Search Results
Abstract
In recent years there has been renewed interest in the Gulf Stream system and its interaction with the mesoscale oceanic eddy field. An important question, not yet adequately addressed, concern the possible generation mechanisms of the mesoscale eddy field and, in general, the problem of radiation of mesoscale energy from a meandering current. This problem has been investigated in a variety of studies, the basic result of which is that, in the quiescent ocean, the far field can transmit energy radiated by a meandering northern current only if the latter has a westward phase speed. All the proposed models are, however, linear. Nonlinear effects may be expected to modify the above results, as indicated by numerical experiments carried out with fully nonlinear models.
In the present study, the question is addressed in the context of a fully nonlinear but simple model, the quasigeostrophic equivalent barotropic potential velocity equation in a zonal channel over variable relief. The meandering current is idealized as a moving northern boundary. First, the case of free nonlinear Rossby wave radiation is studied. Solutions are found in both the weak and highamplitude limit. The latter solutions are symmetric monopoles with closed recirculation regions, strongly similar to the ring shapes observed to be shed by the Gulf Stream.
In the boundaryforced case, the weakly nonlinear problem is thoroughly analyzed and boundaryforced, equilibrium nonlinear solutions are found. The basic effects of nonlinearity can be summarized as follows:
1) Nonlinearity allows for the production of nonlinear radiation in the interior field through a resonance mechanism. The resonant, equilibriumforced solutions obey a forced Kortewegde Vries (KdV) equation and admit, for a specific choice of the forcing, two equilibrium amplitudes.
2) Allowing for a slow time modulation of the northern boundary wave, the resonant interior response obeys the timedependent KdV equation. Numerical experiments show that an initial condition corresponding to the steady equilibrium solution previously found evolves with soliton production in the region affected by the forcing. Thus, the interior response undergoes, on a long time scale, a nonlinear deterministic cascade process leading to nonlinear radiation of shorter wavelength.
3) In the limit of high nonlinearity, and for longwave radiation, it can be shown analytically that the crosschannel structure of the interior field is very different from the structure allowed by the corresponding linear model. In the linear case, over an essentially northwardsloping relief, an eastwardmoving boundary excites a response which, at best, has an oscillatory nature only in some interior, limited region, while exponentially decaying near the northern boundary. Conversely, in the highly nonlinear case the resonant response is oscillatory, i.e., radiating near the northern boundary. For sufficiently high nonlinearity, the excited eddy will have closed recirculation regions which may detach and propagate away from the boundary like Gulf Stream rings.
Abstract
In recent years there has been renewed interest in the Gulf Stream system and its interaction with the mesoscale oceanic eddy field. An important question, not yet adequately addressed, concern the possible generation mechanisms of the mesoscale eddy field and, in general, the problem of radiation of mesoscale energy from a meandering current. This problem has been investigated in a variety of studies, the basic result of which is that, in the quiescent ocean, the far field can transmit energy radiated by a meandering northern current only if the latter has a westward phase speed. All the proposed models are, however, linear. Nonlinear effects may be expected to modify the above results, as indicated by numerical experiments carried out with fully nonlinear models.
In the present study, the question is addressed in the context of a fully nonlinear but simple model, the quasigeostrophic equivalent barotropic potential velocity equation in a zonal channel over variable relief. The meandering current is idealized as a moving northern boundary. First, the case of free nonlinear Rossby wave radiation is studied. Solutions are found in both the weak and highamplitude limit. The latter solutions are symmetric monopoles with closed recirculation regions, strongly similar to the ring shapes observed to be shed by the Gulf Stream.
In the boundaryforced case, the weakly nonlinear problem is thoroughly analyzed and boundaryforced, equilibrium nonlinear solutions are found. The basic effects of nonlinearity can be summarized as follows:
1) Nonlinearity allows for the production of nonlinear radiation in the interior field through a resonance mechanism. The resonant, equilibriumforced solutions obey a forced Kortewegde Vries (KdV) equation and admit, for a specific choice of the forcing, two equilibrium amplitudes.
2) Allowing for a slow time modulation of the northern boundary wave, the resonant interior response obeys the timedependent KdV equation. Numerical experiments show that an initial condition corresponding to the steady equilibrium solution previously found evolves with soliton production in the region affected by the forcing. Thus, the interior response undergoes, on a long time scale, a nonlinear deterministic cascade process leading to nonlinear radiation of shorter wavelength.
3) In the limit of high nonlinearity, and for longwave radiation, it can be shown analytically that the crosschannel structure of the interior field is very different from the structure allowed by the corresponding linear model. In the linear case, over an essentially northwardsloping relief, an eastwardmoving boundary excites a response which, at best, has an oscillatory nature only in some interior, limited region, while exponentially decaying near the northern boundary. Conversely, in the highly nonlinear case the resonant response is oscillatory, i.e., radiating near the northern boundary. For sufficiently high nonlinearity, the excited eddy will have closed recirculation regions which may detach and propagate away from the boundary like Gulf Stream rings.
Abstract
An ocean general circulation model (OGCM) of the North Atlantic Ocean is fitted to the monthly averaged climatological temperatures and salinities of Levitus using the adjoint method, representing a significant step forward with respect to previous steady OGCM assimilations. The inverse approach has two important advantages over purely prognostic calculations: (i) it provides an estimate of the North Atlantic circulation and of its seasonal variability, which is optimally consistent with the OGCM dynamics and with the assimilated hydrography; (ii) it provides optimal estimates of the monthly surface heat and freshwater fluxes consistent with the used climatology, which are the most poorly known surface forcing functions.
