Florent Lyard

Spectroscopy of the world ocean tides from a finite element hydrodynamic model

An atlas of the main components of the tides has been produced on the basis of a finite element hydrodynamic model, with the aim of offering the scientific community, using satellite altimetric data, a prediction of the tidal contribution to sea surface height variations under the ground tracks of the satellites that is totally independent of altimetric measurements. The geographic coverage of the simulations only excludes, temporarily, some marginal seas like the Bay of Fundy. But the design of the model, based on a nonlinear formulation of the shallow water equations, could enable the simulations to be extended to these very singular areas. On the other hand, the Arctic Basin and the Antarctic Circumpolar Basin have been fully resolved, including the under-ice shelf areas of the Weddell Sea and the Ross Sea. Eight constituents, M2, S2, N2, K2, 2N2, K1, O1, and Q1 have been simulated. Five secondary constituents: Mu2, Nu2, L2, T2, and P1, required to insure a priori correct predictions, have been deduced by admittance. The accuracy and precision of these solutions have been estimated by reference to the harmonic constituents data set available from analysis of the entire collection of pelagic, plateau and coastal observations made to date, and archived by International Association for Physical Sciences of the Oceans and International Hydrographie Bureau. Over the deep oceans, these solutions fit the observations to within a few centimeters for the larger components: M2, S2, K1, O1, and a few millimeters for the others, in RMS maximum difference to a standard set of 78 ground truth stations. Over the shelves, the differences are larger, because of the increase in amplitude of the tidal waves, but the flexibility offered by the finite element technique to refine the discretization mesh of the model over the shallow seas enables detailed cotidal maps to be produced along the coasts. One zoom on South Georgia Island, in the South Atlantic Ocean, is presented as an illustration. Finally, the performances of the tidal predictions made on the basis of this new set of solutions was tested by looking at the residual RMS differences at the crossover points of sea level measurements supplied by the TOPEX/POSEIDON mission, when using these predictions. This test provided confirmation of most of the conclusions already drawn on the basis of the previous comparisons with in situ tide gauge data.

A hydrodynamic ocean tide model improved by assimilating a satellite altimeter‐derived data set

An upgraded version of the tidal solutions (FES94.1) is presented, obtained by assimilating an altimeter-derived data set in the finite element hydrodynamic model, following the representer approach. The assimilated data are drawn from the CSR2.0 Texas solutions sampled on a 5° × 5° grid. The assimilation is applied over the Atlantic, Indian, and Pacific Oceans. The standard release of the new FES95.2 solutions is a 0.5° × 0.5° gridded version of the full finite element solutions. The associated tidal prediction model includes 26 constituents. The eight major constituents are drawn directly from the hydrodynamic model: K1, O1, Q1, M2, S2, N2, K2, and 2N2, corrected by assimilation except K2 and 2N2. The other 18 constituents are derived by admittance. Among them are μ2, ν2, L2, T2, M1, P1, J1, and OO1. The quality of these solutions is evaluated by reference to a standard sea truth data set of 95 stations. This quality is significantly improved after the assimilation process is applied: the root-sum-square (RSS) of the differences between solutions and observations, for the eight major constituents, is reduced from 3.8 cm for FES94.1 to 2.8 cm for FES95.2, i.e., a gain of 1 cm. The performances of the prediction model are evaluated by comparing tidal predictions with observations at 59 sites distributed over the world ocean and by looking at the level of variance of the sea surface variability observed by the T/P altimeter at its cross-over track points after tidal correction. These evaluations lead to the same conclusion: this new prediction model performs much better than the one based on FES94.1, because of correction of the major constituents by T/P data assimilation and because of the increase in the number of constituents from 13 to 26. The tidal predictions are at the level of accuracy of those produced by the best recent T/P empirical models.

FES99: A Global Tide Finite Element Solution Assimilating Tide Gauge and Altimetric Information

An improved version of the global hydrodynamic tide solutions [finite element solutions (FESs) FES94, FES95.2.1, and FES98] has been developed, implemented, and validated. The new model is based on the resolution of the tidal barotropic equations on a global finite element grid without any open boundary condition, which leads to solutions independent of in situ data (no open boundary conditions and no assimilation). The accuracy of these ‘‘free’’ solutions is improved by assimilating tide gauge and TOPEX/Poseidon (T/P) altimeter information through a representer assimilation method. This leads to the FES99 version of this model. For the eight main constituents of the tidal spectrum (M 2 ,S 2 ,N 2 ,K 2 ,2 N 2 ,K 1 ,O 1, and Q1), about 700 tide gauges and 687 T/P altimetric measurements are assimilated. An original algorithm is developed to calculate the tidal harmonic constituents at crossover points of the T/P altimeter database. Additional work is performed for the S2 wave by reconsidering the inverse barometer correction. To complete the spectrum, 19 minor constituents have been added by admittance. The accuracy of FES99 is evaluated against the former FESs. First, it is compared to two tide gauge datasets: ST95 (95 open-ocean measurements) and ST739 (739 coastal measurements). For ST95, the root-sum square of the differences between observations and solutions is reduced from 2.8 (FES95.2.1) to 2.4 cm (FES99), a gain of 17% in overall accuracy. Second, the variance of the sea surface variability is calculated and compared for FES95.2.1, FES98, and FES99 at the T/P and the European Remote Sensing Satellite (ERS-2) crossover data points. FES99 performed best, with a residual standard deviation for the independent ERS-2 dataset of 13.5 cm (15.2 cm for FES95.2.1). Third, tidal predictions are implemented for the FESs to provide along-track estimates of the sea surface variability for T/P and ERS-2. Compared to ERS-2, FES99 residuals are 11.8 cm (12.4 cm for FES95.2.1). All the accuracy tests show that FES99 is a significant improvement compared to former FESs both in the deep ocean and along coasts.

