Damien Allain

The FES2022 Global Tide Atlas represents a significant advancement in global tidal modelling, specifically designed to meet the high-resolution tidal correction requirements of modern altimetry missions like the Surface Water and Ocean Topography (SWOT) mission, which demand enhanced resolution and accuracy in the coastal seas. Building on the success of its predecessor FES2014, which performed well in most ocean regions but exhibited residuals issues in coastal, shelf, and polar areas, FES2022 introduces a tenfold increase in mesh resolution, prioritizing coastal and shelf regions. To some extent, this resolution aligns with SWOT’s KaRIn instrument capabilities, ensuring compatibility with its high-resolution ocean elevation measurements in shallow water regions. The bathymetry dataset is a composite of GEBCO_2020 and regional patches from other datasets, with a 2-meter depth threshold to better capture shallow coastal dynamics. The underlying hydrodynamic model (T-UGOm) includes both frequency-domain and time-stepping solvers, with the latter providing more accurate schemes for non-linearities in tides. Bottom friction and wave drag parameters were regionally calibrated. The model also incorporates atmospheric forcing from ERA5 to account for the radiational component of tides when relevant. The data assimilation process uses an ensemble Kalman filter with 358 members, generated by perturbing bathymetry, bottom friction, and wave drag. 16 tidal constituents were assimilated, along with 18 additional waves derived from time-stepping simulations. The assimilation was performed in two iterations (the second one resulting in the final FES2022b atlas) to incorporate the FES2022a Loading and Self-Attraction solution, enhancing the consistency between the model and the observations. The validation of FES2022b demonstrates substantial improvements over FES2014b and other state-of-the-art models. In the frequency domain, the Root Sum Square (RSS) errors for tidal elevations were reduced to 7.6 mm at altimetry crossovers in the deep ocean, 11.3 mm on shelves, and 42.3 mm at tide gauges compared to FES2014b. Temporal validation showed a variance reduction in Sea Surface Height (SSH) of -2.26 cm² for Jason-3 and -5.75 cm² for AltiKa when compared to FES2014b, with even greater reductions (-16.6 cm² for AltiKa) when compared to GOT4.10c. In polar regions, FES2022b significantly reduced the Sentinel-3A SSH variance in the Arctic (Baffin Bay, Siberian Shelf) and Antarctic (Ross and Weddell Seas). Coastal zones benefited from more than 40 cm² of variance reduction within 20 km of the shore. Tidal current validation using 119 current-meter stations showed a 56 % improvement compared to FES2014b, with a global RMSD of 2 cm/s for the major axis of tidal ellipses. GRACE gravity field residuals were also reduced, particularly around the Vancouver Island, from 10 cm to 3 cm EWE (Equivalent Water Elevation). Despite these advancements, some local residual errors persist due to bathymetry inaccuracies, shoreline misalignments, and limited high-latitude data coverage. These issues will be addressed in the future FES release. FES2022 is operational for altimetry de-aliasing corrections and available for download on the AVISO+ website, along with the prediction code on the CNES GitHub. Future improvements will focus on integrating latest bathymetry databases, refining shoreline databases, and enhancing high-latitude coverage of data assimilation through dedicated missions. The model’s unprecedented accuracy in coastal and polar regions makes it a recommended replacement for FES2014 in operational and scientific applications.

The impact of internal and barotropic tides on the vertical and horizontal temperature structure off the Amazon River was investigated during two highly contrasted seasons (AMJ: April–May–June; ASO: August–September–October) over a 3-year period from 2013 to 2015. Twin regional simulations, with and without tides, were used to highlight the general effect of tides. The findings reveal that tides have a cooling effect on the ocean from the surface (∼ 0.3 ^∘C) to above the thermocline (∼ 1.2 ^∘C), while warming it up below the thermocline (∼ 1.2 ^∘C). The heat budget analysis indicates that the vertical mixing is the dominant process driving temperature variations within the mixed layer, while it is associated with both horizontal and vertical advection to explain temperature variations below. The increased mixing in the simulations including tides is attributed to breaking of internal tides (ITs) on their generation sites over the shelf break and offshore along their propagation pathways. Over the shelf, mixing is driven by the dissipation of the barotropic tides. In addition, the vertical terms of the heat budget equation exhibit wavelength patterns typical of mode-1 IT. The study highlights the key role of tides and particularly how IT-related vertical mixing shapes the ocean temperature off the Amazon. Furthermore, we found that tides impact the interactions between the upper ocean interface and the overlying atmosphere. They contribute significantly to increasing the net heat flux between the atmosphere and the ocean, with a notable seasonal variation from 33.2 % in AMJ to 7.4 % in ASO seasons. This emphasizes the critical role of tidal dynamics in understanding regional-scale climate.

