1. ASSIMILATION of Limb measurements at ECMWF: GPS radio occultation
Sean Healy
DA lecture, 4th May, 2007

2. Aim of lecture
Introduce the GPS radio occultation measurement technique.
Explain the basic physics of the measurement. Try to be honest about the strengths and weaknesses of the technique.
Why do we need GPS radio occultation measurements, given that we have millions of satellite measurements?
Summarise first assimilation results at ECMWF.
Point you to web sites that contain useful papers and where you can get GPSRO assimilation software (1D-Var minimisation code, observation operators etc).

3. Outline 1) Limb geometry. 2) GPS radio occultation (RO) measurements.
3) “Classical RO retrieval”.
4) Why are we interested in RO (weighting functions,
vertical resolution, information content).
5) Early 4D-Var assimilation of GPS RO measurements.
6) Useful web sites.
7) Summary and conclusions.

4. Limb geometry
Satellite h
Tangent
height
We are looking at a slice through the atmosphere with a cold space
background. A large proportion signal (radiance or bending) arises
near the tangent height, leading to narrow vertical weighting
functions, but they tend to be quite broad in the horizontal.

5. Radio Occultation Background
Radio occultation (RO) measurements have been used to study planetary atmospheres, such as Mars and Venus, since the 1960’s. Its an active technique, that is based on very simple physics - Snell’s Law of refraction. We simply look at how the paths of radio signals are bent by refractive index gradients in the atmosphere. Much easier than modelling radiative transfer!
The use of RO measurements in the Earth’s atmosphere was originally proposed in 1965, but required the advent of the GPS constellation of satellites to provide a suitable source of radio signals.
In 1996 the proof of concept “GPS/MET” experiment demonstrated useful temperature information could be derived from the GPS RO measurements.

6. GPS RO: Basic idea
The 24 GPS satellites are primarily a tool for positioning and navigation These satellites emit radio signals at L1= GHz and L2=1.2276GHz (~20 cm wavelength).
The path of a GPS signal will be bent by refractive index gradients in the ionosphere and neutral atmosphere.
GPS RO is based on analysing the bending caused by the neutral atmosphere along ray paths between a GPS satellite and a receiver placed on a low-earth-orbiting (LEO) satellite. IE, it’s an active
satellite to satellite measurement!
(The ionospheric signal can be removed by taking a linear combination of the L1 and L2 measurements. We’ll ignore the ionosphere in this lecture, but note GPSRO measurements can also provide useful ionospheric electron density profiles.)

7. GPS RO geometry Setting occultation: as the LEO moves behind the earth
GPS transmitter a
Tangent point
LEO receiver
“eg, CHAMP”
20,200km
800km
The motion of LEO results
in sounding progressively
lower regions of the
atmosphere.
Setting occultation: as the LEO moves behind the earth
we obtain a profile of bending angles, a, as a function of
impact parameter, . The impact parameter is the distance of closest approach for the straight line path. Its directly analogous to angular momentum of a particle.

8. GPS RO
Good vertical resolution. Around 70% of the bending occurs over a ~450km section of ray-path, centred on the tangent point (point closest to surface) – it has a broad horizontal weighting function!
All weather capability: not affected by cloud or rain.
The bending is ~1-2 degree at the surface, falling exponentially with height. The scale-height of the decay is approximately the density scale-height.
A profile of bending angles from ~60km tangent height to the surface takes about 2 minutes. Tangent point drifts in the horizontal by ~150 km during the measurement.

9. The “Classical” retrieval (Or how the planetary scientists invert RO data)
GPS RECEIVERS DO NOT MEASURE BENDING ANGLE DIRECTLY!
In fact, the bending angles,a, and impact parameter values, , are derived from the time derivative of the measured phase delay assuming local spherical symmetry. This is done by assuming that the impact parameter value is constant along the ray-path:
Given bending angle, a, as a function of impact parameter we can estimate the refractive index profile, n, in the region of the tangent point. f r
where f is the angle between the ray-path and the
local radius vector, r is the radius value and n is the
refractive index.
ray-path

10. “Classical” retrieval (2)
If the impact parameter is constant, the bending angle can be
written in terms of the radial gradient of refractive index,
Convenient variable for integration
This integral can be inverted with an Abel transform:
(Note the upper limit.
Extrapolation required
a-priori information used.)
So we can derive the refractive index as a function of radius
from the profile of bending angles as a function of impact parameters.

11. “Classical” retrieval (3)
The refractive index can be written as:
refractivity
“wet term”
(c1 = 77.6 and c2 = 3.73E5
are known constants)
Neglecting the wet term and using the ideal gas law (P=rRT),
the refractivity, N, is linearly proportional to density. Use the
hydrostatic equation to obtain the pressure profile.
“dry term”
a priori

12. “Classical” retrieval (4)
The temperature profile can then be derived with the ideal gas law:
GPSMET experiment (1996): Groups from JPL and UCAR demonstrated that the retrievals agreed with co-located analyses and radiosondes to within 1K between ~5-25km.
EG, See Rocken et al, 1997, JGR, 102, D25,

13. GPS/MET Temperature Sounding (Kursinski et al, 1996, Science, 271, 1107-1110, Fig2a)
GPS/MET - thick solid.
Radiosonde – thin solid.
Dotted ECMWF anal.
(Location 69N, 83W.
01.33 UT, 5th May, 1995)

14. Post GPS/MET
The “proof of concept” GPS/MET mission in 1996 was a major success. This led to a number of missions of opportunity, proposals for a constellation of LEO satellites and first dedicated operational instruments.
Current status:
Missions of opportunity: CHAMP and GRACE-A currently provide a combined total of around 250 occultations per day.
The COSMIC constellation of 6 LEO satellites was launched last year. Currently providing ~1800 occultations per day. Expect 2500 occultations per day by the end of 2007.
The GRAS instrument on METOP will provide measurements soon.

