dataesr/scientific-paragraphs-categorization huggingface dataset:
Model grid settings Since the first truly global ocean atlas (FES2004), the unstructured FES model mesh has been upgraded by using regional patches. The main meshing difficulty consists in dealing with the shoreline details. Present databases 15 contain a high level of coastal details, much more than needed for a global ocean mesh, and that consequently need to be filtered out. Reversely, it is necessary to maintain and assemble together some packets of microislands that will form a macro-obstacle to the tidal propagation. Considering the tedious task of re-meshing most of the ocean shorelines, automated tools have been developed to optimize the meshing operation. The targeted resolution for coastal areas is 10 kilometers or less in terms of triangle side-length (Figure  1 ). The resolution has 20 been augmented to about 1.
Model bathymetry When dealing with tides, bathymetry remains one of the most critical parameters. Several global ocean databases 30 were available at the FES2014 production time (GEBCO, ETOPO, Smith&Sandwell) and their successive releases have shown tremendous improvements during the last ten years. Unfortunately, none of those global databases have the effective resolution nor the accuracy needed to be used directly in our global ocean tides modelling. As for the earlier FES atlases, a composite bathymetry has been built from available global and regional databases. In some cases, a regional digital terrain model (DTM) has been specifically constructed from 35 depth sounding and/or multi-beam data. A special treatment is applied to the Ross and Weddell seas, where the free water column depth must be processed by substracting ice-shelf immersion to the bottom topography, using the RTOPO1 dataset  (Timmermann et al.
). Many regions of the world ocean are now quite well documented in terms of bathymetry, however two major continental shelves, namely the Patagonian shelf and the Siberian shelf, do not match modern standards in any publically available database. Bathymetry selection, reconstruction and 40 merge is a tedious task, and quite uncertain because of the lack of independent validation data. Finally, the most practical way to assess bathymetry changes remains the examination of the tidal solutions computed from the https://doi. org/10. 5194/os-2020-96 Preprint. Discussion started: 16 October 2020 c Author(s) 2020. CC BY 4. 0 License. candidate bathymetry. Naturally this is not a perfect measure of accuracy, as errors in bathymetry can 5 compensate some other modelling errors, but so far we always found consistent results between improvements in bathymetry and tidal solutions.
FES2014 hydrodynamic (assimilation-free) solutions Some parameters of the T-UGOm hydrodynamic model need to be calibrated in order to obtain the most accurate hydrodynamic solution, either to improve model realism or provide useful error compensation. The two main parameters to which the model is the most sensitive are the bottom friction coefficient and the internal tide drag coefficient. Several simulations of the main tidal components (limited to M2, K1, S2 and O1 constituents) have 25 been performed by extensively varying these two parameters, and each resulting simulation was compared to the altimetry and tide gauge validation databases. Figure  2  and Figure  3  show the vector differences between the TPJ1J2 (deep ocean) crossover point database and the hydrodynamic simulations of the FES2004 and FES2014 tidal models, for the M2 and K1 tidal components, respectively.
Several tidal gauges databases have been used within the FES2014 project: a harmonic analysis was 15 performed on time series from GLOSS  (Holgate and al. , 2013)  and SONEL  (Wöppelmannn and Marcos, 2016) , databases, GLOSS being a global observation network and SONEL providing measurements on all French territories; then three validated databases provided by R. Ray have been used  (Ray et al. , 2013) , named Deep_BPR, Shallow and Coastal hereafter and respectively dedicated to deep ocean, shallow waters and coastal regions. 20 The altimetry-derived time series show more processing and accuracy issues, with a strong dependency on the mission orbit and duration (which firstly determine the level of contamination of the tidal analysis by non-tidal ocean signal). Clearly, the twenty years and more duration of the Topex-Poseidon and Jason series on a nearly ten-day repeat orbit allows for deriving outstandingly high-quality along-track and cross-over datasets of tidal harmonic constants.
