dataesr/scientific-paragraphs-categorization huggingface dataset:
Simulated altimetry datasets In this section, we provide a technical description of the two observational datasets used to train 4DVarNet, namely the four nadir and one SWOT plus four nadir configurations. Regarding the pseudo-nadir altimetry dataset, representative of the current pre-SWOT observational altimetric dataset, we use the ground tracks of four altimetric missions (TOPEX/Poseidon, Geosat, Jason-1, and Envisat) picked up from the 2003 constellation to interpolate the NATL60 simulation from 1 October 2012 to 29 September 2013. A Gaussian white noise, with variance σ 2 = (4• • •9) cm 2 , is added to the interpolated NATL60 simulation by the SWOT simulator tool to mimic noise with a spectrum of error consistent with global estimates from the Jason-2 altimeter  (Dufau et al. , 2016).
Evaluation framework Our evaluation framework exploits and extends the one introduced in Le  Guillou et al. (2020) , as follows: -Training and evaluation setting. Because the NATL60 dataset is made of 365 daily simulations, and the reference data used for training never have to be used during the optimization, we train all learning-based models   Overall, we evaluate the performance metrics over the test period from 22 October to 2 December 2012, which is 42 d, corresponding to two SWOT cycles in the SWOT science-phase orbit. In doing so, the test period can be considered uncorrelated to the training and validation period. -Evaluation metrics. We use BOOST-SWOT DC (data challenge) metrics to benchmark the 4DVarNet-SSH scheme with respect to the state-of-the-art SSH interpolation schemes. They comprise the following: -RMSE s (t), for the mean RMSE score (normalized RMSE), -σ RMSE s (t) , for the RMSE(t) standard deviation of the RMSE(t), which gives some information regarding the temporal stability of the reconstruction, -λ x , for which the minimum spatial scale is resolved (wavelength in degrees), -λ t , for which the minimum temporal scale is resolved (wavelength in days), where RMSE s (t) = 1 -RMSE(t) RMS(x) , RMS denotes the root mean square function, N is the number of pixels included in the study domain, and RMSE(t) = 1 N N i=1 (x (t, i) -x(t, i)) 2.
As such, for a given training configuration, we can train an ensemble of 4DVarNet-SSH schemes by running multiple training procedures. We apply this approach to build an ensemble of nine 4DVarNet-SSH schemes for a given training configuration, which comprises a training dataset, the considered 4DVarNet-SSH parameterization, and given training hyperparameters (i. e. , number of epochs, learning rates, and optimizers). For a given observation time window, we then retrieve nine interpolations from which we can compute a me-   dian field and the associated standard deviation. We report the performance metrics for the GULFSTREAM domain of the nine trained models and the median model in Table  5. It reveals the internal variability in the training process. Though it does not reach the best performance, the median model combines a resolved spatial scale below 0.
7 • and a resolved timescale below 5 d, which is only the case for 6 out of 9 of the trained models. Figure  12a  further illustrates this aspect. Interestingly, the standard deviation of the ensemble of 4DVarNet-SSH schemes correlates to the interpolation error, with an R 2 coefficient of determination equal to 0. 86. Even if the scales between the interpolation error and the trainingrelated 4DVarNet internal variability differ (see Fig. 13 ), the latter can be regarded as an indicator of the interpolation error, usually with an appropriate localization of large errors. In future works, we plan to draw from traditional ensemble DA methods or ensemble Gaussian-based simulations to address all the components of the interpolation error related to the data assimilation scheme.
Conclusion and discussion This paper introduced the 4DVarNet-SSH scheme, an endto-end neural architecture for the space-time interpolation of SSH fields from nadir and wide-swath satellite altimetry data. The 4DVarNet-SSH scheme draws from recent methodological development to bridge data assimilation and deep learning with a view to training 4D-Var DA models and solvers from data. Numerical experiments within an OSSE setting support the relevance of the 4DVarNet-SSH scheme with respect to the state of the art. We further discuss our main contributions according to three aspects, namely the added value of a deep learning scheme for satellite altimetry and operational oceanography, the exploitation of upcoming SWOT data, and the ability to scale up learning approaches from regional case studies to the global scale.
