Barotropic Tide Model Research Articles

A Barotropic Tide Model for Global Ocean Based on Rotated Spherical Longitude-Latitude Grids

Ocean modeling and simulation are important for understanding the dynamic processes in the geophysical system, and the simulation of tidal dynamics is of great significance for understanding the dynamic evolution of the ocean. However, there are some problems in existing simulations, including lack of specific standards to produce a desirable discrete spherical mesh for global ocean modelling. Many global ocean numerical models based on conventional longitude-latitude (LL) coordinates suffer from the “pole problem” in regions adjacent to the North Pole due to the convergence of meridians, which seriously hinders global ocean simulations. In this paper, a new longitude-latitude spherical grid coupled with rotated coordinate mapping is proposed to overcome the problem. In the design of the numerical model, for spatial approximation, the finite volume method on staggered C grid is proposed to solve the two-dimensional tidal wave equations for the global ocean. For temporal integration, the third-order Adams-Bashforth method is used to explicitly extrapolate the value on the next time interval half layer, and then the fourth-order implicit Adams-Moulton method is used to correct the water level. Finally, the constructed model is used to simulate the dynamics of two-dimensional tidal waves in the global ocean, and the co-tidal maps of two major diurnal tide and semidiurnal tide components are shown. The results demonstrate that the proposed model can support the simulation of tidal dynamics in the global ocean, especially for the Arctic Ocean.

An Assessment of Global Ocean Barotropic Tide Models Using Geodetic Mission Altimetry and Surface Drifters

AbstractThe 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 M2, S2, N2, K2, K1, O1, P1, and Q1. Variance reduction statistics for smaller tides are generally not accurate enough to differentiate the models’ performance.

Simultaneous Estimation of Ocean Tides and Underwater Topography in the Weddell Sea

AbstractA new model for the M2, S2, K1, and O1 tides in the Weddell Sea is developed by assimilating CryoSat‐2 data into a barotropic tide model. A variational approach is used, which explicitly allows for errors in the water depth, that is, the bottom topography in open water and the water column thickness under floating ice shelves, so that an optimized estimate of the topography is obtained together with the tidal fields. In preparation for assimilation, the sensitivity of the tidal elevation to the interfacial drag at the sea floor and the ice‐water interface (under the floating ice shelves) is investigated; this motivates the development of a new drag parameterization which is more accurate and physically plausible in comparison with the interfacial drag alone. The assimilation of CryoSat‐2 data into the model results in tidal elevations with essentially the same accuracy as previous estimates, which is demonstrated by comparisons with independent in situ data and withheld CryoSat‐2 data. The novelty of the present tidal estimates is that they are consistent with well‐defined dynamics based on the Laplace Tidal Equations—augmented with the new parameterization of drag—and modifications of the prior estimate of underwater topography and water column thickness. Analysis of the sensitivity to the topography finds that, at this level of precision, the topography is not uniquely determined by the observed data.

Analysis of tidal currents in the North Sea from shipboard acoustic Doppler current profiler data

North Sea tidal currents are determined by applying harmonic analysis to ship-borne acoustic Doppler current profiler data recorded from 1999 to 2016, covering large areas of the northern North Sea. Direct current measurement data sets of this magnitude are rare in the otherwise well investigated North Sea, and thus it is a valuable asset in studying and expanding our understanding of its tidal currents and circulation in general. The harmonic analysis is applied to a least squares fit of the current observations at a set of knot points. Results from the harmonic analysis compare favorably to tidal parameters estimated from observations from moored instruments. The analysis shows that the tides are characterized by strong semi-diurnal component, with amplitudes of the principal Lunar constituent ranging from 1.6 cm/s in the Skagerrak to 67 cm/s in the Fair Isle Channel. Diurnal tides are found to be approximately one fifth the strength of the predominant semi-diurnal constituent. Output from a regional barotropic tide model compares well to tidal current determined from the harmonic analysis of the Acoustic Doppler Current Profiler data.

