# Analog Data Assimilation of Along-Track Nadir and Wide-Swath SWOT Altimetry Observations in the Western Mediterranean Sea

Manuel Lopez Radcenco, Ananda Pascual, Laura Gomez-Navarro, Abdeldjalil

Aissa El Bey, Bertrand Chapron, Ronan Fablet

► To cite this version:

Manuel Lopez Radcenco, Ananda Pascual, Laura Gomez-Navarro, Abdeldjalil Aissa El Bey, Bertrand Chapron, et al.. Analog Data Assimilation of Along-Track Nadir and Wide-Swath SWOT Altimetry Observations in the Western Mediterranean Sea. IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing, 2019, 12 (7), pp.2530 - 2540. 10.1109/JSTARS.2019.2903941. hal-02113223

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# Analog Data Assimilation of Along-Track Nadir and Wide-Swath SWOT Altimetry Observations in the Western Mediterranean Sea

Manuel Lopez-Radcenco<sup>D</sup>, Member, IEEE, Ananda Pascual, Laura Gomez-Navarro, Abdeldjalil Aissa-El-Bey<sup>D</sup>, Senior Member, IEEE, Bertrand Chapron, and Ronan Fablet<sup>D</sup>, Senior Member, IEEE

**Abstract**—The growing availability of ocean data brought forth by recent advancements in remote sensing, in situ measurements, and numerical models supports the development of data-driven strategies as a powerful, computationally efficient alternative to model-based approaches for the interpolation of high-resolution, gap-free, regularly gridded sea surface geophysical fields from partial satellite-derived observations. In this paper, we investigate such data-driven strategies for the spatio-temporal interpolation of sea level anomaly (SLA) fields in the Western Mediterranean Sea from satellite-derived altimetry data. We introduce and evaluate the analog data assimilation (AnDA) framework, which exploits patch-based analog forecasting operators within a classic Kalman-based data assimilation scheme. With a view toward the upcoming wide-swath surface water and ocean topography (SWOT) mission, two different types of altimetry data are assimilated: along-track nadir data and wide-swath SWOT altimetry data. Using an observing system simulation experiment, we demonstrate the relevance of AnDA as an improved interpolation method, particularly for mesoscale features in the 20- to 100-km horizontal scale range. Results report an SLA reconstruction RMSE (correlation) improvement of 42% (14%) with respect to optimal interpolation, and show a clear gain when the joint assimilation of SWOT and along-track nadir observations are considered.

**Index Terms**—Interpolation, remote sensing, sea surface, radar altimetry signal sampling.

Manuscript received October 1, 2018; revised January 25, 2019; accepted February 21, 2019. This work was supported in part by ANR under Grant ANR-13-MONU-0014, in part by Labex CominLabs project SEACS, and in part by OSTST project MANATEE. A. Pascual acknowledges support from the Spanish Research Agency and the European Regional Development Fund (Award no. CTM2016-78607-P/PRE-SWOT). (*Corresponding author: Manuel Lopez-Radcenco*.)

M. Lopez-Radcenco, A. Aissa-El-Bey, and R. Fablet are with the IMT Atlantique, Lab-STICC UMR6285, 29200 Brest, France (e-mail: manuel.lopezradcenco@imt-atlantique.fr; abdeldjalil.aissaelbey@telecom-bretagne.eu; ronan.fablet@telecom-bretagne.eu).

A. Pascual is with the Mediterranean Institute for Advanced Studies (IMEDEA) (UIB-CSIC), 07190 Esporles, Spain (e-mail: ananda.pascual@imedea.uib-csic.es).

L. Gomez-Navarro is with Université Grenoble Alpes, CNRS, IRD, IGE, Grenoble, 38400 Saint-Martin-d'Hères, France, and also with the Mediterranean Institute for Advanced Studies (IMEDEA) (UIB-CSIC), 07190 Esporles Spain (e-mail: laura.gomez-navarro@univ-grenoble-alpes.fr).

B. Chapron is with the French Research Institute for Exploitation of the Sea (IFREMER), 29280 Plouzané, France (e-mail: bertrand.chapron@ifremer.fr).

This paper has supplementary downloadable material available at http://ieeexplore.ieee.org, provided by the authors.

Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/JSTARS.2019.2903941

## I. INTRODUCTION

T HANKS to recent advancements in remote sensing, in situ measurements, and numerical models, ever increasing amount of data, coming from a wide range of sources, are gathered daily. However, most of these data sources use different sampling strategies at multiple spatio-temporal resolutions, and usually involve irregular sampling patterns and missing data due to cloud occlusion, satellite orbit, and track geometry. In this context, the processing of such data sets to produce gridded gap-free products is of major interest for both research and industry. The problem of producing a regularly gridded field from irregularly sampled data belongs to the family of inverse problems, which have been extensively studied [10], [30], [33], [35]. In ocean sciences, state-of-the-art methods rely on optimal interpolation (OI) [2], [7], [23], a model-driven approach that involves modeling the spatio-temporal covariance structure of the field to be interpolated, usually under the hypothesis that this covariance structure remains constant in space and time. Such a hypothesis is not always verified, which leads to a lack of accuracy in the representation of the dynamics of smaller scale structures. Indeed, the Gaussian assumption inherent to OI techniques causes smaller scale structures to be smoothened, and it has been verified that it is not possible to recover fine scale structures (between 10 and 100 km) using OI [6], [14], [15]. Such limitation also relates to the inherent track separation in conventional altimeter tracks, governed by the orbit design and sampling strategies of currently space-borne altimetry missions. On the other hand, data assimilation techniques [9] have been regarded as a particularly powerful model-driven tool for the interpolation of high-resolution geophysical fields, provided that the chosen physical model is sufficiently accurate and does not bear a prohibitive computational cost. Nowadays, most alternative methods that do not rely on OI or data assimilation remain mostly model-driven, in spite of the growing availability of massive data sets, issued from both real remote sensing or in situ observations as well as numerical simulations or reanalysis issues, which truly supports the exploration of data-driven approaches as a powerful and efficient alternative [12], [35]. Here, we follow recent developments [11], [12], [25] that explore data-driven approaches for the interpolation of high-resolution geophysical fields. Data-driven approaches aim at exploiting available data sets, which can be considered
to accurately depict the spatio-temporal variability of the fields of interest, to emulate the physical model behind the process of interest, and better capture the spatio-temporal variabilities that may not be accounted for in purely numerical models.

