Water Vapor Retrieved by GNSS Radio Occultation Technique with no External Information

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Water Vapor Retrieved by GNSS Radio Occultation
Technique with no External Information (?)
F. Vespe Agenzia Spaziale Italiana Centro Di
Geodesia Spaziale 75100 Matera (Italy) C.
Benedetto, R. Pacione Telespazio S.p.A. Centro
Di Geodesia Spaziale 75100 Matera (Italy)
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Summary

• Methods for Water Vapor Pressure (PW) Retrieval
  From RO Need External Data
• Description of the Method Proposed for Retrieving
  PW(Without External Data)
• Results and Their Comparison With CHAMP RO, RAOB
  and ECMWF
• Conclusions and Future Development

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Derivation of Water Vapor Iterative Approach
(Kursinski Hajj 2001)

• To solve for Pd, T and Pw it is used
• THE HYDROSTATIC EQUILIBRIUM LAW ?
• THE IDEAL GAS LAW ?

(2)
(3)
Solving (1) for
and combining (2) and (3)
?
So, we have the two equations (1) and (4) in
three unknowns Pd, T and Pw We consider two
different cases
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Derivation of Water Vapor Iterative
Approach(Kursinski Hajj 2001) (Cont.)
DRY AIR

• Pw can be ignored in the upper atmosphere (for
  heights where T?250 K (h250K)
• Given N, both T and P Pd can be solved from
  (1) and (4)

WET AIR

• When in the middle and low troposphere Pw is not
  negligible, it is necessary to have an
  independent knowledge of one of three parameters
  (T, P, Pw) in order to solve for the other two
• h250K is considered as a boundary layer between
  the dry and wet atmosphere
• P and T at a certain boundary layers can be
  taken by ECMWF or NCEP models
• (1) and (4) are solved iteratively as follows

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Derivation of Water Vapor Iterative
Approach(Kursinski Hajj 2001) (Cont.)
WET AIR

• Assume Pw(h) 0 for a first guess
• Integrate (4) to obtain P(h)
• Use P(h) and T(h) in (1) to update Pw(h)
• Repeat step 2. And 3. until convergence.

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Integration of RO Ground GPS Data
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Optimal Estimation Approach
Assuming all Errors as Gaussian, the penalty
function is built as follows
Where yobsvector of measurements y(x)simulated
vector of measurements based on the solution
state vector x (rapresents a profile of
temperature and water vapor a surface
pressure, xa the apriori state vector from an
analysis Sa and Sy are, in turn, the analysis
error covariance and measurement error covariance
plus the covariance forward model which relates
the state vector to the observation
The Solution is
Hx and ?x are the Hessian and the gradient
applied to the penalty function
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The Current Status
Upper Layers (gt50 Km) Too noise
Ihe Iono, Clock and Orbit uncertainties
overwhelm the tiny effects of refractivity
through the outer stratosphere
S/N ratio is good. The atmosphere has no wet
content. The inversion is fully reliable (no
horizontal gradient). The system of 2 equations
hydrostatic equilibrium and refractivity can be
heasily solved.
Stratopause
The atmosphere has a no negligible wet content.
The inversion is not fully reliable (horizontal
gradient). The system of 2 equations
hydrostatic equilibrium and refractivity suffers
of rank deficiency (3 unknows) .
hh250K
Ground Level
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The Hopfield Model
z(r)
hd
P
rd
zo
r
hw
h0
Earth Surface
ro
O
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The Method Proposed(BPV)
THE STEPS

• Fit the Atmosphere refractivity profiles above
  hh250K up to the stratopause retrieved by
  RO (in our case CHAMP data) using the Hopfield
  dry model

• The GPS RO refractivity profiles from level 3
  CHAMP data are used.A Levenberg-Marquardt non
  linear fit is performed having h as variable
  and To and Po as parameters to estimate
  minimizing

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The Method Proposed(BPV)
THE STEPS (Cont.)

• From the estimated parameters To and Po the dry
  refractivity Nd,BPV(h) (magenta line) is computed
  by extrapolating Hopfield model down to the
  ground
• We obtain Nw,BPV(h) ,subtracting the computed
  Nd,BPV(h) from the CHAMP total refractivity
  profiles Nw,BPV(h) NRO(h) - Nd,BPV(h)

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The Method Proposed(BPV)
THE STEPS (Cont.)

