Assessment of DUACS Sentinel-3A Altimetry Data in the Coastal Band of the European Seas: Comparison with Tide Gauge Measurements

: The quality of the Data Uniﬁcation and Altimeter Combination System (DUACS) Sentinel-3A altimeter data in the coastal area of the European seas is investigated through a comparison with in situ tide gauge measurements. The comparison was also conducted using altimetry data from Jason-3 for inter-comparison purposes. We found that Sentinel-3A improved the root mean square di ﬀ erences (RMSD) by 13% with respect to the Jason-3 mission. In addition, the variance in the di ﬀ erences between the two datasets was reduced by 25%. To explain the improved capture of Sea Level Anomaly by Sentinel-3A in the coastal band, the impact of the measurement noise on the synthetic aperture radar altimeter, the distance to the coast, and Long Wave Error correction applied on altimetry data were checked. The results conﬁrmed that the synthetic aperture radar altimeter instrument onboard the Sentinel-3A mission better solves the signal in the coastal band. Moreover, the Long Wave Error processing contributes to reduce the errors in altimetry, enhancing the consistency between the altimeter and in situ datasets.


Introduction
Since 1992, altimeter missions have been providing accurate measurements of sea surface height (SSH) [1]. However, there is still a degree of uncertainty in altimeter measurements and in the geophysical corrections applied in the SSH computation [2][3][4][5]. Traditional altimetry retrievals have often been unable to produce meaningful signals of sea level change in the coastal zone due to the typically shallower water, bathymetric gradients, and shoreline shapes, among other things [6].
In the recent past, a lively international community of scientists has been involved in the research and development of techniques for coastal altimetry, with substantial support from space agencies such as the European Space Agency (ESA), the Centre National d'Études Spatiales (CNES), and other research institutions [7]. Efforts have aimed at extending the capabilities of current altimeters closer to the coastal zone. This includes the application of improved geophysical corrections, data recovery strategies near the coast using new editing criteria, and high-frequency along-track sampling associated with updated quality control procedures [6][7][8][9]. Concerning the geophysical corrections, one of the major improvements is in the tide models where the tidal component is not part of the observed signal [10] and needs to be removed [7].

Tide Gauge Observations
The sea-level records used to compare with satellite altimetry were obtained from the CMEMS In Situ Thematic Assembly Centre (TAC) data repository. The Copernicus catalogue provides data of 485 tide gauge stations along the World Ocean coasts, which are updated within a few weeks or a few months. This dataset covers the time period spanning from January 2010 to the present. Sixhourly tide gauge records were used according to the following procedure ( Figure 1): the 445 tide gauge stations located in the European seas' domain were initially considered for this study. The quality flags of the tide gauge records were checked and observations with anomalous SSH data

Tide Gauge Observations
The sea-level records used to compare with satellite altimetry were obtained from the cmEMS In Situ Thematic Assembly Centre (TAC) data repository. The Copernicus catalogue provides data of 485 tide gauge stations along the World Ocean coasts, which are updated within a few weeks or a few months. This dataset covers the time period spanning from January 2010 to the present. Six-hourly tide gauge records were used according to the following procedure ( Figure 1): the 445 tide gauge stations located in the European seas' domain were initially considered for this study. The quality flags of the tide gauge records were checked and observations with anomalous SSH data (values larger than three times the standard deviation of the time series) or changes in the vertical reference of the tide gauge were rejected. Additionally, tide gauge time series exhibiting a large variance (more than 20 cm 2 ) with respect to altimetry data were removed, as they are considered not representative of ocean sea level changes and are likely related to local features (e.g., river discharge). Only tide gauges with at least a 70% yearly data coverage were selected in order to allow the analysis of the seasonal signal.
The final set consists of 370 stations ( Figure 2). The stations and their information are listed in Table A1. Before they can be compared with altimeter data, tide gauge measurements have to be processed [7,19] to remove oceanographic signals whose temporal periods are not resolved by altimetry, thus avoiding important aliasing errors [6]. First, tidal components were removed from the sea level records using the u-tide software [28]. The annual and semiannual frequencies, mainly driven by steric effect, are kept in the tidal residuals since they are included in the altimetry data.
For consistency with the satellite altimetry data, the atmospherically induced sea level caused by the action of atmospheric pressure and wind was removed from the tidal residuals [7,25,29]. This high-frequency oceanic signal is badly sampled by altimeter measurements. To solve this problem, a combination of high frequencies of a barotropic model forced by pressure and wind (MOG2D) and low frequencies of a classical Inverted Barometer model was applied [30]. We used the DAC available at the Archiving, Validation, and Interpretation of Satellite Oceanographic Data (AVISO) website. The DAC data are provided as 6 h sea level fields on a 1/4 • × 1/4 • regular grid covering the global oceans. For each tide gauge site, the nearest grid point was selected and used to remove the atmospherically induced sea level from observations, previously converted into 6-hourly records [25]. Finally, the 6-hourly tidal residuals were corrected for vertical movements associated with glacial isostatic adjustment (GIA). Indeed, many studies have demonstrated the need for tide gauges to be corrected for vertical crustal land motion when compared to altimeter data, since tide gauges measure the relative sea level with respect to the land where they are grounded [19]. We considered GIA as the only source of vertical land motions and removed its effects from the tidal residuals using the Peltier mantle viscosity model (VM2) [31,32].