Among recent advancements in remote sensing, the surface water and ocean topography (SWOT) satellite mission, a joint effort between the US National Aeronautics and Space Administration, the French Centre Nationale d'Etudes Spatiales and the UK and Canada Space Agencies aim at providing high-resolution altimetry maps for both hydrology and oceanography. Specifically, the SWOT mission will be the first mission to exploit wide-swath Ka-band radar interferometry altimeters producing, for the first time, complete two-dimensional (2-D) wide-swath satellite tracks [8], [16], [17], as seen in Fig. 2. Moreover, the mission's unparalleled high spatial resolution (2 km) should allow us to better capture mesoscale and submesoscale processes [8], [16], which constitutes one of the great challenges within current oceanography research. In preparation for the mission launch in 2021, we explore here the potential of exploiting SWOT-like observations in the context of data-driven methods for the reconstruction of high-resolution altimetry fields.

In previous work [24], we introduced the analog data assimilation (AnDA), a fully data-driven data assimilation framework and we further demonstrated its suitability for the interpolation of high-dimensional geophysical fields, namely sea surface temperature (SST) fields largely obscured by clouds [12] and irregularly sampled satellite-derived sea level anomaly (SLA) fields [12], [25]. Extending on this work, we introduce here the application of this framework to the reconstruction of high-resolution SLA fields from multisource remote sensing data. In particular, we consider and fusion classic nadir along-track altimetry sources [34] as well as wide-swath altimetry, with a view toward the upcoming SWOT mission [8], [16].

The chosen region of interest, the Western Mediterranean Sea, is characterized by small Rossby radii, with smaller scales structures whose reconstruction from satellite data appears as considerably challenging. In this respect, the Mediterranean Sea can be regarded as a small scale ocean laboratory, as a wide variety of global mesoscale and submesoscale ocean processes are also present, at smaller scale, within both the basin and sub-basin scales [1], [31], [40]. As such, developing efficient strategies to correctly capture and represent smaller scales within the Mediterranean Sea is of the utmost importance for the exploitation of the scientific potential that exists within the region.

We exploit here an observing system simulation experiment (OSSE) to demonstrate the relevance of AnDA for the high-resolution reconstruction of SLA fields from irregularly sampled data sources issued from real satellite-derived spatio-temporal sampling patterns, including nadir along-track altimetry and pseudo-SWOT patterns. We compare the proposed approach to state-of-the-art methods and demonstrate both a considerable gain, in terms of reconstruction error, for the reconstruction of smaller scales structures not correctly resolved by current methods, as well as a potential additional gain derived from the joint assimilation of both data sources considered.

The paper is organized as follows. In Section II, we formally introduce the problem of data assimilation, discuss related work, and present the fully data-driven AnDA framework. The considered case-study, data, and OSSE developed to evaluate the performance of AnDA is presented in Section III. In Section IV, we explore the effect of considering and combining different types of altimetric observations involving various spatio-temporal sampling patterns, namely nadir along-track and SWOT observations. Finally, we present our concluding remarks and future work perspectives in Section V.

## II. PROBLEM STATEMENT AND RELATED WORK

### A. Data Assimilation

Data assimilation refers, in a general way, to methods aimed at combining the equations governing the behavior of a dynamical system (which ultimately determine a numerical model) with observations conveying information related to such dynamical system, which can be either direct observations of the system state variables, or a function of such state variables. The objective is to improve reconstruction/forecasting performance of the numerical model by exploiting the additional information introduced by observations. Formally, a state-space formulation is used [9]

$$ \begin{cases} \mathbf{x}(t) = \mathcal{M}(\mathbf{x}(t - \delta t)) \\ \mathbf{y}(t) = \mathcal{H}(\mathbf{x}(t), \Omega(t)) + \eta(t) \end{cases} \quad (1) $$

where $t$ is a discrete time index, $\mathbf{x}$ is the hidden state sequence to be reconstructed, and $\mathbf{y}$ is the observed data sequence. $\mathcal{M}$ is a dynamical model relating the current state $\mathbf{x}(t)$ to the previous state $\mathbf{x}(t - \delta t)$. $\mathcal{H}$ is an observation operator, where $\Omega(t)$ is a mask accounting for missing data at time $t$ and $\eta(t)$ is a random noise process accounting for observation uncertainties.

In classical data assimilation, model $\mathcal{M}$ is applied at each time step to produce an initial forecast $\mathbf{x}^f$. This forecast is then corrected using observation $\mathbf{y}(t)$, by means of either stochastic approaches (such as Kalman [22] or particle filters [19]) aiming at producing the maximum a posteriori estimate (i.e., the most probable state) given the current state and observation sequence, or variational approaches (such as 3-DVAR [28]) aiming at optimizing a cost function that penalizes observation error, by means of gradient-descent approaches, to produce an improved prediction $\mathbf{x}^a$ (referred to as the analysis).

OI, in particular, relies on stochastic data assimilation to produce the MAP estimate of field $\mathbf{x}$, under the hypothesis that it follows a Gaussian distribution with a constant covariance matrix and that the observation operator $\mathcal{H}$ is linear. The length of the considered covariance structure will then represent a tradeoff between model locality, relating to fine scale reconstruction, and observation availability, relating to the size of the gaps to be filled. Given that the Gaussian hypothesis involves spatio-temporally invariant, mean covariance structures that tend to smooth out fine scale details, it should be expected that OI will not be able to fully exploit high-resolution information available in observations from either current or future
altimetry missions, such as SWOT. In this respect, considerable efforts are being made to improve OI [7] or find alternative approaches [12], [25], [43]. Following these efforts, we introduced in [24] the AnDA, a completely data-driven data assimilation approach that exploits available observations to emulate dynamical model $M$, thus avoiding the use of restrictive model hypothesis, such as spatio-temporally invariant covariance structures.

## B. AnDA Framework

The AnDA [24] was introduced as a data-driven alternative to classical data assimilation, and should allow us to tackle the strong dependence of classical data assimilation models on the accuracy and computational efficiency of numerical model $M$. AnDA is based on the hypothesis that dynamical model $M$ can be emulated by exploiting a catalog of realistic observations/simulations of the dynamical system.

