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Abstract
The conservation equations of heat, salt, and mass are combined in such a way that a simple relation is found between the known volume flux of Mediterranean Water entering the North Atlantic Ocean and the effects of lateral and vertical mixing processes. The method is a form of inverse method in which the only unknowns are the vertical and lateral diffusivities. For each isohaline contour on each neutral density surface the authors develop one equation in two unknowns, arguing that other terms that cannot be evaluated are small. By considering several such isohaline contours, the method becomes overdetermined for each density layer, and results are found for both the vertical and lateral diffusivity that vary smoothly in the vertical direction, giving some confidence in the method.
Abstract
The conservation equations of heat, salt, and mass are combined in such a way that a simple relation is found between the known volume flux of Mediterranean Water entering the North Atlantic Ocean and the effects of lateral and vertical mixing processes. The method is a form of inverse method in which the only unknowns are the vertical and lateral diffusivities. For each isohaline contour on each neutral density surface the authors develop one equation in two unknowns, arguing that other terms that cannot be evaluated are small. By considering several such isohaline contours, the method becomes overdetermined for each density layer, and results are found for both the vertical and lateral diffusivity that vary smoothly in the vertical direction, giving some confidence in the method.
Abstract
Hochet and Tailleux (2019), in a comment on Holmes et al. (2019), argue that under the incompressible Boussinesq approximation the “sum of the volume fluxes through any kind of control volume must integrate to zero at all times.” They hence argue that the expression in Holmes et al. (2019) for the change in the volume of seawater warmer than a given temperature is inaccurate. Here we clarify what is meant by the term “volume flux” as used in Holmes et al. (2019) and also more generally in the water-mass transformation literature. Specifically, a volume flux across a surface can occur either due to fluid moving through a fixed surface, or due to the surface moving through the fluid. Interpreted in this way, we show using several examples that the statement from Hochet and Tailleux (2019) quoted above does not apply to the control volume considered in Holmes et al. (2019). Hochet and Tailleux (2019) then derive a series of expressions for the water-mass transformation or volume flux across an isotherm
Abstract
Hochet and Tailleux (2019), in a comment on Holmes et al. (2019), argue that under the incompressible Boussinesq approximation the “sum of the volume fluxes through any kind of control volume must integrate to zero at all times.” They hence argue that the expression in Holmes et al. (2019) for the change in the volume of seawater warmer than a given temperature is inaccurate. Here we clarify what is meant by the term “volume flux” as used in Holmes et al. (2019) and also more generally in the water-mass transformation literature. Specifically, a volume flux across a surface can occur either due to fluid moving through a fixed surface, or due to the surface moving through the fluid. Interpreted in this way, we show using several examples that the statement from Hochet and Tailleux (2019) quoted above does not apply to the control volume considered in Holmes et al. (2019). Hochet and Tailleux (2019) then derive a series of expressions for the water-mass transformation or volume flux across an isotherm
Abstract
The strength of the meridional overturning circulation (MOC) in the North Atlantic is dependent upon the formation of dense waters that occurs at high northern latitudes. Wintertime deep convection in the Labrador and Irminger Seas forms the intermediate water mass known as Labrador Sea Water (LSW). Changes in the rate of formation and subsequent export of LSW are thought to play a role in MOC variability, but formation rates are uncertain and the link between formation and export is complex. We present the first observation-based application of a recently developed regional thermohaline inverse method (RTHIM) to a region encompassing the Arctic and part of the North Atlantic subpolar gyre for the years 2013, 2014, and 2015. RTHIM is a novel method that can diagnose the formation and export rates of water masses such as the LSW identified by their temperature and salinity, apportioning the formation rates into contributions from surface fluxes and interior mixing. We find LSW formation rates of up to 12 Sv (1 Sv ≡ 106 m3 s−1) during 2014–15, a period of strong wintertime convection, and around half that value during 2013 when convection was weak. We also show that the newly convected water is not exported directly, but instead is mixed isopycnally with warm, salty waters that have been advected into the region, before the products are then exported. RTHIM solutions for 2015 volume, heat, and freshwater transports are compared with observations from a mooring array deployed for the Overturning in the Subpolar North Atlantic Program (OSNAP) and show good agreement, lending validity to our results.