Tides and internal tides (IT) in the ocean can significantly affect local to regional ocean temperature and even sea surface temperature (SST), via processes such as vertical mixing, vertical advection and transport of water masses. Offshore of the Amazon River, IT have already been detected and studied; however, their impact on temperature, SST and associated processes are not known in this region. In this work, we use high resolution (1/36°) numerical simulations with and without the tides from an ocean circulation model (NEMO) which explicitly resolves the internal tides (IT), to assess how they can affect ocean temperature in the studied area. We distinguish the analysis for two contrasted seasons, from April to June (AMJ) and from August to October (ASO), since the seasonal stratification off the Amazon River modulates the IT’s response and their influence in temperature. The IT are well reproduced by the model, and are in good agreement with observations, for both their generation and their propagation. The simulation with tides is in better agreement with satellite SST data compared to the simulation without tides. During ASO season, stronger meso-scale currents, deeper and weaker pycnocline are observed in contrast to the AMJ season. Results show that the observed coastal upwelling during ASO season is well reproduced by the model including tides, whereas the no-tide simulation is too warm by +0.3 °C at sea surface. In the subsurface above the thermocline, the tide simulation is cooler by -1.2 °C, and warmer below the thermocline by +1.2 °C compared to the simulation without the tides. The study further highlights that the IT induce vertical mixing on their generation site along the shelf break and on their propagation pathways towards the open ocean. This process explains the cooler temperature at the ocean surface and in the subsurface water above the thermocline and a warming in the deeper layers (below the thermocline). The surface cooling induced in turn an increase of the net heat flux from the atmosphere to the ocean surface, which could induce significant changes in the local and even for the regional tropical Atlantic atmospheric circulation and precipitation. We therefore demonstrate that IT, mainly via vertical diffusivity along their propagation pathways of approximately 700 km offshore, and tides over the continental shelf, play a key role on the temperature structure off the Amazon River mouth, particularly in the coastal cooling enhanced by IT.

Thanks to its current accuracy and maturity, altimetry is considered as a fully operational observing system dedicated to various applications such as climate studies. Altimeter measurements are corrected from several geophysical parameters in order to isolate the oceanic variability and tide correction is one of the most critical. The accuracy of tidal models has been much improved for the last 25 years leading to centimetric accuracy in the open ocean. The last release of the global tidal model, referenced as FES2014b was distributed in mid-2016.The underlying unstructured mesh resolution of FES2014b was increased in areas of interest like shallow waters and on the slope of the continental shelves, and the error of the pure hydrodynamic ocean solution has been divided by a factor of 2 compared to the previous version (FES2004). Still, some significant errors remain in some regions, due to the omission of compound tides and bathymetric errors (in shelf/coastal seas), seasonal sea ice effects, and lack of available data for assimilation (in the high latitudes).To address the reduction of these errors and face the new challenges of the tide correction for HR altimetry, in particular, the forthcoming SWOT mission, a new global tide model FES2022 has been developed, focusing particularly on shallow waters and high latitudes.This new tidal solution uses higher spatial resolution in coastal areas, extending systematically the model mesh to the narrowest coastal systems (fjords, estuaries, …), and the model bathymetry has been upgraded in many places thanks to an international collaboration effort. The hydrodynamic modeling benefits also from further improvements which allow producing very accurate hydrodynamic simulations. The use of the most recent altimeter standards and high inclination altimeters like Cryosat-2, Saral/AltiKa, and even Sentinel-3, also allowed retrieving some tide observations in the highest latitudes to help improving the polar tides modeling. Results show a great improvement in the FES2022 hydrodynamic solution compared to FES2014’s one. The assimilation procedure was conducted, and a specific loading tide solution was produced. The final FES2022 tidal solution was validated in comparison to the FES2014b, EOT20, GOT, and TPXO9v5 models, for the missions Jason 3, Sentinel-3A, and Cryosat-2. Some validations of the new FES2022 tidal current are also presented here.