In this way, at each time step, model $M$ is replaced by a data-driven numerical approximation, thus replacing the model-based forecasting step with a data-driven alternative. Formally, this comes down to the following state-space formulation:

$$ egin{cases} \mathbf{x}(t) = \mathcal{F}(\mathbf{x}(t - \delta t)) \\ \mathbf{y}(t) = \mathcal{H}(\mathbf{x}(t), \Omega(t)) + \eta(t) \end{cases} \quad (2) $$

where $\mathcal{F}$ is an analog forecasting operator. Specifically, for current system state $\mathbf{x}$, and assuming a catalog of past state dynamics large enough to accurately depict the underlying processes is available, operator $\mathcal{F}$ is built from the $K$ most similar states to $\mathbf{x}$ within the catalog, referred to as analogs. Given that the future state of these analogs, known as successors, is known and exists within the catalog, this information can be used to adjust a forecasting model that can be subsequently applied to the current state $\mathbf{x}$ to obtain forecast $\mathbf{x}^f$. In this respect, the procedure relies on the similarity between the current state $\mathbf{x}$ and simulated states stored in the catalog. The idea of analog forecasting was introduced by Lorenz in the context of weather forecasting [29], and relates to approaches such as nonlocal means [3] and nonlocal regularization [35]. In the context of stochastic data assimilation, the analog forecasting operator $\mathcal{F}$ involves the data-driven characterization of the transition probability between analogs and successors $p(\mathbf{x}(t)|\mathbf{x}(t - \delta t))$, so that the analog forecast $\mathbf{x}^f$ is obtained by sampling from the estimated distribution. Assuming a Gaussian prior $\mathbf{x}(t)|\mathbf{x}(t - \delta t) \sim \mathcal{N}(\mu_t, \Sigma_t)$, as in [24], the mean $\mu_t$ and covariance matrix $\Sigma_t$ are estimated from the $K$ nearest neighbors of the current system state within the catalog. Multiple strategies can be used for the estimation of these parameters, and we refer the reader to [12], [24], and [25] for an in-depth discussion. Here, we shall consider a locally linear model that involves fitting a weighted linear regression between the $K$ nearest analogs and their successors. The fitted linear regression is then applied to the current state to obtain mean $\mu_t$. Covariance matrix $\Sigma_t$ then comes to the empirical covariance of the residuals of the fitted linear regression. In this formulation, linear regression weights are introduced to account for the distance between the current state and its analog within the catalog, so that closer analogs will have a stronger contri-

bution to the estimation of the forecasting linear regression. To this end, following [25], a Gaussian kernel, normalized by the median distance between analogs and the current system state, is used.

Once this step is completed, AnDA proceeds similarly to classical data assimilation and exploits a stochastic scheme to combine forecast $\mathbf{x}^f$ with observation $\mathbf{y}$ and produce the analysis $\mathbf{x}^a$. In our current implementation, we consider an Ensemble Kalman filter/smoothen (EnKFS) to assimilate partial observations sampled at a $\delta t$ time step. Importantly, exploiting a stochastic data assimilation approach should allow us to evaluate the spatio-temporal uncertainty associated with the obtained altimetric field reconstruction, as is done in [13] and [25], which is of crucial importance for the scientific usage of an altimetry data product. That being said, the evaluation of the altimetric field reconstruction uncertainty is beyond the scope of this particular work, where we will rather focus on the effects of considering different spatio-temporal sampling strategies on the reconstruction of the finer scale details of the considered altimetry field.

The application of the proposed framework to the reconstruction of high-resolution geophysical fields from irregularly sampled data requires, however, the implementation of a number of strategies to deal with both the 2-D geometry as well as the high-dimensional nature of the data, as explained in the following section.

## C. Multiscale Patch-Based AnDA for High-Dimensional Geophysical Fields

1) **Multi-Scale Decomposition:** Given that we focus on resolving smaller scales not resolved by current methods, and that OI already provides an efficient way of estimating large scale dynamics, AnDA follows classical scale space decomposition principles [32] and exploits a multiscale decomposition

$$ \mathbf{x} = \bar{\mathbf{x}} + d\mathbf{x} + \epsilon \quad (3) $$

so that larger scales $\bar{\mathbf{x}}$ are resolved by means of an OI scheme, while the reconstruction of the anomaly field $d\mathbf{x}$ relies on the proposed AnDA, with unresolved scales being represented by $\epsilon$. We refer the interested reader to [25], particularly Fig. 3, for an in-depth description.

2) **Patch-Based State Space Formulation:** Following recent advancements in image processing [10], [35] and data assimilation issues [12], the 2-D nature of the considered data is tackled by extracting and vectorizing $W_p \times W_p$ overlapping patches of anomaly field $d\mathbf{x} = \mathbf{x} - \bar{\mathbf{x}}$. The AnDA is thus performed independently at the patch level, with the final anomaly field reconstruction being obtained by means of a simple overlapping patch averaging scheme. We denote a patch centered at position $s$ at time $t$ as $P(s, t)$.

3) **EOF-Based Representation of Patches:** Depending on the chosen patch size $W_p$, the vectorized anomaly patches $p(s, t) = \text{vec}(P(s, t))$ may probably involve a high number of dimensions. This is particularly problematic for the proposed framework, given that the analog forecasting is highly sensitive to the curse of dimensionality, as it relies on a $K$ nearest neighbor search, with the relevance of the neighbor selection being highly
degraded as dimension increases. To deal with this drawback, an empirical orthogonal function (EOF)-based decomposition [20] of vectorized anomaly patches $\mathbf{p}(s, t)$ is used

$$ \mathbf{p}(s, t) = \sum_{k=1}^{N_{\text{EOF}}} \alpha_k(s, t) \mathbf{B}_k \quad (4) $$

where $\mathbf{B}_k$ are the EOF basis functions learned from the ensemble of all patches $\mathbf{p}(s, \cdot)$ at location $s$, and $\alpha_k(s, t)$ are the coefficients of the decomposition of patch $\mathbf{p}(s, t)$, at location $s$ and time $t$, onto these EOF basis functions. At each location, only the $N_{\text{EOF}}$ strongest EOF basis functions are retained, so that AnDA is subsequently performed on coefficients $\alpha_k(s, t)$ representing each patch decomposition onto its locally computed EOF basis functions. In this way, analog forecasting (including the nearest neighbor search) and data assimilation are performed on the projection of patches $\mathbf{p}(s, t)$ onto a lower-dimensional space of their EOF-based representation, given by coefficients $\alpha_k(s, t)$, rather than on the high-dimensional space of patches $\mathbf{p}(s, t)$. Particularly, to deal with potentially missing values, e.g., for patches in coastal regions or containing land, a land mask is used at each location to remove land (or other missing) pixels, so that the considered patches only contain valid pixel values. Regarding missing values in partial observations involving irregular sampling patterns, the assimilation step of AnDA is implemented so as to ignore pixels involving missing data. This is achieved by defining, for each observation at each patch location, an appropriate observation operator $\mathcal{H}$ that projects the partial observation from the original spatio-temporal domain onto the reduced EOF-based domain. Specifically, observation operators for each observation at each patch location are built from the EOF basis functions by considering only pixel locations involving observed data, so that unobserved pixels are ignored for the definition of observation operators. Finally, for illustration purposes, a supplementary document presenting examples of the obtained EOF modes and coefficients time series for different patch locations is available alongside the electronic version of this paper.

a) Algorithm flowchart: To better illustrate the proposed algorithm and the interaction between the different strategies presented before, we present in Fig. 1 the flow chart of the proposed AnDA framework. We refer the interested reader to [12], [24], [25], and references there-in for additional details regarding methodological aspects of the AnDA framework.

