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Abstract
The combined problem of determining the ocean circulation and improving the geoid from satellite altimetry is formulated and studied. Minimum variance estimation is used to form optimum estimates of the ocean topography and the geoid. These estimates are a function of the altimeter observations, prior knowledge of the ocean circulation and prior knowledge of the geoid. Particular emphasis is placed on the use of a dynamical ocean model as a source of a priori oceanographic information capable of discriminating between geoid errors and ocean topography. The technique is illustrated in a simulation study of Gulf Stream variability, in which an ocean topography, degraded by noise representing the uncertainty in a gravimetric geoid, is reconstructed by assimilation into an ocean model. At the same time an improved estimate of the geoid is made.
Abstract
The combined problem of determining the ocean circulation and improving the geoid from satellite altimetry is formulated and studied. Minimum variance estimation is used to form optimum estimates of the ocean topography and the geoid. These estimates are a function of the altimeter observations, prior knowledge of the ocean circulation and prior knowledge of the geoid. Particular emphasis is placed on the use of a dynamical ocean model as a source of a priori oceanographic information capable of discriminating between geoid errors and ocean topography. The technique is illustrated in a simulation study of Gulf Stream variability, in which an ocean topography, degraded by noise representing the uncertainty in a gravimetric geoid, is reconstructed by assimilation into an ocean model. At the same time an improved estimate of the geoid is made.
Abstract
An attempt is made to incorporate into a two-layer, zonally averaged, channel ocean model the important transfers achieved by a geostrophic eddy field, using gross parameterizations rather than resolving individual eddy events. It is shown that a representation of the eddy field as an explicit diffuser of potential vorticity can give a reasonable description of the interaction between the eddies and mean flow, provided care is taken to satisfy the attendant constraints that the zonally invariant channel geometry imposes on the eddy fields.
Abstract
An attempt is made to incorporate into a two-layer, zonally averaged, channel ocean model the important transfers achieved by a geostrophic eddy field, using gross parameterizations rather than resolving individual eddy events. It is shown that a representation of the eddy field as an explicit diffuser of potential vorticity can give a reasonable description of the interaction between the eddies and mean flow, provided care is taken to satisfy the attendant constraints that the zonally invariant channel geometry imposes on the eddy fields.
Abstract
Using twice daily synoptic charts, objectively analyzed at the National Meteorological Centre, horizontal eddy fluxes of temperature and quasi-geostrophic potential vorticity are computed for the month Of July 1976, when a blocking anticyclone was centered over western Europe. The local time-averaged eddy variance equations are used to provide a dynamical basis for interpreting the spatial pattern of eddy fluxes, and their relation to mean gradients. It is shown that a rotational non-divergent flux can be identified, the cross-gradient component of which balances the mean flow advection of eddy variance. The remaining flux is the dynamically significant one which helps maintain the block and can be understood in terms of a response to sources and sinks of eddy variance.
Abstract
Using twice daily synoptic charts, objectively analyzed at the National Meteorological Centre, horizontal eddy fluxes of temperature and quasi-geostrophic potential vorticity are computed for the month Of July 1976, when a blocking anticyclone was centered over western Europe. The local time-averaged eddy variance equations are used to provide a dynamical basis for interpreting the spatial pattern of eddy fluxes, and their relation to mean gradients. It is shown that a rotational non-divergent flux can be identified, the cross-gradient component of which balances the mean flow advection of eddy variance. The remaining flux is the dynamically significant one which helps maintain the block and can be understood in terms of a response to sources and sinks of eddy variance.
Abstract
The authors explore the use of the “neutral vectors” of a linearized version of a global quasigeostrophic atmospheric model with realistic mean flow in the study of the nonlinear model's low-frequency variability. Neutral vectors are the (right) singular vectors of the linearized model's tendency matrix that have the smallest eigenvalues; they are also the patterns that exhibit the largest response to forcing perturbations in the linear model. A striking similarity is found between neutral vectors and the dominant patterns of variability (EOFs) observed in both the full nonlinear model and in the real world. The authors discuss the physical and mathematical connection between neutral vectors and EOFs.
