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- Author or Editor: Peter D. Killworth x
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Abstract
The large-scale two-dimensional rheology of a sea ice pack arises from the local contact forces between adjacent does in convergence. It is conventionally modeled by a viscous-plastic constitutive relation to reflect the low or zero stress in a divergent flow field and the rate-independent ridging process in convergence. The authors demonstrate how, for a simple one-dimensional configuration, the elliptical yield curve results in tensile in-plane stresses in divergence that cause a short wave length linear instability. As the ice pack diverges, the ice strength, which is the root cause of the instability, is rapidly reduced, and so, although the model is linearly unstable, it is nonlinearly stable. The practical significance is that the model does not blow up, but systematic grid size-dependent errors associated with the linear instability are introduced throughout the pack. Artificial diffusion terms can be used to prevent the growth of the linear instability. Numerical models must almost always possess artificial diffusion to permit them to run. Here, however, the diffusion is necessary to overcome physical inaccuracies in the model. Diffusion alone is not even a total cure. Generally, diffusive coefficients shrink as a power of the grid size, so as model resolution becomes finer, a previously stable algorithm will become unstable. The problem can be properly posed by constraining the yield curve to lie within the third quadrant of principal stress space.
Abstract
The large-scale two-dimensional rheology of a sea ice pack arises from the local contact forces between adjacent does in convergence. It is conventionally modeled by a viscous-plastic constitutive relation to reflect the low or zero stress in a divergent flow field and the rate-independent ridging process in convergence. The authors demonstrate how, for a simple one-dimensional configuration, the elliptical yield curve results in tensile in-plane stresses in divergence that cause a short wave length linear instability. As the ice pack diverges, the ice strength, which is the root cause of the instability, is rapidly reduced, and so, although the model is linearly unstable, it is nonlinearly stable. The practical significance is that the model does not blow up, but systematic grid size-dependent errors associated with the linear instability are introduced throughout the pack. Artificial diffusion terms can be used to prevent the growth of the linear instability. Numerical models must almost always possess artificial diffusion to permit them to run. Here, however, the diffusion is necessary to overcome physical inaccuracies in the model. Diffusion alone is not even a total cure. Generally, diffusive coefficients shrink as a power of the grid size, so as model resolution becomes finer, a previously stable algorithm will become unstable. The problem can be properly posed by constraining the yield curve to lie within the third quadrant of principal stress space.
Abstract
This paper discusses the errors in surface tracer and flux fields in ocean models induced by using approximate surface boundary conditions involving relaxation toward observed values rather than more physically realistic conditions that involve (often inaccurate) surface fluxes. The authors show theoretically and with a global model example that where there is a net annual surface flux of tracer (balanced by advection), (i) the annual mean surface tracer field is biased compared with the observations and (ii) the annual mean tracer flux is also biased if the surface tracer field has a feedback on the surface tracer advection or diffusion. As previously shown, the amplitude of the annual cycle of tracers is also decreased. The global model indicates that temperature offsets of 1°–2°C (or even greater) and heat flux errors of 30 W m−2 occur in regions of strong advection, such as the equatorial upwelling zone, western boundary currents, and the Antarctic Circumpolar Current. These are all areas crucial for the thermohaline circulation, so that the use of such boundary conditions is likely to yield incorrect estimates for climate simulation models. Zonally integrated meridional heat fluxes may be in error by up to 25%.
Abstract
This paper discusses the errors in surface tracer and flux fields in ocean models induced by using approximate surface boundary conditions involving relaxation toward observed values rather than more physically realistic conditions that involve (often inaccurate) surface fluxes. The authors show theoretically and with a global model example that where there is a net annual surface flux of tracer (balanced by advection), (i) the annual mean surface tracer field is biased compared with the observations and (ii) the annual mean tracer flux is also biased if the surface tracer field has a feedback on the surface tracer advection or diffusion. As previously shown, the amplitude of the annual cycle of tracers is also decreased. The global model indicates that temperature offsets of 1°–2°C (or even greater) and heat flux errors of 30 W m−2 occur in regions of strong advection, such as the equatorial upwelling zone, western boundary currents, and the Antarctic Circumpolar Current. These are all areas crucial for the thermohaline circulation, so that the use of such boundary conditions is likely to yield incorrect estimates for climate simulation models. Zonally integrated meridional heat fluxes may be in error by up to 25%.