Our results for satellite altimetry are in line with other recent studies for other ocean parameters, such as sea surface temperature  (Barth et al. , 2019) , suspended sediments  (Vient et al. , 2022) , and 3D temperature and salinity fields  (Pauthenet et al. , 2022). All these studies support the potential of neural approaches to retrieve finer-scale variabilities from available satellite and/or in situ observations. Regarding satellite altimetry, a future challenge includes the application to real altimetry datasets (see, e. g. , the 2021 Observing System Experiments (OSEs) BOOST-SWOT data challenge at https://github. com/ocean-data-challenges/ 2021a_SSH_mapping_OSE, last access: 2022) and the exploitation of multimodal synergies  (Fablet and Chapron, 2022). -Making the most of SWOT data.
Our study brings new evidence that the wide-swath space-time sampling of the upcoming SWOT mission could lead to a very significant improvement in the reconstruction of mesoscale sea surface dynamics. For the considered case study regions, with contrasting dynamical regimes at play and different revisit times of SWOT orbits, we report relative gains from 20 % to 60 % compared to nadir altimetry data only in terms of RMSE and resolved space-timescales. These results assume an errorfree SWOT product. Therefore, exploring further how these results could generalize to error-prone  (Esteban-Fernandez, 2014; Gaultier and Ubelmann, 2010)  and uncalibrated SWOT data  (Febvre et al. , 2022 ) is a critical challenge. Preliminary preprocessing of the pseudo-SWOT observations  (Metref et al. , 2020)  to filter out the correlated components and avoid major issues in the assimilation and/or learning process of the interpolation methods may also be considered.
The extension of the considered OSSE to multi-SWOT configurations could also provide new means to optimize the deployment of multi-satellite configurations in coming years. -Scaling up to a global scale with a learning-based scheme. Our numerical experiments focused mainly on a regional scale, typically 10 • × 10 • domains, as illustrated by the GULFSTREAM and OSMOSIS regions. The reported results support the relevance of the proposed 4DVarNet-SSH parameterization to account for such regional space-time variabilities. Scaling up to a basin scale or even the global scale naturally arises as a key challenge for future work. Through the built-in features of the PyTorch framework and its associated packages, our open-source code can leverage multi-GPU distribution learning schemes and on-the-fly minibatch generation tools to deal with larger-scale datasets from a computational point of view.
Acknowledgements. This work has been supported by the  LEFE program  (LEFE  MANU  project  IA-OAC ),  CNES  (grant  OSTST DUACS-HR ), and  ANR Projects Melody and OceaniX. It has benefited from  HPC  and  GPU resources from Azure (Microsoft Azure  grant). Financial support. This research has been supported by  GENCI-IDRIS  (grant no. 2020-101030 ). Review statement. This paper was edited by  Xiaomeng Huang  and reviewed by two anonymous referees.
Code and data availability. The open-source 4DVarNet version of the code is available at https://doi. org/10. 5281/zenodo. 7186322 (hgeorgenthum et al. , 2023). The datasets are shared through the BOOST-SWOT data challenge also available on GitHub (https://github. com/ocean-data-challenges/2020a_SSH_mapping_ NATL60, last access: 2022). Video supplement. The animations corresponding to the 4DVarNet comparison to DUACS OI on the BOOST-SWOT DC test period are given for both GULFSTREAM and OSMOSIS domains in the four nadirs and one SWOT plus four nadir configuration. They can be found on the OceaniX-AI YouTube channel under the following: -GULFSTREAM (four nadirs) at https://youtube. com/shorts/ QKXukB_Rd5E  (Beauchamp, 2022a) , -GULFSTREAM (one SWOT plus four nadirs) at https:// youtube. com/shorts/i91Z1pMm4gY (Beauchamp, 2022b) , -OSMOSIS (four nadirs) at https://youtube.
Observations Two sets of observations are jointly analyzed in this paper. The first data set  (project-id: 2017. 1. 00108   0 +6. 4 k BHR71-IRS1 200 o, p 2. 7 q 15 q 44 q 0 -4. 4 q Per-emb-25 294 r 0. 5 h 1. 0 h 68 h 0/I +5. 8 k NGC 1333-IRAS4B 299 e 3. 0 q 4. 4 q 28 g 0 +7. 4 q Ser-SMM3 436 s 3. 2 q 5. 1 q 38 q 0 +7. 6 q TMC1 140 t, u 0. 2 q 0. 9 q 101 q I +5. 2 q Notes. The columns represent 1) Source, 2) d: distance to the source in pc, 3) M env : mass of the envelope in M , 4) L bol : bolometric luminosity in L , 5) T bol : bolometric temperature in K, 6) Class: stage of the protostar, 7) v LSR : local standard of rest velocity in km s -1. References:   2009 ), (i) Neuhäuser & Forbrich (  2008 ), (j) Lindberg et al. (  2014 ), (k) Stephens et al. (  2019 ), (l)     2009 ), (v)   Lindberg et al.