How can we improve a global ocean tide model at a regional scale? A test on the Yellow Sea and the East China Sea

A global ocean model has been developed within the context of TOPEX/Poseidon (T/P) on the basis of a finite element hydrodynamic modeling approach combined with data assimilation based on the representer method. The solution produced at global scale represents a spectacular improvement over what was available before the era of T/P. Typically, the mean discrepancy between the main tidal components and a hundred in situ tide gauges is 1.7 cm for M2 and 1 cm or less for the other components. However, the accuracies of this solution and of that produced by different authors within the T/P tide working group are all worse near coastlines and over continental shelves. This is the case for our finite element solution (FES) FES94.1 solution over the Yellow Sea and the East China Sea (YS-ECS) where the discrepancy is 33 cm for the M2 tide and 9 cm for the K1 tide when compared to a set of 192 tide gauges distributed along the coastlines. This is due largely to the complex geometry of the basin and the limited knowledge of the bathymetry. The aim of this paper is to investigate how our FES model can be improved with a dedicated application focused on one of the most energetic coastal basins: the YS-ECS (∼180 Gigawatts for M2, i.e. 8% of the global energy dissipated in the whole ocean). For this application, a finite grid was implemented with a resolution down to 5 km along the coasts and over the continental shelf break. Particular attention was paid to bathymetry by complementing the ETOP05 database with regional maps. Sensitivity tests to the tuning of the bottom friction and the nonlinear interactions between the diurnal and semidiurnal components allow us to investigate the impact of dissipation parameterization and to produce an optimal solution, without any data assimilation, for nine main components of the tidal spectrum (improvement by a factor of 2). M2 distance to the observations is now ∼17.5 cm (global variance of 92 cm), and K1 is 4 cm (global variance of 21 cm). As nonlinear components are significant over these basins, the two main quarterdiurnal components are calculated. The improvements are explained by five points: (1) the choice of a mixed friction, (2) a refinement of the mesh, (3) a choice of reliable boundary conditions, (4) a refined topography and, (5) the use of a specific friction coefficient 1.5×10−3. Surprisingly, the energy budget for the M2 component leads to a dissipation similar to the value estimated by the global FES94.1. This is a major result of this study, which leads us to the conclusion that when forcing a regional model with sea level boundary conditions along the open limits, the simulated velocity field adjusts to the tuning of friction coefficients in order to dissipate the same amount of energy made available at its open boundaries.

Spreading of the Western Mediterranean Deep Water after winter 2005: Time scales and deep cyclone transport

This work is dedicated to the study of the propagation of the Western Mediterranean Deep Water (WMDW) formed in the Gulf of Lions during the exceptional winter 2005. A simulation of the 1998-2008 period has been carried out with an eddy-resolving Ocean General Circulation Model of the Mediterranean Sea, driven by interannual high-resolution air-sea fluxes. This study first presents a validation of the recently improved model configuration against satellite observations. Then, we assess the ability of the model to reproduce the particularly intense deep convection event of winter 2005 in the Gulf of Lions. A huge volume of very dense water is formed in the simulations at that time (annual formation rate of about 3 Sv). The thermohaline characteristics of the new WMDW allow a monitoring of its deep propagation. We identify several deep cyclones as mainly responsible of the fast spreading of the WMDW southwards in the Western Mediterranean. By comparing Eulerian and Lagrangian approaches, we estimate different transport times of the WMDW by these cyclonic eddies and compare them to those deduced from several observations. Finally, we argue that these cyclones favour the propagation of the WMDW thermohaline characteristics towards the Channel of Sardinia and decrease the volume of WMDW which can reach the Strait of Gibraltar.

