Numerical Ocean Circulation Model Research Articles

Chaotic Lagrangian transport and mixing in the ocean

Dynamical systems theory approach has been successfully used in physical oceanography for the last two decades to study mixing and transport of water masses in the ocean. The basic theoretical ideas have been borrowed from the phenomenon of chaotic advection in fluids, an analogue of dynamical Hamiltonian chaos in mechanics. The starting point for analysis is a velocity field obtained by this or that way. Being motivated by successful applications of that approach to simplified analytic models of geophysical fluid flows, researchers now work with satellite-derived velocity fields and outputs of sophisticated numerical models of ocean circulation. This review article gives an introduction to some of the basic concepts and methods used to study chaotic mixing and transport in the ocean and a brief overview of recent results with some practical applications of Lagrangian tools to monitor spreading of Fukushima-derived radionuclides in the ocean.

A two-time-level split-explicit ocean circulation model (MASNUM) and its validation

A two-time-level, three-dimensional numerical ocean circulation model (named MASNUM) was established with a two-level, single-step Eulerian forward-backward time-differencing scheme. A mathematical model of large-scale oceanic motions was based on the terrain-following coordinated, Boussinesq, Reynolds-averaged primitive equations of ocean dynamics. A simple but very practical Eulerian forward-backward method was adopted to replace the most preferred leapfrog scheme as the time-differencing method for both barotropic and baroclinic modes. The forward-backward method is of second-order of accuracy, computationally efficient by requiring only one function evaluation per time step, and free of the computational mode inherent in the three-level schemes. This method is superior to the leapfrog scheme in that the maximum time step of stability is twice as large as that of the leapfrog scheme in staggered meshes thus the computational efficiency could be doubled. A spatial smoothing method was introduced to control the nonlinear instability in the numerical integration. An ideal numerical experiment simulating the propagation of the equatorial Rossby soliton was performed to test the amplitude and phase error of this new model. The performance of this circulation model was further verified with a regional (northwest Pacific) and a quasi-global (global ocean simulation with the Arctic Ocean excluded) simulation experiments. These two numerical experiments show fairly good agreement with the observations. The maximum time step of stability in these two experiments were also investigated and compared between this model and that model which adopts the leapfrog scheme.

Randomness, Symmetry, and Scaling of Mesoscale Eddy Life Cycles

Abstract It is shown that the life cycles of nonlinear mesoscale eddies, a major component of low-frequency ocean physical variability, have a characteristic structure that differs fundamentally from that which would be expected on the basis of classical interpretations of ocean eddy evolution in terms of mean flow instability and equilibration followed by frictional, radiative, or barotropic decay, or of vortex merger dynamics in quasigeostrophic turbulent cascades. Further, it is found that these life cycles can be accurately modeled in terms of the large-amplitude excursions of a stochastic process. These conclusions, which apply in the corresponding global-mean context, follow from the examination of ensemble-mean and standard deviation time series of normalized eddy amplitude from an automated eddy identification and tracking analysis of a nearly two decade–merged satellite altimeter record of global sea surface height (SSH). The resulting series are found to have several striking and unexpected characteristics, including time-reversal symmetry and approximate self-similarity. Consistent results are obtained from a similar analysis of a 7-yr record of global SSH from a numerical ocean circulation model. The basic qualitative and quantitative statistical properties of these series can be remarkably well reproduced with an extremely simple stochastic model, in which the SSH increments between successive time points are random numbers, and the eddy life cycles are represented by excursions exceeding a given threshold. The stochastic model is found also to predict accurately the empirical autocorrelation structure of the underlying observed SSH field itself, when the autocorrelations are computed along long planetary (Rossby) wave characteristics.

