Sergey Danilov

A finite-element ocean model: principles and evaluation

Abstract 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°.

Scaling, spectra and zonal jets in beta-plane turbulence

A beta-plane approximation of the two-dimensional quasigeostrophic model describes a single layer (barotropic) fluid subjected to a latitudinally varying Coriolis parameter or topography. Rhines (1975) initiated the study of beta-plane turbulence. He predicted the inverse energy cascade into predominantly zonal modes, hence an array of eastward–westward jets, and estimated the jet number (celebrated Rhines scale). He also proposed a k−5 scaling law of zonal energy spectra. Our paper re-examines scaling, spectra, and zonal structure of beta-plane turbulence, based on theoretical predictions and numeric experiments. We show that the inverse cascade gives rise to strong organized zonal jets that evolve a peculiar frontal-band (“saw-tooth”) vorticity profile. Such structure affects all spectral properties of the system, by creating organized sequences of spectral peaks, and thus confounds any putative “scaling behavior.” The frontal-band structure appears consistently in all stochastically forced beta-plane f...

Barotropic Beta-Plane Turbulence in a Regime with Strong Zonal Jets Revisited

Abstract The problem of quantification of barotropic beta-plane turbulence driven by small-scale stochastic forcing into regimes dominated by quasi-periodic zonal jets is revisited. It is shown that the large-scale relative vorticity in such regimes is organized into a sequence of zonal bands. Its zonal mean profile varies approximately linearly within the bands. Its mean negative slope β∗ is less than the meridional gradient of the Coriolis parameter β, and depends on the external parameters (friction, forcing, and β). The neighboring bands are connected through the vorticity fronts where the zonal mean meridional gradient is large and positive. The frontal-band vorticity structure defines piecewise parabolic profiles of asymmetric eastward and westward jets, and strong peaks in the low-k interval of turbulent zonal energy spectra, which store most of the zonal energy. The slope of their envelope depends on the structure of the frontal zones and is always steeper than −4. The presence of peaks invalidate...

Assimilation of sea ice motion in a finite-element sea ice model

[1] A finite-element sea ice model (FESIM) is applied in a data assimilation study with the singular evolutive interpolated Kalman (SEIK) filter. The model has been configured for a regional Arctic domain and is forced with a combination of daily NCEP reanalysis data for 2-m air temperature and 10-m winds with monthly mean humidities from the ECMWF reanalysis and climatological fields for precipitation and cloudiness. We assimilate 3-day mean ice drift fields derived from passive microwave satellite data. Based on multivariate covariances (which describe the statistical relationship between anomalies in different model fields), the sea ice drift data assimilation produces not only direct modifications of the ice drift but also updates for sea ice concentration and thickness, which in turn yield sustainable corrections of ice drift. We use observed buoy trajectories as an independent data set to validate the analyzed sea ice drift field. A good agreement between modeled and observed tracks is achieved already in the reference simulation. Application of the SEIK filter with satellite-derived drift fields further improves the agreement. Spatial and temporal variability of ice thickness increases due to the assimilation procedure; a comparison to thickness data from a submarine-based upward looking sonar indicates that the thickness distribution becomes more realistic. Validation with regard to satellite data shows that the velocity data assimilation has only a small effect on ice concentration, but a general improvement of the ice concentration within the pack is still evident.

Evaluation of a Finite-Element Sea-Ice Ocean Model (FESOM) set-up to study the interannual to decadal variability in the deep-water formation rates

The characteristics of a global set-up of the Finite-Element Sea-Ice Ocean Model under forcing of the period 1958–2004 are presented. The model set-up is designed to study the variability in the deep-water mass formation areas and was therefore regionally better resolved in the deep-water formation areas in the Labrador Sea, Greenland Sea, Weddell Sea and Ross Sea. The sea-ice model reproduces realistic sea-ice distributions and variabilities in the sea-ice extent of both hemispheres as well as sea-ice transport that compares well with observational data. Based on a comparison between model and ocean weather ship data in the North Atlantic, we observe that the vertical structure is well captured in areas with a high resolution. In our model set-up, we are able to simulate decadal ocean variability including several salinity anomaly events and corresponding fingerprint in the vertical hydrography. The ocean state of the model set-up features pronounced variability in the Atlantic Meridional Overturning Circulation as well as the associated mixed layer depth pattern in the North Atlantic deep-water formation areas.

Designing variable ocean model resolution based on the observed ocean variability

If unstructured meshes are refined to locally represent eddy dynamics in ocean circulation models, a practical question arises on how to vary the resolution and where to deploy the refinement. We propose to use the observed sea surface height variability as the refinement criterion. We explore the utility of this method (i) in a suite of idealized experiments simulating a wind-driven double gyre flow in a stratified circular basin and (ii) in simulations of global ocean circulation performed with FESOM. Two practical approaches of mesh refinement are compared. In the first approach the uniform refinement is confined within the areas where the observed variability exceeds a given threshold. In the second one the refinement varies linearly following the observed variability. The resolution is fixed in time. For the double gyre case it is shown that the variability obtained in a high-resolution reference run can be well captured on variable-resolution meshes if they are refined where the variability is high and additionally upstream the jet separation point. The second approach of mesh refinement proves to be more beneficial in terms of improvement downstream the midlatitude jet. Similarly, in global ocean simulations the mesh refinement based on the observed variability helps the model to simulate high variability at correct locations. The refinement also leads to a reduced bias in the upper-ocean temperature

