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## Abstract

A numerical model of a 6-level, baroclinic ocean with a flat bottom and a regular coast line extending from 51.25S to 48.75N is integrated over 125 years of simulated time using a finite-difference analog of the primitive equations. The surface atmospheric conditions which drive the circulation, both mechanically and thermally, are prescribed and depend on latitude only. The numerical integration is done in two phases. In the first phase (100 years), the temperature is predicted from the complete thermal energy equation, while the equations of horizontal motion are linear and the vertical mean current is constant in time. In the second phase (25 years), the complete primitive equations are used, and the coefficients of eddy viscosity and eddy conductivity are reduced.

Integration of the first phase produces western boundary currents in both hemispheres, a surface counter-current at 7N, an eastward undercurrent at the equator, and a narrow band of cold surface water along the equator which is maintained by a narrow belt of strong vertical velocities of the order of 200 cm day^{−1} at the bottom of the first layer. However, the calculated undercurrent and western boundary current speeds are only 25% as strong as those observed, and in the equatorial region the calculated thermocline is too deep.

The most interesting differences in the results of the two phases occur in equatorial regions where the eastward transport by the model undercurrent nearly doubled in the second phase. By comparing the under-current transport predicted by Gill's theory, with that obtained in the first and second phases, respectively, it is shown that density stratification increases the eastward transport by a factor of 4 while increased baroclinity and nonlinear effects increase the transport an additional 75% over the stratified case.

A calculation of the different modes of poleward heat transport in the second phase shows that the mean meridional circulation transports most of the heat, and that the eddies in both the vertical shear current and the vertical mean current transport heat equatorward. An analysis of the energy balance in the second phase of the model shows that, in the mean, kinetic energy is transformed into potential energy and that this is related to the thickness of the thermal boundary layer in the vicinity of the western boundary. There is also a positive, though small, transformation from the kinetic energy of the vertical shear flow to the kinetic energy of the vertical mean flow, which is related to the relatively large lateral eddy viscosity required by the coarse grid.

## Abstract

A numerical model of a 6-level, baroclinic ocean with a flat bottom and a regular coast line extending from 51.25S to 48.75N is integrated over 125 years of simulated time using a finite-difference analog of the primitive equations. The surface atmospheric conditions which drive the circulation, both mechanically and thermally, are prescribed and depend on latitude only. The numerical integration is done in two phases. In the first phase (100 years), the temperature is predicted from the complete thermal energy equation, while the equations of horizontal motion are linear and the vertical mean current is constant in time. In the second phase (25 years), the complete primitive equations are used, and the coefficients of eddy viscosity and eddy conductivity are reduced.

Integration of the first phase produces western boundary currents in both hemispheres, a surface counter-current at 7N, an eastward undercurrent at the equator, and a narrow band of cold surface water along the equator which is maintained by a narrow belt of strong vertical velocities of the order of 200 cm day^{−1} at the bottom of the first layer. However, the calculated undercurrent and western boundary current speeds are only 25% as strong as those observed, and in the equatorial region the calculated thermocline is too deep.

The most interesting differences in the results of the two phases occur in equatorial regions where the eastward transport by the model undercurrent nearly doubled in the second phase. By comparing the under-current transport predicted by Gill's theory, with that obtained in the first and second phases, respectively, it is shown that density stratification increases the eastward transport by a factor of 4 while increased baroclinity and nonlinear effects increase the transport an additional 75% over the stratified case.

A calculation of the different modes of poleward heat transport in the second phase shows that the mean meridional circulation transports most of the heat, and that the eddies in both the vertical shear current and the vertical mean current transport heat equatorward. An analysis of the energy balance in the second phase of the model shows that, in the mean, kinetic energy is transformed into potential energy and that this is related to the thickness of the thermal boundary layer in the vicinity of the western boundary. There is also a positive, though small, transformation from the kinetic energy of the vertical shear flow to the kinetic energy of the vertical mean flow, which is related to the relatively large lateral eddy viscosity required by the coarse grid.