Seasonality is ensured by penalizing field differences between month 13 and month 1 of the forward time integration within each iteration of the adjoint procedure. The primary goal of this work is to estimate largescale oceanic properties important for climate issues and how they are affected by the inclusion of the seasonal cycle. The resultant meridional overturning displays significant seasonal variations. The surface Ekman cell centered at 35°N reaches a maximum intensity of ∼7 Sv (Sv ≡ 10^{6} m^{3} s^{−1}) in wintertime, while the North Atlantic Deep Water cell reaches a maximum strength of ∼19 Sv in summertime. Its annual average is of ∼17 Sv, in good agreement with the recent estimate of Schmitz and McCartney. The poleward heat transport exhibits the strongest seasonal variations, reaching its maximum value of 0.85 × 10^{15} W at ∼25°N in summertime or 0.85 PW (1 PW = 10^{15} W). The annual average at 25°N is ∼0.7 PW, weaker than observational estimates. The dynamical analysis indicates that the wind forcing is the controlling factor for these variations by controlling the timevarying Ekman cell.
Comparison with previous steadystate optimizations of Yu and MalanotteRizzoli shows that the optimization with seasonal forcing produces three major improvements in the inverse results. First, the inclusion of the seasonal cycle greatly improves the estimated hydrography (temperature and salinity fields) by eliminating the basinwide cold bias in the upper ocean and the warm bias in the deep ocean found in the steadystate inversions. As a consequence, the velocity fields are also significantly improved, with a tight and strong Gulf Stream jet.
Second, the monthly optimal estimates of surface heat and freshwater fluxes provide an annual average resembling closely the observational climatological means, a striking contrast to the fluxes estimated in the steady assimilation.
Finally, the most important improvement is in the estimate of the poleward heat transport. The annual mean meridional heat transport shows an increase of ∼0.2 PW at all latitudes with respect to the steadystate heat transport, thus demonstrating the importance of rectification effects of the seasonal cycle.
Abstract
An ocean general circulation model (OGCM) of the North Atlantic Ocean is fitted to the monthly averaged climatological temperatures and salinities of Levitus using the adjoint method, representing a significant step forward with respect to previous steady OGCM assimilations. The inverse approach has two important advantages over purely prognostic calculations: (i) it provides an estimate of the North Atlantic circulation and of its seasonal variability, which is optimally consistent with the OGCM dynamics and with the assimilated hydrography; (ii) it provides optimal estimates of the monthly surface heat and freshwater fluxes consistent with the used climatology, which are the most poorly known surface forcing functions.
Seasonality is ensured by penalizing field differences between month 13 and month 1 of the forward time integration within each iteration of the adjoint procedure. The primary goal of this work is to estimate largescale oceanic properties important for climate issues and how they are affected by the inclusion of the seasonal cycle. The resultant meridional overturning displays significant seasonal variations. The surface Ekman cell centered at 35°N reaches a maximum intensity of ∼7 Sv (Sv ≡ 10^{6} m^{3} s^{−1}) in wintertime, while the North Atlantic Deep Water cell reaches a maximum strength of ∼19 Sv in summertime. Its annual average is of ∼17 Sv, in good agreement with the recent estimate of Schmitz and McCartney. The poleward heat transport exhibits the strongest seasonal variations, reaching its maximum value of 0.85 × 10^{15} W at ∼25°N in summertime or 0.85 PW (1 PW = 10^{15} W). The annual average at 25°N is ∼0.7 PW, weaker than observational estimates. The dynamical analysis indicates that the wind forcing is the controlling factor for these variations by controlling the timevarying Ekman cell.
Comparison with previous steadystate optimizations of Yu and MalanotteRizzoli shows that the optimization with seasonal forcing produces three major improvements in the inverse results. First, the inclusion of the seasonal cycle greatly improves the estimated hydrography (temperature and salinity fields) by eliminating the basinwide cold bias in the upper ocean and the warm bias in the deep ocean found in the steadystate inversions. As a consequence, the velocity fields are also significantly improved, with a tight and strong Gulf Stream jet.
Second, the monthly optimal estimates of surface heat and freshwater fluxes provide an annual average resembling closely the observational climatological means, a striking contrast to the fluxes estimated in the steady assimilation.
Finally, the most important improvement is in the estimate of the poleward heat transport. The annual mean meridional heat transport shows an increase of ∼0.2 PW at all latitudes with respect to the steadystate heat transport, thus demonstrating the importance of rectification effects of the seasonal cycle.