The Influence of Subinertial Internal Tides on Near-Topographic Turbulence at the Mendocino Ridge: Observations and Modeling

AbstractShipboard measurements of velocity and density were obtained in the vicinity of a small channel in the Mendocino Ridge, where flows were predominantly tidal. Measured daily inequalities in transport are much greater than those predicted by a barotropic tide model, with the strongest transport associated with full depth flows and the weakest with shallow, surface-confined flows. A regional numerical model of the area finds that the subinertial K1 (diurnal) tidal constituent generates topographically trapped waves that propagate anticyclonically around the ridge and are associated with enhanced near-topographic K1 transports. The interaction of the baroclinic trapped waves with the surface tide produces a tidal flow whose northward transports alternate between being surface confined and full depth. Full depth flows are associated with the generation of a large-amplitude tidal lee wave on the northward face of the ridge, while surface-confined flows are largely nonturbulent. The regional model demonstrates that, consistent with field observations, near-topographic dissipation over the entire ridge is diurnally modulated, despite the semidiurnal tidal constituent having larger barotropic velocities. It is concluded that at this location it is the bottom-trapped subinertial internal tide that governs near-topographic dissipation and mixing. The effect of the trapped wave on regional energetics is to increase the fraction of converted barotropic–baroclinic tidal energy that dissipates locally.

日本沿岸潮流発電の資源量推定に対する潮流の長期変動の影響

Tidal currents have two types of intrinsic long-term fluctuations. The one is single tidal constituent such as Ssa and the other one is interferences between tidal constituents. The effect of the long-term fluctuation of tides on the resource assessment for tidal current energy generation system near Japan has been described based on the predictions using data-assimilative global barotropic tide model results. It is shown that monthly mean tidal energy flux varies by more than 20% over a year in the most of the prospective areas. The result indicates the intrinsic long-term fluctuations need to be considered in the resource assessment of tidal current power generation system.

Optimizing internal wave drag in a forward barotropic model with semidiurnal tides

A global tuning experiment for the semidiurnal tide is performed with a barotropic model. The model is forced with the M2 equilibrium tide and accounts for the self-attraction and loading (SAL) term. In addition to a quadratic drag, various linear internal wave drag terms adjusted by a scale factor of O(1) are applied. The drag terms include the original Nycander (2005) tensor scheme, the Nycander tensor scheme reduced at supercritical slopes, and their scalar sisters, a Nycander scalar scheme computed for additional abyssal hill roughness, and the Jayne and St. Laurent (2001) scalar scheme. The Nycander scheme does not have a tunable parameter, but to obtain the best tidal solutions, it is demonstrated that some tuning is unavoidable. It is shown that the scalar Nycander schemes yield slightly lower root-mean square (RMS) elevation errors vs. the data-assimilative TPXO tide model than the tensor schemes. Although the simulation with the optimally tuned original Nycander scalar yields dissipation rates close to TPXO, the RMS error is among the highest. The RMS error is lowered for the reduced schemes, which place relatively more dissipation in deeper water. The inclusion of abyssal hill roughness improves the regional agreement with TPXO dissipation rates, without changing the RMS errors. It is difficult to have each ocean basin optimally tuned with the application of a constant scale factor. The relatively high RMS error in the Atlantic Ocean is reduced with a spatially varying scale factor with a larger value in the Atlantic. Our best global mean RMS error of 4.4cm for areas deeper than 1000m and equatorward of 66° is among the lowest obtained in a forward barotropic tide model.

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.

Extracting tidal variability of sea ice concentration from AMSR‐E passive microwave single‐swath data: a case study of the Ross Sea

AbstractThe periodic divergence of stress applied by ocean tidal currents to sea ice affects the time‐averaged ice concentration (Cice) and heat and freshwater fluxes at the ocean surface. We demonstrate that, at sufficiently high latitudes, tidal variability in Cice can be extracted from single‐swath data from the Advanced Microwave Scanning Radiometer–EOS (AMSR‐E) satellite passive microwave sensor, although time intervals between swaths are irregular. For the northwest Ross Sea where tidal currents are large, tidal divergence is the dominant cause of Cice variability in winter, with a range of ±0.2 about a mean of ~0.8. Daily‐averaged Cice values vary from >0.9 at neap tides to ~0.7 at spring tides. Variability at the fundamental tidal periods is about half that expected from an inverse barotropic tide model for the Ross Sea, suggesting that the measured tidal signal in Cice may be used to diagnose sea ice mechanical properties and ice/ocean coupling.

