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We present a new energy backscatter parametrization for primitive equation ocean models at eddy-permitting resolution, specifically for unstructured grids. Traditional eddy parametrizations in terms of viscosity closures lead to excessive dissipation of kinetic energy when used with eddy-permitting meshes. Implemented into the FESOM2 ocean model, the backscatter parametrization leads to a more realistic total dissipation of kinetic energy. It maintains a reservoir of dissipated energy and reinjects this subgrid energy at larger scales at a controlled rate. The separation between dissipation and backscatter scales is achieved by using different-order differential operators and/or spatial smoothing. This ensures numerical model stability. We perform sensitivity studies with different choices of parameter settings and viscosity schemes in a configuration with a baroclinically unstable flow in a zonally reentrant channel with a horizontally uniform mesh. The best backscatter setup substantially improves eddy-permitting simulations at 1/4° and 1/6° resolution, bringing them close to a 1/12° eddy-resolving reference. Improvements are largest for levels of kinetic energy and variability in temperature and vertical velocity. A selected optimal default scheme is then tested in a mixed resolution setup – a channel with narrow transitions between an eddy-permitting and an eddy-resolving subdomain. The backscatter scheme is able to adapt dynamically to the different resolutions and moves the diagnostics closer to the high resolution reference throughout the domain. Our study is a first step toward using backscatter in global variable-mesh ocean models and suggests potential for substantial improvements of ocean mean state and variability at reduced computational cost. • Implementation of kinetic energy backscatter in 3D primitive equation ocean model • Extensive sensitivity studies of backscatter schemes in channel setup • Application to variable grid channel simulation with local grid refinement • Backscatter substantially improves kinetic energy and flow variability. • Similarly good flow representation at 1/4° compared to 1/12° with <5% of costs [ABSTRACT FROM AUTHOR]

Stability and convergence of the modified EVP implementation of the visco-plastic sea ice rheology by Bouillon et al., Ocean Modell., 2013, is analyzed on B- and C-grids. It is shown that the implementation on a B-grid is less restrictive with respect to stability requirements than on a C-grid. On C-grids convergence is sensitive to the discretization of the viscosities. We suggest to adaptively vary the parameters of pseudotime subcycling of the modified EVP scheme in time and space to satisfy local stability constraints. This new approach generally improves the convergence of the modified EVP scheme and hence its numerical efficiency. The performance of the new “adaptive EVP” approach is illustrated in a series of experiments with the sea ice component of the MIT general circulation model (MITgcm) that is formulated on a C-grid. [ABSTRACT FROM AUTHOR]

Abstract: A data assimilation (DA) system has been developed for the operational circulation model of the German Federal Maritime and Hydrographic Agency (BSH) in order to improve the forecast of hydrographic characteristics in the North and Baltic Seas. It is based on the local Singular Evolutive Interpolated Kalman (SEIK) filter algorithm and assimilation of the NOAA AVHRR-derived sea surface temperature (SST). The DA system allows one to improve the agreement of the SST forecast with the satellite observations by 27% on average over the period of October 2007–September 2008. However, a sensitivity analysis of the forecasting system performance shows a significant impact of initial model error statistics on ice fields and bottom temperature. A reinitialisation of model error covariances in accordance with seasonality of the model error statistics was required in order to maintain the predictive skill with respect to these variables. The success of the DA system is quantified by the comparison with independent data from MARNET stations as well as sea ice concentration measurements. In addition, the Maximum Entropy approach is used to assess the system performance and the prior and posterior model error statistics. [Copyright &y& Elsevier]

Abstract: Experiments with idealized geometry are used to compare model solutions of implicit VP- and explicit EVP-solvers in two very different ice-ocean codes: the regular-grid, finite-volume Massachusetts Institute of Technology general circulation model (MITgcm) and the Alfred Wegener Institute Finite Element Ocean Model (FEOM). It is demonstrated that for both codes the obtained solutions of implicit VP-and EVP-solvers can differ significantly, because the EVP solutions tend to have smaller ice viscosities (“weaker” ice). EVP solutions tend to converge only slowly to implicit VP solutions for very small sub-cycling time steps. Variable resolution in the unstructured-grid model FEOM also affects the solution as smaller grid cell size leads to smaller viscosity in EVP solutions. Models with implicit VP-solvers can block narrow straits under certain conditions, while EVP-models are found to always allow flow as a consequence of lower viscosities. [Copyright &y& Elsevier]

