L. Padman, S. Erofeeva, G. Egbert Presentation at

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A Barotropic Inverse Tidal Modelfor the Arctic
Ocean

• S. Erofeeva 1, L. Padman 2, G. Egbert 1
• 1 Oregon State University, Corvallis, OR
• 2 Earth Space Research, Seattle, WA
• Sponsored by NSF Polar Programs (Arctic)

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Why study Arctic tides?

• Tides as noise
• Remove ocean tide and load tide on solid earth
  from satellite gravity records (e.g., GRACE).
• Remove tidal currents from vessel ADCP records.
• Tides as signal
• Tidal currents contribute to ocean mixing,
  rectified mean flows.
• Periodic divergence of tidal currents affects ice
  roughness, mean open water fraction, mean ice
  formation rates.

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Model domain and data sites

• Tide gauge data () prov-ided by A. Proshutinsky
  and G. Kivman
• ERS and TOPEX/Poseidon radar altimetry (lilac and
  yellow dots, respectively) provided by R. Ray and
  B. Beckley
• 7 subdomains.

Water depth (m)
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Steps to obtain an inverse model

• Get a prior solution
• Define bathymetryIBCAO
• Set dynamic equations....linearized SWE
• Choose open boundary conditionsTPXO6.2.
• Assimilate data (EBF 1994, EE 2002)
• Set linearized dynamic equations
• Assign errors in dynamics and data
• Minimize quadratic penalty functional sum of
  dynamics and data misfits weighted with error
  covariances.

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Prior model main features

• 8 constituents M2,S2,N2,K2,K1,O1,P1,Q1
• High resolution (5 km) Bathymetry from IBCAO
• Dynamics is based on shallow water equations
  (SWE) solved by direct matrix factorization.
  Simplifications to the SWE include
• tidal loading and self attraction computed from a
  global model (TPXO6.2)
• linear benthic friction, F(r/H)U, where r is the
  friction velocity, H is the water depth, and U is
  the depth-integrated transport (r0.5 m s-1 for
  semi-diurnal constituents and 2 m s-1 for
  diurnals)
• No sea ice.
• Open boundary conditions taken from the latest
  global tidal model TPXO6.2, 1/4º resolution.

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Tide height fields Semidiurnal (M2)
Diurnal (K1)
(From 5-km inverse solution)
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Elevation comparison of the prior and KP94
semi-diurnals
M2 Amp(Prior)-Amp(KP94) (cm)
White Sea
Canadian Arctic Archipelago
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Elevation comparison of the prior and KP94
diurnals
K1 Amp(Prior)-Amp(KP94) (cm)
Baffin Bay Archipelago
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Inverse model main features

• Corrects 4 most energetic constituents M2, S2,
  K1, O1
• Assimilates 364 cycles of T/P data (11178 sites),
  108 cycles of ERS data (18224 sites), 250-310
  tide gauges per constituent
• Dynamics covariance as in EBF 1994, decorrelation
  length scale 50 km
• Data error set for TG 0.05 cm, estimates for
  satellite 3 cm (up to 20 cm)
• Use effective data assimilation scheme
  implemented in OTIS (OSU Tidal Inversion
  Software) http//www.oce.orst.edu/po/research/tide
  /index.html.

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Elevation comparison of prior and inverse
semi-diurnals
M2 Amp(Inverse)-Amp(Prior) (cm)
White Sea
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Elevation comparison of prior and inverse
diurnals
K1 Amp(Inverse)-Amp(Prior) (cm)
Baffin Bay Archipelago
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Model comparisons to tide gauge data
Semidiurnal M2 Diurnal . K1
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Mean tidal current speed

• The calculation is based on simulating 14 days of
  hourly total tidal speed from the inverse
  solution
• Spring tide maximum speed
• umax?2u

u (cm s-1) logarithmic color scale
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Conclusions

• Averaged over the entire model domain, the M2,
  S2, K1 and O1 tides account for 79, 10, 5 and
  1 of the total (8 constituent) tidal potential
  energy, respectively. Tide height variability is
  overwhelmingly dominated by M2.
• Inverse Arctic tide model is most consistent with
  available tide gauge data and satellite
  altimetry. Long term goal to develop
  dynamics-only models with comparable accuracy.
• Further improvements are likely through increased
  resolution, addition of ice-ocean interactions,
  and more sophisticated dissipation
  parameterizations, including benthic friction and
  the conversion of barotropic tidal energy to
  internal tides .
• The inverse model is available from
  http//www.oce.orst.edu/po/research/tide/Arc.html
  (Fortran-based) and http//www.esr.org/arctic_tide
  s_index.html (Matlab-based).