Method for Comparing Altimeter and In Situ Tide Gauge Records
The comparison method of altimetry with tide gauges consisted of co-locating both datasets in time and space. It was based on a particular track point selected for each tide gauge location as follows: we computed the correlations between each tide gauge record (tidal residuals) and SLA time series corresponding to track points within a radius of 1 degree around the tide gauge site and choose the most correlated track point. A minimum length of time series of 10 months (corresponding to approximately 10 cycles of Sentinel-3A) was set up to allow statistical significance [14]. Statistical analyses were performed between both datasets using all available data pairs (altimetry-tide gauge) for a given region.
The co-located altimeter and tide gauge measurements were analysed in terms of the RMSD and variance of the time series. The RMSD metric is commonly used to examine along-track altimeter data quality [14]. In addition, the robustness of the results was investigated according to [33] using a bootstrap method [34], 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 10 3 iterations were used to ensure that meaningful statistics such as standard deviation could Remote Sens. 2020, 12, 3970 6 of 27 be calculated on the sample of estimated values, thus allowing us to assign measures of accuracy to sample estimates.

Ancillary Data
The Global, Self-consistent, Hierarchical, and High-resolution Geography database (GSHHG) was used to estimate the nearest distance to the coast of the altimetry track points used to compare with tide gauges. The aim was to investigate the degradation of the altimetric signal as we approach the coast. The shorelines in the GSHHG database are constructed entirely from hierarchically arranged closed polygons and are available in five geographical resolutions. The early processing and assembly of the shoreline data is described in [35]. We used the latest data files for version 2.3.7 presently available and released on 15 June 2017 with the original full data resolution.

Comparison of Sentinel-3A and Tide Gauges along the European Coasts
This section presents the statistics of the comparisons performed between the Sentinel-3A altimetry data and the tide gauge observations from the cmEMS catalogue in the coastal region in terms of errors (RMSD) and the variance of the differences between both datasets. The analysis has been conducted for the entire European coast and the following sub-regions: the Mediterranean Sea, the IBI and NWS regions, and the Baltic Sea ( Figure 2). SLA measurements without filtering ( Figure 1) were used. The bootstrapping technique [34] was applied to gain an estimation of the standard errors of the differences between both datasets.
The mean value of the RMSD between the Sentinel-3A satellite altimetry and tide gauges is 6.97 cm. The mean distance between the location of the tide gauge and the location of the corresponding altimeter data with the highest correlation is 80 km with a standard deviation of 33 km. Data from 342 tide gauge stations were compared with the Sentinel-3A data. Thus, 28 stations were rejected from the computation according with the selection criteria described in the previous section. These stations are located in the NWS region, the Mediterranean Sea, and the Arctic Sea (Table A1).
The rejected tide gauge time series showing a variance much larger than that found in the corresponding altimetry time series (RMSD between both datasets larger than 20 cm) were further investigated. We checked the shape of their time series, together with the quality flag data related to SSH, tide gauge position, and recorded atmospheric pressure. The aim was to investigate the presence of outliers in the tide gauge time series due to poor quality control not captured by satellite altimetry responsible for such large discrepancies, which could be corrected by the data providers. A subset of twenty-four tide gauge stations (Table A2) showed abnormal values in variance due to poor quality control that induced substantial RMSD when compared to the Sentinel-3A and Jason-3 altimetry data. This represents 5% of the tide gauge dataset in the European coasts. Figure 3 shows the consistency between the altimetry and tide gauge data computed as follows: where the variance of the tide gauge is associated with the variance of the signal. Consistency is expressed here as the mean square differences between both datasets, computed as the variance of the differences (altimetry-tide gauge) in terms of percentage of the tide gauge variance. This approach has already been applied by [23,24] to compare the satellite altimetry and tide gauge measurements at a global scale. Overall, mean square differences lower than 10% are observed in most of the Baltic Sea ( Figure 3b). Larger mean square differences of around 25% are observed in the Gulf of Finland, whereas they reach values between 15% and 50% and even larger values when in connection region with the North Remote Sens. 2020, 12, 3970 7 of 27 Atlantic Ocean. The mean square differences are between 20% and 50% for stations located in the Mediterranean Sea and the NWS region ( Figure 3a).
If we analyse the results in terms of the RMSD (figure not shown), minimum mean errors of 3.41 cm were obtained in the Mediterranean Sea, whilst they increased until 10.72 cm for the NWS region. These results can be explained by the larger spatio-temporal variability observed in the NWS region (SLA mean variance of 206 cm 2 ) with respect to that found in the Mediterranean basin (SLA mean variance of 47 cm 2 ). Non-tidal variance, which is also larger in the former [36], contributes to the larger RMSD obtained in the NWS region.

Improvements of Sentinel-3A over Jason-3 Satellite Mission
In this section, we conduct an equivalent analysis on Jason-3 data. The Jason-3 satellite mission has an orbit repeat cycle of 9.91 days, whilst Sentinel-3A presents a repeat cycle of 27 days. To make the inter-comparisons between both satellite missions with in situ tide gauge observations comparable, SLA from Jason-3 was sub-sampled to retain every third point along the tracks to emulate the Sentinel-3A cycle. The tide gauge stations (270 stations) common to both satellite missions were used. The results obtained for the whole European coasts are summarised in Table 1.
Notice that the rejected tide gauge stations in the inter-comparison with Jason-3 are mainly located in the central part of the Mediterranean Sea, the Gulf of Finland, the easternmost part of the Baltic Sea, and along most of the Norwegian coast. As a consequence of this, the Arctic region will not be investigated here due to the lack of valid data ( Figure A1). Table 1. Inter-comparison of the satellite altimetry and tide gauge data from the European coasts in terms of the RMSD (cm) and variance (cm 2 ) of the differences between both datasets. The number of tide gauge stations used in the comparison, the mean distance between tide gauges and the most correlated along-track altimetry points, and the number of total data pairs (altimetry-tide gauge) used The largest errors, which reach 100%, are mainly found in the Atlantic shore of the IBI region. This could be due to the imprecisions of the corrections applied (i.e., ocean tide) to the altimeter data.