Numerical Simulation of Barotropic Tides around Taiwan

A 1/12°, 2-D barotropic tide model was used to examine the characteristics of barotropic tides and to improve the accuracy of predicting tidal sea levels and currents in the seas around Taiwan. The form ratio suggests that tides are predominantly semidiurnal in the northern reaches of the Taiwan Strait and mixed of diurnal and semidiurnal elsewhere around Taiwan. When the dominant M2 wave enters the Strait from the north, its amplitude is magnified to ~2 m in the middle, and then decreases rapidly toward the south end of the Strait. The predominance of diurnal tides along the southwest to the south coast of Taiwan is attributed to the quasi-resonance of diurnal waves in the South China Sea. The tidal range is small and tidal currents are weak off the east coast of Taiwan. Barotropic tidal energy is mostly dissipated on the shallow banks of the southwestern Strait. Results summarized from sensitivity tests on the bottom drag coefficient (CD) and horizontal eddy viscosity (AM) indicate that CD = 0.0015 - 0.00175 and AM = 150 m 2 s -1 lead to the best model-data fit when compared to the observed tidal sea levels at ten reference tide-gauge stations around Taiwan. The averaged root-mean-squared (RMS) differences of the simulated tidal sea level for the six principal constituents of O1, P1, K1, N2, M2, and S2 are significantly reduced to 1.3, 0.7, 2.0, 1.6, 5.1, and 3.1 cm, respectively, compared to that calculated from a 0.5° resolution global tide harmonic constant database, NAO.99b (Matsumoto et al. 2000). The averaged RMS differences of barotropic tidal currents (U, V) for O1, K1, M2, and S2 are (0.92, 1.64), (1.17, 0.61), (3.88, 2.37), and (1.52, 1.20) cm s -1 . A database of tidal sea levels and current harmonic constants,

Tidal signals in basin-scale acoustic transmissions

Travel times of acoustic signals were measured between a bottom-mounted source near Oahu and five bottom-mounted receivers located near Washington, Oregon, and California in 1988 and 1989. This paper discusses the observed tidal signals. At three out of five receivers, observed travel times at M2 and S2 periods agree with predictions from a barotropic tide model to within ±30° in phase and a factor of 1.6 in amplitude. The discrepancies at the fourth and fifth receivers can largely be accounted for with a simple model for the generation of baroclinic tides by interactions between the barotropic tides and guyots in the Moonless mountains. These baroclinic tides are phase locked to the astronomical tide-generating forces. A simple model is used to estimate the conversion of energy from barotropic to baroclinic tides by the world’s seamounts. At M2, the conversion amounts to about 1×1018 erg s−1, or about 4% of the total dissipation at M2. Although this estimate is very approximate, it is similar to other published values.

Tidal signals in basin-scale acoustic transmissions

Travel times of acoustic signals were measured between a bottom-mounted source near Oahu and five bottom-mounted receivers located near Washington, Oregon, and California in 1988 and 1989. At three out of five receivers, observed travel times at M2 and S2 periods agree with predictions from a barotropic tide model to within 30 deg in phase and a factor of 1.6-in. amplitude. The discrepancies at the fourth and fifth receivers can be removed, to first order, by including predicted effects of phase-locked baroclinic tides generated by guyots in the Moonless mountains. A simple model is used to estimate the conversion of energy from barotropic to baroclinic tides by the world’s seamounts. At M2, the conversion amounts to about 4% of the total dissipation at M2. Although this estimate is very approximate, it is similar to other published values.