# Impact of altimeter-buoy data-pairing methods on the validation of Sentinel-3A coastal significant wave heights

Guillaume Dodet, Gregoire Mureau, Mickael Accensi, Jean-François Piollé

► To cite this version:

Guillaume Dodet, Gregoire Mureau, Mickael Accensi, Jean-Francois Piollé. Impact of altimeter-buoy data-pairing methods on the validation of Sentinel-3A coastal significant wave heights. Remote Sensing of Environment, 2025, 316, 114483 (12p.). 10.1016/j.rse.2024.114483. hal-04878484

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# Impact of altimeter-buoy data-pairing methods on the validation of Sentinel-3A coastal significant wave heights

Guillaume Dodet a,*, Grégoire Mureau b, Mickaël Accensi a, Jean-François Piollé a

## ARTICLE INFO

Edited by Menghua Wang

**Keywords:**

Coastal altimetry

Data-pairing methods

Sea state variability

Sentinel-3A measurements

## ABSTRACT

Sea state information is critical for a broad range of human activities (e.g. shipping, marine energy, marine engineering) most of them being concentrated along the coastal zone. Satellite altimeter records of significant wave heights (SWH) represent the largest source of sea state observations available to date. However, the quality of altimeter observations is reduced in the coastal zone due to surface heterogeneity within the radar signal footprint. Major difficulties to assess the performance of coastal altimetry in the coastal zone are the reduced number of valid altimeter records and the increased sea state variability, which have recently fostered the development of new methods to pair and compare nearby altimeter and buoy data. In this study, we use a high-resolution numerical wave model implemented over the European coastal waters in order to characterize the spatial variability of sea states in the proximity of coastal in situ buoys, we explore different model-based data-pairing methods to account for coastal sea state variability and we assess their impact on the validation of Sentinel-3A 20Hz SWH measurements. Three Sentinel-3A processing modes are considered: the pseudo low rate mode processing, the SAR processing and the Low Resolution with Range Migration Correction (LR-RMC) processing. Our results indicate major impacts of data-pairing methods on the Sentinel-3A coastal validation and reveals the contribution of more frequent low SWH conditions, poorly resolved by radar altimeters, in the coastal zone as an additional source of errors in coastal altimetry.

## 1. Introduction

Collecting long-term, frequent and accurate coastal sea state information is critical for a broad range of human activities, such as commercial shipping, harbour operations, marine and coastal engineering, or marine energy resource assessment (Ardhuin et al., 2019). A particularly important demand for coastal sea state data concerns extreme wave statistics, since long return period events are currently significantly underestimated in global wave reanalysis (Fanti et al., 2023) while they may have dramatic impacts on the nearshore environments (Casas-Prat et al., 2024). Moreover, accurate coastal sea state information is required for satellite altimetry applications. Indeed, ocean waves are known to modify the scattering properties of the sea surface, with higher reflectivity in the wave troughs than in the wave crests, resulting in an underestimation of the mean sea level of the order of a few percent of the significant wave height (SWH) (Yaplee et al., 1971; Jackson, 1979). This so-called sea state bias still represents one of the major source of errors in satellite altimeter range corrections in the coastal zone (Vignudelli et al., 2019).

Satellite altimeter records of SWH represent the most abundant archive of sea state observations available to date. However, the

quality of altimeter acquisitions is degraded in the coastal zone due to land contamination and sea surface heterogeneities (e.g. natural and oil surface slicks, stretches of calm water in sheltered areas, bottom-induced wave steepening and breaking) within the radar signal footprint (Vignudelli et al., 2019). Over the last decades, increasing efforts have been devoted to enhance the exploitation of altimeter observations closer to the coast using new sensor technologies (e.g. K-band and synthetic aperture radar altimeters), improved waveform retracking algorithms (e.g. Passaro et al., 2018; Tourain et al., 2021; Schlembach et al., 2022), optimized geophysical corrections in the coastal zone (e.g. Fernandes et al., 2015) or dedicated post processing techniques (e.g. Birol et al., 2017).

Among the recent innovations, synthetic aperture radar (SAR) altimetry (also known as delay-Doppler altimetry) appears particularly efficient for monitoring the coastal zone, thanks to a finer along-track-resolution and a lower noise level (Raney, 1998). In this study, we investigate the performance of the SAR Radar Altimeter (SRAL) instrument on-board the Copernicus Sentinel-3A mission, to retrieve SWH in the coastal zone. In particular, different processing methods

<footnote>a Univ Brest, Ifremer, CNRS, IRD, LOPS, Plouzané, F-29280, France</footnote>

<footnote>b Ifremer, IRSI, ISI Service Ingénierie des Systèmes d'Information, Plouzané, F-29280, France</footnote>

<footnote>* Corresponding author.
E-mail address: guillaume.dodet@ifremer.fr (G. Dodet).</footnote>
permitted by this instrument, described in the next Section, will be
compared.

A number of studies have explored the performance of altime-
ter missions for measuring wave heights in the coastal zone based
on comparisons with in situ measurements (e.g. Hithin et al., 2015;
Nencioli and Quartly, 2019; Jiang et al., 2022) and high resolution
numerical wave models (Schlembach et al., 2020; Alday et al., 2022).
Two major difficulties have been identified for the interpretation of
coastal altimeter validation results. On one hand, the number of invalid
altimeter data drastically increases close to the coast so that improved
error metrics (e.g. bias, root-mean-square error) are often obtained at
the expense of a reduced sample size resulting from a more restric-
tive data editing (Schlembach et al., 2020). On the other hand, the
representativeness error due to the spatial and temporal separation
distances between pairs of altimeter and in situ measurements strongly
increases in the coastal zone and customary collocation method based
on fixed thresholds (usually 50 km and 30 min) are no longer adequate.
To overcome these limitations, several authors developed data-pairing
methods for the coastal zone based on numerical wave model re-
sults. Nencioli and Quartly (2019) used wave model hindcast results
over the southwest coast of England in order to define high corre-
lation areas between buoy and surrounding nodes. The selection of
altimeter data to be compared with the buoy data is then based on
these high correlation areas, so that spatial representativeness error is
reduced. Jiang et al. (2022) revisited this experiment and proposed a
dynamic correction to the buoy measurements based on wave model
outputs in order to account for SWH variability without reducing the
number of altimeter-buoy matchups.

