Title: S. Casotto, F. Panzetta
1Tidal Field Refinement from GOCEand GRACE A
sensitivity study
- S. Casotto, F. Panzetta
- Università di Padova, Italy
- and GOCE Italy Consortium
- Sponsored by ASI
2Tidal 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
3Outline
- 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
4Why 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.)
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6Ocean 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.)
7Ocean 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
8Spherical Harmonic Representation
- Amplitude and phase from FES2004 OT model
- 15 constituents (M2, S2, K1, O1 , )
- Harmonic analysis provides harmonic constants
a,b,c,ds
9Ocean Tide Potential
Tidal mass displacement ? Stokes coefficients
variation
- Can compute functionals of gravity
- accelerations
- gravity gradients
10The 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
11The 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
12Extrapolation to minor constituents
.
.
A, B, C, D
.
.
frequency
13Orthotide 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)
14Orthotide method (2/4)
Total tide height as convolution with the TGP
coefficients
harmonic analysis of the convolution weights for
each tidal band
15Orthotide method (3/4)
CONVOLUTION
SH coefficients SH coefficients of
convolution weights of TGP
SH coefficients of tide height
16Orthotide method (4/4)
Obtain variations of the Stokes OT coefficients
Ocean Tide potential
17So 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
18Now
- 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
19Sensitivity analysis GOCE Transverse
perturbations Constituent RMS
20Sensitivity analysis GOCE Spectrum of
transverse perturbations
21OT 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, )
22OT 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
23Orbital 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
24Relative 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
25OT 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)
26OT 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
27OT 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
28Conclusions
- 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
29Future 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
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31Sensitivity analysis GOCE Radial perturbations
Constituent RMS
32Sensitivity analysis GOCE Normal perturbations
Constituent RMS
33Sensitivity analysis GOCE Spectrum of radial
perturbations
34Sensitivity analysis GOCE Spectrum of normal
perturbations