Search Results

You are looking at 11 - 20 of 26 items for

  • Author or Editor: William R. Holland x
  • Refine by Access: All Content x
Clear All Modify Search
William R. Holland and Peter B. Rhines

Abstract

Gyre scale and local vorticity balances are examined for a single numerical experiment designed to elucidate the role of eddies in the oceanic general circulation. Due to the complex nature of the flow, a combination of different analyses is needed. In particular the mean potential vorticity fields are calculated and related to local and global vorticity fluxes. The nature of eddy generation and decay is discussed in terms of eddy enstrophy balances in the fluid. Momentum balances in various parts of the gyre are deduced through the application of the circulation theorem. Fields of eddy diffusivity for the mixing of potential vorticity and heat are determined. The applicability of Sverdrup dynamics in various parts of the fluid and the manner in which the deep abyssal gyres are driven are examined.

The net picture is a complex but consistent one. In the upper layer, eddy generation occurs in the separation region of the eastward jet and in the region of westward return flow. Eddy decay occurs principally at the eastern end of the free jet accompanied by upgradient eddy fluxes of heat and potential vorticity. The lower layer is driven from above by inviscid pressure forcing at the interface., this is accompanied by downgradient potential vorticity flux everywhere in the lower layer. The deep dynamics is essentially a “turbulent” Sverdrup balance, Ū3·∇ Q̄3= ∇·κ ∇Q̄3, driven by eddy rather than wind stresses.

Full access
Albert J. Semtner Jr. and William R. Holland

Abstract

An equatorial ocean experiment has been carried out, using the primitive equation model of Semtner and Mintz (1977) with a highly conservative differencing scheme, with high horizontal resolution (Δx = 0.50°, Δy=0.25°) and with 14 levels in the vertical. A turbulent equilibrium state has been reached for a 3300 km × 2200 km equatorial ocean, driven by constant 0.5 dyn cm−2 wind stress, heated at the surface and cooled at the northern and southern walls.

The predicted surface temperature field shows an upwelling-induced cold region along the equator. The temperatures at the equator near the eastern wall are as much as 6°C colder than in the subequatorial regions. Westward moving waves occur in the temperature field a few degrees north and south of the equator. These waves have periods of 33 days, wavelengths of 800 km, and are symmetric about the equator. Their structure is similar to that of equatorially trapped Rossby waves with n=1 in the vertical and m=1 in the horizontal. Shorter wavelength disturbances are found throughout the thermocline near the equator, and these have periods typical of equatorially trapped inertia-gravity waves. The horizontal temperature field at depth suggests that a number of high baroclinic modes are superposed.

The surface flow in the model is characterized by Ekman drift plus transient geostrophic flow off the equator and by weak and variable flow at the equator. A pressure gradient due to the tilt of the sea surface along the equator largely balances the wind stress on the surface layer. Below the surface, this pressure gradient drives an equatorial undercurrent, which slopes upward to the east and intensifies to a maximum of about 100 cm s−1. The undercurrent meanders, with periods of 100 days or more, by as much as 100 km on either side of the equator. Below the current, westward moving cross-equatorial flows with periods of about 44 days sometimes link up the quasi-geostrophic circulations on opposite sides of the equator. These flows appear to be associated with an antisymmetric (in u and p) Rossby wave of the same period having m = 2.

An analysis of energetics shows that the disturbances on either side of the equator are maintained by baroclinic instability, whereas the equatorial undercurrent exhibits mainly barotropic instability. These instabilities lead to transient circulations whose characteristics are similar to those of equatorially trapped neutral waves. Frictional dissipation is concentrated at the equator, and most of the loss of energy is from the eddy circulations rather than from the mean flow.

Full access
Albert J. Semtner Jr. and William R. Holland

Abstract

The purpose of this paper is to compare two numerical models of vastly different complexity and computational requirements, which have been used recently in a number of midlatitude ocean simulations. Specifically, the two-layer quasi-geostrophic (QG) model of Holland (1978) is compared with the five-level primitive equation (PE) model of Semtner and Mintz (1977) for a wind-driven multi-gyre ocean, with effects of bottom topography and thermal forcing included. The dominant feature of the circulation predicted in the previous PE calculations is a strong free jet, with intense mesoscale transients which are maintained by baroclinic instability.

