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Data assimilation combines forecasts from a numerical model with observations. Most of the current data assimilation algorithms consider the model and observation error terms as additive Gaussian noise, specified by their covariance matrices and , respectively. These error covariances, and specifically their respective amplitudes, determine the weights given to the background (i.e., the model forecasts) and to the observations in the solution of data assimilation algorithms (i.e., the analysis). Consequently, and matrices significantly impact the accuracy of the analysis. This review aims to present and to discuss, with a unified framework, different methods to jointly estimate the and matrices using ensemble-based data assimilation techniques. Most of the methods developed to date use the innovations, defined as differences between the observations and the projection of the forecasts onto the observation space. These methods are based on two main statistical criteria: 1) the method of moments, in which the theoretical and empirical moments of the innovations are assumed to be equal, and 2) methods that use the likelihood of the observations, themselves contained in the innovations. The reviewed methods assume that innovations are Gaussian random variables, although extension to other distributions is possible for likelihood-based methods. The methods also show some differences in terms of levels of complexity and applicability to high-dimensional systems. The conclusion of the review discusses the key challenges to further develop estimation methods for and . These challenges include taking into account time-varying error covariances, using limited observational coverage, estimating additional deterministic error terms, or accounting for correlated noise.

Through the Synthetic Aperture Radar (SAR) embarked on the satellites Sentinel-1A and Sentinel-1B of the Copernicus program, a large quantity of observations is routinely acquired over the oceans. A wide range of features from both oceanic (e.g., biological slicks, icebergs, etc.) and meteorologic origin (e.g., rain cells, wind streaks, etc.) are distinguishable on these acquisitions. This paper studies the semantic segmentation of ten metoceanic processes either in the context of a large quantity of image-level groundtruths (i.e., weakly-supervised framework) or of scarce pixel-level groundtruths (i.e., fully-supervised framework). Our main result is that a fully-supervised model outperforms any tested weakly-supervised algorithm. Adding more segmentation examples in the training set would further increase the precision of the predictions. Trained on 20 × 20 km imagettes acquired from the WV acquisition mode of the Sentinel-1 mission, the model is shown to generalize, under some assumptions, to wide-swath SAR data, which further extents its application domain to coastal areas.

This paper studies different machine learning methods for solving the regression problem of estimating the marine surge value given meteorological data. The marine surge is defined as the difference between the sea level predicted with the tides equations, and the real measured sea level. Different approaches are explored, from linear regression to multilayer perceptrons and recurrent neural networks. Stochastic networks are also considered, as they enable us to calculate a prediction error. These models are compared with a baseline method, which uses physical equations to calculate the surge. We show that all the statistical models outperform the baseline, being the multilayer perceptron the one that performs the best. (It reaches an R2 score of 0.68 and an RMSE of 7.3 cm.)

The Sentinel‐1 mission is part of the European Copernicus program aiming at providing observations for Land, Marine and Atmosphere Monitoring, Emergency Management, Security and Climate Change. It is a constellation of two (Sentinel‐1 A and B) Synthetic Aperture Radar (SAR) satellites. The SAR wave mode (WV) routinely collects high‐resolution SAR images of the ocean surface during day and night and through clouds. In this study, a subset of more than 37,000 SAR images is labelled corresponding to ten geophysical phenomena, including both oceanic and meteorologic features. These images cover the entire open ocean and are manually selected from Sentinel‐1A WV acquisitions in 2016. For each image, only one prevalent geophysical phenomenon with its prescribed signature and texture is selected for labelling. The SAR images are processed into a quick‐look image provided in the formats of PNG and GeoTIFF as well as the associated labels. They are convenient for both visual inspection and machine learning‐based methods exploitation. The proposed dataset is the first one involving different oceanic or atmospheric phenomena over the open ocean. It seeks to foster the development of strategies or approaches for massive ocean SAR image analysis. A key objective was to allow exploiting the full potential of Sentinel‐1 WV SAR acquisitions, which are about 60,000 images per satellite per month and freely available. Such a dataset may be of value to a wide range of users and communities in deep learning, remote sensing, oceanography and meteorology.

Phytoplankton plays a key role in the carbon cycle and supports the oceanic food web. While its seasonal and interannual cycles are rather well characterized owing to the modern satellite ocean color era, its longer time variability remains largely unknown due to the short time-period covered by observations on a global scale. With the aim of reconstructing this longer-term phytoplankton variability, a support vector regression (SVR) approach was recently considered to derive surface Chlorophyll-a concentration (Chl, a proxy of phytoplankton biomass) from physical oceanic model outputs and atmospheric reanalysis. However, those early efforts relied on one particular algorithm, putting aside the question of whether different algorithms may have specific behaviors. Here, we show that this approach can also be applied on satellite observations and can even be further improved by testing performances of different machine learning algorithms, the SVR and a neural network with dense layers (a multi-layer perceptron, MLP). The MLP, thanks to its ability to capture complex non-linear relationships, outperforms the SVR to capture satellite Chl spatial patterns (correlation of 0.75 vs. 0.65 on a global scale, respectively) along with its interannual variability and trend, despite an underestimated amplitude. Among deep learning algorithms, neural network such as MLP models appear to be promising tools to investigate phytoplankton long-term time-series.

