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Eddy viscosity is employed throughout the majority of numerical fluid dynamical models, and has been the subject of a vigorous body of research spanning a variety of disciplines. It has long been recognized that the proper description of eddy viscosity uses tensor mathematics, but in practice it is almost always employed as a scalar due to uncertainty about how to constrain the extra degrees of freedom and physical properties of its tensorial form. This manuscript borrows techniques from outside the realm of geophysical fluid dynamics to consider the eddy viscosity tensor using its eigenvalues and eigenvectors, establishing a new framework by which tensorial eddy viscosity can be tested. This is made possible by a careful analysis of an operation called tensor unrolling, which casts the eigenvalue problem for a fourth‐order tensor into a more familiar matrix‐vector form, whereby it becomes far easier to understand and manipulate. New constraints are established for the eddy viscosity coefficients that are guaranteed to result in energy dissipation, backscatter, or a combination of both. Finally, a testing protocol is developed by which tensorial eddy viscosity can be systematically evaluated across a wide range of fluid regimes. Plain Language Summary: Numerical fluid flow solvers need to dissipate energy in order to remain numerically stable, and this is most often achieved by adding a mechanism to the governing equations called eddy viscosity. Generally the implementation of eddy viscosity boils down to specifying a scalar coefficient that governs the rate of energy dissipation. However, the true mathematical form of eddy viscosity is that of a higher‐order geometric object called a tensor, and the potential advantages of using this form remain unexplored. This paper uses a generalized version of familiar linear algebra operations (eigenvalues, trace, and determinant) to establish new constraints on the eddy viscosity coefficients that promise to open up this parameterization to renewed scrutiny. Key Points: Eddy viscosity is usually employed as a scalar coefficient, but its true form is that of a tensorEigenanalysis can reveal new constraints on the coefficients of the eddy viscosity tensorTensor unrolling can help expose the power of the eigenanalysis, but only if done in a particular way [ABSTRACT FROM AUTHOR]

We present a two‐dimensional, zonally averaged global model of atmospheric transport named MALTA: Model of Averaged in Longitude Transport in the Atmosphere. It aims to be accessible to a broad community of users, with the primary function of quantifying emissions of greenhouse gases and ozone depleting substances. The model transport is derived from meteorological reanalysis data and flux‐gradient experiments using a three‐dimensional transport model. Atmospheric sinks are prescribed loss frequency fields. The zonally averaged model simulates important large‐scale transport features such as the influence on trace gas concentrations of the quasi‐biennial oscillation and variations in inter‐hemispheric transport rates. Stratosphere‐troposphere exchange is comparable to a three‐dimensional model and inter‐hemispheric transport is faster by up to 0.3 years than typical transport times of three‐dimensional models, depending on the metric used. Validation of the model shows that it can estimate emissions of CFC‐11 from an incorrect a priori emissions field well using three‐dimensional (3D) mole fraction fields generated using a different 3D model than which the flux gradient relationships were derived. The model is open source and is expected to be applicable to a wide range of studies requiring a fast, simple model of atmospheric transport and chemical processes for estimating associated emissions or mole fractions. Plain Language Summary: We introduce a simplified global model that simulates the movement of gases in the atmosphere. The main goal of this model is to understand how greenhouse gases and substances that deplete the ozone layer are transported and distributed, and to more accurately estimate their global emissions using concentrations measured in the atmosphere over time. To achieve this, the model uses data from weather analysis and experiments conducted with a more complex three‐dimensional model. The model calculates how gases move across different latitudes and altitudes, and accounts for their chemical loss. The simplified model can accurately reproduce large‐scale atmospheric transport phenomena. The model is publicly available. We expect it to be useful for research that requires a fast and easy to use model to understand large‐scale atmospheric transport and related processes. Key Points: A user‐friendly 2D global atmospheric transport model using transport derived from 3D reanalysis data and flux‐gradient experimentsIntended for use with long‐lived greenhouse gases and ozone‐depleting substancesAn open‐source model, which is applicable to diverse studies on emissions and chemical processes [ABSTRACT FROM AUTHOR]