Abstract
An ocean GCM is used for idealized studies of the Atlantic circulation in a square basin. The subtropical, the tropical, and the equatorial gyres are produced by forcing the model with a wind stress profile having only latitudinal dependence. The goal is to understand the effect of the meridional overturning circulation (MOC) on the Atlantic intergyre exchanges. The MOC is imposed by prescribing an inflow all along the southern boundary and an outflow at the northern boundary. The results indicate that the northward flow of the MOC has a crucial effect on the subtropical–tropical pathways. In this idealized configuration the North Atlantic wind field creates a basinwide potential vorticity barrier. Therefore, the water subducted in the North Atlantic has to flow to the western boundary before turning equatorward. This is shown by the trajectories of floats injected in a band of northern latitudes. The warm water return flow of the MOC inhibits this pathway and reduces the inflow of North Atlantic waters into the equator from 10 Sv in the purely winddriven case to 2 Sv (Sv ≡ 10^{6} m^{3} s^{−1}). Thus, the equatorial thermocline consists mainly of water from the South Atlantic. The analysis of synthetic float trajectories reveals two distinct routes for the return flow of the MOC, the first one occurring in the intermediate layers along the western boundary and the second all across the basin in the surface layer. The surface path starts with water subducting in the South Atlantic subtropical gyre, flowing within the North Brazil Current to the equator, entering the Equatorial Undercurrent (EUC), becoming entrained into the tropical mixed layer, and finally flowing northward in the Ekman layer. The contribution of thermocline water to the MOC return flow is negligible.
Abstract
An ocean GCM is used for idealized studies of the Atlantic circulation in a square basin. The subtropical, the tropical, and the equatorial gyres are produced by forcing the model with a wind stress profile having only latitudinal dependence. The goal is to understand the effect of the meridional overturning circulation (MOC) on the Atlantic intergyre exchanges. The MOC is imposed by prescribing an inflow all along the southern boundary and an outflow at the northern boundary. The results indicate that the northward flow of the MOC has a crucial effect on the subtropical–tropical pathways. In this idealized configuration the North Atlantic wind field creates a basinwide potential vorticity barrier. Therefore, the water subducted in the North Atlantic has to flow to the western boundary before turning equatorward. This is shown by the trajectories of floats injected in a band of northern latitudes. The warm water return flow of the MOC inhibits this pathway and reduces the inflow of North Atlantic waters into the equator from 10 Sv in the purely winddriven case to 2 Sv (Sv ≡ 10^{6} m^{3} s^{−1}). Thus, the equatorial thermocline consists mainly of water from the South Atlantic. The analysis of synthetic float trajectories reveals two distinct routes for the return flow of the MOC, the first one occurring in the intermediate layers along the western boundary and the second all across the basin in the surface layer. The surface path starts with water subducting in the South Atlantic subtropical gyre, flowing within the North Brazil Current to the equator, entering the Equatorial Undercurrent (EUC), becoming entrained into the tropical mixed layer, and finally flowing northward in the Ekman layer. The contribution of thermocline water to the MOC return flow is negligible.
Abstract
An idealized numerical simulation of the tropical Atlantic Ocean is used to study the dynamics of an Atlantic subsurface countercurrent, the South Equatorial Undercurrent (SEUC). The particular structure of the SEUC between 28° and 10°W allows for a reformulation of the transformed Eulerian mean (TEM) equations with which the momentum balance of the SEUC can be explored. With this modified TEM framework, it is shown that between 28° and 10°W the SEUC is maintained against dissipation by the convergence of the Eliassen–Palm flux. The source of this Eliassen–Palm flux is the tropical instability waves that are generated along the shear between the Equatorial Undercurrent and the South Equatorial Current.
Abstract
An idealized numerical simulation of the tropical Atlantic Ocean is used to study the dynamics of an Atlantic subsurface countercurrent, the South Equatorial Undercurrent (SEUC). The particular structure of the SEUC between 28° and 10°W allows for a reformulation of the transformed Eulerian mean (TEM) equations with which the momentum balance of the SEUC can be explored. With this modified TEM framework, it is shown that between 28° and 10°W the SEUC is maintained against dissipation by the convergence of the Eliassen–Palm flux. The source of this Eliassen–Palm flux is the tropical instability waves that are generated along the shear between the Equatorial Undercurrent and the South Equatorial Current.
Abstract
The northern half of the Adriatic Sea is constituted by the continental shelf with very shallow depths (20 m) in the northernmost extremity. In particular, the newcoastal region adjacent to the Italian coastline forms a shallow strip, with isobaths running parallel to the coast and a topography gently increasing towards the interior of the basin. In the region immediately south of the Po River delta—the major source of fresh water input into the Adriatic—important eutrophication phenomena have recently occurred in summer. The controversial question thus arises whether these eutrophication phenomena are to be ascribed to nutrient inputs from local sources or from the Po River waters carried southward parallel to the Italian coastline in the general cyclonic gyre characterizing the Adriatic yearly average circulation. The dynamically important question is, then, whether and how a localized source of freshwater drives the nearcoastal shelf circulation.
To answer this question a multilevel hydrodynamic model coupled with equations for temperature and salinity was constructed to study the northern Adriatic circulation, which in the summer season can be approximated by a twolevel system. The model was run in a basic numerical experiment, with real input data, from 15 September to 16 October 1978, taken as a typical summer test case. The general conclusion of the investigation is that the “signal” of the Po River water, represented by the salinity field, is lost when progressing towards the coastline, even during intense episodes of northeast wind, when significant advective effects are present. In the newcoastal strip, moreover, the total transport in alongshore direction is most often directed northward contrary to what occurs in winter. Dynamical considerations suggest that the nearcoastal circulation is driven by the bottom torque, which dominates the dynamical bounce of forces as soon as an alongshore density gradient is present. The direction of the vertically integrated alongshore flow can be ascribed to this alongshore density gradient, which is significantly influenced by the Po freshwater outflow. Current records and preliminary experimental results seem to confirm the above numerical and dynamical considerations.