An ocean circulation model based on Eulerian forward-backward difference scheme and three-dimensional, primitive equations and its application in regional simulations

A two-time-level, three-dimensional numerical ocean circulation model is established with a two-level, single-step Eulerian time-difference scheme. The mathematical model of the large-scale oceanic motions is based on the terrain-following coordinated, Boussinesq, Reynolds-averaged primitive equations of ocean dynamics. A simple but very practical Eulerian forward-backward method is adopted to replace the most preferred leapfrog scheme as the time-difference method for both barotropic and baroclinic modes. The forward-backward method is of the second order of accuracy, requires only once of the function evaluation per time step, and is free of the computational mode inherent in the three-level schemes. It is superior in many respects to the original leapfrog and Asselin-filtered leapfrog schemes in the practical use. The performance of the newly-built circulation model is tested by simulating a barotropic (tides in marginal seas of China) and a baroclinic phenomenon (seasonal evolution of the Yellow Sea Cold Water Mass), respectively. The three-year time histories of four prognostic variables obtained by the POM model and the two-time-level model are compared in a regional simulation experiment for the northwest Pacific to further show the reliability of the two-level scheme circulation model.

Eddy properties in the Mozambique Channel: A comparison between observations and two numerical ocean circulation models

Analysis of satellite altimetry observations, transports estimates from a mooring array, as well as output from two different numerical ocean circulation models (ROMS and HYCOM), have been used to investigate the mesoscale eddy properties and transport variability in the Mozambique Channel. The power spectral density of model transports at 17°S indicates the models ability to represent the transport variability at mesoscale frequencies (range between 3yr−1 and 10yr−1). The models have shown an exaggerated representation of the lower frequencies (~ <3yr−1), while underestimating the higher frequency signals (~ >10yr−1). The overestimation of the seasonal cycle appears in our case not to be related to a misrepresentation of the mesoscale variability. The eddies were identified using an automatic eddy tracking scheme. Both anticyclonic and cyclonic eddies appeared to have a preferred site of formation within the channel. The density distribution showed that the anticyclones exhibited a bi-modal distribution: the first mode was associated with the typical scale for the oceanic mesoscale turbulence, while the second mode was related to the passage of large rings at a frequency of about 4–7 per year. On the other hand, cyclonic eddies had a single mode distribution that follows the first baroclinic Rossby radius of deformation, which is a typical scale for the oceanic mesoscale surface eddy variability, suggesting that their formation is associated with baroclinic instability. Eddy mean amplitudes per class of radius (<100km), increase linearly with increasing radius, while no linear relationship exists for the rings. Different from the rings, the increase in the amplitude of the eddies was consistent with the increase of their life expectancy and travelling distances.

Tidally induced lateral dispersion of the Storfjorden overflow plume

Abstract. We investigate the flow of brine-enriched shelf water from Storfjorden (Svalbard) into Fram Strait and onto the western Svalbard Shelf using a regional set-up of NEMO-SHELF, a 3-D numerical ocean circulation model. The model is set up with realistic bathymetry, atmospheric forcing, open boundary conditions and tides. The model has 3 km horizontal resolution and 50 vertical levels in the sh-coordinate system which is specially designed to resolve bottom boundary layer processes. In a series of modelling experiments we focus on the influence of tides on the propagation of the dense water plume by comparing results from tidal and non-tidal model runs. Comparisons of non-tidal to tidal simulations reveal a hotspot of tidally induced horizontal diffusion leading to the lateral dispersion of the plume at the southernmost headland of Spitsbergen which is in close proximity to the plume path. As a result the lighter fractions in the diluted upper layer of the plume are drawn into the shallow coastal current that carries Storfjorden water onto the western Svalbard Shelf, while the dense bottom layer continues to sink down the slope. This bifurcation of the plume into a diluted shelf branch and a dense downslope branch is enhanced by tidally induced shear dispersion at the headland. Tidal effects at the headland are shown to cause a net reduction in the downslope flux of Storfjorden water into the deep Fram Strait. This finding contrasts previous results from observations of a dense plume on a different shelf without abrupt topography.

Ocean state estimation from hydrography and velocity observations during EIFEX with a regional biogeochemical ocean circulation model