In this study we consider 70 coastal buoys located in European
coastal waters near Sentinel-3A (S3A) tracks and we use a high-
resolution numerical wave model in order to characterize the spatial
variability of sea states in the proximity of these buoys. These in
situ, satellite and model datasets are presented in the next section
(Section 2). Then, buoy representativeness areas are defined from the
computation of systematic and random errors between the time series
simulated at the station and those of neighbouring grid points. These
areas are then used to compute buoy-altimeter matchup statistics and
estimate altimeter errors with respect to the buoy data. Additional
methods considered in this study are based on the dynamic compar-
ison between model results at the buoy location and at the altimeter
ground measurement, to ensure that (modelled) spatial variability
is low before comparing altimeter and in situ data. These different
methods are presented in Section 3. In Section 4, we first present the
buoy representativeness areas along the coasts of Europe, and then we
analyse the impact of the data-pairing methods on the overall S3A
performance, with a particular attention given to the impact of the
data-pairing methods on the geographical sampling and SWH distri-
bution in coastal altimeter records. Finally, the coastal performance
of S3A SWH measurements (considering PLRM, SAR and LR-RMC
processing) are presented and discussed to the lights of the improved
comprehension of the impact of data-pairing methods. Section 5 pro-
vides a summary of the results and presents some perspectives of
application.

## 2. Datasets

### 2.1. Sentinel-3A

The Copernicus Sentinel-3A (S3A hereafter) mission, launched in
February 2016, is a low Earth polar orbiting satellite operating at an
average altitude of 815 km above the Earth surface with a repeat cycle
of 27 days. It carries onboard a SAR Radar Altimeter (SRAL), which
provides high-resolution SWH measurements. SAR altimetry was first
developed for the European Space Agency (ESA) mission Cryosat for
its measurements over ice (and later extended to small sample regions
of the ocean), but S3A is the first altimeter mission to operate in

SAR mode globally over all surfaces. SAR altimeters present a narrow (~300 m) footprint in the along-track direction, which presents a major advantage in comparison to conventional low rate mode (LRM) altimetry for which the diameter of the altimeter footprint can exceed 10 km during rough sea state conditions (Chelton et al., 1989) making each consecutive 20 Hz measurement (approximately 300 m apart) dependent on each other. The SAR narrow-band footprint results from the coherent processing of radar pulses transmitted at very high rate (ten times as high as for LRM) to localize radar echoes and form multi-looked waveforms (Raney, 1998). Despite its clear advantages in terms of resolution and noise level (Boy et al., 2017), SAR processing proved to be particularly sensitive to the presence of swells for retrieving accurate wave height information (Moreau et al., 2018) and SAR SWH measurements were shown to be positively biased with respect to LRM measurements (Quartly et al., 2020). Moreover, the 20 Hz sampling was found to inadequately sample high frequency ocean wave signals, inducing errors over the entire wavenumber spectrum through spectral aliasing (Rieu et al., 2021; Ehlers et al., 2023). To overcome this issue, Moreau et al. (2021) implemented the Low Resolution with Range Migration Correction (LR-RMC hereafter) method, which uses an alternative averaging (stacking) operation so that all the Doppler beams produced in a radar cycle (4 bursts of 64 beams for the S3 open-burst mode) are incoherently combined to form a multi-beam echo. Contrarily to the narrow-band SAR technique, the LR-RMC processing enlarges the effective footprint to average out the effects of surface waves that are known to impact SAR processing performances. As a consequence, the measurements between successive 20 Hz records are not independent anymore. On the other hand, the number of averaged beams is as high as in current SAR processing, thus providing a noise reduction at least equally good.

The S3A measurements considered in this study are along-track
SWH records at 20 Hz posting rate over the period January 2018 -
December 2020. The SWH measurements are estimated from three dif-
ferent processing methods, namely the Pseudo Low Resolution (PLRM),
SAR and LR-RMC methods. The PLRM and SAR-processed data are
both from the EUMETSAT SRAL/MWR L2 Marine products (https://
www.eumetsat.int/sentinel-3), while the LR-RMC data are from the
ESA Sea State Climate Change Initiative project (Piollé et al., 2022,
https://climate.esa.int/en/projects/sea-state/). For each dataset, data
editing was performed based on the available surface type and quality
flag information.

### 2.2. Wave buoys

The CMEMS In Situ Thematic Assembly Center (CMEMS INSTAC)
is a component of the European Copernicus Marine Service and its
role is to ensure consistent and reliable access to a range of in situ
data for service production and validation. For this purpose, CMEMS
INSTAC collects multi-source/multiplatform data, and performs consis-
tent quality control before distributing the data in a common format to
the CMEMS Marine Forecasting Centres (MFC). The data can be found
at http://www.marineinsitu.eu/. In this study, we considered European
wave buoys moored in locations within 20 km from a S3A track and
at a 1-km minimum distance to the coast. 70 buoys were identified,
with distance to the coast comprised between 2 and 250 km. Almost
70% of these buoys are located within 50 km from the coast while the
remaining 30% provide a means of comparisons between offshore and
coastal environments. The locations of these buoys are shown on Fig. 1.

### 2.3. *High-resolution numerical wave model*

The wave model hindcast used in this study is being developed
at IFREMER in the context of the ResourceCODE project (OCEAN
ERA-Net cofound) with the aim to provide accurate long-term sea
state information for the exploitation of Marine Renewable Energy
(https://resourcecode.ifremer.fr/). It is a regional implementation of
<figure><img src="image_4.png" /><figcaption>**Fig. 1.** Location of the 70 wave buoys (magenta circles) moored within 20 km of Sentinel-3A ground tracks (dashed black lines) selected for this study. The background colorscale shows the SWH field from the high-resolution wave model during Ulla storm (February 14 2014). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)</figcaption></figure>