Improvements of Sentinel-3A over Jason-3 Satellite Mission
In this section, we conduct an equivalent analysis on Jason-3 data. The Jason-3 satellite mission has an orbit repeat cycle of 9.91 days, whilst Sentinel-3A presents a repeat cycle of 27 days. To make the inter-comparisons between both satellite missions with in situ tide gauge observations comparable, SLA from Jason-3 was sub-sampled to retain every third point along the tracks to emulate the Sentinel-3A cycle. The tide gauge stations (270 stations) common to both satellite missions were used. The results obtained for the whole European coasts are summarised in Table 1.
Notice that the rejected tide gauge stations in the inter-comparison with Jason-3 are mainly located in the central part of the Mediterranean Sea, the Gulf of Finland, the easternmost part of the Baltic Sea, Remote Sens. 2020, 12, 3970 8 of 27 and along most of the Norwegian coast. As a consequence of this, the Arctic region will not be investigated here due to the lack of valid data ( Figure A1).
The RMSD between the Jason-3 and tide gauge time series shows a mean value of 7.97 cm, whereas it is reduced to 6.89 cm for the inter-comparison using the Sentinel-3A dataset. Overall, the results from the Jason-3 satellite mission are consistent with those obtained for Sentinel-3A in terms of spatial distribution ( Figure A1).
In the IBI and NWS regions, 81 and 55 common tide gauge stations to Sentinel-3A and Jason-3 missions were respectively identified from the whole tide gauge dataset ( Table 2). The analysis conducted with these stations shows a mean RMSD of 6.62 cm and 10.31 cm, respectively, for the comparison with Sentinel-3A, whilst the mean values for the inter-comparison using the Jason-3 dataset are 7.31 cm for the IBI region and 12.22 cm for the NWS region. Thus, the Sentinel-3A satellite mission improves, respectively, the errors with tide gauges in both regions by 9% and 15%. Table 1. Inter-comparison of the satellite altimetry and tide gauge data from the European coasts in terms of the RMSD (cm) and variance (cm 2 ) of the differences between both datasets. The number of tide gauge stations used in the comparison, the mean distance between tide gauges and the most correlated along-track altimetry points, and the number of total data pairs (altimetry-tide gauge) used in the computation are displayed. The common tide gauge stations for the Sentinel-3A and Jason-3 satellite missions were used. Values in parenthesis show the uncertainties (error bars) computed for the RMSD and variance from the bootstrap method using 10 3 iterations. Finally, the improvement (%) of the Sentinel-3A data in comparison with tide gauges in terms of lower RMSD, lower variance of the differences (altimetry-tide gauge), and lower mean distance between the most correlated altimetry point and tide gauges with respect to Jason-3 is also displayed. SLA measurements without filtering have been used.

European Coasts
Sentinel-3A Jason-3 Improvement In the Baltic and Mediterranean seas (Table 2), where generally lower errors are observed, we identified, respectively, 88 and 38 tide gauge stations common to both missions, showing a mean RMSD of 5.69 cm and 3.47 cm for the comparison with Sentinel-3A, whilst the mean values for the inter-comparison using the Jason-3 data are 6.24 cm and 4.49 cm, respectively. Thus, the Sentinel-3A satellite mission improves the errors with tide gauges in both regions by 9% (23%) in the Baltic (Mediterranean) Sea.
Notice that the mean distance between tide gauge sites and the most correlated altimetry track points is shorter for the Sentinel-3A mission in all the sub-basins investigated except for the Baltic Sea, where the same mean distance is obtained for both satellite missions (Table 2). At first sight, this fact may contribute to the better results obtained for the Sentinel-3A mission. However, a shorter distance between tide gauge and the altimeter co-location point does not always result in a lower RMSD and variance of the differences (tide gauge-altimetry). This fact can be observed in the Baltic Sea, where an overall improvement of Sentinel-3A over Jason-3 is found despite the same mean distance tide gauge-altimetry for both missions. Therefore, this parameter has not a strong impact on the better results obtained with Sentinel-3A, and other reasons for the higher performance of the SAR technology in the coastal zone must be given.
To further investigate the impact of SAR technology on the quality of the Sentinel-3A data close to the coast, we analyse in the following sections how the measurement noise and the approach to the coast affect the retrieval of SLA in both the Sentinel-3A and Jason-3 missions. Moreover, the impact of Remote Sens. 2020, 12, 3970 9 of 27 the LWE processing, associated with geographically correlated errors between neighbouring tracks from different sensors, on the quality of altimetry along-track products will be assessed. The LWE is an empirical correction that aims at removing residual ocean tide and DAC signal, as well as residual orbit error (residual signals induced by the imperfection of the solution used for these corrections).