Abstract
The strength of the meridional overturning circulation (MOC) in the North Atlantic is dependent upon the formation of dense waters that occurs at high northern latitudes. Wintertime deep convection in the Labrador and Irminger Seas forms the intermediate water mass known as Labrador Sea Water (LSW). Changes in the rate of formation and subsequent export of LSW are thought to play a role in MOC variability, but formation rates are uncertain and the link between formation and export is complex. We present the first observation-based application of a recently developed regional thermohaline inverse method (RTHIM) to a region encompassing the Arctic and part of the North Atlantic subpolar gyre for the years 2013, 2014, and 2015. RTHIM is a novel method that can diagnose the formation and export rates of water masses such as the LSW identified by their temperature and salinity, apportioning the formation rates into contributions from surface fluxes and interior mixing. We find LSW formation rates of up to 12 Sv (1 Sv ≡ 106 m3 s−1) during 2014–15, a period of strong wintertime convection, and around half that value during 2013 when convection was weak. We also show that the newly convected water is not exported directly, but instead is mixed isopycnally with warm, salty waters that have been advected into the region, before the products are then exported. RTHIM solutions for 2015 volume, heat, and freshwater transports are compared with observations from a mooring array deployed for the Overturning in the Subpolar North Atlantic Program (OSNAP) and show good agreement, lending validity to our results.
Abstract
The global water cycle is dominated by an atmospheric branch that transfers freshwater away from subtropical regions and an oceanic branch that returns that freshwater from subpolar and tropical regions. Salt content is commonly used to understand the oceanic branch because surface freshwater fluxes leave an imprint on ocean salinity. However, freshwater fluxes do not actually change the amount of salt in the ocean and—in the mean—no salt is transported meridionally by ocean circulation. To study the processes that determine ocean salinity, we introduce a new variable “internal salt” along with its counterpart “internal fresh water.” Precise budgets for internal salt in salinity coordinates relate meridional and diahaline transport to surface freshwater forcing, ocean circulation, and mixing and reveal the pathway of freshwater in the ocean. We apply this framework to a 1° global ocean model. We find that for freshwater to be exported from the ocean’s tropical and subpolar regions to the subtropics, salt must be mixed across the salinity surfaces that bound those regions. In the tropics, this mixing is achieved by parameterized vertical mixing, along-isopycnal mixing, and numerical mixing associated with truncation errors in the model’s advection scheme, whereas along-isopycnal mixing dominates at high latitudes. We analyze the internal freshwater budgets of the Indo-Pacific and Atlantic Ocean basins and identify the transport pathways between them that redistribute freshwater added through precipitation, balancing asymmetries in freshwater forcing between the basins.
Abstract
The global water cycle is dominated by an atmospheric branch that transfers freshwater away from subtropical regions and an oceanic branch that returns that freshwater from subpolar and tropical regions. Salt content is commonly used to understand the oceanic branch because surface freshwater fluxes leave an imprint on ocean salinity. However, freshwater fluxes do not actually change the amount of salt in the ocean and—in the mean—no salt is transported meridionally by ocean circulation. To study the processes that determine ocean salinity, we introduce a new variable “internal salt” along with its counterpart “internal fresh water.” Precise budgets for internal salt in salinity coordinates relate meridional and diahaline transport to surface freshwater forcing, ocean circulation, and mixing and reveal the pathway of freshwater in the ocean. We apply this framework to a 1° global ocean model. We find that for freshwater to be exported from the ocean’s tropical and subpolar regions to the subtropics, salt must be mixed across the salinity surfaces that bound those regions. In the tropics, this mixing is achieved by parameterized vertical mixing, along-isopycnal mixing, and numerical mixing associated with truncation errors in the model’s advection scheme, whereas along-isopycnal mixing dominates at high latitudes. We analyze the internal freshwater budgets of the Indo-Pacific and Atlantic Ocean basins and identify the transport pathways between them that redistribute freshwater added through precipitation, balancing asymmetries in freshwater forcing between the basins.