the WAVEWATCH III (hereafter WW3) spectral wave model on a high-resolution unstructured mesh extending from the south of Spain to the Faroe Islands, and from the western Irish continental shelf to the Baltic Sea (12°W to 13.5°E, 36°N to 63°N). The extension of the model grid is presented on Fig. 1 with an example of simulated SWH field during Ulla storm on February, 14 2014. The hindcast covers a 28-year period, from 1993 to 2020, and gridded outputs are stored every hour. The bathymetry combines data from the EMODnet dataset (EMODnet 2016) and the HOMONIM dataset provided by the French Naval Hydrographic and Oceanographic Service (Shom) with a 0.001° resolution over the Channel and the Bay of Biscay. The spatial mesh contains 328,000 nodes and the resolution ranges from 10 km offshore to 200 m near the coast. The spectral grid consists of 36 directions and 36 exponentially spaced frequencies, from 0.0339 Hz to 0.9526 Hz. The physical parameterization is the T475 parameterization described in Alday et al. (2021), which uses adjusted parameters for the wind-wave generation and swell damping terms. The model is forced along its boundaries with wave spectra generated by a global WW3 wave model hindcast forced with ERA-5 hourly wind fields (Hersbach et al., 2020) and CMEMS-Globcurrent surface current fields (Global Ocean Multi Observation Product, MULTIOBS_GLOPHY_REP_015_004). The regional model is forced by ERA-5 wind fields (with a bias correction for wind speeds larger than 21 m/s), and with currents and water levels reconstructed from the MARS2D and FES2014 tidal harmonics database. Detailed information on the ResourceCODE model implementation and validation can be found in Accensi et al. (2021) and Alday et al. (2022), while implementation and validation of the global wave hindcast are described in Alday et al. (2021).

## 3. Methods

### 3.1. Buoy representativeness area

In order to characterize the spatial variability of the SWH in the vicinity of the buoy, and to quantify the spatial representativeness of the buoy SWH measurements, we implemented a methodology based on the results of the high resolution numerical wave hindcast described in Section 2.3, and adapted from the work of Nencioli and Quartly (2019). In this method, the time-series of simulated SWH at the buoy location is compared to the time-series of simulated SWH at every surrounding node located within a radius of 200 km. The normalized bias (Nbias, Eq. (1)) and the scatter index (SI, Eq. (2)) are computed between the buoy and its neighbouring nodes, to characterize both systematic and random variabilities, respectively. The NBias and SI values are then interpolated over a 200 × 200 km regular grid with 200 m resolution in order to enhance the sampling in offshore regions, where the unstructured grid has a coarser resolution. The area presenting Nbias and SI values lower than 5% is then identified as the buoy representativeness area and a polygon is fitted to encompass this area as closely as possible. The different steps of the methods are illustrated on Fig. 2 for buoy 6200080, which is located near La Rochelle, on the west coast of France.

Note that this method can be applied to other sea state parameters, such as the wave period and direction (as in Mureau et al., 2022), and other geophysical variables for which satellite-in situ collocation is required, for instance to investigate coastal sea level variability near tide gauges.

Given that sea states present significant seasonal, inter-annual, and decadal variability, it is expected that the buoy representativeness areas depend on the time period over which they are computed. In this study, we have considered stationary buoy representativeness areas and we have used a 10-year time window from the model hindcast to compute these areas. The polygon vertices of the representativeness areas for the 70 European buoys considered in this study are provided as Supplementary Material (SM1), so that similar coastal validation activities can be performed.

### 3.2. Data-pairing methods

Data-pairing methods (also known as collocation or matchup detection methods) are required to associate and compare values acquired by distinct measurement systems (model or sensor) at nearby location and time (e.g. satellite and in situ observations). Four data-pairing methods are considered in this study. These methods are based on spatial criteria only since wave buoy measurements usually provide continuous hourly records, giving a maximum separation time between satellite and buoy records of 30 min, which is sufficiently small to consider the sea state to be stationary. The four methods are:

1. The *static* method: it uses a fixed separation distance (radius) from the buoy location to sample all altimeter records within this distance. This method is used in most altimeter CAL/VAL studies based on in situ measurements. The selected threshold is usually 100 km, but it can be relaxed to 300 km in order to increase the number of available data pairs. Conversely, in the coastal zone this distance is often reduced but barely below 20 km to keep a sufficient number of available data pairs (note that with an approximate 65 km separation distance between S3A tracks at European latitudes, around ~60% of the buoys are expected to be within 20 km of a track). In this study we consider four separation distances: 100, 50, 20, and 5 km.

2. The *polygon-based* method: it uses the polygon vertices derived from the buoy representativeness area analysis (see Section 3.1) to sample only the altimeter records within the area (polygon) of low sea state variability. The maximum separation distance is 100 km. This method is adapted from the definition of areas of correlation elaborated by Nencioli and Quartly (2019).
<figure><img src="image_5.png" /><figcaption>Fig. 2. Processing of the buoy representativeness area for buoy 6200080 (near La Rochelle, France). Step1 (left panel): Differences between modelled SWH at buoy location and surrounding nodes are computed over the hindcast duration. Step2 (middle panel): Maps of normalized bias and scatter index are interpolated over 200 km × 200 km grid (thick black dashed lines indicate the 5% isocontour). Step3 (right panel): The intersection (dotted area) between areas with |Nbias| < 5% (thick blue dashed line) and SI < 5% (thick orange dashed line) is used to fit a convex polygon defining the buoy representativeness area (red shaded area). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)</figcaption></figure>

<figure><img src="image_6.png" /><figcaption>Fig. 3. Examples of sampling regions (red shaded area) and altimeter records (blue dots) paired with buoy 6200192 (magenta circle) for the different data-pairing methods. (left) the static method considers only measurements within a fixed separation distance (here 50 km) from the buoy; four distances are considered: 100, 50, 20 and 5 km (black circles); (b) the polygon-based method considers only measurements occurring within the buoy representativeness area estimated from model hindcast; (c) the dynamic collocation method considers only measurements within 100 km from the buoy for which modelled SWH difference between the buoy and the altimeter record is lower than 5%. Black dots represent altimeter records that are not selected for comparisons. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)</figcaption></figure>

3. The dynamic collocation method: it uses model results dynamically (i.e. model results are analysed at the time of altimeter measurements) to sample only the altimeter records for which modelled SWH difference between the buoy and the altimeter locations is below 5%, following Janssen et al. (2007). The maximum separation distance is 100 km.