In the European Iron Fertilization Experiment (EIFEX), the iron hypothesis was tested by an open ocean perturbation experiment. The success of EIFEX owes to the applied experimental strategy; namely to use the closed core of a mesoscale eddy for the iron injection. This strategy not only allowed tracking the phytoplankton bloom within the fertilized patch of mixed-layer water, but also allowed the export of biologically fixed carbon to the deep ocean to be quantified. In this present study, least-squares techniques are used to fit a regional numerical ocean circulation model with four open boundaries to temperature, salinity, and velocity observations collected during EIFEX. By adjusting the open boundary values of temperature, salinity and velocity, an optimized model is obtained that clearly improves the simulated eddy and its mixed layer compared to a first guess representation of the cyclonic eddy. A biogeochemical model, coupled to the optimized circulation model, simulates the evolution of variables such as chlorophyll a and particular organic carbon in close agreement with the observations. The estimated carbon export, however, is lower than the estimates obtained from observations without numerical modeling support. Tuning the sinking parameterization in the model increases the carbon export at the cost of unrealistically high sinking velocities. Repeating the model experiment without adding iron allows more insight into the effects of the iron fertilization. In the model this effect is about 40% lower than in previous estimates in the context of EIFEX. The likely causes for these discrepancies are potentially too high remineralization, inaccurate representation of the bloom-termination in the model, and ambiguity in budget computations and averaging. The discrepancies are discussed and improvements are suggested for the parameterization used in the biogeochemical model components.

Global ocean storage of anthropogenic carbon

Abstract. The global ocean is a significant sink for anthropogenic carbon (Cant), absorbing roughly a third of human CO2 emitted over the industrial period. Robust estimates of the magnitude and variability of the storage and distribution of Cant in the ocean are therefore important for understanding the human impact on climate. In this synthesis we review observational and model-based estimates of the storage and transport of Cant in the ocean. We pay particular attention to the uncertainties and potential biases inherent in different inference schemes. On a global scale, three data-based estimates of the distribution and inventory of Cant are now available. While the inventories are found to agree within their uncertainty, there are considerable differences in the spatial distribution. We also present a review of the progress made in the application of inverse and data assimilation techniques which combine ocean interior estimates of Cant with numerical ocean circulation models. Such methods are especially useful for estimating the air–sea flux and interior transport of Cant, quantities that are otherwise difficult to observe directly. However, the results are found to be highly dependent on modeled circulation, with the spread due to different ocean models at least as large as that from the different observational methods used to estimate Cant. Our review also highlights the importance of repeat measurements of hydrographic and biogeochemical parameters to estimate the storage of Cant on decadal timescales in the presence of the variability in circulation that is neglected by other approaches. Data-based Cant estimates provide important constraints on forward ocean models, which exhibit both broad similarities and regional errors relative to the observational fields. A compilation of inventories of Cant gives us a "best" estimate of the global ocean inventory of anthropogenic carbon in 2010 of 155 ± 31 PgC (±20% uncertainty). This estimate includes a broad range of values, suggesting that a combination of approaches is necessary in order to achieve a robust quantification of the ocean sink of anthropogenic CO2.

On the dynamics of strait flows: an ocean model study of the Aleutian passages and the Bering Strait

A high-resolution numerical ocean circulation model of the Bering Sea (BS) is used to study the natural variability of the BS straits. Three distinct categories of strait dynamics have been identified: (1) Shallow passages such as the Bering Strait and the Unimak Passage have northward, near barotropic flow with periodic pulses of larger transports; (2) wide passages such as Near Straits, Amukta Pass, and Buldir Pass have complex flow patterns driven by the passage of mesoscale eddies across the strait; and (3) deep passages such as Amchitka Pass and Kamchatka Strait have persistent deep return flows opposite in direction to major surface currents; the deep flows persist independent of the local wind. Empirical orthogonal function analyses reveal the spatial structure and the temporal variability of strait flows and demonstrate how mesoscale variations in the Aleutian passages influence the Bering Strait flow toward the Arctic Ocean. The study suggests a general relation between the barotropic and baroclinic Rossby radii of deformations in each strait, and the level of flow variability through the strait, independent of geographical location. The mesoscale variability in the BS seems to originate from two different sources: a remote origin from variability in the Alaskan Stream that enters the BS through the Aleutian passages and a local origin from the interaction of currents with the Bowers Ridge in the Aleutian Basin. Comparisons between the flow in the Aleutian passages and flow in other straits, such as the Yucatan Channel and the Faroe Bank Channel, suggest some universal topographically induced dynamics in strait flows.

