Data-driven approaches, particularly those based on deep learning, are rapidly advancing Earth system modeling. However, their application to ocean forecasting remains limited despite the ocean's pivotal role in climate regulation and marine ecosystems. To address this gap, we present OceanBench, a benchmark designed to evaluate and accelerate global short-range (1–10 days) data-driven ocean forecasting.OceanBench is constructed from a curated dataset comprising first-guess trajectories, nowcasts, and atmospheric forcings from operational physical ocean models, typically unavailable in public datasets due to assimilation cycles. Matched observational data are also included, enabling realistic evaluation in an operational-like forecasting framework.The benchmark defines three complementary evaluation tracks: (i) Model-to-Reanalysis, where models are compared against the reanalysis dataset commonly used for training; (ii) Model-to-Analysis, assessing generalization to a higher-resolution physical analysis; and (iii) Model-to-Observations, Intercomparison and Validation (IV-TT) CLASS-4 evaluation against independent observational data. The first two tracks are further supported by process-oriented diagnostics to assess the dynamical consistency and physical plausibility of forecasts.OceanBench includes key ocean variables: sea surface height, temperature, salinity, and currents, along with standardized metrics grounded in physical oceanography. Baseline comparisons with operational systems and state-of-the-art deep learning models are provided. All data, code, and evaluation protocols are openly available at https://github.com/mercator-ocean/oceanbench, establishing OceanBench as a foundation for reproducible and rigorous research in data-driven ocean forecasting.

Information theory is an outstanding framework for measuring uncertainty, dependence, and relevance in data and systems. It has several desirable properties for real-world applications: naturally deals with multivariate data, can handle heterogeneous data, and the measures can be interpreted. However, it has not been adopted by a wider audience because obtaining information from multidimensional data is a challenging problem due to the curse of dimensionality. We propose an indirect way of estimating information based on a multivariate iterative Gaussianization transform. The proposed method has a multivariate-to-univariate property: it reduces the challenging estimation of multivariate measures to a composition of marginal operations applied in each iteration of the Gaussianization. Therefore, the convergence of the resulting estimates depends on the convergence of well-understood univariate entropy estimates, and the global error linearly depends on the number of times the marginal estimator is invoked. We introduce Gaussianization-based estimates for Total Correlation, Entropy, Mutual Information, and Kullback-Leibler Divergence. Results on artificial data show that our approach is superior to previous estimators, particularly in high-dimensional scenarios. We also illustrate the method's performance in different fields to obtain interesting insights. We make the tools and datasets publicly available to provide a test bed for analyzing future methodologies.

The ocean is a crucial component of the Earth's system. It profoundly influences human activities and plays a critical role in climate regulation. Our understanding has significantly improved over the last decades with the advent of satellite remote sensing data, allowing us to capture essential sea surface quantities over the globe, e.g., sea surface height (SSH). Despite their ever-increasing abundance, ocean satellite data presents challenges for information extraction due to their sparsity and irregular sampling, signal complexity, and noise. Machine learning (ML) techniques have demonstrated their capabilities in dealing with large-scale, complex signals. Therefore we see an opportunity for these ML models to harness the full extent of the information contained in ocean satellite data. However, data representation and relevant evaluation metrics can be the defining factors when determining the success of applied ML. The processing steps from the raw observation data to a ML-ready state and from model outputs to interpretable quantities require domain expertise, which can be a significant barrier to entry for ML researchers. In addition, imposing fixed processing steps, like committing to specific variables, regions, and geometries, will narrow the scope of ML models and their potential impact on real-world applications. OceanBench is a unifying framework that provides standardized processing steps that comply with domain-expert standards. It is designed with a flexible and pedagogical abstraction: it a) provides plug-and-play data and pre-configured pipelines for ML researchers to benchmark their models w.r.t. ML and domain-related baselines and b) provides a transparent and configurable framework for researchers to customize and extend the pipeline for their tasks. In this work, we demonstrate the OceanBench framework through a first edition dedicated to SSH interpolation challenges. We provide datasets and ML-ready benchmarking pipelines for the long-standing problem of interpolating observations from simulated ocean satellite data, multi-modal and multi-sensor fusion issues, and transfer-learning to real ocean satellite observations. The OceanBench framework is available at https://github.com/jejjohnson/oceanbench and the dataset registry is available at https://github.com/quentinf00/oceanbench-data-registry.

In this paper we present an extension of rotation-based iterative Gaussianization (RBIG). Although RBIG has been successfully applied to many tasks, it is limited to medium dimensionality data (on the order of a thousand dimensions). In images its application has been restricted to small image patches or isolated pixels, because the rotation operation in RBIG is based on principal or independent component analysis and these transformations are difficult to learn and scale. Here we present Convolutional RBIG: an extension that alleviates this issue by imposing that the rotation in RBIG is a convolution. We propose to learn convolutional rotations (i.e. orthonormal convolutions) by optimising for the reconstruction loss between the input and an approximate inverse of the transformation using the transposed convolution operation. Additionally, we suggest different regularizers in learning orthonormal convolutions. For example, imposing sparsity in the activations leads to a transformation that extends convolutional independent component analysis to multilayer architectures. We also highlight how statistical properties of the data, such as multivariate mutual information, can be obtained. We illustrate the behavior of the transform with a simple example of texture synthesis, and analyze its properties by visualizing the stimuli that maximize the response in certain feature and layer.

This work introduces a novel method that makes use of machine learning (ML) techniques to classify hyper- and multi spectral observations into optical water types (OWTs). Classification was done using$k$-means clustering, which was followed by a feature relevance step based on the sensitivity analysis (SA) of the predictive mean and variance function of a Gaussian process (GP) regression model. The method was used both in training and predictive mode. The latter allows applying the approach for new unlabeled observations, so that the OWTs and the associated relevant features can automatically be assessed. The methods were studied on hyperspectral synthesized and in situ Arctic data, and were further evaluated on a test image acquired over Arctic seas. Good empirical results encourage wide adoption of the methodology to be applied in operational processing and assessment of water types.

Gaussian processes (GPs) are a class of Kernel methods that have shown to be very useful in geoscience and remote sensing applications for parameter retrieval, model inversion, and emulation. They are widely used because they are simple, flexible, and provide accurate estimates. GPs are based on a Bayesian statistical framework which provides a posterior probability function for each estimation. Therefore, besides the usual prediction (given in this case by the mean function), GPs come equipped with the possibility to obtain a predictive variance (i.e., error bars, confidence intervals) for each prediction. Unfortunately, the GP formulation usually assumes that there is no noise in the inputs, only in the observations. However, this is often not the case in earth observation problems where an accurate assessment of the measuring instrument error is typically available, and where there is huge interest in characterizing the error propagation through the processing pipeline. In this letter, we demonstrate how one can account for input noise estimates using a GP model formulation which propagates the error terms using the derivative of the predictive mean function. We analyze the resulting predictive variance term and show how they more accurately represent the model error in a temperature prediction problem from infrared sounding data.

Gaussian Processes (GPs) are a class of kernel methods that have shown to be very useful in geoscience applications. They are widely used because they are simple, flexible and provide very accurate estimates for nonlinear problems, especially in parameter retrieval. An addition to a predictive mean function, GPs come equipped with a useful property: the predictive variance function which provides confidence intervals for the predictions. The GP formulation usually assumes that there is no input noise in the training and testing points, only in the observations. However, this is often not the case in Earth observation problems where an accurate assessment of the instrument error is usually available. In this paper, we showcase how the derivative of a GP model can be used to provide an analytical error propagation formulation and we analyze the predictive variance and the propagated error terms in a temperature prediction problem from infrared sounding data.