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The turbulent mixing in thin ocean surface boundary layers (OSBL), which occupy the upper 100 m or so of the ocean, control the exchange of heat and trace gases between the atmosphere and ocean. Here we show that current parameterizations of this turbulent mixing lead to systematic and substantial errors in the depth of the OSBL in global climate models, which then leads to biases in sea surface temperature. One reason, we argue, is that current parameterizations are missing key surface‐wave processes that force Langmuir turbulence that deepens the OSBL more rapidly than steady wind forcing. Scaling arguments are presented to identify two dimensionless parameters that measure the importance of wave forcing against wind forcing, and against buoyancy forcing. A global perspective on the occurrence of wave‐forced turbulence is developed using re‐analysis data to compute these parameters globally. The diagnostic study developed here suggests that turbulent energy available for mixing the OSBL is under‐estimated without forcing by surface waves. Wave‐forcing and hence Langmuir turbulence could be important over wide areas of the ocean and in all seasons in the Southern Ocean. We conclude that surface‐wave‐forced Langmuir turbulence is an important process in the OSBL that requires parameterization. Key Points Climate models have biases in the depth of the ocean surface boundary layer Langmuir turbulence is a key process mixing the ocean surface boundary layer Langmuir turbulence deepens the layer more quickly than wind‐forced turbulence

We evaluate the Community ocean Vertical Mixing project version of the K‐profile parameterization (KPP) for modeling upper ocean turbulent mixing. For this purpose, one‐dimensional KPP simulations are compared across a suite of oceanographically relevant regimes against horizontally averaged large eddy simulations (LESs). We find the standard configuration of KPP consistent with LES across many forcing regimes, supporting its physical basis. Our evaluation also motivates recommendations for KPP best practices within ocean circulation models and identifies areas where further research is warranted. The original treatment of KPP recommends the matching of interior diffusivities and their gradients to the KPP‐predicted values computed in the ocean surface boundary layer (OSBL). However, we find that difficulties in representing derivatives of rapidly changing diffusivities near the base of the OSBL can lead to loss of simulation fidelity. To mitigate this difficulty, we propose and evaluate two computationally simpler approaches: (1) match to the internal predicted diffusivity alone and (2) set the KPP diffusivity to 0 at the OSBL base. We find the KPP entrainment buoyancy flux to be sensitive to vertical grid resolution and details of how to diagnose the KPP boundary layer depth. We modify the KPP turbulent shear velocity parameterization to reduce resolution dependence. Additionally, an examination of LES vertical turbulent scalar flux budgets shows that the KPP‐parameterized nonlocal tracer flux is incomplete due to the assumption that it solely redistributes the surface tracer flux. This result motivates further studies of the nonlocal flux parameterization. Key Points The Community ocean Vertical Mixing (CVMix) project version of the K‐profile parameterization (KPP) is compared across a suite of oceanographically relevant regimes against large eddy simulations (LESs) The standard configuration of KPP is consistent with LES results across many ocean simulations, but some adaptations of KPP are proposed to improve comparisons with LES An alternative, computationally simpler, configuration of KPP is proposed to alleviate the need to represent rapidly changing diffusivities near the base of the ocean surface boundary layer