Assessing the fidelity of surface currents from a coastal ocean model and HF radar using drifting buoys in the Middle Atlantic Bight

The rapid expansion of urbanization along the world’s coastal areas requires a more comprehensive and accurate understanding of the coastal ocean. Over the past several decades, numerical ocean circulation models have tried to provide such insight, based on our developing understanding of physical ocean processes. The systematic establishment of coastal ocean observation systems adopting cutting-edge technology, such as high frequency (HF) radar, satellite sensing, and gliders, has put such ocean model predictions to the test, by providing comprehensive observational datasets for the validation of numerical model forecasts. The New York Harbor Observing and Prediction System (NYHOPS) is a comprehensive system for understanding coastal ocean processes on the continental shelf waters of New York and New Jersey. To increase confidence in the system’s ocean circulation predictions in that area, a detailed validation exercise was carried out using HF radar and Lagrangian drifter-derived surface currents from three drifters obtained between March and October 2010. During that period, the root mean square (RMS) differences of both the east–west and north–south currents between NYHOPS and HF radar were approximately 15 cm s−1. Harmonic analysis of NYHOPS and HF radar surface currents shows similar tidal ellipse parameters for the dominant M2 tide, with a mean difference of 2.4 cm s−1 in the semi-major axis and 1.4 cm s−1 in the semi-minor axis and 3° in orientation and 10° in phase. Surface currents derived independently from drifters along their trajectories showed that NYHOPS and HF radar yielded similarly accurate results. RMS errors when compared to currents derived along the trajectory of the three drifters were approximately 10 cm s−1. Overall, the analysis suggests that NYHOPS and HF radar had similar skill in estimating the currents over the continental shelf waters of the Middle Atlantic Bight during this time period. An ensemble-based set of particle tracking simulations using one drifter which was tracked for 11 days showed that the ensemble mean separation generally increases with time in a linear fashion. The separation distance is not dominated by high frequency or short spatial scale wavelengths suggesting that both the NYHOPS and HF radar currents are representing tidal and inertial time scales correctly and resolving some of the smaller scale eddies. The growing ensemble mean separation distance is dominated by errors in the mean flow causing the drifters to slowly diverge from their observed positions. The separation distance for both HF radar and NYHOPS stays below 30 km after 5 days, and the two technologies have similar tracking skill at the 95 % level. For comparison, the ensemble mean distance of a drifter from its initial release location (persistence assumption) is estimated to be greater than 70 km in 5 days.

Geostrophic Adjustment Problems in a Polar Basin

The geostrophic adjustment of a homogeneous fluid in a circular basin with idealized topography is addressed using a numerical ocean circulation model and analytical process models. When the basin is rotating uniformly, the adjustment takes place via excitation of boundary propagating waves and when topography is present, via topographic Rossby waves. In the numerically derived solution, the waves are damped because of bottom friction, and a quasi-steady geostrophically balanced state emerges that subsequently spins-down on a long time scale. On the f-plane, numerical quasi-steady state solutions are attained well before the system's mechanical energy is entirely dissipated by friction. It is demonstrated that the adjusted states emerging in a circular basin with a step escarpment or a top hat ridge, centred on a line of symmetry, are equivalent to that in a uniform depth semicircular basin, for a given initial condition. These quasi-steady solutions agree well with linear analytical solutions for the latter case in the inviscid limit. On the polar plane, the high latitude equivalent to the β-plane, no quasi-steady adjusted state emerges from the adjustment process. At intermediate time scales, after the fast Poincaré and Kelvin waves are damped by friction, the solutions take the form of steady-state adjusted solutions on the f-plane. At longer time scales, planetary waves control the flow evolution. An interesting property of planetary waves on a polar plane is a nearly zero eastward group velocity for the waves with a radial mode higher than two and the resulting formation of eddy-like small-scale barotropic structures that remain trapped near the western side of topographic features. RÉSUMÉ Traduit par la rédaction] Nous étudions l'ajustement géostrophique d'un fluide homogène dans un bassin circulaire ayant une topographie idéalisée à l'aide d'un modèle numérique de circulation océanique et de modèles analytiques de processus. Quand le bassin est en rotation uniforme, l'ajustement se fait par l'excitation d'ondes de propagation aux limites, et en présence de topographie, par des ondes de Rossby topographiques. Dans la solution numériquement dérivée, les ondes sont amorties à cause frottement contre le fond, et un état quasi-stable géostrophiquement équilibré s’établit pour ensuite décélérer sur une longue période de temps. Sur le plan f, les solutions numériques d’états quasi-stables sont atteintes bien avant que l’énergie du système mécanique soit entièrement dissipée par le frottement. Nous démontrons que les états ajustés apparaissant dans un bassin circulaire avec un accore en forme de marche ou une crête en forme de merlon, centrés sur une ligne de symétrie, sont équivalents à ceux d'un bassin semi-circulaire de profondeur uniforme pour une condition initiale donnée. Les solutions quasi-stables s'accordent bien avec les solutions analytiques linéaires pour le dernier cas dans la limite de la non-viscosité. Sur le plan polaire, la haute latitude équivalente au plan β, le processus d'ajustement n'aboutit à aucun état ajusté quasi-stable. Aux échelles de temps intermédiaires, après l'amortissement des ondes rapides de Poincaré et Kelvin par le frottement, les solutions prennent la forme de solutions ajustées d’états stables sur le plan f. Aux échelles de temps plus longues, les ondes planétaires déterminent l’évolution de l’écoulement. Une propriété intéressante des ondes planétaires sur un plan polaire est une vitesse de groupe presque nulle vers l'est pour les ondes ayant un mode radial plus grand que deux et la formation résultante de structures barotropiques de petite échelle de type remous qui demeurent emprisonnées près du bord ouest des caractéristiques topographiques.

