Svetlana Y. Erofeeva

Efficient Inverse Modeling of Barotropic Ocean Tides

Abstract A computationally efficient relocatable system for generalized inverse (GI) modeling of barotropic ocean tides is described. The GI penalty functional is minimized using a representer method, which requires repeated solution of the forward and adjoint linearized shallow water equations (SWEs). To make representer computations efficient, the SWEs are solved in the frequency domain by factoring the coefficient matrix for a finite-difference discretization of the second-order wave equation in elevation. Once this matrix is factored representers can be calculated rapidly. By retaining the first-order SWE system (defined in terms of both elevations and currents) in the definition of the discretized GI penalty functional, complete generality in the choice of dynamical error covariances is retained. This allows rational assumptions about errors in the SWE, with soft momentum balance constraints (e.g., to account for inaccurate parameterization of dissipation), but holds mass conservation constraints. Wh...

Accuracy assessment of global barotropic ocean tide models

The accuracy of state-of-the-art global barotropic tide models is assessed using bottom pressure data, coastal tide gauges, satellite altimetry, various geodetic data on Antarctic ice shelves, and independent tracked satellite orbit perturbations. Tide models under review include empirical, purely hydrodynamic (“forward”), and assimilative dynamical, i.e., constrained by observations. Ten dominant tidal constituents in the diurnal, semidiurnal, and quarter-diurnal bands are considered. Since the last major model comparison project in 1997, models have improved markedly, especially in shallow-water regions and also in the deep ocean. The root-sum-square differences between tide observations and the best models for eight major constituents are approximately 0.9, 5.0, and 6.5 cm for pelagic, shelf, and coastal conditions, respectively. Large intermodel discrepancies occur in high latitudes, but testing in those regions is impeded by the paucity of high-quality in situ tide records. Long-wavelength components of models tested by analyzing satellite laser ranging measurements suggest that several models are comparably accurate for use in precise orbit determination, but analyses of GRACE intersatellite ranging data show that all models are still imperfect on basin and subbasin scales, especially near Antarctica. For the M2 constituent, errors in purely hydrodynamic models are now almost comparable to the 1980-era Schwiderski empirical solution, indicating marked advancement in dynamical modeling. Assessing model accuracy using tidal currents remains problematic owing to uncertainties in in situ current meter estimates and the inability to isolate the barotropic mode. Velocity tests against both acoustic tomography and current meters do confirm that assimilative models perform better than purely hydrodynamic models.

Tides of the Ross Sea and Ross Ice Shelf cavity

Two new ocean tide models for the Ross Sea including the ocean cavity under the Ross Ice Shelf, are described. The optimum model for predicting ice shelf surface height variability is based on assimilation of gravimetry-derived tidal constituents from the Ross Ice Shelf. Synthetic aperture radar interferograms provide an independent test of model performance. The standard deviation of tide height variability is largest under the eastern ice shelf along the Shirase and Siple Coasts, where it can exceed 0.8 m. The maximum peak-to-peak tidal range in this region is ∼3 m. The best predictor for ocean tidal currents north of the ice front is a dynamics-based model that solves the depth-integrated shallow water equations with a linear representation of benthic friction rather than the more usual quadratic form. Tidal currents over the open Ross Sea are dominated by diurnal, topographically trapped vorticity waves. The strongest modelled currents exceed 1 m s−1 at spring tide in a narrow band along the upper continental slope in the north-western Ross Sea. Typical tidal currents in the central continental shelf area of the Ross Sea are 10–20 cm s−1. Under the ice shelf the typical currents are ∼5 cm s−1.

The M2 Internal Tide off Oregon: Inferences from Data Assimilation

A linearized baroclinic, spectral-in-time tidal inverse model has been developed for assimilation of surface currents from coast-based high-frequency (HF) radars. Representer functions obtained as a part of the generalized inverse solution show that for superinertial flows information from the surface velocity measurements propagates to depth along wave characteristics, allowing internal tidal flows to be mapped throughout the water column. Application of the inverse model to a 38 km 3 57 km domain off the mid-Oregon coast, where data from two HF radar systems are available, provides a uniquely detailed picture of spatial and temporal variability of the M2 internal tide in a coastal environment. Most baroclinic signal contained in the data comes from outside the computational domain, and so data assimilation (DA) is used to restore baroclinic currents at the open boundary (OB). Experiments with synthetic data demonstrate that the choice of the error covariance for the OB condition affects model performance. A covariance consistent with assumed dynamics is obtained by nesting, using representers computed in a larger domain. Harmonic analysis of currents from HF radars and an acoustic Doppler profiler (ADP) mooring off Oregon for May‐July 1998 reveals substantial intermittence of the internal tide, both in amplitude and phase. Assimilation of the surface current measurements captures the temporal variability and improves the ADP/solution rms difference. Despite significant temporal variability, persistent features are found for the studied period; for instance, the dominant direction of baroclinic wave phase and energy propagation is always from the northwest. At the surface, baroclinic surface tidal currents (deviations from the depth-averaged current) can be 10 cm s21, 2 times as large as the depth-averaged current. Barotropic-to-baroclinic energy conversion is generally weak within the model domain over the shelf but reaches 5 mW m22 at times over the slopes of Stonewall Bank.