4. The dynamic correction method: it uses the model results dynamically in order to correct the buoy measurement from the modelled SWH gradient between the buoy and the altimeter record location. In its original form, proposed by Jiang (2020), this method gives the possibility to use several buoys, with a weighting scheme based on the inverse squared distance between each buoy and the altimeter records, to characterize more precisely the sea state conditions at the altimeter record location. Note that this method does not constrain the altimeter record sampling and can actually be used in combination with any of the methods presented above. In this study we have considered the method in its simplest form (only one buoy is used for a given location, see Equation 3 in Jiang, 2020) and a fixed maximum separation distance of 50 km.

Examples of sampling obtained with the static, polygon and dynamic collocation methods for buoy 6200192, near Nazaré in Portugal, are shown on Fig. 3. Selected and rejected samples are shown as blue and black dots, respectively. For the static (left panel) and polygon (middle panel) methods, all altimeter records located within the sampling area (red shaded area) are selected, while for the dynamic collocation method (right panel), the sampling area varies at each satellite pass depending on the modelled SWH gradient. However, we see that with this latter method, altimeter records as far as 100 km from the buoy can be selected.

### 3.3. Evaluation of S3A performance

S3A performance in the coastal zone was evaluated through statistical comparisons against buoy SWH records. The selected metrics for these comparisons are the normalized bias (Nbias), the scatter index (SI), and the correlation coefficient (R), computed as follows:

$$ Nbias = \frac{\sum_{i=1}^{n} (A_i - B_i)}{\sum_{i=1}^{n} B_i} \qquad (1) $$
$$SI = \sqrt{\frac{\sum_{i=1}^{n} [(A_i - \bar{A}_i) - (B_i - \bar{B}_i)]^2}{\sum_{i=1}^{n} B_i^2}} \quad (2)$$

$$R = \frac{\sum_{i=1}^{n} (A_i - \bar{A}_i)(B_i - \bar{B}_i)}{\sqrt{\sum_{i=1}^{n} (A_i - \bar{A}_i)^2 \sum_{i=1}^{n} (B_i - \bar{B}_i)^2}} \quad (3)$$

where $A_i$ and $B_i$ are the altimeter and buoy measurements, respectively, and n the number of altimeter-buoy matchups. For the S3A-buoy data comparisons, the metrics were computed using all the data pairs obtained with each of the four data-pairing methods presented previously. As opposed to previous altimeter validation work, in which the altimeter records collocated with buoy data are averaged using along-track neighbour data (which is generally referred to as “super-observations”) to reduce high-frequency noise (Abdalla et al., 2011), we consider here raw altimeter records, without any averaging, in order to estimate the uncertainty associated to the noisy individual 20 Hz record. Similarly, no smoothing was applied to the buoy data and only the buoy SWH recorded at the closest time to the altimeter approach was used for comparison.

# 4. Results and discussion

## 4.1. Wave buoy representativeness areas

SWH representativeness areas were computed for the 70 buoys selected for this study, from the analysis of the high resolution wave hindcast (see Section 2.3). These areas, shown on Fig. 4, exhibit strong heterogeneities in size and shape. In particular, offshore buoys (i.e. with distance to coast larger than 50 km, as defined in this study) are characterized by low and isotropic SWH variability resulting in large and near-circular representativeness areas, with mean and maximum surface areas of 4000 and 10,000 km², respectively (i.e. with an equivalent radius of 35 and 56 km, respectively), while nearshore buoys present very local error gradients resulting in reduced representativeness areas with surface areas as low as 7 km² (i.e. with an equivalent radius of 1.5 km). Buoys at intermediate distance from the coast present significant cross-shore error gradients (not shown here) resulting in anisotropic representativeness areas stretched in the along-shore direction. Note that many buoys moored in the North Sea at more than 100 km from the coast present smaller representativeness areas than several buoys moored in the Atlantic ocean at less than 50 km from the coast (e.g. along the western Portuguese coast), meaning that the distance to the coast is not the only factor influencing sea state variability.

Although it is not the goal of this study to investigate which environmental factors controls the coastal sea state variability depicted by the buoy representativeness area, we hypothesize that coastline geometry, and bathymetry, current and wind gradients are the main factors explaining coastal sea state variability, as investigated by many authors (e.g. Abdalla and Cavaleri, 2002; Ardhuin et al., 2012; Dodet et al., 2019). Several conclusions can be drawn from this preliminary analysis. First, since the most exposed buoys present quasi-circular representativeness areas of roughly 50-km radius, we can say that the (static) 50-km maximum separation distance often used to collocate altimeter and offshore buoy measurements (Zieger et al., 2009; Queffeulou, 2004) may explain at least 5% of systematic and random spatial representativeness errors in standard CAL/VAL studies using offshore buoys only. Then, we see that using the distance to the coast to select buoy data for comparison with (distant) satellite measurements is not sufficient to discriminate buoys with low and high spatial variability, and that other parameters should also be considered (e.g. current and wind gradients, degree of exposure to oceanic swell and wind sea), corroborating the findings of Jiang (2023). Finally, the very confined representativeness areas of some near coastal buoys, such as buoy 6200059 (Cherbourg, France), clearly hinders their use for satellite CAL/VAL activities.

<table><caption>**Table 1**
Percentage of buoys showing the best score for the following parameters: Nval, Nbias, SI, R (see also Fig. 6).</caption><thead><tr><th>Method</th><th>Nval (%)</th><th>Nbias (%)</th><th>SI (%)</th><th>R (%)</th></tr></thead><tbody><tr><td>50km-static</td><td>57<sup>a</sup></td><td>21</td><td>6</td><td>4</td></tr><tr><td>Polygon</td><td>1.5</td><td>16</td><td>29</td><td>29</td></tr><tr><td>Dynamic collocation</td><td>41.5</td><td>40</td><td>44</td><td>40</td></tr><tr><td>Dynamic correction</td><td>57<sup>a</sup></td><td>23</td><td>21</td><td>27</td></tr></tbody></table>

a Note that the 50 km-static and Dynamic correction methods share an equal number of values, hence a similar ranking with these two methods and an overall sum different than 100%.