Synthetic spectral fitting For the spectral analysis, on-source spectra were extracted from the data cubes of the sources of the two data sets. Circular regions centered on source positions (in RA and Dec) with the radius of spectrum extraction corresponding to one-beam onsource are given in Table  3. The number of pixels in radius r of the circular region to be used was computed by dividing the radius of the circular region with the size of one pixel in arcsecond. The spectroscopy used for the targeted molecules and their isotopologs stems from the Cologne Database of Molecular Spectroscopy (CDMS;  Müller et al. 2001 Müller et al. , 2005;; Endres et al. 2016)   1  and the Jet Propulsion Laboratory (JPL) catalog  (Pickett et al. 1998)   2. Line blending in the detected lines was checked with the online database Splatalogue 3.
Synthetic spectral fitting was performed with custom-made Python scripts based on the assumption of local thermal equilibrium (LTE). The input parameters include the full width halfmaximum (FWHM) of the line, column density (N), excitation temperature (T ex ), source size, beam size, and spectral resolution of the observations. Line profiles are assumed to be Gaussian. Further details are provided in section 2. 3 of  Drozdovskaya et al. (2022). For some sources, the number of free parameters (e. g. , source size or T ex ) can be reduced based on information from other observing programs. These are detailed on a sourceby-source basis in the corresponding Appendices. Typically, just two free parameters were fitted at a time by means of a visual inspection and an exploration of a grid of possible values.
Results The spectral setup of the first data set allows the targeted sources to be probed for the emission of the main isotopologs of H 2 S and OCS, v=0, their minor isotopologs (HDS, HD 34 S H 33 2 S, H 34 2 S, 18 OCS, O 13 CS, OC 33 S, 18 OC 34 S), and also the vibrationally excited states of OCS (v 2 =1 ± ). Consequently, sources IRAS 16293 A, IRAS 16293 B, IRAS4A, and IRS7B were probed for all these species. The spectral setup of the second data set allows the other targeted sources (B1-c, BHR71-IRS1, Per-emb-25, IRAS4B, SMM3, and TMC1) to be probed for the main isotopologs of H 2 S and OCS, v=0, their minor isotopologs (HDS, HD 34 S, 18 OCS, OC 33 S, 18 OC 34 S, 18 O 13 CS), as well as the vibrationally excited state of OCS (v 2 =1 -). All the transitions of the detected molecules have E up in the range of 84 -123 K and A i j values of 0.
Acknowledgements. The research was started as part of the  Leiden/ESA   Astrophysics Program for Summer Students  (LEAPS) 2021. M. N. D. acknowledges the support by the  Swiss National Science Foundation (SNSF)   Ambizione  grant no. 180079 , the  Center for Space and Habitability (CSH) Fellowship , and the  IAU Gruber Foundation Fellowship. This paper makes use of the following ALMA data: ADS/JAO. ALMA# 2017. 1. 00108. S and  ADS/JAO. ALMA# 2017. 1. 01350. S. ALMA is a partnership of  ESO  (representing its member states),  NSF (USA)  and  NINS (Japan) , together with  NRC (Canada) ,  MOST  and  ASIAA (Taiwan) , and  KASI (Republic of Korea) , in cooperation with the  Republic of Chile. The  Joint ALMA Observatory  is operated by  ESO ,  AUI/NRAO  and  NAOJ. This research made use of Astropy, a communitydeveloped core Python package for Astronomy (Astropy Collaboration et al.
Acknowledgments J. L. and C. B. were supported by  NASA InSight PSP  Grant  80NSSC18K1679  and S. M. M. by  NASA InSight PSP  Grant  80NSSC18K1622. M. P. P. and W. B. B. were supported by the  InSight  Project at the  Jet Propulsion Laboratory, California Institute of Technology  under a contract with the  National Aeronautics and Space Administration  ( 80NM0018D0004 ). P. L. and M. A. W. are supported by  Agence Nationale de la Recherche  ( MAGIS ,  ANR-19-CE31-0008-08 ;  IdEx Université Paris Cité ,  ANR-18-IDEX-0001 ) and by  CNES  for SEIS science support. This is InSight Contribution Number  278. InSight seismic data presented here (http://dx. doi. org/10. 18715/SEIS. INSIGHT. XB_2016 ) are publicly available through the Planetary Data System (PDS) Geosciences node (InSight SEIS Data Bundle, 2021), the  Incorporated Research Institutions for Seismology (IRIS)   Data Management Center  under network code XB and through the  Data center of Institut de Physique du Globe, Paris.
