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Abstract We propose a multiscale approach for predicting quantities in dynamical systems which is explicitly structured to extract information in both fine-to-coarse and coarse-to-fine directions. Our approach improves model accuracy and stability with minimally increased computation compared to non-multiscale approaches with analogous network architecture. We evaluate our approach on an idealized fluid subgrid parameterization (known as closure) task in which our multiscale networks correct chaotic underlying models to reflect the contributions of unresolved, fine-scale dynamics. 

Abstract Radiative forcing drives warming in the Earth system, leading to changes in sea surface temperatures (SSTs) and associated radiative feedbacks. The link between changes in the top-of-the-atmosphere (TOA) net radiative flux and SST patterns, known as the “pattern effect”, is typically diagnosed by studying the response of atmosphere-only models to SST perturbations. In this work, we diagnose the pattern effect through response theory, by performing idealized warming perturbation experiments from unperturbed data alone. First, by studying the response at short time scales, where the response is dominated by atmospheric variability, we recover results that agree with the literature. Second, by extending the framework to longer time scales, we capture coupled interactions between the slow ocean component and the atmosphere, yielding a novel “sensitivity map” quantifying the response of the net radiative flux to SST perturbations in the coupled system. Here, feedbacks are captured by a spatiotemporal response operator, rather than time-independent maps as in traditional studies. Both formulations skillfully reconstruct changes in externally forced simulations and provide practical strategies for climate studies. The key distinction lies in their perspectives on climate feedbacks. The first formulation, closely aligned with prediction tasks, follows the traditional view in which slow variables, such as SSTs, exert a one-way influence on fast variables. The second formulation broadens this perspective by incorporating spatiotemporal interactions across state variables. This alternative approach explores how localized SST perturbations can alter the coupled dynamics, leading to temperature changes in remote areas and further impacting the radiative fluxes at later times. 

Abstract Surface and upper-ocean measurements of mesoscale eddies have revealed the central role they play in ocean transport, but their interior and deep ocean characteristics remain undersampled and underexplored. In this study, mooring arrays, sampling with high vertical resolution, and a high-resolution global atmosphere–ocean coupled simulation are used to characterize full-depth mesoscale eddy vertical structure. The vertical structure of eddy kinetic energy, e.g., partitioning of barotropic to baroclinic eddy kinetic energy or vertical modal structure, is shown to depend partly on bathymetric slope and roughness. This influence is contextualized alongside additional factors, such as latitude and vertical density stratification, to present a global landscape of vertical structure. The results generally reveal eddy vertical structure to decay with increasing depth, consistent with theoretical expectations relating to the roles of surface-intensified stratification and buoyancy anomalies. However, at high latitudes and where the seafloor is markedly flat and smooth (approximately 20% of the ocean’s area), mesoscale eddy vertical structures are significantly more barotropic by an approximate factor of 2–5. From a climate modeling perspective, these results can inform the construction, implementation, and improvement of energetic parameterizations that account for the underrepresentation of mesoscale eddies and their effects. They also offer expectation as to a landscape of eddy vertical structure to be used in inferring vertical structure from surface measurements. Significance StatementThis work addresses the question of how do ocean seafloor features (bathymetry) affect the vertical structure of ocean currents and eddies? Seafloor features modify eddies in complex ways not often accounted for in global ocean simulations. We analyze high-resolution velocity observations, find diverse structures at four mooring sites, and consider how sloping and rough bathymetry change distributions of eddy kinetic energy throughout the water column. Comparison to theory and model output reveals a relationship between vertical structure and bathymetry. These results show that vertical structures vary significantly with bathymetry, density stratification, and latitude and contribute to model development efforts to reproduce the effects of eddy turbulence without explicit representation. These results also enhance interpretations of more numerous surface observations. 