## 4.2. Sensitivity of S3 coastal validation to data-pairing methods

In Section 3.2 (Fig. 3), we have shown that the choice of the data-pairing method has a strong influence on the geographic sampling of altimeter records to be compared with the buoy measurements. This choice is therefore expected to impact the error metrics computed from these comparisons. In order to investigate the sensitivity of altimeter validation results to the data-pairing methods, we compared Sentinel-3A SAR and buoy data using data pairs given by the static, polygon, dynamic collocation and dynamic correction methods. For each method we computed the relative (with respect to the 100 km-static method) number of data pairs (Nval), the normalized bias (Nbias), the scatter index (SI), and the correlation coefficient (R). Fig. 5 compares the different metrics obtained with the four data-pairing method, the first four bars corresponding to the four separation distances used with the static method (100 km, 50 km, 20 km and 5 km).

Looking at the relative number of data pairs (Nval) obtained with the static method and considering the 100, 50, 20 and 5-km maximum separation distances, we note a rapid decrease of available matchups when the maximum separation distance is reduced, matching the expected inverse-square law of the sampling surface area. Indeed, if we consider that the number of altimeter samples is proportional to the surface area of the considered region, it is therefore inversely proportional to the square of the maximum separation distance. As a result, using a fixed separation distance lower or equal than 20 km reduces the number of samples to less than 5% with respect to the number of samples obtained with a 100-km separation distance. Conversely, the three model-based methods (i.e. the polygon-based, dynamic collocation and dynamic correction methods) preserve between 10 to 35% of data. In terms of normalized bias, we see that Nbias is systematically higher for the four static methods and the dynamic correction method (between 6.9 and 8.8%) than for the polygon and dynamic collocation methods (between 4.9 and 5.4%). Same conclusions can be drawn for SI and R, for which the static and dynamic correction methods shows poorer performance (between 22.2 and 28.0% for SI and between 0.88 and 0.92 for R) than the polygon and dynamic collocation methods (between 20.3 and 20.6% for SI and 0.93 for R). Overall, the dynamic collocation method gives the best score while preserving a significant amount of data (34.8%). The dynamic correction method, which shares the same sampling as the 50-km static method presents slightly better performance than the latter, thanks to the model-based correction. Similar results were obtained when the same analysis was applied to PLRM and LR-RMC data (not shown here). However, we may question whether such conclusions can be drawn for each buoy separately or only for the aggregated dataset. To answer this point, we estimated for each buoy which data-pairing method provides the best score for the four considered parameters (Fig. 6 and Table 1). For this analysis, we only considered the 50 km separation distance for the static method, as it provides the best trade-off between the number of samples and the error metrics. First, we see that the maximum number of samples are either obtained with the 50 km-static or the dynamic collocation methods (first panel). Note that the dynamic correction method uses the same sampling as the 50 km-static method and therefore cannot be differentiated for this parameter (hence blue circles can be swapped
<figure><img src="image_7.png" /><figcaption>**Fig. 4.** Map showing the buoy locations (magenta circles) and buoy representativeness area polygons (light red areas) computed for 70 European buoys selected for this study. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)</figcaption></figure>

<figure><img src="image_8.png" /><figcaption>**Fig. 5.** Relative number of data pairs (Nval), normalized bias (Nbias), scatter index (SI), and correlation coefficient (R) obtained from the comparisons between Sentinel 3A SAR and buoy SWH data for the different data-pairing methods.</figcaption></figure>

with red circles). In terms of spatial distribution, we see that the 50 km-
static method provides the largest number of samples mostly for buoys
located near the coast, while the dynamic collocation methods provides

the largest number of samples for the offshore buoys. This can be
explained by the fact that – as opposed to the 50-km static method
– the dynamic collocation method considers altimeter records within
<figure><img src="image_9.png" /><figcaption>Fig. 6. Spatial distribution of the data-pairing methods providing the best score at each buoy location for the following metrics: relative number of data pairs (Nval), normalized bias (Nbias), scatter index (SI), and correlation coefficient (R) obtained from the comparisons between Sentinel 3A SAR and buoy SWH data.</figcaption></figure>

50–100 km from the buoy for which the modelled SWH difference with the buoy location is small. In offshore conditions, a significant number of altimeter records located between 50–100 km from the buoy satisfy this condition, as opposed to nearshore conditions where SWH variability is much stronger. The number of samples obtained with the polygon-based method is systematically lower due to site-dependent representativeness areas, which hardly cover an equivalent 50-km radius disc area for the most exposed buoys, and can be so small near the coast that no satellite record intersects it (see Section 4.1 and Fig. 4). In terms of Nbias we find that the dynamic collocation method gives the best score (lowest absolute Nbias) for the largest number of buoys (40%), while the polygon method gives the best score for the lowest number of buoys (16%). For SI and R, the three model-based methods are clearly better than the 50 km-static method for most buoys, with the dynamic collocation method showing best scores for 44% and 40% of the buoys, respectively. Similar rankings were obtained when the analysis was applied to the PLRM and LR-RMC datasets (not shown here). This analysis highlights the benefits of using model-based information to compare altimeter with buoy data and indicates that, for the set of buoys considered in this study, the dynamic collocation method outperforms the other methods both in terms of systematic and random errors, while the dynamic correction method preserves the largest number of samples. Nevertheless, our results also indicate that buoy settings should be considered individually to select the most adequate collocation method. Moreover, we recall here that the dynamic correction method can be used in combination with any sampling method, so that its performance could be enhanced by applying the polygon-based or dynamic collocation.

### 4.3. Impact of data-pairing method on sampling geometry and SWH distribution

Several factors may explain increased altimeter-buoy errors in the coastal zone: first, the sampling pattern of altimeter data collocated with coastal buoys is often skewed offshore (wrt. buoy position) because a higher fraction of altimeter data is invalid near the coast. Given that coastal sea states attenuate towards the coast (e.g. Passaro et al., 2021), there is a dominance of higher-than-average altimeter SWH in the selected samples, as explained by Jiang et al. (2022); second, radar altimeter sensors do not have a sufficient range resolution (around 50 cm for Ku-band instruments) to resolve low sea states (Smith and Scharroo, 2015), which could result in increased error level near the coast where sea states are lower on average.

