Simulation of oceanic volume transports through Fram Strait 1995–2005

We discuss the model representation of volume transports through one of the most climate-relevant ocean passages, the Fram Strait. We compare results from a coupled ocean–sea ice model with different resolutions (∼1/12° and ∼1/4°) and measurements from a mooring array along 79° N. The 1/4° model delivers a realistic mean climate state and realistic net volume transports. However, this model fails to reproduce the observed intense barotropic recirculation that reaches far north in Fram Strait. This recirculation is captured in the higher resolution version of the model. Other differences exist in the circulation over the East Greenland Shelf and in the temperature of Atlantic waters in the Fram Strait region as well as in surface heat fluxes. We find that a combination of high-resolution model results and long-term measurements can improve the interpretation of measured and simulated processes and reduce the uncertainties in exchange rates between Arctic and the North Atlantic.     

Eddy-permitting simulations of the sub-polar North Atlantic: impact of the model bias on water mass properties and circulation

Some previous studies demonstrated that model bias has a strong impact on the quality of long-term prognostic model simulations of the sub-polar North Atlantic Ocean. Relatively strong bias of water mass characteristics is observed in both eddy-permitting and eddy-resolving simulations, suggesting that an increase of model resolution does not reduce significantly the model bias. This study is an attempt to quantify the impact of model bias on the simulated water mass and circulation characteristics in an eddy-permitting model of the sub-polar ocean. This is done through comparison of eddy-permitting prognostic model simulations with the results from two other runs in which the bias is constrained by using spectral nudging. In the first run, the temperature and salinity are nudged towards climatology in the whole column. In the second run, the spectral nudging is applied in the surface 30 m layer and at depths below 560 m only. The biases of the model characteristics of the unconstrained run are similar to those reported in previous eddy-permitting and eddy-resolving studies. The salinity in the surface and intermediate waters of the Labrador Sea waters increases with respect to the climatology, which reduces the stability of the water column. The deep convection in the unconstrained run is artificially intensified and the transport in the sub-polar gyre stronger than in the observations. In particular, the transport of relatively salty and warm Irminger waters into the Labrador Sea is unrealistically high. While the water mass temperature and salinity in the run with spectral nudging in the whole column are closest to the observations, the depth of the winter convection is underestimated in the model. The water mass characteristics and water transport in the run with spectral nudging in the surface and deep layers only are close to observations and at the same time represent well the deep convection in terms of its intensity and position. The source of the bias in the prognostic model run is discussed.     

On the developments of spectral wave models: numerics and parameterizations for the coastal ocean

The development of numerical wave models for coastal applications, including coupling with ocean circulation models, has spurred an ongoing effort on theoretical foundations, numerical techniques, and physical parameterizations. Some important aspects of this effort are reviewed here, and results are shown in the case of the French Atlantic and Channel coast using version 4.18 of the WAVEWATCH III ^R model. Compared to previous results, the model errors have been strongly reduced thanks to, among other things, the introduction of currents, coastal reflection, and bottom sediment types. This last item is described here for the first time, allowing unprecedented accuracy at some sites along the French Atlantic Coast. The adequate resolution, necessary to represent strong gradients in tidal currents, was made possible by the efficiency brought by unstructured grids. A further increase in resolution, necessary to resolve surf zones and still cover vast regions,will require further developments in numerical methods.     

A modeling study of the role that bottom topography plays in Gulf Stream dynamics and in influencing the tilt of mean sea level along the US East Coast

Two aspects of the interactions between the Gulf Stream (GS) and the bottom topography are investigated: 1. the spatial variations associated with the north-south tilt of mean sea level along the US East Coast and 2. the high-frequency temporal variations of coastal sea level (CSL) that are related to Gulf Stream dynamics. A regional ocean circulation model is used to assess the role of topography; this is done by conducting numerical simulations of the GS with two different topographies–one case with a realistic topography and another case with an idealized smooth topography that neglects the details of the coastline and the very deep ocean. High-frequency oscillations (with a 5-day period) in the zonal wind and in the GS transport are imposed on the model; the source of the GS variability is either the Florida Current (FC) in the south or the Slope Current (SC) in the north. The results demonstrate that the abrupt change of topography at Cape Hatteras, near the point where the GS separates from the coast, amplifies the northward downward mean sea level tilt along the coast there. The results suggest that idealized or coarse resolution models that do not resolve the details of the coastline may underestimate the difference between the higher mean sea level in the South Atlantic Bight (SAB) and the lower mean sea level in the Mid-Atlantic Bight (MAB). Imposed variations in the model’s GS transport can generate coherent sea level variability along the coast, similar to the observations. However, when the bottom topography in the model is modified (or not well resolved), the shape of the coastline and the continental shelf influence the propagation of coastal-trapped waves and impact the CSL variability. The results can explain the different characteristics of sea level variability in the SAB and in the MAB and help understand unexpected water level anomalies and flooding related to remote influence of the GS.     

