Satellite Altimetry OCTAS lecture January 2005,

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Satellite AltimetryOCTAS lecture January 2005,

• Ole B. Andersen.

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Content

• The radar altimetric observations (1)
• Altimetry data
• Contributors to sea level
• Crossover adjustment
• From altimetry to Gravity and Geoid (2)
• Geodetic theory
• FFT for global gravity fields
• Least Squares Collocation
• Global Marine Altimetric Gravity Field (3)
• Accuracy assesment
• Applications

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Content 2

• Radar altimetry Frontiers (4)
• Altimetric gravity field in shallow water
• Altimetric gravity field in polar regions
• Merging altimetry with airborne data.
• Mean sea surface and ocean variability
• Time variation (5)
• Long Term Sea Level Change.
• El Nino Monitoring
• Ocean Tides.
• Real Time altimetry
• Laser Altimetry (6).
• Difference with radar altimetry
• Gravity from ICESAT
• High resolution Ice-rif monitoring

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Altimetric Observations 2
Accurate ranging to the sea surface is based On
accurate time-determination. P. Berry will give
much more on this.
Typical ocean waveforms Registred at 20 Hz The
20 Hz height values are Too noisy and averaged to
give 1 Hz values (7 km averaging).
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Sampling the Sea Surface (Quick Time Movie).
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OngoingSatellitemissions
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Sampling the sea surface.
1 Day
3 Days
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Orbit Parameters
The coverage of the sea surface depends on the
orbit parameters (inclination of the orbit plane
and repeat period).
TOPEX/JASON - 10 Days
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5 ongoing missions JASON-1 TOPEX
TDM GFO ERS-2 ENVISAT. One/two track every
day. Real time altimetry (JASON) 4-6 hours
5-7 cm accuracy.
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GEOSAT / GFO ERS1 / ERS2 / ENVISAT
ERM
GM
ERS GM mission 1994 GEOSAT GM mission 1985
GEOSATERS GM data is ESSENTIAL for high
resolution Gravity Field mapping.
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The orbital height of the space craft minus the
altimeter radar ranging to the sea
surface corrected for path delays and
environmental corrections Yields the sea
surface height
where N is the geoid height above the
reference ellipsoid, ? is the ocean
topography, e is the error The Sea surface
height mimicks the geoid. MSS N MDT e
-gt GOCINA OCTAS
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Altimetric observations
The magnitudes of the contributors ranges up
to The geoid NREF /- 100 meters
Terrain effect NDTM /- 30
centimeters Residual geoid ?N /- 2
meters Mean dynamic topography ?MDT /-
1.5 meter Time varying Dyn topography ?(t)
/- 5 meters. (Tides storms El Nino)
What We want for Global Gravity is So we need
to account for the rest.
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Remove - Restore.

• Remove-restore technique enhancing signal to
  noise.
• Remove a global spherical harmonic geoid model
  (EGM96)
• Remove terrain effect
• Remove Mean dynamic topography from model.
• Restore the EGM96 global gravity field
• Restore the Terrain effect
• PROBLEM
• What about time varying signals
• What about Errors.

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Time Varying Signal Errors.
Tides contribute nearly 80 to sea level
variability. removed using Ocean tide Model
(AG95, GOT, FES2002, NAO99) Time variable signals
are averaged out in ERM data but not in GM data.

• eorbit is the radial orbit error
• etides is the errors due to remaining tidal
  errors
• erange is the error on the range corrections.
• eretrak is the errors due to retracking
• enoise is the measurement noise.

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Errorstime varying signals.

• ERM data. Most timeerror average out.
• Geodetic mission data ?(t) is not reduced
• Must limit errors to avoid orange skin effect
• NOTICE ERRORS ARE LONG WAVELENGTH

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Enhancing the altimetry for gravity

• Two approaches to limit long wavelength (time
  error signal).
• Use sea surface slopes
• Using crossover adjustment.
• Motivation for crossover
• The residual geoid signal is stationary at each
  location.
• Consequently the residual geoid observations /sea
  surface height observations
• should be the same on ascending and descending
  tracks at crossing locations.
• Timevarying Dynamic sea level orbital related
  signals should not be the same, and should be
• Motivation for sea surface slopes
• Theoretically straight forward wrt gravity field
  computation.
• Using sea surface slopes reduces long wavelength
  errors
• THERE IS LITTLE (IF NO) NEED FOR XOVER
  ADJUSTMENT.
• Short wavelength part of dynamic topography is
  enhanced
• At extreme latitudes only east-west slopes are
  represented
• At Equator mainly north-south slope are
  represented.

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Crossover Adjustment

• dkhi-hj.
• dAxv
• where x is vector containing the unknown
  parameters for the
• track-related errors.
• v is residuals that we wish to minimize
• Least Squares Solution to this is
• Constraint is needed cTx0
• Case of bias mean bias is zero

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Crossover adjustment 2.

• Modelling track related errors.
• Bias (short tracks) Rank 1
• Bias Tilt (medium tracks) Rank 4
• Higher order (long tracks) Rank 6
• Rank deficiencý can be solved by fixing arcs
  (arbitrerely).
• Better to apply minimum variance of free surface
  constraint. (free cross over adjustment)

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Before
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After Crossover
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Data are now ready for computing gravity /
geoid.

• Corrected the range for as many known signals as
  possible.
• Removed Long wavelength Geoid part will be
  restored.
• Limited errors time varying signal (Long
  wavelength).
• Still small long wavelength errors can be seen in
  sea surface heights. This will be treated in the
  subsequent Least Squares Collocation
  interpolation procedure.