A Methodological Review Of Radio Occultation Analysis Of Atmospheric And Ionospheric Structures

A methodological review of radio occultation analysis
of atmospheric and ionospheric structures

Victor H. Rios*
*Department of Physics, UNT, CONICET
Argentina

Content of poster presentation
1) The GNSS radio occultation
principle
2) Data processing and exemplar
results
-----------------------------------------------

GPS
Glonass
Galileo
------------60–90
sources
in spaceAbundant signals !!!

GPS Signal Coverage
Two L-band frequencies:

L1: 1.58 GHz
L2: 1.23 GHz

~3000 km

The LEO tracks the GPS phase
while the signal is occulted to
determine the Doppler

The velocity of GPS relative to LEO
must be estimated to ~0.2 mm/sec
(20 ppb) to determine precise
temperature profiles

Radio Occultation Observation
During a GPS occultation a GPSreceiver in LEO 'sees' the GPS SV set
or rise behind the Earth's limb while the
signal slices through the atmosphere.
The GPS receiver in LEO observes
the change of the delay of the signal
between the GPS and the LEO that is
related to slowing and bending of the
signal path.

The change of the delay allows for reconstruction of the bending angle α and
then the vertical refractivity profile atthe ray tangent point.
The refractivity allows for reconstruction of the pressure, temperature and
humidity in the neutral atmosphere and electron density in the ionosphere

Refractivity
Refractivity

N = 10 6 (n − 1)

c
n
Atmospheric refractive index = c / v
where
is the light
v
velocity
in a vacuum and P is the light velocity in the atmosphere
P
n
N = 77.6
(1)
•
•

••
•

T

+ 3.73 × 105
(2)

T

w
2

− 40.3 × 10 6

f

e
2

(3)

Hydrostatic dry (1) and wet (2) terms dominate below 70 km
Wet term (2) becomes important in the troposphere and can
constitute up to 30% of refractivity at the surface in the tropics
In the presence of water vapor, external information information is
needed to obtain temperature and water vapor
Liquid waterand aerosols are generally ignored
Ionospheric term (3) dominates above 70 km

Determining Bending from observed Doppler (I)

Bending angle
α
Φ
Transmitted
wave fronts

Earth

ψ

∆x

v

k

Wave vector of
received
wave fronts

From orbit determination we know the location of source and
We know the receiver orbit v . Thus we know Φ
1
v
v
v
fd =
=
=
cosψ = f T cos ψWe measure Doppler frequency shift:
∆t ∆x λ
c
Thus we know

ψ. And compute the bending angle α = Φ − ψ

Determining Bending from observed Doppler (II)
GPS

VT


eT
Φ

T

α

a

rT

a


eR
Φ

R

LEO

rR

VR

Earth

- The projections of transmitter and receiver orbital motion on the ray path produces a Doppler frequency shift
- After correction forclock and relativistic effects, the Doppler shift, fd, of the transmitter frequency, fT, is given as

fd =

(

)

fT
f
V T • eˆ T + V R • eˆ R = − T (V T r c o s φ T + V
c
c

The Snell's law:

rT sin( Φ T ) = rR sin( Φ R ) = a

θ
T

s in φ T + V R r c o s φ R − V

θ
R

s in φ R

)

- impact parameter

where: c is the speed of light and the other variables are defined inthe figure with V Tr and V Tq
representing the radial and azimuthal components of the transmitting spacecraft velocity.
From Doppler + orbits + Snell's law we obtain bending angle as a function of impact parameter

Abel inversion
∫

Total bending angle of a plain curved ray is α = dl / ρ where dl is
the differential path length, and ρ is the local curvature radius of the ray.
Withaccount for expression for ρ in polar coordinates and the Snell's law:
∞

α ( a ) = − 2a ∫

a

dn / dx
n

x −a
2

2

dx

where x = rn ( r ) is the "refractional radius". This equation can be inverted
2
2
by substitution of the variables u = x , v = a and by use of the
Abel transform:

1
n( x ) = exp 
π

∞

α (a)

x

a2 − x2

∫


da  - the so-called "Abel...