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- Author or Editor: Robert Hallberg x
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Abstract
In isopycnal coordinate ocean models, diapycnal diffusion must be expressed as a nonlinear difference equation. This nonlinear equation is not amenable to traditional implicit methods of solution, but explicit methods typically have a time step limit of order Δt ⩽ h 2/κ (where Δt is the time step, h is the isopycnal layer thickness, and κ is the diapycnal diffusivity), which cannot generally be satisfied since the layers could be arbitrarily thin. It is especially important that the diffusion time integration scheme have no such limit if the diapycnal diffusivity is determined by the local Richardson number. An iterative, implicit time integration scheme of diapycnal diffusion in isopycnal layers is suggested. This scheme is demonstrated to have qualitatively correct behavior in the limit of arbitrarily thin initial layer thickness, is highly accurate in the limit of well-resolved layers, and is not significantly more expensive than existing schemes. This approach is also shown to be compatible with an implicit Richardson number–dependent mixing parameterization, and to give a plausible simulation of an entraining gravity current with parameters like the Mediterranean Water overflow through the Straits of Gibraltar.
Abstract
In isopycnal coordinate ocean models, diapycnal diffusion must be expressed as a nonlinear difference equation. This nonlinear equation is not amenable to traditional implicit methods of solution, but explicit methods typically have a time step limit of order Δt ⩽ h 2/κ (where Δt is the time step, h is the isopycnal layer thickness, and κ is the diapycnal diffusivity), which cannot generally be satisfied since the layers could be arbitrarily thin. It is especially important that the diffusion time integration scheme have no such limit if the diapycnal diffusivity is determined by the local Richardson number. An iterative, implicit time integration scheme of diapycnal diffusion in isopycnal layers is suggested. This scheme is demonstrated to have qualitatively correct behavior in the limit of arbitrarily thin initial layer thickness, is highly accurate in the limit of well-resolved layers, and is not significantly more expensive than existing schemes. This approach is also shown to be compatible with an implicit Richardson number–dependent mixing parameterization, and to give a plausible simulation of an entraining gravity current with parameters like the Mediterranean Water overflow through the Straits of Gibraltar.
Abstract
Substantial bottom topography in a basin with planetary vorticity gradients strongly affects the vertical structure of the linear topographic and planetary Rossby waves that spin up the ocean circulation. There is no barotropic mode with large amplitude topography and stratification. It is shown that the lowest frequency two-layer quasigeostrophic waves that exist with stratification, planetary vorticity gradients, and large-amplitude bottom topography are more strongly concentrated in the vertical than Burger number 1 scaling would indicate (for most orientations of the wavevector) except where the bottom slope is nearly meridional. This concentration increases with decreasing frequency. Ray tracing in an ocean basin suggests that the two layers are linearly coupled in regions with parallel or antiparallel topographic and planetary vorticity gradients, but elsewhere small amplitude motion in the two layers is largely independent. Continuity within isopycnal layers implies that most of the circulation remains within isopycnal layers, even in the regions of linear coupling. The strength of surface(bottom)-intensified flow driven by coupling to bottom(surface)-intensified flow is approximately twice as strong as the surface(bottom) projection of the bottom(surface)-intensified flow. Primitive equation simulations concur with the quasigeostrophic results and indicate that the localized linear coupling between surface- and bottom-intensified flow pertains to a continuous stratification.
Abstract
Substantial bottom topography in a basin with planetary vorticity gradients strongly affects the vertical structure of the linear topographic and planetary Rossby waves that spin up the ocean circulation. There is no barotropic mode with large amplitude topography and stratification. It is shown that the lowest frequency two-layer quasigeostrophic waves that exist with stratification, planetary vorticity gradients, and large-amplitude bottom topography are more strongly concentrated in the vertical than Burger number 1 scaling would indicate (for most orientations of the wavevector) except where the bottom slope is nearly meridional. This concentration increases with decreasing frequency. Ray tracing in an ocean basin suggests that the two layers are linearly coupled in regions with parallel or antiparallel topographic and planetary vorticity gradients, but elsewhere small amplitude motion in the two layers is largely independent. Continuity within isopycnal layers implies that most of the circulation remains within isopycnal layers, even in the regions of linear coupling. The strength of surface(bottom)-intensified flow driven by coupling to bottom(surface)-intensified flow is approximately twice as strong as the surface(bottom) projection of the bottom(surface)-intensified flow. Primitive equation simulations concur with the quasigeostrophic results and indicate that the localized linear coupling between surface- and bottom-intensified flow pertains to a continuous stratification.
