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Abstract Through the implementation of a streaming filter, output of numerical ocean simulations can be band‐pass filtered at tidal frequencies while the model is running, yielding time series of sinusoidal motions consisting of tidal signals in the filter's target frequency band. The filtering algorithm is developed from a system of two ordinary differential equations that represents the motion of a damped harmonic oscillator. The filter's response to a broadband input signal is unity at its target frequency but vanishes toward the low and high frequency limits. The decay of the filter response is controlled by a dimensionless parameter, which determines the filter's bandwidth. As a result, the filter allows signals within a small frequency band around its target frequency to pass through, while blocking signals outside of its target frequency band. In this work, the filtering algorithm is implemented into the barotropic solver of the Modular Ocean Model version 6 (MOM6) for determining the instantaneous tidal velocities of the semi‐diurnal and diurnal tides. Utilizing the filters, the frequency‐dependent internal wave drag is applied to the semi‐diurnal and diurnal frequency bands separately. The simulation results suggest that the performance of the algorithm is consistent with the filter transfer function in Fourier space. Potential applications of the algorithm also include de‐tiding the model output for nested regional ocean models, especially those for the purpose of operational forecasting. 

Abstract Internal waves generated by the interaction of the surface tides with topography are known to propagate long distances and lead to observable effects such as sea level variability, ocean currents, and mixing. In an effort to describe and predict these waves, the present work is concerned with using geographically distributed data from satellite altimeters and drifting buoys to estimate and map the baroclinic sea level associated with the M₂, S₂, N₂, K₁, and O₁tides. A new mapping methodology is developed, based on a mixedL₁/L₂-norm optimization, and compared with previously developed methods for tidal estimation from altimeter data. The altimeter and drifter data are considered separately in their roles for estimating tides and for cross-validating estimates obtained with independent data. Estimates obtained from altimetry and drifter data are found to agree remarkably well in regions where the drifter trajectories are spatially dense; however, heterogeneity of the drifter trajectories is a disadvantage when they are considered alone for tidal estimation. When the different data types are combined by using geodetic mission altimetry to cross validate estimates obtained with either exact-repeat altimetry or drifter data, and subsequently averaging the latter estimates, the estimates significantly improve on the previously published HRET8.1 model, as measured by their utility for predicting sea level and surface currents in the open ocean. The methodology has been applied to estimate the annual modulations of M₂, which are found to have much smaller amplitudes compared to those reported in HRET8.1, and suggest that the latter estimates of these tides were not reliable. Significance StatementThe mechanical and thermodynamic forcing of the ocean occurs primarily at very large scales associated with the gravitational perturbations of the sun and moon (tides), atmospheric wind stress, and solar insolation, but the frictional forces within the ocean act on very small scales. This research addresses the question of how the large-scale tidal forcing is transformed into the smaller-scale motion capable of being influenced by friction. The results show where internal waves are generated and how they transport energy across ocean basins to eventually be dissipated by friction. The results are useful to scientists interested in mapping the flows of mechanical energy in the ocean and predicting their influences on marine life, ocean temperature, and ocean currents. 

Abstract The geographical variability, frequency content, and vertical structure of near‐surface oceanic kinetic energy (KE) are important for air‐sea interaction, marine ecosystems, operational oceanography, pollutant tracking, and interpreting remotely sensed velocity measurements. Here, KE in high‐resolution global simulations (HYbrid Coordinate Ocean Model; HYCOM, and Massachusetts Institute of Technology general circulation model; MITgcm), at the sea surface (0 m) and at 15 m, are compared with KE from undrogued and drogued surface drifters, respectively. Global maps and zonal averages are computed for low‐frequency (<0.5 cpd), near‐inertial, diurnal, and semidiurnal bands. Both models exhibit low‐frequency equatorial KE that is low relative to drifter values. HYCOM near‐inertial KE is higher than in MITgcm, and closer to drifter values, probably due to more frequently updated atmospheric forcing. HYCOM semidiurnal KE is lower than in MITgcm, and closer to drifter values, likely due to inclusion of a parameterized topographic internal wave drag. A concurrent tidal harmonic analysis in the diurnal band demonstrates that much of the diurnal flow is nontidal. We compute simple proxies of near‐surface vertical structure—the ratio 0 m KE/(0 m KE + 15 m KE) in model outputs, and the ratio undrogued KE/(undrogued KE + drogued KE) in drifter observations. Over most latitudes and frequency bands, model ratios track the drifter ratios to within error bars. Values of this ratio demonstrate significant vertical structure in all frequency bands except the semidiurnal band. Latitudinal dependence in the ratio is greatest in diurnal and low‐frequency bands. 

This dataset of Harmonic Constants for Baroclinic Tide Prediction was produced by Edward Zaron (Oregon State University) and Shane Elipot (University of Miami). It provides sea surface height and ocean surface currents associated with the predictable astronomical tide at the M2, S2, N2, K1, and O1 frequencies. The tidal harmonic constants, in-phase and quadrature with respect to the equilibrium potential, are provided on a latitude/longitude at 1/20-deg resolution. Using the software available at the Github repository, the dataset can be used to predict baroclinic tidal sea surface height and surface ocean currents at arbitrary time and location throughout the world oceans. 

Abstract The accuracy of three data-constrained barotropic ocean tide models is assessed by comparison with data from geodetic mission altimetry and ocean surface drifters, data sources chosen for their independence from the observational data used to develop the tide models. Because these data sources do not provide conventional time series at single locations suitable for harmonic analysis, model performance is evaluated using variance reduction statistics. The results distinguish between shallow and deep-water evaluations of the GOT410, TPXO9A, and FES2014 models; however, a hallmark of the comparisons is strong geographic variability that is not well summarized by global performance statistics. The models exhibit significant regionally coherent differences in performance that should be considered when choosing a model for a particular application. Quantitatively, the differences in explained SSH variance between the models in shallow water are only 1%–2% of the root-mean-square (RMS) tidal signal of about 50 cm, but the differences are larger at high latitudes, more than 10% of 30-cm RMS. Differences with respect to tidal currents variance are strongly influenced by small scales in shallow water and are not well represented by global averages; therefore, maps of model differences are provided. In deep water, the performance of the models is practically indistinguishable from one another using the present data. The foregoing statements apply to the eight dominant astronomical tides M 2 , S 2 , N 2 , K 2 , K 1 , O 1 , P 1 , and Q 1 . Variance reduction statistics for smaller tides are generally not accurate enough to differentiate the models’ performance.