Investigation of the “optimal forcing patterns”—the left singular vectors—proves to be less fruitful. The neutral modes have equivalent barotropic vertical structure, but their optimal forcing patterns are baroclinic and seem to be associated with low-level heating. But the horizontal patterns of the forcing patterns are not robust and are sensitive to the form of the inner product used in the singular vector decomposition analysis. Additionally, applying “optimal” forcing patterns as perturbations to the full nonlinear model does not generate the response suggested by the linear model.
Abstract
The authors explore the use of the “neutral vectors” of a linearized version of a global quasigeostrophic atmospheric model with realistic mean flow in the study of the nonlinear model's low-frequency variability. Neutral vectors are the (right) singular vectors of the linearized model's tendency matrix that have the smallest eigenvalues; they are also the patterns that exhibit the largest response to forcing perturbations in the linear model. A striking similarity is found between neutral vectors and the dominant patterns of variability (EOFs) observed in both the full nonlinear model and in the real world. The authors discuss the physical and mathematical connection between neutral vectors and EOFs.
Investigation of the “optimal forcing patterns”—the left singular vectors—proves to be less fruitful. The neutral modes have equivalent barotropic vertical structure, but their optimal forcing patterns are baroclinic and seem to be associated with low-level heating. But the horizontal patterns of the forcing patterns are not robust and are sensitive to the form of the inner product used in the singular vector decomposition analysis. Additionally, applying “optimal” forcing patterns as perturbations to the full nonlinear model does not generate the response suggested by the linear model.
Abstract
The role of “neutral vectors” in midlatitude air–sea interaction is studied in a simple coupled model. Neutral vectors—the right singular vectors of the linearized atmospheric model tendency matrix with the smallest singular values—are shown to act as pattern-specific amplifiers of ocean SST anomalies and dominate coupled behavior.
These ideas are developed in the framework of a previously developed analytical coupled model, which described the mutual interaction across the sea surface of atmospheric and oceanic Rossby waves. A numerical model with the same physics is developed that permits the consideration of nontrivial background conditions. It is shown that the atmospheric modes that are least damped, and thus the patterns most easily energized by stochastic forcing, are neutral vectors.
Abstract
The role of “neutral vectors” in midlatitude air–sea interaction is studied in a simple coupled model. Neutral vectors—the right singular vectors of the linearized atmospheric model tendency matrix with the smallest singular values—are shown to act as pattern-specific amplifiers of ocean SST anomalies and dominate coupled behavior.
These ideas are developed in the framework of a previously developed analytical coupled model, which described the mutual interaction across the sea surface of atmospheric and oceanic Rossby waves. A numerical model with the same physics is developed that permits the consideration of nontrivial background conditions. It is shown that the atmospheric modes that are least damped, and thus the patterns most easily energized by stochastic forcing, are neutral vectors.
Abstract
Many recent observations have described fronts in the interior of the ocean at locations far away from any lateral boundaries. Some of these fronts are observed to be associated with considerable mass transports, which suggests that they participate importantly in setting the water mass structure of the ocean interior, and represent considerable local departures from linear Sverdrup dynamics. In this paper, a simple analytic theory of interior fronts is developed. The main features of this theory are that the fronts are highly inertial and anisotropic, and reside on the edge of a somewhat larger scale interior inertial recirculation. The recirculation is taken to be modonlike; the dynamic height difference across the edge of the recirculation supports an interior jet, which is clockwise around the edge of the recirculation and carries water from the subpolar into the subtropical gyre. Unlike in previous theories of interior fronts, all of the transports, both in the large-scale and the fronts, are “anomalous” and in excess of any wind-driven transport. The fronts themselves represent interior, deformation-scale boundary layers, which are necessary to smoothly join the baroclinic parts of the inertial recirculation and the sluggish Sverdrup zones. The authors speculate on the role of these dynamics in the LDE jet.