Abstract
The meridional Ekman transport in a zonally reentrant channel may be balanced by diabatic circulations, standing eddies associated with topography, or by Lagrangian mean eddy mass fluxes. A simple model is used to explore the interaction between these mechanisms. A key assumption of this study is that diabatic forcing in the poleward edge of the channel acts to create lighter fluid, as is the case with net freshwater fluxes into the Southern Ocean. For weak wind forcing or strong diabatic constraint, a simple scaling argument accurately predicts the level of baroclinic shear. However, given our understanding of the relative magnitudes of Ekman flux and deep upwelling, this is not the appropriate parameter range for the Antarctic Circumpolar Current. With stronger wind stresses, eddies are prominent, with baroclinic instability initially developing in the vicinity of large topography. Arguments have been advanced by a number of authors that baroclinic instability should limit the velocity shear, leading to a stiff upper limit on the transport of the current. However, in the simulations presented here baroclinic instability is largely confined to the region of topographic highs, and the approach to a current that is independent of the wind stress occurs gradually. Several recent parameterizations of transient eddy fluxes do not reproduce key features of the observed behavior.
Abstract
The meridional Ekman transport in a zonally reentrant channel may be balanced by diabatic circulations, standing eddies associated with topography, or by Lagrangian mean eddy mass fluxes. A simple model is used to explore the interaction between these mechanisms. A key assumption of this study is that diabatic forcing in the poleward edge of the channel acts to create lighter fluid, as is the case with net freshwater fluxes into the Southern Ocean. For weak wind forcing or strong diabatic constraint, a simple scaling argument accurately predicts the level of baroclinic shear. However, given our understanding of the relative magnitudes of Ekman flux and deep upwelling, this is not the appropriate parameter range for the Antarctic Circumpolar Current. With stronger wind stresses, eddies are prominent, with baroclinic instability initially developing in the vicinity of large topography. Arguments have been advanced by a number of authors that baroclinic instability should limit the velocity shear, leading to a stiff upper limit on the transport of the current. However, in the simulations presented here baroclinic instability is largely confined to the region of topographic highs, and the approach to a current that is independent of the wind stress occurs gradually. Several recent parameterizations of transient eddy fluxes do not reproduce key features of the observed behavior.
Abstract
The dynamics that govern the spreading of a convectively formed water mass in an ocean with sloping boundaries are examined using an isopycnal model that permits the interface between the layers to intersect the sloping boundaries. The simulations presented here use a two-layer configuration to demonstrate some of the pronounced differences in a baroclinically forced flow between the response in a basin with a flat bottom and vertical walls and a more realistic basin bounded by a sloping bottom. Each layer has a directly forced signal that propagates away from the forcing along the potential vorticity (PV) contours of that layer. Paired, opposed boundary currents are generated by refracted topographic Rossby waves, rather than Kelvin waves. It is impossible to decompose the flow into globally independent baroclinic and barotropic modes; topography causes the barotropic (i.e., depth averaged) response to buoyancy forcing to be just as strong as the baroclinic response. Because layer PV contours diverge, boundary currents are pulled apart at different depths even in weakly forced, essentially linear, cases. Such barotropic modes, often described as “caused by the JEBAR effect,” are actually dominated by strong free flow along PV contours. With both planetary vorticity gradients and topography, the two layers are linearly coupled. This coupling is evident in upper-layer circulations that follow upper-layer PV contours but originate in unforced regions of strong lower-layer flow. The interior ocean response is confined primarily to PV contours that are either directly forced or strongly coupled at some point to directly forced PV contours of the other layer. Even when the forcing is strong enough to generate a rich eddy field in the upper layer, the topographic PV gradients in the lower layer stabilize that layer and inhibit exchange of fluid across PV contours. The dynamic processes explored in this study are pertinent to both nonlinear flows (strongly forced) and linear flows (weakly forced and forerunners of strongly forced). Both small (f plane) and large (full spherical variation of the Coriolis parameter) basins are included. Transequatorial basins, in which the geostrophic contours are blocked, are not described here.