Numerical modeling with application to tracking marine debris

This paper describes different numerical models of ocean circulation the output of which can be applied to study patterns and pathways of drifting marine debris. The paper focuses on model output that is readily available rather than on numerical models that could be configured and run locally. These include operational models from the US Navy (the Navy Layered Ocean Model (NLOM), Coastal Ocean Model (NCOM), and Hybrid Coordinate Ocean Model (HYCOM)), data assimilating reanalysis models (the Simple Ocean Data Assimilation (SODA), the Global Ocean Data Assimilation Experiment (GODAE) models), and the European Center for Medium-Range Weather Forecasts (ECMWF) ocean reanalysis (Ocean Reanalysis System, ECMWF/ORA-S3). The paper describes the underlying physics in each model system, limitations, and where to obtain the model output.

On the modeling of the 2010 Gulf of Mexico Oil Spill

Abstract Two oil particle trajectory forecasting systems were developed and applied to the 2010 Deepwater Horizon Oil Spill in the Gulf of Mexico. Both systems use ocean current fields from high-resolution numerical ocean circulation model simulations, Lagrangian stochastic models to represent unresolved sub-grid scale variability to advect oil particles, and Monte Carlo-based schemes for representing uncertain biochemical and physical processes. The first system assumes two-dimensional particle motion at the ocean surface, the oil is in one state, and the particle removal is modeled as a Monte Carlo process parameterized by a one number removal rate. Oil particles are seeded using both initial conditions based on observations and particles released at the location of the Maconda well. The initial conditions (ICs) of oil particle location for the two-dimensional surface oil trajectory forecasts are based on a fusing of all available information including satellite-based analyses. The resulting oil map is digitized into a shape file within which a polygon filling software generates longitude and latitude with variable particle density depending on the amount of oil present in the observations for the IC. The more complex system assumes three (light, medium, heavy) states for the oil, each state has a different removal rate in the Monte Carlo process, three-dimensional particle motion, and a particle size-dependent oil mixing model. Simulations from the two-dimensional forecast system produced results that qualitatively agreed with the uncertain “truth” fields. These simulations validated the use of our Monte Carlo scheme for representing oil removal by evaporation and other weathering processes. Eulerian velocity fields for predicting particle motion from data-assimilative models produced better particle trajectory distributions than a free running model with no data assimilation. Monte Carlo simulations of the three-dimensional oil particle trajectory, whose ensembles were generated by perturbing the size of the oil particles and the fraction in a given size range that are released at depth, the two largest unknowns in this problem. 36 realizations of the model were run with only subsurface oil releases. An average of these results yields that after three months, about 25% of the oil remains in the water column and that most of the oil is below 800 m.