Impact of the Measurement Noise on the Retrieval of SLA in the Coastal Area
To check the impact of the measurement noise on the SRAL instrument onboard the Sentinel-3A mission, the inter-comparison between satellite altimetry and in situ tidal records in the European coasts is repeated but using the Lanczos low-pass filtered SLA available in cmEMS altimetric products (Section 2.1 and Figure 1). The outcomes are then compared with the inter-comparison conducted in the previous section. The same tide gauge sites and data points for the inter-comparisons using filtered SLA and SLA measurements without filtering from the Sentinel-3A mission were used to make the outcomes comparable. As a consequence, the statistics for the SLA measurements displayed in Table 3 slightly differ from those shown in Table 1 due to the different tide gauge sites and data pairs used.
The variance of the Sentinel-3A altimetry data diminished by 2% when using the filtered data (Table 3). This is an expected result due to higher frequencies being subtracted from the SLA time series in the filtering procedure. This fact decreased the RMSD by 0.3% when comparing the filtered SLA with Remote Sens. 2020, 12, 3970 10 of 27 tide gauge records with respect to that obtained when using the SLA without filtering. The variance of the differences (altimetry-tide gauge) was also reduced by 1% when using the Sentinel-3A filtered data. However, it is worth noting that the improvements in the inter-comparisons (RMSD reduction) when using filtered SLA are negligible. Table 3. The same as Table 1 but for the inter-comparison using Lanczos low-pass filtered SLA and SLA measurements without filtering for the Sentinel-3A and Jason-3 satellite missions. Common tide gauge stations for each satellite mission have been used.

European Coasts
Sentinel-3A Improv. Filtered S-3A This procedure was repeated using the Jason-3 dataset (Table 3). A reduction threefold larger (6%) in the variance of the filtered SLA with respect to the SLA without filtering is observed. This underscores the expected larger measurement noise in the unfiltered SLA from the Jason-3 Low Resolution Mode mission compared to the SAR mission [37,38]. As a result, a reduction of 2.3% in the RMSD was obtained when using filtered data. Additionally, the variance of the differences (altimetry-tide gauge) diminished by 5% when using the Jason-3 filtered data.

Effects of the Coastal Distance on Altimeter Data
The quality of retrieved altimeter signal decays with closer distance to the coast, because radar return from the land and bright target causes the typical shape of waveform to deviate [14,39]. To investigate the degradation of the altimeter signal and its performance as we approach the coast, an additional comparison between satellite altimetry from both Sentinel-3A and Jason-3 and in situ tidal records in the European coasts was conducted.
First, we estimated the distance to the coast of all track points within a radius of 1 degree around a given tide gauge by using the GSHHG dataset. Then, the closest altimetry track point to the coast (ctp hereafter) and the most correlated altimetry point (mcp hereafter) along the track of the ctp were identified. This provides two altimeter time series from track points along the same track from a given mission but with a different or equal distance to the coast (the latter if ctp and mcp match up) to compare against the same tide gauge. SLA measurements without filtering ( Figure 1) were used. Finally, statistics (RMSD and variance) for the inter-comparisons of satellite ctp and mcp with tide gauges were obtained. Differences between statistics when using the altimetry mcp and ctp against the same tide gauge will provide an estimation of the degradation of the altimetry signal as we approach the coast.
To obtain comparable results between the Sentinel-3A and Jason-3 missions, tide gauge sites exhibiting altimetry ctp with a similar distance to coast for both missions were identified. A maximum difference for the distance to the coast of ctp from the Sentinel-3A and Jason-3 missions for a given tide gauge site of 1 km was allowed. Only tide gauge sites showing a distance to coast of the altimetry mcp lower than 40 km were kept. This ensures the analysis in the nearest coastal zone of the European Seas, where the data quality can be affected by the impact of land and islands near the coast. Twenty-seven common tide gauge stations keeping the aforementioned selection criteria were identified.
Overall, the inter-comparisons between SLA measurements and tidal residuals improved in terms of RMSD and variance when using the altimetry mcp time series for both missions. This is an expected result, although the altimetry ctp is located closer to tide gauges and also closer to coast than the altimetry mcp for both missions (Table 4). Table 4. The same as Table 1 but for the inter-comparison using the altimetry closest track point to coast (ctp) and the most correlated altimetry point (mcp) with tide gauge records computed along the satellite track of ctp (see text for details) for the twenty-seven common tide gauge stations showing a similar distance with the altimetry ctp for Sentinel-3A and Jason-3 (a maximum difference of 1 km is allowed). The distance (km) of mcp and ctp to both tide gauges (TG) and coast and the degradation (in percentage) of the altimetry signal, computed as the differences between mcp and ctp, are also shown.

European Coasts
Sentinel The mean distance to tide gauges is lower for the Sentinel-3A dataset for both the mcp and ctp due to the reduction in the cross-track distance in the Sentinel-3A orbit with respect to Jason-3. The RMSD increased from 6.78 cm to 7.95 cm when we approach the coast (from the mcp location to the ctp location) for the Sentinel-3A dataset and from 7.91 cm to 8.74 cm for the Jason-3 dataset. These results suggest an impact of the distance to coast on the data quality for both missions.
The degradation of the altimeter signal, estimated here as the difference in the percentage of statistics between the altimetry mcp and ctp computations for a single mission, shows a mean value for the RMSD of 15% for the Sentinel-3A mission when we approach the coast from around 13 km to 5 km and of 10% for the Jason-3 mission. The degradation in the variance of the differences (altimetry-tide gauge) was 22% for Sentinel-3A and 20% for the Jason-3 dataset. Despite this lower degradation in the Jason-3 dataset, a superior performance of the Sentinel-3A dataset in terms of the lower along-track RMSD and a lower variance of the differences (altimetry-tide gauge) against the same tide gauges was obtained, also showing a mean distance of the ctp 300 m closer to coast than that of the Jason-3 dataset ( Table 4). The number of points used for both altimeters is similar, at 456 for Sentinel-3A and 442 for Jason-3, this suggesting a reasonable comparison.
The altimetry variance exhibited an enhancement of 5% for the Sentinel-3A dataset when we approached the coast, whilst it reached 10% for the Jason-3 mission (Table 4). This twofold increase in the latter can be associated with a larger impact of the measurement noise on altimeters onboard the Jason-3 close to coast, as was shown in the previous section. This fact again confirms that the SRAL instrument better solves the signal in the coastal band.

