Numerical Ocean Circulation Model Research Articles

Biological production models as elements of coupled, atmosphere‐ocean models for climate research

Process models of phytoplankton production are discussed with respect to their suitability for incorporation into global‐scale numerical ocean circulation models. Exact solutions are given for integrals over the mixed layer and the day of analytic, wavelength‐independent models of primary production. Within this class of model, the bias incurred by using a triangular approximation (rather than a sinusoidal one) to the variation of surface irradiance through the day is computed. Efficient computation algorithms are given for the nonspectral models. More exact calculations require a spectrally sensitive treatment. Such models exist but must be integrated numerically over depth and time. For these integrations, resolution in wavelength, depth, and time are considered and recommendations made for efficient computation. The extrapolation of the one‐(spatial)‐dimension treatment to large horizontal scale is discussed.

Variations in the structure of the anticyclonic gyres found in the Alboran Sea

Historical satellite, aircraft, and in situ data have shown that two anticyclonic gyres (the western and eastern Alboran gyres) are major ocean features of the Alboran Sea. An examination of several years of satellite imagery indicates that large variations in the surface expression of these two gyres occur and that on occasion one or the other gyre disappears (the disappearance of both gyres at the same time was not seen). The initial disappearance of either gyre occurs on a time scale of a week to 2 weeks, whereas the return may take from 3 weeks to 2 months. Various forcing mechanisms, i.e., winds, mass flux inflow through the Straits of Gibraltar and Sicily, and/or density, have been used in numerical ocean circulation models to study the dynamics of the western Mediterranean Sea. Various model results show relationships similar to those shown by the satellite imagery. However, no single forcing mechanism has been positively identified as the source of the disappearances, and the events may be a result of a combination of forcing mechanisms.

A review of sea ice and ocean modeling relevant to the Labrador and Newfoundland shelves

Numerical and analytical models of sea ice and ocean circulation are reviewed from a viewpoint of their application to the Labrador and Newfoundland shelves. Seasonal variabilities of sea ice and ocean circulation have not been reported in numerical models. The difficulty comes from the importance of both stratification and bottom topography. Sea ice should be included for seasonal cycle calculations. Individual mechanisms of variabilities with time scales ranging from a day to a month have been studied extensively using various models so that the coupling of these models will make it possible to test the predictability of sea ice and ocean circulation. The data collected during LIMEX'87 and '89 provide verification of the models.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Model Simulation of the Cretaceous Ocean Circulation

Three-dimensional numerical ocean circulation model experiments that were designed to evaluate the circulation characteristics for the mid-Cretaceous ( approximately 100 million years ago) show that the primary direction of flow through the Tethys Ocean was eastward; in contrast, a westward flowing circumglobal Tethys current has been a consistent feature of earlier reconstructions of Cretaceous ocean circulation. The model studies demonstrate that (i) ocean circulation is sufficiently sensitive to the role of continental positions, sea level, and climate to limit the application of modern analogs to past circulations, and (ii) reconstructions based on limited biogeographic data may not provide unique surface circulation patterns.

Adjustment of the Ocean under Buoyancy Forces. Part II: The Role of Planetary Waves

A numerical ocean general circulation model is used to investigate the early stages in the adjustment to equilibrium of an ocean initially at rest with imposed uniform meridional potential temperature gradients, which yield density gradients representative of those observed in the North Atlantic. The main feature of the adjustment during the early stages (the first year) is the formation and decay of a “subtropical” (warm core) and a “subpolar” (cold core) density gyre. The gyres are formed by the irreversible winding-up of the initially zonal isotherms by first baroclinic mode, coastally-trapped, dissipative Kelvin waves. This phase and the north–south asymmetry arising from the variation in viscous–diffusive Kelvin wave properties with latitude were discussed in Part I of this series. Within a month β-effects become significant, especially in the evolution of the southern gyre, which develops a distinct east–west asymmetry through western intensification and long planetary wave propagation of boundary information from the east. In the north, penetration of boundary information into the interior is attributed to diffusive effects, because the maximum allowable planetary wave frequency is lower than that of the Kelvin wave signal. This phase in the adjustment is described in Part A of the present paper. A simple model based on the quasi-geostrophic potential vorticity equation for a single vertical mode is used to explain and quantitatively assess the effects of finite spatial resolution and viscous and diffusive processes on the Kelvin wave–planetary wave dynamics. The longshore temperature gradients at the middle depths of the ocean are considerably reduced by first baroclinic mode Kelvin wave propagation. The adjustment then enters another phase characterized by the destruction of the density gyres by either planetary wave or diffusive processes, there being no further significant Kelvin wave propagation. This phase is described and investigated in Part B, using the simple model developed in Part A with modified boundary conditions.

