Validation of ocean tide models around Antarctica

1. Validation of ocean tide models around Antarctica Matt King, Nigel Penna, Peter Clarke, Ian Thomas University of Newcastle upon Tyne, United Kingdom

2. Above GRACE error budget Introduction • Challenges of tide modelling in circum-Antarctic oceans • Poor bathymetry/grounding line definitions • Lack of data to assimilate (south of T/P cutoff) • Model physics developments required • Results in inaccurate and/or unvalidated models • The need for accurate ocean tide models • Altimetry –ICESat, ERS/EnviSat RA2 • GRACE • Mismodelled tidal signals alias • S2->162 days, K2->4 y with ~100% admittance • Sub-cm tidal prediction required RMS of gravity from ocean tide model differences (AG95, FES94.2) of M2, S2, K1, and O1 combined associated with harmonic degrees 1-50. From Knudsen et al. http://research.kms.dk/~pk/pubs/grace

3. Tidal characteristics (CATS02.01) Topex/Poseidon cutoff

4. Inter-model agreement (7 models) CATS02.01, CADA00.10, FES2004, CSR4, GOT00.2, NAO.99b, TPXO6.2

5. Tide Models to Validate • Global • TPXO6.2 – 0.25 x 0.25°; Assimilates T/P, TG • TPXO7.0 – 0.25 x 0.25°; Assimilates T/P + Jason, ERS (M2 & O1), TG • FES99 – 0.25 x 0.25°; T/P, TG • FES2004 – 0.125 x 0.125°; T/P, ERS • CSR4 – 0.5 x 0.5°; T/P • GOT00.2 - 0.5 x 0.5°; T/P, ERS • NAO.99b - 0.5 x 0.5°; T/P • Regional • MTOs.05 – 0.125 x 0.083° (south of 30°S); T/P • CATS02.01 – 0.25 x 0.083° (south of 58°S) • CADA00.10 - 0.25 x 0.083°; T/P; 37 TG, GPS and gravity sites

6. Relative accuracy assessment • Using onshore GPS and gravity data • Ocean tides periodically load Earth’s surface and it deforms (3d) • In Antarctica, this is up to ~80mm amplitude (shown) • Measurable by GPS (15 sites shown) and gravity (AMUN) • Fully independent measure of relative accuracy, over large spatial scales (hundreds of km) • Complements the use of TG data at discrete, but relatively few, points Maximum ocean tide loading displacement (mm), based on CATS02.01 + TPXO6.1

7. Ocean tide loading displacements • Daily GPS data analysed using GIPSY Precise Point Positioning (PPP) • Solid earth tide (IERS96), astronomical argument and mean nodal corrections applied • Daily site coordinates and other parameters (tropospheric zenith and gradient, clocks) estimated as normal • Ambiguity terms not fixed to integers • Daily estimates (and VCV) combined to produce final estimates of OTL displacement at each site • Model estimates • Tide Model + Green’s Functions using SPOTL software (D. Agnew) • CATS02.01/CADA00.10/MTOs.05 supplemented north of northern domains • Misfit statistic - sum of squares of complex misfits (S2)

8. Validation against VLBI • Compared (5-10y GPS data) against estimates from VLBI [Petrov & Ma, JGR, 2003] at 21 co-located sites • Fits with modelled values (TPXO6.2) similar in both Radial (shown) and North component • Fit with VLBI ~10-20% better in East component • GPS not good at K1 and K2 • VLBI not good at K1 (worse than GPS) • Very good agreement between GPS and model at N2, O1 (all components) Misfit - Radial Component

9. Antarctic Results All constituents No K1/K2 3d Radialonly Schenewerk et al. GPS Results

10. Results

11. Results

12. Results

13. Fits at most sites on average <1mm2 per constituent for at least one model TPXO6.2, FES2004, CATS02.01, CADA00.10 fit best CSR4, NAO.99b not appropriate near large ice shelves Results

14. U E N GPS K1 and K2 biases Local N is 0° phase • Computed misfit with TPXO6.2 • Residuals as phasor plots • K1 • Approx. repeat period of GPS constellation • Misfits up to 5mm • No evidence for regional correlation in misfits • Multipath and/or orbit mismodelling+local effects

15. U E N K1 and K2 biases Local N is 0° phase • K2 • Orbital period of each satellite (approx.) • Misfits >2mm • North-East ~=90° • K2 estimates also drift in time • Suggestive of satellite-specific range bias • Satellite/block-specific phase centre offsets [e.g., Ge et al., GRL, 2005]

16. Gravity FES99 FES2004 TPXO7.0 CADA00.10 MTOs.05 TPXO6.2 South Pole gravity • No semi-diurnal/diurnal body tides • Relative gravity analysis of Knopoff et al. Units: uGal, same scale

17. South Pole gravity • No semi-diurnal/diurnal body tides • Relative gravity analysis of Knopoff et al. Units: uGal, same scale

18. Conclusions • GPS and VLBI have a similar capability to retrieve harmonic site displacements • TPXO6.2 presently the most accurate model for circum-Antarctic oceans (~5-7cm RMS for 4 constituents [King and Padman, GRL, 2005]) • CSR4 and NAO.99b are inaccurate near large ice shelves • FES2004 used in GRACE analysis; improvements could be found using TPXO6.2 around Antarctica • Further improvements in model accuracy • Better grounding-line and bathymetry (esp. under ice shelves) • Accurate data to assimilate with widespread geographical coverage (ice shelves) • GPS, IceSat, ERS/EnviSat • Theoretical developments in tide model physics