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This study addresses the boundary artifacts in machine‐learned (ML) parameterizations for ocean subgrid mesoscale momentum forcing, as identified in the online ML implementation from a previous study (Zhang et al., 2023, https://doi.org/10.1029/2023ms003697). We focus on the boundary condition (BC) treatment within the existing convolutional neural network (CNN) models and aim to mitigate the “out‐of‐sample” errors observed near complex coastal regions without developing new, complex network architectures. Our approach leverages two established strategies for placing BCs in CNN models, namely zero and replicate padding. Offline evaluations revealed that these padding strategies significantly reduce root mean squared error (RMSE) in coastal regions by limiting the dependence on random initialization of weights and restricting the range of out‐of‐sample predictions. Further online evaluations suggest that replicate padding consistently reduces boundary artifacts across various retrained CNN models. In contrast, zero padding sometimes intensifies artifacts in certain retrained models despite both strategies performing similarly in offline evaluations. This study underscores the need for BC treatments in CNN models trained on open water data when predicting near‐coastal subgrid forces in ML parameterizations. The application of replicate padding, in particular, offers a robust strategy to minimize the propagation of extreme values that can contaminate computational models or cause simulations to fail. Our findings provide insights for enhancing the accuracy and stability of ML parameterizations in the online implementation of ocean circulation models with coastlines. Plain Language Summary This study focuses on improving machine learning (ML) models used to predict ocean forces near coastlines, where errors arise because these models lack information in the area. We investigated how boundary conditions are handled in existing convolutional neural network models to reduce these errors without creating complex new architectures. By using two methods, that is, zero padding and replicate padding, we found that replicate padding significantly decreases prediction errors in coastal areas. While zero padding sometimes worsens issues in certain models, our results show that replicate padding is more reliable for effectively minimizing extreme value errors. This work highlights the importance of proper boundary condition treatment in ML models for coastal applications, ultimately aiming to enhance the accuracy and reliability of ocean circulation predictions. Key Points This study validates specialized boundary condition treatments in CNN models to reduce boundary artifacts in ocean parameterizations This approach can be applied directly to already trained CNN models to ensure accurate and stable implementation of mesoscale eddies parameterizations Replicate padding outperforms zero padding by minimizing boundary artifacts and preventing extreme values that compromise simulations

Mesoscale eddies play an important role in transport of heat and biogeochemical tracers in the global ocean circulation. Resolving these energetic eddies, however, is challenging in ocean general circulation models (OGCM) because it requires a horizontal grid spacing of ≲1/8° that is computationally expensive. As a result, we are required to parameterize mesoscale eddy effects on large‐scale ocean flows. In this work, we introduce a new subgrid‐scale (SGS) model that is developed based on a Taylor series expansion of resolved variables to parameterize subgrid mesoscale eddy transports and momentum fluxes in OGCM. We have performed an a priori study to evaluate the performance of our new gradient model using high‐resolution ocean simulations. Our results show that the gradient model well predicts the actual SGS thickness fluxes in the zonal and meridional directions in coarse‐resolution simulations with the grid spacing ≳1/4°. The unresolved kinetic energy at the ocean surface is also skillfully estimated. More importantly, unlike current mesoscale eddy parameterizations, which are mainly developed based on an assumption of flat bottom ocean, our new SGS model can capture the structure of unresolved standing meanders at the ocean surface. We have also developed a dynamic procedure for setting in non‐dimensional parameters in our new parameterization through a non‐ad hoc and tuning‐free method. Overall, this work suggests that implementing the gradient model in OGCM can improve the model accuracy with an affordable computational cost in eddy‐permitting and non‐eddying simulations. Plain Language Summary Mass, momentum and heat transports in the global ocean circulation can be significantly influenced by mesoscale eddies. In ocean models, however, it is not computationally affordable to resolve these energetic eddies; hence, we need to parameterize their effects on large‐scale resolved motions. In this work, we propose a new generation of subgrid mesoscale eddy parameterizations based on the gradient of resolved velocity and thickness. Our new model is evaluated using coarse‐grained ocean simulations, where both actual and gradient‐based‐parameterized subgrid transports are computed. The new subgrid parameterization can reduce biases in coarse‐resolution ocean models by skillfully representing unresolved volume and momentum fluxes, leading to higher accuracy in the prediction of zonal and meridional transports with a reasonable computational cost. Key Points A new subgrid mesoscale eddy parameterization based on the gradients of resolved variables are introduced in ocean modeling The gradient model can skillfully reproduce unresolved volume transport and momentum fluxes in non‐eddying and eddy‐permitting ocean resolutions Unlike current subgrid mesoscale models, the gradient model can capture the structure of unresolved standing meanders at the ocean surface