Impact of the Long Wavelength Error Correction Applied on Satellite Altimetry
SLA in DUACS-DT2018 processing is provided to data users after removing several disturbances affecting the altimeter measurements such as high-frequency oceanic signals, ocean tides, and Long Wavelength Error correction (LWE). The LWE is an empirical correction that aims at removing residual ocean tide and DAC signal as well as residual orbit error. An LWE reduction algorithm based on Optimal Interpolation (see for instance [1,3]) is applied. This optimal-interpolation based empirical correction contributes to remove high-frequency variability in the altimetry SLA due to noise (errors in corrections) and high-frequency signals close to the coast that are not fully corrected by the application of the corrections to minimise the other two aforementioned errors [40].
In this section, we investigate the possible impact of the LWE correction applied to Sentinel-3A and Jason-3 datasets on both the retrieval of SLA in the coastal zone and the inter-comparisons with in situ measurements performed. To do that, LWE correction applied to SLA was subtracted from the altimetry time series to obtain uncorrected SLA as follows: Then, the SLA uncorr time series were compared with tide gauge records according to the procedure described in previous sections. Finally, the outcomes from this new computation were compared with the inter-comparison conducted by using the corrected SLA. In this analysis, SLA measurements without filtering have been used.
The variance associated with the LWE correction applied on SLA from Sentinel-3A mission ( Figure 4) shows low values close to 0 cm 2 for most of the tide gauge sites located in the Baltic and Mediterranean Seas and in the southernmost part of the IBI region; whereas a larger variability exhibiting values larger than 25 cm 2 was found in the north-easternmost part of the latter and in the NWS region. Such variability is associated with the LWE absorbing part of the residual errors in ocean tide correction and DAC and also part of the remaining "long-wavelength" signal that can contribute to the SLA discrepancy between neighbouring tracks. Similar results were obtained for the LWE correction applied to SLA from the Jason-3 mission (figure not shown).
Remote Sens. 2020, 12, x FOR PEER REVIEW 12 of 35 Mediterranean Seas and in the southernmost part of the IBI region; whereas a larger variability exhibiting values larger than 25 cm 2 was found in the north-easternmost part of the latter and in the NWS region. Such variability is associated with the LWE absorbing part of the residual errors in ocean tide correction and DAC and also part of the remaining "long-wavelength" signal that can contribute to the SLA discrepancy between neighbouring tracks. Similar results were obtained for the LWE correction applied to SLA from the Jason-3 mission (figure not shown). The RMSD between the corrected SLA from Sentinel-3A (Jason-3) and the tide gauge records (Table 5) diminished by 10% (3%) with respect to that obtained when using uncorrected SLA. In addition, the variance of the differences between both datasets reduced by 18% (5%) when using corrected SLA. Thus, LWE correction leads to a better agreement between the altimeter datasets and the tide gauges. As we did for the comparisons conducted in the previous sections, here we have considered the same tide gauge sites and data points for the inter-comparisons using corrected and uncorrected SLA from the Sentinel-3A mission to make the outcomes comparable. Thus, the statistics for corrected SLA displayed in Table 5 slightly differ from those shown in Table 1 due to the different tide gauge sites and data points used. The same applies to the Jason-3 dataset. Table 5. Inter-comparison of the LWE-corrected and -uncorrected SLA from the Sentinel-3A and Jason-3 satellite missions and tide gauge data in the European coasts in terms of the RMSD (cm) and variance (cm 2 ) of the differences between the datasets. The number of tide gauge stations used in the comparison, the mean distance between tide gauges and the most correlated along-track altimetry The RMSD between the corrected SLA from Sentinel-3A (Jason-3) and the tide gauge records (Table 5) diminished by 10% (3%) with respect to that obtained when using uncorrected SLA. In addition, the variance of the differences between both datasets reduced by 18% (5%) when using corrected SLA. Thus, LWE correction leads to a better agreement between the altimeter datasets and the tide gauges. As we did for the comparisons conducted in the previous sections, here we have considered the same tide gauge sites and data points for the inter-comparisons using corrected and uncorrected SLA from the Sentinel-3A mission to make the outcomes comparable. Thus, the statistics for corrected SLA displayed in Table 5 slightly differ from those shown in Table 1 due to the different tide gauge sites and data points used. The same applies to the Jason-3 dataset. Table 5. Inter-comparison of the LWE-corrected and -uncorrected SLA from the Sentinel-3A and Jason-3 satellite missions and tide gauge data in the European coasts in terms of the RMSD (cm) and variance (cm 2 ) of the differences between the datasets. The number of tide gauge stations used in the comparison, the mean distance between tide gauges and the most correlated along-track altimetry points, and the number of total data pairs (altimetry-tide gauge) used in the computation are displayed. The common tide gauge stations for each satellite mission have been used. Values in parentheses show the uncertainties (error bars) computed for the RMSD and variance from the bootstrap method using 10 3 iterations. Finally, the improvement (%) of the LWE-corrected SLA data from Sentinel-3A and Jason-3 in the comparison with tide gauges, in terms of the lower RMSD and lower variance of the differences (altimetry-tide gauge) with respect to the LWE-uncorrected SLA data, is also displayed. SLA measurements without filtering have been used.

