The climatological mean barotropic vorticity budget is analyzed to investigate the relative importance of surface wind stress, topography and nonlinear advection in dynamical balances in a global ocean simulation. In addition to a pronounced regional variability in vorticity balances, the relative magnitudes of vorticity budget terms strongly depend on the length-scale of interest. To carry out a length-scale dependent vorticity analysis in different ocean basins, vorticity budget terms are spatially filtered by employing the coarse-graining technique. At length-scales greater than 10o (or roughly 1000 km), the dynamics closely follow the Topographic-Sverdrup balance in which bottom pressure torque, surface wind stress curl and planetary vorticity advection terms are in balance. In contrast, when including all length-scales resolved by the model, bottom pressure torque and nonlinear advection terms dominate the vorticity budget (Topographic-Nonlinear balance), which suggests a prominent role of oceanic eddies, which are of Ο(10-100) km in size, and the associated bottom pressure anomalies in local vorticity balances at length-scales smaller than 1000 km. Overall, there is a transition from the Topographic-Nonlinear regime at scales smaller than 10o to the Topographic-Sverdrup regime at length-scales greater than 10o. These dynamical balances hold across all ocean basins; however, interpretations of the dominant vorticity balances depend on the level of spatial filtering or the effective model resolution. On the other hand, the contribution of bottom and lateral friction terms in the barotropic vorticity budget remains small and is significant only near sea-land boundaries, where bottom stress and horizontal friction generally peak.

Algorithms to determine regions of interest in large or highly complex and nonlinear data is becoming increasingly important. Novel methodologies from computer science and dynamical systems are well placed as analysis tools, but are underdeveloped for applications within the Earth sciences, and many produce misleading results. I present a novel and general workflow, the Native Emergent Manifold Interrogation (NEMI) method, which is easy to use and widely applicable. NEMI is able to quantify and leverage the highly complex ‘latent’ space presented by noisy, nonlinear and unbalanced data common in the Earth sciences. NEMI uses dynamical systems and probability theory to strengthen associations, simplifying covariance structures, within the data with a manifold, or a Riemannian, methodology that uses domain specific charting of the underlying space. On the manifold, an agglomerative clustering methodology is applied to isolate the now observable areas of interest. The construction of the manifold introduces a stochastic component which is beneficial to the analysis as it enables latent space regularization. NEMI uses an ensemble methodology to quantify the sensitivity of the results noise. The areas of interest, or clusters, are sorted within individual ensemble members and co-located across the set. A metric such as a majority vote, entropy, or similar the quantifies if a data point within the original data belongs to a certain cluster. NEMI is clustering method agnostic, but the use of an agglomerative methodology and sorting in the described case study allows a filtering, or nesting, of clusters to tailor to a desired application.

The North Atlantic ocean is key to climate through its role in heat transport and storage. Climate models suggest that the circulation is weakening but the physical drivers of this change are poorly constrained. Here, the root mechanisms are revealed with the explicitly transparent machine learning method Tracking global Heating with Ocean Regimes (THOR). Addressing the fundamental question of the existence of dynamical coherent regions, THOR identifies these and their link to distinct currents and mechanisms such as the formation regions of deep water masses, and the location of the Gulf Stream and North Atlantic Current. Beyond a black box approach, THOR is engineered to elucidate its source of predictive skill rooted in physical understanding. A labeled dataset is engineered using an explicitly interpretable equation transform and k-means application to model data, allowing theoretical inference. A multilayer perceptron is then trained, explaining its skill using a combination of layerwise relevance propagation and theory. With abrupt CO2 quadrupling, the circulation weakens due to a shift in deep water formation regions, a northward shift of the Gulf stream and an eastwards shift in the North Atlantic Current. If CO2 is increased 1% yearly, similar but weaker patterns emerge influenced by natural variability. THOR is scalable and applicable to a range of models using only the ocean depth, dynamic sea level and wind stress, and could accelerate the analysis and dissemination of climate model data. THOR constitutes a step towards trustworthy machine learning called for within oceanography and beyond.

The trustworthiness of neural networks is often challenged because they lack the ability to express uncertainty and explain their skill. This can be problematic given the increasing use of neural networks in high stakes decision-making such as in climate change applications. We address both issues by successfully implementing a Bayesian Neural Network (BNN), where parameters are distributions rather than deterministic, and applying novel implementations of explainable AI (XAI) techniques. The uncertainty analysis from the BNN provides a comprehensive overview of the prediction more suited to practitioners’ needs than predictions from a classical neural network. Using a BNN means we can calculate the entropy (i.e. uncertainty) of the predictions and determine if the probability of an outcome is statistically significant. To enhance trustworthiness, we also spatially apply the two XAI techniques of Layer-wise Relevance Propagation (LRP) and SHapley Additive exPlanation (SHAP) values. These XAI methods reveal the extent to which the BNN is suitable and/or trustworthy. Using two techniques gives a more holistic view of BNN skill and its uncertainty, as LRP considers neural network parameters, whereas SHAP considers changes to outputs. We verify these techniques using comparison with intuition from physical theory. The differences in explanation identify potential areas where new physical theory guided studies are needed.