Vertical mixing parameterizations in ocean models are formulated on the basis of the physical principles that govern turbulent mixing. However, many parameterizations include ad hoc components that are not well constrained by theory or data. One such component is the eddy diffusivity model, where vertical turbulent fluxes of a quantity are parameterized from a variable eddy diffusion coefficient and the mean vertical gradient of the quantity. In this work, we improve a parameterization of vertical mixing in the ocean surface boundary layer by enhancing its eddy diffusivity model using data‐driven methods, specifically neural networks. The neural networks are designed to take extrinsic and intrinsic forcing parameters as input to predict the eddy diffusivity profile and are trained using output data from a second moment closure turbulent mixing scheme. The modified vertical mixing scheme predicts the eddy diffusivity profile through online inference of neural networks and maintains the conservation principles of the standard ocean model equations, which is particularly important for its targeted use in climate simulations. We describe the development and stable implementation of neural networks in an ocean general circulation model and demonstrate that the enhanced scheme outperforms its predecessor by reducing biases in the mixed‐layer depth and upper ocean stratification. Our results demonstrate the potential for data‐driven physics‐aware parameterizations to improve global climate models. Plain Language Summary The upper region of the ocean is highly energetic and is responsible for transferring mass, energy and biogeochemical tracers between the atmosphere and the deeper regions of the ocean. This transport takes place because of turbulent swirling motions, which are found to be of varying sizes. Climate models cannot represent all of these motions because smaller‐scale swirls are complex and require additional computational resources. As we cannot neglect those small swirls, we try to approximate their effects on larger‐scale motions using mathematical models. These models have a few ad hoc or empirical assumptions that lead to uncertainty when these climate models are used to project the future climate. To reduce this uncertainty, we augment an existing model of turbulent swirling process with machine learning, which replaces some ad hoc approximations with data‐driven neural networks. Neural networks can learn those missing processes more accurately than a traditional physics‐based model. The neural networks are shown to improve physics in climate simulations. Although we only touch on one component in an ocean climate model, this approach can be replicated to improve any other component that was using ad hoc assumptions and replace them with data‐driven models using techniques from machine learning. Key Points We improve a parameterization of vertical mixing in the ocean surface boundary layer using neural networks Neural networks are trained to predict the diffusivity of second moment closure and maintain energetic constraints of the original parameterization The improved scheme reduces biases of mixed layer depth and thermocline in an atmospherically forced ocean model

Six recent Langmuir turbulence parameterization schemes and five traditional schemes are implemented in a common single‐column modeling framework and consistently compared. These schemes are tested in scenarios versus matched large eddy simulations, across the globe with realistic forcing (JRA55‐do, WAVEWATCH‐III simulated waves) and initial conditions (Argo), and under realistic conditions as observed at ocean moorings. Traditional non‐Langmuir schemes systematically underpredict large eddy simulation vertical mixing under weak convective forcing, while Langmuir schemes vary in accuracy. Under global, realistic forcing Langmuir schemes produce 6% (−1% to 14% for 90% confidence) or 5.2 m (−0.2 m to 17.4 m for 90% confidence) deeper monthly mean mixed layer depths than their non‐Langmuir counterparts, with the greatest differences in extratropical regions, especially the Southern Ocean in austral summer. Discrepancies among Langmuir schemes are large (15% in mixed layer depth standard deviation over the mean): largest under wave‐driven turbulence with stabilizing buoyancy forcing, next largest under strongly wave‐driven conditions with weak buoyancy forcing, and agreeing during strong convective forcing. Non‐Langmuir schemes disagree with each other to a lesser extent, with a similar ordering. Langmuir discrepancies obscure a cross‐scheme estimate of the Langmuir effect magnitude under realistic forcing, highlighting limited understanding and numerical deficiencies. Maps of the regions and seasons where the greatest discrepancies occur are provided to guide further studies and observations. Key Points Six Langmuir turbulence parameterization schemes and five non‐Langmuir schemes are compared in a common single‐column modeling framework A suite of test cases of various scenarios are used, including typical global ocean conditions using JRA55‐do Significant discrepancies among schemes are found and sorted by locations, seasons, and forcing regimes