Abstract Mass loss from the Antarctic ice sheet is projected to continue over the coming century. The resultant sea level change will have a regional pattern that evolves over time as the ocean adjusts. Accurate estimation of this evolution is crucial for local communities. Current state-of-the-art climate models typically do not couple ice sheets to the atmosphere–ocean system, and the impact of ice sheet melt has often been studied by injecting meltwater at the model ocean surface. However, observational evidence suggests that most Antarctic meltwater enters the ocean at depth through ice shelf basal melt. A previous study has demonstrated that the regional sea level pattern at a given time depends on meltwater injection depth. Here, we introduce a 2.5-layer model to investigate this dependence and develop a theory for the associated adjustment mechanisms. We find mechanisms consistent with previous literature on the ocean adjustment to changes in forcing, whereby a slower Rossby wave response off the eastern boundary follows a fast response from the western boundary current and Kelvin waves. We demonstrate that faster baroclinic Rossby waves near the surface than at depth explain the injection depth dependence of the adjustment in the 2.5-layer model. The identified Rossby wave mechanism may contribute to the dependence of the ocean’s transient adjustment on meltwater injection depth in more complex models. This work highlights processes that could cause errors in the projection of the time-varying pattern of sea level rise using surface meltwater input to represent Antarctica’s freshwater forcing. Significance StatementSea level rise is expected to be larger in some locations than in others. Accurate projections of the pattern of sea level change, which changes in time as the ocean adjusts, are essential information for local communities. One of the factors that leads to uncertainty in the local sea level change due to Antarctic melt is the depth at which this meltwater is input into an ocean model. We propose a mechanism for a faster response of sea level around the basin when meltwater is injected at the ocean surface compared to when it is injected well below the surface. This mechanism has implications for projections of the regional sea level response to Antarctic melt. 

Ocean mesoscale eddies are often poorly represented in climate models, and therefore, their effects on the large scale circulation must be parameterized. Traditional parameterizations, which represent the bulk effect of the unresolved eddies, can be improved with new subgrid models learned directly from data. Zanna and Bolton (ZB20) applied an equation‐discovery algorithm to reveal an interpretable expression parameterizing the subgrid momentum fluxes by mesoscale eddies through the components of the velocity‐gradient tensor. In this work, we implement the ZB20 parameterization into the primitive‐equation GFDL MOM6 ocean model and test it in two idealized configurations with significantly different dynamical regimes and topography. The original parameterization was found to generate excessive numerical noise near the grid scale. We propose two filtering approaches to avoid the numerical issues and additionally enhance the strength of large‐scale energy backscatter. The filtered ZB20 parameterizations led to improved climatological mean state and energy distributions, compared to the current state‐of‐the‐art energy backscatter parameterizations. The filtered ZB20 parameterizations are scale‐aware and, consequently, can be used with a single value of the non‐dimensional scaling coefficient for a range of resolutions. The successful application of the filtered ZB20 parameterizations to parameterize mesoscale eddies in two idealized configurations offers a promising opportunity to reduce long‐standing biases in global ocean simulations in future studies. 

Abstract. Accurate estimation of changes in the global hydrological cycle over the historical record is important for model evaluation and understanding future trends. Freshwater flux trends cannot be accurately measured directly, so quantification of change often relies on ocean salinity trends. However, anthropogenic forcing has also induced ocean transport change, which imprints on salinity. We find that this ocean transport affects the surface salinity of the saltiest regions (the subtropics) while having little impact on the surface salinity in other parts of the globe. We present a method based on linear response theory which accounts for the regional impact of ocean circulation changes while estimating freshwater fluxes from ocean tracers. Testing on data from the Community Earth System Model large ensemble, we find that our method can recover the true amplification of freshwater fluxes, given thresholded statistical significance values for salinity trends. We apply the method to observations and conclude that from 1975–2019, the hydrological cycle has amplified by 5.04±1.27 % per degree Celsius of surface warming. 

Subgrid parameterizations of mesoscale eddies continue to be in demand for climate simulations. These subgrid parameterizations can be powerfully designed using physics and/or data‐driven methods, with uncertainty quantification. For example, Guillaumin and Zanna (2021) proposed a Machine Learning (ML) model that predicts subgrid forcing and its local uncertainty. The major assumption and potential drawback of this model is the statistical independence of stochastic residuals between grid points. Here, we aim to improve the simulation of stochastic forcing with generative models of ML, such as Generative adversarial network (GAN) and Variational autoencoder (VAE). Generative models learn the distribution of subgrid forcing conditioned on the resolved flow directly from data and they can produce new samples from this distribution. Generative models can potentially capture not only the spatial correlation but any statistically significant property of subgrid forcing. We test the proposed stochastic parameterizations offline and online in an idealized ocean model. We show that generative models are able to predict subgrid forcing and its uncertainty with spatially correlated stochastic forcing. Online simulations for a range of resolutions demonstrated that generative models are superior to the baseline ML model at the coarsest resolution.