### III. CASE STUDY AND DATA

We illustrate the relevance of the proposed approach by implementing an OSSE, considering a case-study region in the Western Mediterranean Sea (36.5°N to 40°N, 1.5°E to 8.5°E). As previously explained, this is a highly dynamic region where both mesoscale and submesoscale processes are present, with a considerably challenging reconstruction of small scale features and a high scientific potential as a small scale ocean laboratory.

<figure><img src="image_2.png" /><figcaption>Fig. 1. AnDA flowchart. AnDA is applied to fine scale detail field $dx = x - \bar{x}$ (anomaly with respect to OI-resolved large scale field $\bar{x}$). It involves extracting overlapping patches so that $dx$ is interpolated independently for each patch. At the patch level, AnDA applies EOF to the high-resolution training data set $dx_{\text{training}}$ to obtain a lower-dimensional catalog of EOF coefficients, and projects current SLA detail field estimate $dx(t)$ and partial observation $y(t)$ onto the training data set EOF basis functions. A Gaussian linear model is then estimated from the nearest neighbors of the current SLA detail field $dx(t)$ in the catalog and used for prediction. Partial observation $y(t)$ is subsequently used to further improve prediction by exploiting an EnKFS. The final step comes to the projection of the improved prediction produced by the EnKFS from the reduced EOF-based domain onto the original spatio-temporal domain, and the averaging of overlapping patches to obtain the final predicted altimetry field $dx(t + dt)$.</figcaption></figure>

#### A. Data

A synthetic ground-truth data set of daily high-resolution SLA fields from 2010 to 2013 is generated using the Western Mediterranean Operational Forecasting System (WMOP) numerical model from SOCIB [21]. WMOP is a regional reparametrization of the Regional Ocean Modeling System (ROMS) model nested in the Mediterranean Ocean Forecasting System (MFS), focused on producing high-resolution realistic ocean dynamics simulations in the Mediterranean Sea. The original grid resolution of the model varies between 1.8 and 2.2 km (~ 1/50°). We refer interested readers to [21] for an in-depth discussion of implementation details and validation of the WMOP model. For this experiment, however, high-resolution SLA fields produced by WMOP are down-sampled to a 1/20° resolution.

#### B. Observing System Simulation Experiment

The generated ground-truth SLA fields data set is split into a training data set comprising years 2010–2012, from which the catalog is created, and a test data set comprising year 2013, which serves as ground-truth for the generation of synthetic observations and the evaluation of reconstruction performance.

Synthetic observations emulating satellite altimetry are generated using the proposed OSSE, which exploits spatio-temporal locations derived from real satellite tracks from a four altimeter configuration (comprising Jason-2, Cryosat-2, Saral-Altika, and Hy-2A satellite missions) in 2014. The year 2014 was chosen as reference because it provides the greatest number of spatio-temporal locations from real airborne altimetry missions.
Following [34], acquisition noise is simulated by means of an additive Gaussian white noise of variance $\sigma_n^2 = 3$ cm$^2$.

SWOT-like observations, on the other hand, are generated from the ground-truth high-resolution SLA fields using the SWOT simulator [17], provided by the SWOT science team. Synthetic observations obtained with the SWOT simulator are produced by linearly interpolating the ground-truth fields onto a synthetically generated SWOT-like 2-km resolution grid computed using expected orbit characteristics of the SWOT mission. Additionally, the SWOT simulator emulates most noise sources expected to influence the mission once launched. According to the SWOT mission error budget [8], this includes both correlated noise sources, related to the novel radar interferometry based altimetry technique, its sampling spatio-temporal geometry and atmospheric perturbations (e.g., roll, phase, timing, baseline dilation, and wet troposphere errors), and uncorrelated noise related to sensor acquisition error (e.g., KaRIn sensor noise). In [27], we demonstrated the high sensitivity of AnDA to correlated noise sources. Taking these results into account, we consider here synthetic SWOT observations involving uncorrelated noise sources only, under the assumption that a pre-processing scheme can be exploited to filter correlated noise sources [18] or take it into account into the correlation structure of data assimilation schemes [39].

Both types of synthetic observations are linearly interpolated onto a regular 1/20° grid to match the high-resolution ground-truth SLA fields.

### C. Pseudo-Observations

To further investigate alternative sampling strategies, two different synthetic observation generation methods are explored. The first strategy comes to simply considering observations at times $t_0, t_0 + \delta t, \dots, t_0 + n\delta t, \dots$ etc., with $\delta t = 1$ days, directly. Alternatively, the second strategy relies on building pseudo-observations by accumulating observations on a time window $t_0 \pm D$ days centered at current day $t_0$. Additionally, nadir along-track and SWOT observations (or pseudo-observations) from the same day $t_0$ can also be combined, which allows for the seamless fusion of both data sources within the AnDA framework. An illustration of this principle and a visual comparison of these two strategies is presented in Fig. 2. We consider here a time window $t_0 \pm D$ of size $D = 5$ days, which was the optimal window size obtained in a parameter sensitivity analysis experiment [27].

## IV. NADIR ALONG-TRACK VERSUS SWOT DATA

To evaluate the effect of different observation sampling patterns, we consider both nadir along-track observations and pseudo-SWOT wide-swath observations, and compare the performance of AnDA when assimilating both types of observations separately, as well as a combination of them. For all the reported experiments, performance is measured by means of the root mean square error (in m) and correlation coefficient, for both the predicted SLA field and the gradient of the predicted SLA field ($\nabla$SLA). The default parameter settings considered are: patch size $W_p = 30$ pixels ($\sim 150$ km), $K = 25$ neighbors,