Sensitivity of simulated extent and future evolution of marine suboxia to mixing intensity

Geological and hydrographic records contain evidence of substantial past variations in the oxygenation of the global ocean. Numerical models predicts a future decrease of marine oxygen levels under global warming. Using a global biogeochemical-climate model in which diapycnal mixing is parametrised as the sum of the regionally heterogenous tidal and homogenous background vertical mixing, we here show that simulated total oceanic oxygen content and the extent of marine suboxia are both sensitive to the strength of background vertical mixing. Eight otherwise identical configurations of the model were spun up under pre-industrial conditions for different vertical diffusivities ranging from background values of 0.01 cm 2/s to 0.5 cm 2/s. This range corresponds to various observational estimates and to values currently used in numerical ocean circulation models. Whereas the simulated total oceanic oxygen content is larger for larger mixing intensities, the simulated suboxic volume displays a maximum at intermediate diffusivities of about 0.2 cm 2/s. The intensity of vertical mixing also determines the evolution of suboxic areas under projected 21st century CO 2 emissions: while all model configurations predict a decline in total oceanic oxygen, the simulated extent of marine suboxia shows a 21st century expansion only for mixing rates higher than 0.2 cm 2/s, whereas the suboxic volume declines for lower mixing rates despite an overall loss of marine oxygen. Differences in the poorly constrained mixing parameterisation can thus lead to qualitatively different estimates about the future evolution of marine suboxia under projected climate change.

Iron conservation by reduction of metalloenzyme inventories in the marine diazotroph Crocosphaera watsonii

The marine nitrogen fixing microorganisms (diazotrophs) are a major source of nitrogen to open ocean ecosystems and are predicted to be limited by iron in most marine environments. Here we use global and targeted proteomic analyses on a key unicellular marine diazotroph Crocosphaera watsonii to reveal large scale diel changes in its proteome, including substantial variations in concentrations of iron metalloproteins involved in nitrogen fixation and photosynthesis, as well as nocturnal flavodoxin production. The daily synthesis and degradation of enzymes in coordination with their utilization results in a lowered cellular metalloenzyme inventory that requires ∼40% less iron than if these enzymes were maintained throughout the diel cycle. This strategy is energetically expensive, but appears to serve as an important adaptation for confronting the iron scarcity of the open oceans. A global numerical model of ocean circulation, biogeochemistry and ecosystems suggests that Crocosphaera's ability to reduce its iron-metalloenzyme inventory provides two advantages: It allows Crocosphaera to inhabit regions lower in iron and allows the same iron supply to support higher Crocosphaera biomass and nitrogen fixation than if they did not have this reduced iron requirement.

The role of the Alaskan Stream in modulating the Bering Sea climate

A numerical ocean circulation model with realistic topography, but with an idealized forcing that includes only lateral transports is used to study the role of the Alaskan Stream (AS) in modulating the Bering Sea (BS) variability. Sensitivity experiments, each one with a different strength of the AS transport reveal a nonlinear BS response. An increase of AS transport from 10 to 25 Sv causes warming (∼0.25°C mean, ∼0.5°C maximum) and sea level rise in the BS shelf due to increased transports of warmer Pacific waters through the eastern passages of the Aleutian Islands, but an increase of AS transport from 25 to 40 Sv had an opposite impact on the BS shelf with a slight cooling (∼−0.1°C mean, ∼−0.5°C maximum). As the AS transport increases, flows through passages farther downstream in the western Aleutian Islands are affected and the variability in the entire BS is reduced. Transport variations of ∼0.1Sv in the Bering Strait are found to be correlated with mesoscale variations of the AS and associated transport variations in the Aleutian Islands passages. These results have important implications for understanding the observed variations in the Bering Strait and potential future climate variations in the Arctic Ocean.