Abstract
The dynamics that govern the spreading of a convectively formed water mass in an ocean with sloping boundaries are examined using an isopycnal model that permits the interface between the layers to intersect the sloping boundaries. The simulations presented here use a two-layer configuration to demonstrate some of the pronounced differences in a baroclinically forced flow between the response in a basin with a flat bottom and vertical walls and a more realistic basin bounded by a sloping bottom. Each layer has a directly forced signal that propagates away from the forcing along the potential vorticity (PV) contours of that layer. Paired, opposed boundary currents are generated by refracted topographic Rossby waves, rather than Kelvin waves. It is impossible to decompose the flow into globally independent baroclinic and barotropic modes; topography causes the barotropic (i.e., depth averaged) response to buoyancy forcing to be just as strong as the baroclinic response. Because layer PV contours diverge, boundary currents are pulled apart at different depths even in weakly forced, essentially linear, cases. Such barotropic modes, often described as “caused by the JEBAR effect,” are actually dominated by strong free flow along PV contours. With both planetary vorticity gradients and topography, the two layers are linearly coupled. This coupling is evident in upper-layer circulations that follow upper-layer PV contours but originate in unforced regions of strong lower-layer flow. The interior ocean response is confined primarily to PV contours that are either directly forced or strongly coupled at some point to directly forced PV contours of the other layer. Even when the forcing is strong enough to generate a rich eddy field in the upper layer, the topographic PV gradients in the lower layer stabilize that layer and inhibit exchange of fluid across PV contours. The dynamic processes explored in this study are pertinent to both nonlinear flows (strongly forced) and linear flows (weakly forced and forerunners of strongly forced). Both small (f plane) and large (full spherical variation of the Coriolis parameter) basins are included. Transequatorial basins, in which the geostrophic contours are blocked, are not described here.
Abstract
The Modeling Eddies in the Southern Ocean (MESO) project uses numerical sensitivity studies to examine the role played by Southern Ocean winds and eddies in determining the density structure of the global ocean and the magnitude and structure of the global overturning circulation. A hemispheric isopycnal-coordinate ocean model (which avoids numerical diapycnal diffusion) with realistic geometry is run with idealized forcing at a range of resolutions from coarse (2°) to eddy-permitting (1/6°). A comparison of coarse resolutions with fine resolutions indicates that explicit eddies affect both the structure of the overturning and the response of the overturning to wind stress changes. While the presence of resolved eddies does not greatly affect the prevailing qualitative picture of the ocean circulation, it alters the overturning cells involving the Southern Ocean transformation of dense deep waters and light waters of subtropical origin into intermediate waters. With resolved eddies, the surface-to-intermediate water cell extends farther southward by hundreds of kilometers and the deep-to-intermediate cell draws on comparatively lighter deep waters. The overturning response to changes in the winds is also sensitive to the presence of eddies. In noneddying simulations, changing the Ekman transport produces comparable changes in the overturning, much of it involving transformation of deep waters and resembling the mean circulation. In the eddy-permitting simulations, a significant fraction of the Ekman transport changes are compensated by eddy-induced transport drawing from lighter waters than does the mean overturning. This significant difference calls into question the ability of coarse-resolution ocean models to accurately capture the impact of changes in the Southern Ocean on the global ocean circulation.
Abstract
The Modeling Eddies in the Southern Ocean (MESO) project uses numerical sensitivity studies to examine the role played by Southern Ocean winds and eddies in determining the density structure of the global ocean and the magnitude and structure of the global overturning circulation. A hemispheric isopycnal-coordinate ocean model (which avoids numerical diapycnal diffusion) with realistic geometry is run with idealized forcing at a range of resolutions from coarse (2°) to eddy-permitting (1/6°). A comparison of coarse resolutions with fine resolutions indicates that explicit eddies affect both the structure of the overturning and the response of the overturning to wind stress changes. While the presence of resolved eddies does not greatly affect the prevailing qualitative picture of the ocean circulation, it alters the overturning cells involving the Southern Ocean transformation of dense deep waters and light waters of subtropical origin into intermediate waters. With resolved eddies, the surface-to-intermediate water cell extends farther southward by hundreds of kilometers and the deep-to-intermediate cell draws on comparatively lighter deep waters. The overturning response to changes in the winds is also sensitive to the presence of eddies. In noneddying simulations, changing the Ekman transport produces comparable changes in the overturning, much of it involving transformation of deep waters and resembling the mean circulation. In the eddy-permitting simulations, a significant fraction of the Ekman transport changes are compensated by eddy-induced transport drawing from lighter waters than does the mean overturning. This significant difference calls into question the ability of coarse-resolution ocean models to accurately capture the impact of changes in the Southern Ocean on the global ocean circulation.