In order to investigate how the different data-pairing methods influence the spatial sampling, Fig. 7 (left) shows histograms of the relative distance to the coast computed as the difference between the altimeter distance to the coast and the buoy distance to the coast, with

altimeter records selected with three different data-pairing methods (50-km static, polygon and dynamic collocation). Positive values correspond to altimeter-buoy matchups when the satellite is at a greater distance from the coast than the buoy and negative values correspond to altimeter-buoy matchups when the satellite is at a lower distance from the coast than the buoy. In the former (resp. latter) case, the altimeter is likely to measure higher (resp. ) SWH than the buoy, although the inverse is also possible in certain coastal configurations. For this analysis, only matchups obtained with buoys located within 50 km from the coast were used. We see that the distributions are all right-skewed, regardless of the data-pairing method. The histogram of the 50 km static method (green) is bounded at 50 km on either side of the buoy location, as expected, with 64% of positive values. The polygon method (orange) samples a lower number of values than the other methods, mostly bounded between –25 km and 60 km, and 64% of positive values. The histogram of the dynamic collocation method (blue) is the most skewed, bounded between –50 km and 100 km, and showing the highest excess of positive values (74%). Assuming that waves have generally more energy offshore than on the shoreward side of the buoy (see for instance Figure 2 of Mureau et al., 2022), we could expect a larger proportion of large waves with this last method, which could partially explain the larger bias obtained with this method in comparison to the other model-based methods (see Figure 5). On the SWH histograms shown on Fig. 7 (right), we see that the choice of the method has a significant impact not only on the total number of samples but also on the sampling distribution, with a higher proportion of low sea state (below 1 m) with the static method.

In order to investigate the impact of the significant wave height on the systematic and random errors between altimeter and buoy measurements, the NBias and SI parameters were computed as a function of the buoy SWH (Fig. 8, left). Only altimeter records and buoys located at more than 50 km from the coast were considered in order to reduce the impact of any coastal effects (e.g. land contamination of the footprint). We see that NBias is almost constant (around 4%) for SWH between 2–6 m and rapidly increases for SWH below 1 m, exceeding 100% for the 0–0.5 m bin. For SI, the increase is more gradual and becomes significant for SWH below 2 m, exceeding 110% for the 0–0.5 m bin. On the right panel of Fig. 8, the median and the range between the 25th and 75th percentiles of SWH are plotted as a function of the distance to the coast, for both buoy and S3A measurements. We see that the proportion of SWH below 2 m increases towards the coast, and represents more than half of the samples between 0–10 km. Given this higher proportion of calm sea states in the coastal zone, and the increased errors for low sea states, we can expect stronger (positive) systematic and random errors when altimeter measurements are compared to near coastal buoys, even when model-based collocation method is used. Such increased error is not directly related to coastal interference with the altimeter radar
<figure><img src="image_10.png" /><figcaption>**Fig. 7.** Histograms of the relative distance to the coast computed as the altimeter minus the buoy distance to the coast (left), and SWH (right) for the 50 km-static (green), polygon (orange) and dynamic collocation (blue) methods. Only matchups with buoys located within 50 km from the coast are considered here. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)</figcaption></figure>

<figure><img src="image_11.png" /><figcaption>**Fig. 8.** (Left) Nbias (blue) and SI (red) between S3A SAR and buoy data as a function of buoy SWH. Only buoy and altimeter data located at more than 50 km from the coast are used. (Right) Median (line) and range between the 25th and 75th percentiles (shaded area) of SWH computed over bins of 10-km as a function of the distance to the coast. The dynamic collocation method is used to select altimeter data. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)</figcaption></figure>

signal and its significant contribution to the uncertainties on coastal altimeter-derived SWH record is still little documented in existing coastal altimetry studies.

### 4.4. Evaluation of S3A coastal performance

In the previous section we have shown that the use of any of the three model-based data-pairing methods (polygon, dynamic col- location, and dynamic correction) to compare S3A and in situ data significantly reduced the spatial representativeness errors induced by the strong SWH spatial variability in the vicinity of the coastal buoys. Moreover, we have shown that the higher fraction of low sea states to- wards the coast may explain larger errors near the coast. In this section we will examine the coastal performance of S3A SWH measurements in the light of these findings, considering three S3A processing techniques: PLRM, SAR and LR-RMC. The dynamic collocation method is used to

pair S3A with buoy data as it was shown to provide the best results for the largest number of buoys while preserving a large amount of data.

Fig. 9 shows the normalized bias and the scatter index between S3A (PLRM, SAR and LR-RMC) and in situ data for each buoy as a function of the distance between the buoy and the nearest coastline. First, we see that most (67%) of the European buoys are located within 50 km from the coast, while the furthest offshore buoys (namely A121 and A122 amidst the North Sea) are moored as far as 240 km from the coast. The mean SWH for each buoy varies between 0.8 m and 3.6 m. The first pattern common to all S3A products is the increased error towards the coast. More specifically, the range of the normalized bias increases from [-2; 20]% in the 50-250 km coastal strip to [-5; 95]% in the 2-50 km coastal strip. Likewise, the range of SI increases from [11; 25]% in the 50-250 km coastal strip to [10; 100]% in the 2-50 km coastal strip. Moreover, the systematic error is positive for a large majority of the buoys, indicating an overestimate of S3A SWH data wrt. buoy data, which is particularly pronounced near the coast,
<figure><img src="image_12.png" /><figcaption>**Fig. 9.** Nbias (upper panels) and SI (lower panels) computed from the differences between S3A PLRM (left panels), SAR (middle panels) and LR-RMC (right panels) and buoy SWH data at each buoy as a function of the distance of the buoy to the coast. The data-pairing is based on the dynamic collocation method. Colorscale indicates the mean SWH at the location of each buoy.</figcaption></figure>

particularly with the S3A PLRM processing. If we now compare the mean error values in the different products (see values indicated in each subpanel of Fig. 9), we can see the clear improvement of SAR and LR-RMC data compared to the PLRM data. The mean normalized bias decreases from 18.6% (PLRM) to 5.6% (LR-RMC) and the mean SI decreases from 45.7% (PLRM) to 20% (LR-RMC). On average the LR-RMC processing presents the best performance, with a reduction of the error of approximately 20% with respect to SAR-processed data. This improved performance of LR-RMC with respect to SAR processing can be attributed to the larger effective footprint inducing correlated along-track data and averaging out the effects of long ocean waves (swells) that are known to impact SAR-mode measurements (Rieu et al., 2021), and to the smaller incoherent integration time limiting surface movement effects (Moreau et al., 2021). The fact that S3A performance starts decreasing from 50 km-onwards despite lower effective footprint areas could be the result of two factors: first, the buoy distance to the coast does not necessarily reflect the actual position of the paired altimeter records, which may occur closer to the coast; then, the average SWH records decrease towards the coast, which result in higher fraction of low SWH that are measured with limited accuracy by radar altimeters (see Fig. 8).