The mixing of tracers by mesoscale eddies, parameterized in many ocean general circulation models (OGCMs) as a diffusive‐advective process, contributes significantly to the distribution of tracers in the ocean. In the ocean interior, diffusive contribution occurs mostly along the direction parallel to local neutral density surfaces. However, near the surface of the ocean, small‐scale turbulence and the presence of the boundary itself break this constraint and the mesoscale transport occurs mostly along a plane parallel to the ocean surface (horizontal). Although this process is easily represented in OGCMs with geopotential vertical coordinates, the representation is more challenging in OGCMs that use a general vertical coordinate, where surfaces can be tilted with respect to the horizontal. We propose a method for representing the diffusive horizontal mesoscale fluxes within the surface boundary layer of general vertical coordinate OGCMs. The method relies on regridding/remapping techniques to represent tracers in a geopotential grid. Horizontal fluxes are calculated on this grid and then remapped back to the native grid, where fluxes are applied. The algorithm is implemented in an ocean model and tested in idealized and realistic settings. Horizontal diffusion can account for up to 10% of the total northward heat transport in the Southern Ocean and Western boundary current regions of the Northern Hemisphere. It also reduces the vertical stratification of the upper ocean, which results in an overall deepening of the surface boundary layer depth. Finally, enabling horizontal diffusion leads to meaningful reductions in the near‐surface global bias of potential temperature and salinity. Plain Language Summary: Mesoscale ocean eddies, which are analogous to the weather systems in the atmosphere, are crucial to the distribution of heat, salt, carbon, and nutrients throughout the global ocean. Most of the ocean models used in climate simulations do not have enough horizontal resolution to resolve these eddies and, therefore, their effects must be parameterized. In the ocean interior, where no appreciable heat or mass is exchanged across density surfaces, the mixing of tracers due to mesoscale eddies occurs along surfaces of constant density. However, as ocean boundaries are approached, mixing occurs on a plane parallel to the boundary. For example, near the surface of the ocean, which is where the scheme presented here is designed to work, this plane is mostly horizontal. There is a class of ocean models that use a vertical coordinate system whose layer thicknesses can vary horizontally, thus complicating the implementation of horizontal diffusive parameterizations. This paper presents and evaluates a method that allows horizontal fluxes to be calculated and applied within the surface layer of this class of ocean models. Key Points: General vertical coordinate ocean models lack the option to shift diffusive fluxes from neutral surfaces to a purely horizontal directionRegridding/remapping techniques are used to represent tracers in z*‐coordinates, where horizontal fluxes are easily appliedThe method reduces global tracer biases in forced simulations, regardless of the coordinate system employed [ABSTRACT FROM AUTHOR]

During the austral summer of 2017/2018, the Tasman Sea experienced an intense marine heatwave over an extensive area. It persisted for approximately 3 months and caused substantial ecological impacts. The marine heatwave was understood to have been driven primarily by increased net downward heat flux associated with a high pressure system. However, it has been unclear why the marine heatwave persisted. Using an ultra‐high‐resolution (∼1 km) regional ocean model simulation, the drivers, dynamics, and persistence of the 2017/2018 marine heatwave are explored in detail. It is found that a burst of warm water advection helped to initiate the event, but a shallower than usual mixed layer, coupled with near continuous net downward air‐sea heat flux, caused the marine heatwave to persist. Submesoscale dynamics were found to be relatively unimportant to the marine heatwave's persistence. Plain Language Summary: Marine heatwaves are occurrences when the ocean temperature is much warmer than usual for an extended period. A large‐scale marine heatwave, lasting around 3 months, occurred in the Tasman Sea between Australia and New Zealand during the austral summer of 2017/2018, causing severe impacts on the local marine ecology. The marine heatwave is known to have been driven by atmospheric heating, but it is unclear why it lasted as long as it did. Using an ultra‐high‐resolution ocean model simulation, a clearer picture has emerged of how ocean dynamics helped to initiate the marine heatwave, while heating by the atmosphere and a shallower than normal mixed layer caused it to persist. Key Points: An ultra‐high‐resolution simulation explored the drivers and ocean dynamics in maintaining the record 2017/2018 Tasman Sea marine heatwaveA warm water burst helped to initiate it, but a shallower than usual mixed layer and ongoing atmospheric heating caused it to persistSubmesoscale dynamics were found to be relatively unimportant [ABSTRACT FROM AUTHOR]