The reduced sensitivity of mean Southern Ocean zonal transport with respect to surface wind stress magnitude changes, known as eddy saturation, is studied in an idealized analytical model. The model is based on the assumption of a balance between surface wind stress forcing and bottom dissipation in the planetary geostrophic limit, coupled to the GEOMETRIC form of the Gent–McWilliams eddy parameterization. The assumption of a linear stratification, together with an equation for the parameterized domain integrated total eddy energy, enables the formulation of a two component dynamical system, which reduces to the non‐linear oscillator of Ambaum and Novak (2014, https://doi.org/10.1002/qj.2352) in a Hamiltonian limit. The model suggests an intrinsic oscillatory time scale for the Southern Ocean, associated with a combination of mean shear erosion by eddies and eddy energy generation by the mean shear. For Southern Ocean parameters the model suggests that perturbing the system via stochastic wind forcing may lead to relatively large excursions in eddy energy. Plain Language Summary The Southern Ocean volume transport is linked to the global stratification to the north of the Southern Ocean. It is thus of interest to understand how the Southern Ocean volume transport responds to changes in the forcing. Eddy saturation in this case refers to the weak sensitivity of the Southern Ocean volume transport to changes in wind forcing, and this phenomenon is investigated in this work within the context of an idealized but analytically and mathematically tractable model. The model mathematically formalizes the physical arguments presented in previous works, and leads to closed form expressions for model response time scales, namely an oscillation and decay time scale. Random but sustained perturbations can be included in the model, and statistics of the model response can still be derived analytically. The simple model here advances our understanding of the governing processes related to the phenomenon of eddy saturation, with possible implications for understanding the ocean's global overturning circulation. Key Points A simplified model of the Antarctic Circumpolar Current is presented exhibiting eddy saturation and frictional control in equilibrium An intrinsic oscillatory time scale is identified that can be excited by stochastic wind forcing and results in decadal variability The eddy energy is found to be particularly sensitive to stochastic wind forcing whereas the thermal wind transport is not

Depth‐averaged eddy buoyancy diffusivities across continental shelves and slopes are investigated using a suite of eddy‐resolving, process‐oriented simulations of prograde frontal currents characterized by isopycnals tilted in the opposite direction to the seafloor, a flow regime commonly found along continental margins under downwelling‐favorable winds or occupied by buoyant boundary currents. The diagnosed cross‐slope eddy diffusivity varies by up to three orders of magnitude, decaying from O104m2/s$\\mathcal{O}\\left(1{0}^{4}\\hspace*{.5em}{\\mathrm{m}}^{2}/\\mathrm{s}\\right)$in the relatively flat‐bottomed region to O10m2/s$\\mathcal{O}\\left(10\\hspace*{.5em}{\\mathrm{m}}^{2}/\\mathrm{s}\\right)$over the steep continental slope, consistent with previously reported suppression effects of steep topography on baroclinic eddy fluxes. To theoretically constrain the simulated cross‐slope eddy fluxes, we examine extant scalings for eddy buoyancy diffusivities across prograde shelf/slope fronts and in flat‐bottomed oceans. Among all tested scalings, the GEOMETRIC framework developed by D. P. Marshall et al. (2012, https://doi.org/10.1175/JPO-D-11-048.1) and a parametrically similar Eady scale‐based scaling proposed by Jansen et al. (2015, https://doi.org/10.1016/j.ocemod.2015.05.007) most accurately reproduce the diagnosed eddy diffusivities across the entire shelf‐to‐open‐ocean analysis regions in our simulations. This result relies upon the incorporation of the topographic suppression effects on eddy fluxes, quantified via analytical functions of the slope Burger number, into the scaling prefactor coefficients. The predictive skills of the GEOMETRIC and Eady scale‐based scalings are shown to be insensitive to the presence of along‐slope topographic corrugations. This work lays a foundation for parameterizing eddy buoyancy fluxes across large‐scale prograde shelf/slope fronts in coarse‐resolution ocean models. Plain Language Summary Understanding the future climate relies on numerical predictions from climate models. However, these models are limited in accuracy because they cannot resolve all crucial processes in the climate system due to computational resource limitations. One such process is the oceanic “mesoscale” turbulence (swirling ocean flows that are tens to hundreds of kilometers wide) across continental margins. These flows impact coastal circulation and ecosystems by mediating material exchanges between coastal and open‐ocean environments. By running computer simulations that can explicitly resolve mesoscale turbulence, we show that heat transport by mesoscale flows becomes less efficient over continental margins than that in the open ocean, due to the presence of the sloping seafloor. After taking this reduced efficiency into account, we are able to predict the heat transport by mesoscale flows across continental margins by adapting established theories for the open‐ocean environment. This work provides a basis for improving the performance of climate models, especially near coastal regions. Key Points Process simulations of eddy buoyancy fluxes across prograde shelf and slope fronts are conducted The GEOMETRIC scaling and the Eady scale‐based scaling for eddy buoyancy fluxes are adapted to continental slopes A basis for parameterizing eddy buoyancy fluxes across prograde fronts is presented