A coarse resolution North Atlantic ocean circulation model: an intercomparison study with a paleoceanographic example

Paleoreconstructions suggest that during the Last Glacial Maximum (LGM) the North Atlantic circulation was noticeably different from its present state. However, the glacial salt conveyor belt is believed to be similar to the present-day’s conveyor, albeit weaker and shallower because of an increased freshwater flux in high-latitudes. We present here the investigation of the conveyor operation based on ocean circulation modelling using two numerical models in parallel. The GFDL primitive equation model and a planetary geostrophic model are employed to address the problem of the paleocirculation modelling in cases of uncertain and sparse data comprising the glacial surface boundary conditions. The role of different simplifications that may be used in the ocean climate studies, including the role of grid resolution, bottom topography, coast-line, etc., versus glacial-interglacial changes of the ocean surface climatology is considered. The LGM reverse conveyor gyre appeared to be the most noticeable feature of the glacial-to-interglacial alteration of the ocean circulation. The reversed upper-ocean conveyor, weaker and subducting ‘normal’ conveyor in the intermediate depths, and the change of the deep-ocean return flow route are robust signatures of the glacial North Atlantic climate. The results are found to be ‘model-independent’ and fairly insensitive to all factors other than the onset of the glacial surface conditions.     

The roles of surface heat flux and ocean heat transport convergence in determining Atlantic Ocean temperature variability

The temperature variability of the Atlantic Ocean is investigated using an eddy-permitting (1/4°) global ocean model (ORCA-025) forced with historical surface meteorological fields from 1958 to 2001. The simulation of volume-averaged temperature and the vertical structure of the zonally averaged temperature trends are compared with those from observations. In regions with a high number of observations, in particular above a depth of 500 m and between 22° N and 65° N, the model simulation and the dataset are in good agreement. The relative contribution of variability in ocean heat transport (OHT) convergence and net surface heat flux to changes in ocean heat content is investigated with a focus on three regions: the subpolar and subtropical gyres and the tropics. The surface heat flux plays a relatively minor role in year-to-year changes in the subpolar and subtropical regions, but in the tropical North Atlantic, its role is of similar significance to the ocean heat transport convergence. The strongest signal during the study period is a cooling of the subpolar gyre between 1970 and 1990, which subsequently reversed as the mid-latitude OHT convergence transitioned from an anomalously weak to an anomalously strong state. We also explore whether model OHT anomalies can be linked to surface flux anomalies through a Hovmöller analysis of the Atlantic sector. At low latitudes, increased ocean heat gain coincides with anomalously strong northward transport, whereas at mid-high latitudes, reduced ocean heat loss is associated with anomalously weak heat transport.     

On the influence of adequate Weddell Sea characteristics in a large-scale global ocean circulation model

Global ocean circulation models usually lack an adequate consideration of high-latitude processes due to a limited model domain or insufficient resolution. Without the processes in key areas of the global thermohaline circulation, the characteristics and flow of deep and bottom waters cannot be modeled realistically. In this study, a high-resolution (~20 km) ocean model focused on the Weddell Sea sector of the Southern Ocean is combined with a low-resolution (2^° × 2^°) global ocean model applying the state estimation technique. Temperature, salinity, and velocity data on two Weddell Sea sections from the regional model are used as constraints for the large-scale model in addition to satellite altimetry and sea-surface temperatures. The differences between the model with additional constraints and without document that the Weddell Sea circulation exerts significant influence on the course of the Antarctic Circumpolar Current with consequences for Southern Ocean water mass characteristics and the spreading of deep and bottom waters in the South Atlantic. Furthermore, a warming trend in the period 1993–2001 was found in the Weddell Sea and adjacent basins in agreement with float measurements in the upper Southern Ocean. Teleconnections to the North Atlantic are suggested but need further studies to demonstrate their statistical significance.     

