The problem of parameterizing the eddy flux of a potential vorticity is discussed. The traditional diffusion parameterization is complemented by the inclusion of the rotational component. The new scheme is analyzed using a quasi-geostrophic model of the dynamics of the barotropic flow in a zonal channel with a nonflat bottom. An analytical solution of the problem is found and the influence of topography on the flow disturbances is discussed. An equation for the eddy potential enstrophy is used, which makes it possible to relate the diffusion and rotational coefficients.

Обсуждается проблема параметризации вихревого потока потенциального вихря. Традиционная диффузионная параметризация дополняется включением ротационного компонента. Для анализа новой схемы используется квазигеострофическая модель динамики баротропного течения в зональном канале с неплоским дном. Находится аналитическое решение задачи и обсуждается влияние топографии на возмущения потока. Показано, что уравнение для вихревой потенциальной энстрофии, позволяет связать диффузионные и ротационные коэффициенты.

With the polar regions opening up to more marine activities but iceberg numbers more likely to increase than decline as a result of global warming, the risk from icebergs to shipping and offshore facilities is increasing. The NW Atlantic iceberg hazard has been well monitored by the International Ice Patrol for a century, but many other polar regions have little detailed climatological knowledge of the iceberg risk. Here, we develop a modelling approach to assessing iceberg hazard. This uses the region of the Falklands Plateau and its shipping routes for a case study, but the approach has general geographical applicability and can be used for assessing iceberg hazard for routes or fixed locations. The iceberg risk for a number of locations selected from the main shipping routes in the SW Atlantic is assessed by using an iceberg model, forced by the output from a high-resolution ocean model. The iceberg model was seeded with icebergs around the edge of the modelled region using a number of scenarios for the seeding distribution, based on a combination of idealised, modelled and observed iceberg fluxes from the Southern Ocean. This enabled us to determine measures of iceberg risk linked to a mix of starting location and the likelihood of icebergs being encountered in such a position. For our study area, the main area of iceberg risk is linked to the East Falklands Current, but small, yet nonzero, risk covers much of the east and north of the region.

The question of whether the coefficient of diffusivity of potential vorticity by mesoscale eddies is positive is studied for a zonally reentrant barotropic channel using the quasigeostrophic approach. The topography is limited to the first mode in the meridional direction but is unlimited in the zonal direction. We derive an analytic solution for the stationary (time independent) solution. New terms associated with parameterized eddy fluxes of potential vorticity appear both in the equations for the mean zonal momentum balance and in the kinetic energy balance. These terms are linked with the topographic form stress exerted by parameterized eddies. It is demonstrated that in regimes with zonal flow (analogous to the Antarctic Circumpolar Current), the coefficient of eddy potential vorticity diffusivity must be positive.

An efficient approach to ocean–iceberg modelling provides a means for assessing prospects for seasonal forecasting of iceberg distributions in the northwest Atlantic, where icebergs present a hazard to mariners each spring. The stand-alone surface (SAS) module that is part of the Nucleus for European Modelling of the Ocean (NEMO) is coupled with the NEMO iceberg module (ICB) in a “SAS-ICB” configuration with horizontal resolution of 0.25°. Iceberg conditions are investigated for three recent years, 2013–2015, characterized by widely varying iceberg distributions. The relative simplicity of SAS-ICB facilitates efficient investigation of sensitivity to iceberg fluxes and prevailing environmental conditions. SAS-ICB is provided with daily surface ocean analysis fields from the global Forecasting Ocean Assimilation Model (FOAM) of the Met Office. Surface currents, temperatures and height together determine iceberg advection and melting rates. Iceberg drift is further governed by surface winds, which are updated every 3 h. The flux of icebergs from the Greenland ice sheet is determined from engineering control theory and specified as an upstream flux in the vicinity of Davis Strait for January or February. Simulated iceberg distributions are evaluated alongside observations reported and archived by the International Ice Patrol. The best agreement with observations is obtained when variability in both upstream iceberg flux and oceanographic/atmospheric conditions is taken into account. Including interactive icebergs in an ocean–atmosphere model with sufficient seasonal forecast skill, and provided with accurate winter iceberg fluxes, it is concluded that seasonal forecasts of spring/summer iceberg conditions for the northwest Atlantic are now a realistic prospect.

The problem of simulating ocean general circulation is considered using an approach developed by G.I. Marchuk. Most attention is focused on problems associated with the application of multi-component-splitting and adjoint-equation methods and with the parameterization of turbulent-exchange processes. The statement of the problem, an algorithm of its solution, and the results of the four-dimensional temperature and salinity data assimilation in a model of World Ocean hydrodynamics are discussed. This algorithm yields qualitatively reliable results, and its main features are modularity, usability, and the possibility of using efficient implicit schemes.