In order to investigate these impacts, the error metrics were binned as a function of the altimeter distance to the coast (Fig. 10). We see that the errors increase towards the coast and that the normalized bias is mostly positive (around 5%) for all products. Yet, in comparison to the previous analysis using the buoy positions instead of the altimeter positions (Fig. 9), the bias increase occurs closer to the coast, at around 40 km for PLRM and 20 km for SAR-processed data. For LR-RMC the bias remains very stable (between 0%–10%) up to 1 km from the coast (see zoom over the 0–20 km coastal strip on the left panels). For SI, we see that the error starts increasing at around 70 km for PLRM data. For SAR-processed data SI presents a sharp increase at around 7 km from the coast. And here again, LR-RMC data remains very stable (between 10%–22%) up to 1 km from the coast. Finally, the correlation coefficient R confirm the previous tendencies, with decreasing values at around 70 km for PLRM data, a sharp decrease at around 10 km for SAR-processed data, and a much more stable trend (above 0.9) for LR-RMC data. The decreased R values between 250 and 300 km likely result from the reduced sampling size in this region. If we compare the three products, we see that the biases are very similar (slightly lower for PLRM) in the 50–300 km region, while they become much lower

for SAR and LR-RMC data in the 0–50 km region. For SI and R, there is a significant offset between PLRM error level on one side, and SAR and LR-RMC error level on the other side. Also, the systematically lower SI and R values obtained with LR-RMC compared to SAR can be explained by the better spatial average of the surface elevation resulting from the larger effective footprint and mitigating the swell impact, and the lower incoherent integration time (0.05 s compared to 2.5 s for the unfocused SAR data processing), limiting possible surface movement effects. The shoreward increase in the SI and R offset between SAR and LR-RMC could be the signature of the impact of long ocean wave effects on SAR-processed measurements, as wave frequency and directional spread both reduce near the coast due to coastal sheltering, depth-induced refraction and fetch reduction. Overall, the LR-RMC data give the best scores in both offshore and nearshore waters, confirming the excellent performance of the LR-RMC processing method. In the 0–20 km region, the average scores for LR-RMC are: NBias = 2.9%, SI = 17.2% and R = 0.94. The number of valid values was also binned as a function of the distance to the coast. While these numbers are fairly similar between products up to 7 km from the coast, we can see that it drops more rapidly for LR-RMC in the 1–7 km region. This reflects the different data-editing information provided for each product which are more or less stringent in the coastal zone. With the LR-RMC product, this information seems to be particularly efficient to reject invalid altimeter record in the coastal zone, as also evidenced by Schlembach et al. (2020), which likely contributes to the improved performance compared to the SAR-processed data.

To estimate the contribution of inaccurate low sea state measurements on this coastal performance analysis, we computed the same metrics after excluding all buoy measurements below 1 m. The results are represented as dashed lines on Fig. 10. Overall, we note a systematic reduction of Nbias and SI, which is more pronounced in the 0–20 km coastal strip. This effect is particularly visible on PLRM and SAR-processed measurements within 0–5 km from the coast, with NBias reducing from 18% to 10% and from 13% to 3%, and SI reducing from 40% to 36% and from 39% to 31%, for PLRM and SAR respectively. Finally, the impact of the different data-pairing methods on the S3A coastal performance analysis is investigated. The Nbias and SI are computed considering all altimeter measurements within 0–10 km, 10–20 km and 20–50 km from the coast obtained with the different data-pairing methods (Table 2). Overall we note a large spread of the metrics when different data-pairing methods are used, which confirms
<figure><img src="image_13.png" /><figcaption>Fig. 10. Nbias (top-row panels), SI (second-row panels), R (third-row panels) and number of valid values NVal (bottom-row panels) computed from the differences between S3A PLRM (green circles), SAR (orange circles) and LR-RMC (purple circles), and buoy SWH data as a function of the distance of the altimeter record to the coast. The right panels present the results over the 0–300 km range, using bins of 10-km width shifted every 5 km, and the left panels correspond to a zoom over the 0–20 km range, using bins of 1-km width. Dashed lines represent the same metrics after excluding all buoy measurements below 1 m. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)</figcaption></figure>

<caption>Table 2</caption>

Nbias and SI between buoy and S3A SWH measurements (PLRM, SAR and LR-RMC), for altimeter data in the following coastal regions: 0–10 km, 10–20 km and 20–50 km from the coast.

<table><thead><tr><th rowspan="2">Method</th><th colspan="2">PLRM</th><th colspan="2">SAR</th><th colspan="2">LR-RMC</th></tr><tr><th>Nbias (%)</th><th>SI (%)</th><th>Nbias (%)</th><th>SI (%)</th><th>Nbias (%)</th><th>SI (%)</th></tr></thead><tbody><tr><td colspan="7" style="text-align: left;">0–10 km</td></tr><tr><td>Static 50 km</td><td>18.2</td><td>49.8</td><td>1.7</td><td>49.1</td><td>-3.0</td><td>29.9</td></tr><tr><td>Polygon</td><td>13.0</td><td>37.8</td><td>9.2</td><td>26.2</td><td>8.5</td><td>17.6</td></tr><tr><td>Dynamic collocation</td><td>19.0</td><td>42.2</td><td>11.7</td><td>33.7</td><td>6.3</td><td>20.3</td></tr><tr><td>Dynamic correction</td><td>53.7</td><td>63.0</td><td>26.0</td><td>51.7</td><td>10.0</td><td>24.3</td></tr><tr><td colspan="7" style="text-align: left;">10–20 km</td></tr><tr><td>Static 50 km</td><td>24.8</td><td>48.9</td><td>7.0</td><td>31.5</td><td>4.0</td><td>25.3</td></tr><tr><td>Polygon</td><td>14.8</td><td>44.3</td><td>8.9</td><td>24.9</td><td>6.9</td><td>18.8</td></tr><tr><td>Dynamic collocation</td><td>17.2</td><td>45.0</td><td>6.9</td><td>25.2</td><td>5.1</td><td>19.0</td></tr><tr><td>Dynamic correction</td><td>27.9</td><td>49.9</td><td>9.2</td><td>27.7</td><td>6.0</td><td>19.9</td></tr><tr><td colspan="7" style="text-align: left;">20–50 km</td></tr><tr><td>Static 50 km</td><td>17.7</td><td>43.6</td><td>9.8</td><td>26.7</td><td>8.2</td><td>21.7</td></tr><tr><td>Polygon</td><td>9.3</td><td>37.5</td><td>4.0</td><td>22.3</td><td>2.7</td><td>16.5</td></tr><tr><td>Dynamic collocation</td><td>9.2</td><td>38.6</td><td>5.4</td><td>22.5</td><td>4.5</td><td>17.1</td></tr><tr><td>Dynamic correction</td><td>13.6</td><td>42.5</td><td>6.0</td><td>23.6</td><td>4.5</td><td>18.0</td></tr></tbody></table>