Moreover the altimetry dataset benefits from new altimeter standards, which allow a better 25 observation of the tidal signals: GDR-D and REAPER orbits, ERA-INTERIM Dynamic Atmospheric Correction for ERS and TOPEX missions, improved wet tropospheric, sea sate bias and ionospheric corrections, and new mean profiles computed on a 20-year period  (Carrère and Lyard, 2003; Carrere et al, 2016). TOPEX-Interleaved track (noted TPN-J1N) also provides an accurate crossover dataset, but still with a higher error level than the 20 years of TP-Jason series, due to the shorter period of 6 years available. ERS/Envisat series and GFO series do 30 not have the same level of accuracy, as their orbits offer higher space coverage at the price of a lower temporal coverage (time sampling of 35 days for ERS/Envisat and 17 days for GFO).
The time under-sampling of tidal observations affects the apparent tidal periods (aliasing effect) which depend on the true tidal periods and on the mission temporal repetitivity. Because of the red nature of the ocean energy spectra, the contamination of the tidal signal by non-tidal signals will increase with the value of the aliased period. The TP/Jason orbit was 35 deliberately chosen to maintain the aliased period in a reasonable range. Reversely, sun-synchronous orbits (such as ERS/Envisat/Altika) are disadvantageous in that matter: not only the S1 and S2 tides are projected on an infinite period (mean state), but many other tidal constituents show a rather large aliased period (cf Table  2 ). This would prevent us to use ERS/Envisat derived data, and concentrate only on the Topex/Jason dataset, however the inclination of Topex/Jason is rather low and ERS/Envisat remains the only choice for very high 40 latitudes and polar seas.
Thus for the purpose of the FES2014 tide model, crossovers and along-track data from TOPEX/Jason-1/Jason-2 were preferred and were completed with some crossover data from TPN-J1N and ERS-https://doi. org/10. 5194/os-2020-96 Preprint. Discussion started: 16 October 2020 c Author(s) 2020. CC BY 4. 0 License. Envisat series in some shallow water regions and at high latitudes respectively. Table  3 presents the altimeter  5  dataset used for the estimation of the harmonic constants within the FES2014 project.
Tidal loading effect As the standard tidal atlases are targeting on the ocean tide component, a tidal loading correction needs to be applied on the altimeter measurements (in addition to the so-called solid earth deformation correction). In a first step, the GOT4v8ac tidal loading model was applied  (Ray 2013) , taking into account the recent correction of the 10 tidal geo-center motion proposed by  Desai and Ray (2014). These data have been used in the data assimilation process for the preliminary version of the ocean tide model, noted FES2014a. In a second step, a new tidal loading atlas was computed from this FES2014a ocean solution, noted "FES2014a tidal loading" (cf. section 6. 3). Then,18); this FES2014a tidal loading solution was used to produce a second version of the altimeter dataset, which was assimilated into the final version of the tide model named FES2014b.
SpEnOI assimilation code 5 The SpEnOI (Spectral Ensemble Optimal Interpolation) data assimilation code is an evolution of the CADOR data assimilation code  (Lyard 1997 , used up to FES2004), based on a variational approach using representer method, originally inspired from  Bennett and MacIntosh, 1982. The main difference lies in the fact that CADOR uses a variational formulation to infer the tidal elevation error covariance matrix, using an adjoint system. If the variational approach is quite well designed to capture model errors arising from the right-hand side of the tidal 10 equations (linear forcing terms), it turns to be poorly tractable to account for bathymetry-derived and non-linear terms (bottom friction) errors that usually dominate modelling errors in coastal and shelf seas. For these reason, an ensemble approach has been privileged to improve the realism and flexibility of the modelling errors prescriptions.
