The Tropical CycloneJet Streak Interaction:

1
The Tropical Cyclone-Jet Streak Interaction The
Role of Upper Tropospheric Inertial Stability in
Tropical Cyclone Intensification Eric Rappin
Department of Atmospheric and Oceanic
Sciences/University of Wisconsin - Madison
Maximum Surface Azimuthal Wind (m/s) Tropopause
Relative Vorticity -f (blue) , 0 (red) , f
(green)
Objective To gain a quantitative insight into
tropical cyclone intensification rates that occur
during a tropical cyclone jet streak (trough)
interaction.
2. Idealized Modeling
1. Introduction
Motivation
The Model

• It is generally accepted that the maximum
  potential intensity (MPI) a tropical cyclone can
  attain is controlled by sea surface temperature
  (SST) and by the thermodynamic state of the
  environment (Emanuel 1986 Holland 1997).
• Tropical cyclones not close to their MPI however
  can be significantly effected by
  hurricane-trough interaction. That is, the rate
  of intensification is highly dependent upon the
  state of the shallow outflow layer.
• A vorticity source above an intensifying tropical
  cyclone will not only force large scale ascent
  and therefore more wide spread convection, but
  will also decrease the Rossby radius of
  deformation so the tropical cyclone will be
  forced to expend more energy to vent its
  outflow from the storm core than otherwise. On
  the other hand, regions of weak inertial
  stability aloft provide a weaker resisting force
  so that the outflow expands more freely (less
  work needs to be done to vent the outflow against
  the radial pressure gradient).
• These ideas were first expressed qualitatively by
  Holland and Merrill (1984) in their description
  of a tropical cyclone life cycle in the
  Australian/south-west Pacific region. They
  suggested that to intensify beyond a minimal
  strength tropical cyclone needed to interact with
  its environment. This interaction is initiated
  with the passage of a subtropical jet streak
  poleward of the tropic cyclone. The anticyclonic
  outflow that wraps tightly around the storm core
  is then free to expand poleward into the region
  of weak inertial stability on the anticyclonic
  shear side of the jet streak.
• For a more detailed description of this
  interaction a brief study of Super Typhoon Oscar
  is presentedin the following section

• This study used ECMWF-TOGA 2.5 degree Global
  Surface and Upper Air Analyses provided by UCAR.
• Storm relative coordinates were used in all wind
  plots and were calculated from the best the Best
  Track Data Set provided by JTWC. In the lower
  right is a table with dates and maximum wind
  speeds taken from the same data.
• Oscar began rapid intensification just after 0Z
  September 14 and intensified into a super typhoon
  around 06Z September 15. Oscar remained a super
  typhoon until 0Z September 17 where it passed
  just offshore of Tokyo with 125 knot winds.
• In the earliest stages of intensification Oscar
  has moved into a region of climatologically high
  SSTs (not shown) so it is reasonable to believe
  that the air-sea interaction was responsible for
  the initial strengthening.
• At 12Z on the 14th and continuing on through 0Z
  on the 15th, the infrared satellite images show
  enhanced convection on the north side of Oscar as
  the anticyclonic outflow increasingly detaches
  from the outflow to the north. The expansion of
  Oscars outflow into the weak inertial stability
  (measured as low absolute vorticity on an
  isentropic surface) is also evident. A word of
  caution should be noted as the outflow to the
  south continues as is clearly seen in the wind
  filed. As discussed in Merrill and Velden (1996)
  the outflow to the south is at a higher altitude
  where little water vapor exists and is more
  associated with core convection (conservation of
  saturated equivalent potential temperature in
  moist adiabatic ascent results in ventilation of
  core convection on higher theta surfaces as a
  result of the theta max in the boundary layer
  storm core). Though no eyewall replacement
  cycles are observed here (lack of high spatial
  and temporal resolution) the enhancement of
  convection to the north of Oscar does not lead to
  significant weakening.
• Also visible during these times is an upper
  leverl vortex to the west of Oscar. This vortex
  acts to accelerate Oscar to the north towards
  the strong band of westerlies. As Oscar
  continues to intensify the outflow continues to
  expand to the northeast into the anticyclonic
  shear side of the jet streak.
• Enhanced ageostrophic motion in the jet entrance
  region and the resultant coriolis forcing of this
  motion leads to strengthening of the jet streak
  by more then 20m/s by 12Z on September 16.
  Should Oscar have not been at its MPI it is
  possible that a positive feedback could have been
  setup where the tropical cyclone strengthenss the
  jet streak which decreases the inertial stability
  and allows for easier ventilation and to further
  tropical cyclone intensification.
• The tropical cyclone-trough interaction is also
  considered to be detrimental to intensification
  as a result of enhanced vertical shear in the
  core region. Note that vertical shear for the
  case of Oscar is not a factor until the last time
  shown.