the strong impact of the sampling on the results. These spreads are particularly pronounced in the 0–10 km region, and less pronounced in the 20–50 km region. We see that the best scores are systematically obtained with the polygon or dynamic collocation methods, while the dynamic correction method presents significant improvements with respect to static method, mostly in the 20–50 km region. In the 0–10 km region, this model-based method can even reduce the performance, possibly because of inaccurate model results in the near coastal zone. Comparing the different S3A processing modes, the LR-RMC clearly outperforms the PLRM and SAR-processed data, possibly due to its larger effective footprint (inducing dependencies between consecutive measurements) and smaller incoherent integration time, as well as its improved flagging of outliers.

## 5. Conclusion

Sea state variability is strongly enhanced in the coastal zone due to interactions between waves, currents, winds, bathymetry and coastline geometry. In Section 4.1, we have used a high-resolution wave hindcast

in order to estimate the spatial scales over which the SWH measured by European coastal buoys can be considered homogeneous (in a statistical sense). Our results show that these so-called buoy representativeness areas (here defined as the region where the modelled spatial representativeness systematic and random errors are below 5%) vary strongly in size and shape, depending on the buoy environmental settings, and can be as small as an equivalent disk's radius of 1.5 km for some highly sheltered nearshore buoy locations (see Fig. 2). Knowing that the conventional data-pairing (or collocation) methods used to compare altimeter and in situ data in deep water usually assumes sea state homogeneity over 50 to 100 km, it is clear that such methods cannot be directly applied for the validation of coastal altimeter SWH data without impairing the results. To demonstrate it, we computed in Section 3.2 statistical error metrics over samples obtained with several data-pairing methods, accounting or not for sea state variability, for comparing S3A and in situ SWH in the coastal zone. Our results confirm the efficiency of model-based data-pairing methods to reduce spatial representativeness errors related to coastal sea state variability, while preserving a sufficiently large sample from the population. For instance,
in comparison to the 50-km static collocation method, the dynamic collocation method gives a 30% lower Nbias and a 22% lower SI for a 22% larger sampling size (see Fig. 5). We also investigated the impact of the data-pairing methods on the geographical sampling and SWH distribution of coastal measurements and we showed that the seaward asymmetry of the coastal sampling (altimeter records are more frequent seaward of the buoy location) could partially explain positive biases observed between S3A and buoy measurements, and that the increased fraction of low values (below 1 m) in the SWH distribution could induce a significant increase of the altimeter measurement uncertainties in the coastal zone. While this impact could be highly significant in coastal altimetry validation results, it has been little documented so far. Having gained a better understanding of the role of data-pairing methods on coastal altimetry validation, we evaluated its impact on the coastal performance of S3A SWH measurements obtained with the PLRM, SAR and LR-RMC processing methods (Section 4.4). Our results show that all three products present increased error levels in the 0–50 km region. This can be explained by model limitations to reproduce the real world sea state variability and by the lower sea state conditions that characterized sheltered near-coastal region and that are inaccurately measured by Ku-band altimeter sensors. Ignoring these low sea state measurements significantly reduces the range of error levels in the 0–50 km region, particularly for the SAR and LR-RMC data (see Fig. 9). These comparisons clearly show the improved performance of SAR and LR-RMC products compared to PLRM, in both offshore and coastal waters (see Fig. 10). They also reveal the consistency of the S3A LR-RMC measurements up to 1 km from the coast partially due to the filtering effect inherent to LR-RMC processing and by an efficient data-editing procedure, which results in stable error metrics over the 0–20 km region, with average NBias = 2.4%, SI = 18.9% and R = 0.95. However, these findings were shown to be highly dependent on the selected data-pairing method and the buoy dataset, which requires deeper analysis in future coastal validation studies. Given the development of dedicated SAR altimetry coastal processors, such as the COastal Retracker for SAR ALtimetry (CORAL V1, Schlembach et al. 2022) or the one developed within the SAR Radar Altimetry for Coastal Zone and Inland Water Level project (HYDRO-COASTAL, https://www.satoc.eu/projects/hydrocoastal/index.html), it seems particularly relevant to apply optimized data-pairing methods in order to assess the performance of these processors in the coastal zone.

### CRediT authorship contribution statement

**Guillaume Dodet:** Writing – review & editing, Investigation, Methodology, Conceptualization. **Grégoire Mureau:** Investigation, Methodology. **Mickaël Accensi:** Resources. **Jean-François Piollé:** Resources.

### Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

### Acknowledgements

This research is funded by the European Space Agency (ESA) through the Sea State CCI project of the Climate Change Initiative (CCI) (ESA ESRIN, Contract 4000123651/18/I-NB), by the French Centre National d'Etudes Spatiale (CNES) through the SEASTAC project (N° 220641/00), and by the European Organisation for the Exploitation of Meteorological Satellites (EUMETSAT) through the COPAS project (EUM/CO/22/4600002662/CLo V1A).

## Appendix A. Supplementary data

Supplementary material related to this article can be found online at https://doi.org/10.1016/j.rse.2024.114483.

### Data availability

Data will be made available on request.

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