Data Availability Statement The data sets used in this study are achieved and released by InSight Mars SEIS Data Service and are available to the science community (InSight Mars SEIS Data Service, 2019; InSight Marsquake Service, 2022). Data sets (both the raw data and the deglitched data in SAC format, after removing the instrument response) for this research are available on the Zenodo repository: https://doi. org/10. 5281/zenodo. 7325555 (Li, Beghein, et al. , 2022). The InSight_KKS21GP model is available on the IPGP Data Center (https://doi. org/10. 18715/IPGP. 2021. kpmqrnz8).
More than 29 years of altimeter data have been recently reprocessed by the multi satellite Data Unification and Altimeter Combination System (DUACS) and made available under the name of DT2021 processing through the Copernicus Marine Service (CMEMS) and the Copernicus Climate Change (C3S) Service. New standards have been applied and various geophysical correction parameters were updated compared to the previous release in order to improve the product quality. This paper describes the assessment of this new release through the comparison of both all satellites and two satellites products with external in situ tide gauge measurements in the coastal areas of the European Seas. The aim is to quantify the improvements on the previous DT2018 processing version on the retrieval of sea level in the coastal zone.
The results confirmed that the new DT2021 processing version better solves the signal in the coastal band. Moreover, the all satellites dataset provided more accurate sea level measurements when comparing with tide gauges respect to the climatic two satellites dataset due to the better performance of the former for the assessment of higher than climatic frequency signals. On the opposite, we found the two satellite dataset the most suitable product for the assessment of long term sea level time series in the coastal zone due to its larger stability to the detriment of the all satellites dataset.
, 2021) ; and the Mediterranean and Black Seas are applied  (Jousset et al. , 2020 (Jousset et al. , ,2022)). (iv) an improved Long Wavelength Error (LWE) correction has been computed to remove local SLA residual biases between neighbouring altimeter tracks. (v) and finally, the DT2021 products version includes an upgraded mapping parameterisation that contributes to improve the mesoscale signal visible on L4 products. A complete description of the different evolutions implemented in the DUACS DT2021 products version can be found in CMEMS-SL-QUID (2022). The validation (quality check) of altimetry products is a key step in the data processing pipe to assess and characterise the errors associated with the altimetry measurements. This issue is crucial in the coastal zone, where traditional altimetry have been often unable to produce meaningful signals of sea level change due to the typically shallower water, bathymetric gradients, and shoreline shapes, among others  (Vignudelli et al.
These authors reported a global reduction of 0. 6% in variance with respect to the previous processing (DUACS DT2014 dataset). Pascual et al. (2006 Pascual et al. ( , 2009) )  investigated the consistency between previous versions of the altimeter L4 gridded products and tide gauge data from the PSMSL repository in the coastal zone reporting mean square differences between the two datasets ranging between 30% and 90% in the European coasts. More recently,  Sánchez-Román et al. (2020)  assessed the quality of DUACS L3 products in the coastal band of the European Seas through comparison with independent tide gauge measurements. These authors reported a mean root mean square (rms) difference between both datasets lower than 7 cm for the whole region, with mean values ranging around less than 4 cm in the   2022 ) reports improved results when using the latest reprocessing with a reduction in variance of the differences between altimetry and tide gauges ranging between 0.
2% and more than 5% of the tide gauge signal in the European coasts; with respect to the previous product version. This paper focuses on improvements of the latest reprocessing of DUACS Delayed Time (DT) reanalysis (referred hereinafter as DT2021) in the retrieval of sea level in the coastal band of the European Seas with respect to the previously available reprocessed products (referred hereafter as DT2018). To do that, we conduct an intercomparison of L4 global altimetry gridded products and in situ tide gauges located along the European coasts from the Copernicus Catalogue. The performance of the DT2021 processing all satellites and two satellites versions on the sea level retrieval is also assessed. The paper is organized as follows: the SLA data used, the tide gauge dataset, and the method for comparing altimeter and in situ measurements are detailed in section 2.