Impact of tidal mixing with different scales of bottom roughness on the general circulation

The current study deals with a parameterization of diapycnal diffusivity in an ocean model. The parameterization estimates the diapycnal diffusivity depending on the location of tidal-related energy dissipation over rough topography. The scheme requires a bottom roughness map that can be chosen depending on the scales of topographic features. Here, we implement the parameterization on an ocean general circulation model, and we examine the sensitivity of the modeled circulations to different spatial scales of the modeled bottom roughness. We compare three simulations that include the tidal mixing scheme using bottom roughness calculated at three different ranges of spatial scales, with the largest scale varying up to 200 km. Three main results are discussed. First, the dependence of the topographic spectra with depth, characterized by an increase in spectral energy over short length scales in the deep ocean, influences the vertical profile of the diffusivity. Second, the changes in diffusivities lead to different equilibrium solutions in the Atlantic meridional overturning circulation and bottom circulation. In particular, the lower cell of the Atlantic overturning and the bottom water transport in the Pacific Ocean are stronger for stronger diffusivities at the corresponding basins and depths, and the strongest when using the small-scale roughness map. Third, a comparison of the density fields of the three simulations with the density field of World Ocean Atlas dataset, from which the models are initialized, shows that among the simulations with three different roughness maps, the one using small-scale bottom roughness map has the smallest density bias.

     

Impact of tidal mixing with different scales of bottom roughness on the general circulation

The current study deals with a parameterization of diapycnal diffusivity in an ocean model. The parameterization estimates the diapycnal diffusivity depending on the location of tidal-related energy dissipation over rough topography. The scheme requires a bottom roughness map that can be chosen depending on the scales of topographic features. Here, we implement the parameterization on an ocean general circulation model, and we examine the sensitivity of the modeled circulations to different spatial scales of the modeled bottom roughness. We compare three simulations that include the tidal mixing scheme using bottom roughness calculated at three different ranges of spatial scales, with the largest scale varying up to 200?km. Three main results are discussed. First, the dependence of the topographic spectra with depth, characterized by an increase in spectral energy over short length scales in the deep ocean, influences the vertical profile of the diffusivity. Second, the changes in diffusivities lead to different equilibrium solutions in the Atlantic meridional overturning circulation and bottom circulation. In particular, the lower cell of the Atlantic overturning and the bottom water transport in the Pacific Ocean are stronger for stronger diffusivities at the corresponding basins and depths, and the strongest when using the small-scale roughness map. Third, a comparison of the density fields of the three simulations with the density field of World Ocean Atlas dataset, from which the models are initialized, shows that among the simulations with three different roughness maps, the one using small-scale bottom roughness map has the smallest density bias.     

Topographic effects on the wind‐driven ocean circulation

Abstract

This is a study of the influence of bottom topography of an ocean basin on the wind‐driven, barotropic ocean circulation. A detailed investigation is made of the role of vorticity transfer to the ocean bottom in the presence of varying topography. It is shown that the wind‐driven gyre over the topography of the North Atlantic has a transport in the western part of the basin only half of that obtained in an ocean of constant depth.     

Numerical study of three-dimensional shelf circulation on the Scotian Shelf using a shelf circulation model

A numerical shelf circulation model was developed for the Scotian Shelf, using a nested-grid setup consisting of a three-dimensional baroclinic inner model embedded inside a two-dimensional barotropic outer model. The shelf circulation model is based on the Princeton Ocean Model and driven by three-hourly atmospheric forcing provided by a numerical weather forecast model and by tidal forcing specified at the inner model's open boundaries based on pre-calculated tidal harmonic constants. The outer model simulates the depth-mean circulation forced by wind and atmospheric pressure fields over the northwest Atlantic Ocean with a horizontal resolution of 1/12°. The inner model simulates the three-dimensional circulation over the Gulf of St. Lawrence, the Scotian Shelf, and the adjacent slope with a horizontal resolution of 1/16°. The performance of the shelf circulation model is assessed by comparing model results with oceanographic observations made along the Atlantic coast of Nova Scotia and in the vicinity of Sable Island (on the Scotian Shelf) during two periods: October 2000–March 2001 and April–June 2002. Analysis of model results on Sable Island Bank indicates that tidal currents account for as much as ∼80% of the total variance of near-bottom currents, and currents driven by local winds account for ∼30% of the variance of the non-tidal near-bottom currents. Shelf waves generated remotely by winds and propagating into the region also play an important role in the near-bottom circulation on the bank.     

