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Abstract A data‐driven emulator for the baroclinic double gyre ocean simulation is presented in this study. Traditional numerical simulations using partial differential equations (PDEs) often require substantial computational resources, hindering real‐time applications and inhibiting model scalability. This study presents a novel approach employing Fourier neural operators to address these challenges in an idealized double‐gyre ocean simulation. We propose a deep learning approach capable of learning the underlying dynamics of the ocean system, complementing the classical methods. Additionally, we show how Fourier neural operators allow us to train the network at one resolution and generate ensembles at a different resolution. We find that there is an intermediate time scale where the prediction skill is maximized. 

Abstract The World Climate Research Programme (WCRP) envisions a world “that uses sound, relevant, and timely climate science to ensure a more resilient present and sustainable future for humankind.” This bold vision requires the climate science community to provide actionable scientific information that meets the evolving needs of societies all over the world. To realize its vision, WCRP has created five Lighthouse Activities to generate international commitment and support to tackle some of the most pressing challenges in climate science today. The overarching goal of the Lighthouse Activity on Explaining and Predicting Earth System Change is to develop an integrated capability to understand, attribute, and predict annual to decadal changes in the Earth system, including capabilities for early warning of potential high impact changes and events. This article provides an overview of both the scientific challenges that must be addressed, and the research and other activities required to achieve this goal. The work is organized in three thematic areas: (i) monitoring and modeling Earth system change; (ii) integrated attribution, prediction, and projection; and (iii) assessment of current and future hazards. Also discussed are the benefits that the new capability will deliver. These include improved capabilities for early warning of impactful changes in the Earth system, more reliable assessments of meteorological hazard risks, and quantitative attribution statements to support the Global Annual to Decadal Climate Update and State of the Climate reports issued by the World Meteorological Organization. 

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. 

Operational ocean forecasting systems (OOFSs) are complex engines that must execute ocean models with high performance to provide timely products and datasets. Significant computational resources are then needed to run high-fidelity models, and, historically, the technological evolution of microprocessors has constrained data-parallel scientific computation. Today, graphics processing units (GPUs) offer a rapidly growing and valuable source of computing power rivaling the traditional CPU-based machines: the exploitation of thousands of threads can significantly accelerate the execution of many models, ranging from traditional HPC workloads of finite difference, finite volume, and finite element modelling through to the training of deep neural networks used in machine learning (ML) and artificial intelligence. Despite the advantages, GPU usage in ocean forecasting is still limited due to the legacy of CPU-based model implementations and the intrinsic complexity of porting core models to GPU architectures. This review explores the potential use of GPU in ocean forecasting and how the computational characteristics of ocean models can influence the suitability of GPU architectures for the execution of the overall value chain: it discusses the current approaches to code (and performance) portability, from CPU to GPU, including tools that perform code transformation, easing the adaptation of Fortran code for GPU execution (like PSyclone), the direct use of OpenACC directives (like ICON-O), the adoption of specific frameworks that facilitate the management of parallel execution across different architectures, and the use of new programming languages and paradigms. 

Process-based modelling offers interpretability and physical consistency in many domains of geosciences but struggles to leverage large datasets efficiently. Machine-learning methods, especially deep networks, have strong predictive skills yet are unable to answer specific scientific questions. In this Perspective, we explore differentiable modelling as a pathway to dissolve the perceived barrier between process-based modelling and machine learning in the geosciences and demonstrate its potential with examples from hydrological modelling. ‘Differentiable’ refers to accurately and efficiently calculating gradients with respect to model variables or parameters, enabling the discovery of high-dimensional unknown relationships. Differentiable modelling involves connecting (flexible amounts of) prior physical knowledge to neural networks, pushing the boundary of physics-informed machine learning. It offers better interpretability, generalizability, and extrapolation capabilities than purely data-driven machine learning, achieving a similar level of accuracy while requiring less training data. Additionally, the performance and efficiency of differentiable models scale well with increasing data volumes. Under data-scarce scenarios, differentiable models have outperformed machine-learning models in producing short-term dynamics and decadal-scale trends owing to the imposed physical constraints. Differentiable modelling approaches are primed to enable geoscientists to ask questions, test hypotheses, and discover unrecognized physical relationships. Future work should address computational challenges, reduce uncertainty, and verify the physical significance of outputs. 

Automatic differentiation (AutoDiff) in machine learning is largely restricted to expressions used for neural networks (NN), with the depth rarely exceeding a few tens of layers. Compared to NN, numerical simulations typically involve iterative algorithms like time steppers that lead to millions of iterations. Even for modest-sized models, this may yield infeasible memory requirements when applying the adjoint method, also called backpropagation, to time-dependent problems. In this situation, checkpointing algorithms provide a trade-off between recomputation and storage. This paper presents the package Checkpointing.jl that leverages expression transformations in the programming language Julia and the package ChainRules.jl to automatically and transparently transform loop iterations into differentiated loops. The user may choose between various checkpointing algorithm schemes and storage devices. We describe the unique design of Checkpointing.jl and demonstrate its features on an automatically differentiated MPI implementation of Burgers’ equation on the Polaris cluster at the Argonne Leadership Computing Facility.