• The model used in this study was developed and
  modified to accommodate varying inertial
  stability at the tropopause level by Dr. Kerry
  Emanuel (a more detailed description can be found
  in Emanuel 1994).
• The model is axisymmetric with two layers. One
  representing the boundary layer and the other the
  troposphere.
• The constraining balance condition of the model
  is thermal wind balance which is obtained by
  assuming slantwise neutral ascent, hydrostatic
  and gradient wind balance. The assumption of
  slantwise neutral ascent leads to the use of
  potential radius (a measure of angular momentum)
  as the model coordinate. Furthermore, the
  balance condition above requires the use of a
  Sawyer-Eliassen type equation to diagnose the
  secondary circulation.
• A cumulus parameterization based on equilibrium
  maintenance of the boundary layer entropy is
  used. Updraft mass fluxes are determined by an
  assumed equilibrium of surface latent heat fluxes
  and cumulus downdraft fluxes. If the boundary
  layer entropy exceeds the tropospheric saturated
  entropy then the boundary layer entropy is
  communicated to the upper layer along the given
  potential radius.
• The model was modified in such a way so that the
  relative vorticity at the tropopause can be
  varied in the Sawyer-Eliassen type equation. Once
  the relative vorticity was chosen it was fixed
  for the entire time integration. All prognostic
  variables were left to evolve unperturbed (except
  for the change in forcing).
• Three runs of the model were carried out. The
  runs had upper level relative vorticities of f
  (zero inertial stability), 0, and f (strong
  inertial stability), respectively. Here f was
  taken to be a subtropical value. All initial
  parameters were left constant (I.e. initial
  vortex dimensions kept constant).

Tropopause Relative Vorticity -f
Results

• The time evolution of the maximum surface
  tangential winds display in the upper right shows
  that all three runs do eventually reach roughly
  the same intensity. The rate at which this
  intensity is reached is different in all three
  cases. The case with the weakest inertial
  stability aloft reached steady state most
  rapidly.
• Notice that during rapid intensification all
  three cases proceed at the same rate. The
  difference between the three cases is the time
  needed to reach the point just prior to rapid
  deepening. According to Emanuel (1994) , the
  period prior to deepening is the time required to
  saturate the boundary layer so that convective
  downdrafts no longer quash boundary layer entropy
  increases.
• Also visible in the evolution plot are a series
  of eyewall replacement cycles for the first two
  cases. Emanuel (1994) noted the existence of
  eyewall replacement cycles when the initial
  relative humidity of the troposphere is high. The
  entropy fields, 8 days into the integration,
  reveal that the mid-level entropy minimum is
  most rapidly eroded for the first case (zero
  inertial stability case). It is evident that, in
  the context of this model, decreased inertial
  stability aloft results in the cessation of
  convective downdrafts by tropospheric moistening
  and to a more rapid development of a warm core
  vortex.
• Large scale moistening in the troposphere is
  accomplished by detrainment from convective
  clouds. Therefore, early convection seems to be
  more rigorous with weak inertial stability aloft
  which is consistent with continuity
  considerations.
• Also shown to the right are plots of vertical
  motion and radial flow (both computed from the
  streamfunction field) at 8 days. Radial motions
  cannot not be detected for the third case. After
  8 days this vortex is not much stronger then the
  initial vortex. Development of a strong outflow
  jet along with vigorous vertical motion is
  observed in the first two cases. The plots also
  reveal eyewall contraction with deepening.
• For the case of zero inertial stability aloft, a
  second eyewall replacement cycle occurs (shown
  to the right) after steady state has been
  achieved at about 22 days into the integration.
  Following this replacement, a series of chaotic
  replacement cycles occurs which leads to the
  eventual decay of the vortex. Emanuel (1989)
  found that when the size of the initial vortex
  became to large, too much energy when into
  maintaining the outflow anticyclone and the
  vortex failed to spin up. A plot of the outflow
  anticyclone at 30 hours shows the outflow
  anticyclone of the first case to be significantly
  larger and more intense then that out of the
  second case. I?t is therefore reasonable to
  believe that with the continued forcing of
  anticyclonic relative vorticity aloft in the
  first case that there was not enough energy to
  maintain the vortex after a certain period of
  time. Although this reasoning seems counter to
  the discussion provided in the first section it
  must be remembered that in the case study the
  large scale jet streak was present to provide
  energy to vent outflow against the pressure
  gradient and to force subsidence against positive
  stability in the far environment. In the
  idealized model there was no external system to
  provide this energy so it came at the expense of
  the tropical cyclone.