Abstract: A newly developed global Finite Element Sea Ice–Ocean Model (FESOM) is presented. The ocean component is based on the Finite Element model of the North Atlantic (FENA) but has been substantially updated and extended. In addition to a faster realization of the numerical code, state-of-the-art parameterizations of subgrid-scale processes have been implemented. A Redi/GM scheme is employed to parameterize the effects of mesoscale eddies on lateral tracer distribution. Vertical mixing and convection are parameterized as a function of the Richardson number and the Monin–Obukhov length. A finite element dynamic-thermodynamic sea ice–model has been developed and coupled to the ocean component. Sea ice thermodynamics have been derived from the standard AWI sea ice model featuring a prognostic snow layer but neglecting internal heat storage. The dynamic part offers the viscous-plastic and elastic-viscous-plastic rheologies. All model components are discretized on a triangular/tetrahedral grid with a continuous, conforming representation of model variables. The coupled model is run in a global configuration and forced with NCEP daily atmospheric reanalysis data for 1948–2007. Results are analysed with a slight focus on the Southern Hemisphere. Many aspects of sea ice distribution and hydrography are found to be in good agreement with observations. As in most coarse-scale models, Gulf Stream transport is underestimated, but transports of the Kuroshio and the Antarctic Circumpolar Current appear realistic. The seasonal cycles of Arctic and Antarctic sea ice extents and Antarctic sea ice thickness are well captured; long- and short-term variability of ice coverage is found to be reproduced realistically in both hemispheres. The coupled model is now ready to be used in a wide range of applications. [Copyright &y& Elsevier]

Abstract: A new version of the 3D finite-element primitive-equation ocean model (FEOM) based on tetrahedron partitioning of the computational domain is applied to simulate the North Atlantic circulation at eddy-permitting resolution (1/15°–2°). It relies on a horizontally refined mesh in regions of steep topography and allows the sloping bottom to be represented within the z-coordinate vertical discretization, similar to the so-called shaved-cell approach. It is the first time this approach is used to model large-scale ocean circulation. The FEOM performance in the North Atlantic is compared with that of the finite-difference models of similar resolution of the DYNAMO project. The meridional overturning circulation and heat transport of FEOM agree well with those of the DYNAMO project models, while the mean sea surface height demonstrates the presence of the Gulf Stream recirculation reproduced only by the ISOPYCNIC model of DYNAMO. The annual mean transports of the Gulf Stream and Deep Western Boundary Current at 27°N are of 37Sv and 17Sv with core velocities of about 1m/s and 12cm/s respectively. Due to flexibility in mesh refinement the FEOM provides a tool for modelling the influence of small-scale phenomena unresolved by current climate models on large-scale ocean circulation. [Copyright &y& Elsevier]

We describe a three-dimensional (3D) finite-element ocean model designed for investigating the large-scale ocean circulation on time scales from years to decades. The model solves the primitive equations in the dynamical part and the advection–diffusion equations for temperature and salinity in the thermodynamical part. The time-stepping is implicit. The 3D mesh is composed of tetrahedra and has a variable resolution. It is based on an unstructured 2D surface mesh and is stratified in the vertical direction. The model uses linear functions for horizontal velocity and tracers on tetrahedra, and for surface elevation on surface triangles. The vertical velocity field is elementwise constant. An important ingredient of the model is the Galerkin least-squares stabilization used to minimize effects of unresolved boundary layers and make the matrices to be inverted in time-stepping better conditioned. The model performance was tested in a 16-year simulation of the North Atlantic using a mesh covering the area between 7° and 80° N and providing variable horizontal resolution from 0.3° to 1.5°. [Copyright &y& Elsevier]