The identification of vortices in a fluid flow is a dynamically interesting problem that has practical applications in oceanography due to the outsized role eddies play in water mass, heat, and tracer transport. Here a new Eulerian scheme is developed to detect both vortices and strongly strained fronts, which are both ubiquitous in the World Ocean. The new scheme is conceptually linked to the well-known Okubo–Weiss parameter, but is extended to quasigeostrophic flows by recognizing the strong role played by vertical shear in ocean dynamics. Adapted from the λ 2 criterion for vortex identification, the scheme considers the curvature of the pressure field as the differentiator between vortical and strained flow structures, and it is shown that its underlying geometry also exhibits characteristics of quasigeostrophic flow. The uses and skill of the scheme are demonstrated using a high-resolution regional ocean simulation, and prospects for its use with observational products are discussed. [ABSTRACT FROM AUTHOR]

Identifying internal waves in complex flow fields is a long‐standing problem in fluid dynamics, oceanography and atmospheric science, owing to the overlap of internal waves temporal and spatial scales with other flow regimes. Lagrangian filtering—that is, temporal filtering in a frame of reference moving with the flow—is one proposed methodology for performing this separation. Here we (a) describe an improved implementation of the Lagrangian filtering methodology and (b) introduce a new freely available, parallelized Python package that applies the method. We show that the package can be used to directly filter output from a variety of common ocean models including MITgcm, Regional Ocean Modeling System and MOM5 for both regional and global domains at high resolution. The Lagrangian filtering is shown to be a useful tool to both identify (and thereby quantify) internal waves, and to remove internal waves to isolate the non‐wave flow field. Plain Language Summary: Ocean flows are a superposition of many different flow phenomena including eddies, jets, currents, and waves. Quantifying a particular phenomenon therefore requires a method to identify and separate that phenomenon from others in the flow, in order to be able to assess the associated energy and energetic exchanges. Here we present a new implementation of a method to identify a particular phenomenon known as "internal waves"—hourly to daily oscillatory motions which propagate three‐dimensionally throughout the ocean, driving mixing and thereby supporting the global ocean circulation. The method involves a combination of a coordinate transformation and a high‐pass temporal filter. Here we describe a newly released, freely available, efficient and user‐friendly open‐source Python package that implements the method. Key Points: A new open source parallelized Python package to perform Lagrangian filtering is now availableThe package implements an improved method for filtering internal waves from high‐resolution numerical model outputThe package may be applied to directly filter output from a number of common ocean models including MITgcm, Regional Ocean Modeling System and MOM5 [ABSTRACT FROM AUTHOR]

Tropical modes of variability, including the Madden‐Julian Oscillation (MJO) and the El Niño‐Southern Oscillation (ENSO), are challenging to represent in climate models. Previous studies suggest their fundamental dependence on zonal asymmetry, but such dependence is rarely addressed with fully coupled ocean dynamics. This study fills the gap by using fully coupled, idealized Community Earth System Model (CESM) and comparing two nominally ocean‐covered configurations with and without a meridional boundary. For the MJO‐like intraseasonal mode, its separation from equatorial Kelvin waves and the eastward propagation of its convective and dynamic signals depend on the zonal gradient of the mean state. For the ENSO‐like interannual mode, in the absence of the ocean's meridional boundary, a circum‐equatorial dominant mode emerges with distinct ocean dynamics. The interpretation of the dependence of these modes on zonal asymmetry is relevant to their representation in realistic climate models. Plain Language Summary: In Earth's tropical regions, recurring patterns—such as El Niño and atmospheric waves that come with storm clusters—have a large influence on the global weather and climate. These patterns are also challenging to represent in modern climate models. Previous studies suggest that the behavior of these patterns depends on the east‐west contrast in the Pacific ocean, but these studies typically focus on the atmosphere while ignoring relevant actions in the ocean, or vice versa. In this study, we address the question by using a state‐of‐the‐art climate model with a full‐blown atmosphere and ocean. We compare two designs with simplified continental shapes, one with east‐west contrast and the other without. The behavior of atmospheric waves is more realistic with an east‐west contrast. On the other hand, in a global ocean with no land blocking the east‐west direction and therefore no east‐west contrast, phenomena similar to El Niño can still occur around the equator, but with different ocean processes. Understanding the essential conditions for these patterns will contribute to better climate models for prediction, helping with the preparation for and mitigation of extreme weather and climate events. Key Points: Two idealized coupled models, with and without a meridional ocean boundary, show Madden‐Julian Oscillation (MJO)‐ and El Niño‐Southern Oscillation (ENSO)‐relevant modes of tropical variabilityZonal asymmetry affects the distinction of an MJO‐like intraseasonal mode from equatorial Kelvin wavesWithout the ocean's meridional boundary and the associated ENSO‐type dynamics, an interannual mode still persists around the equator [ABSTRACT FROM AUTHOR]

