Radio Occultation and Multipath Behavior

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Radio Occultation and Multipath Behavior
Kent Bækgaard Lauritsen Danish Meteorological
Institute (DMI), Denmark
2nd GRAS SAF User Workshop, 11-13 June 2003
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Outline of the Talk

• Introduction
• Multipath behavior
• Inversion of 1-ray and multipath signals
• Back-propagation
• Canonical transform methods
• Conclusions and outlook

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Radio Occultation Geometry
Impact parameter
Bending angle
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Radio Occultation Signal
Physical signal E, B ? Measured signal
u(t) u(t) uEM Receiver noise tracking
errors Receiver - small noise will not
cause problems - tracking errors need to be
known in order to be able to correct for
them Two tracking modes - closed loop
phase-locked loop (PLL) - open loop raw
signal
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Wave Optics Simulation Example
Standard atmosphere
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Water Vapor and Multipath
Tropics dense water vapor layers will in general
give rise to multipath propagation of radio
signals Critical refraction condition -
ducting of rays
Horizontal gradients - normally, one
assumes spherical symmetry in order to obtain
the refractivity N(r) from ?(p) using the Abel
transform
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Multipath Example
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Schematic Ray Manifold
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Inversion of 1-Ray Signal
Measured signal
Doppler shift (wave vector along the t
coordinate)
Bending angle, ?(p), obtainable from ?(t) (using
geometry) Refractivity, N(r), using the Abel
transform ( spherical symmetry) Atmospheric
quantities P, T, q,
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Inversion of Multipath Signal
Measured, multi-ray representation
u(t) t-representation, with caustic with 3 rays
at a given time, t
Map to a 1-ray representation
uz(z) z-representation with 1 ray at any given
value of the coordinate z
Wave vector along the z-coordinate
Bending angle, ?(p), obtainable from ?(z)
Phase space (z, ?) are new coordinates,
replacing (y,ky)
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Back-Propagation Method
Back-propagation maps the measured field u(t) to
a new field with x ? xB
?B known from the Greens function for the
Helmholtz equation
Wave vector along the yB-coordinate
Bending angle, ?(p), obtainable from kB
Phase space (yB,kB) are new coordinates in the
(y,ky) phase space
Does yB uniquely define the rays? - no, real and
imaginary caustics may overlap - multipath tend
to be reduced, thus results are slightly improved
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Back-Propagation Plane at xB
yB
xB
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Impact Parameter Representation
Physical insight for a spherical symmetric
atmosphere, the impact parameter, p, uniquely
defines a ray Gorbunov with horizontal gradient
s the assumption will be fulfilled to a good
approximation Thus, choose z p and map the
measured field to the p-representation up(p)
Mathematical physics provides the recipe for
calculating up(p)
where F is a Fourier integral operator (FIO) with
phase function being equal to the generating
function for the canonical transform from the
old to the new (p, ?) coordinates note, there
are infinitely many Fs that map to the
p-representation
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Schematic Drawing of the p-Representation
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Canonical Transform Method
Map to the 1-ray p-representation
Wave vector along the p-coordinate
Bending angle, ?(p), obtainable from ?(p)
e(p) ?x(p) (plus a correction when the
GPS satellite is at a finite position)
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Canonical Transform Method of Type 2
Canonical transform (of type 1) - Gorbunovs
original CT method which involves first doing
back-propagation - FIO, F, based on a
canonical transform from (yB, kB) to (p, ?)
coordinates
Canonical transform (of type 2) - CT method
based on directly mapping the measured field u(t)
to the p-representation, up(p) FSI -
FIO, F2, based on a canonical transform from (t,
?) to (p, ?) coordinates - up(p) can be chosen
to be identical to the one obtained by a CT of
type 1 - GPS satellite is not assumed
stationary
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Conclusions and Outlook

• Radio occultations and multipath behavior
• Water vapor, critical refraction, receiver
  tracking errors
• Mapping from multi-ray to 1-ray representation
• Multi-ray caustics
• 1-ray Impact parameter representation
• Inversion methods
• Standard methods handle 1-ray signals
• Back-propagation can reduce multi-ray behavior
• Canonical transform methods handle multi-ray
  behavior
• Gorbunovs original CT CT without
  back-propagation (CT of type 2)
• Increased vertical resolution (about 50 m)
• Improved product accuracy