An established iceberg module, ICB, is used interactively with the Nucleus for European Modelling of the Ocean (NEMO) ocean model in a new implementation, NEMO–ICB (v1.0). A 30-year hindcast (1976–2005) simulation with an eddy-permitting (0.25°) global configuration of NEMO–ICB is undertaken to evaluate the influence of icebergs on sea ice, hydrography, mixed layer depths (MLDs), and ocean currents, through comparison with a control simulation in which the equivalent iceberg mass flux is applied as coastal runoff, a common forcing in ocean models. In the Southern Hemisphere (SH), drift and melting of icebergs are in balance after around 5 years, whereas the equilibration timescale for the Northern Hemisphere (NH) is 15–20 years. Iceberg drift patterns, and Southern Ocean iceberg mass, compare favourably with available observations. Freshwater forcing due to iceberg melting is most pronounced very locally, in the coastal zone around much of Antarctica, where it often exceeds in magnitude and opposes the negative freshwater fluxes associated with sea ice freezing. However, at most locations in the polar Southern Ocean, the annual-mean freshwater flux due to icebergs, if present, is typically an order of magnitude smaller than the contribution of sea ice melting and precipitation. A notable exception is the southwest Atlantic sector of the Southern Ocean, where iceberg melting reaches around 50% of net precipitation over a large area. Including icebergs in place of coastal runoff, sea ice concentration and thickness are notably decreased at most locations around Antarctica, by up to ~ 20% in the eastern Weddell Sea, with more limited increases, of up to ~ 10% in the Bellingshausen Sea. Antarctic sea ice mass decreases by 2.9%, overall. As a consequence of changes in net freshwater forcing and sea ice, salinity and temperature distributions are also substantially altered. Surface salinity increases by ~ 0.1 psu around much of Antarctica, due to suppressed coastal runoff, with extensive freshening at depth, extending to the greatest depths in the polar Southern Ocean where discernible effects on both salinity and temperature reach 2500 m in the Weddell Sea by the last pentad of the simulation. Substantial physical and dynamical responses to icebergs, throughout the global ocean, are explained by rapid propagation of density anomalies from high-to-low latitudes. Complementary to the baseline model used here, three prototype modifications to NEMO–ICB are also introduced and discussed.

Parameterization of mesoscale eddies is an important problem of modern ocean dynamics and modeling. The most widely used scheme is the so-called Gent-McWilliams parameterization, which describes the eddy-induced transport of tracers, including temperature, density, and isopycnal thickness (TH). An alternative scheme, proposed by Green and Welander, deals with parameterizing eddy fluxes of potential vorticity (PV). Many recent studies propose using it, for it includes the effect of eddy Reynolds stresses that may influence mean flows. These two schemes are compared in the simplest configuration of two-layer quasigeostrophic channel flow, which enables analytical solutions for zonal-mean fields. It is shown how the parameterizations shape the zonally averaged zonal velocity profiles, with special attention paid to the role of the Reynolds stresses and momentum conservation. The zonally averaged zonal velocity profiles are sensitive to the amplitude and profiles of TH and PV diffusivities. For small enough diffusivities the TH parameterization may lead to solutions resembling those for the PV parameterization if it uses the diffusivity of the latter; that is, it may mimic the impact of the Reynolds stresses on the mean flow.

Integral constraints for momentum and energy impose restrictions on parameterizations of eddy potential vorticity (PV) fluxes. The impact of these constraints is studied for a wind-forced quasigeostrophic two-layer zonal channel model with variable bottom topography. The presence of a small parameter, given by the ratio of Rossby radius to the width of the channel, makes it possible to find an analytical/asymptotic solution for the zonally and time-averaged flow, given diffusive parameterizations for the eddy PV fluxes. This solution, when substituted in the constraints, leads to nontrivial explicit restrictions on diffusivities. The system is characterized by four dimensionless governing parameters with a clear physical interpretation. The bottom form stress, the major term balancing the external force of wind stress, depends on the governing parameters and fundamentally modifies the restrictions compared to the flat bottom case. While the analytical solution bears an illustrative character, it helps to see certain nontrivial connections in the system that will be useful in the analysis of more complicated models of ocean circulation. A numerical solution supports the analytical study and confirms that the presence of topography strongly modifies the eddy fluxes.

NEMO-ICB (v1.0): interactive icebergs in the NEMO ocean model globally configured at coarse and eddy-permitting resolution R. Marsh, V. O. Ivchenko, N. Skliris, S. Alderson, G. R. Bigg, G. Madec, A. Blaker, and Y. Aksenov University of Southampton, National Oceanography Centre, Southampton, UK National Oceanography Centre, Southampton, UK Department of Geography, University of Sheffield, Sheffield, UK LOCEAN-IPSL, CNRS-IRD-UPMC-MNHN, Paris, France

