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In this work, a stochastic representation based on a physical transport principle is proposed to account for mesoscale eddy effects on the large‐scale oceanic circulation. This stochastic framework arises from a decomposition of the Lagrangian velocity into a smooth‐in‐time component and a highly oscillating noise term. One important characteristic of this random model, without any external forcing and damping, is that it conserves the total energy of the resolved flow for any realization. The proposed stochastic formulation is successfully implemented in a well established multi‐layered quasi‐geostrophic dynamical core. The empirical spatial correlation of the unresolved noise is calibrated from the eddy‐resolving simulation data. In particular, a stationary correction drift can be introduced in the noise through Girsanov transformation. This non‐intuitive term appears to be important in reproducing on a coarse mesh the eastward jet of the wind‐driven double‐gyre circulation. In addition, a projection method has been proposed to constrain the noise to act along the iso‐surfaces of the vertical stratification. The resulting noise enables us to improve the intrinsic low‐frequency variability of the large‐scale current. Plain Language Summary: Accurate numerical simulation of the ocean and the atmosphere is important for understanding complex patterns in climate science. Unfortunately, the high‐dimensional geophysical fluid dynamics contain a wide range of spatio‐temporal scales with complex interactions. In order to maintain affordable computational time, only large‐scale representations of the geophysical flows of interest are simulated. However, the effect of the unresolved scales on the resolved component must be carefully taken into account to minimize the errors of truncation. In the present work, we stick to a specific stochastic formulation that represents the physical principles of the resolved large scales and parameterizes the statistical properties of the unresolved small scales. Such random formulation is successfully tested in numerical simulations of a simplified ocean mesoscale model, in which the structure of the unresolved flow is calibrated from a finite sequence of reference data. The resulting model enables to represent accurately the statistics of the resolved flow component. In addition, numerical results show that an adequate modeling of the unresolved dynamics leads to a significant improvement of the intrinsic variability for the large‐scale ocean models. These findings are important for future developments of ocean and atmosphere climate models. Key Points: A stochastic transport formulation is used to parameterize the effects of the unresolved eddies on the resolved flowThe structure of unresolved flow is calibrated from data and a projection method is proposed to parameterize its dynamicsThe proposed random models on coarse resolutions enable to reproduce the eastward jet and the intrinsic variability of ocean wind‐driven circulation [ABSTRACT FROM AUTHOR]

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 conductedThe GEOMETRIC scaling and the Eady scale‐based scaling for eddy buoyancy fluxes are adapted to continental slopesA basis for parameterizing eddy buoyancy fluxes across prograde fronts is presented [ABSTRACT FROM AUTHOR]

Gyres are prominent surface structures in the global ocean circulation that often interact with the sea floor in a complex manner. Diagnostic methods, such as the depth‐integrated vorticity budget, are needed to assess exactly how such model circulations interact with the bathymetry. Terms in the vorticity budget can be integrated over the area enclosed by streamlines to identify forces that spin gyres up and down. In this article we diagnose the depth‐integrated vorticity budgets of both idealized gyres and the Weddell Gyre in a realistic global model. It is shown that spurious forces play a significant role in the dynamics of all gyres presented and that they are a direct consequence of the Arakawa C‐grid discretization and the z‐coordinate representation of the sea floor. The spurious forces include a numerical beta effect and interactions with the sea floor which originate from the discrete Coriolis force when calculated with the following schemes: the energy conserving scheme; the enstrophy conserving scheme; and the energy and enstrophy conserving scheme. Previous studies have shown that bottom pressure torques provide the main interaction between the depth‐integrated flow and the sea floor. Bottom pressure torques are significant, but spurious interactions with bottom topography are similar in size. Possible methods for reducing the identified spurious topographic forces are discussed. Spurious topographic forces can be alleviated by using either a B‐grid in the horizontal plane or a terrain‐following vertical coordinate. Plain Language Summary: Gyres are large scale circulations in the world ocean that often interact with the sea floor. It is important to develop a method to assess how the representation of the sea floor in models affects gyre circulations. By calculating how model forces generate vorticity (the tendency to rotate) in the flow, we are able to determine the forces acting with and against the gyre circulation. We apply this method to results from a simplified double gyre model and the Weddell Gyre in a realistic global model. We show that spurious forces which emerge from the layout of the model grid play an important role in the presented gyre circulations. The spurious forces originate from the calculation of the Coriolis acceleration in the model. In previous studies, it has been argued that gyre circulations interact with the sea floor primarily by forming pressure gradients; here we show that contributions from pressure gradients are significant, but the spurious forces are similar in size and also emerge from interactions with the sea floor. We discuss possible approaches to reduce the identified spurious forces by considering alternative grid layouts. The spurious forces can be alleviated by using a B‐grid or a terrain‐following vertical coordinate. Key Points: The vorticity budget is used to identify forces spinning gyres up and down when integrated over the area enclosed by streamlinesSpurious topographic forces and a numerical beta effect emerge from the Coriolis acceleration when using a C‐grid with z‐coordinatesThe identified spurious forces are significant in both an idealized gyre configuration and the Weddell Gyre in a realistic global model [ABSTRACT FROM AUTHOR]

Parameterizations of unresolved turbulent processes often compromise the fidelity of large‐scale ocean models. In this work, we argue for a Bayesian approach to the refinement and evaluation of turbulence parameterizations. Using an ensemble of large eddy simulations of turbulent penetrative convection in the surface boundary layer, we demonstrate the method by estimating the uncertainty of parameters in the convective limit of the popular "K‐Profile Parameterization." We uncover structural deficiencies and propose an alternative scaling that overcomes them. Plain Language Summary: Climate projections are often compromised by significant uncertainties which stem from the representation of physical processes that cannot be resolved—such as clouds in the atmosphere and turbulent swirls in the ocean—but which have to be parameterized. We propose a methodology for improving parameterizations in which they are tested against, and tuned to, high‐resolution numerical simulations of subdomains that represent them more completely. A Bayesian methodology is used to calibrate the parameterizations against the highly resolved model, to assess their fidelity and identify shortcomings. Most importantly, the approach provides estimates of parameter uncertainty. While the method is illustrated for a particular parameterization of boundary layer mixing, it can be applied to any parameterization. Key Points: A Bayesian methodology can be used to probe turbulence parameterizations and better understand their biases and uncertaintiesParameterization parameter distributions, learned using high‐resolution simulations, can be used as prior distributions for climate studies [ABSTRACT FROM AUTHOR]