Abstract
Many recent observations have described fronts in the interior of the ocean at locations far away from any lateral boundaries. Some of these fronts are observed to be associated with considerable mass transports, which suggests that they participate importantly in setting the water mass structure of the ocean interior, and represent considerable local departures from linear Sverdrup dynamics. In this paper, a simple analytic theory of interior fronts is developed. The main features of this theory are that the fronts are highly inertial and anisotropic, and reside on the edge of a somewhat larger scale interior inertial recirculation. The recirculation is taken to be modonlike; the dynamic height difference across the edge of the recirculation supports an interior jet, which is clockwise around the edge of the recirculation and carries water from the subpolar into the subtropical gyre. Unlike in previous theories of interior fronts, all of the transports, both in the large-scale and the fronts, are “anomalous” and in excess of any wind-driven transport. The fronts themselves represent interior, deformation-scale boundary layers, which are necessary to smoothly join the baroclinic parts of the inertial recirculation and the sluggish Sverdrup zones. The authors speculate on the role of these dynamics in the LDE jet.
Abstract
A continuously stratified, steady thermocline model is formulated in which a mixed layer of variable depth and density overlies a stratified thermocline. Rather than prescribe the distribution of density and vertical velocity at the top of the permanent themocline, we explicitly represent the dynamics of the vertically homogeneous layer layer that overlies it; the density distribution at the sea surface, the depth of the mixed layer, and the structure of the thermocline are all found for prescribed patterns of Ekman pumping and surface buoyancy fluxes. If the potential vorticity of the thermocline is assumed to have a uniform value on isopycnal surfaces, it is shown that the problem can be reduced to one of finding the distribution of a single scalar field, the mixed-layer density, by the method of characteristics. Given this field and knowledge of the potential vorticity distribution in the thermocline, all other variables of the model can be found. The resulting model seems ideally suited to the study of the interaction of a mixed layer with a stratified thermocline, since it explicitly represents the lateral geostrophic flow through the sloping base of the mixed layer.
Idealized solutions are presented for both subtropical and subtrophical and in which, in response to patterns of wind and diabatic forcing, isopycnals outcrop into a mixed layer of variable thickness and density. The effect of both warming and cooling of the mixed layer on the structure of the gyre is investigated.
Abstract
A continuously stratified, steady thermocline model is formulated in which a mixed layer of variable depth and density overlies a stratified thermocline. Rather than prescribe the distribution of density and vertical velocity at the top of the permanent themocline, we explicitly represent the dynamics of the vertically homogeneous layer layer that overlies it; the density distribution at the sea surface, the depth of the mixed layer, and the structure of the thermocline are all found for prescribed patterns of Ekman pumping and surface buoyancy fluxes. If the potential vorticity of the thermocline is assumed to have a uniform value on isopycnal surfaces, it is shown that the problem can be reduced to one of finding the distribution of a single scalar field, the mixed-layer density, by the method of characteristics. Given this field and knowledge of the potential vorticity distribution in the thermocline, all other variables of the model can be found. The resulting model seems ideally suited to the study of the interaction of a mixed layer with a stratified thermocline, since it explicitly represents the lateral geostrophic flow through the sloping base of the mixed layer.
Idealized solutions are presented for both subtropical and subtrophical and in which, in response to patterns of wind and diabatic forcing, isopycnals outcrop into a mixed layer of variable thickness and density. The effect of both warming and cooling of the mixed layer on the structure of the gyre is investigated.