Ensembles construction In the ensemble assimilation approach, a large number of simulations is run in order to describe the model errors. This ensemble of simulations is generated by varying the parameters and input datasets to which the model is the most sensitive. In the case of the FES2014 tidal model, the perturbations were made on the bottom friction 20 coefficient, the tide drag coefficient, the bathymetry and the LSA. All the simulations were validated against the altimetry and the tide gauge databases, in order to identify potential outliers. In addition, the dispersion of the ensembles and the distance of the ensemble mean to the reference hydrodynamic simulation were computed, in order to verify that the ensembles were centered on the reference. In total, the whole ensemble contains 432 simulation members for each tidal constituent, built by following the methodology described in the next sections.
In addition to severe computational cost (SpEnOI code is solving assimilation problem in the data space), the data of the whole dataset is not optimal. First TPN/J1N and E1/E2/EN data can contain errors larger than the one of the prior solution and associated error bars are not fully reliable, so their inclusion can degrade the resulting data assimilation accuracy. Second, previous studies have shown that a limited subset of high-quality data can perform as well as the full dataset. Thirdly, it is the long-going objectives of FES atlases to 10 keep the weight of data assimilation at the lowest possible level and preserve as much as feasible the hydrodynamic properties of the solutions (needed for instance to perform energy budgets). So the selection of the observations for the data assimilation process is driven by several constraints: the computing limitations in terms of memory, which are directly linked to the number of assimilated observations; the homogeneous repartition of the assimilated observations all over the global ocean; the necessity to constrain more closely the model with the 15 observations in problematic regions (i.
e. where problems have been identified in the hydrodynamic solution, mostly linked with deficient bathymetry). In addition, the quality and the availability (in particular in the coastal regions) of the altimetry data are also important aspects in the selection. Actually, due to the 20 years of data available on the TP/J1/J2 orbit, the tidal constituents retrievals at the TP/J1/J2 crossover points and along the tracks are more accurate than the tidal retrievals at the TPN/J1N and E1/E2/EN crossover points. However, the 20 Topex/Jason orbit is limited to 66° in latitude, which means that the E1/E2/EN data will be needed as a complement in the high latitudes. The altimetry assimilation dataset was built in two steps. First, a systematic decimation was performed, following the criteria detailed in Table  4.
A threshold on the error estimate on the M2 tidal constituents was also used as a selection criterion. As some observations will provide accurate estimate for some given tidal 25 component and show strong error for another ones, data were then decimated specifically by applying a threshold value to the error estimate associated with the considered tidal component. In particular, regarding the S2 tidal constituent, no E1/E2/EN data were selected, because of its infinite aliasing period (sun-synchronous orbit). The second step of the construction of the altimetry assimilation dataset consisted in re-ingesting TP/J1/J2 30 crossover and along-track data that were discarded by the spatial decimation in regions where the model needed more close constraints, using an empirical, iterative procedure.
The final dataset of altimetry crossover points selected for the data assimilation process is presented on Figure  9 , with a specific color for each altimetry mission. One can notice there are fewer observations in the major ocean surface circulation areas (Gulf Stream, Kuroshio, Agulhas Current), because of the potentially large contamination by meso-scale dynamics. In the sub-35 Antarctic region, the seasonal presence of sea ice limits the availability of usable E1/E2/EN altimetry data and will be rejected by the numerical Raighley criterion at harmonic analysis step. The TP/J1/J2 along-track data, showed on Figure  10 , clearly enables to densify the assimilation dataset on the shelves and near the coasts, where the amplitude of the tide and the errors of the model are the largest and tidal wavelength the shortest.
The tide gauge dataset for the data assimilation process was built from several initial tidal records distributions: neighbor stations was systematically verified. In total, the tide gauge database contains 600 stations (Figure  11 ) 5 with a relatively homogeneous geographical repartition. Finally, iterative data assimilation experiences proved the need for some additional observations in very peculiar regions, where neither tide gauge nor standard altimetry data were available. Dedicated coastal altimetry-derived tidal observations provided by the CTOH (TP/J1/J2) were used to better constrain the model in these specific cases: 1 point North of Tierra del Fuego, 1 point in the Pamlico Bay (North Carolina) and 2 points between 10 Southern islands of Japan. The total assimilation dataset contains 12 622 observations for the M2 tidal component and slightly less for the other components, depending on the error estimate associated with the tidal constituents or because of constituent-specific aliasing issues.
