In recent years, machine learning (ML) has been proposed to devise data-driven parametrizations of unresolved processes in dynamical numerical models. In most cases, the ML training leverages high-resolution simulations to provide a dense, noiseless target state. Our goal is to go beyond the use of high-resolution simulations and train ML-based parametrization using direct data, in the realistic scenario of noisy and sparse observations. The algorithm proposed in this work is a two-step process. First, data assimilation (DA) techniques are applied to estimate the full state of the system from a truncated model. The unresolved part of the truncated model is viewed as a model error in the DA system. In a second step, ML is used to emulate the unresolved part, a predictor of model error given the state of the system. Finally, the ML-based parametrization model is added to the physical core truncated model to produce a hybrid model. The DA component of the proposed method relies on an ensemble Kalman filter while the ML parametrization is represented by a neural network. The approach is applied to the two-scale Lorenz model and to MAOOAM, a reduced-order coupled ocean-atmosphere model. We show that in both cases, the hybrid model yields forecasts with better skill than the truncated model. Moreover, the attractor of the system is significantly better represented by the hybrid model than by the truncated model.This article is part of the theme issue ‘Machine learning for weather and climate modelling’.

The reconstruction from observations of high-dimensional chaotic dynamics such as geophysical flows is hampered by (ⅰ) the partial and noisy observations that can realistically be obtained, (ⅱ) the need to learn from long time series of data, and (ⅲ) the unstable nature of the dynamics. To achieve such inference from the observations over long time series, it has been suggested to combine data assimilation and machine learning in several ways. We show how to unify these approaches from a Bayesian perspective using expectation-maximization and coordinate descents. In doing so, the model, the state trajectory and model error statistics are estimated all together. Implementations and approximations of these methods are discussed. Finally, we numerically and successfully test the approach on two relevant low-order chaotic models with distinct identifiability.

Progress within physical oceanography has been concurrent with the increasing sophistication of tools available for its study. The incorporation of machine learning (ML) techniques offers exciting possibilities for advancing the capacity and speed of established methods and for making substantial and serendipitous discoveries. Beyond vast amounts of complex data ubiquitous in many modern scientific fields, the study of the ocean poses a combination of unique challenges that ML can help address. The observational data available is largely spatially sparse, limited to the surface, and with few time series spanning more than a handful of decades. Important timescales span seconds to millennia, with strong scale interactions and numerical modelling efforts complicated by details such as coastlines. This review covers the current scientific insight offered by applying ML and points to where there is imminent potential. We cover the main three branches of the field: observations, theory, and numerical modelling. Highlighting both challenges and opportunities, we discuss both the historical context and salient ML tools. We focus on the use of ML in situ sampling and satellite observations, and the extent to which ML applications can advance theoretical oceanographic exploration, as well as aid numerical simulations. Applications that are also covered include model error and bias correction and current and potential use within data assimilation. While not without risk, there is great interest in the potential benefits of oceanographic ML applications; this review caters to this interest within the research community.

A new algorithm for classification of sea ice types on Sentinel-1 Synthetic Aperture Radar (SAR) data using a convolutional neural network (CNN) is presented. The CNN is trained on reference ice charts produced by human experts and compared with an existing machine learning algorithm based on texture features and random forest classifier. The CNN is trained on two datasets in 2018 and 2020 for retrieval of four classes: ice free, young ice, first-year ice and old ice. The accuracy of our classification is 90.5% for the 2018-dataset and 91.6% for the 2020-dataset. The uncertainty is a bit higher for young ice (85%/76% accuracy in 2018/2020) and first-year ice (86%/84% accuracy in 2018/2020). Our algorithm outperforms the existing random forest product for each ice type. It has also proved to be more efficient in computing time and less sensitive to the noise in SAR data. The code is publicly available.