Rapid restratification of the ocean surface boundary layer in the Indonesian-Australian Basin was captured in austral spring 2018, under the conditions of low wind speed and clear sky during the suppressed phase of Madden–Julian Oscillations (MJOs). Despite sunny days, strong diurnal variations of sea surface temperature (SST) were not observed until the wind speed became extremely low, because the decreasing wind speed modulated the latent heat flux. Combined with the horizontal advection of ocean current, the reduced upward heat loss inhibited the nighttime convective mixing and facilitated the restratification of the subsurface ocean layers. The surface mixed layer was thus shoaled up to 40 m in two days. The restratified upper ocean then sustained high SSTs by trapping heat near the sea surface until the onset of the MJO convection. This restratification process might be initialized under the atmospheric downwelling conditions during the suppressed phase of MJOs. The resulted high SSTs may affect the development and trajectories of MJOs, by enhancing air-sea heat and moisture fluxes as the winds pick up. Simulating this detailed interaction between the near-surface ocean and atmospheric features of MJOs remains a challenge, but with sufficient vertical resolution and realistic initial conditions, several features of the observations can be well captured.

While various parameterizations of vertical turbulent fluxes at different levels of complexity have been proposed, each has its own limitations. For example, simple first‐order closure schemes such as the K‐Profile Parameterization (KPP) lack energetic constraints; two‐equation models like k−ɛ$k-\\varepsilon $directly solve an equation for the turbulent kinetic energy but do not account for non‐diffusive fluxes, and high‐order closures that include the high‐order transport terms are computationally expensive. To address these, we extend the Assumed‐Distribution Higher‐Order Closure (ADC) framework originally proposed for the atmospheric boundary layer and apply it to the ocean surface boundary layer. By assuming a probability distribution function relationship between the vertical velocity and tracers, all second‐order and higher‐order moments are exactly constructed and turbulence closure is achieved in the ADC scheme. In addition, this ADC parameterization has full energetic constraints and includes non‐diffusive fluxes without the computational cost of a full higher‐order closure scheme. We have tested the ADC scheme against a combination of large eddy simulation (LES), KPP, and k−ɛ$k-\\varepsilon $for surface buoyancy‐driven convective mixing and found that the ADC scheme is robust with different vertical resolutions and compares well to the LES results. Plain Language Summary The upper ocean (order of few tens of meters depth from the surface) has a substantial influence on our climate and weather systems. Specifically, upper ocean mixing processes play a key role in modulating global heat budget in the ocean and atmosphere by mixing heat deeper into the ocean or warming the atmosphere above. Accurate representation of the effects of these mixing processes on the global climate and in ocean models is crucial for understanding our current and changing climate. However, current mixing schemes used in these models have shown significant biases. We present a new physically‐motivated mixing scheme for the upper ocean inspired by atmospheric mixing schemes. Results show that the proposed mixing scheme can simulate upper ocean mixing efficiently, suggesting its potential use in climate and ocean models to help reduce model biases. Key Points A new physically‐motivated, PDF‐based parameterization of ocean surface boundary layer turbulence is presented The non‐diffusive fluxes are included naturally and the scheme provides a closed set of equations with realizable closure assumptions The mixing scheme accurately predicts the effects of convective turbulence across different vertical resolutions

Turbulent motions in the thin ocean surface boundary layer control exchanges of momentum, heat and trace gases between the atmosphere and ocean. However, present parametric equations of turbulent motions that are applied to global climate models result in systematic or substantial errors in the ocean surface boundary layer. Significant mixing caused by surface wave processes is missed in most parametric equations. A Large Eddy Simulation model is applied to investigate the wave-induced mixed layer structure. In the wave-averaged equations, wave effects are calculated as Stokes forces and breaking waves. To examine the effects of wave parameters on mixing, a series of wave conditions with varying wavelengths and heights are used to drive the model, resulting in a variety of Langmuir turbulence and wave breaking outcomes. These experiments suggest that wave-induced mixing is more sensitive to wave heights than to the wavelength. A series of numerical experiments with different wind intensities-induced Stokes drifts are also conducted to investigate wave-induced mixing. As the wind speed increases, the influence depth of Langmuir circulation deepens. Additionally, it is observed that breaking waves could destroy Langmuir cells mainly at the sea surface, rather than at deeper layers.