Idealized models can reveal insights into Earth's climate system by reducing its complexities. However, their potential is undermined by the scarcity of fully coupled idealized models with components comparable to contemporary, comprehensive Earth System Models. To fill this gap, we compare and contrast the climates of two idealized planets which build on the Simpler Models initiative of the Community Earth System Model (CESM). Using the fully coupled CESM, the Aqua configuration is ocean‐covered except for two polar land caps, and the Ridge configuration has an additional pole‐to‐pole grid‐cell‐wide continent. Contrary to most sea surface temperature profiles assumed for atmosphere‐only aquaplanet experiments with the thermal maximum on the equator, the coupled Aqua configuration is characterized by a global cold belt of wind‐driven equatorial upwelling, analogous to the eastern Pacific cold tongue. The presence of the meridional boundary on Ridge introduces zonal asymmetry in thermal and circulation features, similar to the contrast between western and eastern Pacific. This zonal asymmetry leads to a distinct climate state from Aqua, cooled by ∼2°C via the radiative feedback of clouds and water vapor. The meridional boundary of Ridge is also crucial for producing a more Earth‐like climate state compared to Aqua, including features of atmospheric and ocean circulation, the seasonal cycle of the Intertropical Convergence Zone, and the meridional heat transport. The mean climates of these two basic configurations provide a baseline for exploring other idealized ocean geometries, and their application for investigating various features and scale interactions in the coupled climate system. Plain Language Summary: Simplified climate models can improve our understanding of the Earth's climate system by stripping down its complexities. For example, atmospheric scientists often use idealized models with fixed sea surface temperature that is uniform in the east‐west direction. Meanwhile, oceanographers often use box‐shaped models driven by fixed wind. Although simplified models with full atmosphere‐ocean interactions are few, previous studies have shed light on fundamental processes governing Earth's climate, including the poleward transport of energy. However, the coarse "pixel size" and overly reduced components are hard to relate to contemporary models for international climate assessments. To bridge this gap, we present two simplified models within components and resolution similar to that of state‐of‐the‐art climate models. The nominally ocean‐covered model, without continents blocking the east‐west direction, develops a global cold belt of upwelling around the equator. In contrast, the model with an additional pole‐to‐pole strip continent is more Pacific‐like with a western pool and eastern cold tongue. While broadly consistent with previous works, these new models show more details in the tropical region that affect the Hadley cells and rainfall. The capability of these simplified models is promising for addressing atmosphere‐ocean interactions of scientific and societal interests, such as El Niño and hurricanes. Key Points: Two baseline examples of fully coupled CESM with idealized ocean geometry capture many features of Earth's circulationThe nominally ocean‐covered coupled model has a global cold belt of equatorial upwelling and corresponding "reverse Hadley" cellsThe addition of a pole‐to‐pole strip continent leads to zonal asymmetry that makes the model's circulation more Pacific‐like [ABSTRACT FROM AUTHOR]

Ocean ventilation is the process by which climatically important tracers such as heat and carbon are exchanged between the atmosphere and ocean interior. In this paper a series of numerical simulations are used to study the interaction of submesoscales and a topographically steered jet in driving rapid ventilation. The ventilation is found to increase both as a function of wind stress and model resolution, with a submesoscale-resolving 1/1208 model exhibiting the largest ventilation rate. The jet in this simulation is found to be persistently unstable to submesoscale instabilities, which are known to feature intense vertical circulations. The vertical tracer transport is found to scale as a function of the eddy kinetic energy and mean isopycnal slope, whose behaviors change as a function of the wind stress and due to the emergence of a strong potential vorticity gradient due to the lateral shear of the jet. These results highlight the importance of jet- submesoscale interaction as a bridge between the atmosphere and the ocean interior. [ABSTRACT FROM AUTHOR]

