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Abstract The marine atmospheric boundary layer (ABL) and oceanic boundary layer (OBL) are a two-way coupled system. At the ocean surface, the ABL and OBL share surface fluxes of momentum and buoyancy that incorporate variations in sea surface temperature (SST) and currents. To investigate the interactions, a coupled ABL–OBL large-eddy simulation (LES) code is developed and exercised over a range of atmospheric stability. At each time step, the coupling algorithm passes oceanic currents and SST to the atmospheric LES, which in turn computes surface momentum, temperature, and humidity fluxes driving the oceanic LES. Equations for each medium are time advanced using the same time step but utilize different grid resolutions: the horizontal grid resolution in the ocean is approximately four times finer, e.g., (Δx_o, Δx_a) = (1.22, 4.88) m. Interpolation and anterpolation (its adjoint) routines connect the atmosphere and ocean surface layers. In the simplest setup of a statistically horizontally homogeneous flow, the largest scale ABL turbulent shear-convective rolls leave an imprint on the OBL currents in the upper layers. This result is shown by comparing simulations that use coupling rules that are applied either instantaneously at everyx–ygrid point or averaged across anx–yplane. The spanwise scale of the ABL turbulence is ∼1000 m, while the depth of the OBL is ∼20 m. In these homogeneous, fully coupled cases, the large-scale spatially intermittent turbulent structures in the ABL modulate SST, currents, and the connecting momentum and buoyancy fluxes, but the mean profiles in each medium are only slightly different. 

Abstract Langmuir turbulence, a dominant process in the ocean surface boundary layer, drives substantial vertical mixing that influences temperature, salinity, mixed layer depth, and biogeochemical tracer distributions. While direct resolution of Langmuir turbulence in ocean and climate models remains computationally prohibitive, its effects are commonly parameterized, frequently within established turbulent mixing frameworks like the K‐profile parameterization (KPP). This study utilizes a modified KPP that determines boundary layer depth through an integral criterion, diverging from the conventional KPP's dependence on the bulk Richardson number. The modified KPP demonstrates markedly lower sensitivity to model vertical resolution than its conventional counterpart. Building upon this modified KPP framework, we introduce an innovative parameterization scheme for Langmuir mixing effects. We evaluate the performance of this new scheme against existing approaches using a one‐dimensional (1D) column model across four different scenarios, incorporating validation against both large eddy simulation (LES) results and field measurements. Our analysis reveals that the new Langmuir mixing scheme, explicitly designed for the modified KPP framework, performs competitively while maintaining reduced sensitivity to vertical resolution. 

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.’ 

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 Realistic computational simulations in different oceanic basins reveal prevalent prograde mean flows (in the direction of topographic Rossby wave propagation along isobaths; aka topostrophy) on topographic slopes in the deep ocean, consistent with the barotropic theory of eddy-driven mean flows. Attention is focused on the western Mediterranean Sea with strong currents and steep topography. These prograde mean currents induce an opposing bottom drag stress and thus a turbulent boundary layer mean flow in the downhill direction, evidenced by a near-bottom negative mean vertical velocity. The slope-normal profile of diapycnal buoyancy mixing results in downslope mean advection near the bottom (a tendency to locally increase the mean buoyancy) and upslope buoyancy mixing (a tendency to decrease buoyancy) with associated buoyancy fluxes across the mean isopycnal surfaces (diapycnal downwelling). In the upper part of the boundary layer and nearby interior, the diapycnal turbulent buoyancy flux divergence reverses sign (diapycnal upwelling), with upward Eulerian mean buoyancy advection across isopycnal surfaces. These near-slope tendencies abate with further distance from the boundary. An along-isobath mean momentum balance shows an advective acceleration and a bottom-drag retardation of the prograde flow. The eddy buoyancy advection is significant near the slope, and the associated eddy potential energy conversion is negative, consistent with mean vertical shear flow generation for the eddies. This cross-isobath flow structure differs from previous proposals, and a new one-dimensional model is constructed for a topostrophic, stratified, slope bottom boundary layer. The broader issue of the return pathways of the global thermohaline circulation remains open, but the abyssal slope region is likely to play a dominant role. 

Estuaries, as connectors between land and ocean, have complex interactions of river and tidal flows that affect the transport of buoyant materials like floating plastics, oil spills, organic matter, and larvae. This study investigates surface-trapped buoyant particle transport in estuaries by using idealized and realistic numerical simulations along with a theoretical model. While river discharge and estuarine exchange flow are usually expected to export buoyant particles to the ocean over subtidal timescales, this study reveals a ubiquitous physical transport mechanism that causes retention of buoyant particles in estuaries. Tidally varying surface convergence fronts affect the aggregation of buoyant particles, and the coupling between particle aggregation and oscillatory tidal currents leads to landward transport at subtidal timescales. Landward transport and retention of buoyant particles is greater in small estuaries, while large estuaries tend to export buoyant particles to the ocean. A dimensionless width parameter incorporating the tidal radian frequency and lateral velocity distinguishes small and large estuaries at a transitional value of around 1. Additionally, higher river flow tends to shift estuaries toward seaward transport and export of buoyant particles. These findings provide insights into understanding the distribution of buoyant materials in estuaries and predicting their fate in the land–sea exchange processes. 

Recent years have seen a surge in interest for leveraging neural networks to parameterize small-scale or fast processes in climate and turbulence models. In this short paper, we point out two fundamental issues in this endeavor. The first concerns the difficulties neural networks may experience in capturing rare events due to limitations in how data is sampled. The second arises from the inherent multiscale nature of these systems. They combine high-frequency components (like inertia-gravity waves) with slower, evolving processes (geostrophic motion). This multiscale nature creates a significant hurdle for neural network closures. To illustrate these challenges, we focus on the atmospheric 1980 Lorenz model, a simplified version of the Primitive Equations that drive climate models. This model serves as a compelling example because it captures the essence of these difficulties. 

Abstract Release of iron (Fe) from continental shelves is a major source of this limiting nutrient for phytoplankton in the open ocean, including productive Eastern Boundary Upwelling Systems. The mechanisms governing the transport and fate of Fe along continental margins remain poorly understood, reflecting interaction of physical and biogeochemical processes that are crudely represented by global ocean biogeochemical models. Here, we use a submesoscale‐permitting physical‐biogeochemical model to investigate processes governing the delivery of shelf‐derived Fe to the open ocean along the northern U.S. West Coast. We find that a significant fraction (∼20%) of the Fe released by sediments on the shelf is transported offshore, fertilizing the broader Northeast Pacific Ocean. This transport is governed by two main pathways that reflect interaction between the wind‐driven ocean circulation and Fe release by low‐oxygen sediments: the first in the surface boundary layer during upwelling events; the second in the bottom boundary layer, associated with pervasive interactions of the poleward California Undercurrent with bottom topography. In the water column interior, transient and standing eddies strengthen offshore transport, counteracting the onshore pull of the mean upwelling circulation. Several hot‐spots of intense Fe delivery to the open ocean are maintained by standing meanders in the mean current and enhanced by transient eddies and seasonal oxygen depletion. Our results highlight the importance of fine‐scale dynamics for the transport of Fe and shelf‐derived elements from continental margins to the open ocean, and the need to improve representation of these processes in biogeochemical models used for climate studies. 

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.