dataesr/scientific-paragraphs-categorization huggingface dataset:
The temporal undersampling 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 longer the aliased period, the larger the contamination of the tidal signal by non-tidal signals. The TOPEX/Jason orbit was deliberately chosen to maintain the aliased period in a reasonable range. Conversely, Sun-synchronous orbits (such as ERS/Envisat/AltiKa) are disadvantageous in that matter: not only are the S1 and S2 tides projected on an infinite period (mean state), but many other tidal constituents show a rather large aliased period (see Table  2 ). This would pre-vent us from using 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 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 complemented with some crossover data from TPN/J1N and ERS/Envisat series in some shallowwater regions and at high latitudes, respectively. Table  3  presents the altimeter dataset used for the estimation of the harmonic constants within the FES2014 project.
Tidal loading effect As the standard tidal atlases are targeted on the ocean tide component, a tidal loading correction needs to be applied to 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 tidal geocentre 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, denoted FES2014a. In a second step, a new tidal loading atlas was computed from this FES2014a ocean solution, denoted "FES2014a tidal loading" (see Sect. 6. 3). Then, 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.
This turns into an ill-defined harmonic system and consequently larger errors in the harmonic constants deduced from its solving. Neither high-latitude dataset manual editing nor entire dataset rejection were options, the former being a gigantic task and the latter an extremely damaging loss of data in already poorly documented regions. Instead, we directly examined the ratio between the diagonal and extra-diagonal terms in the numerical harmonic matrix, and we used an analogy with the Rayleigh criterion for continuous time series (and the corresponding harmonic matrix) to decide on a maximum ratio (extra-diagonal / diagonal) above which the frequency separation was considered deficient. The maximum ratio is set by analogy with the Rayleigh criterion. Ideally, i. e. in the case of quasi-infinite time series, the harmonic matrix will be quasi-diagonal.
Ensemble construction In the ensemble assimilation approach, a large number of simulations are 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 coefficient, the internal tide drag coefficient, the bathymetry and the LSA. All the simulations were validated against the altimetry and the TG 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 centred on the reference. In total, the whole ensemble contains 432 simulation members for each tidal constituent, https://doi.
Perturbation of the model bathymetry Several approaches are possible for the hydrodynamic model bathymetry perturbations, such as linear combinations of various datasets or modifications in specific regions using either 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 what we call "gridone", 1 min resolution from GEBCO, and Smith and Sandwell, 15. 1 release, in each of the 19 regions displayed in Fig. 8  and chosen either for their dynamical impact on tidal solutions or for the large uncertainties of the reference bathymetry quality (such as the Patagonian shelf). However, the construction of the ensemble simulations has highlighted that the two bathymetry perturbations in the Weddell Sea (southern Atlantic Ocean) resulted in solutions showing errors in semi-diurnal tides up to 2-4 times larger than the average simulations, with a large increase of errors in the whole Atlantic Ocean, in the Indian Ocean and in the southern Pacific Ocean.
This comes from the free water depth reduction due to the Weddell Sea ice-shelf immersion, which has been corrected in our reference bathymetry, but not in the gridone and Smith and Sandwell patches because of project schedule constraints. Despite being considered as potentially critical for the model error space, the Weddell Sea region was discarded from the bathymetry patch ensemble construction, whose effective set contains 36 members. A few additional members have been added from the perturbations of the model minimal depth threshold. It is usually set to 10 m in the T-UGOm hydrodynamic global ocean model. Depth threshold aims to minimize frequency-domain modelling validity limitations in very shallow waters (T-UGOm has the ability to modulate the threshold as a function of local tidal range; it was not used in FES2014 to avoid additional complexity in the model configuration setting) but more importantly to deal with the existence of unrealistically shallow depths in most bathymetry datasets.
The depths found in most bathymetry databases in the 0-10 m (and probably 0-20 m) range are anything but reliable. In most places, the depths linearly vary with distance from 0 m at coastline to the 10 m isobaths, which is not the usual morphology one will find in the true ocean. Such artificial, very-shallow-water patches can have a damaging impact on the bottom friction https://doi. org/10. 5194/os-17-615-2021 Ocean Sci. , 17, 615-649, 2021.
