On the Assimilation of GPS Occultation Measurements

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On the Assimilation of GPS Occultation
Measurements

• X. Zou
• Florida State University

COSMIC Radio Occultation Science Workshop, 21-23
August, 2002
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Outline
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Introduction
Forward modeling of bending angle
.
Impact of observational weightings
.
An effort toward assimilating GPS refractivity
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GPS/MET data
1. Phase delay caused by the bending of the radio
signal at
two frequencies 1227.6 MHz, 1575.4 MHz
2. Doppler frequency shift estimated by the time
derivative of phase delay
3. Bending angle and impact parameter derived
from Doppler frequency shift based on
satellite geometry (impact parameter is
assumed constant at GPS and LEO)
4. Refractivity calculated from bending angle
through the Abel inversion (the refractivity
is assumed spherically symmetric)
5. Temperature and pressure retrieved from
refractivity using the hydrostatic equation
and neglecting water vapor
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Why bending angle?

• The total effect of atmospheric refractivity
  along the ray path can be included through
• a raytracing procedure.
• The effect of the ionosphere can be removed by
• combining two bending angles into one.
• Computational cost can be reduced by carrying out
  raytracing on multiple processors.
• Providing a benchmark for developing a fast and
  accurate GPS refractivity assimilation method.

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Assimilating a in a 3D-Var system
bending angle
Cost function
other observations
Gradient
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Ray-tracing model
The GPS bending angle is derived through an
integration of the following ray equation
where
, s is the length of the ray, n is the
refractive index, and
is the Cartesian coordinate vector.
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Refractivity
Local refractivity
GPS-derived refractivity
n
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Concerns from Data Assimilation

• Forward observation operator is accurate and fast
• Error structures are simple and can be estimated
• Adjoint of the observation operator is fast

The scheme must be as accurate as possible with
affordable computational cost.
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A bending angle observation operator

• It is a 2D raytracing model.
• The oblateness effect of the Earth is removed.
• The latitudinal variation of the gravity
  acceleration is included.
• The forward model uses 0.02 seconds per ray using
  the fourth-order Runge-Kutta method. It is
  reduced by more than half using the second-order
  alternating direction implicit method.

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Issues related to the forward modeling of GPS
bending angle

• Computational cost
• Impact of a bias removal
• Accuracy dependence on the vertical resolution
• A modified integration strategy

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RK versus ADI
Runge-Kutta (RK) method --- 4th order
Alternating direction implicit (ADI) --- 2nd order
For simulating one occultation with 300 rays, RK
uses 5.9 CPU seconds and ADI uses 2.3 seconds
For a total of 133 GPS/MET occultation
CPU (s)
ADI is 2.6 times less expensive than RK. The
fractional diff. is less than 0.04!
RK
983
381
ADI
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Parallelization of the GPS Raytracing Operators
and Theirs Incorporation in the NCEP SSI 3D-Var
System
For 50 iterations (including 2 outer loops), the
wall clock time required by SSI at T62L28
resolution is
13000 seconds on CRAY J90 800 seconds on IBM
SP
Ratio 1/16
if 108 occultation profiles (each with 30 rays)
are included, and
21200 seconds on CRAY J90 1100 seconds on IBM SP
Ratio 1/19
if 200 occultation profiles are included.
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A bias correction
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q analysis with and without the bias correction
The radiosonde sounding is located at (144W,
28S) at 00 UTC June 29, 1995.
without bias correction
The GPS/MET occultation is located at (144W,
27S) at 23 UTC June 28, 1995.
guess
with bias correction
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What causes bias?
It is caused by an inconsistency between
observational data and their simulations
generated by the observation operator.
The radius of local curvature of the earth at the
mean perigee point is used in the raytracing
operator.
The radius of local curvature of the earth at the
perigee point of the lowest ray is used in
GPS/MET.
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vertical resolution
The refractivity is assumed spherically symmetric
2 Hz --- 120 rays 5 Hz --- 300 rays per
occultation 10 Hz --- 600 rays
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Impact of observational weightings
Fifty-two GPS/MET soundings are selected from 837
GPS/MET soundings available during 20-30 June
1995.
Three observational weightings are tested.
The analysis of T and q from the assimilation of
bending angle using three different weightings
are compared with nearby radiosonde observations.
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56 radiosonde stations collocated with 52 GPS/MET
occultations