The configuration of the QG experiment is designed to approximate closely that of the PE experiment, while retaining as much of the simplicity of the Holland (1978) model as possible. The QG model spins up to a state of statistical equilibrium, which is characterized by a meandering jet and by mid-ocean mesoscale eddies with periods and wavelengths much like those in the PE experiment. The time-mean circulations and the distributions of eddy energy in both models are very similar. An energy analysis shows that the free jet in the QG model is more barotropically unstable than in the PE model; however, by reducing the QG upper layer depth to be closer to the thickness of the free jet in the PE model (200 m), this discrepancy disappears. Excellent agreement is also obtained between the volume-integrated energetics of the two models, provided one uses the same lateral diffusion coefficients for momentum and heat in both models.

To gain more insight into physical processes, the computational speed of the QG model is exploited to make additional experiments on the influences of bottom topography, thermal forcing and increased vertical resolution. Bottom topography is found to intensify the upper layer jet and to change substantially the pattern of the deep mean flow. While the presence or absence of topography does not alter the degree of baroclinic versus barotropic instability when the upper layer is 500 m thick, topography does cause a greater proportion of baroclinic instability when the upper layer is thinner. Thermal forcing strengthens the flow in both layers. The use of a three-layer QG model removes the arbitrariness associated with the choice of upper layer thickness: the dominant baroclinic instability of the free jet remains and is concentrated at the interface of the upper two layers.

The results of the present intercomparison suggest that QG simulations will produce the same basic dynamics as PE models in the type of problem considered, using a fraction of the computer time. The saying in computer resources can be profitably applied to understanding the important effects of parameter variations on the oceanic general circulation.

Full access
William R. Holland and Liang B. Lin

Abstract

Numerical experiments on the wind-driven ocean circulation in a closed basin show that mesoscale eddiescan appear spontaneously during the integration of the equations of motion for a baroclinic ocean. For somevalues of the basic parameters governing the flow, the solutions reach a steady state while for other valuesfinite-amplitude eddies remain a part of the final statistically steady state. In the eddying cases the solutionscan be regarded as a mean flow upon which is superimposed a set of eddies which propagate westward at afew kilometers per day. The eddies typically have horizontal wavelengths of a few hundred kilometers.

Analyses of die energetics show the eddies to be generated by the process of baroclinic instability. Thepotential energy of the mean flow is released to supply energy to the eddies. The computed Reynoldsstresses, while small compared to the terms in the geostrophic balance of the mean momentum equations, dohave a strong influence on the mean circulation and, in fact, the deep mean circulation is driven entirelyby the eddies. If the flow were steady, there would be no flow in the deep layer in this model. Finally, thecomputed curl of the Reynolds stresses shows that the vorticity balance of the mean flow is strongly affected by the presence of mesoscale eddies.

In the first part of this report we describe the two-layer model and discuss its numerical formulation.Then the results of a preliminary eddy experiment are discussed in detail, showing the spontaneous growthof baroclinic eddies and describing the final statistical steady state that occurs. Energetic analyses andvorticity balances show the important role played by the eddies in determining the character of the oceanicgeneral circulation.

Part II of this paper will discuss a variety of experiments which explore the dependence of results on thebasic parameters and boundary conditions governing the model. In particular the dependence of resultson wind stress magnitude and distribution, lateral viscosity coefficient, basin size, and boundary conditions(free slip and no slip) will be examined.

Full access
William R. Holland and Alan D. Hirschman

Abstract

A series of numerical experiments are carried out to simulate the three-dimensional circulation in the North Atlantic Ocean and to examine the dynamics therein. The calculations are partly diagnostic in that the density field is not predicted but is given from observations. The main predicted quantities are the velocity and pressure fields.