It should also be noticed that the M4 tidal component received a special treatment for the construction of the data assimilation dataset. Indeed, the non-linear M4 tidal component mostly develops on the continental shelves. 15 Because of it small amplitude in the open ocean, it is difficult to separate M4 signal from the other ocean signals with similar space and temporal scales, and the noise-to-signal ration in M4 analysis is much too large to provide appropriate data to the assimilation. Consequently, only shelves and coastal seas data have been kept from the M4 initial assimilation dataset. The complete M4 assimilation dataset contains altimetry crossover points from TP/J1/J2, TPN/J1N and E1/E2/EN, along track data from TP/J1/J2, the four CTOH TP/J1/J2 coastal points 20 previously mentioned and only one tide gauge, the Avon Mouth station, in the Bay of Bristol (UK).
Validation in the frequency domain The validation in the frequency domain (i. e. of constituent harmonic constants) enables to easily identify and locate potential deficiencies in tidal atlases. The performance of the tidal model can be quite different from one region to another, but also from one tidal component to another. Such as for the hydrodynamic simulations, the optimal tidal atlas (i. e. with data assimilation) has been validated by computing the vector differences between 25 the observations (altimetry and tide gauges) for each tidal component. Figure  12  shows the vector differences between the tide gauge databases provided by R. Ray (and used as validation databases in  Stammer et al, 2015)  and the most recent global tidal models, for four main tidal components (M2, K1, S2 and O1).
Here, it must be reminded that the deep ocean tide gauge database was included in the assimilation dataset for FES2014b. As a consequence, it is expected that the vector difference between this database and the FES2014b tidal model is 30 very low (still, it indicates that this dataset was found to be self-consistent in the data assimilation process). However, the comparison to the other databases (shelf and coastal) shows the overall excellent performance of the FES2014b tidal atlas, whatever the considered tidal component. This highlights the rather uniform accuracy of the FES2014b atlas, compared to some other competing atlases that sometimes show uneven accuracy estimates, also strongly depending on the tidal constituent. 35 In this validation against tide gauges data, FES2014b and TPXO9 (recently released, April 2020,  Egbert and Erofeeva, 2002)  show the best agreement with data.
Tidal currents Tidal currents have been estimated on the finite element mesh with the discontinuous P1 discretization (one estimate in the middle of each element, estimated separately for each triangle, see Figure  18 ). The FES2014 tidal currents benefited from the data assimilation of the tidal elevations data through the dynamical correlation 15 computed from the assimilation ensemble. The tidal currents are provided on a 1/16° grid like the elevations. Contrary to sea surface elevation, where tides is the major contributor in most ocean regions, the validation of the tidal currents is quite challenging as it requires long-enough (several months to years) accurate current meter time series to accurately extract current harmonic constants from the tidal harmonic analysis. In addition, to be useful for consistent comparisons, the current meter gauges must be moored in sites that are representative of the 20 surrounding tidal dynamics.
Energy budget Barotropic tides energy budget is basically a very valuable diagnostics to examine the model performances and 20 accuracy, and to understand more precisely how tidal dynamics works as an energy generation, transport and dissipation mechanism. It can also be a proxy of the interactions of ocean tides with ocean circulation and stratification (bottom friction and internal tides drag rates of work) and be a feeding parameter to general ocean circulation models that do not solve explicitly for the tides and need to parameterize their effects, mostly on mixing. Energy budget has been estimated both from the prior, dynamically balanced tidal solutions (thanks to 25 their unprecedented accuracy), and from the data assimilation solutions. The latter are of course more accurate in elevation and currents, but are not perfectly balanced (dynamically consistent).