15. But why are we interested in GPS RO for NWP?
Even with COSMIC, the GPSRO data numbers are quite small. There
is already a massive number of satellite data assimilated into
NWP models - of order millions of satellite radiances with the latest
high-resolution IR sounders.
1) GPS RO can be assimilated without bias correction*. They are
good for highlighting model errors/biases. Most other satellite
observations require bias correction. Climate applications.
2) GPS RO (limb sounders in general) have sharper weighting
functions in the vertical and therefore have good vertical
resolution properties. The GPSRO measurements can “see”
vertical structures that are in the “null space” of the satellite radiances.
*The observed refractivity values are biased low near the surface. See Ao et al, JGR,
2003, D18, 4577, doi: /2002JD

16. Limitations of classical retrieval
The classical GPS retrieval is good for developing a physical
understanding of the measurement technique, but it is not
recommended as a practical retrieval method for either
NWP or climate applications because:
1) Above ~35 km, the temperature retrievals are very sensitive
to noise (e.g., residual ionospheric signal) and the introduction of a
priori information. Information content is low above 35km – signal
to noise falls exponentially with height!
2) We also need a-priori information to derive temperature and
humidity information from the measurements near the surface
(The “water-vapour” ambiguity N(T,Q).)
Better to use 1D-Var retrievals, where the observation operator, H(x),
simulates refractivity or bending angle from the model state. The
observation operators can also be used in a 4D/3D Var assimilation
system.

17. 1D-Var retrieval The 1D-Var retrieval minimises the cost function:
The observation operator -
simulating bending angles or
refractivity from the forecast
state.
The 1D-Var approach provides a framework for testing
observation operators that we might use in 3D/4D-Var
assimilation.
We can also investigate various information content measures.

18. 1D bending angle weighting function (Normalised with the peak value)
Weighting function peaks at the pressure levels above and below the
ray tangent point. Bending related to vertical gradient of refractivity:
Increase the T on the
lower level – reduce the
N gradient – less bending!
upper level – increase
N gradient more bending!
(See also Eyre, ECMWF Tech Memo. 199.)
Very sharp weighting function in the vertical – we can resolve structures
that nadir sounders cannot!

19. Useful 1D-Var diagnostics
1D-Var provides an estimate of the solution error covariance matrix
It also gives vertical resolution diagnostics – the averaging kernel.

20. 1D-Var information content (Collard+Healy, 2003) QJRMS, 2003, v129, 2741-2760
RO provides good temperature information
between hPa. IASI retrieval performed
with 1000 channels, RO has 120 refractivity
values. (Refractivity errors are vertically correlated because of the Abel transform).
RO humidity error estimates are over-optimistic near the surface. The observed refractivity values are known to be biased near the surface – as noted earlier.
RO provides very little humidity information
above 400hPa. The “wet” refractivity is small compared to the assumed observation error.

21. Vertical resolution (1D-Var averaging kernels – how well a retrieval can reproduce a spike)

22. Assimilation of GPSRO at ECMWF
We currently assimilate GPS RO bending angle profiles by evaluating the 1D bending angle integral.
So we treat the GPS RO measurement as though it is a profile measurement. We have 2D bending angle operators built into the assimilation code as well, but these are not yet used in operations.

23. Impact on ECMWF operational analyses
We would expect improvements in the stratospheric temperatures. The fit to radiosonde temperatures is improved (eg, 100 hPa, SH).
GPSRO used in operations
since 12th December, 2007.

24. Mean analysis/increments over Antarctica for Feb. 2007
Mean temperature increment
Black = GPSRO included
Red = No GPSRO measurements assimilated

25. Useful web-sites
The COSMIC homepage This contains latest information on the status of COSMIC and a extensive list of papers with some links to .pdfs of the papers.
The GRAS-SAF homepage
You can find lists GRAS-SAF publications
Links to GPS RO monitoring pages at the Met Office (Data quality, data flow of COSMIC, GRACE-A, CHAMP and GRAS soon).
In addition, you can register and download for the GRAS-SAF’s Radio Occultation Processing Package (ROPP). This F90 software package containing pre-processing software modules,1D-Var minimization code, bending angle and refractivity observation operators and their tangent-linears and adjoints.

26. Summary GPS RO is a satellite-to-satellite limb measurement.
Outlined the basic physics of the GPS RO technique and the classical retrieval.
Measurements do not require bias correction. This may be important for climate applications. The observation operators are quite simple. Very good vertical resolution, but poor horizontal resolution (~450 km average). Also, be wary of classical temperature retrievals above 35 km. They mainly contain a-priori information.
Information content studies suggest GPS RO should provide good temperature information in the upper troposphere and lower/mid stratosphere. First impact studies and results in operations support this. Nice results over Antarctica, where a known model/assimilation problem has been corrected.