Abstract
The northern half of the Adriatic Sea is constituted by the continental shelf with very shallow depths (20 m) in the northernmost extremity. In particular, the newcoastal region adjacent to the Italian coastline forms a shallow strip, with isobaths running parallel to the coast and a topography gently increasing towards the interior of the basin. In the region immediately south of the Po River delta—the major source of fresh water input into the Adriatic—important eutrophication phenomena have recently occurred in summer. The controversial question thus arises whether these eutrophication phenomena are to be ascribed to nutrient inputs from local sources or from the Po River waters carried southward parallel to the Italian coastline in the general cyclonic gyre characterizing the Adriatic yearly average circulation. The dynamically important question is, then, whether and how a localized source of freshwater drives the nearcoastal shelf circulation.
To answer this question a multilevel hydrodynamic model coupled with equations for temperature and salinity was constructed to study the northern Adriatic circulation, which in the summer season can be approximated by a twolevel system. The model was run in a basic numerical experiment, with real input data, from 15 September to 16 October 1978, taken as a typical summer test case. The general conclusion of the investigation is that the “signal” of the Po River water, represented by the salinity field, is lost when progressing towards the coastline, even during intense episodes of northeast wind, when significant advective effects are present. In the newcoastal strip, moreover, the total transport in alongshore direction is most often directed northward contrary to what occurs in winter. Dynamical considerations suggest that the nearcoastal circulation is driven by the bottom torque, which dominates the dynamical bounce of forces as soon as an alongshore density gradient is present. The direction of the vertically integrated alongshore flow can be ascribed to this alongshore density gradient, which is significantly influenced by the Po freshwater outflow. Current records and preliminary experimental results seem to confirm the above numerical and dynamical considerations.
Abstract
In Part I of the present work we performed assimilation experiments with a multilayer, quasigeostrophic (QG) eddyresolving model of the ocean general circulation. In Part I we studied the quasilinear, steady state and the assimilated data were density measured along hydrographic sections. The major result of this study was that the most effective sections are long, meridional ones located at distance from the western boundary. The model estimates are significantly improved over the entire region extending from the data section to the western boundary itself.
In this second part we extend the study to the more realistic timedependent, fully eddyresolving ocean. Again we capitalize upon the two assumptions that the available models are imperfect and that data are measured only locally at meridional sections. The location of the sections are chosen according to (i) distance from the western boundary; (ii) energetics of the region. Also, here we compare assimilation of density alone versus density and velocity.
A crucial problem emerges when assimilating data into a fully nonlinear, timedependent model, that is the problem of model predictability The assimilated data can in fact be viewed as “perturbations” introduced into the model at a specific location. The important question is then: is data insertion performed only locally, i.e., along sections, sufficient to “drive” the model to the reference ocean overcoming the model inherent loss of predictability.
Different data sections are compared and the model performance is quantified monitoring two global rms (root mean square) errors, the rms DIFF1 between the model with inserted data and the reference ocean and the rms DIFF2 between the model with inserted data and without.
Two major results emerge from the present study. First, and differently from the quasilinear steady case, a single data section is very ineffective in driving the model towards the reference ocean over time scales of ∼100 days, comparable with the time scale of predictability loss. The rmserror DIFF2 is used to quantify the effectiveness of the different section as the “true” rmserror DIFF1 exhibits only random fluctuations around a mean equilibration value. The overall error level depends upon the balance between criteria (i) and (ii) above. Results are rationalized by dynamical considerations showing that the internal boundary forcing provided by the data insertion is equivalent to an additional stresscurl (vorticity source) imposed impulsively along a line in each layer. Also, the assimilation of barotropic and baroclinic information versus baroclinic only (velocity and density versus density only) has no effect on the error levels and error growth rates on the short time scale of mesoscale variability. In general, the error growth rates are not significantly different for any of the considered sections, both for the global rms errors measured over the entire basin and for local rmserrors measured over localized regions. On the short time scale of mesoscale variability, all the considered sections are equally ineffective.
A single section of data is shown instead to be quite effective in driving the model to the reference ocean if the data insertion process is carried out for time durations longer than the model equilibration time. With ten years of data assimilation, the climatological mean of the model becomes extremely similar to the climatological mean of the reference ocean. This result can now be quantified using the “true” rmserror DIFF1, which exhibits an unambiguous decreasing trend during the last years of assimilation, thus improving the estimate of the climatology up to 25%. Thus, single hydrographic sections might still be useful in providing a better model climatology if time series of data were available longer than the model equilibration time.
Abstract
In Part I of the present work we performed assimilation experiments with a multilayer, quasigeostrophic (QG) eddyresolving model of the ocean general circulation. In Part I we studied the quasilinear, steady state and the assimilated data were density measured along hydrographic sections. The major result of this study was that the most effective sections are long, meridional ones located at distance from the western boundary. The model estimates are significantly improved over the entire region extending from the data section to the western boundary itself.
In this second part we extend the study to the more realistic timedependent, fully eddyresolving ocean. Again we capitalize upon the two assumptions that the available models are imperfect and that data are measured only locally at meridional sections. The location of the sections are chosen according to (i) distance from the western boundary; (ii) energetics of the region. Also, here we compare assimilation of density alone versus density and velocity.