Abstract
An eddy-permitting numerical ocean model is used to investigate the variability of the meridional overturning circulation (MOC). Both wind stress and fluctuations of the seawater density contribute to MOC changes on subannual and seasonal time scales, whereas the interannual variability mainly reflects changes in the density field. Even on subannual and seasonal time scales, a significant fraction of the total MOC variability is due to changes of the density field in the upper 1000 m of the ocean. These changes reflect perturbations of the isopycnal structure that travel westward as Rossby waves. Because of a temporally changing phase difference between the eastern and western boundaries, the Rossby waves affect the MOC by modifying the basinwide east–west density gradient. Both the numerical model used in this study and calculations based on Rossby wave theory suggest that this effect can account for an MOC variability of several Sverdrups (Sv ≡ 106 m3 s−1). These results have implications for the interpretation of variability signals inferred from hydrographic sections and might contribute to the understanding of the results obtained from the Rapid Climate Change (RAPID) monitoring array deployed at 26°N in the North Atlantic Ocean.
Abstract
An eddy-permitting numerical ocean model is used to investigate the variability of the meridional overturning circulation (MOC). Both wind stress and fluctuations of the seawater density contribute to MOC changes on subannual and seasonal time scales, whereas the interannual variability mainly reflects changes in the density field. Even on subannual and seasonal time scales, a significant fraction of the total MOC variability is due to changes of the density field in the upper 1000 m of the ocean. These changes reflect perturbations of the isopycnal structure that travel westward as Rossby waves. Because of a temporally changing phase difference between the eastern and western boundaries, the Rossby waves affect the MOC by modifying the basinwide east–west density gradient. Both the numerical model used in this study and calculations based on Rossby wave theory suggest that this effect can account for an MOC variability of several Sverdrups (Sv ≡ 106 m3 s−1). These results have implications for the interpretation of variability signals inferred from hydrographic sections and might contribute to the understanding of the results obtained from the Rapid Climate Change (RAPID) monitoring array deployed at 26°N in the North Atlantic Ocean.
Abstract
The study of barotropic structure and its effects on oceanic ring stability has yielded seemingly conflicting results. Some studies suggest that the stability of a given ring profile is as sensitive to the sense of the barotropic mode as it is to the vertical shear, while others suggest the vertical shear is the sole dominant effect. Here numerical evidence that supports both views is presented. Warm rings with a favorable barotropic structure can retain their monopole nature while cold rings do not. These results are of interest given the observed long lifetimes of oceanic rings.
As evidence a series of initial value integrations is presented. The initial ring profile consists of an exponential profile decaying as the cube of the radial distance, rather than as the squared decay law of the commonly used Gaussian. The reasons for this choice are that previous studies have examined the Gaussian initial condition extensively and recent analysis suggests the Gaussian profile has special stability properties.
The authors find that the barotropic mode affects the coherence of warm rings, yielding essentially stable, monopolar structures for the case that the initial deep flow is in the same sense as the surface flow (i.e., in the“co-rotating” case), even if the initial underlying ring is linearly unstable. Thus, warm rings remain dominantly monopolar, although an underlying, weak tripole is often seen in the final state. Cold rings in the oceanic parameter regime, on the other hand, experience no such stabilizing effects from deep structure. Quasigeostrophic dynamics fails to capture the stabilization tendencies of warm rings with corotating deep flow, suggesting the effect is related to the finite-amplitude thickness changes of a warm ring. The transition from an unstable, warm monopolar initial state to an effectively stable, warm initial monopolar state is a sensitive function of the barotropic mode. Finally, beta-plane experiments demonstrate the robustness of the primitive equation result.
Thus, it is suggested that the barotropic component of a warm ring can enhance ring stability as a monopole by providing for the existence of a nearby tripolar state to which the ring evolves and thereafter remains. The observed stability of cold rings, however, remains a mystery.
Abstract
The study of barotropic structure and its effects on oceanic ring stability has yielded seemingly conflicting results. Some studies suggest that the stability of a given ring profile is as sensitive to the sense of the barotropic mode as it is to the vertical shear, while others suggest the vertical shear is the sole dominant effect. Here numerical evidence that supports both views is presented. Warm rings with a favorable barotropic structure can retain their monopole nature while cold rings do not. These results are of interest given the observed long lifetimes of oceanic rings.
As evidence a series of initial value integrations is presented. The initial ring profile consists of an exponential profile decaying as the cube of the radial distance, rather than as the squared decay law of the commonly used Gaussian. The reasons for this choice are that previous studies have examined the Gaussian initial condition extensively and recent analysis suggests the Gaussian profile has special stability properties.