Wave group focusing gives rise to the formation of large gravity waves at the surface of the ocean, some of which are called rogue waves and represent a natural hazard for ships and offshore platforms. For safety purposes, it is crucial to predict when and where these large waves will appear and how large they will be. This work focuses on crest velocities, a quantity that is relatively easy to extract from sea surface elevation fields. It is shown that there is a direct link between crest velocity gradient and wave group linear dispersive focusing. Studying analytically the focusing of one-dimensional Gaussian wave packets under linear evolution makes it possible to derive estimates of quantities at focus, based only on crest velocity measurements. In this way, the focusing time, focusing size and focusing amplitude (relative to instantaneous amplitude) of an isolated Gaussian wave packet can be estimated. Our work is also applicable to second-order non-linear waves. Limitations due to higher-order non-linear effects are studied in numerical simulations of the non-linear Schrödinger equation.

More than twelve satellite scatterometers have operated since 1992 through the present, providing the main source of surface wind vector observations over global oceans. In this study, these scatterometer winds are used in combination with radiometers and synthetic aperture radars (SAR) for the better determination and characterization of high spatial and temporal resolution of regional surface wind parameters, including wind speed and direction, wind stress components, wind stress curl, and divergence. In this paper, a 27-year-long (1992–2018) 6-h satellite wind analysis with a spatial resolution of 0.125° in latitude and longitude is calculated using spatial structure functions derived from high-resolution SAR data. The main objective is to improve regional winds over three major upwelling regions (the Canary, Benguela, and California regions) through the use of accurate and homogenized wind observations and region-specific spatial and temporal wind variation structure functions derived from buoy and SAR data. The long time series of satellite wind analysis over the California upwelling, where a significant number of moorings is available, are used for assessing the accuracy of the analysis. The latter is close to scatterometer wind retrieval accuracy. This assessment shows that the root mean square difference between collocated 6-h satellite wind analysis and buoys is lower than 1.50 and 1.80 m s−1 for offshore and nearshore locations, respectively. The temporal correlation between buoy and satellite analysis winds exceeds 0.90. The analysis accuracy is lower for 1992–1999 when satellite winds were mostly retrieved from ERS-1 and/or ERS-2 scatterometers. To further assess the improvement brought by this new wind analysis, its data and data from three independent products (ERA5, CMEMS, and CCMP) are compared with purely scatterometer winds over the Canary and Benguela regions. Even though the four products are generally similar, the new satellite analysis shows significant improvements, particularly in the upwelling areas.

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In light of growing interest in data-driven methods for oceanic, atmospheric, and climate sciences, this work focuses on the field of data assimilation and presents the analog data assimilation (AnDA). The proposed framework produces a reconstruction of the system dynamics in a fully data-driven manner where no explicit knowledge of the dynamical model is required. Instead, a representative catalog of trajectories of the system is assumed to be available. Based on this catalog, the analog data assimilation combines the nonparametric sampling of the dynamics using analog forecasting methods with ensemble-based assimilation techniques. This study explores different analog forecasting strategies and derives both ensemble Kalman and particle filtering versions of the proposed analog data assimilation approach. Numerical experiments are examined for two chaotic dynamical systems: the Lorenz-63 and Lorenz-96 systems. The performance of the analog data assimilation is discussed with respect to classical model-driven assimilation. A Matlab toolbox and Python library of the AnDA are provided to help further research building upon the present findings.

Machine learning techniques are attractive tools to establish statistical models with a high degree of non linearity. They require a large amount of data to be trained and are therefore particularly suited to analysing remote sensing data. This work is an attempt at using advanced statistical methods of machine learning to predict the bias between Sea Surface Temperature (SST) derived from infrared remote sensing and ground “truth” from drifting buoy measurements. A large dataset of collocation between satellite SST and in situ SST is explored. Four regression models are used: Simple multi-linear regression, Least Square Shrinkage and Selection Operator (LASSO), Generalised Additive Model (GAM) and random forest. In the case of geostationary satellites for which a large number of collocations is available, results show that the random forest model is the best model to predict the systematic errors and it is computationally fast, making it a good candidate for operational processing. It is able to explain nearly 31% of the total variance of the bias (in comparison to about 24% for the multi-linear regression model).