Abstract
The Southern Hemisphere westerly winds have intensified in recent decades associated with a positive trend in the southern annular mode (SAM). However, the response of the Antarctic Circumpolar Current (ACC) transport and eddy field to wind forcing remains a topic of debate. This study uses global eddy-permitting ocean circulation models driven with both idealized and realistic wind forcing to explore the response to interannual wind strengthening. The response of the barotropic and baroclinic transports and eddy field of the ACC is found to depend on the spatial pattern of the changes in wind forcing. In isolation, an enhancement of the westerlies over the ACC belt leads to an increase of both barotropic and baroclinic transport within the ACC envelope, with lagged enhancement of the eddy kinetic energy (EKE). In contrast, an increase in wind forcing near Antarctica drives a largely barotropic change in transport along closed f/H contours (“free mode”), with little change in eddy activity. Under realistic forcing, the interplay of the SAM and the El Niño–Southern Oscillation (ENSO) influences the spatial distribution of the wind anomalies, in particular the partition between changes in the wind stress over the ACC and along f/H contours. This study finds that the occurrence of a negative or positive ENSO during a positive SAM can cancel or double the wind anomalies near Antarctica, altering the response of the ACC and its eddy field. While a negative ENSO and positive SAM favors an increase in EKE, a positive ENSO and positive SAM lead to barotropic transport changes and no eddy response.
Abstract
The Southern Hemisphere westerly winds have intensified in recent decades associated with a positive trend in the southern annular mode (SAM). However, the response of the Antarctic Circumpolar Current (ACC) transport and eddy field to wind forcing remains a topic of debate. This study uses global eddy-permitting ocean circulation models driven with both idealized and realistic wind forcing to explore the response to interannual wind strengthening. The response of the barotropic and baroclinic transports and eddy field of the ACC is found to depend on the spatial pattern of the changes in wind forcing. In isolation, an enhancement of the westerlies over the ACC belt leads to an increase of both barotropic and baroclinic transport within the ACC envelope, with lagged enhancement of the eddy kinetic energy (EKE). In contrast, an increase in wind forcing near Antarctica drives a largely barotropic change in transport along closed f/H contours (“free mode”), with little change in eddy activity. Under realistic forcing, the interplay of the SAM and the El Niño–Southern Oscillation (ENSO) influences the spatial distribution of the wind anomalies, in particular the partition between changes in the wind stress over the ACC and along f/H contours. This study finds that the occurrence of a negative or positive ENSO during a positive SAM can cancel or double the wind anomalies near Antarctica, altering the response of the ACC and its eddy field. While a negative ENSO and positive SAM favors an increase in EKE, a positive ENSO and positive SAM lead to barotropic transport changes and no eddy response.
Abstract
The rate at which the ocean moves heat from the tropics toward the poles, and from the surface into the interior, depends on diabatic surface forcing and diffusive mixing. These diabatic processes can be isolated by analyzing heat transport in a temperature coordinate (the diathermal heat transport). This framework is applied to a global ocean sea ice model at two horizontal resolutions (1/4° and 1/10°) to evaluate the partioning of the diathermal heat transport between different mixing processes and their spatial and seasonal structure. The diathermal heat transport peaks around 22°C at 1.6 PW, similar to the peak meridional heat transport. Diffusive mixing transfers this heat from waters above 22°C, where surface forcing warms the tropical ocean, to temperatures below 22°C where midlatitude waters are cooled. In the control 1/4° simulation, half of the parameterized vertical mixing is achieved by background diffusion, to which sensitivity is explored. The remainder is associated with parameterizations for surface boundary layer, shear instability, and tidal mixing. Nearly half of the seasonal cycle in the peak vertical mixing heat flux is associated with shear instability in the tropical Pacific cold tongue, highlighting this region’s global importance. The framework presented also allows for quantification of numerical mixing associated with the model’s advection scheme. Numerical mixing has a substantial seasonal cycle and increases to compensate for reduced explicit vertical mixing. Finally, applied to Argo observations the diathermal framework reveals a heat content seasonal cycle consistent with the simulations. These results highlight the utility of the diathermal framework for understanding the role of diabatic processes in ocean circulation and climate.