Recent developments of the explicit elastic-viscous-plastic (EVP) solvers call for a new comparison with implicit solvers for the equations of viscous-plastic sea ice dynamics. In Arctic sea ice simulations, the modified and the adaptive EVP solvers, and the implicit Jacobian–free Newton–Krylov (JFNK) solver are compared against each other. The adaptive EVP method shows convergence rates that are generally similar or even better than those of the modified EVP method, but the convergence of the EVP methods is found to depend dramatically on the use of the replacement pressure (RP). Apparently, using the RP can affect the pseudo-elastic waves in the EVP methods by introducing extra non-physical oscillations so that, in the extreme case, convergence to the VP solution can be lost altogether. The JFNK solver also suffers from higher failure rates with RP implying that with RP the momentum equations are stiffer and more difficult to solve. For practical purposes, both EVP methods can be used efficiently with an unexpectedly low number of sub-cycling steps without compromising the solutions. The differences between the RP solutions and the NoRP solutions (when the RP is not being used) can be reduced with lower thresholds of viscous regularization at the cost of increasing stiffness of the equations, and hence the computational costs of solving them. [ABSTRACT FROM AUTHOR]

Abstract: Hydrographic observations in deep Fram Strait evidence a plume of Storfjorden Brine-enriched Shelf Water in 1986, 1988 and 2002. The plume spreads along the continental slope over 600km away from its formation area and reaches 2000m depth. The plume is 30 to 80m thick in the deep layer of Fram Strait; it is almost 0.4°C warmer and 0.06 more saline than the ambient water. The velocity of the plume, observed by a moored current meter in Fram Strait, is 12.60±4.70cms−1 .The hydrographic properties of the plume are used to study entrainment. A streamtube model with four entrainment parameterizations is applied. Two Froude-number dependent parameterizations lead to mixing mostly happening over the shelf break, where the Froude number is large. This is in agreement with the traditional view, but is inconsistent with the observed temperature and salinity of the Storfjorden plume. Therefore further entrainment assumptions (a constant and a volume-dependent entrainment) are tested. The volume-dependent entrainment scheme yields the best representation of entrainment in the Storfjorden plume. Our results emphasize the necessity of strong mixing in the deep layers in Fram Strait to achieve an agreement with observed properties of the plume. [Copyright &y& Elsevier]

Abstract: Unstructured meshes suggest a number of advantages in tide modeling by resolving coastlines and providing refinements where it is required. We investigate the performance of several unstructured grid methods (finite element and finite volume) and time stepping schemes with respect to their accuracy and computational cost in simulating the tide in the North Sea. On a triangular mesh, we compare solutions of one finite volume and two finite element approaches with the amplitude and phase of observation data. All models show reasonable agreement and we explain the differences. By comparing CPU times for one tidal cycle we get the computational efficiency of the temporal discretization schemes (Euler semi-implicit, leapfrog explicit, Runge–Kutta and Adams–Bashforth). Although numerical solvers involve more computational loads per time step, we give the preference to the semi-implicit models, as the increased time step size reduces the total computational time considerably. [Copyright &y& Elsevier]

Many questions in ocean and climate modelling require the combined use of high resolution, global coverage and multi-decadal integration length. For this combination, even modern resources limit the use of traditional structured-mesh grids. Here we compare two approaches: A high-resolution grid nested into a global model at coarser resolution (NEMO with AGRIF) and an unstructured-mesh grid (FESOM) which allows to variably enhance resolution where desired. The Agulhas system around South Africa is used as a testcase, providing an energetic interplay of a strong western boundary current and mesoscale dynamics. Its open setting into the horizontal and global overturning circulations also requires global coverage. Both model configurations simulate a reasonable large-scale circulation. Distribution and temporal variability of the wind-driven circulation are quite comparable due to the same atmospheric forcing. However, the overturning circulation differs, owing each model's ability to represent formation and spreading of deep water masses. In terms of regional, high-resolution dynamics, all elements of the Agulhas system are well represented. Owing to the strong nonlinearity in the system, Agulhas Current transports of both configurations and in comparison with observations differ in strength and temporal variability. Similar decadal trends in Agulhas Current transport and Agulhas leakage are linked to the trends in wind forcing. Although the number of 3D wet grid points used in FESOM is similar to that in the nested NEMO, FESOM uses about two times the number of CPUs to obtain the same model throughput (in terms of simulated model years per day). This is feasible due to the high scalability of the FESOM code. [ABSTRACT FROM AUTHOR]