Sampling strategies and model assimilation of altimetric data for ocean monitoring and prediction

Numerical forecasts using simulated altimeter data are generated in order to examine the assimilation of altimeter‐derived sea surface heights into numerical ocean circulation models. A one‐layer reduced gravity primitive equation circulation model of the Gulf of Mexico is utilized; the Gulf of Mexico is chosen because of its amenability to modeling and the ability of low vertical mode models to reproduce many of the observed dynamical features of gulf circulation. The simulated data are obtained by flying a hypothetical altimeter over the model ocean and sampling the model sea surface in a manner similar to a real altimeter. The data are used to examine spatial sampling requirements for accurate resolution of oceanic eddies and, in forecast mode, the assimilation of asynoptic altimeter data into numerical models. Results indicate that for a stationary circular eddy, approximately two tracks (either ascending or descending) across the eddy are sufficient to ensure adequate spatial resolution. An irregularly shaped eddy may require three or four tracks. In addition, the study reveals that if the track spacing is sufficient to resolve the height field of an eddy, the along‐track geostrophic velocity component is determined with equivalent accuracy to that of the cross track component. Simulated Gulf of Mexico circulation forecasts suggest that the numerical model can effectively assimilate asynoptic altimeter measurements. Optimum sampling strategies for a single beam altimeter and intermittent updating of the nowcast/forecast are examined.

Initial Testing of a Numerical Ocean Circulation Model Using a Hybrid (Quasi-Isopycnic) Vertical Coordinate

Abstract An ocean circulation model, developed for the study of mesoscale to gyre-scale circulation and heat transport, is described and tested. The model employs density as vertical coordinate except in the immediate vicinity of possible coordinate surface intersections with the ocean surface. Test simulations are carried out for a double-gyre ocean basin of the type used by Holland (1978), but with better resolution in the upper 1000 m of the model ocean. The final state of a 5-year coarse-mesh (50 km resolution on a 2400 km × 1200 km domain) spin-up is used as the initial state for mesoscale experimentation on a 25 km mesh. Basin energetics, as well as mean mass transport streamfunction and mean potential vorticity fields are given for three mesoscale experiments, in which the magnitude and formulation of lateral dissipation are varied. Each of these experiments, run for approximately five years, exhibits vigorous mesoscale activity associated with western boundary current separation and the free jet. ...

Model Studies of the Wind-Driven Transient Circulation in the Middle Atlantic Bight. Part 1: Adiabatic Boundary Conditions

Abstract A numerical model of the wind-driven transient ocean circulation in the Middle Atlantic Bight is described. The model incorporates realistic topography and covers the continental shelf between the coast and the 200 m isobath from Cape Hatteras to the southern tip of Nova Scotia. The traditional shallow-water dynamics are used, i.e., the vertically integrated and linearized equations for the flow of a homogeneous fluid driven by atmospheric pressure and wind stress fluctuations and damped by a quadratic bottom stress. The equations are integrated in time using a simple modification of Platzman's (1972) finite-difference scheme, with a 12.7 km grid spacing. At the coast, normal flow is required to vanish; at non-coastal boundaries, the equivalent surface elevation is held fixed. Several classes of initial value experiments are used to study the free and forced modes of this model, and the damped flow driven by a spatially uniform and stationary wind stress and by an idealized travelling synoptic-sc...

Numerical models of ocean circulation and climate interaction

This article reviews recent advances in ocean circulation models and climate interactions. Related reviews of one‐dimensional models and models of equatorial and polar regions are given in this Quadrennial Report by Garwood [1979], O'Brien [1979] and Baker [1979], respectively. Related reviews of climate are given in the Meteorology section of the Quadrennial Report by Gates [1979], Kutzbach [1979], Perry [1979], and Rotty and Marland [1979].Several detailed review articles on ocean circulation models and climate were written in the last four years. National Academy of Sciences [1975], U. S. Committee for GARP [1975] and WMO/ICSU [1975] give the status at the beginning of this review period while Pond and Bryan [1976] and Holland [1977a] represent more recent reviews. Kraus [1977] contains review articles on modeling the upper ocean, while Gribbin [1978] contains review articles on the ocean's role in climatic change. The latest detailed reviews of ocean circulation models and their relation to climate were presented at a JOC/SCOR Joint Study Conference held in Helsinki in May, 1977 [WMO/ICSU, 1977]. Many of these reviews will be published in a forthcoming issue of Dynamics of Atmospheres and Oceans. The present review begins with studies of the possible effect of ocean temperature variabilities on the atmosphere, and then proceeds to studies using idealized basin models, world ocean models, and finally coupled ocean‐atmosphere models.