<table><caption>TABLE I
ROOT MEAN SQUARE ERROR (CORRELATION) FOR ANDA SLA RECONSTRUCTION WHEN CONSIDERING CLASSIC NADIR ALONG-TRACK OBSERVATIONS ($AT_D$), WIDE-SWATH SWOT OBSERVATIONS ($SWOT_D$), AND A FUSION OF NADIR ALONG-TRACK AND SWOT OBSERVATIONS</caption><thead><tr><th>Setting</th><th>SLA</th><th>∇SLA</th></tr></thead><tbody><tr><td>AT<sub>0</sub></td><td>0.02395 (0.9186)</td><td>0.005507 (0.6989)</td></tr><tr><td>AT<sub>5</sub></td><td>0.01978 (0.9457)</td><td>0.004699 (0.7660)</td></tr><tr><td>SWOT<sub>0</sub></td><td>0.01810 (0.9543)</td><td>0.004436 (0.7857)</td></tr><tr><td>SWOT<sub>5</sub></td><td>0.01920 (0.9502)</td><td>0.004345 (0.7913)</td></tr><tr><td>AT<sub>0</sub> + SWOT<sub>0</sub></td><td>0.01742 (0.9576)</td><td>0.004375 (0.7934)</td></tr><tr><td>AT<sub>5</sub> + SWOT<sub>5</sub></td><td>0.01876 (0.9523)</td><td>0.004318 (0.7952)</td></tr><tr><td>AT<sub>5</sub> + SWOT<sub>0</sub></td><td><b>0.01687 (0.9607)</b></td><td><b>0.004286 (0.8051)</b></td></tr><tr><td>OI</td><td>0.02927 (0.8451)</td><td>0.006655 (0.6052)</td></tr><tr><td>NNLD</td><td>0.02115 (0.6965)</td><td>0.004506 (0.5893)</td></tr></tbody></table>

For each type of observations, both daily observations ($D = 0$) and observations accumulated on a time window $t_0 \pm D$ with $D = 5$ days are considered. Best Result in **bold**. Results for OI [7] and NNLD [26] given as reference.

$\delta t = 1$ days, $N_{EOF} = 9$ EOF components. These settings relate to optimal parameter values obtained from a parameter sensitivity analysis experiment [27].

Table I presents SLA and $\nabla$SLA RMSE and correlation results obtained when considering nadir along-track data, SWOT data and a combination of both nadir along-track and SWOT data (which may be regarded as equivalent to considering the nadir along-track data that is part of the SWOT configuration) for current observations only and for observations accumulated on a time window $t_0 \pm D$ with $D = 5$ days. Reconstruction performance of OI [7], and of a data-driven locally adapted convolution-based non-negative decomposition approach are included as reference. The second data-driven approach considered, non-negative linear decomposition (NNLD), was introduced in [26] for the interpolation of irregularly sampled geophysical fields. This super-resolution model locally applies convolutional operators to reconstruct the SLA field from an optimally interpolated initial guess. The convolutional operators considered vary in space and time according to a patch-level representation. To this end, convolutional operators are decomposed onto an operator basis learned in the model training step, so that they can then be fitted locally (in space and time) from the available altimetry data in a given spatio-temporal neighborhood. The OI SLA reconstruction was obtained from nadir along-track observations with a standard covariance parametrization considering a temporal correlation scale of 10 days and a spatial correlation scale of 100 km. The NNLD SLA reconstruction, on the other hand, employs a globally fitted dictionary-based convolutional model that is then locally adjusted in $2^\circ \times 2^\circ$ overlapping regions, and considers nadir along-track data accumulated on a 21-day window.

From Table I, a first interesting result is that considering SWOT observations for the current day only (without accumulation) is already enough to outperform OI, NNLD, and AnDA when considering only along-track data. Particularly, our results suggest a mean normalized root mean square error (nRMSE, computed by normalizing the RMSE by the variance of the ground-truth high-resolution SLA fields) gain of around 2.8%
<figure><img src="image_3.png" /><figcaption>Fig. 2. Examples of pseudo-observations generated for 9th March, 2013 from the ground-truth SLA fields by considering either observations at current day $t_0$ or observations accumulated over a time window $t_0 \pm D$ with $D = 5$ days, for both classic nadir along-track altimetry (noted as AT$_D$) and pseudo-SWOT observations (noted as SWOT$_D$). (a) Nadir along-track observations accumulated on a time window $t_0 \pm D$ with $D = 5$ days (noted as AT$_5$). (b) Daily SWOT observations (noted as SWOT$_0$). (c) Fusion of daily nadir along-track observations accumulated on a time window $t_0 \pm D$ with $D = 5$ days and daily SWOT observations (noted as AT$_5$ + SWOT$_0$).</figcaption></figure>

for the whole year 2013 and 6.2% for days when at least one SWOT track is observed (with respect to the assimilation of 5-days accumulated along-track data only), which clearly implies that the performance gain relates to the availability of SWOT observations. This is in agreement with previous studies [4], [37] that suggest that SWOT observations should be able to provide as much information as four conventional altimeters for the reconstruction of mesoscale features. Indeed, for days when a SWOT swath exists within the considered region, the surface coverage of such swath is considerably larger than the surface coverage of the 5-day accumulated nadir along-track observations, which partially explains the increased reconstruction performance. Moreover, our results suggest that days involving a loss in reconstruction performance are, as expected, days where no SWOT observation exist and which thus involve a loss in observation coverage. For such days, AnDA relies solely on the analog forecasting scheme to produce a prediction when considering daily SWOT observations, whereas when considering 5-days accumulated nadir along-track data, there is always some partial information conveyed by observations available every day for AnDA to assimilate.

Another interesting, yet counterintuitive, result is that performance seems to decrease when accumulating SWOT observations over a time window $t_0 \pm D$ days. We hypothesize that wide-swath observations, given their 2-D nature and higher continuous spatial coverage, are prone to capturing moving/changing structures multiple times as observations are accumulated, thus creating inconsistent SLA observations leading to the reconstruction of fictitious structures. Accumulating SWOT observations will thus tend to increase the sensitivity of AnDA to changes occurring in the SLA field during the days over which observations are accumulated. In this respect, accumulating observations over multiple days seems to be an appropriate strategy to improve AnDA SLA reconstruction performance for nadir along-track data, whereas for SWOT data AnDA seems to be prone to issues arising from inconsistencies between accumulated observations.

## A. Altimetric Data Fusion

Not surprisingly, when considering the fusion of nadir along-track and SWOT data, the best strategy involves the fusion of

accumulated nadir along-track observations over a time window of $D = 5$ days, thus increasing the spatial coverage of nadir along-track data, and SWOT observations captured on the current day only, thus fully exploiting the 2-D nature and added information provided by SWOT without being negatively affected by the increased sensitivity of AnDA to inconsistencies between accumulated SWOT observations.