We evaluate the mean circulation patterns, water mass distributions, and tropical dynamics of the North and Equatorial Pacific Ocean based on a suite of global ocean-sea ice simulations driven by the CORE-II atmospheric forcing from 1963-2007. The first three moments (mean, standard deviation and skewness) of sea surface height and surface temperature variability are assessed against observations. Large discrepancies are found in the variance and skewness of sea surface height and in the skewness of sea surface temperature. Comparing with the observation, most models underestimate the Kuroshio transport in the Asian Marginal seas due to the missing influence of the unresolved western boundary current and meso-scale eddies. In terms of the Mixed Layer Depths (MLDs) in the North Pacific, the two observed maxima associated with Subtropical Mode Water and Central Mode Water formation coalesce into a large pool of deep MLDs in all participating models, but another local maximum associated with the formation of Eastern Subtropical Mode Water can be found in all models with different magnitudes. The main model bias of deep MLDs results from excessive Subtropical Mode Water formation due to inaccurate representation of the Kuroshio separation and of the associated excessively warm and salty Kuroshio water. Further water mass analysis shows that the North Pacific Intermediate Water can penetrate southward in most models, but its distribution greatly varies among models depending not only on grid resolution and vertical coordinate but also on the model dynamics. All simulations show overall similar large scale tropical current system, but with differences in the structures of the Equatorial Undercurrent. We also confirm the key role of the meridional gradient of the wind stress curl in driving the equatorial transport, leading to a generally weak North Equatorial Counter Current in all models due to inaccurate CORE-II equatorial wind fields. Most models show a larger interior transport of Pacific subtropical cells than the observation due to the overestimated transport in the Northern Hemisphere likely resulting from the deep pycnocline. [ABSTRACT FROM AUTHOR]

In this paper we compare the simulated Arctic Ocean in 15 global ocean–sea ice models in the framework of the Coordinated Ocean-ice Reference Experiments, phase II (CORE-II). Most of these models are the ocean and sea-ice components of the coupled climate models used in the Coupled Model Intercomparison Project Phase 5 (CMIP5) experiments. We mainly focus on the hydrography of the Arctic interior, the state of Atlantic Water layer and heat and volume transports at the gateways of the Davis Strait, the Bering Strait, the Fram Strait and the Barents Sea Opening. We found that there is a large spread in temperature in the Arctic Ocean between the models, and generally large differences compared to the observed temperature at intermediate depths. Warm bias models have a strong temperature anomaly of inflow of the Atlantic Water entering the Arctic Ocean through the Fram Strait. Another process that is not represented accurately in the CORE-II models is the formation of cold and dense water, originating on the eastern shelves. In the cold bias models, excessive cold water forms in the Barents Sea and spreads into the Arctic Ocean through the St. Anna Through. There is a large spread in the simulated mean heat and volume transports through the Fram Strait and the Barents Sea Opening. The models agree more on the decadal variability, to a large degree dictated by the common atmospheric forcing. We conclude that the CORE-II model study helps us to understand the crucial biases in the Arctic Ocean. The current coarse resolution state-of-the-art ocean models need to be improved in accurate representation of the Atlantic Water inflow into the Arctic and density currents coming from the shelves. [ABSTRACT FROM AUTHOR]