Eddies and the general circulation of numerical model gyres: An energetic perspective

Energy budgets for the long‐time‐averaged circulation of mesoscale resolution numerical ocean circulation model (EGCM) experiments are the only widely used analysis methods that permit investigation into the eddy‐mean flow interaction of these model oceanic systems. All published energy results from the closed basin EGCM experiments are presented here in nondimensional form to facilitate comparison of the various types of behavior. The ubiquitous basin‐averaged energy analysis method is necessarily sensitive to changes in model forcing and dissipative processes, and it is shown that several natural energy measures of eddy‐mean flow interaction are strongly correlated with forcing and dissipation choices. In particular, it is found that by these energy measures, eddies are relatively unimportant in the mean flow when the horizontal momentum subgrid scale process corresponds to constant coefficient viscosity, but they are much more important when this process is modeled by a constant coefficient biharmonic operator. Energy budgets over subrogions of the full domain should offer increased insight into model mechanisms, but the use of quasi‐geostrophic dynamics can severely limit the number of independent energy pathways in the flow. Owing to these constraints the published regional two‐layer quasi‐geostrophic energy budgets offer information beyond that of the basin budgets. It is suggested that the assumptions of these quasi‐geostrophic models also limit the generality of inferences about the role of vertical processes based on these calculations. In none of the energy budgets reported is there significant direct driving of a mean flow by Reynolds stress work, and in only one case does mean buoyancy work act to try to increase mean flow kinetic energy. From these budgets it appears that if eddies are energetically important in the model flows, their only unambiguous role is as a pathway to dissipation. Further more detailed regional analysis is necessary to see if this result continues to hold when smaller horizontal subregions of the domain are analyzed. Such analysis activity, as well as more attention to alternative means of investigating eddy‐mean flow interaction, appears to be needed.

The relationship between the grid size and the coefficient of nonlinear lateral eddy viscosity in numerical ocean circulation models

When a constant coefficient of lateral eddy viscosity v 0 is used in ocean circulation models, a false computational space oscillation is generated in the western boundary region if v 0 is smaller than a critical value. The use of a nonlinear eddy viscosity coefficient based upon two-dimensional turbulence theory is shown to permit the use of an eddy viscosity which, away from the western boundary region, is at least an order of magnitude smaller than the above critical value.

Analytical and numerical studies of ocean circulation

This report, while concerning primarily those analytical and numerical models of quasi‐steady circulation of the oceans and adjacent seas, also recognizes similar important studies pertaining to lakes, estuaries, and the continental shelf. (Note, however, that coastal upwelling studies are covered in a separate report.) The accompanying bibliography includes representative papers from abroad as well as from the United States. Several review papers are included with the new contributions, published since the beginning of 1971; moreover, the list includes some papers that this reporter is aware of which will be published in 1975. Several of the latter, although carrying the date 1975, are papers presented at the Symposium on Numerical Models of Ocean Circulation which was held in October 1972, at Durham, New Hampshire; the proceedings will appear as a publication of the U.S. National Academy of Science.

A numerical model of the wind-Driven ocean circulation in a circular basin

Abstract The governing vorticity equation for the two-dimensional flow of a viscous homogeneous fluid on a β-plane is integrated numerically, and steady state results are presented for several values for the Reynolds number. The model and numerical techniques are similar to those used by Bryan (1963) with the important exception that we consider here a circular basin. The interior flow is forced by a negative uniform wind stress curl and the intense western boundary current is adequately resolved by means of variable grid spacing. For the highly non-linear case of Re = 20, the western boundary current undergoes distinct separation from the boundary before the end of the western boundary is reached. A strong vortex with intense recirculation develops in the northwest quadrant of the basin with damped stationary Rossby waves occurring in the transition region between boundary current and interior. The numerical solutions are then compared with streak photographs obtained with the sliced-cylinder laboratory ...

An Approximate Equation of State for Numerical Models of Ocean Circulation

An Approximate Equation of State for Numerical Models of Ocean Circulation