DETECTION OF UPPER LEVEL TURBULENCE
VIA GPS OCCULTATION METHODS
Larry Cornman
National Center
for
Atmospheric Research
USA
Turbulence is a significant operational problem
•
1983-1997 accident statistics in US
• 1,438 injuries
• 609 fatalities (mainly GA, only 1 commercial)
• 70% (commercial) of weather related accidents
• Cost to U.S. airlines alone exceeds $135M USD/year
• Only 35% were forecast!
• 1999: severe encounters = 6288, extreme = 16
National Center for Atmospheric Research
Turbulence Scales of Motion
“Turbulent”
eddies
Large eddies
10’s
km
Small eddies
cm
Aircraft responds to scales
from few m – few km
energy
cascade
Energy
NWP
resolution
Mesoscale
model
resolution
turbulence
no
turbulence
1 eddy size
Turbulence Detection And Forecasting:
Past Approaches
Current Observation System -Voice Pilot Reports (PIREP’s)
– Currently, the only source of
real-time observations
– Inadequate spatial and
temporal accuracy
– Not all pilots report
– Lack of null reports
– Subjective measure
– Dissemination of turbulence
information is poor
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Turbulence Detection And Forecasting:
Past Approaches
Current Advisory and Warning
System - Airmets & Convective
SigMets
– Human-generated product
– Gives an overly broad picture
in both time and space
– Better dissemination of
information is required
National Center for Atmospheric Research
GPS-Turbulence Feasibility Efforts
Is there “signal in the signal”?
or:
What is one person’s noise is another’s signal…
GPS/MET occultation through turbulence?
National Center for Atmospheric Research
Theoretical Background
• As a microwave signal passes through a field
with fluctuating index of refraction, the signal
amplitude and phase will also fluctuate –
proportional to the fluctuating field.
• Scattering theory tells us the form of the
proportionality – given a set of assumptions.
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Theoretical Background, cont’d
• Assumptions:
– The effects of ray bending are negligible.
– The turbulence is isotropic on the spatial scales of
interest.
– The transmitter and receiver velocities are
constant over the sampling time.
– Weak scattering theory is applicable.
– Ionospheric and attenuation effects are negligible.
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Problem Geometry
R is the distance from the GPS to the LEO, and z1 is
the distance from the GPS to the turbulence.
Theoretical amplitude frequency spectrum in the
coordinate system of the GPS. (Phase spectrum
is very similar.)
4
SA ( f ) 
VE

q

2 f
VE
2

q
 z1  
2
sin  z1 1   
2k  R  

 (q)
qdq
1
 q 2  2 f
 2

VE 


Where, the effective velocity is:
VE  VLEO
z1
 z1 
 VGPS 1    VATM . ( z1 )
R
 R
A phase screen approximation is used for the input
spectrum:
R
 (q)  2 k 2   n ( q, z ) dz
0
n (q, z ) is the spectrum of the index of
refraction fluctuations. Using a von Karman
spectrum gives:
2 2
 (q ) 
2 k Cn Z
11
 2 1 
 q  L20 
6
Where it is assumed that the turbulence is only
contained in a region Z in length
Therefore, the proportionality between the
measured amplitude spectrum and the turbulence
spectrum – given all the inherent assumptions –
is:
C Z
S A ( f )  Const. 
 I A ( L0 ,VE , k , z1 , R; f )
VE
2
n
Where I A is the integral from above.
The phase spectrum has a similar structure.
The turbulence intensity information is contained in
2
C
the term n Z , which unfortunately is a function
of the unknown size of the turbulent region.
GPS-Turbulence Feasibility Efforts
• Using GPS/MET data to investigate the question.
• Looking at data from upper troposphere, lower
stratosphere:
– Negligible humidity effects.
– Altitude of commercial transport aircraft in cruise.
• Analyzing short segments of measured, detrended
amplitude (SNR) and phase time series and
comparing to theory.
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Occultation 546: Raw Amplitude and Altitude (via phase)
Occultation 546 : Raw and detrended amplitude
Occultation 546 : Amplitude and Phase Spectra,
measured and model.
Occultation 546 : Amplitude and Phase Structure Functions,
measured and model.
Occultation 586: Raw Amplitude and Altitude (via phase)
Occultation 586 : Amplitude and Phase Spectra,
measured and model.
Occultation 586 : Amplitude and Phase Structure Functions,
measured and model.
Occultation 641: Raw Amplitude and Altitude (via phase)
Occultation 641 : Amplitude and Phase Spectra,
measured and model.
Occultation 641 : Amplitude and Phase Structure Functions,
measured and model.
Summary and Future Work
• Occultation data from GPS-MET is consistent
with theoretical turbulence and scattering models
– especially amplitude data.
• More cases will be analyzed; issues with phase
will be investigated.
• Fine-scale numerical modeling and GPS signal
simulation will be used to look into:
– The effect of shear layers on turbulence estimation.
– Investigate the relationship between index of refraction
fluctuations and velocity fluctuations.
National Center for Atmospheric Research