Abstract

Several simple numerical experiments are conducted, using both single- and double-hemisphere ocean basins under symmetric steady forcing to study de ocean's thermohaline circulation. It is shown that a stable steady state obtained under a restoring surface boundary condition on salinity becomes unstable upon a switch to a flux boundary condition. The polar halocline catastrope of F. Bryan occurs. It is shown that further integration of this collapsed state ultimately yields a steady, stable one-cell circulation with the approach being essentially chaotic but with significant energy at decadal period. The two-hemisphere ocean passes through many stages in which violent overturning occurs O(80 × 10¹ m³ a⁻¹). These flushes occurs in both hemispheres and are of one-cell structure. The time period between them Bushes varies from seveal hundred to about one thousand years.

A single 12-vertical-level hemispheric basin, spun up from an initial state of rest under mixed boundary conditions (restoring boundary condition on temperature and flux boundary condition on salinity), never reaches a study gate. Three characteristic stages are observed in the integration: a stage where the system oscillates with decadal time scale, a stage when the system undergoes a violent overturning flush, and a Quiescent stage in which either deep water is forming or the themohaline circulation is in a collapsed state. These three characteristic stage are also present in 33 level single- and double-hemisphere runs. The decadal time wide is associated primarily with the advection of positive salinity anomalies into the region of deep-water formation from the midocean region between the subtropical and subpolar gyres. Upon increasing the resolution to 33 levels a steady is reached. The resulting steady state is fundamentally different from the one obtained under the same resolution and restoring boundary conditions in that it is more energetic and has much warmer basin mean temperature. These differences are due to a change in the location of deep-water formation.

The dependence of the results on the type a convection scheme used, vertical resolution and time-stepping procedure (synchronous or asynchronous integration) is also studied in order to separate physical processes from those that might be numerical artifacts. Sufficient vertical resolution is shown to be important in obtaining realistic models of the thermohaline circulation. It is shown that a steady state, which is stable under asynchronous integration and mixed boundary conditions may become unstable upon a switch to synchronous integration. It is also shown that the steady state obtained under restoring boundary conditions only changes slightly upon a switch to synchronous integration. Under mixed boundary conditions the steady state is shown to be very sensitive to the choice of surface tracer time step even while integrating asynchronously. Upon a Switch in this time step a polar halocline catastrophe way be induced.

The implications of the present study for future ocean climate modles are discussed.

Abstract

A series of numerical experiments is conducted with a three-dimensional ocean general circulation model and a two-dimensional counterpart both designed for efficient integration over diffusive (millennial) time scales. With strong steady salinity fluxes (salting at low latitudes and freshening at high), basin mean temperature and several other diagnostics show a series of self-sustaining oscillations. The oscillations termed deep decoupling oscillations, exhibit halocline catastrophes at regular intervals, followed by warming deep decoupled phases (when the deep overturning is weak), cooling flushes, and in the lower range of salinity forcing, a coupled phase when the deep ocean advective/diffusive heat balance is almost, but not quite, met. It is suggested that oscillations arise when a steady overturning circulation encounters a contradiction: the poleward salt and heat transport needed to maintain convection in the polar ocean requires more overturning than is consistent with the reduced thermocline depth that results. This hypothesis is supported by the sensitivity to variations in the vertical diffusivity: increased vertical diffusivity stabilizes oscillating solutions into steady, thermally direct circulations.

Although deep decoupling oscillations appear in both two- and three-dimensional models, they occur over a much broader range of forcing in the three-dimensional model. This is shown to be due to heat and salt transports by the horizontal plane (gyre) motions in the three-dimensional model that intensify in the upper polar ocean in response to the formation of a halocline and eventually destabilize it. Increasing the wind stress in the three-dimensional model and the horizontal diffusivity in the two-dimensional model stabilizes oscillating solutions. The amplitude, shape, and period of the oscillations are also sensitive to the strength of the salinity forcing.

Another kind of oscillation, termed a loop oscillation, with a smaller amplitude and an overturning time scale, is found in some of the more weakly forced experiments with both models. These oscillations are shown to be a result of the advection of salinity anomalies by the deep overturning, affecting its strength in a manner that leads to their further amplification by feedback from the salinity flux boundary condition. A simple thermohaline loop model demonstrates the essential advective mechanism for this kind of oscillation.