The authors find that the barotropic mode affects the coherence of warm rings, yielding essentially stable, monopolar structures for the case that the initial deep flow is in the same sense as the surface flow (i.e., in the“co-rotating” case), even if the initial underlying ring is linearly unstable. Thus, warm rings remain dominantly monopolar, although an underlying, weak tripole is often seen in the final state. Cold rings in the oceanic parameter regime, on the other hand, experience no such stabilizing effects from deep structure. Quasigeostrophic dynamics fails to capture the stabilization tendencies of warm rings with corotating deep flow, suggesting the effect is related to the finite-amplitude thickness changes of a warm ring. The transition from an unstable, warm monopolar initial state to an effectively stable, warm initial monopolar state is a sensitive function of the barotropic mode. Finally, beta-plane experiments demonstrate the robustness of the primitive equation result.
Thus, it is suggested that the barotropic component of a warm ring can enhance ring stability as a monopole by providing for the existence of a nearby tripolar state to which the ring evolves and thereafter remains. The observed stability of cold rings, however, remains a mystery.
Abstract
The design and implementation of a midlatitude basin-scale coupled climate model are described. The development of the model is motivated by the clear indications of important low-frequency midlatitude ocean variability in ocean-only models and the lack of the same in coupled climate models. Currently, the best comprehensive coupled climate models run at resolutions far coarser than those needed to model intrinsic ocean variability. The model presented here is an attempt to explicitly include ocean eddies within the framework of an idealized climate setting. It is proposed that the model will help resolve how intrinsic ocean variability is altered by coupling and the extent to which such variability may force the climate. The objective of this paper is to describe the theory behind the model formulation and its implementation.
The basic model consists of a quasigeostrophic channel atmosphere coupled to a simple, rectangular quasigeostrophic ocean. Heat and momentum exchanges between the ocean and the atmosphere are mediated via mixed-layer models, and the system is driven by steady, latitudinally dependent incident solar radiation. Model spinup is described, some basic descriptors of the solution are discussed, and it is argued that the model exhibits skill in capturing essential features of the midlatitude climate system.
Abstract
The design and implementation of a midlatitude basin-scale coupled climate model are described. The development of the model is motivated by the clear indications of important low-frequency midlatitude ocean variability in ocean-only models and the lack of the same in coupled climate models. Currently, the best comprehensive coupled climate models run at resolutions far coarser than those needed to model intrinsic ocean variability. The model presented here is an attempt to explicitly include ocean eddies within the framework of an idealized climate setting. It is proposed that the model will help resolve how intrinsic ocean variability is altered by coupling and the extent to which such variability may force the climate. The objective of this paper is to describe the theory behind the model formulation and its implementation.
The basic model consists of a quasigeostrophic channel atmosphere coupled to a simple, rectangular quasigeostrophic ocean. Heat and momentum exchanges between the ocean and the atmosphere are mediated via mixed-layer models, and the system is driven by steady, latitudinally dependent incident solar radiation. Model spinup is described, some basic descriptors of the solution are discussed, and it is argued that the model exhibits skill in capturing essential features of the midlatitude climate system.
Abstract
A midlatitude coupled ocean–atmosphere model is used to investigate interactions between the atmosphere and the wind-driven ocean circulation. This model uses idealized geometry, yet rich and complicated dynamic flow regimes arise in the ocean due to the explicit simulation of geostrophic turbulence. An interdecadal mode of intrinsic ocean variability is found, and this mode projects onto existing atmospheric modes of variability, thereby controlling the time scale of the atmospheric modes. It is also shown that ocean circulation controls the time scale of the SST response to wind forcing, and that coupled feedback mechanisms thus modify variability of the atmospheric circulation. It is concluded that ocean–atmosphere coupling in the midlatitudes is unlikely to produce new modes of variability but may control the temporal behavior of modes that exist in uncoupled systems.
Abstract
A midlatitude coupled ocean–atmosphere model is used to investigate interactions between the atmosphere and the wind-driven ocean circulation. This model uses idealized geometry, yet rich and complicated dynamic flow regimes arise in the ocean due to the explicit simulation of geostrophic turbulence. An interdecadal mode of intrinsic ocean variability is found, and this mode projects onto existing atmospheric modes of variability, thereby controlling the time scale of the atmospheric modes. It is also shown that ocean circulation controls the time scale of the SST response to wind forcing, and that coupled feedback mechanisms thus modify variability of the atmospheric circulation. It is concluded that ocean–atmosphere coupling in the midlatitudes is unlikely to produce new modes of variability but may control the temporal behavior of modes that exist in uncoupled systems.
Abstract
A version of the Bryan–Cox–Semtner numerical ocean general circulation model, adapted to include a free surface, is described. The model is designed for the following uses: tidal studies (a tidal option is explicitly included); assimilation of altimetric data (since the surface elevation is now a prognostic variable); and in situations where accurate relaxation to obtain the streamfunction in the original model is too time consuming. Comparison is made between a 300-year run of the original model and the free-surface version, using a very coarse North Atlantic calculation as the basis. The results are very similar, differing only in the streamfunction over topography; this is to be expected, since the treatment of topographic torques on the barotropic flow differs because of the nature of the modifications.