Abstract
This paper discusses a numerical closure, motivated from the ideas of Smagorinsky, for use with a biharmonic operator. The result is a highly scale-selective, state-dependent friction operator for use in eddy-permitting geophysical fluid models. This friction should prove most useful for large-scale ocean models in which there are multiple regimes of geostrophic turbulence. Examples are provided from primitive equation geopotential and isopycnal-coordinate ocean models.
Abstract
This paper discusses a numerical closure, motivated from the ideas of Smagorinsky, for use with a biharmonic operator. The result is a highly scale-selective, state-dependent friction operator for use in eddy-permitting geophysical fluid models. This friction should prove most useful for large-scale ocean models in which there are multiple regimes of geostrophic turbulence. Examples are provided from primitive equation geopotential and isopycnal-coordinate ocean models.
Abstract
The correlation between observed values of atmospheric greenhouse trapping and sea surface temperature is found to vary seasonally. Atmospheric greenhouse trapping is defined here as the difference between infrared emissions from the earth's surface and infrared emissions from the top of the atmosphere through cloudless skies. Infrared surface emissions are calculated from known sea surface temperatures, and emissions from the top of the atmosphere are taken from direct satellite measurements. Atmospheric greenhouse trapping at the same sea surface temperature is greater in the winter than in the summer over temperate oceans. In subtropical latitudes, the opposite is true. At surface temperatures above approximately 298 K, atmospheric greenhouse trapping is found to increase even more rapidly from regions of lower sea surface temperature to regions of higher surface temperature than infrared surface emissions. The causes for this “super” greenhouse effect are explored, and four processes are found to contribute. Water vapor continuum absorption and thermodynamically controlled increases in water vapor concentration at constant relative humility with increasing atmospheric temperature are found to make significant contributions, but do not explain the entire super greenhouse effect. To explain the observations of atmospheric greenhouse trapping, the atmosphere, and in particular the upper and middle troposphere, must be increasingly moist over the warmest sea surface temperatures, while the atmospheric temperature profile becomes increasingly unstable. Regions with these high sea surface temperatures are also increasingly subject to deep convection, which suggests that convection moistens the upper and middle troposphere in regions of convective activity relative to nonconvective regions, resulting in the super greenhouse effect. Dynamic processes, along with local thermodynamic process. are required to explain the observed super greenhouse effect.
Abstract
The correlation between observed values of atmospheric greenhouse trapping and sea surface temperature is found to vary seasonally. Atmospheric greenhouse trapping is defined here as the difference between infrared emissions from the earth's surface and infrared emissions from the top of the atmosphere through cloudless skies. Infrared surface emissions are calculated from known sea surface temperatures, and emissions from the top of the atmosphere are taken from direct satellite measurements. Atmospheric greenhouse trapping at the same sea surface temperature is greater in the winter than in the summer over temperate oceans. In subtropical latitudes, the opposite is true. At surface temperatures above approximately 298 K, atmospheric greenhouse trapping is found to increase even more rapidly from regions of lower sea surface temperature to regions of higher surface temperature than infrared surface emissions. The causes for this “super” greenhouse effect are explored, and four processes are found to contribute. Water vapor continuum absorption and thermodynamically controlled increases in water vapor concentration at constant relative humility with increasing atmospheric temperature are found to make significant contributions, but do not explain the entire super greenhouse effect. To explain the observations of atmospheric greenhouse trapping, the atmosphere, and in particular the upper and middle troposphere, must be increasingly moist over the warmest sea surface temperatures, while the atmospheric temperature profile becomes increasingly unstable. Regions with these high sea surface temperatures are also increasingly subject to deep convection, which suggests that convection moistens the upper and middle troposphere in regions of convective activity relative to nonconvective regions, resulting in the super greenhouse effect. Dynamic processes, along with local thermodynamic process. are required to explain the observed super greenhouse effect.