A crucial problem emerges when assimilating data into a fully nonlinear, timedependent model, that is the problem of model predictability The assimilated data can in fact be viewed as “perturbations” introduced into the model at a specific location. The important question is then: is data insertion performed only locally, i.e., along sections, sufficient to “drive” the model to the reference ocean overcoming the model inherent loss of predictability.
Different data sections are compared and the model performance is quantified monitoring two global rms (root mean square) errors, the rms DIFF1 between the model with inserted data and the reference ocean and the rms DIFF2 between the model with inserted data and without.
Two major results emerge from the present study. First, and differently from the quasilinear steady case, a single data section is very ineffective in driving the model towards the reference ocean over time scales of ∼100 days, comparable with the time scale of predictability loss. The rmserror DIFF2 is used to quantify the effectiveness of the different section as the “true” rmserror DIFF1 exhibits only random fluctuations around a mean equilibration value. The overall error level depends upon the balance between criteria (i) and (ii) above. Results are rationalized by dynamical considerations showing that the internal boundary forcing provided by the data insertion is equivalent to an additional stresscurl (vorticity source) imposed impulsively along a line in each layer. Also, the assimilation of barotropic and baroclinic information versus baroclinic only (velocity and density versus density only) has no effect on the error levels and error growth rates on the short time scale of mesoscale variability. In general, the error growth rates are not significantly different for any of the considered sections, both for the global rms errors measured over the entire basin and for local rmserrors measured over localized regions. On the short time scale of mesoscale variability, all the considered sections are equally ineffective.
A single section of data is shown instead to be quite effective in driving the model to the reference ocean if the data insertion process is carried out for time durations longer than the model equilibration time. With ten years of data assimilation, the climatological mean of the model becomes extremely similar to the climatological mean of the reference ocean. This result can now be quantified using the “true” rmserror DIFF1, which exhibits an unambiguous decreasing trend during the last years of assimilation, thus improving the estimate of the climatology up to 25%. Thus, single hydrographic sections might still be useful in providing a better model climatology if time series of data were available longer than the model equilibration time.
Abstract
One of the most important forthcoming synoptic datasets for ocean circulation studies will he the seasurface height data provided by the TOPEX /POSEIDON satellite. The TOPEX/POSEIDON project is in the planning stage and must still decide upon the particular characteristics of the satellite track. The repeat period will be between 10 and 20 days for a variety of technical and strategic reasons. These choices win give a global coverage with spatial resolution (eastwest or northsouth separation of crossover points) in midlatitudes of roughly 2.8° of latitude and longitude for a 10day repeat orbit and 1.4° of latitude and longitude for a 20day repeat orbit. Thus, the crucial question we address in the present study is: what is the effect of changing space or time resolution or both upon the success of a numerical model in reconstructing a fourdimensional picture a the ocean circulation through the assimilation of altimetric data?
To answer this question we carry out a series of numerical experiments with a threelayer, eddyresolving quasigeostrophic model of the ocean circulation in which we systematically vary the space and time resolutions of the data available for assimilation experiments. The experiments are carded out under the “best possible” conditions for the assimilation to be successful, namely: (i) the model is “perfect"; (ii) the data have no errors; and (iii) the data are dynamically compatible with the model since they are simulated by the model itself in a control run.
We reach the following conclusions. In principle, assimilation of altimetric data with a simple relaxation (“nudging”) technique can be very successful in driving the assimilation model to the control run even in the deep layers for which no data are supplied. This is achieved with a “nearly perfect” spacetime resolution surface height dataset in which data are supplied at every model grid point and every 0.5 day in time. The residual errors after one year of continuous assimilation amount to less than 10% in all three layers. When the altimetric data are provided along tracks with a given realistic separation (but complete time information), the decrease in space resolution degrades the model estimates somewhat. With data provided at every time step but a track separation of 280 km and making use of the best choice of assimilation procedures we have found that the residual rms errors amount to about 45% after six years of continuous assimilation. While the patterns of the circulation are somewhat different from those of the control run and the flow intensifies are slightly underestimated, the correspondences between the assimilation run and the control run are considerable. When the altimetric data are provided with a realistic time sampling period (but with space resolution at every grid point), the intensity of the flow fields also are somewhat underestimated, especially in the deep layer. The assimilation procedure is again capable, however, of reproducing quite faithfully the flow patterns throughout the water column.
When the altimetric data are assimilated along the actual tracks, that is only at the track gridpoints and at the actual time of arrival, the best assimilation results achieved with TOPEX repeat periods of 10 or 20 days are about equally effective for improving the model estimates of the circulation. The residual errors after 6 years of continuous time assimilation are from 60% to 70% for both 10 and 20day repeats. Apparently, the tradeoff between space and time resolutions just about compensate for each other. The results show that under the best of conditions (small errors, good model) a single satellite makes only minor improvements in the model estimates, and it cannot reconstruct the details of the mesoscale eddy field.
It should be kept in mind that these results depend on the space and time scales of motion in the region to be studied. Moreover, the conclusions reached here depend, to an unknown extent, on the assimilation technique used. Better techniques might allow us to better differentiate between the different spacetime choices for TOPEX and to reproduce the actual oceanic circulation more faithfully.