The Arctic Ocean simulated in 14 global ocean-sea ice models in the framework of the Coordinated Ocean-ice Reference Experiments, phase II (CORE-II) is analyzed in this study. The focus is on the Arctic liquid freshwater (FW) sources and freshwater content (FWC). The models agree on the interannual variability of liquid FW transport at the gateways where the ocean volume transport determines the FW transport variability. The variation of liquid FWC is induced by both the surface FW flux (associated with sea ice production) and lateral liquid FW transport, which are in phase when averaged on decadal time scales. The liquid FWC shows an increase starting from the mid-1990s, caused by the reduction of both sea ice formation and liquid FW export, with the former being more significant in most of the models. The mean state of the FW budget is less consistently simulated than the temporal variability. The model ensemble means of liquid FW transport through the Arctic gateways compare well with observations. On average, the models have too high mean FWC, weaker upward trends of FWC in the recent decade than the observation, and low consistency in the temporal variation of FWC spatial distribution, which needs to be further explored for the purpose of model development. [ABSTRACT FROM AUTHOR]

The Arctic Ocean simulated in fourteen global ocean-sea ice models in the framework of the Coordinated Ocean-ice Reference Experiments, phase II (CORE II) is analyzed. The focus is on the Arctic sea ice extent, the solid freshwater (FW) sources and solid freshwater content (FWC). Available observations are used for model evaluation. The variability of sea ice extent and solid FW budget is more consistently reproduced than their mean state in the models. The descending trend of September sea ice extent is well simulated in terms of the model ensemble mean. Models overestimating sea ice thickness tend to underestimate the descending trend of September sea ice extent. The models underestimate the observed sea ice thinning trend by a factor of two. When averaged on decadal time scales, the variation of Arctic solid FWC is contributed by those of both sea ice production and sea ice transport, which are out of phase in time. The solid FWC decreased in the recent decades, caused mainly by the reduction in sea ice thickness. The models did not simulate the acceleration of sea ice thickness decline, leading to an underestimation of solid FWC trend after 2000. The common model behavior, including the tendency to underestimate the trend of sea ice thickness and March sea ice extent, remains to be improved. [ABSTRACT FROM AUTHOR]

Simulated inter-annual to decadal variability and trends in the North Atlantic for the 1958–2007 period from twenty global ocean – sea-ice coupled models are presented. These simulations are performed as contributions to the second phase of the Coordinated Ocean-ice Reference Experiments (CORE-II). The study is Part II of our companion paper (Danabasoglu et al., 2014) which documented the mean states in the North Atlantic from the same models. A major focus of the present study is the representation of Atlantic meridional overturning circulation (AMOC) variability in the participating models. Relationships between AMOC variability and those of some other related variables, such as subpolar mixed layer depths, the North Atlantic Oscillation (NAO), and the Labrador Sea upper-ocean hydrographic properties, are also investigated. In general, AMOC variability shows three distinct stages. During the first stage that lasts until the mid- to late-1970s, AMOC is relatively steady, remaining lower than its long-term (1958–2007) mean. Thereafter, AMOC intensifies with maximum transports achieved in the mid- to late-1990s. This enhancement is then followed by a weakening trend until the end of our integration period. This sequence of low frequency AMOC variability is consistent with previous studies. Regarding strengthening of AMOC between about the mid-1970s and the mid-1990s, our results support a previously identified variability mechanism where AMOC intensification is connected to increased deep water formation in the subpolar North Atlantic, driven by NAO-related surface fluxes. The simulations tend to show general agreement in their temporal representations of, for example, AMOC, sea surface temperature (SST), and subpolar mixed layer depth variabilities. In particular, the observed variability of the North Atlantic SSTs is captured well by all models. These findings indicate that simulated variability and trends are primarily dictated by the atmospheric datasets which include the influence of ocean dynamics from nature superimposed onto anthropogenic effects. Despite these general agreements, there are many differences among the model solutions, particularly in the spatial structures of variability patterns. For example, the location of the maximum AMOC variability differs among the models between Northern and Southern Hemispheres. [ABSTRACT FROM AUTHOR]