Abstract
The rate at which the ocean moves heat from the tropics toward the poles, and from the surface into the interior, depends on diabatic surface forcing and diffusive mixing. These diabatic processes can be isolated by analyzing heat transport in a temperature coordinate (the diathermal heat transport). This framework is applied to a global ocean sea ice model at two horizontal resolutions (1/4° and 1/10°) to evaluate the partioning of the diathermal heat transport between different mixing processes and their spatial and seasonal structure. The diathermal heat transport peaks around 22°C at 1.6 PW, similar to the peak meridional heat transport. Diffusive mixing transfers this heat from waters above 22°C, where surface forcing warms the tropical ocean, to temperatures below 22°C where midlatitude waters are cooled. In the control 1/4° simulation, half of the parameterized vertical mixing is achieved by background diffusion, to which sensitivity is explored. The remainder is associated with parameterizations for surface boundary layer, shear instability, and tidal mixing. Nearly half of the seasonal cycle in the peak vertical mixing heat flux is associated with shear instability in the tropical Pacific cold tongue, highlighting this region’s global importance. The framework presented also allows for quantification of numerical mixing associated with the model’s advection scheme. Numerical mixing has a substantial seasonal cycle and increases to compensate for reduced explicit vertical mixing. Finally, applied to Argo observations the diathermal framework reveals a heat content seasonal cycle consistent with the simulations. These results highlight the utility of the diathermal framework for understanding the role of diabatic processes in ocean circulation and climate.
Abstract
Mixing along sloping isopycnals plays a key role in the transport and uptake of heat and carbon by the ocean. This mixing is quantified by a lateral diffusivity, which can be measured by tracking the lateral spreading of point release tracer patches. We present a definition for the area of a tracer patch, the time derivative of which provides the lateral diffusivity. To accurately estimate the diffusivity, an ensemble mean concentration field of many tracer release experiments is required. We use numerical experiments to quantify how accurately the “true” lateral diffusivity (obtained from the ensemble mean concentration field) can be estimated from a single tracer release experiment (one ensemble member). To simulate observational campaigns, we also estimate the diffusivity from a single tracer release that is spatially and/or temporally subsampled, quantifying how the error between the estimated diffusivity and the true diffusivity grows as this sampling resolution worsens. We perform these numerical experiments in a two-layer quasigeostrophic model of turbulent flow on a β plane, using an ensemble of 50 passive tracer release experiments, each initialized as a 2D Gaussian but with differing realizations of the turbulent flow. We find that the diffusivity estimates from the single tracer releases have a relative root-mean-square error (RMSE) of 1.43% from the true diffusivity. Subsampling a single tracer release experiment every 956 km increases the relative RMSE from the true diffusivity to 3.1%; also subsampling every 277 days raises this figure to 6.5%.