Abstract
One of the most important forthcoming synoptic datasets for ocean circulation studies will he the seasurface height data provided by the TOPEX /POSEIDON satellite. The TOPEX/POSEIDON project is in the planning stage and must still decide upon the particular characteristics of the satellite track. The repeat period will be between 10 and 20 days for a variety of technical and strategic reasons. These choices win give a global coverage with spatial resolution (eastwest or northsouth separation of crossover points) in midlatitudes of roughly 2.8° of latitude and longitude for a 10day repeat orbit and 1.4° of latitude and longitude for a 20day repeat orbit. Thus, the crucial question we address in the present study is: what is the effect of changing space or time resolution or both upon the success of a numerical model in reconstructing a fourdimensional picture a the ocean circulation through the assimilation of altimetric data?
To answer this question we carry out a series of numerical experiments with a threelayer, eddyresolving quasigeostrophic model of the ocean circulation in which we systematically vary the space and time resolutions of the data available for assimilation experiments. The experiments are carded out under the “best possible” conditions for the assimilation to be successful, namely: (i) the model is “perfect"; (ii) the data have no errors; and (iii) the data are dynamically compatible with the model since they are simulated by the model itself in a control run.
We reach the following conclusions. In principle, assimilation of altimetric data with a simple relaxation (“nudging”) technique can be very successful in driving the assimilation model to the control run even in the deep layers for which no data are supplied. This is achieved with a “nearly perfect” spacetime resolution surface height dataset in which data are supplied at every model grid point and every 0.5 day in time. The residual errors after one year of continuous assimilation amount to less than 10% in all three layers. When the altimetric data are provided along tracks with a given realistic separation (but complete time information), the decrease in space resolution degrades the model estimates somewhat. With data provided at every time step but a track separation of 280 km and making use of the best choice of assimilation procedures we have found that the residual rms errors amount to about 45% after six years of continuous assimilation. While the patterns of the circulation are somewhat different from those of the control run and the flow intensifies are slightly underestimated, the correspondences between the assimilation run and the control run are considerable. When the altimetric data are provided with a realistic time sampling period (but with space resolution at every grid point), the intensity of the flow fields also are somewhat underestimated, especially in the deep layer. The assimilation procedure is again capable, however, of reproducing quite faithfully the flow patterns throughout the water column.
When the altimetric data are assimilated along the actual tracks, that is only at the track gridpoints and at the actual time of arrival, the best assimilation results achieved with TOPEX repeat periods of 10 or 20 days are about equally effective for improving the model estimates of the circulation. The residual errors after 6 years of continuous time assimilation are from 60% to 70% for both 10 and 20day repeats. Apparently, the tradeoff between space and time resolutions just about compensate for each other. The results show that under the best of conditions (small errors, good model) a single satellite makes only minor improvements in the model estimates, and it cannot reconstruct the details of the mesoscale eddy field.
It should be kept in mind that these results depend on the space and time scales of motion in the region to be studied. Moreover, the conclusions reached here depend, to an unknown extent, on the assimilation technique used. Better techniques might allow us to better differentiate between the different spacetime choices for TOPEX and to reproduce the actual oceanic circulation more faithfully.
Abstract
Many coastal regions in the world ocean are characterized by wellmixed conditions to shelf depth in the density field during the winter season. In these situations it is appropriate to construct a model based on the assumption that the shelf is vertically well mixed. Such a model has been constructed assuming that (i) vertical mixing of momentum is stronger than either horizontal mixing or inertial effects; (ii) the density field is also vertically well mixed, i.e., varies only in horizontal at zero order in the expansion in the vertical Peclet number, (iii) the crossshelf scale is small compared to the alongshelf scale; (iv) depth varies only in crossshelf direction. The transport streamfunction equation and the advective density equation can then be combined into a single model equation by noting that in the vertically wellmixed flow, density is conserved as it is advected along streamlines.
This model is used to study two different configurations quite common for shelf circulations in the world ocean. The first configuration considers the effect of a deep baroclinic ocean in driving the shelf circulation. Past studies show that a barotropic deepocean pressure gradient cannot drive significant shelf flow and that the continental slope effectively “insulates”the shelf from the deep ocean. Thus, the basic question we want to answer is: how does the baroclinic structure of a deep ocean flow affect its ability to penetrate the shelf and determine its circulation? The second configuration to which the model is applied is that of a coastal current driven by an alongshore buoyancy source, such as a river discharge or an alongshore jet.
In all model applications studied, the basic mechanism by which the flow is able to cross topography is bottom friction. In the first situation the flow is driven by prescribing the velocity and density at the outer edge of the shelf. Three types of shelf forcing by the deep ocean are studied: a wide inflow, a narrow inflow and forcing by a Gulf Stream ring. A specific application is made to the northern Adriatic coastal shelf forced by a dense water pool formed in wintertime in the Adriatic interior. In all cases, the main conclusion for the baroclinic deepocean inflow onto the wellmixed shelf is that, like in the barotropic case, the tendency for the flow to follow isobaths is much stronger than the degree to which bottom friction allows crossisobath motion. The deep ocean inflow forces a horizontal boundary layer against the shelf edge. The width of this boundary layer, and therefore the shelf penetration, is larger if the drag coefficient is higher, the latitude lower or the bottom slope weaker. Also, surfaceintensified deep ocean flows penetrate the shelf few strongly than bottom intensified flows.