To further illustrate the gain brought forward by considering additional SWOT data, Fig. 3 depicts the ground-truth SLA and $\nabla$SLA fields [see Fig. 3(a) and (b)], as well as the interpolated SLA and $\nabla$SLA fields for the AnDA assimilation of classic nadir along-track observations accumulated on a time window $t_0 \pm D$ with $D = 5$ days [see Fig. 3(e) and (f)], for the AnDA assimilation of daily SWOT observations [see Fig. 3(g) and (h)] and for the AnDA assimilation of a combination of daily nadir along-track observations accumulated on a time window $t_0 \pm D$ with $D = 5$ days and daily SWOT observations [see Fig. 3(i) and (j)]. We also include the SLA and $\nabla$SLA fields interpolated by OI as reference [see Fig. 3(c) and (d)]. In agreement with Table I, the SLA field reconstructed from daily SWOT data appears closer to the ground-truth SLA field than the reconstruction obtained when considering 5-days accumulated nadir along-track observations. Moreover, the reconstruction improvement associated with considering additional SWOT data appears clearly in the presented results, especially in the western region south off Mallorca, where the sampling provided by SWOT observations [see Fig. 2(b)] helps better reconstruct warm structures that are not present for OI or AnDA using nadir along-track observations only. A completely opposite behavior involving the smoothing of details can be observed for all considered cases in the eastern part of the considered region, where the sparse sampling provided by nadir along-track observations [see Fig. 2(a)] only is not enough to accurately reconstruct finer scale details. As far as gradient fields reconstruction is concerned, it seems clear that AnDA is able to better reconstruct fine scale features and details when the fusion of 5-days accumulated nadir along-track data and daily SWOT data are considered.

To study the temporal consistency of previous results, Fig. 4 presents the time series of the daily spatially averaged nRMSE for the SLA reconstruction obtained with OI, the AnDA SLA reconstruction using nadir along-track observations accumulated
<figure><img src="image_4.png" /><figcaption>Fig. 3. AnDA SLA reconstruction results for 9th March, 2013. Real high-resolution ground-truth SLA and SLA gradient fields: (a) SLA<sub>GT</sub> and (b) ∇SLA<sub>GT</sub>. OI SLA and SLA gradient reconstruction obtained from nadir along-track observations with a standard covariance parametrization considering a temporal correlation scale of ten days and a spatial correlation scale of 100 km: (c) SLA<sub>OI</sub> and (d) ∇SLA<sub>OI</sub>. AnDA SLA and SLA gradient reconstruction when considering nadir along-track observations accumulated on a time window t<sub>0</sub> ± D with D = 5 days [noted as AT<sub>5</sub> and depicted in Fig. 2(a)]: (e) SLA<sub>AT<sub>5</sub></sub> and (f) ∇SLA<sub>AT<sub>5</sub></sub>. AnDA SLA and SLA gradient reconstruction when considering daily SWOT observations [noted as SWOT<sub>0</sub> and depicted in Fig. 2(b)]: (g) SLA<sub>SWOT<sub>0</sub></sub> and (h) ∇SLA<sub>SWOT<sub>0</sub></sub>. AnDA SLA and SLA gradient reconstruction when considering a combination of daily nadir along-track observations accumulated on a time window t<sub>0</sub> ± D with D = 5 days and daily SWOT observations [noted as AT<sub>5</sub> + SWOT<sub>0</sub> and depicted in Fig. 2(c)]: (i) SLA<sub>AT<sub>5</sub> + SWOT<sub>0</sub></sub> and (j) ∇SLA<sub>AT<sub>5</sub> + SWOT<sub>0</sub></sub>.</figcaption></figure>
<figure><img src="image_5.png" /><figcaption>Fig. 4. Time series of the daily spatially averaged nRMSE for the AnDA reconstruction of SLA fields. Reported results correspond to the OI SLA reconstruction obtained from nadir along-track observations with a standard covariance parametrization considering a temporal correlation scale of ten days and a spatial correlation scale of 100 km (OI), the AnDA SLA reconstruction using nadir along-track observations accumulated on a time window $t_0 \pm D$ with $D = 5$ days (AT$_5$), the AnDA SLA reconstruction using daily SWOT observations (SWOT$_0$) and the AnDA SLA reconstruction using a combination of daily nadir along-track observations accumulated on a time window $t_0 \pm D$ with $D = 5$ days and daily SWOT observations (AT$_5$ + SWOT$_0$).</figcaption></figure>

on a time window $t_0 \pm D$ with $D = 5$ days (AT$_5$), the AnDA SLA reconstruction using daily SWOT observations (SWOT$_0$) and the AnDA SLA reconstruction using a combination of daily nadir along-track observations accumulated on a time window $t_0 \pm D$ with $D = 5$ days and daily SWOT observations (AT$_5$ + SWOT$_0$). Results depicted in Fig. 4 are consistent with previous results (see Fig. 3), with AnDA considerably outperforming OI, and nRMSE values getting smaller as we consider the AnDA SLA reconstruction using nadir along-track observations accumulated on a time window $t_0 \pm D$ with $D = 5$ days (AT$_5$), the AnDA SLA reconstruction using daily SWOT observations (SWOT$_0$) and the AnDA SLA reconstruction using a combination of daily nadir along-track observations accumulated on a time window $t_0 \pm D$ with $D = 5$ days and daily SWOT observations (AT$_5$ + SWOT$_0$). As previously stated, the best reconstruction performance is obtained with the AnDA assimilation of a combination of daily along-track observations accumulated on a time window $t_0 \pm D$ with $D = 5$ days and daily SWOT observations (AT$_5$ + SWOT$_0$). If we compute the radially averaged power spectra as a spatial domain average (Fig. 5) we can see that, effectively, considering additional SWOT data helps improve the reconstruction performance of AnDA, with the joint AnDA assimilation of nadir along-track and SWOT data outperforming the AnDA assimilation of nadir along-track observations only for most spatial scales in the mesoscale/submesoscale range. Moreover, despite the similarity between the spectra of the assimilation of daily SWOT data and the joint assimilation of 5-days accumulated nadir along-track data and daily SWOT observations, we can observe that the joint assimilation helps better constrain the spectrum of the reconstructed SLA field, particularly for the smaller scales, where the joint assimilation produces a spectrum closer to the real ground-truth SLA spectrum. As expected, OI clearly underestimates the high-resolution finer details of the ground-truth

<figure><img src="image_6.png" /><figcaption>Fig. 5. Radially averaged power spectra for AnDA SLA reconstruction results on 9th March, 2013. Reported power spectra correspond to the high-resolution ground-truth SLA field (GT), the OI SLA reconstruction obtained from nadir along-track observations with a standard covariance parametrization considering a temporal correlation scale of ten days and a spatial correlation scale of 100 km (OI), the AnDA SLA reconstruction using nadir along-track observations accumulated on a time window $t_0 \pm D$ with $D = 5$ days (AT$_5$), the AnDA SLA reconstruction using daily SWOT observations (SWOT$_0$) and the AnDA SLA reconstruction using a combination of daily nadir along-track observations accumulated on a time window $t_0 \pm D$ with $D = 5$ days and daily SWOT observations (AT$_5$ + SWOT$_0$).</figcaption></figure>

