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## 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

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.

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## 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

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.

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## 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 × 10^{1} m^{3} 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

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 × 10^{1} m^{3} 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.

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## 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 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.

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## 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 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.

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## 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

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.

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## 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.

## 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.

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## Abstract

The authors identify and describe the important dynamical mechanisms that explain the significant sensitivity of the Atlantic thermohaline circulation to the parameterization of heat and salt transports by mesoscale eddies in numerical models. In particular, the effects of the Gent–McWilliams (GM) scheme, which has a strong flattening effect on isopycnals, and a simple horizontal diffusion scheme are considered and compared. Two control runs, one with each scheme, exhibit very different circulations and density structures. To analyze the dynamical reasons for the differences between the control runs, a number of numerical experiments with regionally varying diffusion coefficients are carried out, emphasizing the effects of different schemes in key regions. The main effect of eddies in the Southern Ocean in nature is to shoal the subsurface isopycnal surfaces, thus increasing the density of the northward inflow of relatively dense intermediate waters into the Atlantic—as will be seen, this is more effectively done by the GM parameterization of the eddies. The resulting increase in the subsurface density at low latitudes decreases the meridional density contrast with the high latitudes of the North Atlantic, shoals the pycnocline, and consequently weakens the meridional overturning. By contrast, the effect of the eddy transports in the western boundary current in the Northern Hemisphere on the strength of the North Atlantic Deep Water (NADW) formation is shown to be smaller. The Northern Hemisphere upwelling and horizontal flow structure is strongly affected by local eddy transports, and the outflow of the NADW is very sensitive to the Northern Hemisphere eddy transports as a result. The original scaling of Gnanadesikan is modified to include the effects of horizontal mixing in low latitudes. The results confirm the leading role of the Southern Ocean eddies in affecting the strength of NADW formation, while the Northern Hemisphere horizontal mixing mostly affects local upwelling. The eddy transports in the Southern Ocean also affect the properties of Antarctic Bottom Water, which influences the vertical penetration of the NADW overturning cell as well as the density of the deep ocean.

## Abstract

The authors identify and describe the important dynamical mechanisms that explain the significant sensitivity of the Atlantic thermohaline circulation to the parameterization of heat and salt transports by mesoscale eddies in numerical models. In particular, the effects of the Gent–McWilliams (GM) scheme, which has a strong flattening effect on isopycnals, and a simple horizontal diffusion scheme are considered and compared. Two control runs, one with each scheme, exhibit very different circulations and density structures. To analyze the dynamical reasons for the differences between the control runs, a number of numerical experiments with regionally varying diffusion coefficients are carried out, emphasizing the effects of different schemes in key regions. The main effect of eddies in the Southern Ocean in nature is to shoal the subsurface isopycnal surfaces, thus increasing the density of the northward inflow of relatively dense intermediate waters into the Atlantic—as will be seen, this is more effectively done by the GM parameterization of the eddies. The resulting increase in the subsurface density at low latitudes decreases the meridional density contrast with the high latitudes of the North Atlantic, shoals the pycnocline, and consequently weakens the meridional overturning. By contrast, the effect of the eddy transports in the western boundary current in the Northern Hemisphere on the strength of the North Atlantic Deep Water (NADW) formation is shown to be smaller. The Northern Hemisphere upwelling and horizontal flow structure is strongly affected by local eddy transports, and the outflow of the NADW is very sensitive to the Northern Hemisphere eddy transports as a result. The original scaling of Gnanadesikan is modified to include the effects of horizontal mixing in low latitudes. The results confirm the leading role of the Southern Ocean eddies in affecting the strength of NADW formation, while the Northern Hemisphere horizontal mixing mostly affects local upwelling. The eddy transports in the Southern Ocean also affect the properties of Antarctic Bottom Water, which influences the vertical penetration of the NADW overturning cell as well as the density of the deep ocean.

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## Abstract

Four different datasets of monthly mean new-equatorial Pacific sea surface temperature for 1982–83 are compared, and the space-time regions for which there was consensus that cooling or warming took place, are determined. There was consensus that warming took place east of the date line, averaged over the period July-December 1982, and that the warming progressed eastward from the central Pacific. There was also consensus that weak cooling took place in April 1983, and that substantial cooling occurred in June-July 1983, generally over the central and eastern Pacific. However, the analyses tend to agree on the sign of SST change only in periods of cooling or warming in excess of 1°C/month; quantitative agreement at the level of 0.5°C/month or better is almost never found.

SST changes in five ocean-circulation model hindcasts of the 1982–83 period (differing only in that each used a different analyzed monthly mean surface wind stress field to drive the ocean), are compared with the observations and with each other. There is agreement that net warming occurred in the July-December 1982 period and cooling in mid-1983. The heat budgets of these experiments indicate that the major model central Pacific warmings occurred primarily from anomalous eastward surface advection of warm water. Further, east zonal advection remains significant but a diminished cooling tendency from meridional advection can also be important; different hindcasts differ on the relative importance of these terms. Surface heat flux changes do not contribute to the warmings. The reduced cooling tendency from meridional advection is consistent with diminished surface Ekman divergence, suggesting that southward transport of warm north equatorial counter current water was not a major factor in the model warmings. The hindcasts do not agree on the relative importance of local or remote forcing of the eastward surface currents; while there is clear evidence of remote forcing in some hindcasts in particular regions, local forcing is also often significant. The main 1983 midocean cooling began because of increased vertical advection of cool water; but once cooling began horizontal advection often contributed. Further east, where the easterlies generally return later than they do in midocean, upwelling and horizontal advection all can be important. Again no model consensus exists concerning the details of SST evolution.