In the two examples studied of flow entering the shelf region near shore, i.e. a coastal river outflow and a coastal jet, it is again shown that the vertical shear of the shore inflow again determines the overall flow pattern. Because of bottom friction, a light alongshore jet or a low density river, i.e., surface intensified flow, expands across the topography more slowly than a bottom intensified flow, such as a high density river or a heavy jet.
Abstract
Many coastal regions in the world ocean are characterized by wellmixed conditions to shelf depth in the density field during the winter season. In these situations it is appropriate to construct a model based on the assumption that the shelf is vertically well mixed. Such a model has been constructed assuming that (i) vertical mixing of momentum is stronger than either horizontal mixing or inertial effects; (ii) the density field is also vertically well mixed, i.e., varies only in horizontal at zero order in the expansion in the vertical Peclet number, (iii) the crossshelf scale is small compared to the alongshelf scale; (iv) depth varies only in crossshelf direction. The transport streamfunction equation and the advective density equation can then be combined into a single model equation by noting that in the vertically wellmixed flow, density is conserved as it is advected along streamlines.
This model is used to study two different configurations quite common for shelf circulations in the world ocean. The first configuration considers the effect of a deep baroclinic ocean in driving the shelf circulation. Past studies show that a barotropic deepocean pressure gradient cannot drive significant shelf flow and that the continental slope effectively “insulates”the shelf from the deep ocean. Thus, the basic question we want to answer is: how does the baroclinic structure of a deep ocean flow affect its ability to penetrate the shelf and determine its circulation? The second configuration to which the model is applied is that of a coastal current driven by an alongshore buoyancy source, such as a river discharge or an alongshore jet.
In all model applications studied, the basic mechanism by which the flow is able to cross topography is bottom friction. In the first situation the flow is driven by prescribing the velocity and density at the outer edge of the shelf. Three types of shelf forcing by the deep ocean are studied: a wide inflow, a narrow inflow and forcing by a Gulf Stream ring. A specific application is made to the northern Adriatic coastal shelf forced by a dense water pool formed in wintertime in the Adriatic interior. In all cases, the main conclusion for the baroclinic deepocean inflow onto the wellmixed shelf is that, like in the barotropic case, the tendency for the flow to follow isobaths is much stronger than the degree to which bottom friction allows crossisobath motion. The deep ocean inflow forces a horizontal boundary layer against the shelf edge. The width of this boundary layer, and therefore the shelf penetration, is larger if the drag coefficient is higher, the latitude lower or the bottom slope weaker. Also, surfaceintensified deep ocean flows penetrate the shelf few strongly than bottom intensified flows.
In the two examples studied of flow entering the shelf region near shore, i.e. a coastal river outflow and a coastal jet, it is again shown that the vertical shear of the shore inflow again determines the overall flow pattern. Because of bottom friction, a light alongshore jet or a low density river, i.e., surface intensified flow, expands across the topography more slowly than a bottom intensified flow, such as a high density river or a heavy jet.
Abstract
In this work we take a first step in the process of assimilating data into models of the ocean general circulation. The goals is not prediction but rather understanding how the data insertion process affects, and is affected by, the dynamics governing the model. The chosen model ocean is steady, weakly nonlinear and highly frictional Strong vertical friction plays the role of eddy fluxes in driving the circulation in the deep layers.
In the data insertion process we capitalize upon the two principles that (i) the available dynamical models are imperfect; (ii) oceanographic data are measured locally. Three major questions are addressed; 1) what is the influence of local data insertion in terms of improving estimates of the model general circulation? 2) how does the model dynamics affect the spreading of information from the data insertion region? 3) what can we learn about the model physics from the effects of data insertion
Density (or temperature) measurements along long hydrographic or tomographic sections or arrays are chosen as data. We vary the location of the section as well as its orientation. In our highly frictional ocean, the most effective sections are meridional, long and located at a distance from the western boundary. Model estimates are then significantly improved over the broad region extending from the data section to the western boundary itself.
Advective effects are minimal and influence the spreading of information only in the intense western boundary current. Rather, the structure of the gyre interior manifests itself through a quite important steering effect exerted by the motion in the intermediate layer upon the spread of information in the surface layer. Due to this effect the region southwest of the data section is consistently preferred for the improvement of the estimates. Simple analytical computations are carried out to rationalize the numerical results. This effect is likely to persist in more realistic, fully eddyresolving simulations in which the interfacial eddy stresses would play the role here given to vertical friction.
The dependence of spreading of information upon the internal physics and/or external forcing is used to examine what is imperfect in the model parameterizations. In a simple analytical example we scan the twodimensional parameter space defined by internal friction and wind stress amplitude. The “correct” values of the above parameters cannot be inferred by this simple scanning due to the nonuniqueness of the solution.
Abstract
In this work we take a first step in the process of assimilating data into models of the ocean general circulation. The goals is not prediction but rather understanding how the data insertion process affects, and is affected by, the dynamics governing the model. The chosen model ocean is steady, weakly nonlinear and highly frictional Strong vertical friction plays the role of eddy fluxes in driving the circulation in the deep layers.