SLA fields, whereas results obtained with AnDA approximate the ground-truth considerably better. For smaller scales between the pixel size and the patch overlap size (~5–25 km), AnDA tends to overestimate the spectrum, which we believe relates to both border effects due to the patch-based formulation (which we have observed during our tests) and to the presence of KaRIn pixel-wise Gaussian observation noise [since our experiments show this effect to be considerably less strong when noise-free observations are considered (not shown here)]. To limit such effects, a filtering stage was considered in postprocessing after the AnDA SLA reconstruction, which introduces a compromise between filtering patch-based high-frequency noise and smoothing out fine scale details. Moreover, in order to avoid excessively long computational times, overlapping patches are computed on a regular subgrid involving a shift of 5 pixels between neighboring patches. In this way, less patches are computed to obtain the final reconstruction, which limits computational time, but also introduces more high-frequency noise due to patch averaging. In this regard, considering a smaller shift between overlapping patches would help limit the presence of patch-based high-frequency noise, but would also require a considerable increase in computational time. Finally, the joint assimilation of nadir along-track and SWOT data seems to help further limit these effects to some extent. For illustration purposes, an example of the high-pass filtered SLA field depicting the content of spatial scales under 20 km, where these effects can be clearly observed, is included in the supplementary document available alongside the electronic version of this paper.

Finally, we further support previous results by analyzing the time series of the observation coverage (given as the ratio between the number of observed pixels and the total number of pixels in the considered region, excluding land pixels) for a combination of daily nadir along-track observations accumu-
<figure><img src="image_7.png" /><figcaption>Fig. 6. (Top) Observation coverage (given as the ratio between the number of observed pixels and the total number of pixels in the considered region, excluding land pixels) time series for a combination of daily nadir along-track observations accumulated on a time window $t_0 \pm D$ with $D = 5$ days and daily SWOT observations. (Bottom) Time series of the AnDA SLA reconstruction nRMSE gain obtained when adding daily SWOT observations to 5-days accumulated along-track data (given by $nRMSE_{AT_5} - nRMSE_{AT_5+SWOT_0}$). The red filling indicates periods during which there is a positive nRMSE gain when considering additional SWOT data (i.e., $nRMSE_{AT_5+SWOT_0} \le nRMSE_{AT_5}$).</figcaption></figure>

lated on a time window $t_0 \pm D$ with $D = 5$ days and daily SWOT observations, and the time series of the nRMSE gain obtained when adding SWOT observations to the nadir along-track data accumulated on a time window of size $t_0 \pm D$ with $D = 5$ days (given by $nRMSE_{AT_5} - nRMSE_{AT_5+SWOT_0}$). The red filling in Fig. 6 indicates periods during which there is a positive nRMSE gain when considering additional SWOT data (i.e., $nRMSE_{AT_5+SWOT_0} \le nRMSE_{AT_5}$).

In Fig. 6 (top), one can easily differentiate the contribution of nadir along-track observations, producing a smaller, more stable low frequency wave around 0.05, and that of SWOT observations, producing a train of spikes associated with the increased coverage produced by SWOT swaths. This spike pattern is highly correlated to the nRMSE gain time series depicted in Fig. 6 (bottom) ($R = 0.60, p < 0.001$), where a similar peak pattern can be observed. This indicates that the observed nRMSE gain is mainly associated with the increased surface coverage brought forth by SWOT observations. Indeed, our results suggest a mean nRMSE gain of around 5.0% for the whole year 2013 and 7.0% for days when at least one SWOT track is observed (with respect to the assimilation of 5-days accumulated along-track data only), which supports the conclusion that the observed performance gain relates to the availability of SWOT observations. Finally, it should also be noted that both accumulating nadir along-track observations over a time window $t_0 \pm D$ days and the use of wide-swath SWOT observations (or a combination of both) have proven to be effective strategies to outperform both OI and NNLD. Indeed, when compared to OI and NNLD, AnDA presents lower RMSE levels and higher correlation coefficients, which indicates that mesoscale structures are being better recovered.

V. CONCLUSION

We developed an application of the AnDA framework for the interpolation and reconstruction of high-resolution SLA fields from satellite altimetry data in the Western Mediterranean Sea. With a view toward the upcoming SWOT altimetry mission, we exploited an OSSE to evaluate the performance of AnDA

for the assimilation of irregularly sampled altimetry data involving different spatio-temporal sampling patterns, namely satellite nadir along-track data and wide-swath SWOT data. In this respect, the AnDA framework may be regarded as a means to exploit high-resolution numerical simulation data sets for the reconstruction of SLA fields from partial satellite observations. Reported results support the relevance of AnDA with respect to state-of-the-art approaches (OI [7], [34] and NNLD [26]) for the high-resolution reconstruction of SLA fields. We report an improvement of 30% (27%) in terms of $\nabla$SLA RMSE (correlation) with respect to OI when considering nadir along-track data only. We also demonstrated the relevance of SWOT observations to better constrain AnDA in order to improve the reconstruction of mesoscale features and show an improvement of 42% (12%) in terms of SLA RMSE (correlation) with the joint assimilation of SWOT and nadir along-track observations. Nevertheless, AnDA has proven to be considerably sensitive to correlated noise sources associated with the SWOT mission. In this respect, additional preprocessing should be carried out to filter correlated noises in SWOT data [18] or take it into account into the correlation structure of data assimilation schemes [39].

Future work will focus on combining these strategies with the AnDA framework in order to develop useful tools to process real observations from the future SWOT altimetry mission. In this respect, the joint assimilation of SWOT observation gradients and nadir along-track SLA data should be explored as a possible alternative to deal with the correlated noise sources present in SWOT data. Other interesting research avenues include the combination of different sources of altimetry data as well as considering additional ocean dynamical tracers (e.g., SST and sea surface salinity). Another promising research direction involves further studying the effect of incoherent internal tides and internal gravity waves on SWOT data. Indeed, recent studies [5], [36], [38] suggest that internal tides and internal gravity waves become significant for spatial scales below 100 km. In this respect, the transition scale, the scale at which unbalanced wave motions become stronger than balanced geostrophic motions depends on latitude, season, and eddy activity (with larger transition scales in high latitudes, during summer and/or for regions with low eddy activity) [38], [41]. Internal tides and internal gravity waves may then introduce high-frequency noise at the surface level, which will then directly influence SWOT measurements [5], [42]. While the coherent component of internal tides is predictable and can be corrected, internal tides may also interact with mesoscale currents, which affects their propagation and makes them incoherent with astronomical forcing [5]. Incoherent internal tides, along with internal gravity waves, are then considerably more difficult to predict and will thus pose a major challenge for the SWOT mission [5], [42]. This implies, thus, that internal tides and internal gravity waves are both an object to be studied by means of SWOT observations, as well as a factor to be corrected to study geostrophic flows [5], [36], [41]. Indeed, several studies [5], [36], [38], [41], [42] point out that characterizing, predicting, and correcting incoherent internal tides and internal gravity waves will be a major issue for the exploitation of SWOT data. Further investigating how these phenomena influence SWOT observations and the assimilation of SWOT observations, alone or combined with conventional along-track
data, seems like a key issue for future research. Moreover, in-
corporating advancements dealing with these issues to AnDA
seems particularly relevant to efficiently exploit real SWOT
observations once the satellite is airborne. In this regard, our
results should be considered as an upper-bound on the possible
improvement we may expect for the reconstruction of altime-
try fields from observations from the future SWOT altimetry
mission. Finally, further exploring the exploitation of structural
information present in wide-swath observations, for example, by
means of numerically resolved gradients or finite size Lyapunov
exponents, is also an appealing research direction.