This study uses a large eddy simulation （LES） model to investigate the turbulence processes in the ocean surface boundary layer at Zhangzi Island offshore. Field measurements at Zhangzi Island （39°N, 122°E） during July 2009 are used to drive the LES model. The LES results capture a clear diurnal cycle in the oceanic turbulence boundary layer. The process of the heat penetration and heat distribution characteristics are analyzed through the heat flux results from the LES and their differences between two diurnal cycles are discussed as well. Energy balance and other dynamics are investigated which show that the tide-induced shear production is the main source of the turbulence energy that balanced dissipation. Momentum flux near the surface shows better agreement with atmospheric data computed by the eddy correlation method than those computed by bulk formula.

The South Atlantic Convergence Zone (SACZ) is an atmospheric system occurring in austral summer on the South America continent and sometimes extending over the adjacent South Atlantic. It is characterized by a persistent and very large, northwest-southeast-oriented, cloud band. Its presence over the ocean causes sea surface cooling that some past studies indicated as being produced by a decrease of incoming solar heat flux induced by the extensive cloud cover. Here we investigate ocean–atmosphere interaction processes in the Southwestern Atlantic Ocean (SWA) during SACZ oceanic episodes, as well as the resulting modulations occurring in the oceanic mixed layer and their possible feedbacks on the marine atmospheric boundary layer. Our main interests and novel results are on verifying how the oceanic SACZ acts on dynamic and thermodynamic mechanisms and contributes to the sea surface thermal balance in that region. In our oceanic SACZ episodes simulations we confirm an ocean surface cooling. Model results indicate that surface atmospheric circulation and the presence of an extensive cloud cover band over the SWA promote sea surface cooling via a combined effect of dynamic and thermodynamic mechanisms, which are of the same order of magnitude. The sea surface temperature (SST) decreases in regions underneath oceanic SACZ positions, near Southeast Brazilian coast, in the South Brazil Bight (SBB) and offshore. This cooling is the result of a complex combination of factors caused by the decrease of solar shortwave radiation reaching the sea surface and the reduction of horizontal heat advection in the Brazil Current (BC) region. The weakened southward BC and adjacent offshore region heat advection seems to be associated with the surface atmospheric circulation caused by oceanic SACZ episodes, which rotate the surface wind and strengthen cyclonic oceanic mesoscale eddy. Another singular feature found in this study is the presence of an atmospheric cyclonic vortex Southwest of the SACZ (CVSS), both at the surface and aloft at 850 hPa near 24°S and 45°W. The CVSS induces an SST decrease southwestward from the SACZ position by inducing divergent Ekman transport and consequent offshore upwelling. This shows that the dynamical effects of atmospheric surface circulation associated with the oceanic SACZ are not restricted only to the region underneath the cloud band, but that they extend southwestward where the CVSS presence supports the oceanic SACZ convective activity and concomitantly modifies the ocean dynamics. Therefore, the changes produced in the oceanic dynamics by these SACZ events may be important to many areas of scientific and applied climate research. For example, episodes of oceanic SACZ may influence the pathways of pollutants as well as fish larvae dispersion in the region.

This paper is concerned with a complete asymptotic analysis as These boundary layers, which are the main center of interest of the present paper, exhibit several types of peculiar behaviour. First, the size of the boundary layer on the western and eastern boundary, which had already been computed by several authors, becomes formally very large as one approaches northern and southern portions of the boudary, i.e. pieces of the boundary on which the normal is vertical. This phenomenon is known as geostrophic degeneracy. In order to avoid such singular behaviour, previous studies imposed restrictive assumptions on the domain Moreover, when the domain Eventually, the effect of boundary layers is non-local in several aspects. On the first hand, for algebraic reasons, the boundary layer equation is radically different on the west and east parts of the boundary. As a consequence, the Sverdrup equation is endowed with a Dirichlet condition on the East boundary, and no condition on the West boundary. Therefore western and eastern boundary layers have in fact an influence on the whole domain