The results of the basic experiment are compared with observations. The surface currents are quite similar to observations based upon ship drift data, and the surface pressure field is nearly identical to the height of the free surface constructed from a level-of-no-motion hypothesis. The deep pressure variations are nowhere flat or level, however, and the predicted deep currents are quite complex. They are, in fact, strongly controlled by bottom topography and tend to follow f/H contours, where f is the Coriolis parameter and H the depth. The Gulf Stream transport is quite large, reaching a maximum value of 81×106 m3 sec−1, despite the lack of important inertial effects in the western boundary current. Subsidiary experiments show that this large transport value results from an important interaction between the variable density field and bottom topography in the western North Atlantic. When in one experiment the density field was a homogeneous one and in another the depth was constant, the maximum transports in the western boundary current were only 14 and 28×106 m3 sec−1, respectively.

Other experiments show that the details of the wind-stress distribution are unimportant when the density field is known; the density field contains most of the information about the long term wind driving. For example, when the wind stress is set equal to zero everywhere (but the density field is maintained in its observed configuration), the Gulf Stream transport is reduced by only 5%. Thus, the pressure torques associated with bottom topography provide the main vorticity input. Finally, it is shown that the results discussed in the basic experiment are not very sensitive to the details of the density field used in the calculation. When these data are highly smoothed and used in a subsidiary calculation, the important features, such as the enhanced transport in the Gulf Stream and the topographic steering of currents in the deep ocean, are unchanged.

Full access
Antonietta Capotondi, William R. Holland, and Paola Malanotte-Rizzoli

Abstract

The improvement in the climatological behavior of a numerical model as a consequence of the assimilation of surface data is investigated. The model used for this study is a quasigeostrophic (QG) model of the Gulf Stream region. The data that have been assimilated are maps of sea surface height that have been obtained as the superposition of sea surface height variability deduced from the Geosat altimeter measurements and a mean field constructed from historical hydrographic data. The method used for assimilating the data is the nudging technique. Nudging has been implemented in such a way as to achieve a high degree of convergence of the surface model fields toward the observations.

Comparisons of the assimilation results with available in situ observations show a significant improvement in the degree of realism of the climatological model behavior, with respect to the model in which no data are assimilated. The remaining discrepancies in the model mean circulation seem to be mainly associated with deficiencies in the mean component of the surface data that are assimilated. On the other hand, the possibility of building into the model more realistic eddy characteristics through the assimilation of the surface eddy field proves very successful in driving components of the mean model circulation that are in relatively good agreement with the available observations. Comparisons with current meter time series during a time period partially overlapping the Geosat mission show that the model is able to “correctly” extrapolate the instantaneous surface eddy signals to depths of approximately 1500 m. The correlation coefficient between current meter and model time series varies from values close to 0.7 in the top 1500 m to values as low as 0.1–0.2 in the deep ocean.

Full access
Antonietta Capotondi, Paola Malanotte-Rizzoli, and William R. Holland

Abstract

The dynamical consequences of constraining a numerical model with sea surface height data have been investigated. The model used for this study is a quasigeostrophic model of the Gulf Stream region. The data that have been assimilated are maps of sea surface height obtained as the superposition of sea surface height variability deduced from the Geosat altimeter measurements and a mean field constructed from historical hydrographic data. The method used for assimilating the data is the nudging technique. Nudging has been implemented in such a way as to achieve a high degree of convergence of the surface model fields toward the observations. The assimilations of the surface data is thus equivalent to the prescription of a surface pressure boundary condition. The authors analyzed the mechanisms of the model adjustment and the characteristics of the resultant equilibrium state when the surface data are assimilated. Since the surface data are the superposition of a mean component and an eddy component, in order to understand the relative role of these two components in determining the characteristics of the final equilibrium state, two different experiments have been considered: in the first experiment only the climatological mean field is assimilated, while in the second experiment the total surface streamfunction field (mean plus eddies) has been used. It is shown that the model behavior in the presence of the surface data constraint can be conveniently described in terms of baroclinic Fofonoff modes. The prescribed mean component of the surface data acts as a “surface topography” in this problem. Its presence determines a distortion of the geostrophic contours in the subsurface layers, thus constraining the mean circulation in those layers. The intensity of the mean flow is determined by the inflow/outflow conditions at the open boundaries, as well as by eddy forcing and dissipation.