## Abstract

A multilevel primitive equation, ocean circulation model with surface layer physics is used to study the interannual variability of sea surface temperatures (SST) in the central midlatitude North Pacific Ocean. Results from a 10-year model simulation (hindcast) driven by observed winds are analyzed and compared with observations.

The hindcast SSTs exhibit a significant amount of nonseasonal variability despite being damped toward a regular annual cycle by the thermal boundary condition at the surface. This variability is due to the horizontal and vertical redistribution of heat by currants and by parameterized turbulence processes caused by the winds. The resulting hindcast SST anomalies are correlated with observed SST anomalies at a statistically significant level over a large part of the central midlatitude North Pacific Ocean. This suggests that wind forcing by itself, through the mechanisms noted before, makes an important contribution to the development of SST anomalies in this area. The hindcast and observed SST anomalies do not compare well in the northwest and in the southeast part of the midlatitude North Pacific, suggesting that local wind forcing by itself is relatively unimportant for SST anomaly generation in these locations.

Throughout the midlatitude North Pacific, however, the hindcast SST anomalies are only about one-third as intense as the observed anomalies. It is suggested that this discrepancy is due to the absence of forcing by anomalous surface heat fluxes in the model hindcast.

## Abstract

A multilevel primitive equation, ocean circulation model with surface layer physics is used to study the interannual variability of sea surface temperatures (SST) in the central midlatitude North Pacific Ocean. Results from a 10-year model simulation (hindcast) driven by observed winds are analyzed and compared with observations.

The hindcast SSTs exhibit a significant amount of nonseasonal variability despite being damped toward a regular annual cycle by the thermal boundary condition at the surface. This variability is due to the horizontal and vertical redistribution of heat by currants and by parameterized turbulence processes caused by the winds. The resulting hindcast SST anomalies are correlated with observed SST anomalies at a statistically significant level over a large part of the central midlatitude North Pacific Ocean. This suggests that wind forcing by itself, through the mechanisms noted before, makes an important contribution to the development of SST anomalies in this area. The hindcast and observed SST anomalies do not compare well in the northwest and in the southeast part of the midlatitude North Pacific, suggesting that local wind forcing by itself is relatively unimportant for SST anomaly generation in these locations.

Throughout the midlatitude North Pacific, however, the hindcast SST anomalies are only about one-third as intense as the observed anomalies. It is suggested that this discrepancy is due to the absence of forcing by anomalous surface heat fluxes in the model hindcast.

## Abstract

The coefficients *A _{n}* and

*B*, and the percentage of the total height variance accounted for by each harmonic were computed for the first three longitudinal harmonics of 5-day mean 500-mb. height-contour charts at each 10° of latitude from 20° N. to 80° N. from December 1, 1959, to May 31, 1960. The phase angles and amplitudes of the first three harmonics were computed at 30° N., 50° N., and 70° N. and plotted as a function of time. Retrogression of the waves was found at high and low latitudes, while relatively stationary conditions prevailed at middle latitudes. The correlation coefficient between the contribution of the sum of the first three harmonics and the entire wave train was found to be almost +0.9.

_{n}## Abstract

The coefficients *A _{n}* and

*B*, and the percentage of the total height variance accounted for by each harmonic were computed for the first three longitudinal harmonics of 5-day mean 500-mb. height-contour charts at each 10° of latitude from 20° N. to 80° N. from December 1, 1959, to May 31, 1960. The phase angles and amplitudes of the first three harmonics were computed at 30° N., 50° N., and 70° N. and plotted as a function of time. Retrogression of the waves was found at high and low latitudes, while relatively stationary conditions prevailed at middle latitudes. The correlation coefficient between the contribution of the sum of the first three harmonics and the entire wave train was found to be almost +0.9.