This study assesses the capability of a coarse-resolution ocean model to replicate the response of the Southern Ocean Meridional Overturning Circulation (MOC) to intensified westerlies, focusing on the role of the eddy transfer coefficient ( κ ). κ is a parameter commonly used to represent the velocities induced by unresolved eddies. Our findings reveal that a stratification-dependent κ , incorporating spatiotemporal variability, leads to the most robust eddy-induced MOC response, capturing 82% of the reference eddy-resolving simulation. Decomposing the eddy-induced velocity into its vertical variation (VV) and spatial structure (SS) components unveils that the enhanced eddy compensation response primarily stems from an augmented SS term, while the introduced VV term weakens the response. Furthermore, the temporal variability of the stratification-dependent κ emerges as a key factor in enhancing the eddy compensation response to intensified westerlies. The experiment with stratification-dependent κ exhibits a more potent eddy compensation response compared to the constant κ , attributed to the structure of κ and the vertical variation of the density slope. These results underscore the critical role of accurately representing κ in capturing the response of the Southern Ocean MOC and emphasize the significance of the isopycnal slope in modulating the eddy compensation mechanism.

The authors characterize impacts on heat in the ocean climate system from transient ocean mesoscale eddies. Their tool is a suite of centennial-scale 1990 radiatively forced numerical climate simulations from three GFDL coupled models comprising the Climate Model, version 2.0–Ocean (CM2-O), model suite. CM2-O models differ in their ocean resolution: CM2.6 uses a 0.1° ocean grid, CM2.5 uses an intermediate grid with 0.25° spacing, and CM2-1deg uses a nominal 1.0° grid. Analysis of the ocean heat budget reveals that mesoscale eddies act to transport heat upward in a manner that partially compensates (or offsets) for the downward heat transport from the time-mean currents. Stronger vertical eddy heat transport in CM2.6 relative to CM2.5 accounts for the significantly smaller temperature drift in CM2.6. The mesoscale eddy parameterization used in CM2-1deg also imparts an upward heat transport, yet it differs systematically from that found in CM2.6. This analysis points to the fundamental role that ocean mesoscale features play in transient ocean heat uptake. In general, the more accurate simulation found in CM2.6 provides an argument for either including a rich representation of the ocean mesoscale in model simulations of the mean and transient climate or for employing parameterizations that faithfully reflect the role of eddies in both lateral and vertical heat transport.

With the ongoing expansion of wind energy onshore and offshore, large-scale wind-farm-flow effects in a temporally- and spatially-heterogeneous atmosphere become increasingly relevant. Mesoscale models equipped with a wind-farm parametrization (WFP) can be used to study these effects. Here, we conduct a systematic literature review on the existing WFPs for mesoscale models, their applications and findings. In total, 10 different explicit WFPs have been identified. They differ in their description of the turbine-induced forces, and turbulence-kinetic-energy production. The WFPs have been validated for different target parameters through measurements and large-eddy simulations. The performance of the WFP depends considerably on the ability of the mesoscale model to simulate the background meteorological conditions correctly as well as on the model set-up. The different WFPs have been applied to both onshore and offshore environments around the world. Here, we summarize their findings regarding (1) the characterizations of wind-farm-flow effects, (2) the environmental impact of wind farms, and (3) the implication for wind-energy planning. Since wind-farm wakes can last for several tens of kilometres downstream depending on stability, surface roughness and terrain, neighbouring wind farms need to be taken into account for regional planning of wind energy. Their environmental impact is mostly confined to areas close to the farm. The review suggests future work should include benchmark-type validation studies with long-term measurements, further developments of mesoscale model physics and WFPs, and more interactions between the mesoscale and microscale community.