Abstract
A version of the Bryan–Cox–Semtner numerical ocean general circulation model, adapted to include a free surface, is described. The model is designed for the following uses: tidal studies (a tidal option is explicitly included); assimilation of altimetric data (since the surface elevation is now a prognostic variable); and in situations where accurate relaxation to obtain the streamfunction in the original model is too time consuming. Comparison is made between a 300-year run of the original model and the free-surface version, using a very coarse North Atlantic calculation as the basis. The results are very similar, differing only in the streamfunction over topography; this is to be expected, since the treatment of topographic torques on the barotropic flow differs because of the nature of the modifications.
Abstract
Eddy-resolving quasigeostrophic simulations of wind-driven circulation in a large ocean basin are presented. The results show that strong modes of low-frequency variability arise in many parameter regimes and that the strength of these modes depends upon the presence of inertial recirculations in the flow field. The inertial recirculations arise through advection of anomalous potential vorticity by the western boundary current and are barotropized by the effect of baroclinic eddies in the flow. The mechanism of low-frequency oscillations is explored with reference to previous studies, and it is found that the observed mode can be linked to the gyre mode but is strongly modified by the effect of eddies.
Abstract
Eddy-resolving quasigeostrophic simulations of wind-driven circulation in a large ocean basin are presented. The results show that strong modes of low-frequency variability arise in many parameter regimes and that the strength of these modes depends upon the presence of inertial recirculations in the flow field. The inertial recirculations arise through advection of anomalous potential vorticity by the western boundary current and are barotropized by the effect of baroclinic eddies in the flow. The mechanism of low-frequency oscillations is explored with reference to previous studies, and it is found that the observed mode can be linked to the gyre mode but is strongly modified by the effect of eddies.
Abstract
Numerical models are used to test whether the sea surface height (SSH) can be used as an indicator for the variability of Atlantic meridional oceanic mass transports. The results suggest that if the transports over the western boundary current region and those in the eastern part of the basin are considered separately, significant correlations (0.3–0.9) are found between zonal SSH differences and the meridional transports in the top 1100 m. Much weaker correlations are found for the basinwide transport, which corresponds to the surface branch of the meridional overturning circulation (MOC). For the eastern and western branches of the meridional transport, combining the SSH signal with the baroclinic structure obtained from Rossby wave theory enables calculation of a quantitative estimate of the transport variability in the top 1100 m. The results of the method are less convincing for the variability of the MOC. The reason for this is that even small relative errors in the variability of the eastern and western branches can be large compared with the MOC variability. These errors project onto the sum of the eastern and western transports and therefore onto the surface branch of the MOC. Nevertheless, being able to infer transport anomalies from SSH signals in the eastern and western parts of the Atlantic might prove useful in interpreting MOC observations from the U.K. Natural Environment Research Council Rapid Climate Change (RAPID) mooring array at 26°N, which show a large subannual variability that is mainly due to changes at the western boundary. Transports inferred from the SSH could help to identify the origin of this variability and whether transport anomalies propagate into the western boundary region from the basin interior or from other latitudes.
Abstract
Numerical models are used to test whether the sea surface height (SSH) can be used as an indicator for the variability of Atlantic meridional oceanic mass transports. The results suggest that if the transports over the western boundary current region and those in the eastern part of the basin are considered separately, significant correlations (0.3–0.9) are found between zonal SSH differences and the meridional transports in the top 1100 m. Much weaker correlations are found for the basinwide transport, which corresponds to the surface branch of the meridional overturning circulation (MOC). For the eastern and western branches of the meridional transport, combining the SSH signal with the baroclinic structure obtained from Rossby wave theory enables calculation of a quantitative estimate of the transport variability in the top 1100 m. The results of the method are less convincing for the variability of the MOC. The reason for this is that even small relative errors in the variability of the eastern and western branches can be large compared with the MOC variability. These errors project onto the sum of the eastern and western transports and therefore onto the surface branch of the MOC. Nevertheless, being able to infer transport anomalies from SSH signals in the eastern and western parts of the Atlantic might prove useful in interpreting MOC observations from the U.K. Natural Environment Research Council Rapid Climate Change (RAPID) mooring array at 26°N, which show a large subannual variability that is mainly due to changes at the western boundary. Transports inferred from the SSH could help to identify the origin of this variability and whether transport anomalies propagate into the western boundary region from the basin interior or from other latitudes.