Because the observations do not agree on the sign of SST change during much of the 1982–83 period, improved SST data is needed in order to document the behavior of the ocean through future ENSO periods. Better forcing data will be needed to carry out improved ocean-model validation studies, and to explore the mechanisms likely responsible for SST change through entire ENSO cycles.

## Abstract

Four different datasets of monthly mean new-equatorial Pacific sea surface temperature for 1982–83 are compared, and the space-time regions for which there was consensus that cooling or warming took place, are determined. There was consensus that warming took place east of the date line, averaged over the period July-December 1982, and that the warming progressed eastward from the central Pacific. There was also consensus that weak cooling took place in April 1983, and that substantial cooling occurred in June-July 1983, generally over the central and eastern Pacific. However, the analyses tend to agree on the sign of SST change only in periods of cooling or warming in excess of 1°C/month; quantitative agreement at the level of 0.5°C/month or better is almost never found.

SST changes in five ocean-circulation model hindcasts of the 1982–83 period (differing only in that each used a different analyzed monthly mean surface wind stress field to drive the ocean), are compared with the observations and with each other. There is agreement that net warming occurred in the July-December 1982 period and cooling in mid-1983. The heat budgets of these experiments indicate that the major model central Pacific warmings occurred primarily from anomalous eastward surface advection of warm water. Further, east zonal advection remains significant but a diminished cooling tendency from meridional advection can also be important; different hindcasts differ on the relative importance of these terms. Surface heat flux changes do not contribute to the warmings. The reduced cooling tendency from meridional advection is consistent with diminished surface Ekman divergence, suggesting that southward transport of warm north equatorial counter current water was not a major factor in the model warmings. The hindcasts do not agree on the relative importance of local or remote forcing of the eastward surface currents; while there is clear evidence of remote forcing in some hindcasts in particular regions, local forcing is also often significant. The main 1983 midocean cooling began because of increased vertical advection of cool water; but once cooling began horizontal advection often contributed. Further east, where the easterlies generally return later than they do in midocean, upwelling and horizontal advection all can be important. Again no model consensus exists concerning the details of SST evolution.

Because the observations do not agree on the sign of SST change during much of the 1982–83 period, improved SST data is needed in order to document the behavior of the ocean through future ENSO periods. Better forcing data will be needed to carry out improved ocean-model validation studies, and to explore the mechanisms likely responsible for SST change through entire ENSO cycles.

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## Abstract

In this paper, the atmospheric circulations on an equatorial beta plane in response to steady tropical heating are investigated by analytically solving a set of linear equations. Special emphasis is placed on the horizontal structure of forced response under the different combinations of momentum damping and thermal damping, as well as the effect of the zonal domain on the forced responses. Two zonal domains are considered: a zonally cyclic domain and a zonally unbounded domain.

The linear model is decomposed in terms of the vertical eigenfunctions in a vertically semi-infinite domain. A new feature of the solution is the existence of a continuous spectrum corresponding to energy propagation out the top of the troposphere. The resulting shallow-water equations are then solved using a method similar to that of Gill.

Since the zonal decay scale is proportional to the inverse of the square root of the product of the Rayleigh friction rate and the Newtonian cooling rate, the solutions in a zonally unbounded domain can be good approximations for the solutions in a zonally cyclic domain only when both Rayleigh friction and Newtonian cooling are large enough. When either Rayleigh friction or Newtonian cooling is very weak, the solutions are essentially zonally uniform regardless of the longitudinal location of the heat source in a zonally cyclic domain except in a very narrow zone along the equator.

The characteristic meridional scale of the shallow-water system is the equatorial radius of deformation of the shallow-water system multiplied by the fourth root of the ratio between the Rayleigh friction rate and the Newtonian cooling rate. Therefore, the characteristic meridional scale is very large for the Rayleigh friction–dominant case, and the forced response can extend far outside the heating latitude. In contrast, in the Newtonian cooling–dominant case the characteristic meridional scale is very small and the forced response is confined to the heating latitudes.

The implications of these solutions for both the thermally driven surface winds and the zonally uniform low-frequency variation in pressure and temperature in the upper half of the tropical troposphere are also discussed.

## Abstract

In this paper, the atmospheric circulations on an equatorial beta plane in response to steady tropical heating are investigated by analytically solving a set of linear equations. Special emphasis is placed on the horizontal structure of forced response under the different combinations of momentum damping and thermal damping, as well as the effect of the zonal domain on the forced responses. Two zonal domains are considered: a zonally cyclic domain and a zonally unbounded domain.

The linear model is decomposed in terms of the vertical eigenfunctions in a vertically semi-infinite domain. A new feature of the solution is the existence of a continuous spectrum corresponding to energy propagation out the top of the troposphere. The resulting shallow-water equations are then solved using a method similar to that of Gill.

Since the zonal decay scale is proportional to the inverse of the square root of the product of the Rayleigh friction rate and the Newtonian cooling rate, the solutions in a zonally unbounded domain can be good approximations for the solutions in a zonally cyclic domain only when both Rayleigh friction and Newtonian cooling are large enough. When either Rayleigh friction or Newtonian cooling is very weak, the solutions are essentially zonally uniform regardless of the longitudinal location of the heat source in a zonally cyclic domain except in a very narrow zone along the equator.

The characteristic meridional scale of the shallow-water system is the equatorial radius of deformation of the shallow-water system multiplied by the fourth root of the ratio between the Rayleigh friction rate and the Newtonian cooling rate. Therefore, the characteristic meridional scale is very large for the Rayleigh friction–dominant case, and the forced response can extend far outside the heating latitude. In contrast, in the Newtonian cooling–dominant case the characteristic meridional scale is very small and the forced response is confined to the heating latitudes.

The implications of these solutions for both the thermally driven surface winds and the zonally uniform low-frequency variation in pressure and temperature in the upper half of the tropical troposphere are also discussed.