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The Role of Mixed Boundary Conditions in Numerical Models of the Ocean's Climate

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  • 1 Department of Meteorology, McGill University, Montreal, Quebec, Canada
  • | 2 Joint Institude for the study of the Atmosphere and Ocean, University of Washington, Seattle, Washington
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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 × 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

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.

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