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The severe changes in climate resulting in the polar oceans getting warmer – with drastic consequences to their physical, biogeochemical, and biological state – require forecasting systems that can accurately simulate and skilfully predict the state of the ice cover and its temporal evolution. Sea-ice processes significantly impact ocean circulation, water mass formation and modifications, and air–sea fluxes. They comprise vertical processes, mainly related to thermodynamics, and horizontal ones, due to internal sea-ice mechanics and motion. We provide an overview on how these processes can be modelled and how operational systems work, in combination with data assimilation techniques, to enhance accuracy and reliability. We also emphasise the need for advancing research on improving such numerical techniques by highlighting current limits and ways forward. 

Artificial intelligence and machine learning are accelerating research in Earth system science, with huge potential for impact and challenges in ocean prediction. Such algorithms are being deployed on different aspects of the forecasting workflow with the aim of improving its speed and skill. They include pattern classification and anomaly detection; regression and diagnostics; and state prediction from nowcasting to synoptic, sub-seasonal, and seasonal forecasting. This brief review emphasizes scientific machine learning methods that have the capacity to embed domain knowledge; to ensure interpretability through causal explanation, to be robust and reliable; to involve effectively high-dimensional statistical methods, supporting multi-scale and multi-physics simulations aimed at improving parameterization; and to drive intelligent automation, as well as decision support. An overview of recent numerical developments is discussed, highlighting the importance of fully data-driven ocean models for future expansion of ocean forecasting capabilities. 

Abstract Recent advances in explainable artificial intelligence (XAI) methods show promise for understanding predictions made by machine learning (ML) models. XAI explains how the input features are relevant or important for the model predictions. We train linear regression (LR) and convolutional neural network (CNN) models to make 1-day predictions of sea ice velocity in the Arctic from inputs of present-day wind velocity and previous-day ice velocity and concentration. We apply XAI methods to the CNN and compare explanations to variance explained by LR. We confirm the feasibility of using a novel XAI method [i.e., global layerwise relevance propagation (LRP)] to understand ML model predictions of sea ice motion by comparing it to established techniques. We investigate a suite of linear, perturbation-based, and propagation-based XAI methods in both local and global forms. Outputs from different explainability methods are generally consistent in showing that wind speed is the input feature with the highest contribution to ML predictions of ice motion, and we discuss inconsistencies in the spatial variability of the explanations. Additionally, we show that the CNN relies on both linear and nonlinear relationships between the inputs and uses nonlocal information to make predictions. LRP shows that wind speed over land is highly relevant for predicting ice motion offshore. This provides a framework to show how knowledge of environmental variables (i.e., wind) on land could be useful for predicting other properties (i.e., sea ice velocity) elsewhere. Significance StatementExplainable artificial intelligence (XAI) is useful for understanding predictions made by machine learning models. Our research establishes trustability in a novel implementation of an explainable AI method known as layerwise relevance propagation for Earth science applications. To do this, we provide a comparative evaluation of a suite of explainable AI methods applied to machine learning models that make 1-day predictions of Arctic sea ice velocity. We use explainable AI outputs to understand how the input features are used by the machine learning to predict ice motion. Additionally, we show that a convolutional neural network uses nonlinear and nonlocal information in making its predictions. We take advantage of the nonlocality to investigate the extent to which knowledge of wind on land is useful for predicting sea ice velocity elsewhere. 

Abstract. In sequential estimation methods often used in oceanic and general climatecalculations of the state and of forecasts, observations act mathematicallyand statistically as source or sink terms in conservation equations for heat, salt, mass, and momentum.These artificial terms obscure the inference of the system's variability or secular changes.Furthermore, for the purposes of calculating changes inimportant functions of state variables such as total mass and energy orvolumetric current transports, results of both filter and smoother-based estimates are sensitive to misrepresentationof a large variety of parameters, including initial conditions, prioruncertainty covariances, and systematic and random errors in observations.Here, toy models of a coupled mass–spring oscillator system and of a barotropic Rossby wave system are used todemonstrate many of the issues that arise from such misrepresentations.Results from Kalman filter estimates and those from finite intervalsmoothing are analyzed.In the filter (and prediction) problem, entry of data leads to violation ofconservation and other invariant rules.A finite interval smoothing method restores the conservation rules, butuncertainties in all such estimation results remain. Convincing trend andother time-dependent determinations in “reanalysis-like” estimates require a full understanding of models, observations, and underlying error structures. Application of smoother-type methods that are designed for optimal reconstruction purposes alleviate some of the issues. 

Physics-based simulations of Arctic sea ice are highly complex, involving transport between different phases, length scales, and time scales. Resultantly, numerical simulations of sea ice dynamics have a high computational cost and model uncertainty. We employ data-driven machine learning (ML) to make predictions of sea ice motion. The ML models are built to predict present-day sea ice velocity given present-day wind velocity and previous-day sea ice concentration and velocity. Models are trained using reanalysis winds and satellite-derived sea ice properties. We compare the predictions of three different models: persistence (PS), linear regression (LR), and a convolutional neural network (CNN). We quantify the spatiotemporal variability of the correlation between observations and the statistical model predictions. Additionally, we analyze model performance in comparison to variability in properties related to ice motion (wind velocity, ice velocity, ice concentration, distance from coast, bathymetric depth) to understand the processes related to decreases in model performance. Results indicate that a CNN makes skillful predictions of daily sea ice velocity with a correlation up to 0.81 between predicted and observed sea ice velocity, while the LR and PS implementations exhibit correlations of 0.78 and 0.69, respectively. The correlation varies spatially and seasonally: lower values occur in shallow coastal regions and during times of minimum sea ice extent. LR parameter analysis indicates that wind velocity plays the largest role in predicting sea ice velocity on 1-day time scales, particularly in the central Arctic. Regions where wind velocity has the largest LR parameter are regions where the CNN has higher predictive skill than the LR. 

Abstract Differentiable Earth system models (ESMs) enable powerful applications such as sensitivity analysis, gradient‐based calibration, state estimation, boundary flux inversions, uncertainty quantification, and online machine learning. Reverse‐mode automatic differentiation (AD) efficiently provides gradients for such tasks, yet models have rarely included this capability because of complex, bespoke numerical algorithms. As part of theDifferentiable programming in Julia for Earth system modeling (DJ4Earth)initiative, we present improved capabilities of the AD tool Enzyme.jl and the new compiler transpilation tool Reactant.jl, augmented by sophisticated checkpointing algorithms, which, together make general‐purpose AD tractable and efficient for full‐fledged ESM components written in Julia. Operating at the low‐level virtual machine intermediate representation or multi‐level intermediate representation compiler levels, these frameworks support mutable memory, custom kernels, and compiler optimizations before and after differentiation. Julia‐specific challenges related to just‐in‐time compilation and garbage collection are handled efficiently. Reactant further enables automatic performance portability across central processing units, graphics processing units, and tensor processing units, facilitating use of emerging AI‐customized high‐performance computing architectures. We demonstrate these frameworks on four Julia‐based ESM components featuring diverse spatial discretizations and numerical algorithms: the rotating‐sphere shallow water model ShallowWaters.jl, the finite‐volume ocean model Oceananigans.jl, the finite‐element ice sheet model DJUICE.jl, and the spectral atmospheric model SpeedyWeather.jl. Across these ESM components, our tools compute efficient and correct gradients. These results establish a foundation for differentiable, high‐performance and performance‐portable ESMs that can integrate neural networks for unresolved processes, trained online, enabling next‐generation hybrid physics–machine learning ESMs constrained by physical dynamics and observations.