In the data insertion process we capitalize upon the two principles that (i) the available dynamical models are imperfect; (ii) oceanographic data are measured locally. Three major questions are addressed; 1) what is the influence of local data insertion in terms of improving estimates of the model general circulation? 2) how does the model dynamics affect the spreading of information from the data insertion region? 3) what can we learn about the model physics from the effects of data insertion
Density (or temperature) measurements along long hydrographic or tomographic sections or arrays are chosen as data. We vary the location of the section as well as its orientation. In our highly frictional ocean, the most effective sections are meridional, long and located at a distance from the western boundary. Model estimates are then significantly improved over the broad region extending from the data section to the western boundary itself.
Advective effects are minimal and influence the spreading of information only in the intense western boundary current. Rather, the structure of the gyre interior manifests itself through a quite important steering effect exerted by the motion in the intermediate layer upon the spread of information in the surface layer. Due to this effect the region southwest of the data section is consistently preferred for the improvement of the estimates. Simple analytical computations are carried out to rationalize the numerical results. This effect is likely to persist in more realistic, fully eddyresolving simulations in which the interfacial eddy stresses would play the role here given to vertical friction.
The dependence of spreading of information upon the internal physics and/or external forcing is used to examine what is imperfect in the model parameterizations. In a simple analytical example we scan the twodimensional parameter space defined by internal friction and wind stress amplitude. The “correct” values of the above parameters cannot be inferred by this simple scanning due to the nonuniqueness of the solution.
Abstract
Ocean Acoustic Tomography was proposed by Munk and Wunsch as a method for making measurements of ocean variability over large areas. After the successful demonstration of the feasibility of the idea in the 1981 threedimensional Mesoscale Experiment the tomography group has proposed a new experiment to be carried out in the Eastern Pacific Ocean, on ranges as long as the subtropical gyre scale.
This paper address the question of which average quantities of importance for the ocean general circulation and ocean climate can be measured by tomography and with what accuracy. The paper focuses upon the following quantities i) measurement of the heat content vertical profile horizontally averaged over a tomographic section; ii) time variability of the average heat content, or average pycnocline displacement, at different depths; iii) measurement of the average pycnocline slope at different depths.
To answer the above question the tomographic experiment is simulated in a given model ocean, using Holland's eddyresolving general circulation quasigeostrophic model. The results of the modeling simulations can be summarized as follows.

The tomographic technique bars upon the use of inverse methods to reconstruct the interior sound speed perturbation field, or, equivalently, the heat content field. Over ranges as long as the gyre scale, the typical result of a single inversion is to provide an ocean with warm or cold biases. A simple iterative procedure allows the removal of these biases. The final estimates of the mean heat content (averaged over the tomographic section) at different depths is very good.

Through a timeevolution experiment carried out for the duration of a full year, the time evolution of the average pycnocline displacement can be monitored at various depths. Thus tomography can measure the frequency spectrum of the average pycnocline displacement in layers below the surface mixed layer in which the circulation is basically winddriven.

The initial estimate of the average heat content can be significantly improved through a better specification of the statistics of the region, like the inclusion of a spatial mean in the horizontal covariance function for the sound speed perturbation. In particular, the inclusion of an inhomogeneous covariance modeling longscale pycnocline trends allow us to estimate the average pycnocline slope at various depths. The obtained slope estimates are very good. Measurement of isopycnal slopes averaged in time could be used for βspiral calculations. Thus, simple “density” tomography would provide a tool to evaluate the absolute velocity field and not only the geostrophic velocity shear.
Abstract
Ocean Acoustic Tomography was proposed by Munk and Wunsch as a method for making measurements of ocean variability over large areas. After the successful demonstration of the feasibility of the idea in the 1981 threedimensional Mesoscale Experiment the tomography group has proposed a new experiment to be carried out in the Eastern Pacific Ocean, on ranges as long as the subtropical gyre scale.
This paper address the question of which average quantities of importance for the ocean general circulation and ocean climate can be measured by tomography and with what accuracy. The paper focuses upon the following quantities i) measurement of the heat content vertical profile horizontally averaged over a tomographic section; ii) time variability of the average heat content, or average pycnocline displacement, at different depths; iii) measurement of the average pycnocline slope at different depths.
To answer the above question the tomographic experiment is simulated in a given model ocean, using Holland's eddyresolving general circulation quasigeostrophic model. The results of the modeling simulations can be summarized as follows.

The tomographic technique bars upon the use of inverse methods to reconstruct the interior sound speed perturbation field, or, equivalently, the heat content field. Over ranges as long as the gyre scale, the typical result of a single inversion is to provide an ocean with warm or cold biases. A simple iterative procedure allows the removal of these biases. The final estimates of the mean heat content (averaged over the tomographic section) at different depths is very good.

Through a timeevolution experiment carried out for the duration of a full year, the time evolution of the average pycnocline displacement can be monitored at various depths. Thus tomography can measure the frequency spectrum of the average pycnocline displacement in layers below the surface mixed layer in which the circulation is basically winddriven.

The initial estimate of the average heat content can be significantly improved through a better specification of the statistics of the region, like the inclusion of a spatial mean in the horizontal covariance function for the sound speed perturbation. In particular, the inclusion of an inhomogeneous covariance modeling longscale pycnocline trends allow us to estimate the average pycnocline slope at various depths. The obtained slope estimates are very good. Measurement of isopycnal slopes averaged in time could be used for βspiral calculations. Thus, simple “density” tomography would provide a tool to evaluate the absolute velocity field and not only the geostrophic velocity shear.