Lowest astronomical tides are commonly used in hydrographic services as the reference level for nautical charts and terrain models. It is also a valuable data in maritime engineering and risk assessments studies. The FES2014 LAT (and HAT, highest astronomical tides) chart has been computed from an eighteen-year tidal prediction (to account for nodal fluctuation in tidal amplitudes) based on all available tidal constituent in the FES2014 atlas (Figure  24 ). Mean lowest lower tides (MLLW) and mean highest higher tides (MHHW) levels (as 15 used by NOAA) could be obtained in a similar way. FES2014 LAT is routinely used at LEGOS to convert bathymetry from hydrographic services into ocean mean-level bathymetry as needed in numerical ocean modelling, especially in coastal and near-shore configurations.
Conclusions Despite the tremendous efforts devoted worldwide to improve tidal corrections for altimetry during the last two 20 decades, we still face challenging issues in shelf and coastal seas, as well as in high latitude oceans, where the atlases accuracy remains too limited for a precise altimetry data processing. Considering this matter, the FES2014 atlas can be considered as a very significant step forward, keeping close to others atlases in the deep ocean but showing a lot of improvements in shallow water seas, and some significant ones in the high latitude seas. 25 After proper, competitive evaluation procedures, it has been selected for CNES/NASA/ESA/EUMETSAT operational and re-processing altimetry data de-aliasing correction, and more recently as the standard correction in ITRF conventions.
Thanks to the (accidental) unusual delay between FES2014 atlas release and this publication, the project team and the user's community could accumulate extensive experience on FES2014 atlas performances in tidal prediction/correction domain. Namely, beside space-borne applications, it is now widely 30 and successfully used for regional modelling and in situ data processing applications, supporting our confidence in its remarkable accuracy. As a matter of fact, one can consider that, even five years after its release, FES2014 is well placed in the most useful global ocean tide atlases short list because of its extended tidal spectrum (34 constituents, among which 15 were optimally adjusted by data assimilation), its unprecedented accuracy in shelf and coastal seas and its coastal details grid flexibility.
35 The forthcoming SWOT altimetry mission will especially profit from these specific characteristics as it will offer coastal and near-shore nearly continuous, high resolution coverage. However the FES project team is already making plans to design the next FES atlas generation, with emphasis to SWOT mission requirements and needs, which should be available within three years or so. Thinking about more detailed shallow water observation detiding, the improvement of the hydrodynamic model will be one of the critical issues, and will need to aggregate 40 further accurate world-wide bathymetry, which is a tedious and complicated task as the attempt to access national hydrographic services data is often frustrating, especially when existing data public release is limited by https://doi. org/10.
5194/os-2020-96 Preprint. Discussion started: 16 October 2020 c Author(s) 2020. CC BY 4. 0 License. non-scientific considerations. To some extent, we foresee that future atlases improvements and overall accuracy 5 will be locally strongly correlated with the level of cooperation of national services in this matter. New or improved space-borne bathymetry estimates (gravimetry/sea surface inversion, IceSAT-2 laser processing, surface wave's wavelength inversion from optical data) might hopefully ease the issue, especially in remote or poorly accessible ocean parts, but open-minded international cooperation and eased public data access remain a key factor for next generation tidal products. Meanwhile, we believe that FES2014 tidal atlas will remain a 10 useful base for tidal prediction and correction, as well in terms of surface elevation and tidal currents, in present or future altimetric or gravimetric satellite observations and in many maritime applications.
For each of these ten regions, the non-dimensional wave drag coefficient was locally varied over seven values ranging around the global value set for the reference hydrodynamic simulation (75). The wave drag perturbations ensemble of wave drag perturbations finally contains 70 simulations. Bathymetry: Several approaches are possible for the hydrodynamic model bathymetry perturbations such as 15 linear combinations of various datasets or modifications in specific regions from synthetic or heterogeneous bathymetry dataset. The latter was used in the case of the FES2014 model, as it enables to better control the perturbations and to choose the most responsive regions. The reference hydrodynamic model bathymetry is replaced by depths extracted from gridone, 1 minute resolution from GEBCO and Smith&Sandwell, 15.