Coupled mesoscale–microscale simulations are required to provide time-varying weather-dependent inflow and forcing for large-eddy simulations under general flow conditions. Such coupling necessarily spans a wide range of spatial scales (i.e., ~10 m to ~10 km). Herein, we use simulations that involve multiple nested domains with horizontal grid spacings in the terra incognita (i.e., km) that may affect simulated conditions in both the outer and inner domains. We examine the impact on simulated wind speed and turbulence associated with forcing provided by a terrain with grid spacing in the terra incognita. We perform a suite of simulations that use combinations of varying horizontal grid spacings and turbulence parameterization/modeling using the Weather Research and Forecasting (WRF) Model using a combination of planetary boundary layer (PBL) and large-eddy simulation subgrid-scale (LES-SGS) models. The results are analyzed in terms of spectral energy, turbulence kinetic energy, and proper orthogonal decomposition (POD) energy. The results show that the output from the microscale domain depends on the type of turbulence model (e.g., PBL or LES-SGS model) used for a given horizontal grid spacing but is independent of the horizontal grid spacing and turbulence modeling of the parent domain. Simulation using a single domain produced less POD energy in the first few modes compared to a coupled simulation (one-way nesting) for similar horizontal grid spacing, which highlights that coupled simulations are required to accurately pass the mesoscale features into the microscale domain.

A subgrid‐scale eddy parameterization is developed, which makes use of an explicit eddy kinetic energy budget and can be applied at both “non‐eddying” and “eddy‐permitting” resolutions. The subgrid‐scale eddies exchange energy with the resolved flow in both directions via a parameterization of baroclinic instability (based on the established formulation of Gent and McWilliams) and biharmonic and negative Laplacian viscosity terms. This formulation represents the turbulent cascades of energy and enstrophy consistent with our current understanding of the turbulent eddy energy cycle. At the same time, the approach is simple and general enough to be readily implemented in ocean climate models, without adding significant computational cost. The closure has been implemented in the Modular Ocean Model Version 6 and tested in the “Neverworld” configuration, which employs an idealized analytically defined topography designed as a testbed for mesoscale eddy parameterizations. The parameterization performs well over a range of resolutions, seamlessly connecting non‐eddying and eddy‐resolving regimes. Key Points A scale‐aware energy budget‐based eddy parameterization is introduced Bidirectional energy transfer between resolved flow and subgrid scales can be represented The parameterization allows for a smooth transition between non‐eddying and eddying resolution regimes

A new wind farm parameterization has been developed for the mesoscale numerical weather prediction model, the Weather Research and Forecasting model (WRF). The effects of wind turbines are represented by imposing a momentum sink on the mean flow; transferring kinetic energy into electricity and turbulent kinetic energy (TKE). The parameterization improves upon previous models, basing the atmospheric drag of turbines on the thrust coefficient of a modern commercial turbine. In addition, the source of TKE varies with wind speed, reflecting the amount of energy extracted from the atmosphere by the turbines that does not produce electrical energy. Analyses of idealized simulations of a large offshore wind farm are presented to highlight the perturbation induced by the wind farm and its interaction with the atmospheric boundary layer (BL). A wind speed deficit extended throughout the depth of the neutral boundary layer, above and downstream from the farm, with a long wake of 60-km e-folding distance. Within the farm the wind speed deficit reached a maximum reduction of 16%. A maximum increase of TKE, by nearly a factor of 7, was located within the farm. The increase in TKE extended to the top of the BL above the farm due to vertical transport and wind shear, significantly enhancing turbulent momentum fluxes. The TKE increased by a factor of 2 near the surface within the farm. Near-surface winds accelerated by up to 11%. These results are consistent with the few results available from observations and large-eddy simulations, indicating this parameterization provides a reasonable means of exploring potential downwind impacts of large wind farms.