Abstract

A two-dimensional (in a vertical and meridional plane) model for steady equatorial undercurrents is described. Compared to the primitive equation model, the zonal pressure gradient and associated zonal temperature gradients (both vary vertically) are prescribed in this model, and all other terms involving zonal variations are ignored. With zonal pressure gradients resembling actual ocean gradients, model undercurrents agree well with observations as far as the main features are concerned. In particular, the model simulates a stronger undercurrent in the Pacific than in the Atlantic, suggesting that a weaker zonal wind stress, a shallower thermocline, a more surface-confined zonal pressure gradient, and an associated larger magnitude of near-surface zonal temperature gradient around 30°W in the Atlantic than around 150°W in the Pacific, which is related to the longitudinal structure of the zonal wind stress and longitudinal basin extent, are the cause of this difference. An argument based on geostrophy and heat balance is also given.

The model is used to examine the dynamic nature and heat balance of steady equatorial undercurrents for a symmetric circulation about the equator. With a full, nonlinear heat balance, an undercurrent is generated in both linear and nonlinear dynamic balances, but the dynamical features are different in the two cases. In the nonlinear dynamic case, vertical-momentum transports play a key role; in the linear dynamic case, though the eastward zonal pressure gradient provides a necessary forcing, the existence of the undercurrent also relies on the meridional diffusive momentum transport near the surface, which is positive instead of negative. For a doubling of zonal wind stress and a fixed vertical profile of zonal pressure gradient, the speed of the undercurrent core increases by about 25% in the nonlinear case but remains unchanged in the linear case; surface temperature increases by about 1.3 K in the nonlinear case and decreases by 3 K in the linear case.

Within the undercurrent core, the dominant momentum balance is between the zonal pressure gradient and meridional diffusive friction, and the heat balance is between zonal and vertical advections. It is proposed that the position of the undercurrent core relative to the thermocline reflects different advective heat balances: the undercurrent core is above (or below) the thermocline if the net heat advection balance tends to heat (or cool). The fact that the undercurrent core is more or less in the thermocline suggests that three-dimensional advective heat transports almost cancel each other.

Abstract

No abstract available.

Abstract

In order to test certain aspects of the ENSO mechanism proposed by Suarez and Schopf and by Battisti and Hirst, we force a shallow water ocean with 28 years of observed (FSU) winds and decompose both the atmospheric forcing and ocean response into equatorial modes.

The proposed mechanism was verified in the following sense. For each warm phase of the cycle, a downwelling Kelvin mode directly forced by the weakening of the trade winds in the central Pacific was found. The same wind anomaly forces an upwelling gravest Rossby mode which propagates freely westward and reflects as a freely propagating Kelvin mode at the western boundary. This Kelvin mode returns to the scene of the original warming and acts as a retarded forcing (of opposite sign) eventually switching the phase of the oscillation from warm to cold. The cold phase then proceeds by the same mechanism but with modes of opposite signs, to eventually switch to the warm phase.

The contribution of the higher Rossby modes to this process is estimated. It is found that almost all the Kelvin response in the western Pacific results from the reflection of the gravest symmetric equatorial Rossby mode so that the ENSO cycle is defined by the interaction of only two ocean modes, the Kelvin and lowest Rossby mode. These modes are sometimes forced directly by the wind as part of an intrinsic coupled atmosphere–ocean mode and sometimes propagate freely where the wind forcing is negligible. The distinction between these two manifestations of the ocean modes is of the greatest importance and is stressed throughout the paper.

The case of the warm event of 1976 is an interesting example of the failure of the switching mechanism, and is discussed in the conclusion.

Abstract

In centered difference models of ocean circulation, two grid-point computational modes can be excited if grid Reynolds and Peclet numbers are greater than two. The Bryan-Cox General Circulation Model (GCM) is used to show the dramatic effect that this instability has on the equatorial thermohaline circulation. In many recent numerical calculations researchers have used 12 vertical levels. It is shown that this resolution produces an artificial cell at the equator when typical values of the vertical diffusivity and viscosity parameters are used. This artifical cell rotates counter to the primary cell driven by deep water formation at high latitudes, is driven by downwelling at the eastern boundary near the equator and is 40% the strength of the primary cell for the parameters used in the present study. When the vertical resolution is increased the cell vanishes. It is suggested therefore that higher vertical resolution should be used in Bryan-Cox GCM deep-ocean modeling studies when current values of the vertical diffusivity and viscosity parameters are used.

Abstract

The implicit vertical diffusion (IVD) convective adjustment scheme in common use in ocean general circulation models (OGCMs) could have large residual static gravitational instability at each time step. An iterative and explicit scheme is devised, based on similar physical considerations as the ones for the IVD scheme. It guarantees a complete removal of static instability in a vertical water column and is more efficient than the IVD scheme in overall spinup of the model.