Long-term ocean simulations in FESOM: evaluation and application in studying the impact of Greenland Ice Sheet melting

The Finite Element Sea-ice Ocean Model (FESOM) is formulated on unstructured meshes and offers geometrical flexibility which is difficult to achieve on traditional structured grids. In this work, the performance of FESOM in the North Atlantic and Arctic Ocean on large time scales is evaluated in a hindcast experiment. A water-hosing experiment is also conducted to study the model sensitivity to increased freshwater input from Greenland Ice Sheet (GrIS) melting in a 0.1-Sv discharge rate scenario. The variability of the Atlantic Meridional Overturning Circulation (AMOC) in the hindcast experiment can be explained by the variability of the thermohaline forcing over deep convection sites. The model also reproduces realistic freshwater content variability and sea ice extent in the Arctic Ocean. The anomalous freshwater in the water-hosing experiment leads to significant changes in the ocean circulation and local dynamical sea level (DSL). The most pronounced DSL rise is in the northwest North Atlantic as shown in previous studies, and also in the Arctic Ocean. The released GrIS freshwater mainly remains in the North Atlantic, Arctic Ocean and the west South Atlantic after 120 model years. The pattern of ocean freshening is similar to that of the GrIS water distribution, but changes in ocean circulation also contribute to the ocean salinity change. The changes in Arctic and sub-Arctic sea level modify exchanges between the Arctic Ocean and subpolar seas, and hence the role of the Arctic Ocean in the global climate. Not only the strength of the AMOC, but also the strength of its decadal variability is notably reduced by the anomalous freshwater input. A comparison of FESOM with results from previous studies shows that FESOM can simulate past ocean state and the impact of increased GrIS melting well.

On the impact of wind forcing on the seasonal variability of Weddell Sea Bottom Water transport

The seasonal variability of Weddell Sea Bottom Water (WSBW) transport and its driving mechanisms are examined using FESOM simulations. Pronounced seasonal variability is present in both the Filchner shelf water export rate and the WSBW transport rate near the Antarctic Peninsula (AP) tip. The variabilities at both locations are linked to the surface wind forcing. The Filchner shelf water export rate responds to the onshore propagating density anomaly, which is caused by the wind-induced variation of the isopycnal depression at the coast. The variability near the AP tip originates from upstream variations at the Filchner Depression and from seasonal variability of the Weddell gyre strength.

Can sea surface height be used to estimate oceanic transport variability

The relation between the sea surface height and the meridional transport across a zonal section at 26.5°N in the North Atlantic is studied by using an eddy resolving ocean state estimate simulated with the Massachusetts Institute of Technology general circulation model. It is shown that the correlation between the zonal sea surface height difference and transport can be substantially increased if the steric height contribution from the seasonal thermocline is removed. The latter explains a substantial part of sea surface height variability, but its effect on transport is weak. It is also found that the zonal steric height difference correlates well with the transport after the contribution of the seasonal thermocline has been removed. There is a similar agreement (with correlation coefficient of 0.63 for the full signal and 0.89 for the mean seasonal cycle) between the meridional transport and steric height based on observations from the Rapid Climate Change (RAPID) project.

Multiscale modeling of coastal, shelf, and global ocean dynamics

In contemporary ocean science, modeling systems that inte-grate understanding of complex multiscale phenomena andutilize efficient numerics are paramount. Many of todaysfundamental ocean science questions involve multiple scalesand multiple dynamics. A new generation of modeling sys-tems would allow to study such questions quantitatively bybeing less restrictive dynamically and more efficient numeri-cally than more traditional systems.Suchmultiscaleoceanmodelingisthethemeofthistopicalcollection.Twolargeinternational workshopswereorganizedonthistheme,oneinCambridge,USA(IMUM2010),andonein Bremerhaven, Germany (IMUM2011). Contributions fromthe scientific community were encouraged on all aspects ofmultiscale ocean modeling from ocean science and dynamicsto the development of new computational methods and sys-tems. Building on previous meetings (e.g., Deleersnijder andLermusiaux 2008; Deleersnijder et al. 2010), the workshopdiscussionsandthefinalcontributionstothetopicalcollectionare summarized next.Thescientificapplicationdomainsdiscussedandpresentedranged from estuaries to the global ocean, including coastalregionsandshelfseas.Multi-resolutionmodelingofphysical,biological, chemical, and sea ice processes as well as air–seainteractions were described. The multiscale dynamics consid-ered involved hydrostatic, non-hydrostatic, turbulent, and seasurface processes.Computational results and discussions emphasized multi-resolution simulations using unstructured and structuredmeshes,aimingtowidentherange ofresolvedscalesinspaceand time. They included finite volume and finite elementspatial discretizations, high-order schemes, preconditioners,solver issues, grid generation, adaptive modeling, data assim-ilation,couplingwithatmosphericorbiogeochemicalmodels,and distributed computing. The advantages of using unstruc-tured meshes and related approaches in particular multi-gridembedding, nesting systems, wavelets, and other multiscaledecompositions were discussed. Techniques for the study ofmulti-resolution results, visualization, optimization, modelevaluations,anduncertaintyquantificationwerealsoexamined.1 Multiscale interdisciplinary dynamicsA number of manuscripts in the topical collection focus onmultiscale interdisciplinary dynamics, specifically oceanphysics and ice interactions, physical–biogeochemical inter-actions, and physical–sediment–coast interactions.