We characterise the representation of the Southern Ocean water mass structure and sea ice within a suite of 15 global ocean-ice models run with the Coordinated Ocean-ice Reference Experiment Phase II (CORE-II) protocol. The main focus is the representation of the present (1988–2007) mode and intermediate waters, thus framing an analysis of winter and summer mixed layer depths; temperature, salinity, and potential vorticity structure; and temporal variability of sea ice distributions. We also consider the interannual variability over the same 20 year period. Comparisons are made between models as well as to observation-based analyses where available. The CORE-II models exhibit several biases relative to Southern Ocean observations, including an underestimation of the model mean mixed layer depths of mode and intermediate water masses in March (associated with greater ocean surface heat gain), and an overestimation in September (associated with greater high latitude ocean heat loss and a more northward winter sea-ice extent). In addition, the models have cold and fresh/warm and salty water column biases centred near 50°S. Over the 1988–2007 period, the CORE-II models consistently simulate spatially variable trends in sea-ice concentration, surface freshwater fluxes, mixed layer depths, and 200–700 m ocean heat content. In particular, sea-ice coverage around most of the Antarctic continental shelf is reduced, leading to a cooling and freshening of the near surface waters. The shoaling of the mixed layer is associated with increased surface buoyancy gain, except in the Pacific where sea ice is also influential. The models are in disagreement, despite the common CORE-II atmospheric state, in their spatial pattern of the 20-year trends in the mixed layer depth and sea-ice. [ABSTRACT FROM AUTHOR]

In the framework of the second phase of the Coordinated Ocean-ice Reference Experiments (CORE-II), we present an analysis of the representation of the Antarctic Circumpolar Current (ACC) and Southern Ocean meridional overturning circulation (MOC) in a suite of seventeen global ocean–sea ice models. We focus on the mean, variability and trends of both the ACC and MOC over the 1958–2007 period, and discuss their relationship with the surface forcing. We aim to quantify the degree of eddy saturation and eddy compensation in the models participating in CORE-II, and compare our results with available observations, previous fine-resolution numerical studies and theoretical constraints. Most models show weak ACC transport sensitivity to changes in forcing during the past five decades, and they can be considered to be in an eddy saturated regime. Larger contrasts arise when considering MOC trends, with a majority of models exhibiting significant strengthening of the MOC during the late 20th and early 21st century. Only a few models show a relatively small sensitivity to forcing changes, responding with an intensified eddy-induced circulation that provides some degree of eddy compensation, while still showing considerable decadal trends. Both ACC and MOC interannual variabilities are largely controlled by the Southern Annular Mode (SAM). Based on these results, models are clustered into two groups. Models with constant or two-dimensional (horizontal) specification of the eddy-induced advection coefficient κ show larger ocean interior decadal trends, larger ACC transport decadal trends and no eddy compensation in the MOC. Eddy-permitting models or models with a three-dimensional time varying κ show smaller changes in isopycnal slopes and associated ACC trends, and partial eddy compensation. As previously argued, a constant in time or space κ is responsible for a poor representation of mesoscale eddy effects and cannot properly simulate the sensitivity of the ACC and MOC to changing surface forcing. Evidence is given for a larger sensitivity of the MOC as compared to the ACC transport, even when approaching eddy saturation. Future process studies designed for disentangling the role of momentum and buoyancy forcing in driving the ACC and MOC are proposed. [ABSTRACT FROM AUTHOR]

Highlights: [•] Global mean sea level simulated in interannual CORE simulations. [•] Regional sea level patterns simulated in interannual CORE simulations. [•] Theoretical foundation for analysis of global mean sea level and regional patterns. [ABSTRACT FROM AUTHOR]

Highlights: [•] Phase II of the Coordinated Ocean-ice Reference Experiments (CORE-II) is introduced. [•] Solutions from CORE-II simulations from eighteen participating models are presented. [•] Mean states in the North Atlantic with a focus on AMOC are examined. [•] The North Atlantic solutions differ substantially among the models. [•] Many factors, including parameterization choices, contribute to these differences. [ABSTRACT FROM AUTHOR]