Discussion
The quality of DUACS Sentinel-3A SAR altimetric 1 Hz in the coastal band of the European Seas, estimated here through comparison with independent tide gauge measurements, revealed a mean RMSD between both datasets lower than 7 cm for the whole region, with mean values ranging around less than 4 cm in the Mediterranean basin and around 10 cm for the NWS region.
Previous works have compared in situ measurements from tide gauges and altimetry data in the European coasts.
The tide gauge records from the PSMSL-i.e., [5,20,25] or GLOSS/CLIVAR [23,24,26]-have been mainly considered. The PSMSL repository presents a dense tide gauge network in the European coasts similar to that found in the cmEMS repository, but it is based on monthly average sea level records. [41,42] conducted a regional calibration of the Sentinel-3A data at higher temporal scales by using tide gauge measurements included in the cmEMS repository, but it was focused on the German coasts of the German Bight and of the Baltic Sea. Thus, to our present knowledge, this is the first time that the dense cmEMS tide gauge dataset is used to compare with Sentinel-3A data in the whole European coasts.
The performance of the Sentinel-3A data in the coastal zone of the Gulf of Finland (Baltic Sea) was investigated by [43] through the comparison with tide gauge records from the Estonian Environment Agency. Such records are not included in the cmEMS repository. These authors found an overall RMSD between both datasets of 7 cm based on the inter-comparison with three tide gauge sites. This RMSD is larger than the one obtained here for the Baltic Sea (5.69 cm, Table 2). However, we used 88 tide gauge stations distributed along the whole basin, this allowing a more robust computation.
Ref. [42] compared, among others, the tide gauge sites of Kiel and Warnemünde with the 1 Hz Sentinel-3A data. The tide gauge processing included the tidal correction, whilst DAC and GIA correction were not applied. These authors found a standard deviation of altimeter and tide gauge difference of 3.3 (3.8) cm for the Kiel (Warnemünde) tide gauge station, which is slightly different to those obtained here, 4.0 (6.8) cm, for the same stations. This is probably due to the different tide gauge processing applied and stresses the impact of such processing on the consistency with altimetry data.
To investigate more in depth the quality of the Sentinel-3A data, a time series for the inter-comparisons conducted in the Mediterranean and Baltic seas is plotted in Figure 5. The tide gauge time series in the former (panel a) shows an annual cycle peaking in October, with an amplitude close to 30 cm. This is an expected result related to the steric effect in the basin that is properly captured by the Sentinel-3A altimetry data. However, this is out of the scope of this paper, because the length of the time series analysed is very short for properly investigating seasonal variability, so in the following we briefly summarise the features found. related to some inter-annual variability. This rise in SSH is captured by the Sentinel-3A dataset and also by in situ tide gauge measurements. As a consequence, the annual minimum in SLA observed in previous years in March-April is located in 2018 in May. This signal has not been detected in the other sub-regions investigated by either altimetry or tide gauge measurements.
The tide gauge time series in the Baltic Sea (Figure 5b) show an annual cycle peaking close to December with an amplitude of around 60 cm; this is quite similar to that found for the NWS region (figure not shown). The tide gauge time series exhibit much more inter-annual variability than that of the Mediterranean Sea. The larger seasonal signal observed in the Baltic Sea is attributed to water mass variations within the basin linked to steric changes in the nearby North Atlantic Ocean and river discharges, as well as meteorological forcing, and amplified due to the presence of shallow waters [44]. The quality of the Sentinel-3A dataset was also assessed by comparing it with the Jason-3 performance (RMSD and variance) obtained for the inter-comparisons with tide gauges conducted for the entire European coast and the different sub-regions investigated. The results are reported in Table 1 for the whole domain and in Table 2 for the different sub-basins clearly show the superior performance of the Sentinel-3A dataset with respect to Jason-3 in the coastal band in terms of the lower along-track RMSD and lower variance in the differences (altimetry-tide gauge) against the same tide gauges, despite their different ground tracks.
The Sentinel-3A satellite mission improves both the RMSD by 13% and the variance (altimetrytide gauge) by 25% with respect to the Jason-3 dataset in the European coasts. Figure 6 shows an example of the comparison between Jason-3 and tidal residuals at the tide gauge site of Aranmore (IBI region). A low correlation between both datasets was obtained, thus leading to poorer results than those for the Sentinel-3A mission (figure not shown). Additionally, the mean of the distance between the tide gauge sites and the most correlated altimetry track points used to conduct the inter- A sudden increase in SLA is observed in spring 2018 (black square in Figure 5), promoting a second maximum around March 2018 which is not observed in the previous year, being probably related to some inter-annual variability. This rise in SSH is captured by the Sentinel-3A dataset and also by in situ tide gauge measurements. As a consequence, the annual minimum in SLA observed in previous years in March-April is located in 2018 in May. This signal has not been detected in the other sub-regions investigated by either altimetry or tide gauge measurements.
The tide gauge time series in the Baltic Sea ( Figure 5b) show an annual cycle peaking close to December with an amplitude of around 60 cm; this is quite similar to that found for the NWS region (figure not shown). The tide gauge time series exhibit much more inter-annual variability than that of the Mediterranean Sea. The larger seasonal signal observed in the Baltic Sea is attributed to water mass variations within the basin linked to steric changes in the nearby North Atlantic Ocean and river discharges, as well as meteorological forcing, and amplified due to the presence of shallow waters [44].
The quality of the Sentinel-3A dataset was also assessed by comparing it with the Jason-3 performance (RMSD and variance) obtained for the inter-comparisons with tide gauges conducted for the entire European coast and the different sub-regions investigated. The results are reported in Table 1 for the whole domain and in Table 2 for the different sub-basins clearly show the superior performance of the Sentinel-3A dataset with respect to Jason-3 in the coastal band in terms of the lower along-track RMSD and lower variance in the differences (altimetry-tide gauge) against the same tide gauges, despite their different ground tracks.
The Sentinel-3A satellite mission improves both the RMSD by 13% and the variance (altimetry-tide gauge) by 25% with respect to the Jason-3 dataset in the European coasts. Figure 6 shows an example of the comparison between Jason-3 and tidal residuals at the tide gauge site of Aranmore (IBI region). A low correlation between both datasets was obtained, thus leading to poorer results than those for the Sentinel-3A mission (figure not shown). Additionally, the mean of the distance between the tide gauge sites and the most correlated altimetry track points used to conduct the inter-comparison reduced by 9% when using the Sentinel-3A altimetry data. This is due to the reduction in the cross-track distance in the Sentinel-3A orbit with respect to Jason-3, which promotes a higher probability of finding a Sentinel-3A track closer to a given tide gauge station. Similar results were found for the different sub-regions investigated.
Remote Sens. 2020, 12, x FOR PEER REVIEW 15 of 35 comparison reduced by 9% when using the Sentinel-3A altimetry data. This is due to the reduction in the cross-track distance in the Sentinel-3A orbit with respect to Jason-3, which promotes a higher probability of finding a Sentinel-3A track closer to a given tide gauge station. Similar results were found for the different sub-regions investigated. Lanczos low-pass filtered SLA from Sentinel-3A and Jason-3 were compared with tidal records from the tide gauge sites common to both missions. Overall, the inter-comparisons between the filtered SLA and in situ measurements improved when using the altimetry data from Sentinel-3A in all the regions investigated (Table 6). For the entire European coast, the RMSD was reduced 12% more for the Sentinel-3A satellite mission than for the Jason-3 one. The variance of the differences between both datasets reduced 22% more for the Sentinel-3A mission. Table 6. Summary of the improvements (%) of the Sentinel-3A mission in comparison with tide gauges in terms of the lower RMSD, lower variance of the differences (altimetry-tide gauge), and lower mean distance between the most correlated altimetry point and tide gauges with respect to Jason-3 in the European coasts and the different sub-regions investigated. The analysis is similar to that shown in Tables 1 and 2 (last column), but using filtered SLA data.