The two convective schemes are compared in an ocean model that is in a state of interdecadal limit cycles. While the model solution with either of these two schemes is characterized by interdecadal oscillations, the variability is different in each scheme. The primary oscillation has a period of about 11 years, but the basin mean kinetic energy shows large differences. The 11-year cycle is modulated by a 33-year oscillation with the IVD scheme, while it is modulated by a 22-year cycle with the complete scheme. The amplitude of the variation of kinetic energy with the IVD scheme is also about twice as large as that with a complete adjustment scheme. It is therefore suggested that complete and incomplete convective schemes can lead to different model variability when convective changes in temperature and salinity have large variations over a short period of time.

Abstract

Oceanic interdecadal thermohaline oscillations are investigated with a coarse-resolution version of the Geophysical Fluid Dynamics Laboratory Modular Ocean Model. The geometry of the model is a box with a depth of 5000 m and a longitudinal width of 60°, spanning latitudes from 14.5° to 66.5°N. The model ocean is forced by a zonal wind stress, a heat flux parameterized by restoring the surface temperature toward a reference value, and a specified surface freshwater flux. Zonal wind stress, reference temperature, and freshwater flux are all longitudinally uniform, time-independent, and vary meridionally.

It is shown that the ocean model can be in a state of interdecadal oscillations, and a physical mechanism is explained. For these oscillatory solutions, both surface mean heat flux and basin mean kinetic energy vary with interdecadal periods. Temperature and salinity budget analyses reveal that these oscillations depend primarily on advective and convective processes. Horizontal advective heat transports from the subtropical region warm the subsurface water in the subpolar region, destablize the water column, and thereby enhance convection. Convection, in turn, induces surface cyclonic and equatorward flows, which, together with horizontal diffusion and surface freshwater input, transport subpolar fresh water into convecting regions, subsequently weakening or suppressing convection. During an oscillation, convection vertically homogenizes the water column, increases the surface salinity, creates a larger meridional gradient of surface salinity, and increases the efficiency of surface advective freshening in the convective region. The periodic strengthening and weakening of convection caused by subsurface advective warming and surface freshening in the subpolar region results in model interdecadal oscillations.

These advective and convective interdecadal oscillations are not sensitive to either the detailed distribution of subpolar freshwater flux or the horizontal diffusivity. They are mainly a result of halocline and inverted thermocline structure in the subpolar region, maintained by horizontal advective subsurface heating and surface freshening processes.

Abstract

Seasonal heat transport is examined in a simple, linear shallow-water model on the equatorial beta plane. It is found in this model that meridional transport by the seasonally varying western boundary current is of the same magnitude but opposite phase to the seasonally varying interior transport and therefore tends to cancel.

Abstract

Restoring boundary conditions, wherein the temperature and salinity are restored to surface target fields of temperature and salinity, are traditionally used for studies of the ocean circulation in ocean general circulation models. The canonical problem with these boundary conditions is that, when the target fields are chosen as the observed fields, accurate simulation of the surface fields of temperature and salinity would imply that the surface fluxes and therefore the ocean heat transports approach zero, a clearly unrealistic situation. It is clear that the target fields cannot be chosen as the observed fields. A simple but effective method of modifying conventional restoring boundary conditions is introduced, designed to keep the calculated values of surface temperature and salinity as close to observations as possible. The technique involves calculating the optimal target fields in the restoring boundary conditions by an iterative procedure. The method accounts for oceanic processes, such as advection and eddy mixing in the derivation of the new boundary conditions. A reduced version of this method is introduced that produces comparable results but offers greater simplicity in implementation. The simplicity of the method is particularly attractive in idealized studies, which often employ restoring surface boundary conditions. The success of the new method is, however, limited by several factors that cannot be easily compensated by the adjustment of the target profiles. These factors include inaccurate model dynamics, errors in the observations, and the too-simplified form of restoring surface boundary conditions themselves. The application of the method in this study with a coarse-resolution model leads to considerable improvements of the simulation of sea surface temperature (SST) and sea surface salinity (SSS). Both amplitude and phase of the annual cycle in SST greatly improve. The resulting magnitudes of surface heat and freshwater fluxes increase on average, and the meridional heat transport gets stronger. However, the fluxes in some regions remain unrealistic, notably the too-strong freshwater forcing of the western boundary currents in the Northern Hemisphere. Southern Ocean cooling and freshening are also likely to be too strong. The subsurface values of temperature improve greatly, proving that a large part of errors in the subsurface temperature distribution in our model can be corrected by reducing errors at the surface. In contrast, the reduction of errors in surface salinity fails to improve uniformly the simulated subsurface salinity values.