Abstract
The transport of mass between a mixed layer, exposed to mechanical and thermodynamic forcing, and an adiabatic thermocline is studied for gyre-scale motions. It is shown that if the mixed layer can be represented by a vertically homogeneous layer, whose base velocity and potential density are continuous, then, at any instant, the rate at which fluid is subducted per unit area of the sloping mixed-layer base, S, is given bywhere h is the depth of the mixed layer, Qb = −fρ̄−1∂ρ/∂z| z−h is th large-scale potential vorticity is the base, ℋnet is the heat input per unit area less that which warms the Ekman drift, α E , Cw , and ρ̄ are the volume expansion coefficient, heat capacity, and mean density of water, respectively. It is assumed that the mixed layer is convectively controlled and much deeper than the layer directly stirred by the wind. The field of S is studied in a steady thermocline model in which patterns of Ekman pumping and diabatic heating drive flow to and from a mixed layer overlying a stratified thermocline.
Abstract
The transport of mass between a mixed layer, exposed to mechanical and thermodynamic forcing, and an adiabatic thermocline is studied for gyre-scale motions. It is shown that if the mixed layer can be represented by a vertically homogeneous layer, whose base velocity and potential density are continuous, then, at any instant, the rate at which fluid is subducted per unit area of the sloping mixed-layer base, S, is given bywhere h is the depth of the mixed layer, Qb = −fρ̄−1∂ρ/∂z| z−h is th large-scale potential vorticity is the base, ℋnet is the heat input per unit area less that which warms the Ekman drift, α E , Cw , and ρ̄ are the volume expansion coefficient, heat capacity, and mean density of water, respectively. It is assumed that the mixed layer is convectively controlled and much deeper than the layer directly stirred by the wind. The field of S is studied in a steady thermocline model in which patterns of Ekman pumping and diabatic heating drive flow to and from a mixed layer overlying a stratified thermocline.
Abstract
A flux form of the Potential vorticity (PV) equation is applied to study the creation and transport of potential vorticity in an ocean gyre; generalized PV fluxes (J vectors) and the associated PV flux fines are used to map the creation, by buoyancy forcing, of PV in the mixed layer and its transport as fluid is subducted through the base of the mixed layer into the thermocline. The PV flux lines can either close on themselves (recirculation) or begin and end on the boundaries (ventilation). Idealized thermocline solutions are diagnosed using J vectors, which vividly illustrate the competing process of recirculation through western boundary currants and subduction from the surface.
Potential vorticity flux vectors are then used to quantify the flux of mass passing invisidly through a surface across which potential vorticity changes discontinuously but at which potential density and velocity are continuous. Such a surface might be the base of the oceanic mixed layer or, in a meteorological context, the tropopause. It is shown that, at any instant, the normal flux of fluid per unit area across such a surface is given, very generally, bywhere u is the velocity and n is the normal vector to the surface. Here ω is the absolute vorticity; B = −gDσ/Dt is the buoyancy forcing, with D/Dt the substantial derivative and σ the potential density; Q = −ρ−1ω·∇σ is the potential vorticity; ρ the in situ density., and g the gravitational acceleration. Square brackets denote the change in the enclosed quantity across the surface.
Abstract
A flux form of the Potential vorticity (PV) equation is applied to study the creation and transport of potential vorticity in an ocean gyre; generalized PV fluxes (J vectors) and the associated PV flux fines are used to map the creation, by buoyancy forcing, of PV in the mixed layer and its transport as fluid is subducted through the base of the mixed layer into the thermocline. The PV flux lines can either close on themselves (recirculation) or begin and end on the boundaries (ventilation). Idealized thermocline solutions are diagnosed using J vectors, which vividly illustrate the competing process of recirculation through western boundary currants and subduction from the surface.
Potential vorticity flux vectors are then used to quantify the flux of mass passing invisidly through a surface across which potential vorticity changes discontinuously but at which potential density and velocity are continuous. Such a surface might be the base of the oceanic mixed layer or, in a meteorological context, the tropopause. It is shown that, at any instant, the normal flux of fluid per unit area across such a surface is given, very generally, bywhere u is the velocity and n is the normal vector to the surface. Here ω is the absolute vorticity; B = −gDσ/Dt is the buoyancy forcing, with D/Dt the substantial derivative and σ the potential density; Q = −ρ−1ω·∇σ is the potential vorticity; ρ the in situ density., and g the gravitational acceleration. Square brackets denote the change in the enclosed quantity across the surface.
