Application of GPS Slant Water Vapor Tomography to an IHOP Storm Case with Simple Constraints

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Application of GPS Slant Water Vapor Tomography
to an IHOP Storm Casewith Simple Constraints

• Y. F. Xie, J. Braun,
• A. E. MacDonald and R. H. Ware

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Outline

• GPS application in meteorology.
• Development of a GPS tomography
• A variational approach based on GPS
  slants
• Incompleteness of GPS slant observation
• Schemes to resolve the incompleteness.
• Numerical experiments
• Real time GPS observation experiments over
  IHOP area.
• Conclusions.

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References

• MacDonald, A., Y. Xie, and R. Ware, 2002
  Diagnosis of Three-Dimensional Water Vapor Using
  Slant Observations from a GPS Network, Monthly
  Weather Review, 130,386-397.
• Xie, Y., J. Braun, A., MacDonald, and R. Ware,
  2004 IHOP GPS Water Vapor Retrieval. In
  preparation.

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1. The GPS application

• The most interesting application Integrated
  Slant Water Vapor
• Water vapor variability is largely responsible
  for signal errors (delays) in GPS positioning
• Verification of the accuracy of the delays led to
  a new atmospheric remote sensing tool
• ground-based GPS observation network.
• For example FSL/GPS-Met.

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GPS slant delay
These delays are integrations of refractivity
along GPS ray paths between GPS receivers and
satellites
D ?r N ds
Where N Cdry Pd/T C1Pw/T C2Pw/T2
GPS software Bernese can convert these delays
into integrated water vapor along these ray
paths, Dq ? q dl, where q water vapor.
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GPS tomography

• GPS tomography is a direct analysis of GPS
• observations independent of other obs or
• NWP models.
• For example, study of GPS slant water
• vapor through double-differencing under the
• zero mean assumption.

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2. GPS tomography

• Minimizing the differences between observed
  integrated water vapor (Dobs) and integrated
  water vapor (D) along the same ray paths
  estimated using the control grid function (q).
• The cost function is
• minimize ?(D Dobs)2

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2. GPS tomography (continue)

• GPS slants cannot uniquely determine a
  solution to the GPS tomography problem. We call
  this incompleteness of these integrated water
  vapor.
• A more complex example

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2. GPS tomography (continue)

• Schemes for resolving the incompleteness
• A. Other water vapor observations.
• In our OSSE experiments, water vapor
  observations from microwave profilers are used.
• B. Simple physical constraints.
• In our real data experiments, some simple
  physical constraints are used, for examples,
  non-negativeness and exponential decay with
  height.

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GPS tomography with simple constraints

• minimize ?(D Dobs)2
• subject to qi,j,k 0
• qi j k 10e-z, k large
• (g/m3)

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Recursive filter

• Due to limited information provided by
  GPS slant observations, an analysis is restricted
  over certain scales. That is, a grid analysis is
  correlated between its gridpoints.
• A. Multigrid technique (used in OSSE)
• B. Recursive filter. (used in here)

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3. Numerical Experiments.

• OSSE experiments.
• Using mesoscale model water vapor fields as
  nature, e.g., QNH from FSL and MM5 from NCAR
• High accuracy line integrations of these water
  vapor fields along GPS slant paths from ideal
  ground GPS network to existing GPS satellites are
  computed. They are used as GPS observations.
• Adding 16 microwave profiler observation sites
  and solving the GPS tomography problem to
  generate three-dimensional water vapor
  distributions.

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3. Numerical Experiments (cont.)
Tomography analysis
Nature from QNH
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3. Numerical Experiments (Cont.)
Tomography analysis
Nature from QNH
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3. Numerical Experiments (Cont.)
Vertical profile (Moist)
Vertical profile (dry)
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3. Numerical Experiments (Cont.)

• Real time GPS data over IHOP area
• Bernese 4.2 is used to process the GPS slant
  delays from 25 ground-based GPS sites over IHOP
  (International H2O Project) during June 12-13,
  2002.
• The domain is over the right center of IHOP.
  (see the right figure)

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GPS slant observations

• Over this domain, there are 25 GPS sites
• Elevation angle down to 7 degree
• Collection of GPS slant during a half hour time
  interval.

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3. Numerical Experiments (Cont.)

• Collect data over a half hour time interval and
  treat them as one time observations (assuming
  large-scale water vapor does not change much).
• Add some simple physical constraints, requiring
  water vapor field is not negative and restricting
  water vapor close to an exponential decay
  function with height at the top 5 levels. The
  water vapor control grid is 21 21 21 over a
  500km by 500km by 10km domain.
• Solve the GPS tomography problem with the simple
  constraints and a recursive filter.

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3. Numerical Experiments (Cont.)
Jun. 13, 2002, 0000UTC
Goes water vapor image
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3. Numerical Experiments (Cont.)
Jun. 12, 2004, 2200UTC
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Comparison with Sounding

• At the central facility
• of IHOP, we plot the
• sounding data (red)
• and our tomography
• analysis (black).

Jun. 13, 2002, 0000UTC
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4. Conclusions

• In a separate study, we found a GPS receiver
  network with 100km density could provide useful
  information for mesocale water vapor analysis
• The GPS tomography provides a direct and
  independent analysis of GPS slants comparing to
  other data assimilation techniques, such as,
  3DVAR or 4DVAR. It helped to discover and solve
  the incompleteness of GPS slant observation
• GPS integrated water vapor observations provide a
  practical mesoscale water vapor observations and
  analysis for improving weather research and
  forecasts
• The study here shows the GPS slant retrieval
  contains useful information under the
  double-differencing and zero mean assumption.
• Future work would focus on improvement of
  mesoscale water vapor forecasts from GPS
  tomography and 3DVAR/4DVAR.

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