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Abstract This work proposes a general framework for analyzing noise-driven transitions in spatially extended non-equilibrium systems and explaining the emergence of coherent patterns beyond the instability onset. The framework relies on stochastic parameterization formulas to reduce the complexity of the original equations while preserving the essential dynamical effects of unresolved scales. The approach is flexible and operates for both Gaussian noise and non-Gaussian noise with jumps. Our stochastic parameterization formulas offer two key advantages. First, they can approximate stochastic invariant manifolds when these manifolds exist. Second, even when such manifolds break down, our formulas can be adapted through a simple optimization of its constitutive parameters. This allows us to handle scenarios with weak time-scale separation where the system has undergone multiple transitions, resulting in large-amplitude solutions not captured by invariant manifolds or other time-scale separation methods. The optimized stochastic parameterizations capture then how small-scale noise impacts larger scales through the system’s nonlinear interactions. This effect is achieved by the very fabric of our parameterizations incorporating non-Markovian (memory-dependent) coefficients into the reduced equation. These coefficients account for the noise’s past influence, not just its current value, using a finite memory length that is selected for optimal performance. The specific memory function, which determines how this past influence is weighted, depends on both the strength of the noise and how it interacts with the system’s nonlinearities. Remarkably, training our theory-guided reduced models on a single noise path effectively learns the optimal memory length for out-of-sample predictions. This approach retains indeed good accuracy in predicting noise-induced transitions, including rare events, when tested against a large ensemble of different noise paths. This success stems from our hybrid approach, which combines analytical understanding with data-driven learning. This combination avoids a key limitation of purely data-driven methods: their struggle to generalize to unseen scenarios, also known as the ‘extrapolation problem.’ 

A general, variational approach to derive low-order reduced models from possibly non-autonomous systems is presented. The approach is based on the concept of optimal parameterizing manifold (OPM) that substitutes more classical notions of invariant or slow manifolds when the breakdown of “slaving” occurs, i.e., when the unresolved variables cannot be expressed as an exact functional of the resolved ones anymore. The OPM provides, within a given class of parameterizations of the unresolved variables, the manifold that averages out optimally these variables as conditioned on the resolved ones. The class of parameterizations retained here is that of continuous deformations of parameterizations rigorously valid near the onset of instability. These deformations are produced through the integration of auxiliary backward–forward systems built from the model’s equations and lead to analytic formulas for parameterizations. In this modus operandi, the backward integration time is the key parameter to select per scale/variable to parameterize in order to derive the relevant parameterizations which are doomed to be no longer exact away from instability onset due to the breakdown of slaving typically encountered, e.g., for chaotic regimes. The selection criterion is then made through data-informed minimization of a least-square parameterization defect. It is thus shown through optimization of the backward integration time per scale/variable to parameterize, that skilled OPM reduced systems can be derived for predicting with accuracy higher-order critical transitions or catastrophic tipping phenomena, while training our parameterization formulas for regimes prior to these transitions takes place. 

Abstract In Eastern boundary upwelling systems, such as the California Current System (CCS), seasonal upwelling brings low oxygen and low pH waters to the continental shelf, causing ocean acidification and hypoxia (OAH). The location, frequency, and intensity of OAH events is influenced by a combination of large‐scale climatic trends, seasonal changes, small‐scale circulation, and local human activities. Here, we use results from two 20‐year long submesoscale‐resolving simulations of the Northern and Southern U.S. West Coast (USWC) for the 1997–2017 period, to describe the characteristics and drivers of OAH events. These simulations reveal the emergence of hotspots in which seasonal declines in oxygen and pH are accompanied by localized short‐term extremes in OAH. While OAH hotspots show substantial seasonal variability, significant intra‐seasonal fluctuations occur, reflecting the interaction between low‐ and high‐frequency forcings that shape OAH events. The mechanisms behind the seasonal decreases in pH and oxygen vary along the USWC. While remineralization remains the dominant force causing these declines throughout the coast, physical transport partially offsets these effects in Southern and Central California, but contributes to seasonal oxygen loss and acidification on the Northern Coast. Critically, the seasonal decline is not sufficient to predict the occurrence and duration of OAH extremes. Locally enhanced biogeochemical rates, including shallow benthic remineralization and rapid wind‐driven transport, shape the spatial and temporal patterns of coastal OAH. 

Abstract Eddies play a crucial role in shaping ocean dynamics by affecting material transport, and generating spatio‐temporal heterogeneity. However, how eddies at different scales modulate biogeochemical transformation rates remains an open question. Applying a multi‐scale decomposition to a numerical simulation, we investigate the respective impact of mesoscale and submesoscale eddies on nutrient transport and biogeochemical cycling in the California Current System. First, the non‐linear nature of nutrient uptake by phytoplankton results in a 50% reduction in primary production in the presence of eddies. Second, eddies shape the vertical transport of nutrients with a strong compensation between mesoscale and submesoscale. Third, the eddy effect on nutrient uptake is controlled by the covariance of temperature, nutrient and phytoplankton fluctuations caused by eddies. Our results shed new light on the tight interaction between non‐linear fluid dynamics and ecosystem processes in realistic eddy regimes, which remain largely under‐resolved by global Earth system models. 