Abstract
The annual rate at which mixed-layer fluid is transferred into the permanent thermocline—that is, the annual subduction rate S ann and the effective subduction period 𝒯eff—is inferred from climatological data in the North Atlantic. From its kinematic definition, S ann is obtained by summing the vertical velocity at the base of the winter mixed layer with the lateral induction of fluid through the sloping base of the winter mixed layer. Geostrophic velocity fields, computed from the Levitus climatology assuming a level of no motion at 2.5 km, are used; the vertical velocity at the base of the mixed layer is deduced from observed surface Ekman pumping velocities and linear vorticity balance. A plausible pattern of S ann is obtained with subduction rates over the subtropical gyre approaching 100 m/yr—twice the maximum rate of Ekman pumping.
The subduction period 𝒯eff is found by viewing subduction as a transformation process converting mixed-layer fluid into stratified thermocline fluid. The effective period is that period of time during the shallowing of the mixed layer in which sufficient buoyancy is delivered to permit irreversible transfer of fluid into the main thermocline at the rate S ann. Typically 𝒯eff is found to be 1 to 2 months over the major part of the subtropical gyre, rising to 4 months in the tropics.
Finally, the heat budget of a column of fluid, extending from the surface down to the base of the seasonal thermocline is discussed, following it over an annual cycle. We are able to relate the buoyancy delivered to the mixed layer during the subduction period to the annual-mean buoyancy forcing through the sea surface plus the warming due to the convergence of Ekman heat fluxes. The relative importance of surface fluxes (heat and freshwater) and Ekman fluxes in supplying buoyancy to support subduction is examined using the climatologist observations of Isemer and Hasse, Schmitt et al., and Levitus. The pumping down of fluid from the warm summer Ekman layer into the thermocline makes a crucial contribution and, over the subtropical gyre, is the dominant term in the thermodynamics of subduction.
Abstract
The annual rate at which mixed-layer fluid is transferred into the permanent thermocline—that is, the annual subduction rate S ann and the effective subduction period 𝒯eff—is inferred from climatological data in the North Atlantic. From its kinematic definition, S ann is obtained by summing the vertical velocity at the base of the winter mixed layer with the lateral induction of fluid through the sloping base of the winter mixed layer. Geostrophic velocity fields, computed from the Levitus climatology assuming a level of no motion at 2.5 km, are used; the vertical velocity at the base of the mixed layer is deduced from observed surface Ekman pumping velocities and linear vorticity balance. A plausible pattern of S ann is obtained with subduction rates over the subtropical gyre approaching 100 m/yr—twice the maximum rate of Ekman pumping.
The subduction period 𝒯eff is found by viewing subduction as a transformation process converting mixed-layer fluid into stratified thermocline fluid. The effective period is that period of time during the shallowing of the mixed layer in which sufficient buoyancy is delivered to permit irreversible transfer of fluid into the main thermocline at the rate S ann. Typically 𝒯eff is found to be 1 to 2 months over the major part of the subtropical gyre, rising to 4 months in the tropics.
Finally, the heat budget of a column of fluid, extending from the surface down to the base of the seasonal thermocline is discussed, following it over an annual cycle. We are able to relate the buoyancy delivered to the mixed layer during the subduction period to the annual-mean buoyancy forcing through the sea surface plus the warming due to the convergence of Ekman heat fluxes. The relative importance of surface fluxes (heat and freshwater) and Ekman fluxes in supplying buoyancy to support subduction is examined using the climatologist observations of Isemer and Hasse, Schmitt et al., and Levitus. The pumping down of fluid from the warm summer Ekman layer into the thermocline makes a crucial contribution and, over the subtropical gyre, is the dominant term in the thermodynamics of subduction.