NWS Region
These results confirm that the SRAL instrument better solves the signal in the coastal band than altimeters onboard Jason-3 even when filtered SLA is used. The improvement of Sentinel-3A is higher for the NWS region with respect to the surrounding areas due to poorer performance (not shown) obtained for the Jason-3 mission in the region, which is probably related to the higher significant wave height signal and thus higher noise measurement (1 Hz bump; [17]) for this mission. Similar results were found for the inter-comparison conducted in the Baltic Sea and IBI region, indicating a poorer improvement of Sentinel-3A over Jason-3 in the area. The reduced noise measurement observed in Sentinel-3A contributes to improving the consistency with tide gauge measurements, but it does not explain by itself the improved performances of the Sentinel-3A mission compared to Jason-3.
To further investigate this, the LWE correction applied to the altimetry was checked. We found that the LWE correction diminished the variance of the SLA time series from Sentinel-3A used to Lanczos low-pass filtered SLA from Sentinel-3A and Jason-3 were compared with tidal records from the tide gauge sites common to both missions. Overall, the inter-comparisons between the filtered SLA and in situ measurements improved when using the altimetry data from Sentinel-3A in all the regions investigated (Table 6). For the entire European coast, the RMSD was reduced 12% more for the Sentinel-3A satellite mission than for the Jason-3 one. The variance of the differences between both datasets reduced 22% more for the Sentinel-3A mission. Table 6. Summary of the improvements (%) of the Sentinel-3A mission in comparison with tide gauges in terms of the lower RMSD, lower variance of the differences (altimetry-tide gauge), and lower mean distance between the most correlated altimetry point and tide gauges with respect to Jason-3 in the European coasts and the different sub-regions investigated. The analysis is similar to that shown in Tables 1 and 2 (last column), but using filtered SLA data. These results confirm that the SRAL instrument better solves the signal in the coastal band than altimeters onboard Jason-3 even when filtered SLA is used. The improvement of Sentinel-3A is higher for the NWS region with respect to the surrounding areas due to poorer performance (not shown) obtained for the Jason-3 mission in the region, which is probably related to the higher significant wave height signal and thus higher noise measurement (1 Hz bump; [17]) for this mission. Similar results were found for the inter-comparison conducted in the Baltic Sea and IBI region, indicating a poorer improvement of Sentinel-3A over Jason-3 in the area. The reduced noise measurement observed in Sentinel-3A contributes to improving the consistency with tide gauge measurements, but it does not explain by itself the improved performances of the Sentinel-3A mission compared to Jason-3.