Abstract
Mixing along sloping isopycnals plays a key role in the transport and uptake of heat and carbon by the ocean. This mixing is quantified by a lateral diffusivity, which can be measured by tracking the lateral spreading of point release tracer patches. We present a definition for the area of a tracer patch, the time derivative of which provides the lateral diffusivity. To accurately estimate the diffusivity, an ensemble mean concentration field of many tracer release experiments is required. We use numerical experiments to quantify how accurately the “true” lateral diffusivity (obtained from the ensemble mean concentration field) can be estimated from a single tracer release experiment (one ensemble member). To simulate observational campaigns, we also estimate the diffusivity from a single tracer release that is spatially and/or temporally subsampled, quantifying how the error between the estimated diffusivity and the true diffusivity grows as this sampling resolution worsens. We perform these numerical experiments in a two-layer quasigeostrophic model of turbulent flow on a β plane, using an ensemble of 50 passive tracer release experiments, each initialized as a 2D Gaussian but with differing realizations of the turbulent flow. We find that the diffusivity estimates from the single tracer releases have a relative root-mean-square error (RMSE) of 1.43% from the true diffusivity. Subsampling a single tracer release experiment every 956 km increases the relative RMSE from the true diffusivity to 3.1%; also subsampling every 277 days raises this figure to 6.5%.
Abstract
The strength and structure of the Southern Hemisphere meridional overturning circulation (SMOC) is related to the along-isopycnal and vertical mixing coefficients by analyzing tracer and density fields from a hydrographic climatology. The meridional transport of Upper Circumpolar Deep Water (UCDW) across the Antarctic Circumpolar Current (ACC) is expressed in terms of the along-isopycnal (K) and diapycnal (D) tracer diffusivities and in terms of the along-isopycnal potential vorticity mixing coefficient (K PV). Uniform along-isopycnal (<600 m2 s−1) and low vertical mixing (10−5 m2 s−1) can maintain a southward transport of less than 60 Sv (Sv = 106 m2 s−1) of UCDW across the ACC, which is distributed largely across the South Pacific and east Indian Ocean basins. For vertical mixing rates of O(10−4 m2 s−1) or greater, the inferred transport is significantly enhanced. The transports inferred from both tracer and density distributions suggest a ratio K to D of O(2 × 106) particularly on deeper layers of UCDW. Given the range of observed southward transports of UCDW, it is found that K = 300 ± 150 m2 s−1 and D = 10−4 ± 0.5 × 10−4 m2 s−1 in the Southern Ocean interior. A view of the SMOC is revealed where dense waters are converted to lighter waters not only at the ocean surface, but also on depths below that of the mixed layer with vertical mixing playing an important role.
Abstract
The strength and structure of the Southern Hemisphere meridional overturning circulation (SMOC) is related to the along-isopycnal and vertical mixing coefficients by analyzing tracer and density fields from a hydrographic climatology. The meridional transport of Upper Circumpolar Deep Water (UCDW) across the Antarctic Circumpolar Current (ACC) is expressed in terms of the along-isopycnal (K) and diapycnal (D) tracer diffusivities and in terms of the along-isopycnal potential vorticity mixing coefficient (K PV). Uniform along-isopycnal (<600 m2 s−1) and low vertical mixing (10−5 m2 s−1) can maintain a southward transport of less than 60 Sv (Sv = 106 m2 s−1) of UCDW across the ACC, which is distributed largely across the South Pacific and east Indian Ocean basins. For vertical mixing rates of O(10−4 m2 s−1) or greater, the inferred transport is significantly enhanced. The transports inferred from both tracer and density distributions suggest a ratio K to D of O(2 × 106) particularly on deeper layers of UCDW. Given the range of observed southward transports of UCDW, it is found that K = 300 ± 150 m2 s−1 and D = 10−4 ± 0.5 × 10−4 m2 s−1 in the Southern Ocean interior. A view of the SMOC is revealed where dense waters are converted to lighter waters not only at the ocean surface, but also on depths below that of the mixed layer with vertical mixing playing an important role.
Abstract
A method is developed for estimating the along-isopycnal and vertical mixing coefficients (K and D) and the absolute velocity from time-averaged hydrographic data. The method focuses directly on transports down tracer gradients on isopycnals. When the tracer considered is salinity or an appropriate variable for heat, this downgradient transport constitutes the along-isopycnal component of the thermohaline overturning circulation. In the method, a geostrophic streamfunction is defined that is related on isopycnals by tracer contours and by the thermal wind relationship in the vertical. Volume and tracer conservation constraints are also included. The method is overdetermined and avoids much of the signal-to-noise error associated with differentiating hydrographic data in conventional inverse methods. The method is validated against output of a layered model. It is shown to resolve both K and D, the downgradient isopycnal transport, and the mean flow on isopycnals in the North Pacific and South Atlantic.