_{n}## Abstract

A 10-level primitive equation ocean circulation model is used to investigate the formation and evolution of large-scale thermal anomalies in the central North Pacific Ocean during the fall and winter of 1976–77. A simplified parameterization of the effects of turbulent vertical mixing produced by wind stirring and surface cooling is included in the model. The numerical experiments consist of prescribed change experiments in which monthly mean ocean temperature anomalies, observed down to 400 m by the North Pacific Experiment (NORPAX), are used to define the prescribed changes (anomalies) in the initial conditions and observed monthly mean anomalies of surface winds, and surface heat fluxes are used to define the prescribed changes in the atmospheric forcing.

Oceanic processes are investigated by comparing several prescribed change experiments with observations. With anomalous wind forcing, horizontal advection by anomalous wind-driven surface (Ekman) currents and anomalous wind mixing contribute to the development of a large-scale cold anomaly in the upper 100 m of the central North Pacific in qualitative agreement with the observed anomaly development. The effects of anomalous horizontal advection are primarily confined to the upper 50 m while anomalous wind mixing produces strong cooling down to 125 m and warming below that. The inclusion of anomalous surface heat fluxes improves the simulation and is especially important for the development of a shallow warm anomaly to the east of the large-scale cold anomaly. In all the experiments the pattern correlation between simulated and observed temperature anomalies is greatest near the surface (r≈0.88) and decreases with depth (r≈0.25 at 262 m).

## Abstract

A 10-level primitive equation ocean circulation model is used to investigate the formation and evolution of large-scale thermal anomalies in the central North Pacific Ocean during the fall and winter of 1976–77. A simplified parameterization of the effects of turbulent vertical mixing produced by wind stirring and surface cooling is included in the model. The numerical experiments consist of prescribed change experiments in which monthly mean ocean temperature anomalies, observed down to 400 m by the North Pacific Experiment (NORPAX), are used to define the prescribed changes (anomalies) in the initial conditions and observed monthly mean anomalies of surface winds, and surface heat fluxes are used to define the prescribed changes in the atmospheric forcing.

Oceanic processes are investigated by comparing several prescribed change experiments with observations. With anomalous wind forcing, horizontal advection by anomalous wind-driven surface (Ekman) currents and anomalous wind mixing contribute to the development of a large-scale cold anomaly in the upper 100 m of the central North Pacific in qualitative agreement with the observed anomaly development. The effects of anomalous horizontal advection are primarily confined to the upper 50 m while anomalous wind mixing produces strong cooling down to 125 m and warming below that. The inclusion of anomalous surface heat fluxes improves the simulation and is especially important for the development of a shallow warm anomaly to the east of the large-scale cold anomaly. In all the experiments the pattern correlation between simulated and observed temperature anomalies is greatest near the surface (r≈0.88) and decreases with depth (r≈0.25 at 262 m).

## Abstract

No abstract available.

## Abstract

No abstract available.

## Abstract

The error in computing the pressure gradient force near steep topography using terms following (σ) coordinates is investigated in an ocean model using the family of vertical differencing schemes proposed by Arakawa and Suarez. The truncation error is estimated by substituting known buoyancy profiles into the finite difference hydrostatic and pressure gradient terms. The error due to “hydrostatic inconsistency,” which is not simply a space truncation error, is also documented. The results show that the pressure gradient error is spread throughout the water column, and it is sensitive to the vertical resolution and to the placement of the grid points relative to the vertical structure of the buoyancy field being modeled. Removing a reference state, as suggested for the atmosphere by Gary, reduces the truncation error associated with the two lowest vertical modes by a factor of 2 to 3. As an example, the error in computing the pressure gradient using a standard 10-level primitive equation model applied to buoyancy profiles and topographic slopes typical of the California Current region corresponds to a false geostrophic current of the order of 10–12 cm s^{−1}. The analogous error in a hydrostatically consistent 30-level model with the reference state removed is about an order of magnitude smaller.