Tides and internal tides (IT) in the ocean can significantly affect local to regional ocean temperature, including sea surface temperature (SST), via physical processes such as diffusion (vertical mixing) and advection (vertical and horizontal) of water masses. Offshore of the Amazon River, strong IT have been detected by satellite observations and well modelled ; however, their impact on temperature, SST and the identification of the associated processes have not been studied so far. In this work, we use high resolution (1/36°) numerical simulations with and without the tides from an ocean circulation model (NEMO). This model explicitly resolves the internal tides (IT) and is therefore suitable to assess how they can affect ocean temperature in the studied area. We distinguish the analysis for two contrasted seasons, from April to June (AMJ) and from August to October (ASO), since the seasonal stratification off the Amazon River modulates the IT’s response and their influence in temperature. The generation and the propagation of the IT in the model are in good agreement with observations. The SST reproduced by the simulation including tides is in better agreement with satellite SST data compared to the simulation without tides. During ASO season, stronger meso-scale currents, deeper and weaker pycnocline are observed in contrast to the AMJ season. The observed coastal upwelling during ASO season is better reproduced by the model including tides, whereas the no-tide simulation is too warm by +0.3 °C for the SST. In the subsurface above the thermocline, the tide simulation is cooler by −1.2 °C, and warmer below the thermocline by +1.2 °C compared to the simulation without the tides. The IT induce vertical mixing on their generation site along the shelf break and on their propagation pathways towards the open ocean. This process mainly explains the cooler temperature at the ocean surface and is combined with vertical and horizontal advection to explain the cooling in the subsurface water above the thermocline and a warming in the deeper layers below the thermocline. The surface cooling induced in turn an increase of the net heat flux from the atmosphere to the ocean surface, which could induce significant changes in the local and even for the regional tropical Atlantic atmospheric circulation and precipitation. We therefore demonstrate that IT, via vertical mixing and advection along their propagation pathways, and tides over the continental shelf, can play a role on the temperature structure off the Amazon River mouth, particularly in the coastal cooling enhanced by the IT. Keywords: internal tides, Amazon continental shelf and slope, temperature, modeling, satellite data, mixing, heat flux.

Since the mid-1990s, a series of FES (finite element solution) global ocean tidal atlases has been produced and released with the primary objective to provide altimetry missions with tidal de-aliasing correction at the best possible accuracy. We describe the underlying hydrodynamic and data assimilation design and accuracy assessments for the latest FES2014 release (finalized in early 2016), especially for the altimetry de-aliasing purposes. The FES2014 atlas shows extremely significant improvements compared to the standard FES2004 and (intermediary) FES2012 atlases, in all ocean compartments, especially in shelf and coastal seas, thanks to the unstructured grid flexible resolution, recent progress in the (prior to assimilation) hydrodynamic tidal solutions, and use of ensemble data assimilation technique. Compared to earlier releases, the available tidal constituent's spectrum has been significantly extended, the overall resolution has been augmented, and additional scientific byproducts such as loading and self-attraction, energy diagnostics, or lowest astronomical tides have been derived from the atlas and are available. Compared to the other available global ocean tidal atlases, FES2014 clearly shows improved de-aliasing performance in most of the global ocean areas and has consequently been integrated in satellite altimetry geophysical data records (GDRs) and gravimetric data processing and adopted in recently renewed ITRF standards (International Terrestrial Reference System, 2020). It also provides very accurate open-boundary tidal conditions for regional and coastal modelling.

This study proposes a new methodology for implementing the barotropic tide in an ocean general circulation model (OGCM). The assumptions underlying this methodology are that the best barotropic tide solutions are computed by specialized models and that the fields that should be accurately reproduced by the OGCM are the transport fields from the specialized tide model. The target/reference solution for the OGCM is thus the projection of the tide model on the OGCM grid, for each tidal harmonic.The proposed methodology involves little change of the OGCM modeland yields almost exactly the reference solution, with a cost that is belowmost of the current methodologies. It relies on the modification of the tidepotential, or more accurately, on the replacement of all terms associatedwith the tide (tide potential, self attraction and loading, tide dissipation,  ...) by a general tide forcing term in the barotropic momentum equationwhich is calculated from the –known- reference solution.The tide forcing terms can be tricky to calculate as they depend on details of the OGCM numerical schemes (for both temporal and spatial operators). A general procedure, automatically adapting the chosen schemes, is proposed for their calculation, so that the procedure is independent of the model.  Tests with academic configurations are first proposed to validate the methodology and its implementation, and the OGCM is chosen to be the NEMO (Nucleus for European Modelling of the Ocean) model.A global ¼° configuration with realistic bathymetry and with FES tide solutions (Finite Element Solution) are then performed. Current tests show that when FES solutions are crudely interpolated on the NEMO grid, the methodology exactly reproduces the FES fluxes, but the associates NEMO SSH is very noisy in regions where FES has high resolution. This problem is currently addressed. To get rid of this problem, fluxes must be carefully integrated along each grid cell, so that the reproduced SSH is exactly an average of the FES SSH within the NEMO grid cell. Hopefully, we will be able to present final –clean- solutions at the conference.