Abstract
This study examines the relative roles of the Arctic freshwater exported via different pathways on deep convection in the North Atlantic and the Atlantic meridional overturning circulation (AMOC). Deep water feeding the lower branch of the AMOC is formed in several North Atlantic marginal seas, including the Labrador Sea, Irminger Sea, and the Nordic seas, where deep convection can potentially be inhibited by surface freshwater exported from the Arctic. The sensitivity of the AMOC and North Atlantic to two major freshwater pathways on either side of Greenland is studied using numerical experiments. Freshwater export is rerouted in global coupled climate models by blocking and expanding the channels along the two routes. The sensitivity experiments are performed in two sets of models (CM2G and CM2M) with different control simulation climatology for comparison. Freshwater via the route east of Greenland is found to have a larger direct impact on Labrador Sea convection. In response to the changes of freshwater route, North Atlantic convection outside of the Labrador Sea changes in the opposite sense to the Labrador Sea. The response of the AMOC is found to be sensitive to both the model formulation and mean-state climate.
Abstract
This study examines the relative roles of the Arctic freshwater exported via different pathways on deep convection in the North Atlantic and the Atlantic meridional overturning circulation (AMOC). Deep water feeding the lower branch of the AMOC is formed in several North Atlantic marginal seas, including the Labrador Sea, Irminger Sea, and the Nordic seas, where deep convection can potentially be inhibited by surface freshwater exported from the Arctic. The sensitivity of the AMOC and North Atlantic to two major freshwater pathways on either side of Greenland is studied using numerical experiments. Freshwater export is rerouted in global coupled climate models by blocking and expanding the channels along the two routes. The sensitivity experiments are performed in two sets of models (CM2G and CM2M) with different control simulation climatology for comparison. Freshwater via the route east of Greenland is found to have a larger direct impact on Labrador Sea convection. In response to the changes of freshwater route, North Atlantic convection outside of the Labrador Sea changes in the opposite sense to the Labrador Sea. The response of the AMOC is found to be sensitive to both the model formulation and mean-state climate.
Abstract
Turbulent mixing driven by breaking internal tides plays a primary role in the meridional overturning and oceanic heat budget. Most current climate models explicitly parameterize only the local dissipation of internal tides at the generation sites, representing the remote dissipation of low-mode internal tides that propagate away through a uniform background diffusivity. In this study, a simple energetically consistent parameterization of the low-mode internal-tide dissipation is derived and implemented in the Geophysical Fluid Dynamics Laboratory Earth System Model with GOLD component (GFDL-ESM2G). The impact of remote and local internal-tide dissipation on the ocean state is examined using a series of simulations with the same total amount of energy input for mixing, but with different scalings of the vertical profile of dissipation with the stratification and with different idealized scenarios for the distribution of the low-mode internal-tide energy dissipation: uniformly over ocean basins, continental slopes, or continental shelves. In these idealized scenarios, the ocean state, including the meridional overturning circulation, ocean ventilation, main thermocline thickness, and ocean heat uptake, is particularly sensitive to the vertical distribution of mixing by breaking low-mode internal tides. Less sensitivity is found to the horizontal distribution of mixing, provided that distribution is in the open ocean. Mixing on coastal shelves only impacts the large-scale circulation and water mass properties where it modifies water masses originating on shelves. More complete descriptions of the distribution of the remote part of internal-tide-driven mixing, particularly in the vertical and relative to water mass formation regions, are therefore required to fully parameterize ocean turbulent mixing.
Abstract
Turbulent mixing driven by breaking internal tides plays a primary role in the meridional overturning and oceanic heat budget. Most current climate models explicitly parameterize only the local dissipation of internal tides at the generation sites, representing the remote dissipation of low-mode internal tides that propagate away through a uniform background diffusivity. In this study, a simple energetically consistent parameterization of the low-mode internal-tide dissipation is derived and implemented in the Geophysical Fluid Dynamics Laboratory Earth System Model with GOLD component (GFDL-ESM2G). The impact of remote and local internal-tide dissipation on the ocean state is examined using a series of simulations with the same total amount of energy input for mixing, but with different scalings of the vertical profile of dissipation with the stratification and with different idealized scenarios for the distribution of the low-mode internal-tide energy dissipation: uniformly over ocean basins, continental slopes, or continental shelves. In these idealized scenarios, the ocean state, including the meridional overturning circulation, ocean ventilation, main thermocline thickness, and ocean heat uptake, is particularly sensitive to the vertical distribution of mixing by breaking low-mode internal tides. Less sensitivity is found to the horizontal distribution of mixing, provided that distribution is in the open ocean. Mixing on coastal shelves only impacts the large-scale circulation and water mass properties where it modifies water masses originating on shelves. More complete descriptions of the distribution of the remote part of internal-tide-driven mixing, particularly in the vertical and relative to water mass formation regions, are therefore required to fully parameterize ocean turbulent mixing.