(i) Each radiosonde has more than 5-levels of
observations. (ii) Their distances to at least
one GPS/MET sounding is less than 200 km.
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Most of the selected GPS/MET soundings (Those
collocated with radiosondes), are found in the
mid-latitudes.
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Three different weightings
1. Background and observation differences
2. Forward model errors
3. Theoretical estimate by
from Palmer et al. (2000)
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Differences between simulated and observed GPS
refractivity
without assimilation
after EXP1
after EXP2
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Differences between simulated local refractivity
and observed GPS/MET refractivity
without assimilation
after EXP1
after EXP2
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Left
Right
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In the NH mid-latitudes, temperature analysis is
improved at all levels except for the mean error
in EXP2.
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Moisture analysis
.
The positive bias errors in the NCEP
background fields are mostly removed by all
three experiments except in the low
troposphere south of 40N .
.
The rms errors are consistently reduced
everywhere by all three experiments.
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GPS-9 (16E,50N)
Vertical profiles of q (left) and dT (right)
for GPS-9 located at (16E, 50N)
before
after
radiosonde
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GPS-30 (94E,60N)
Vertical profiles of q (left) and dT (right)
for GPS-30 located at (94E, 60N)
before
after
radiosonde
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Temperature analysis
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Specific humidity analysis
90S-40N, 10 40N-60N, 30 60N-90N, 16
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The mean and rms errors for temperature and
specific humidity analyses compared to
radiosonde data.
T(K)
guess
EXP1
EXP2
EXP3
bias
0.26 (0.26)
0.20 (0.20)
-0.05 (-0.02)
0.20 (0.20)
rms
1.83 (1.83)
1.69 (1.66)
1.70 (1.66)
1.71 (1.69)
q (g/kg)
guess
EXP1
EXP2
EXP3
bias
0.13 (0.21)
-0.06 (0.01)
-0.13 (-0.06)
-0.09 (-0.02)
rms
0.91 (0.97)
0.82 (0.81)
0.84 (0.83)
0.82 (0.80)
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Inconsistency is noticed for 10 soundings
between the two types of obs. compared to the
NCEP background fields.
Guess-RAD
Guess-GPS
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Toward assimilating GPS refractivity
Why refractivity?

• The computational cost is low to assimilate N.
• A priori separation of temperature and moisture
• information is not required.
• A weighted average might be sufficient to account
• for the integrated effect of the atmosphere
  to GPS
• measurements.

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Assimilating N in a 3D-Var system
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Summary
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• Compared with nearby radiosonde observations, the
  bending angle assimilation improves both the
  temperature and specific humidity analyses with
  the first and third weightings.
• The consistency between the forward model and
  observations must be carefully maintained to
  guarantee the accuracy.
• The wallclock time of raytracing can be
  significantly reduced by paralleling the
  raytracing code and its adjoint and making them
  run efficiently on IBM-SP2 computers.

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Future plans

• Test the sensitivity of bending angle
  assimilation results to the use of a non-diagonal
  observation error covariance matrix.
• Develop an effective and accurate method of
• assimilating GPS refractivity
• Explore the benefit of the high-resolution and
  high-altitude features of GPS/MET measurements
  for NWP (such as convective triggering,
  stratospheric analysis, etc.)

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More details can be found in

• Zou et al., 1999 A raytracing operator and its
  adjoint for the use
• of GPS/MET refraction angle
  measurements. J. G. R., 104,
• 22301-22318.
• Zou et al., 2000 Use of GPS/MET refraction
  angles in 3D variational
• analysis. Q. J. Roy. Met. Soc., 126,
  3013-3040.
• Liu et al., 2001 The impact of 837 GPS/MET
  bending angle profiles on
• assimilation and forecasts for the
  period June 20-30, 1995. J. G. R.,
• 106, 31771-31786.
• Zou et al., 2002 A statistical estimate of
  errors in the calculation of radio
• occultation bending angles caused by a
  2D approcimation of raytracing
• and the assumption of spherical
  symmetry of the atmosphere. JTECH,
• 19, 51-64.
• Shao and Zou, 2002 On the observational
  weighting and its impact on
• GPS/MET bending angle assimilation. J.
  G. R., (accepted)

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Acknowledgment
Dr. Steve Mango, Integrated Program Office of
NOAA National Polar-Orbiting Operational
Environmental Satellite System under SMC/CIPN
project order no. Q000C1737600086.
Drs. Pamela Stephen, J. Fein and Melinda Peng,
National Science Foundation under project no.
ATM-9812729.