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<figure><img src="image_8.png" /></figure>

**Manuel Lopez-Radcenco** (M'19) was born in Salto, Uruguay, in 1988. He received the B.Eng. degree from the Faculty of Engineering, University of the Oriental Republic of Uruguay, Montevideo, Uruguay, in 2015, the Ms.Eng. degree from Télécom Bretagne, Brest, France, in 2015, and the master's degree in signal and image processing from Télécom Bretagne and Université de Rennes 1, Rennes, France, in 2015. In 2018, he received the Ph.D. degree in signal processing from IMT Atlantique Bretagne-Pays de la Loire (formerly Télécom Bretagne), Brest, France.

His main research interests include machine learning, stochastic processes, statistical modeling, and applications to remote sensing, geosciences, and physical oceanography.

<figure><img src="image_9.png" /></figure>

**Abdeldjalil Aissa-El-Bey** (SM'12) was born in Algiers, Algeria, in 1981. He received the State Engineering degree from École Nationale Polytechnique, Algiers, Algeria, in 2003, the M.S. degree in signal processing from Supélec and Paris XI University, Orsay, France, in 2004, and the Ph.D. degree in signal and image processing from the École Nationale Supérieure des Télécommunications, Paris, France, in 2007.

In 2007, he joined the Department of Signal and Communications, IMT Atlantique Bretagne-Pays de la Loire (formerly Télécom Bretagne), Brest, France, as an Associate Professor, and has been a Professor since 2015. He was a Visiting Researcher with Fujitsu Laboratories, Japan, and the Department of Electrical and Electronic Engineering, University of Melbourne, Melbourne, Australia, in 2010 and 2015, respectively. His research interests include blind source separation, blind system identification and equalization, statistical signal processing, wireless communications, and adaptive filtering.

<figure><img src="image_10.png" /></figure>

**Ananda Pascual** received the Ph.D. degree in physical oceanography from the University of the Balearic Islands, Palma, Spain, in 2003.

She spent two years as a Marie-Curie Postdoctoral Fellow with CLS Space Oceanography Division, Toulouse, France, from 2003 to 2005. From 2006 to 2008, she was a Ramon y Cajal (tenure-track) Researcher with IMEDEA(CSIC-UIB), Mallorca, Spain. Since 2008, she has been a Research Scientist with the Spanish Research Council (CSIC), IMEDEA. She is currently the Head of the Department of Oceanography and Global Change, IMEDEA. Her research interests include physical oceanography, meso and submesoscale dynamics, and operational oceanography. She investigates physical ocean processes combining remote-sensing, numerical simulations, and multiplatform *in situ* data. In 2017, she was the Co-Director of the GODAE-Ocean View International School: New Frontiers in Operational Oceanography. She serves as the Co-Chair of the Scientific and Technical Advisory Committee, Copernicus Marine and Monitoring Service.

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**Bertrand Chapron** received the Ph.D. degree in fluid mechanics from Aix-Marseille University, Marseille, France, in 1988.

He is currently a Senior Research Scientist with the Laboratoire d'Océanographie Physique et Spatiale, L'Institut Français de Recherche pour l'Exploitation de la Mer, Brest, France. He has been the Co-Investigator or the Principal Investigator in several ESA (ENVISAT RA2, ASAR, and SMOS), NASA, and CNES (TOPEX and JASON) projects. He has contributed to the development of several algorithms for geophysical parameter retrieval from altimeters, radiometers, or SAR. He is co-responsible for the ENVISAT ASAR-Wave Mode algorithms and scientific preparation for the ENVISAT and S1 wind, wave, and current. He has collaborated in studies that demonstrated the high potential of radiometers for wind retrieval in extreme conditions and the possibility of doing directional ocean waves spectrum from Sentinel-2. He has authored more than 80 publications in refereed journals in applied mathematics, physical oceanography (upper ocean dynamics), and electromagnetic wave theory, and its application to ocean surface remote sensing.

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**Laura Gomez-Navarro** was born in Barcelona, Spain, in 1992. She received the B.Sc. degree in marine sciences from the University of Las Palmas de Gran Canaria, Las Palmas, Spain, in 2014, and the M.Sc. degree in marine physics from the University of Bretagne Occidentale, Brest, France, in 2016. She is currently working toward the Ph.D. degree with French Centre Nationale d'Etudes Spatiales and European FP7 funding, at the University of Grenoble Alpes, Grenoble, France, and IMEDEA (CSIC-UIB), Mallorca, Spain.

She works on the observability of oceanic turbulence by the SWOT mission. Her research interests include submesoscale dynamics, satellite altimetry, biophysical interactions, and the study of oceanic processes by using different sources of data.

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**Ronan Fablet** (SM'09) received the graduate degree from the École Nationale Supérieure de l'Aéronautique et de l'Espace, Toulouse, France, in 1997, and the Ph.D. degree in signal processing and telecommunications from the University of Rennes, Rennes, France, in 2001.

In 2002, he was a National Institute of Research in Computer Science and Automation Fellow with Brown University, Providence, RI, USA. From 2003 to 2007, he held a full-time research position with IFREMER Brest in the field of signal and image processing applied to fisheries science. In 2008, he joined the Signal and Communications Department, IMT Atlantique Bretagne-Pays de la Loire (formerly Télécom Bretagne), as an Associate Professor, and has been a Professor since 2012. In 2011, he was a Visiting Researcher with Institut de Recherche pour le Développement/Instituto del Mar del Perú, Peru (Peruvian Sea Research Institute). His main research interests include statistical methods for signal processing and computer vision and applications to ocean remote sensing.