Isotachs and Streamlines 355 Theta Surface
Vertical Wind Shear 850-250 mb Layer
Absolute Vorticity and Winds 355 Theta Surface
Tropopause Relative Vorticity 0
1200 UTC 14 September 1995
Tropopause Relative Vorticity f
0000 UTC 15 September 1995
Relative Vorticity at Boundary Layer Top (scaled
by f) Time 22.1 Days
Azimuthal Velocity at Tropopause at 30
hrs. Specified Relative Vorticity -f (Blue) , 0
(Red)
1200 UTC 15 September 1995
4. Acknowledgements
3. Conclusions/Future Work
Appreciation goes to Dr. Kerry Emanuel for
modifying his model for this experiment and his
constructive comments. The author would also
like to thank Dr. Greg Tripoli for his
enlightening ideas and conversation. Infrared
satellite images were provided by the CIMMS
tropical cyclone group at the University of
Wisconsin-Madison.

• A close look at the the tropical cyclone-trough
  interaction with focus on the role of the jet,
  lying between the warm tropical cyclone outflow
  and cold trough, revealed that the inertial
  stability of the upper troposphere can play a
  significant role on intensification.
• A brief overview of super typhoon Oscar suggested
  that while initial deepening was likely due to
  the air-sea interaction, intensification to and
  maintenance of super typhoon strength occurred as
  outflow from Oscar expanded into the weak
  inertial stability on the anticyclonic shear side
  of the strengthening jet streak. Though the data
  set used has poor resolution for tropical
  cyclone studies, the study is still an indicator
  that the interaction deserves closer inspection.
• An idealized model (Emanuel 1994) was used to
  test the effect of upper tropospheric inertial
  stability on an axisymmetirc tropical cyclone.
  It was found that while rapid intensification
  rates remained constant, early intensification
  was more pronounced for weaker inertial stability
  due to quicker moistening of the troposphere by
  enhanced convection.

1200 UTC 16 September 1995

• There is still no clear picture in the
  meteorology community as to whether the
  tropical-cyclone jet streak interaction is
  beneficial or detrimental to intensification.
  Numerous studies have looked at eddy angular
  momentum and potential vorticity fluxes to
  quantify the interaction with mixed results.
• A three dimensional model is being developed to
  include the jet streak and the effects of shear
  into this idealized modeling study. It is hoped
  that with the freedom to choose relative
  orientation, separation, and strength a more
  complete understanding of the interaction can be
  obtained. It is also felt that with explicit
  treatment of convection it will be possible to
  determine, to a limited degree, the response of
  the tropical cyclone core to external forcing.

5. References
Bosart, L., W. Bracken, J. Molinari, C. Velden,
and P. Black, 2000 Environmental influences on
the rapid intensification of Hurricane Opal
(1995) over the Gulf of Mexico. Mon. Wea. Rev.,
128, 322-352 Emanuel, K, A. 1986 An air-sea
interaction for tropical cyclones. Part I
Steady state maintenance. J. Atmos. Sci., 43,
585-605. _______, 1989 The finite-amplitude
nature of tropical cyclogenesis. J. Atmos. Sci.,
46, 3431-3456 _______, 1994 The behavior of a
simple hurricane model using a convective scheme
based on subcloud-layer entropy equilibrium. J.
Atmos. Sci., 52, 3959-3968. Holland, G, J. 1997
The maximum potential intensity of tropical
cyclones. J. Atmos. Sci., 54,
2519-2541. _______, and R. Merrill, 1984 On the
dynamics of tropical cyclone structural changes.
Quart.. J. R. Met. Soc., 110, 723-745. Merrill,
R, T. and C. Velden, 1996 A three-dimensional
analysis of the outflow layer of Supertyphoon
Flo (1990). Mon. Wea. Rev., 124, 47-63.
0000 UC 17 September 1995