Energetics of the M2 barotropic ocean tides: an estimate of bottom friction dissipation from a hydrodynamic model

Abstract The aim of this paper is to present a detailed energy budget of the M2 ocean tides over the world ocean, based on the hydrodynamic tidal solution FES94.1 which includes not only the characteristics of the sea surface tidal elevations, but also of the tidal currents. Global and regional budgets are given. The global energy input by astronomical forcing, deduced from the (2,2) spherical harmonic development of the M2 sea surface elevation solution, is 2.35 TW (lower by 0.1 TW than for the new altimetric solutions produced recently directly from satellite observations). One major feature emerging from the present analysis is that a quarter of this energy input takes place over the South Atlantic Ocean. On the other hand, ocean tides work against astronomical forcing over three areas: Eastern Indian Ocean, southwest of the South American Continent, and around New Zealand. This energy is dissipated (in FES94.1) by bottom friction over the main continental shelves, but the outstanding feature is that 40% of the tidal energy is dissipated over the North Atlantic Ocean. Energy is thus redistributed from the areas of energy input to feed the areas of dissipation. The Pacific Ocean, the Indian Ocean and the South Atlantic Ocean receive more energy in total than they dissipate, in contrast with the Atlantic Ocean and the Arctic Ocean, where a large deficit must be compensated by a net influx of energy from the other basins. One third of the total M2 energy input by astronomical forcing over the world ocean flows northwards through the Equatorial Atlantic. Detailed energy dissipation estimates are computed over the different areas of energy dissipation and compared to the previous estimates published in the literature.

On the statistical stability of the M2 barotropic and baroclinic tidal characteristics from along‐track TOPEX/Poseidon satellite altimetry analysis

An along-track analysis of 7 years of TOPEX/Poseidon (T/P) data has been performed on the global ocean over the period 1993-1999. Such long time series allow us to determine the semidiurnal tidal component very accurately, while resolving the aliasing problems, at least for the main tidal wave M2. As already inferred by other authors, this along-track analysis detects the surface signatures of the internal tides signal that maintains coherence with the M2 astronomical forcing. By analyzing the T/P data in different periods of 3 years or more, the stability of the M2 tidal characteristics is demonstrated for the barotropic component as well as for the baroclinic signal observed in the altimetric data. This stability varies with location. For the barotropic component the dispersion of the results as a function of the length and period of analysis is only significant over the areas of ocean mesoscale activity (noise impact) and of large barotropic tidal signal (separating the different components of the tidal signal proves difficult). The baroclinic tidal signal appears to be surprisingly stable over many areas located around strong topographic gradients like submarine ridges. A methodology has been developed to draw a map of these areas. This can be of help for ocean modelers to specify areas of higher vertical mixing associated with internal tidal wave activity and for those who assimilate altimetric data in their models by giving guidance on where to increase the uncertainty of the altimeter data over these areas.

Barotropic tides of the Southern Indian Ocean and the Amery Ice Shelf cavity

The 8 main tidal constituents were computed using a finite element, hydrodynamic ocean tide model over the South Indian Ocean region. The discretization of the domain is of the order of 100 km over the deep ocean and a few hundred meters near the coast. Such refinement in the grid resolution enables wave propagation and damping on the continental shelves to be solved correctly. The model used the GEBCO 1-minute global bathymetric grid which was improved with updated topographic data. The model solutions show good agreement with in-situ observations and Topex-Poseidon altimeter measurements and are significantly better than previously published solutions. We obtain a combined standard deviation of 1.4 cm for differences of our new regional model against independent observations compared to about 2.5 cm for the other tide models. The greatest improvements are found around the Kerguelen Islands, around Antarctica and beneath the Amery Ice Shelf and can be explained by the high grid resolution used and the particular attention given to the accuracy of the bathymetry in those regions.

Improving ocean tide predictions by using additional semidiurnal constituents from spline interpolation in the frequency domain

The improvement in accuracy that can be obtained by increasing the number of constituents in the model at present used for tidal height corrections in the GDRs of satellite altimetric measurements is analysed by referring to the performance of the Harmonic Method in predicting tides at a selected number of locations in the world where observations of sea level variations are available. Given the interest in such improvements, a way of extending the existing data set is proposed, without the need to run a new model of the worlds oceans: the method relies on the concept of admittance. Worlds oceans maps are derived for five additional constituents, and the differences in predicted heights resulting from these improvements are evaluated.

The tides in the Arctic Ocean from a finite element model

The two main diurnal (i.e., K1 and O1) and semidiurnal (i.e., M2 and S2) tidal waves have been computed from a hydrodynamic, finite element, spectral model. The spatial resolution of the model varies from a few kilometers at the coastline to 100 km in the deepest regions. An optimization of the open boundary conditions has been performed to improve the solution accuracy. The bottom topography used in this model has been originally extracted from the Earth Topography 5-minutes Grid (ETOPO5) and corrected from various sources of data. The impact of the input parameters like the friction coefficient, the loading effects, and the parameterisation of the additional friction due to the Arctic ice cover is investigated. The tidal elevations are compared to a set of in situ observations and validated. They also are compared to the Kowalik and Proshutinsky [1993] model. These comparisons mainly show good agreement between the two models. Nevertheless, significant differences are observed where small wavelength structures are produced by the topographic trapping of the tidal energy. The velocities associated with the elevations are also presented. The potential rate of work, the dissipation, and the energy fluxes are computed from these elevations and velocities. Because of the uncertainties of the velocities at the open boundaries, we are restricted to a qualitative analysis of the energy equation terms, which appears to be consistent with the previous studies on Arctic tides.