Tides and tidally generated waves play a key role in modulating the heat budget of the nearshore environment, which can significantly affect the ecology of the coastal and reef zones. The high spatial resolution required to resolve such waves in numerical models means that diagnosing wave-generated heat fluxes (WHFs) has so far only been possible over very limited areas. Because many marine ecosystems that are affected by WHFs, such as coral reefs, are patchily distributed within domains of hundreds of kilometers, an alternative to fully wave-resolving models is needed to identify thermal refugia and guide conservation efforts over larger regions. In this study, a one-way nested series of regional ocean simulations has been conducted to study the role of waves in driving high-frequency temperature variations in the Coral Triangle and to develop a method for identifyingWHFin coarser-resolution models. Afiltering method using Lagrangian particles is used to separate the wave component of the flow, which is used to diagnose the wave energy and to identify locations experiencing large, high-frequency temperature variability. These locations are shown to possess three key characteristics: large time-mean wave kinetic energy, shallow depth, and a steep bathymetric gradient that gives access to a nearby source of cold, subthermocline water. A function of the wave kinetic energy and bathymetric slope is found to closely correlate with areas of maximal temperature variance, suggesting its use as a convenient and readily calculable metric to locate thermal refugia in observations or numerical experiments over large spatial domains. [ABSTRACT FROM AUTHOR]

Oceanic mesoscale eddies are known to diffuse and stir tracers, and the development of skillful eddy closures is aided considerably by the accurate diagnosis of these processes from eddy‐resolving model statistics. In this work a multiple‐tracers inversion method is applied to a global mesoscale eddy‐resolving simulation, with the intent to solve for the eddy transport tensor that describes the eddy diffusion (symmetric part) and stirring (antisymmetric part). Special emphasis is placed on diagnosing the anisotropy of the horizontal transport, which is described by the eigenvalues and eigenvectors of the 2×2 horizontal symmetric subtensor. Global diagnoses of these quantities, along with an examination of their vertical structures, are used to recommend an algorithm for extending the Gent and McWilliams and Redi parameterizations to include anisotropic effects. Plain Language Summary: Tracer transport by ocean mesoscale eddies is usually parameterized using a flux‐gradient relationship with a scalar transport coefficient for the horizontal fluxes. Using a scalar coefficient implies that the transport is horizontally isotropic. There exist many mechanisms that may lead to anisotropic transport, however, and parameterizing this anisotropy requires a (symmetric) tensor coefficient. We diagnose this tensor coefficient using a high‐resolution global ocean model with an inversion method that uses multiple passive tracers. The statistics from the diagnosis allow us to explore the properties of the flow that govern the anisotropy, and to recommend an anisotropic extension of extant tracer parameterization schemes. Key Points: Anisotropic eddy diffusivity is diagnosed with a multiple tracers inversion techniqueAn eigendecomposition of the horizontal diffusion tensor determines the 3‐D parameterized transportThis diagnosis informs an anisotropic extension to the GM‐Redi parameterization [ABSTRACT FROM AUTHOR]

Submesoscale dynamics are hypothesized to play a leading-order role in setting the stratification of the mixed layer via the interaction of submesoscale eddies and surface forcing. Previous studies of such interactions have generally focused on the time-evolving characteristics of submesoscale turbulence, such as the spindown of a baroclinically unstable front. This paper focuses instead on the equilibrium dynamics of the oceanic mixed layer, where forcing and dissipation are in balance, through a combination of scaling analysis and numerical simulations. The steady dynamics are well described by a turbulent thermal wind balance, with external forcing parameterized by a strong vertical diffusivity κ. Scaling laws are developed for the characteristic vertical length scale L υ, ageostrophic velocity scales U and V, buoyancy frequency N2, and eddy buoyancy flux , which are appropriate for a turbulent mixed layer whose stratification is equilibrated against strong vertical mixing. A suite of numerical simulations is developed to test these scalings for different values of κ and lateral buoyancy gradient. The scaling relations are shown to be very robust across all simulations, and this allows the new scaling for to be directly compared against an extant parameterization in the forcing scenarios explored here. [ABSTRACT FROM AUTHOR]