Abstract Eastern boundary upwelling systems (EBUSs) host equatorward wind-driven near-surface currents overlying poleward subsurface undercurrents. Various previous theories for these undercurrents have emphasized the role of poleward alongshore pressure gradient forces (APFs). Energetic mesoscale variability may also serve to accelerate undercurrents via mesoscale stirring of the potential vorticity gradient imposed by the continental slope. However, it remains unclear whether this eddy rectification mechanism contributes substantially to driving poleward undercurrents in EBUS. This study isolates the influence of eddy rectification on undercurrents via a suite of idealized simulations forced either by alongshore winds, with or without an APF, or by randomly generated mesoscale eddies. It is found that the simulations develop undercurrents with strengths comparable to those found in nature in both wind-forced and randomly forced experiments. Analysis of the momentum budget reveals that the along-isobath undercurrent flow is accelerated by isopycnal advective eddy momentum fluxes and the APF and retarded by frictional drag. The undercurrent acceleration may manifest as eddy momentum fluxes or as topographic form stress depending on the coordinate system used to compute the momentum budget, which reconciles these findings with previous work that linked eddy acceleration of the undercurrent to topographic form stress. The leading-order momentum balance motivates a scaling for the strength of the undercurrent that explains most of the variance across the simulations. These findings indicate that eddy rectification is of comparable importance to the APF in driving poleward undercurrents in EBUSs and motivate further work to diagnose this effect in high-resolution models and observations and to parameterize it in coarse-resolution ocean/climate models. 

Abstract Oceanic mixing, mostly driven by the breaking of internal waves at small scales in the ocean interior, is of major importance for ocean circulation and the ocean response to future climate scenarios. Understanding how internal waves transfer their energy to smaller scales from their generation to their dissipation is therefore an important step for improving the representation of ocean mixing in climate models. In this study, the processes leading to cross-scale energy fluxes in the internal wave field are quantified using an original decomposition approach in a realistic numerical simulation of the California Current. We quantify the relative contribution of eddy–internal wave interactions and wave–wave interactions to these fluxes and show that eddy–internal wave interactions are more efficient than wave–wave interactions in the formation of the internal wave continuum spectrum. Carrying out twin numerical simulations, where we successively activate or deactivate one of the main internal wave forcing, we also show that eddy–near-inertial internal wave interactions are more efficient in the cross-scale energy transfer than eddy–tidal internal wave interactions. This results in the dissipation being dominated by the near-inertial internal waves over tidal internal waves. A companion study focuses on the role of stimulated cascade on the energy and enstrophy fluxes. 

Abstract Fjord circulation modulates the connection between marine‐terminating glaciers and the ocean currents offshore. These fjords exhibit both overturning and horizontal recirculations, which are driven by water mass transformation at the head of the fjord via subglacial discharge plumes and distributed meltwater plumes. However, little is known about how various fjord characteristics influence the interaction between 3D fjord circulation and glacial melt. In this study, high‐resolution numerical simulations of idealized glacial fjords demonstrate that recirculation strength controls melt, which feeds back on overturning and recirculation. The relationships between overturning, recirculation, and melt rate are well predicted by vorticity balance, reduced‐order melt parameterizations, and empirical scaling arguments. These theories allow us to take into account the near‐glacier horizontal velocities, which yield improved predictions of fjord overturning, recirculation, and glacial melt. 

Abstract A set of realistic coastal simulations in California allows for the exploration of surface gravity wave effects on currents (WEC) in an active submesoscale current regime. We use a new method that takes into account the full surface gravity wave spectrum and produces larger Stokes drift than the monochromatic peak-wave approximation. We investigate two high-wave events lasting several days—one from a remotely generated swell and another associated with local wind-generated waves—and perform a systematic comparison between solutions with and without WEC at two submesoscale-resolving horizontal grid resolutions (dx= 270 and 100 m). WEC results in the enhancement of open-ocean surface density and velocity gradients when the averaged significant wave heightH_sis relatively large (>4.2 m). For smaller waves, WEC is a minor effect overall. For the remote swell (strong waves and weak winds), WEC maintains submesoscale structures and accentuates the cyclonic vorticity and horizontal convergence skewness of submesoscale fronts and filaments. The vertical enstrophyζ²budget in cyclonic regions (ζ/f> 2) reveals enhanced vertical shear and enstrophy production via vortex tilting and stretching. Wind-forced waves also enhance surface gradients, up to the point where they generate a small-submesoscale roll-cell pattern with high vorticity and divergence that extends vertically through the entire mixed layer. The emergence of these roll cells results in a buoyancy gradient sink near the surface that causes a modest reduction in the typically large submesoscale density gradients. 

Abstract Previous studies have concluded that the wind-input vorticity in ocean gyres is balanced by bottom pressure torques (BPT), when integrated over latitude bands. However, the BPT must vanish when integrated over any area enclosed by an isobath. This constraint raises ambiguities regarding the regions over which BPT should close the vorticity budget, and implies that BPT generated to balance a local wind stress curl necessitates the generation of a compensating, nonlocal BPT and thus nonlocal circulation. This study aims to clarify the role of BPT in wind-driven gyres using an idealized isopycnal model. Experiments performed with a single-signed wind stress curl in an enclosed, sloped basin reveal that BPT balances the windsonlywhen integrated over latitude bands. Integrating over other, dynamically motivated definitions of the gyre, such as barotropic streamlines, yields a balance between wind stress curl and bottom frictional torques. This implies that bottom friction plays a nonnegligible role in structuring the gyre circulation. Nonlocal bottom pressure torques manifest in the form of along-slope pressure gradients associated with a weak basin-scale circulation, and are associated with a transition to a balance between wind stress and bottom friction around the coasts. Finally, a suite of perturbation experiments is used to investigate the dynamics of BPT. To predict the BPT, the authors extend a previous theory that describes propagation of surface pressure signals from the gyre interior toward the coast along planetary potential vorticity contours. This theory is shown to agree closely with the diagnosed contributions to the vorticity budget across the suite of model experiments.