During the 1990s, a large number of new tidal atlases were developed, primarily to provide accurate tidal corrections for satellite altimetry applications. During this decade, the French tidal group (FTG), led by C. Le Provost, produced a series of finite element solutions (FES) tidal atlases, among which FES2004 is the latest release, computed from the tidal hydrodynamic equations and data assimilation. The aim of this paper is to review the state of the art of tidal modelling and the progress achieved during this past decade. The first sections summarise the general FTG approach to modelling the global tides. In the following sections, we introduce the FES2004 tidal atlas and validate the model against in situ and satellite data. We demonstrate the higher accuracy of the FES2004 release compared to earlier FES tidal atlases, and we recommend its use in tidal applications. The final section focuses on the new dissipation term added to the equations, which aims to account for the conversion of barotropic energy into internal tidal energy. There is a huge improvement in the hydrodynamic tidal solution and energy budget obtained when this term is taken into account.

https://hpiers.obspm.fr/combinaison/documentation/articles/Modelling_Ocean_Tides_Lyard_FES2004.pdf

Modelling the global ocean tides: modern insights from FES2004

The Multi-GNSS Experiment (MGEX) of the International GNSS Service (IGS) - Achievements, prospects and challenges

[1] A global simulation of the ocean response to atmospheric wind and pressure forcing has been run during the Topex/Poseidon (T/P) period (1992–2002), using a new hydrodynamic finite element (FE) model, MOG2D-G. Model outputs are compared to in situ observations with tide gauge data (TG) and bottom pressure gauge data (BPR), and also with T/P altimetric cross over points (noted CO). Intercomparisons were performed over the 1993–1999 period. The model correction reduces the sea level variance by more than 50% at TG locations, and by more than 15% at T/P CO, when compared to the classical inverse barometer correction (IB). The model impact differs between high and low latitudes: in the very energetic high latitudes areas, MOG2D-G is efficient in reducing the variance, while at low latitudes, the results are similar to the IB static response. In shallow water, the model shows an oceanic response very different from the IB response. In conclusion, MOG2D-G models the high frequency (HF) atmospheric forced variability of the global ocean with unprecedented accuracy.

/pdf/modeling-the-barotropic-response-of-the-global-ocean-to-3101cvrpsd.pdf

Modeling the barotropic response of the global ocean to atmospheric wind and pressure forcing - comparisons with observations

We present a new global model of plate motions and strain rates in plate boundary zones constrained by horizontal geodetic velocities. This Global Strain Rate Model (GSRM v.2.1) is a vast improvement over its predecessor both in terms of amount of data input as in an increase in spatial model resolution by factor of ∼2.5 in areas with dense data coverage. We determined 6739 velocities from time series of (mostly) continuous GPS measurements; i.e., by far the largest global velocity solution to date. We transformed 15,772 velocities from 233 (mostly) published studies onto our core solution to obtain 22,511 velocities in the same reference frame. Care is taken to not use velocities from stations (or time periods) that are affected by transient phenomena; i.e., this data set consists of velocities best representing the interseismic plate velocity. About 14% of the Earth is allowed to deform in 145,086 deforming grid cells (0.25° longitude by 0.2° latitude in dimension). The remainder of the Earth's surface is modeled as rigid spherical caps representing 50 tectonic plates. For 36 plates we present new GPS-derived angular velocities. For all the plates that can be compared with the most recent geologic plate motion model, we find that the difference in angular velocity is significant. The rigid-body rotations are used as boundary conditions in the strain rate calculations. The strain rate field is modeled using the Haines and Holt method, which uses splines to obtain an self-consistent interpolated velocity gradient tensor field, from which strain rates, vorticity rates, and expected velocities are derived. We also present expected faulting orientations in areas with significant vorticity, and update the no-net rotation reference frame associated with our global velocity gradient field. Finally, we present a global map of recurrence times for Mw=7.5 characteristic earthquakes.

A geodetic plate motion and Global Strain Rate Model

As continental ice from Antarctica reaches the grounding line and begins to float, its underside melts into the ocean. Results obtained with satellite radar interferometry reveal that bottom melt rates experienced by large outlet glaciers near their grounding lines are far higher than generally assumed. The melting rate is positively correlated with thermal forcing, increasing by 1 meter per year for each 0.1°C rise in ocean temperature. Where deep water has direct access to grounding lines, glaciers and ice shelves are vulnerable to ongoing increases in ocean temperature.

/pdf/rapid-bottom-melting-widespread-near-antarctic-ice-sheet-195vczq4dl.pdf

Rapid Bottom Melting Widespread near Antarctic Ice Sheet Grounding Lines

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.

/pdf/fes99-a-global-tide-finite-element-solution-assimilating-3hi1h34r4j.pdf

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

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.

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 new version of the FES hydrodynamic finite element tide model combined with a revised data assimilation procedure is now available. The CEFMO hydrodynamic model previously used to obtain the solution FES94.1 was improved and the assimilation method based on the representer approach was revised. A careful selection of in situ tide gauge data from different data banks allowed us to build a collection of about 700 data values for each of the eight computed waves (M2, S2, N2, K2, 2N2, K1, O1 and Q1), which were assimilated. Eighteen other constituents of the tide spectrum were derived by admittance and three long period waves were added. Referred to as FES98, these new solutions are available on a 0.25° × 0.25° gridded version of the full finite element solutions. This paper presents these new FES solutions and proposes a brief analysis of the improvements of the new approach with respect to the former FES94.1 and FES95.2.1 solutions.

https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/1999GL011315

Fabien Lefevre

Papers

Modelling the global ocean tides: modern insights from FES2004

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

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

FES98: A new global tide finite element solution independent of altimetry