• The dry density, the dry pressure and the
  temperature profiles are computed by the
  hidrostatic equilibrium and the ideal gas laws

• The wet pressure profile is computed from the
  Smith and Weintraub equation by the total or the
  wet refractivity, e.s.

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The Method Proposed(BPV)
THE STEPS (Cont.)

• Apply the iterative method, but using as
  external source the values obtained by the BPV
  method instead of those recovered by NCEP/ECMWF
  models, (we achieved the convergence after only
  an iteration!)

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The Test Sites
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The Data Used for the Validation of the Method

• The CHAMP level 3 data. The Water Vapor Profiles
  have been retrieved with the method of Gorbunov
  Sokolovskiy (Wickert et al. 2001)
• The RAOB data have been taken on line from the
  university of Wyoming (http//weather.uwyo.edu/upp
  erair/sounding.html)
• ECMWF data

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RAOB Profiles

To compute the water vapor pressure Pw from
RAOB data (relative humidity RH and temperature
T) it is used the GoffGratch Formulation for
the saturation vapor pressure es Pw RH es
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Results of Data Fitting with Hopfield Model
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RAOB - GFZ - BPV Refractivity Profiles
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RAOB-GFZ-ECMWF-BPV Wet Pressure Profiles
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RAOB-GFZ-ECMWF-BPV Temperature Profiles
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GFZ-BPV Pwet Residuals
(Pwet GFZ- Pwet BPV)
(Pwet GFZ- Pwet BPV)/ Pwet GFZ
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GFZ-BPV Pwet Residuals (Cont.)
(Pwet GFZ- Pwet BPV)
(Pwet GFZ- Pwet BPV)/ Pwet GFZ
Mean-0.380 STD 0.778
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Pwet Residuals
(RAOB-GFZ)/RAOB RECIFE Mean-0.553
STD0.866 GUAM Mean-0.011 STD0.613 BREST Mean
0.122 STD0.552 (RAOB-BPV)/RAOB RECIFE Mean-0
.081 STD0.416 GUAM Mean 0.171
STD0.546 BREST Mean-0.035 STD0.583
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Pwet Residuals
(ECMWF-GFZ)/ECMWF RECIFE Mean-0.11
STD0.21 GUAM Mean0.30 STD0.18 BREST Mean
0.29 STD0.27 (ECMWF-BPV)/ECMWF RECIFE Mean0.19
STD0.33 GUAM Mean0.38 STD0.27 BREST Mean
0.15 STD0.32
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Temperature Residuals
(RAOB-BPV)/RAOB e RECIFE Mean-0.005
STD0.010 GUAM Mean-0.006 STD0.009 BREST Mean
-0.02 STD0.015 (RAOB-GFZ)/RAOB RECIFE Mean0.1
1 STD0.06 GUAM Mean0.11 STD0.05 BREST Mean
0.06 STD0.04
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Temperature Residuals
(ECMWF-GFZ)/ECMWF e e RECIFE Mean0.11
STD0.05 GUAM Mean0.10 STD0.05 BREST Mean
0.06 STD0.04 (ECMWF-BPV)/ECMWF RECIFE Mean-0.0
06 STD0.010 GUAM Mean-0.01
STD0.008 BREST Mean -0.02 STD0.013
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Conclusions and Future Plans

• It is possible from RO data to retrieve Pw
  without using external information (ECMWF, NCEP,
  or Ground GPS)
• The BPV method proposed works and has the same
  performances (it is only slightly wetter) of
  those currently adopted (i.e. CHAMP data) at
  least, for water vapor retrieval
• The method, on the other side, improves
  significantly the temperature profiles of CHAMP
• Other more refined atmosphere models could be
  adopted for fitting the data but Hopfield model
  seems to be a quite good tool for extrapolating
  dry refractivity profiles down to Earth ground
  (Kaniuth 1986 re-estimated the costants in the
  formula using RAOB data but he refined slightly
  the model). Possible alternatives MSISE90 model
  
• The method will be apply directly to the bending
  angles (i.e. before the Abel inversion is
  performed). The drawback is its non-linearity.
  The approach has been set up.
• The method proposed dont replace the current
  methods but could be an helpful integration of
  them