Wave phenomena in radar meteorology

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Wave phenomena in radar meteorology

• Chris Westbrook

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Rayleigh (small size compared to wavelength)
Reflectivity, Z - Measure of intensity reflected
back to radar
Almost no phase difference (uniform E -
field) across particle wave blind to details,
scatters Isotropically according to how much
material
is there
eg. Rain Radar l10cm drop1mm
back scatter cross section (intensity)
radar wavelength
RAL Chilbolton
Doppler radar Measure frequency shift (the
police car effect) gives reflectivity weighted
average fall speed

• Includes (unknown) contribution
• from velocity of the air (updraft/downdraft)
• can remove this effect using
• two wavelengths (soon!)

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EXAMPLE THUNDERSTORM 28th JULY 2000
Reflectivity RED / PURPLE HEAVY RAIN
At the tropopause, the cloud spreads out
horizontally to form cirrus anvil clouds.
Strong ascending motion can be seen in the
regions of heaviest precipitation. At the
tropopause, the cloud spreads out horizontally to
form cirrus anvil clouds.
Doppler velocity RED TOWARDS RADAR BLUE AWAY
FROM RADAR
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Polarisation measurements

• Differential polarisability
• Bigger drops arent spherical, but oblate
  (pancake)
• drop is more easily polarised in horizontal
• direction than in the vertical, so ZH gt ZV
• Look at ratio ZDR ? provides estimate of drop size

ZDR ? 0 dB (ZH ZV)
1 mm
3 mm
ZDR 1.5 dB (ZH gt ZV)
4.5 mm
ZDR 3 dB (ZH gtgt ZV)
Differential phase shift fdp Flattened drops -
Horizontally polarised component is slowed down
more than the vertically polarised component ?
difference in phase between H and V
Less influenced by largest drops, but data can be
noisy. Helps distinguish big rain drops from
hailstones (which are spherical and so fdp0)
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Observations
Cold front 20th October 2000
melting layer
(time scale 1¼ hours)
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Clear air returns
Refractive index variations in clear air can
produce radar returns if length scale is ?
l/2 Waves from each layer add up constructively
and in phase (like Bragg scattering in crystals)
Allows you to see the boundary layer, Edges of
clouds Turbulence. insects?
Bulge, indicative of storm
Boundary layer
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Ice clouds
Cover about ¼ of earths surface typically
important for radiation budget / climate etc.
Want to interpret observations in terms of how
much ice is in the cloud, how big the ice
particles are, how fast theyre falling etc
Need to model the scattering properties of ice
particles in clouds
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First few hundred metres
Diffusion of water vapour onto ice
Pristine crystals Columns, Plates, Bullet
rosettes
Lower Altitudes
Sedimentation at different speeds
AGGREGATES - (complicated!)
Cloud radars wavelength and ice particle size
are comparable
PARTICLE SHAPE MATTERS!
Previous studies concentrate only on pristine
crystals We want to try and model the scattering
from aggregates Timely, since next month
CloudSat 3mm radar will be in space.
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Aggregation model
Mean field approach big box of snowflakes, pick
pairs to collide with probability proportional
to
Then, to get the statistics right, pick a random
trajectory from possible ones encompassed by and
track particles to see if they actually do
collide if so, stick them together.
(aggregates of bullet rosette crystals)
UNIVERSALITY Statistically self-similar
structure fractal dimension of 2 Also
self-similar size distribution.
Real ice aggregates from a cirrus cloud In the USA
Simulated aggregates
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Rayleigh-Gans theory (Born approximation)
k 2p/l
For small particles, wave only sees particle
volume, not particle shape. (Rayleigh regime)
APPROXIMATE PARTICLE BYASSEMBLY OF SMALL
VOLUME ELEMENTS dv
k
If particle size and wavelength are comparable
(cloud radar / ice particles) then we need a more
sophisticated theory
Phase shift between centre of mass and element at
position r is kr So for back-scatter the total
phase difference in the scattered wave is 2kr
(ie. there and back)
r
dv
Assume 1. each volume element sees only the
applied wave 2. the elements scatter in the same
way as an equivalent volume sphere (amplitude
dv / l2) NO INTERACTION BETWEEN VOLUME
ELEMENTS. So just add up the scattered amplitude
of each element a phase factor exp(I 2kr)
Small particle limit (kr?0) reduces to Rayleigh
sphere formula, ie. intensity volume2 / l4
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So the scattered intensity (radar cross section)
is
Dimensionless function f - tells you the
deviation from the Rayleigh formula
with Increasing size r

• The form factor f is easy to calculate, and
  allows you (for a given shape) to parameterise
  the scattering in terms of
• the particle volume,
• characteristic particle length r (relative to the
  wavelength).

Universal form factor for aggregates irrespective
of the pristine crystals that compose them (as
long as crystals much smaller than wavelength)
f s / s (Rayleigh formula)
LIMITATION OF RAYLEIGH-GANS Assumes no
interaction between volume elements (low density
/ weak dielectric / small kr limit) Good for
first approximation, but is this really all ok?
to appear in the January edition of Q. J. Royal
Met. Soc. (Westbrook CD, Ball RC Field PR
Radar scattering by aggregate snowflakes)
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The discrete (coupled) dipole approximation DDA
Approximate particle by an assembly of
polarisable, INTERACTING dipoles
applied

• Each dipole is polarised in response to
• The incident applied field
• The field from all the other dipoles

etc..
Now instead of simple volume integral of
Rayleigh-Gans, have 3N coupled linear equations
to solve
Electric field at k
Electric field at j
polarisability of dipole k
Applied field at j
Tensor characterising fall off of the E field
from dipole k, as measured at j
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Results

• Would like to parameterise the increased
  backscatter must depend on
• Volume fraction of ice ie. Volume / (4pr3/3)
• Size of aggregate relative to wavelength kr

• USE DDA CALCULATIONS TO
• WORK OUT FUNCTIONS S AND Y
• THEN ONLY NEED r AND v TO
• CACLULATE THE SCATTERING.

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Acknowledgements / Ads etc.
John Nicol (sws04jcn_at_reading.ac.uk) for the clear
air boundary layer image. Robin Hogan
(r.j.hogan_at_reading.ac.uk) for advice and an old
presentation from which the animations were
robbed. Robin Ball (Physics, Warwick) and Paul
Field (NCAR), collaboration on ice aggregation
Rayleigh-Gans work. Photographs of pristine snow
crystals were from www.snowcrystals.com
(Caltech) For more information on the radar
group at Reading www.met.reading.ac.uk/radar
and on my work www.reading.ac.uk/sws04cdw
Chris Westbrook Room 2U04, Meteorology c.d.westbro
ok_at_reading.ac.uk