Combining T/P altimetric data with hydrographic data to estimate the mean dynamic topography of the North Atlantic and improve the geoid

The mean dynamic topography of the surface of the North Atlantic is estimated using an inverse model of the ocean circulation constrained by hydro-graphic and altimetric observations. In the North Atlantic, altimetric observations have no significant impact on the topography estimate because of the limited precision of available geoid height models. They have a significant impact, however, when uncertainties in the density field are increased to simulate interpolation errors in regions where hydrographic data are scarce. This result, which moderates the conclusion drawn by Ganachaud and co-workers of no significant contribution of altimetric observations to the determination of the large-scale steady circulation, reflects the simple idea that altimetric data are most useful near the surface of the ocean and in areas where the hydrography is poorly determined. One application of the present inverse estimate of the mean dynamic topography is to compute a geoid height correction over the North Atlantic which reduces the uncertainty in the geoid height expanded to spherical harmonic 40 down to a level of about 5 cm.     

Resolution issues in numerical models of oceanic and coastal circulation

The baroclinic and barotropic properties of ocean processes vary on many scales. These scales are determined by various factors such as the variations in coastline and bottom topography, the forcing meteorology, the latitudinal dependence of the Coriolis force, and the Rossby radius of deformation among others. In this paper we attempt to qualify and quantify scales of these processes, with particular attention to the horizontal resolution necessary to accurately reproduce physical processes in numerical ocean models. We also discuss approaches taken in nesting or down-scaling from global/basin-scale models to regional-scale or shelf-scale models. Finally we offer comments on how vertical resolution affects the representation of stratification in these numerical models.     

Three-dimensional numerical modelling of wind-driven circulation in a homogeneous lake

A three-dimensional numerical model has been developed to study wind-induced circulation patterns in a shallow homogeneous lake with a complex bathymetry. The governing equations are the unsteady Reynolds-Averaged Navier–Stokes equations in which the non-hydrostatic pressure distribution has been included. The model was tested against analytical solutions and laboratory data for wind-induced currents and then applied to Esthwaite Water, a small lake in Cumbria, UK. The model was used to study the main model parameters and to generate typical circulation patterns for a variety of conditions in the lake. Simulations showed that a non-hydrostatic pressure distribution did not have any noticeable influence on the overall circulation pattern in the lake. However, comparisons with field data at some measurement stations in the near-shore region with sharply varying bottom topography showed that the hydrodynamic pressure component had some influence on the vertical velocity profile.     

Benchmarking the mesoscale variability in global ocean eddy-permitting numerical systems

The role of data assimilation procedures on representing ocean mesoscale variability is assessed by applying eddy statistics to a state-of-the-art global ocean reanalysis (C-GLORS), a free global ocean simulation (performed with the NEMO system) and an observation-based dataset (ARMOR3D) used as an independent benchmark. Numerical results are computed on a 1/4 ^° horizontal grid (ORCA025) and share the same resolution with ARMOR3D dataset. This “eddy-permitting” resolution is sufficient to allow ocean eddies to form. Further to assessing the eddy statistics from three different datasets, a global three-dimensional eddy detection system is implemented in order to bypass the need of regional-dependent definition of thresholds, typical of commonly adopted eddy detection algorithms. It thus provides full three-dimensional eddy statistics segmenting vertical profiles from local rotational velocities. This criterion is crucial for discerning real eddies from transient surface noise that inevitably affects any two-dimensional algorithm. Data assimilation enhances and corrects mesoscale variability on a wide range of features that cannot be well reproduced otherwise. The free simulation fairly reproduces eddies emerging from western boundary currents and deep baroclinic instabilities, while underestimates shallower vortexes that populate the full basin. The ocean reanalysis recovers most of the missing turbulence, shown by satellite products , that is not generated by the model itself and consistently projects surface variability deep into the water column. The comparison with the statistically reconstructed vertical profiles from ARMOR3D show that ocean data assimilation is able to embed variability into the model dynamics, constraining eddies with in situ and altimetry observation and generating them consistently with local environment.     