Tide Predictions in Shelf and Coastal Waters: Status and Prospects

The challenges of supplying accurate tide corrections for satellite altimetry in shelf and near-coastal environments are reviewed. Relative to the deep ocean, tides in shallow water are generally larger and shorter wavelength. Nonlinearity further complicates tide prediction because of the multitude of additional compound tides and overtides that must be accounted for and because standard deep-ocean methods of inferring minor tides are inapplicable. Development of accurate shelf and coastal tide models with high spatial resolution requires assimilation of high-quality data; for most of the globe, the Topex/Poseidon and Jason time series constitutes the primary source. Data assimilation with nested high-resolution models tied to lower resolution global models appears feasible, but it places severe demands on the accuracy and resolution of bathymetry data. Some envisioned next-generation altimeter missions, capable of mapping the ocean topography at very high resolution, could relax these demands by providing direct tidal measurements at the requisite scales.

Assimilation of Ship-Mounted ADCP Data for Barotropic Tides: Application to the Ross Sea

The application of a generalized inverse approach for assimilating vessel-mounted acoustic Doppler current profiler (VM-ADCP) data into numerical solutions of barotropic tides is described. The derived estimates of tidal currents can be used to detide the VM-ADCP data and expose underlying mean circulation. The methodology is illustrated with data assimilation models of tidal currents in the Ross Sea. The prior solution, obtained by solving the nonlinear shallow-water equations by time stepping with a linear bottom friction parameterization and elevation of open boundary conditions obtained from a circumAntarctic tide model, provides reasonably good fit to most available moored current meter data. Two inverse solutions were obtained: one assimilating moored current meter records and the other assimilating three cruises of VM-ADCP data. Fitting either the mooring time series or the VM-ADCP records leads to only small changes relative to the prior solution currents, except over the shelf break where short length scale, energetic diurnal topographic vorticity waves are present. It is shown that the dynamics embedded in the representer functions provides reasonable tidal corrections even with no prior information about forcing at open boundaries.

Long-Period Tidal Variations in the Length of Day

A new model of long-period tidal variations in length of day is developed. The model comprises 80 spectral lines with periods between 18.6 years and 4.7 days, and it consistently includes effects of mantle anelasticity and dynamic ocean tides for all lines. The anelastic properties follow Wahr and Bergen; experimental confirmation for their results now exists at the fortnightly period, but there remains uncertainty when extrapolating to the longest periods. The ocean modeling builds on recent work with the fortnightly constituent, which suggests that oceanic tidal angular momentum can be reliably predicted at these periods without data assimilation. This is a critical property when modeling most long-period tides, for which little observational data exist. Dynamic ocean effects are quite pronounced at shortest periods as out-of-phase rotation components become nearly as large as in-phase components. The model is tested against a 20 year time series of space geodetic measurements of length of day. The current international standard model is shown to leave significant residual tidal energy, and the new model is found to mostly eliminate that energy, with especially large variance reduction for constituents Sa, Ssa, Mf, and Mt.

The Atlantic Water boundary current north of Svalbard in late summer

Data from a shipboard hydrographic/velocity survey carried out in September 2013 of the region north of Svalbard in the Nansen Basin are analyzed to characterize the Atlantic Water (AW) boundary current as it flows eastward along the continental slope. Eight meridional transects across the current, spanning an alongstream distance of 180 km, allow for a detailed description of the current and the regional water masses. During the survey the winds were light and there was no pack-ice. The mean section reveals that the boundary current was O(40 km) wide, surface-intensified, with a maximum velocity of 20 cm/s. Its mean transport during the survey was 3.11 ± 0.33 Sv, of which 2.31 ± 0.29 Sv was AW. This suggests that the two branches of AW entering the Arctic Ocean via Fram Strait—the Yermak Plateau branch and the Svalbard branch—have largely combined into a single current by 30°E. At this location the boundary current meanders with a systematic change in its kinematic structure during offshore excursions. A potential vorticity analysis indicates that the flow is baroclinically unstable, consistent with previous observations of AW anticyclones offshore of the current as well as the presence of a near-field cyclone in this data set. Our survey indicates that only a small portion of the boundary current is diverted into the Kvitoya Trough (0.17 ± 0.08 Sv) and that the AW temperature/salinity signal is quickly eroded within the trough.