Abstract

A model of the convectively driven mixed layer is used to interpret BOMEX Phase III data. It is concluded that the compensating downdrafts and the moisture transports due to trade cumulus must be included explicitly in any theory of the dynamics of the tropical mixed layer.

Abstract

The effect of nonlinearities on a previously investigated coupled atmosphere–ocean basin mode is examined. The nonlinearity in the thermodynamic equation for sea surface temperature arises mainly from the dependence of subsurface temperature on the thermocline depth anomaly in the parameterization of entrainment into the mixed layer. This nonlinearity ultimately suppresses the linear growth of the unstable mode and equilibrates it at a finite amplitude. Because this nonlinearity acts differently for warm and cold states, the warm states are enhanced at finite amplitude. It is found that multiple equilibrium states appear as the coupling coefficient increases and as the reflection coefficient of the oceanic Rossby mode at the western boundary decreases. The finite-amplitude warm equilibrium state turns out to be stable, but the finite-amplitude cold state is unstable. The explicit inclusion of the dependence of the coupling strength on the warm and cold sea surface temperature anomalies modulates the sinusoidal-like oscillation and increases the period, but aperiodic solutions could not be obtained.

Abstract

The fundamental modes of oscillation of a coupled atmosphere–ocean basin system in the presence of a spatially varying oceanic basic state are investigated by formulating and solving an eigenvalue problem, thereby extending the work of Hirst. The model reduces essentially to the linearized Zebiak and Cane model as discussed by Battisti and Hirst. With conventionally chosen basic states, the unstable eigenmode closely resembles the El Niño–Southern Oscillation (ENSO) cycle in these models.

It is shown that the unstable low-frequency eigenfunction consists primarily of a Kelvin mode and a gravest equatorial Rossby mode, and the oscillation can be understood in particularly simple term essentially those proposed by Suarez and Schopf and others. The oscillatory nature of the ENSO cycle can be explained by a transition mechanism resulting from the interaction of these two equatorial (but not necessarily propagating) modes. A growing unstable positive wind anomaly in the central Pacific produces a growing eastward-propagating downwelling Kelvin mode and a growing westward-propagating upwelling equatorial Rossby mode. The down-welling Kelvin mode propagates eastward and enhances the growing warm phase of the ENSO. On the other hand, the upwelling Rossby mode propagates westward and produces an upwelling Kelvin mode via rejection at the western boundary. This growing Kelvin mode propagates to the central and eastern Pacific where it then grows without propagation, cools the warm anomaly, eventually changes the phase of the warm event to cold, and therefore switches the sign of the air–sea coupled instability in the eastern Pacific. The regular ENSO cycle is the repeated application of this mechanism.

The nature of the propagation of the ENSO anomalies is shown to be sensitive to the meridional profile of the upwelling velocity near the equator. The sea surface temperature (SST) anomaly changes synchronously (i.e., without propagation) in the eastern Pacific only if the entrainment velocity is tightly confined meridionally to the equator, while it begins to propagate eastward if the entrainment velocity expands in the meridional direction, all other parameters held constant.

In examining the parameter dependence of the unstable modes, it was found that two nonoscillatory solutions appear as a transition from the oscillatory solution as the air–sea coupling parameter and the Rayleigh friction parameter of the ocean are increased.

Abstract

Arakawa's recent parameterization of the effects of a cumulus ensemble on the large-scale environment is applied to the problem of conditional instability of the second kind (CISK). In particular, Charney's linear, two-level, line-symmetry CISK model of the ITCZ is re-examined using a simplified non-entraining cloud version of the Arakawa scheme. It is found that the growth rate is maximum, in fact infinite, at some reasonable mesoscale rather than at cumulus scale as is characteristic of Charney's solution. A more accurate semi-analytic model of CISK is considered and it is found that a separable, line-symmetric CISK solution is always possible under very general conditions. In both the two-level and semi-analytic models of CISK, it is proved that a necessary condition for the existence of a growing solution is that the mass flux into the clouds exceeds the Ekman pumping out of the boundary layer, or equivalently, that the air between the clouds must subside and therefore heat the environment by adiabatic compression.

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

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

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

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

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

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.