Full access
Frank O. Bryan, Claus W. Böning, and William R. Holland

Abstract

This paper describes, and establishes the dynamical mechanisms responsible for, the large-scale, time-mean, midlatitude circulation in a high-resolution model of the North Atlantic basin. The model solution is compared with recently proposed transport schemes and interpretations of the dynamical balances operating in the sub-tropical gyre. In particular, the question of the degree to which Sverdrup balance holds for the subtropical gyre is addressed. At 25°N, thermohaline-driven bottom flows cause strong local departures from the Sverdrup solution for the vertically integrated meridional mass transport, but these nearly integrate to zero across the interior of the basin. In the northwestern region of the subtropical gyre, in the vicinity of the Gulf Stream, higher-order dynamics become important, and linear vorticity dynamics is unable to explain the model's vertically integrated transport. In the subpolar gyre, the model transport bears little resemblance to the Sverdrup prediction, and higher-order dynamics are important across the entire longitudinal extent of the basin.

The sensitivity of the model transport amplitudes, patterns, and dynamical balances are estimated by examining the solutions under a range of parameter choices and for four different wind stress forcing specifications. Taking into account a deficit of 7–10 Sv (Sv ≡ 106 m3 s−1) in the contribution of the model thermohaline circulation to the meridional transports at 25°N, the wind stress climatology of Isemer and Hasse appears to yield too strong of a circulation, while that derived from the NCAR Community Climate Model yields too weak of a circulation. The Hellerman and Rosenstein and ECMWF climatologies result in wind-driven transports close to observational estimates at 25°N. The range between cases for the annual mean southward transport in the interior above 1000 m is 14 Sv, which is 40%–70% of the mean transport itself. There is little sensitivity to the model closure parameters at this latitude. At 55°N, in the subpolar gyre, there is little sensitivity of the model solution to the choice of either closure parameters or wind climatology, despite large differences in the Sverdrup transports implied by the different wind stress datasets. Large year to year variability of the meridional transport east of the Bahamas makes it difficult to provide robust estimates of the sensitivity of the Antilles and deep western boundary current systems to forcing and parameter changes.

Full access
Jacques Verron, Christian Le Provost, and William R. Holland

Abstract

High resolution ocean general circulation model experiments were carried out to investigate the effects of a midocean ridge on the eddy field and the mean circulation on the basin scale. A quasigeostrphic two-layer model was used. Long term statistics were computed for a detailed comparison with the flat bottom case. An eddy-driven anticyclonic gyre, locked over the topography, appears as a new feature of the deep circulation pattern. The eddy energy radiation in both layers is strongly constrained by the topography. Insofar as surface currents are concerned, the ridge acts, to a limited extent, as a new western boundary for the eastern basin.

Full access
William R. Holland, Julianna C. Chow, and Frank O. Bryan

Abstract

The National Center for Atmospheric Research (NCAR) Ocean Model has been developed for use in NCAR’s Climate System Modeling project, a comprehensive development of a coupled ocean–atmosphere–sea ice–land surface model of the global climate system. As part of this development, new parameterizations of diffusive mixing by unresolved processes have been implemented for the tracer equations in the model. Because the strength of the mixing depends upon the density structure under these parameterizations, it is possible that local explicit mixing may be quite small in selected locations, in contrast to the constant diffusivity model generally used. When a spatially centered advection scheme is used in the standard model configuration, local overshooting of tracer values occurs, leading to unphysical maxima and minima in the fields. While the immediate problem is a local Gibbs’s phenomenon, there is the possibility that such local tracer anomalies might propagate by advection and diffusion far from the source, causing inaccuracies in the tracer fields globally.

Because of these issues, a third-order upwind scheme was implemented for the advection of tracers. Numerical experiments show that this scheme is computationally efficient compared to alternatives (such as the flux-corrected transport scheme) and that it works well with other aspects of the model, such as acceleration (important for spinup efficiency) and the new mixing parameterizations. The scheme mimimizes overshooting effects while keeping the dissipative aspect of the advective operator reasonably small. The net effect is to produce solutions in which the large-scale fields are affected very little while local extrema are nearly (but not completely) removed, leading to physically much more realistic tracer patterns.

Full access