Since the mid-1990’s, a series of Finite Element Solution (FES) global ocean tidal atlases has been produced and released with the primary objective to provide altimetry missions with tidal de-aliasing correction at the best possible accuracy. We describe the underlying hydrodynamic and data assimilation designs for the last FES2014 release (finalized in early 2016), and some accuracy assessments especially for the altimetry de-aliasing purposes. The FES2014 atlas shows extremely significant improvements compared to the FES2004 (Lyard et al. 2006) and (intermediary) FES2012 atlases, in all ocean regions, especially in shelf and coastal seas; these advances are due to the unstructured grid flexible resolution, recent progress in the (prior to assimilation) hydrodynamic tidal solutions and to the use of an ensemble data assimilation technique. Compared to earlier releases, the FES2014 available tidal constituents spectrum has been significantly extended, the overall resolution augmented; some new additional scientific by-products have been derived from the atlas and are available, including the loading and self-attraction effects, energy diagnostics or the lowest astronomical tides . Compared to the other available global ocean tidal atlases, FES2014 clearly shows improved de-aliasing performances in most of the global ocean areas. It has consequently been integrated in satellite altimetry and gravimetry data processing, and adopted in recently renewed ITRF standards. It also provides very accurate open boundary tidal conditions for regional and coastal modelling.

Intense equatorward western boundary currents transit the Solomon Sea, where active mesoscale structures exist with energetic internal tides. In this marginal sea, the mixing induced by these features can play a role in the observed water mass transformation. The objective of this paper is to document the M2 internal tides in the Solomon Sea and their impacts on the circulation and water masses, based on two regional simulations with and without tides. Since the Solomon Sea is under the influence of ENSO, the characteristics of the internal tides are also analyzed for two contrasted conditions: the January–March 1998 El Niño and the April–June 1999 La Niña. The generation, propagation, and dissipation of the internal tides are sensitive to changes in stratification and mesoscale activity, and these differ between these contrasted El Niño and La Niña case studies. Mode 1 is the dominant vertical mode to propagate baroclinic tidal energy within the Solomon Sea, but mode 2 becomes more energetic during the El Niño period when the stratification is closer to the surface. The La Niña period with a higher level of mesoscale activity exhibits more incoherent internal tides. These results illustrate the complexity of predicting internal tides in marginal seas in order to clearly observe meso- and submesoscale signatures from altimetric missions, including the future Surface Water Ocean Topography (SWOT) mission. Diapycnal mixing induced by tides contributes to a stronger erosion of the salinity maximum of the upper thermocline water and to cooling of the surface temperature interacting with the atmosphere. Such effects are particularly visible in quieter regions, where particles may experience the tidal effects over a longer time. However, when averaged over the Solomon Sea, the tidal effect on water mass transformation is an order of magnitude less than that observed at the entrance and exits of the Solomon Sea. These localized sites appear crucial for diapycnal mixing, since most of the baroclinic tidal energy is generated and dissipated locally here, and the different currents entering/exiting the Solomon Sea merge and mix. Finally, the extreme ENSO condition case studies suggest the strong role of local circulation changes, as well as stratification changes, in modifying the internal tides.

Consequences of tidal dynamics on hydro-sedimentary processes are a recurrent issue in estuarine and coastal processes studies, and accurate tidal solutions are a prerequisite for modeling sediment transport, especially in macro-tidal regions. The motivation for the study presented in this publication is to implement and optimize a model configuration that will satisfy this prerequisite in the frame of a larger objective in order to study the sediment dynamics and fate from the Red River Delta to the Gulf of Tonkin from a numerical hydrodynamical–sediment coupled model. Therefore, we focus on the main tidal constituents to conduct sensitivity experiments on the bathymetry and bottom friction parameterization. The frequency-domain solver available in the hydrodynamic unstructured grid model T-UGOm has been used to reduce the computational cost and allow for wider parameter explorations. Tidal solutions obtained from the optimal configuration were evaluated from tide measurements derived from satellite altimetry and tide gauges; the use of an improved bathymetry dataset and fine friction parameter adjustment significantly improved our tidal solutions. However, our experiments seem to indicate that the solution error budget is still dominated by bathymetry errors, which is the most common limitation for accurate tidal modeling.