Abstract. NEMO-ICB features interactive icebergs in the NEMO ocean model. Simulations with coarse (2°) and eddy-permitting (0.25°) global configurations of NEMO-ICB are undertaken to evaluate the influence of icebergs on sea-ice, hydrography and transports, through comparison with control simulations in which the equivalent iceberg mass flux is applied as coastal runoff, the default forcing in NEMO. Comparing a short (14 year) spin-up of the 0.25° model with a computationally cheaper 105 year spin-up of the 2° configuration, calving, drift and melting of icebergs is evidently near equilibrium in the shorter simulation, justifying closer examination of iceberg influences in the eddy-permitting configuration. Freshwater forcing due to iceberg melt is most pronounced in southern high latitudes, where it is locally dominant over precipitation. Sea ice concentration and thickness in the Southern Ocean are locally increased with icebergs, by up to ~ 8 and ~ 25% respectively. Iceberg melting reduces surface salinity by ~ 0.2 psu around much of Antarctica, with compensating increases immediately adjacent to Antarctica, where coastal runoff is suppressed. Discernible effects on salinity and temperature extend to 1000 m. At many locations and levels, freshening and cooling indicate a degree of density compensation. However, freshening is a dominant influence on upper ocean density gradients across much of the high-latitude Southern Ocean, leading to weaker meridional density gradients, a reduced eastward transport tendency, and hence an increase of ~ 20% in westward transport of the Antarctic Coastal Current.

Abstract. Ocean heat storage is an essential component of the climate system and there is considerable interest in its accurate evaluation. There are a number of heat storage products produced by many different groups. These products are derived from Argo as well as other platforms, for example XBT and CTD, in the last decade. Here we compare two heat storage estimates for the North Atlantic 0–2000 m from 10° to 70° N. One derived solely from Argo data whilst the other is derived from Argo and other platforms. It is found that there is a positive trend in heat storage over the period 1999–2010. This trend is influenced by a strong air–sea interaction event in 2009–2010, and this reduces the upward trend 1999–2008 identified previously. Both data sets are consistent with each other for the layer 0–1000 m on a timescale of beyond 1 yr. There are significant differences at sub-annual time scales and in the layer 1000–2000 m.

Relative sea level change is estimated with a combination of methods. First a melting scenario with reasonable fresh water input from Greenland ice sheet, glaciers in Alaska or West-Antarctica between 50 and 200 Gt per year are assumed and used as sources in a global Finite Element Sea-Ice Ocean Model (FESOM). The model calculates the evolution of ocean volume and mass using a non linear free sea surface. Other driving forces are atmospheric surface fluxes from NCEP reanalysis and river runoff from hydrologic modelling. The resulting sea level change due to inflow of mass, steric expansion and redistribution as a consequence of ocean dynamic reactions are calculated relative to the geoid. Geoid changes as a response to the changed mass distribution and the associated uplift are calculated in a second step and are augmented by rotational feedback. Finally glacio-isostatic adjustment is used to correct for ongoing vertical movements. A significant fraction of the sea level variations at the North Atlantic coasts can already be explained by our reference experiment (no extra melting prescribed). Including ice sheet melting substantially improves the comparison between modelled sea level and PSMSL tide gauge records.

We compare ocean dynamic topography estimates from an ensemble of ocean circulation hindcasts, performed with the Finite Element Sea-ice Ocean Model (FESOM), to the estimates of dynamic topography from Aviso, CSIRO, Altimetry Data System (GFZ Potsdam), operational ocean reanalysis by ECMWF (ORAS4) and to the Argo based product from JAMSTEC. The ensemble members used for the hindcasts differ by their initialization and by the model meshes. The meshes have been refined in various key regions for the large-scale ocean circulation,such as the equatorial belt or Denmark Strait, and also the background resolution was varied.We compare both the model sea level mean and variability. The modelled interannual variability agrees with the data within the spread of different datasets while the ENSO mode explains the major part of comparison between data and model. The model ensemble members under the same forcing differ primarily in the deep water formation regions. The largest discrepancies between model and data are also seen in these regions.

The problem of numerical simulation of the Baltic Sea large-scale circulation is considered. The Baltic Sea numerical model is based on the two previous models: the model of ocean dynamics developed at the Institute of Numerical Mathematics of the RAS and the FRESCO model of marine hydroecosystem developed at the Estonian Marine Institute, University of Tartu. The model is based on primitive equations written in spherical sigma coordinates with a free surface in the hydrostatic and Boussinesq approximations.The structure of numerical algorithm is described. The algorithm is based on the method of multicomponent splitting and includes splitting by physical processes and spatial coordinates. The equations of sea dynamics are written in a symmetrized form. The problem is split into several energetically balanced subsystems (splitting by physical processes). Each subsystem can be additionally split into subsystems of a simpler structure (splitting by spatial coordinates).The numerical experiment consists in the calculation of the Baltic Sea hydrodynamic fields with the spatial horizontal resolution of similar to 3.5 km and 25 vertical s sigma-levels nonuniformly distributed over the depth. The atmospheric forcing is calculated according to the Era-Interim data, the calculation period is 2 years: 2007 and 2008. The results of numerical simulation demonstrate good resemblance to observation data, as well as the results of the Baltic Sea dynamics computation obtained from other models.

The relationship between the zonal transport across the Drake Passage and meridional pressure difference is studied by using an eddy resolving ocean state estimate simulated with the Massachusetts Institute of Technology general circulation model. The analysis is performed for monthly and yearly time series. The results show that while the meridional surface pressure difference alone can already explain a substantial part of transport variability, the pressure at 1000m gives the highest correlation. The contribution of sea surface elevation versus steric height signal are discussed.