Sea level anomaly data The DUACS reprocessed L4 global satellite SLA maps used in this study correspond to both the DT2021  (Faugère et al. , 2022)  and DT2018 product  (Taburet et al. , 2019)  versions. SLA gridded products cover the global ocean with a spatial and temporal resolution of respectively ¼ of a degree and 1 day. We used two different SLA datasets for each one of the DUACS product versions: the all satellites L4 global gridded product disseminated via the CMEMS and the two satellites L4 global gridded product distributed via the C3S. The first one is computed with a satellite constellation including all the available altimeters at a given time (ranging from 2 to 7 over the period considered in this study). As a consequence, the errors are not constant in time since they depend on the number of satellites used.
This product focuses on the mesoscale mapping capacity of the altimeter data together with the stability of the overall dataset. The two satellites SLA dataset is obtained by merging a steady number of altimeters (two) in the satellite constellation. Two satellites is the minimum requirement to retrieve mesoscale signals in delayed time conditions. (Pascual et al. , 2006; Dibarboure et al. , 2011). This fact also promotes nearly consistent errors during the whole time period (some variation of the error can occur related to changes of the two satellites constellation). This product focuses on the stability of the global mean sea level (MSL), even if this implies potential reduction of the spatial sampling of the ocean. The reader is referred to Fig. 1  in  Sánchez-Román et al. (2020)  for more information about the DUACS procedure flowchart applied to the altimetry data; and also to the processing of the tide gauge data used to compare with https://doi.
org/10. 5194/egusphere-2023-63 Preprint. Discussion started: 18 January 2023 c Author(s) 2023. CC BY 4. 0 License. altimetry (next section). The time period investigated spans from 1 January 1993 to 31 May 2020 due to the presently availability of DUACS DT2018 products. A complete description of the SLA datasets can be found in CMEMS-SL-QUID (2022).
Tide gauge observations The sea level records used to compare with satellite altimetry were extracted from the Copernicus Catalogue (www. marineinsitu. eu). The tide gauge stations located in the European Seas' domain were initially considered for this study. Following the methodology described in  Sánchez-Román et al. (2020) , the quality flags of the tide gauge records were checked in order to remove observations with no quality check; potentially and bad data; and changes in the vertical reference of the tide gauge. Also, observations with values larger than three times the standard deviation of the time series were rejected. The final dataset consists of 213 tide gauge stations (Fig. 1 ) with time series exhibiting between 90% and 100% of valid data. The stations and their information are listed in Table  A1  in the Appendix A.
Before they can be compared with altimeter data, tide gauge measurements have to be processed  (Valladeau et al. , 2012; Cipollini et al. , 2017; Sánchez-Román et al. , 2020)  to remove oceanographic signals whose temporal periods are not resolved by altimetry, thus avoiding important aliasing errors  (Vignudelli et al. , 2019). We applied the methodology described in  Sánchez-Román et al. (2020). In the following we summarise the corrections applied to the tide gauge records: • correction of oceanic tidal effects by filtering tidal components. We used the u-tide software  (Codiga, 2011). The annual and semiannual frequencies are kept in the tidal residuals since they are included in the altimetry data. • Removal of the atmospherically induced sea level caused by the action of atmospheric pressure and wind  (Dorandeu and Le Traon, 1999; Carrère and Lyard, 2003).
Method for comparing altimeter and in situ tide gauge records The comparison method of altimetry with tide gauges consisted of collocating both datasets in time and space. As a first step, a 15 day low pass Loess filter was applied to altimetry and tide gauge time series to remove the high frequencies that cannot https://doi. org/10. 5194/egusphere-2023-63 Preprint. Discussion started: 18 January 2023 c Author(s) 2023. CC BY 4. 0 License. be resolved by the altimetric data  (Pascual et al. , 2009; Ballarotta et al. , 2019; Sánchez-Román et al. , 2020). Then, we computed the correlations between each tide gauge record and SLA time series corresponding to grid points within a radius of 1 degree around the tide gauge site and choose the most correlated altimetry point. We used only long term monitoring stations with a lifetime of more than three years in order to allow statistical significance.
Statistical analyses were performed using all available data pairs (altimetry-tide gauge). The collocated altimeter and tide gauge measurements were analysed in terms of the rms difference and variance of the time series. In addition, the robustness of the results was investigated according to  Sánchez-Román et al. (2017 , 2020)  using a bootstrap method  (Efron and Tibshirani, 1986) , which allows us to estimate quantities related to a dataset by averaging estimates from multiple data samples. To do that, the dataset is iteratively resampled with replacement. A total of 1. 000 iterations were used to ensure that meaningful statistics such as standard deviation could be calculated on the sample of estimated values, thus allowing us to assign measures of accuracy to sample estimates  (Sánchez-Román et al.