A multi-envelope vertical coordinate system for numerical ocean modelling

A multi-envelope generalised coordinate system for numerical ocean modelling is introduced. In this system, computational levels are curved and adjusted to multiple ‘virtual bottoms’ (aka envelopes) rather than following geopotential levels or the actual bathymetry. This allows defining computational levels which are optimised to best represent different physical processes in different sub-domains of the model. In particular, we show how it can be used to improve the representation of tracer advection in the ocean interior. The new vertical system is compared with a widely used z-partial step scheme. The modelling skill of the models is assessed by comparison with the analytical solutions or results produced by a model with a very high-resolution z-level grid. Three idealised process-oriented numerical experiments are carried out. Experiments show that numerical errors produced by the new scheme are much smaller than those produced by the standard z-partial step scheme at a comparable vertical resolution. In particular, the new scheme shows superiority in simulating the formation of a cold intermediate layer in the ocean interior and in representing dense water cascading down a steep topography.     

Baroclinic and topographic influences on the transport in western boundary currents

Abstract

One of the central unsolved theoretical problems of the large scale ocean circulation is concerned with explaining the very large transports measured in western boundary currents such as the Gulf Stream and the Kuroshio. The only theory up to now that can explain the size of these transports is that of non-linear recirculation in which the advective terms in the momentum equations became important near the western boundary. In this paper an alternative explanation is suggested. When bottom topography and baroclinic effects are included in a wind-driven ocean model it is shown that the western boundary current can have a transport larger than that predicted from the wind stress distribution even when the nonlinear advective terms are ignored. The explanation lies in the presence of pressure torques associated with bottom topography which can contribute to the vorticity balance in the same sense as the wind stress curl.

Three numerical experiments have been carried out to explore the nature of this process using a three dimensional numerical model. The first calculation is done for a baroclinic ocean of constant depth, the second for a homogeneous ocean with an idealized continental slope topography, and the third for a baroclinic ocean with the same continental slope topography. The nature of the vorticity balance and of the circulation around closed paths is examined in each case, and it is shown that bottom pressure torques lead to enhanced transport in the western boundary current only for the baroclinic case with variable depth.     

Assessing the credibility of a series of computational fluid dynamic simulations of open channel flow

Recent developments in numerical algorithms have enabled the construction of three‐dimensional models for the prediction of flows in open channels. These advances encompass improvements in both numerical solutions and the process representation required for an accurate system definition. However, to date, there is still little agreement on how to assess systematically and report the credibility of these simulations. This paper addresses this problem by adopting a Grid Convergence Index approach. The results indicate, for two simple hypothetical cases, a zero‐degree confluence and a meander bend, that the numerical code can be verified to an acceptable numerical standard. However, it is shown that this does not mean that verification is complete, as the literature implies, as whilst the discretization resolution may be sufficient to verify one of the model variables it does not imply that every variable has converged. Furthermore, the scheme may still be insufficient to capture all the processes of interest that are operating within the chosen environment. Copyright © 2003 John Wiley & Sons, Ltd.     

Space discontinuous Galerkin method for shallow water flows—kinetic and HLLC flux,and potential vorticity generation

In this paper, a second order space discontinuous Galerkin (DG) method is presented for the numerical solution of inviscid shallow water flows over varying bottom topography. Novel in the implementation is the use of HLLC and kinetic numerical fluxes¹ in combination with a dissipation operator, applied only locally around discontinuities to limit spurious numerical oscillations. Numerical solutions over (non-)uniform meshes are verified against exact solutions; the numerical error in the L₂-norm and the convergence of the solution are computed. Bore–vortex interactions are studied analytically and numerically to validate the model; these include bores as “breaking waves” in a channel and a bore traveling over a conical and Gaussian hump. In these complex numerical test cases, we correctly predict the generation of potential vorticity by non-uniform bores. Finally, we successfully validate the numerical model against measurements of steady oblique hydraulic jumps in a channel with a contraction. In the latter case, the kinetic flux is shown to be more robust.