European Coasts
To further investigate this, the LWE correction applied to the altimetry was checked. We found that the LWE correction diminished the variance of the SLA time series from Sentinel-3A used to compare with tide gauges by 21% in the European coasts (Table 5). This fact translates to better results in terms of the RMSD and variance of the differences (altimetry-tide gauge) when compared with tidal residuals. Similar results were obtained from the Jason-3 dataset. If we compare the outcomes reported in Table 5 for both satellite missions, a larger improvement in statistics was obtained for the Sentinel-3A dataset with respect to Jason-3. This leads to an overall larger impact of LWE correction on SLA from the Sentinel-3A mission.
If the LWE correction is not applied to both altimetry datasets, better results in terms of lower RMSD and variance (altimetry-tide gauge) were still obtained for the Sentinel-3A mission for all the regions investigated (Table 7). If these results are compared with those reported in Tables 1 and 2, computed from the LWE-corrected SLA, we observe an overall lower improvement in Sentinel-3A over Jason-3 when LWE-uncorrected SLA is used for all the regions investigated except for the IBI region. This fact stresses the higher residual high-frequency LWE for the Sentinel-3A mission shown in Table 5. Table 7. Summary of the improvements (%) of the Sentinel-3A mission in the comparison with tide gauges in terms of the lower RMSD, lower variance of the differences (altimetry-tide gauge), and lower mean distance between the most correlated altimetry point and tide gauges with respect to Jason-3 in the European coasts, and the different sub-regions investigated. The analysis is similar to that shown in Tables 1 and 2 (last column) but using LWE-uncorrected SLA data.

European Coasts
Med. Sea IBI Region NWS Region Baltic Sea The opposite behaviour found in the IBI region-that is, the lightly larger improvement in the Sentinel-3A mission with respect to Jason-3 when using the LWE-uncorrected SLA-could be due to the different location and number of altimetry points used to compare with tide gauges. However, the improvements obtained were only in the range of 1-2%.
These results demonstrate that LWE processing contributes to reducing errors in altimetry, enhancing the consistency between the altimeter and in situ datasets. However, it does not explain alone the better results obtained for the SAR technology in the retrieval of SLA close to the coast. Nonetheless, these outcomes again confirm the better capabilities of SRAL with respect to the altimeters onboard Jason-3 in the retrieval of SLA close to the coast in the European seas.
We have given the reasons why we decided to focus on the reference 1 Hz altimetry data instead of using high-rate (i.e., 20 Hz) SLAs. We realise that the use of high-frequency 20 Hz products could produce better results, and this analysis is in our future plans when these products will be available for the whole oceanographic community.

Conclusions
We have performed an assessment of the Sentinel-3A L3 along-track DUACS dataset in the coastal area of the European seas over a period of two and half years from May 2016 to September 2018. This validation was conducted by comparing the equivalent SLAs derived from 6-h sampled tide gauges over the same period in the whole domain and the following sub-regions: the Mediterranean and Baltic Seas and the IBI and NWS regions. Tide gauge records disseminated on cmEMS were used.
The mean value of the RMSD between 1 Hz SLA from Sentinel-3A and tide gauges for the whole European coasts was 6.97 cm. This showed some variability according to the different regions investigated: minimum mean values of 3.41 cm were observed in the Mediterranean Sea and maximum ones (10.72 cm) in the NWS region. These results can be explained by the larger spatio-temporal variability observed in the NWS region with respect to that found in the Mediterranean basin. Non-tidal variance, which is also larger in the former, contributes to the larger RMSD obtained in the NWS region. The assessment was also conducted using altimetry data from Jason-3 for inter-comparison purposes. The Sentinel-3A dataset showed a lower RMSD and variance of the differences (altimetry-tide gauge) in the European coasts.
The impact of the measurement noise on the SRAL instrument was checked by repeating the inter-comparisons but using filtered SLA. The results showed that the variance of altimetry data diminished by 2% when using filtered SLA from Sentinel-3A due to higher frequencies being subtracted from the SLA time series in the filtering procedure. As a consequence, an error 0.3% lower when comparing filtered SLA with tide gauge records with respect to that obtained when using the unfiltered data was obtained. Additionally, the variance of the differences between both datasets reduced by 1% when using the filtered data.
The outcomes from the Jason-3 dataset confirmed the better results obtained from filtered SLA, although much larger discrepancies were found between filtered and unfiltered SLA when comparing with tide gauge records with respect to those obtained for the Sentinel-3A mission. This fact emphasises that the Jason-3 dataset is affected by a higher measurement noise than Sentinel-3A, and also that SRAL instrument onboard the Sentinel-3A mission better solves the signal in the coastal band. This was doubly confirmed from the computations conducted using only filtered SLA from the Sentinel-3A and Jason-3 missions, and also from the analysis of the signal degradation when we approach the coast.
The impact of the LWE correction applied to satellite altimetry was also assessed. The RMSD between the LWE-corrected SLA from the Sentinel-3A and tide gauge records was 10% lower than that obtained when using uncorrected SLA, and the variance of the differences (altimetry-tide gauge) was also reduced by 18%. This is due to a depletion in the variance of SLA due to the LWE correction, which contributes to filtering out part of the residual high-frequency signals not removed after applying other geophysical corrections with respect to uncorrected data. The results for the whole domain and the four sub-regions investigated showed an overall improvement of the Sentinel-3A over Jason-3 when using the LWE-uncorrected SLA for all the regions. Thus, the Sentinel-3A mission still provided better results than the Jason-3 along the European coasts even if the LWE correction was not applied to both. Appendix A Table A1. List of tide gauge records with their location and the time period analysed. Bold stations were used in the inter-comparisons with altimetry data, whilst non-bold ones were rejected because they presented spurious data and/or did not keep the selection criteria described in the text.

Region
Station  Figure A1. Spatial distribution of the correlations (panels a,c) and relative variance reduction between tide gauge and SLA [variation(tide gauge-altimeter)]/variation(tide gauge); units are the percent of the tide gauge variance (panels b,d) for the inter-comparisons between Sentinel-3A (left column) and Jason-3 (right column) with tide gauge time series conducted in the European coasts. Unfiltered SLA and tide gauge stations common to both satellite missions have been used.