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S. Casotto, F. Panzetta

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Title: A Barotropic Inverse Tidal Model for the Arctic Ocean Author: coas Last modified by: Stefano Created Date: 1/5/2004 7:37:24 PM Document presentation format – PowerPoint PPT presentation

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Title: S. Casotto, F. Panzetta


1
Tidal Field Refinement from GOCEand GRACE A
sensitivity study
  • S. Casotto, F. Panzetta
  • Università di Padova, Italy
  • and GOCE Italy Consortium
  • Sponsored by ASI

2
Tidal Field Refinement from GOCE?
  • S. Casotto, F. Panzetta
  • Università di Padova, Italy
  • and GOCE Italy Consortium
  • Sponsored by ASI

S. Casotto, F. Panzetta Università di Padova,
Italy and GOCE Italy Consortium
3
Outline
  • Tide field representation
  • Sidebands and sensitivity of satellite orbits to
    ocean tides
  • Rationale for ocean tide parameter estimation
    from GOCE
  • Roadmap to using GOCE other missions for OT
    extraction

4
Why study ocean tides?
  • Tides as noise
  • Remove ocean tide and load tide from satellite
    gravity records (e.g., GOCE, GRACE)
  • Remove tidal currents from Acoustic Doppler
    Current Profiler (ADCP) records
  • Tides as signal
  • Oceanographic applications (tidal currents in
    ocean mixing, mean flows, ice formation rates,
    etc.)
  • Geodetic applications (satellite perturbations,
    tidal loading and station displacements, etc.)

5
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6
Ocean Tide Representations
  • Harmonic constituents
  • Doodson (1921)
  • FES2004 OT model
  • Response method
  • Originally due to Munk Cartwright (1966)
  • Orthotides variant due to Groves Reynolds
    (1975)
  • Orthotides are orthogonal over time
  • CSR3.0, etc.
  • Proudman functions
  • Orthogonal over space
  • MASCONS (Mass Concentrations)
  • Usually for localized sensitivity (Ray et al.)

7
Ocean Tide Constituent
  • k Doodson number of the tide constituent
  • tide amplitude
  • tide phase
  • Doodson Warburg phase correction
  • Doodson argument
  • t mean lunar time
  • s mean longitude of the Moon
  • h mean longitude of the Sun
  • p mean longitude of the lunar perigee
  • N negative mean longitude of the lunar node
  • ps mean longitude of the solar perigee

8
Spherical Harmonic Representation
  • Amplitude and phase from FES2004 OT model
  • 15 constituents (M2, S2, K1, O1 , )
  • Harmonic analysis provides harmonic constants
    a,b,c,ds

9
Ocean Tide Potential
Tidal mass displacement ? Stokes coefficients
variation
  • Can compute functionals of gravity
  • accelerations
  • gravity gradients

10
The Response Method (1/2)
Tide height field as a weighted sum of
past, present and future values of the Tide
Generating Potential (TGP)
TGP coefficients cnm(t) due to Sun, Moon, Planets
11
The Response Method (2/2)
Define admittance G as FT of impulse response
MC credo of smoothness ? Linear in each tidal
band m k1
Basis for extrapolation to minor constituents
frequencies
12
Extrapolation to minor constituents
.
.
A, B, C, D
.
.
frequency
13
Orthotide method (1/4)
Tide height as a linear combination of orthotides
CSR3.0
Orthotides result from a convolution with TGP
coefficients
orthotide constants (Groves Reynolds, 1975)
14
Orthotide method (2/4)
Total tide height as convolution with the TGP
coefficients
harmonic analysis of the convolution weights for
each tidal band
15
Orthotide method (3/4)
CONVOLUTION
SH coefficients SH coefficients of
convolution weights of TGP
SH coefficients of tide height
16
Orthotide method (4/4)
Obtain variations of the Stokes OT coefficients
Ocean Tide potential
17
So far
  • Constituents Orthotides
  • FES2004 into orthotides representation
  • Extract any constituent from CSR4.0
  • Constituents suitable for frequency analysis
  • variant due to Groves Reynolds (1975)
  • Orthotides allow efficient computation of
    gravitational perturbations on satellite orbits
    economy of representation

18
Now
  • Ocean tide model improvement from space missions
  • Altimetry (TPX/Poseidon, Jason, )
  • Orbit perturbation analysis very classical,
    goes back to 1970s
  • Sensitivity study
  • Use constituents over entire tide spectrum to
    identify OT coefficients (solution set)
  • Beware of aliasing, resonances (orbit is
    sun-synchronous) and other perturbations
  • Parameter estimation
  • Based on constituents
  • Based on orthotides some caveats
  • Based on mascons