Data selection As described in Sect. 3, the TG and altimetry sea surface height observations were processed with a harmonic analysis in order to retrieve the tidal harmonic constituents (amplitude and phase lag) for about 15 tidal components (M2, K1, S2, O1, etc. ) and the associated error estimates. The altimetry data were processed at the crossover points for the TP/J1/J2, TPN/J1N, and E1/E2/EN series, and along the tracks for the TP/J1/J2 series. This means a large amount of data, with more than 9000 crossover points for each of the TP/J1/J2 and TPN/J1N series, about 64 000 crossover points for the E1/E2/EN series, and many more points along the TP/J1/J2 tracks. In addition to severe computational cost (SpEnOI code is solving an assimilation problem in the data space), using data of the entire dataset is not optimal.
First, TPN/J1N and E1/E2/EN data can contain errors larger than those of the prior solutions, 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-standing objectives of FES atlases to keep the weight of data assimilation at the lowest possible level and preserve as feasible of 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 the following general guidelines: keep the overall assimilation dataset as limited as feasible, giving priority to the TP/J1/J2 crossover data, with a partial decimation especially at high latitudes to favour the homogeneous repartition of the assimilated observations all over the global ocean, and add (possibly decimated) alongtrack TP/J1/J2 data to constrain more closely the model with the observations in problematic regions, i.
e. where problems have been identified in the hydrodynamic solution, mostly linked with deficient bathymetry. Those regions lie mostly in shelf and coastal seas, where data could also be taken from TPN/J1N and E1/E2/EN along-track/crossover datasets. However, due to the 20 years of data available during the TP/J1/J2 orbit at FES2014 production era, the tidal constituents' retrievals at the TP/J1/J2 crossover points and Ocean Sci. , 17, 615-649, 2021 https://doi. org/10. 5194/os-17-615-2021 along the tracks are more accurate than the tidal retrievals at the TPN/J1N and E1/E2/EN crossover points. Consequently, TPN/J1N and E1/E2/EN along-track/crossover datasets were not used, except in some rare exceptions. Of course, with the TOPEX/Jason orbit being limited to 66 • in latitude, the E1/E2/EN data are definitely needed as a complement in the northern high latitudes (E1/E2/EN data were not considered as being accurate enough in southern 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 of the M2 tidal constituents was also used as a selection criterion. As some observations provide accurate estimates for some given tidal components and show strong errors for other ones, data were 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 of re-ingesting TP/J1/J2 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 in Fig. 9 , with a specific colour 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 mesoscale dynamics (the non-tidal ocean dynamic contamination is estimated by looking at sea surface signal spectral energy close to the considered constituent's aliased frequency, and data showing values higher than the thresholds given in Table  4  are dismissed from the assimilation dataset). In the sub-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 Rayleigh criterion at harmonic analysis step.
The TP/J1/J2 along-track data, shown in Fig. 10 , clearly enable us 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 TG dataset for the data assimilation process was obtained from several tidal datasets: the WOCE/GLOSS coastal database, open-ocean BPR database provided by R. Ray (and used as validation dataset in  Stammer et al. , 2014) , an openocean BPR database in Antarctica compiled by LEGOS, an Arctic database from  Kowalik and Proshutinsky (1994) , the International Hydrographic Office (IHO) dataset, the research of  Gjevik et al. (1994) , and some additional data compiled by LEGOS, and four TG stations of R. Ray's shelf database, located north of Florida.
Any inevitable redundancies due to neighbouring observations were identified, and the consistency between the neighbouring stations was systematically verified. In total, the TG database contains 600 stations (Fig. 11 ) with a relatively homogeneous geographical distribution. For efficiency reasons, and because the TG time series needed to compute numerical error estimates https://doi. org/10. 5194/os-17-615-2021 Ocean Sci. , 17, 615-649, 2021 TP/J1/J2 along-track data Shelves 20 km 1 cm 6024 Figure  10. TP/J1/J2 along-track data selected for the data assimilation. were not available for the full dataset, the TG data error estimates were fixed arbitrarily and empirically to 3 mm for the deep ocean stations and to 1 cm for the shelf and coastal stations. The idea was to limit the constraints on the model at the tide gauge stations on the shelf and close to the coast in order to avoid drawing the solution to fit some very local tide features observed by the coastal stations that may be inconsistent with the larger-scale tidal patterns that can be accurately solved at the resolution and/or bathymetry of the model.
