.
  Investigate the parameter space involving initial
  vortex structure (intensity, wind profile shape,
  swirl ratio), physics (precipitation loading and
  cloud microphysics effects), convection
  (distribution and mass fluxes of updrafts and
  downdrafts), and surface properties (transfer
  coefficients for drag and heat).
• Real storm experiments determine role of
  genesis mode in eye formation (a storms
  pedigree) and the role of the environment.
  Determine what mechanisms prevented eye formation
  in past storms.
• Evaluation of HWRFs structure and intensity
  forecasts during eye formation.

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Model Goals and Diagnostics

• To determine useful measures of the model
  vortex's intensity, aspect ratio, swirl
  parameter, inflow angle, and inflow source
  radius.
• To examine the evolution of the momentum, E, and
  potential vorticity (PV) fields during eye
  formation.
• To diagnose the strength of the induced axial
  subsidence and determine the contributive
  mechanisms (i.e. by comparing the subsidence
  predicted from balanced dynamical theory to the
  subsidence observed in the model).
• To compute Lagrangian parcel back-trajectories
  from the eyewall and eye during eye formation.
  This should help determine the source
  characteristics for these two types of air and
  shed light on the mass recycling rates in the
  incipient eye (following Cram et al., 2006).
  Budgets of angular momentum, thermodynamic
  energy, moisture, kinetic energy, and PV of the
  eye and eyewall air can then be computed along
  the parcel trajectories.
• To test the sensitivity of eye formation to
  surface fluxes. These fluxes could be held fixed,
  or allowed to vary through a coupling of the
  air-sea interface.

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Avenues of Inquiry

• What is the most useful way to define the eye?
  Are there different types or classes of eyes
  (i.e. rapidly rotating vs. weakly rotating)?
• What are salient mechanisms and dynamics that
  drive a single-cell vortex structure to a
  two-cell vortex structure?
• What role does central subsidence play in eye
  formation?
• What forces the subsidence? Can subsidence
  trigger eye formation?
• Convection must obviously play an important role
  in eye formation, but what role? What role does
  the convective strength play? The distribution
  and concentration of convective elements and
  their radial distance from the storm center?
  Their morphology and geometrical arrangement into
  rings, spiral bands, or clusters?
• It is also believed that friction plays a
  critical role in eye formation. What is that
  role? As the storm intensifies, are feedbacks
  between the sea state and the resulting
  frictional drag exerted on the atmosphere
  important for eye formation? What are the
  microphysical effects of increasing sea spray on
  the storm's cloud and precipitation microphysics?
• What role does intensification play during eye
  formation? Is eye formation an instability
  process triggered at an intensity threshold? If
  so, what is the nature of the trigger and the
  actual intensity threshold for eye formation?
  What is the least intense tropical cyclone to
  sport a bona de eye? What is the most intense
  storm to not possess a clearly defined eye?

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• Is eye formation a bifurcation phenomenon, with
  multiple states of equilibria? If so, what
  mechanisms are responsible for pushing a storm
  back and forth between equilibria states? Can a
  phase space diagram be constructed for eye
  formation? What are the relevant parameters of
  this phase space?
• Are there multiple dynamical pathways to eye
  formation, or do all intensification routes lead
  to one common eye formation pathway, perhaps
  dictated purely by geometry and friction?
• If there are multiple modes of eye formation,
  which one is optimal for the greatest
  intensification rate? How much of the storm's
  actual realized maximum intensity depends on the
  storm's initial structure and the route it
  followed to get there?
• What are the relationships between overall storm
  size and initial eye size? Eye size and
  intensification rate? Eye size and a storm's
  ultimate realized intensity? What role does the
  environment play in these relationships?
• How much of constraint does initial structure
  place on the final mature structure?
• What role do asymmetries play in eye formation?
  At what threshold do asymmetric mixing processes
  become important as the storm strengthens?
• What is the exact role of gravity waves during
  eye formation? Of vortex Rossby waves?
• What determines the eye shape and eyewall slope
  in real storms? How is eye shape affected by
  intensity or rate of intensification? Movement?
  Shear?
• Why do some storms rapidly intensify as they form
  eyes, yet others do not? Are there commonalities
  in the developing eyes of storms which
  subsequently undergo rapid intensification in the
  hurricane stage?
• What role does eye and eyewall buoyancy play
  during eye formation?

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Willoughby (1995)
Willoughby (1995)
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Hurricane Inez (1966)
From Hawkins and Imbembo (1976)
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Hawkins and Imbembo (1976)
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Hawkins and Imbembo (1976)
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lt- Response to heat source centered at the
radius of maximum winds in a baroclinic vortex
Response to a momentum source -gt
Shapiro and Willoughby (1982)
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• Shapiro and Willoughby (1982) find that the
  vortex is sensitive to the location of heat and
  momentum sources, with the largest vortex
  response occurring when sources are located at or
  just inside the RMW
• Character of vortex response to symmetric forcing
  depends critically only on the vortex intensity
  (not aspect ratio)
• At vmax gt 35 m s-1, the character of the response
  changes dramatically due to increased inertial
  stability in the core and recirculation inside
  the RMW forms an eye
• Theory describes vortex response to given
  forcings at various vortex intensities, but does
  not explain initial vortex structure evolution
• Does not include effects such as eddy momentum or
  cumulus momentum fluxes, boundary layer effects

Shapiro and Willoughby (1982)
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Schubert and Hack (1982)