## Abstract

The error in computing the pressure gradient force near steep topography using terms following (σ) coordinates is investigated in an ocean model using the family of vertical differencing schemes proposed by Arakawa and Suarez. The truncation error is estimated by substituting known buoyancy profiles into the finite difference hydrostatic and pressure gradient terms. The error due to “hydrostatic inconsistency,” which is not simply a space truncation error, is also documented. The results show that the pressure gradient error is spread throughout the water column, and it is sensitive to the vertical resolution and to the placement of the grid points relative to the vertical structure of the buoyancy field being modeled. Removing a reference state, as suggested for the atmosphere by Gary, reduces the truncation error associated with the two lowest vertical modes by a factor of 2 to 3. As an example, the error in computing the pressure gradient using a standard 10-level primitive equation model applied to buoyancy profiles and topographic slopes typical of the California Current region corresponds to a false geostrophic current of the order of 10–12 cm s^{−1}. The analogous error in a hydrostatically consistent 30-level model with the reference state removed is about an order of magnitude smaller.

## Abstract

By employing a heat budget analysis appropriate to zonally and time averaged conditions within the atmosphere, it is shown that the net downward heat flux *Q* at the ocean's surface can be expressed as *Q* = *Q*
_{2} (*T _{A}**–

*T*), where

_{s}*T** is an apparent atmospheric equilibrium temperature,

_{A}*T*the sea surface temperature, and

_{s}*Q*

_{2}a coefficient determined from the zonally and time averaged data. The latter coefficient, which is of the order of 70 ly day

^{−1}(°C)

^{−1}, varies with latitude by as much as 20%. It is suggested that the use of the above relation as a flux-type thermal boundary condition would allow for large-scale thermal coupling of ocean and atmosphere. The more common use of specified

*T*as a boundary condition clearly does not allow for such coupling.

_{s}## Abstract

By employing a heat budget analysis appropriate to zonally and time averaged conditions within the atmosphere, it is shown that the net downward heat flux *Q* at the ocean's surface can be expressed as *Q* = *Q*
_{2} (*T _{A}**–

*T*), where

_{s}*T** is an apparent atmospheric equilibrium temperature,

_{A}*T*the sea surface temperature, and

_{s}*Q*

_{2}a coefficient determined from the zonally and time averaged data. The latter coefficient, which is of the order of 70 ly day

^{−1}(°C)

^{−1}, varies with latitude by as much as 20%. It is suggested that the use of the above relation as a flux-type thermal boundary condition would allow for large-scale thermal coupling of ocean and atmosphere. The more common use of specified

*T*as a boundary condition clearly does not allow for such coupling.

_{s}## Abstract

The tendency equations for shear and curvature vorticity are interpreted as a function of the terms that modify speed and direction on in a fluid element. The tendency equations consistent with this interpretation do not contain time derivative on the right-hand side, and the interchange terms are kinematically independent of the shear and curvature vorticity tendencies. It is shown that an understanding of the anholonomic reference frame in which these equations are formulated, and the directional derivatives in this frame, is fundamental for the correct formulation and interpretation of the equations. Previous formulations, none of which have the above properties, are discussed and compared with those proposed here.

Since shear and curvature vorticity and their rate of change are not Galilean invariant quantities, the above equations only represent relationships between kinematic and dynamic quantities that hold when the different terms are referred to the same reference system. When the equations are referred to a system of axes fixed to the earth, the new results show that both shear and curvature vorticity tendencies depend explicitly on the earth's rotation, although only the curvature tendency depends on the beta effect.

The authors define the interchange between shear and curvature vorticity as the amount of vorticity that is cancelled when the shear and curvature tendencies are added. Except for special cases (e.g., when the flow is horizontally nondivergent and therefore relative vorticity is conserved) this interchange between shear and curvature vorticity cannot be identified with a unique collection of interchange terms on the right-hand side of the tendency equations.

## Abstract

The tendency equations for shear and curvature vorticity are interpreted as a function of the terms that modify speed and direction on in a fluid element. The tendency equations consistent with this interpretation do not contain time derivative on the right-hand side, and the interchange terms are kinematically independent of the shear and curvature vorticity tendencies. It is shown that an understanding of the anholonomic reference frame in which these equations are formulated, and the directional derivatives in this frame, is fundamental for the correct formulation and interpretation of the equations. Previous formulations, none of which have the above properties, are discussed and compared with those proposed here.