Finally, iterative data assimilation experiments proved the need for some additional observations in particular regions, where neither TG nor standard altimetry data were available. Dedicated coastal altimetry-derived tidal observations provided by the French Observation Service dedicated to satellite altimetry studies (Centre of Topography of the Oceans and the Hydrosphere, denoted CTOH, http: //ctoh. legos. obs-mip. fr/, last access: 28 March 2021), based on the harmonic analysis of TP/J1/J2 GDRs, were used to better constrain the model in these specific cases: one point north of Tierra del Fuego, one point in the Pamlico Sound (North Carolina), and two points between the 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 estimates associated with the tidal constituents or because of constituentspecific aliasing issues.
It should also be noticed that the M4 tidal component received a special treatment for the construction of the assimilation dataset. Indeed, the non-linear M4 tidal component mostly develops on the continental shelves. Because of its small amplitude in the open ocean, it is difficult to sepa-Ocean Sci. , 17, 615-649, 2021 https://doi. org/10. 5194/os-17-615-2021.
The prediction code used for the time domain validations presented in Sect. 5. 3 is the operational TOPEX/Jason GDR processing code. The tidal prediction software is available on a Bitbucket deposit: https://bitbucket. org/cnes_aviso/fes/src/master/ (last access: 28 March 2021). It is appropriate not only for use with FES atlases but also with other popular atlases, such as GOT or TPXO releases. Without getting deep into the details, the tidal prediction includes all tidal constituents provided by an atlas, but it also uses inference technique to add some significant missing astronomical constituents when not given as a prediction input file (namely µ2, ν2, L2, T2, λ2, 2N2, ε2, η2, 2Q1, σ 1, ρ1, M1-1, M1-2, χ1, π 1, ϕ1, θ 1, J1, OO1), and a quite comprehensive number of long-period constituents (up to 106 from second-degree terms and 17 from third-degree terms of the gravitational tidal potential) are added using the tidal equilibrium approximation.
The FES2014 atlas is originally designed for the tidal de-aliasing correction of the altimetry sea surface height ob-Ocean Sci. , 17, 615-649, 2021 https://doi. org/10. 5194/os-17-615-2021 Figure  12. Vector differences (cm) between the TG databases and the global tidal models, for M2, K1, S2, and O1. The deep group is made of abyssal plain TGs; the shelf is made of tides gauges located in upper 500 m depth limit. The coastal group is made of TGs collected in coastal databases such as GLOSS. servations, for which the mission accuracy requirements are set to 2 cm in the open ocean, so each (accurate) contribution to the tidal spectrum is of importance. Another asset of the FES2014 atlas is the supplying of six long-period tidal components (Mf, Mm, Mtm, MSqm, Sa, and Ssa; see previous comment about MSf) computed from the dynamical model forced with gravitational forces.
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. As for the hydrodynamic simulations, the optimal tidal atlas (i. e. with data assimilation) has been validated by computing the vector differences between the observations (altimetry and TGs) for each tidal component. Figure  12  shows the vector differences between the TG databases provided by R. Ray (and used as validation databases in  Stammer et al. , 2014)  and the most recent global tidal models, for four main tidal components (M2, K1, S2, and O1). Here, it must be reminded that most of the deep ocean TG 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/FES2014c tidal model should be very low (still, it indicates that this dataset was found to be self-consistent in the data assimilation process). To a lesser extent, shelf and coastal datasets inevitably contain some assimilated data. Actually, the amount of quality TG data is not large enough to allow for a distinct data assimilation and well-balanced validation datasets. Moreover, if a quality-checked validation dataset's data demonstrates some divergence with the atlas solution, it would be then extremely useful to include it in the final dataset for assimilation. In addition, because of the ensemble or data representer's approach, the assimilation solution will not easily fit the TG data if not consistent with model error covariance and other data, including https://doi.
org/10. 5194/os-17-615-2021 Ocean Sci. , 17, 615-649, 2021 Figure  13. Variance reduction differences (cm 2 ) at tidal gauge sites from GLOSS network, when using the FES2014b atlas versus the GOT4v10 atlas. Analysis computed over the 2007 to 2011 time period. Blue colours indicate a higher variance reduction when using FES2014b tidal correction. Tidal corrections made for both models with their native constituents' spectrum (i. e. not restricted to their common constituents). altimetry data. Internally, we also made consistency checks by assimilating altimetry data only, then compared solutions with TG data and reached very close numbers. So there is a favourable but moderate bias in terms of accuracy when comparing our final solution with the validation dataset. Still, the comparison to the other databases (shelf and coastal) shows the overall excellent performance of the FES2014b tidal atlas, whatever the considered tidal component.