Identifying and quantifying nonconservative energy production/destruction terms in hydrostatic Boussinesq primitive equation models

This paper seeks to illustrate the point that physical inconsistencies between thermodynamics and dynamics usually introduce nonconservative production/destruction terms in the local total energy balance equation in numerical ocean general circulation models (OGCMs). Such terms potentially give rise to undesirable forces and/or diabatic terms in the momentum and thermodynamic equations, respectively, which could explain some of the observed errors in simulated ocean currents and water masses. In this paper, a theoretical framework is developed to provide a practical method to determine such nonconservative terms, which is illustrated in the context of a relatively simple form of the hydrostatic Boussinesq primitive equation used in early versions of OGCMs, for which at least four main potential sources of energy nonconservation are identified; they arise from: (1) the “hanging” kinetic energy dissipation term; (2) assuming potential or conservative temperature to be a conservative quantity; (3) the interaction of the Boussinesq approximation with the parameterizations of turbulent mixing of temperature and salinity; (4) some adiabatic compressibility effects due to the Boussinesq approximation. In practice, OGCMs also possess spurious numerical energy sources and sinks, but they are not explicitly addressed here. Apart from (1), the identified nonconservative energy sources/sinks are not sign definite, allowing for possible widespread cancellation when integrated globally. Locally, however, these terms may be of the same order of magnitude as actual energy conversion terms thought to occur in the oceans. Although the actual impact of these nonconservative energy terms on the overall accuracy and physical realism of the oceans is difficult to ascertain, an important issue is whether they could impact on transient simulations, and on the transition toward different circulation regimes associated with a significant reorganization of the different energy reservoirs. Some possible solutions for improvement are examined. It is thus found that the term (2) can be substantially reduced by at least one order of magnitude by using conservative temperature instead of potential temperature. Using the anelastic approximation, however, which was initially thought as a possible way to greatly improve the accuracy of the energy budget, would only marginally reduce the term (4) with no impact on the terms (1), (2) and (3).

Large bio-geographical shifts in the north-eastern Atlantic Ocean: From the subpolar gyre, via plankton, to blue whiting and pilot whales

Pronounced changes in fauna, extending from the English Channel in the south to the Barents Sea in the north-east and off Greenland in the north-west, have occurred in the late 1920s, the late 1960s and again in the late 1990s. We attribute these events to exchanges of subarctic and subtropical water masses in the north-eastern North Atlantic Ocean, associated with changes in the strength and extent of the subpolar gyre. These exchanges lead to variations in the influence exerted by the subarctic or Lusitanian biomes on the intermediate faunistic zone in the north-eastern Atlantic. This strong and persistent bottom-up bio-physical link is demonstrated using a numerical ocean general circulation model and data on four trophically connected levels in the food chain – phytoplankton, zooplankton, blue whiting, and pilot whales. The plankton data give a unique basin-scale depiction of these changes, and a long pilot whale record from the Faroe Islands offers an exceptional temporal perspective over three centuries. Recent advances in simulating the dynamics of the subpolar gyre suggests a potential for predicting the distribution of the main faunistic zones in the north-eastern Atlantic a few years into the future, which might facilitate a more rational management of the commercially important fisheries in this region.

The Depth-Dependent Current and Wave Interaction Equations: A Revision

AbstractThis is a revision of a previous paper dealing with three-dimensional wave-current interactions. It is shown that the continuity and momentum equations in the absence of surface waves can include waves after the addition of three-dimensional radiation stress terms, a fairly simple alteration for numerical ocean circulation models. The velocity that varies on time and space scales, which are large compared to inverse wave frequency and wavenumber, is denoted by ûα and, by convention, is called the “current.” The Stokes drift is labeled uSα and the mean velocity is Uα ≡ ûα + uSα. When vertically integrated, the results here are in agreement with past literature.Surface wind stress is empirical, but transfer of the stress into the water column is a function derived in this paper. The wave energy equation is derived, and terms such as the advective wave velocity are weighted vertical integrals of the mean velocity. The wave action equation is not an appropriate substitute for the wave energy equation when the mean velocity is depth dependent.

A Surface Wave Model for Coupling with Numerical Ocean Circulation Models

AbstractA surface wave model is developed with the intention of coupling it to three-dimensional ocean circulation models. The model is based on a paper by Mellor wherein depth-dependent coupling terms were derived. To be compatible with circulation models and to be numerically economical, this model is simplified compared to popular third-generation models. However, the model does support depth and current refraction, deep and shallow water, and proper coupling with depth-variable currents.The model is demonstrated for several simple scenarios culminating in comparisons of model calculations with buoy data during Hurricane Katrina and with calculations from the model Simulating Waves Nearshore (SWAN); for these calculations, coupling with the ocean was not activated.