Rossby Wave Radiation from Tropical Cyclones

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Rossby Wave Radiation from Tropical Cyclones

• Kyle Krouse1, Adam Sobel1,2, Lorenzo Polvani1,2

1Department of Applied Physics and Applied
Mathematics 2Department of Earth and
Environmental Sciences Columbia University NE
Tropical Conference MIT Endicott House June 18,
2007
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TCs, being vortices, radiate Rossby waves in the
presence of PV gradients
Snapshot of 850 hPa Abs. vorticity and wind from
NCEP Reanalysis, from Sobel and Bretherton (2000)
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This energy dispersion can lead to genesis of a
second TC (e.g. Frank 1982 Davidson and Hendon
1989)
TC Jelawat inducing TC Ewinar in WNP, Aug., 2000.
From Li et al, 2003
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What controls whether or to what extent wave
radiation occurs? What sets the wavelength?
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We look at this process with simple numerical
experiments

• Shallow water equations on sphere
• Mass equation forced by relaxation to specified
  function of position,
• he is a constant plus a Gaussian depression
  time scale also Gaussian, minimum at mass sink
  center (so no far-field damping of waves)
• This produces a vortex we move it by forcibly
  moving the mass sink at a constant velocity
• Velocity and amplitude of mass sink are varied

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Westward vortex motion is necessary in order to
obtain a zonal wave train as in observations
Note U here is defined as the opposite of the
vortex translation velocity Ugt0 westward
vortex motion
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Moderate nonlinearity makes wave train more zonal
but doesnt otherwise change results much
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The linear dispersion relation for Rossby waves
explains why only westward-moving vortices radiate
In the presence of uniform background flow U,
So Ugt0 (westerly flow for stationary obstacle
resting environment viewed from reference frame
of westward-moving vortex) gives steady solution
(!0)
k zonal wavenumber n meridional wavenumber
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What is U?

• Not the translation velocity of the TC
• Rather, the difference between that and the
  steering flow of the waves
• Either vertical or horizontal shear could provide
  this difference for vertical, need steering
  levels to be different

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? vs. U for n 0, 1, 2 and c 50 m/s (linear
runs)
obs
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? vs. U for n 0, 1, 2 and c 50 m/s (nonlinear
runs)
obs
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The prediction is that easterly vertical shear or
cyclonic horizontal shear will be necessary for
wave radiation, and that stronger shear-gt larger
wavelength
PV contour
z or y
Mean zonal flow
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Implications of horizontal shear, in more
synoptic language
Monsoon trough good for wave radiation
Recurvature bad
y
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Easterly shear also inhibits vertical
propagation, trapping energy in troposphere (good
for our disturbances)
z
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Test these hypotheses using best-track data for
west Pacific, combined with NCEP Reanalysis to
define large-scale flow

• Look for cases where new TC appears to east of
  old one, less than 5000 km away (threshold not
  critical)
• First one is mother, 2nd is daughter TC for
  which daughter never forms is other
• 1517 storms, 676 mothers (44), 972 others (64)
  (totalgt100 because some daughters have gt1
  mother string of pearls)
• Look at histograms of large-scale horizontal and
  vertical shear of zonal wind averaged over large
  regions centered on storm (for vertical shear) or
  between mother and daughter (for horizontal shear)

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• Distributions are very different, and sign of
  difference is
• consistent with theory

Vertical shear (850-250, opposite of
standard definition)
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• Distributions are very different, and sign of
  difference is
• consistent with theory

Horizontal shear at 850 hPa
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• Wavelength is unrelated to shear, in
  contradiction to theory

Wavelength vs. horiz. shear vector
Wavelength mean stdev in horiz. hear vector
bins, theoretical dispersion relation
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Conclusions

• Dynamics of stationary Rossby waves seems to
  explain some basic features of multiple cyclone
  events conditions under which they occur, and
  zonal scale
• Easterly vertical shear and cyclonic horizontal
  shear are favorable, opposite unfavorable
• From event to event, wavelength differences do
  not seem to be explainable by differences in
  shear, so other dynamics must be relevant at this
  level of detail