In addition, seasonal ice in the Arctic Ocean is furthermore diminishing the number of available valid observations and hence potentially increasing the uncertainty on the variance reduction estimates. Some independent validation was performed to compare FES2012 and FES2014 (see  Ray et al. , 2019)  and showed the clear improvement in FES2014, except for M2 in the Kara and Laptev seas, where comparison with Al-tiKa measurements shows a slightly weaker performance of FES2014. Unfortunately, the lack of a more comprehensive TG dataset makes any stronger conclusions quite difficult to draw. FES2014b also strongly reduces the variance compared to GOT4v10 in northern high latitudes, except for a slight rise of variance noted north of Baffin Bay when comparing to the GOT model. To pursue the analysis further to the coast, we consider along-track sea-level anomalies (SLAs) calculated from 1 Hz altimetric measurements.
Acknowledgements. The authors warmly thank  David Griffin  from  CSIRO (Australia)  for providing the depth-averaged ADCP current time series at the  IMOS stations around Australia  and for all of the fruitful discussions about the comparison with the FES2014 tidal currents. The authors are also grateful to  Pascal Gégout  ( GET, France ) and  Jean-Paul Boy  ( ITES, France ) for their assistance in developing the unstructured grid loading/self-attraction software, and to  David Greenberg  ( BIO, Canada ) for his long-lasting support in providing expertise and data for the Hudson Bay and  Canadian Archipelago modelling. Finally , the authors acknowledge their colleagues from the OSTST tidal community for their long-lasting support and collaborations, with a special thought for  Richard Ray (GSFC, USA ).
Financial support. The  FES2014  project has been supported by the  French space agency (CNES ; grant nos. 131678 ,  160306 , and  161431 ; general grant framework no. 14026 ) and by  OSTST/TOSCA (INSU)  scientific funding. Review statement. This paper was edited by  Philip Woodworth  and reviewed by  Michael Foreman ,  Edward Zaron , and  Jason Otero Torres.
Code availability. Codes have not yet been assigned a DOI. The prediction code used for the present study is freely available at the following git repository: https://bitbucket. org/cnes_aviso/fes/ src/master/ (last access: 9 April 2021), managed by the Aviso team. Complementary codes for post-processing and tidal analysis are freely available at the SIROCCO French national service website (https://sirocco. obs-mip. fr/, last access: 9 April 2021), hosted by the Observatoire Midi-Pyrénées, Toulouse, France. Data availability. FES2014 data have not yet been assigned a DOI. They are freely available at the Aviso website https://www. aviso. altimetry. fr/en/data/products/auxiliary-products/ global-tide-fes. html (last access: 9 April 2021). Auxiliary data can be requested from the SIROCCO French national service (https://sirocco.
Study Area Ninety-four large lakes (>100 km 2 ) with LSWT observations of the Along Track Scanning Radiometer Reprocessing for Climate: Lake Surface Water Temperature and Ice Cover (ARC-Lake) data set in China were chosen as study areas to calibrate and improve the FLake model performance. Lake boundaries were extracted from the HydroLAKES data set  (Messager et al. , 2016) , as well as lake areas, lake depths and altitudes. These lakes account for nearly 50% of lake areas in China and vary in surface area (100. 8-4,266. 6 km 2 ), depth (1-120 m), altitude (0-5,198 m), and geographic location (Figure  1 ). The studied lakes were divided into six subregions to demonstrate the simulations of LSWT according to geographical and climatic features (Ma HUANG ET AL. et al. , 2011; Zhang et al. , 2019).
Geomorphometric Characteristics of Lakes HydroLAKES data set version 1. 0 estimates the volumes of all global lakes with surface areas greater than 10 ha using a geostatistical model based on surrounding topography information  (Messager et al. , 2016). HUANG ET AL. The data set also provides other additional lake characteristics required by FLake, including lake boundary, lake mean depth, lake surface area and latitude/longitude of lake center coordinates. A basic assumption of the geostatistical model is that the topography around the lake is a reliable predictor variable of its bathymetry. The model has been trained and validated on 12,150 existing records of lake depth obtained from 14 national and international datasets. Overall, the lake depths from HydroLAKES match well with reference depths  (Messager et al.