Since shear and curvature vorticity and their rate of change are not Galilean invariant quantities, the above equations only represent relationships between kinematic and dynamic quantities that hold when the different terms are referred to the same reference system. When the equations are referred to a system of axes fixed to the earth, the new results show that both shear and curvature vorticity tendencies depend explicitly on the earth's rotation, although only the curvature tendency depends on the beta effect.

The authors define the interchange between shear and curvature vorticity as the amount of vorticity that is cancelled when the shear and curvature tendencies are added. Except for special cases (e.g., when the flow is horizontally nondivergent and therefore relative vorticity is conserved) this interchange between shear and curvature vorticity cannot be identified with a unique collection of interchange terms on the right-hand side of the tendency equations.

## Abstract

It is shown, from hydrographic data, that the eastward flowing Atlantic jet (AJ) in the Alboran Sea has zero or positive relative vorticity. This holds even when the AJ curves anticyclonically around the western and eastern Alboran gyres. This feature is due to the presence of large positive shear vorticity mainly caused by the interaction between the AJ and the slow westward flow of Mediterranean Water on the northern side of the AJ. It is also shown that the AJ acquires negative curvature vorticity at the same time that it acquires positive shear vorticity at the exit of the Strait of Gibraltar. This feature is described in terms of a shear and curvature conversion. It is found that the cross-stream variation of alongstream geopotential differences is the main term in this vorticity interchange description of the AJ in the western Alboran Sea.

## Abstract

It is shown, from hydrographic data, that the eastward flowing Atlantic jet (AJ) in the Alboran Sea has zero or positive relative vorticity. This holds even when the AJ curves anticyclonically around the western and eastern Alboran gyres. This feature is due to the presence of large positive shear vorticity mainly caused by the interaction between the AJ and the slow westward flow of Mediterranean Water on the northern side of the AJ. It is also shown that the AJ acquires negative curvature vorticity at the same time that it acquires positive shear vorticity at the exit of the Strait of Gibraltar. This feature is described in terms of a shear and curvature conversion. It is found that the cross-stream variation of alongstream geopotential differences is the main term in this vorticity interchange description of the AJ in the western Alboran Sea.

## Abstract

The role of surface-generated mixing in determining the seasonal variation of the ocean thermal structure is investigated using a one-dimensional numerical model. The model contains vertical eddy diffusion with a constant coefficient *K _{H}* = 0.5 cm

^{2}s

^{−1}, an instantaneous convective adjustment mechanism as commonly used in oceanic general circulation models, and a simple parameterization of surface-generated wind and convective mixing based on recent mixed-layer theories. Forcing on the seasonal time scale is accomplished by prescribing the atmospheric solar radiation, longwave radiation, wind speed, temperature and dew point to vary sinusoidally with the annual period. Results of model integrations show that surface-generated wind and convective mixing are responsible for producing many features which are observed in the real ocean including the occurrence of two sea surface temperature maxima—one in summer and another in early fall.

## Abstract

The role of surface-generated mixing in determining the seasonal variation of the ocean thermal structure is investigated using a one-dimensional numerical model. The model contains vertical eddy diffusion with a constant coefficient *K _{H}* = 0.5 cm

^{2}s

^{−1}, an instantaneous convective adjustment mechanism as commonly used in oceanic general circulation models, and a simple parameterization of surface-generated wind and convective mixing based on recent mixed-layer theories. Forcing on the seasonal time scale is accomplished by prescribing the atmospheric solar radiation, longwave radiation, wind speed, temperature and dew point to vary sinusoidally with the annual period. Results of model integrations show that surface-generated wind and convective mixing are responsible for producing many features which are observed in the real ocean including the occurrence of two sea surface temperature maxima—one in summer and another in early fall.