Importantly, an understanding is established of both the physics underlying the method and the circumstances necessary for an inverse method to determine the mixing rates and the absolute velocity. If mixing is neglected, the method is the Bernoulli inverse method. At the limit of zero weight on the tracer-contour equations the method is a conventional box inverse method. Comparisons are drawn between each method and their relative merits are discussed. A new closed expression for the absolute velocity is also presented.
Abstract
A method is developed for estimating the along-isopycnal and vertical mixing coefficients (K and D) and the absolute velocity from time-averaged hydrographic data. The method focuses directly on transports down tracer gradients on isopycnals. When the tracer considered is salinity or an appropriate variable for heat, this downgradient transport constitutes the along-isopycnal component of the thermohaline overturning circulation. In the method, a geostrophic streamfunction is defined that is related on isopycnals by tracer contours and by the thermal wind relationship in the vertical. Volume and tracer conservation constraints are also included. The method is overdetermined and avoids much of the signal-to-noise error associated with differentiating hydrographic data in conventional inverse methods. The method is validated against output of a layered model. It is shown to resolve both K and D, the downgradient isopycnal transport, and the mean flow on isopycnals in the North Pacific and South Atlantic.
Importantly, an understanding is established of both the physics underlying the method and the circumstances necessary for an inverse method to determine the mixing rates and the absolute velocity. If mixing is neglected, the method is the Bernoulli inverse method. At the limit of zero weight on the tracer-contour equations the method is a conventional box inverse method. Comparisons are drawn between each method and their relative merits are discussed. A new closed expression for the absolute velocity is also presented.
Abstract
The tracer-contour inverse method is used to infer mixing and circulation in the eastern North Atlantic. Solutions for the vertical mixing coefficient D, the along-isopycnal mixing coefficient K, and a geostrophic streamfunction Ψ are all direct outputs of the method. The method predicts a vertical mixing coefficient O(10−5 m2 s−1) in the upper 1000 m of the water column, consistent with in situ observations. The method predicts a depth-dependent along-isopycnal mixing coefficient that decreases from O(1000 m2 s−1) close to the mixed layer to O(100 m2 s−1) in the interior, which is also consistent with observations and previous hypotheses. The robustness of the result is tested with a rigorous sensitivity analysis including the use of two independently constructed datasets.
This study confirms the utility of the tracer-contour inverse method. The results presented support the hypothesis that vertical mixing is small in the thermocline of the subtropical Atlantic Ocean. A strong depth dependence of the along-isopycnal mixing coefficient is also demonstrated, supporting recent parameterizations for coarse-resolution ocean models.
Abstract
The tracer-contour inverse method is used to infer mixing and circulation in the eastern North Atlantic. Solutions for the vertical mixing coefficient D, the along-isopycnal mixing coefficient K, and a geostrophic streamfunction Ψ are all direct outputs of the method. The method predicts a vertical mixing coefficient O(10−5 m2 s−1) in the upper 1000 m of the water column, consistent with in situ observations. The method predicts a depth-dependent along-isopycnal mixing coefficient that decreases from O(1000 m2 s−1) close to the mixed layer to O(100 m2 s−1) in the interior, which is also consistent with observations and previous hypotheses. The robustness of the result is tested with a rigorous sensitivity analysis including the use of two independently constructed datasets.
This study confirms the utility of the tracer-contour inverse method. The results presented support the hypothesis that vertical mixing is small in the thermocline of the subtropical Atlantic Ocean. A strong depth dependence of the along-isopycnal mixing coefficient is also demonstrated, supporting recent parameterizations for coarse-resolution ocean models.