19
Sensitivity analysis GOCE Transverse
perturbations Constituent RMS
20
Sensitivity analysis GOCE Spectrum of
transverse perturbations
21
OT parameter estimation
  • Rationale
  • Exceptionally low orbit of GOCE is highly
    sensitive to tidal perturbations
  • Tidal perturbation power distributed across OT
    spectrum, not fully intercepted by the 15
    constituents of FES2004
  • Official GOCE orbits do not account for
    admittance tides
  • Official orbit accuracy at the 1-3 cm level may
    leave residual power containing OT signal
  • More power, constraints, complementarity from
    other high accuracy missions (GRACE, )

22
OT parameter estimation
  • Input data
  • GOCE GPS phase measurements orbit fit residuals
  • GOCE GRADIO measurement residuals not enough
    sensitivity
  • GRACE GPS residuals KBRR residuals
  • Model dynamics
  • Orbit perturbations due to OT only
  • OT field representation
  • Measurement models
  • SST h-l range
  • SST l-l range rate

23
Orbital Dynamics due to OT
  • Kaula-type linear theory
  • Available in Orbit Elements or RTN Cartesian
  • Limited by use of reference secularly precessing
    Keplerian orbit
  • Need for multi-arc approach
  • Integral equations
  • Also linearized orbit perturbations (Xu, 2008
    Schneider, 1968)
  • Can use any reference trajectory
  • Relative orbit methods
  • Can use any reference trajectory no multi-arc
    needed
  • Brute force numerical integration
  • Need entire force field

24
Relative Orbital Dynamics Approach
  • Can refer to any reference trajectory as the
    intermediary orbit to evaluate the perturbations
  • Single integration arc over 180-day nominal GOCE
    mission
  • No need for the partials w.r.t. reference orbit
  • Not officially available from the project
  • Still need the orbit fit residuals
  • We learned yesterday that the residuals are being
    made availlable
  • Tracking observations are available, but not
    equivalent
  • Otherwise entire OD process is to be redone

25
OT Representation
  • Classical constituents
  • Provides the best identification of relevant
    parameters in this selective application
  • Use of response background model still possible
    and more efficient, also in view of decoupling
    from sensitive constituents
  • MASCONS
  • Well-posed inverse problem due to applicable
    constraints
  • Already applied to GRACE (Ray al.) for
    localized sensitivity
  • Response/Orthotides
  • Critical if used in parameter inversion tuned
    to specific satellite, not sensitive to entire
    spectrum (better suited to altimeter-based
    inversion)

26
OT parameter inversion (1/2)
  • Possible misidentification of relevant OT
    coefficients
  • Use of SVD techniques for inversion of normal
    equations can help solve the singularity
  • Deep resonances
  • adopt Colombos model (essentially ODE solution
    with multiple eigenvalues)
  • Sideband constituents associated with longer
    periods than mission length
  • Possibly not a problem due to foreseen total
    mission length

27
OT parameter inversion (2/2)
  • Sideband constituents not used in official
    products
  • Sideband constituents were considered in
    preliminary studies, but are not in current
    official GOCE processing standards
  • If official GOCE orbits have absorbed residual
    tidal signal
  • OT inversion incomplete, try new POD estimates
  • Hopefully not necessary
  • Inclusion of data from other missions, like GRACE
  • Apply the same reference orbit philosophy
  • Model instrumental (RR) measurements (Cheng,
    2002)
  • Build on current experience, e.g. within Darota

28
Conclusions
  • Tools were developed for handling several ocean
    tides representations and transforming between
    them
  • Interpolation/extrapolation to minor constituents
    available
  • Linear perturbation analysis using numerical
    integration underway as verification of
    analytical approach for identification of
    sensitive parameters
  • System dynamics representation identified
  • Input data identified
  • Economy of representations is based on excellent
    quality of reference official GOCE (as well as
    GRACE) orbits

29
Future work
  • Need to study all details of GOCE orbit
    processing standards
  • Refine interpolation/extrapolation to sidebands
    nonlinearity corrections
  • Develop integral equation solution capability
  • Develop hybrid response method/mascons model to
    represent ocean tides
  • Verify ideas by running numerical simulations
  • Build on experience within GOCE-Italy
  • Use data to squeeze out residual power

30
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31
Sensitivity analysis GOCE Radial perturbations
Constituent RMS
32
Sensitivity analysis GOCE Normal perturbations
Constituent RMS
33
Sensitivity analysis GOCE Spectrum of radial
perturbations
34
Sensitivity analysis GOCE Spectrum of normal
perturbations
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