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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
Many recent studies have been devoted to atmospheric Patterns that persist beyond the synoptic time scale, such as those known as blocking events. In the present paper we explore the possibility that blocking patterns can be modeled with a local approach. We propose a truncated model that is a timedependent, highly nonlinear extension of our earlier analytical theory. In this theory, stationary coherent structures were found as asymptotic solutions of the inviscid, quasigeostrophic potential vorticity equation with a mean zonal wind with vertical and horizontal shear, in the limit of weak dispersion and weak nonlinearity. The truncated model is obtained by projecting the potential vorticity equation onto the orthonormal basis defined by the lowest order problem of the asymptotic theory and then suitably truncating the number of modes. The timeevolution of the model is investigated numerically with different truncations.
The steady solutions were antisymmetric dipoles, with the anticyclone north of the cyclone; they have an equivalent barotropic vertical structure and are meridionally as well as zonally trapped. We suggest that this solution could model the persistent patterns associated with blocking events that satisfy Rex's definition. An extensive series of numerical experiments is carried out to investigate the persistence of the steady solutions and their stability to different superimposed perturbations. The result is that, in an environment as turbulent as the real atmosphere, a typical estimate of the robustness (predictability) of the solution is of the order of 10 to 12 days. Such persistence is consistent with observations of blocking patterns.
Abstract
Many recent studies have been devoted to atmospheric Patterns that persist beyond the synoptic time scale, such as those known as blocking events. In the present paper we explore the possibility that blocking patterns can be modeled with a local approach. We propose a truncated model that is a timedependent, highly nonlinear extension of our earlier analytical theory. In this theory, stationary coherent structures were found as asymptotic solutions of the inviscid, quasigeostrophic potential vorticity equation with a mean zonal wind with vertical and horizontal shear, in the limit of weak dispersion and weak nonlinearity. The truncated model is obtained by projecting the potential vorticity equation onto the orthonormal basis defined by the lowest order problem of the asymptotic theory and then suitably truncating the number of modes. The timeevolution of the model is investigated numerically with different truncations.
The steady solutions were antisymmetric dipoles, with the anticyclone north of the cyclone; they have an equivalent barotropic vertical structure and are meridionally as well as zonally trapped. We suggest that this solution could model the persistent patterns associated with blocking events that satisfy Rex's definition. An extensive series of numerical experiments is carried out to investigate the persistence of the steady solutions and their stability to different superimposed perturbations. The result is that, in an environment as turbulent as the real atmosphere, a typical estimate of the robustness (predictability) of the solution is of the order of 10 to 12 days. Such persistence is consistent with observations of blocking patterns.
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
Many recent theoretical and observational studies have been devoted to the understanding of atmospheric patterns that persist beyond the synoptic time scale. These patterns are known as blocking events.
Properties of blocking events emerging from the observational evidence are consistent with the properties of nonlinear, i.e., coherent, localized structures characterized by locking of phases and phase speeds which are amplitude dependent.
In the present paper we develop a nonlinear, analytical theory with solutions in the form of stationary, coherent structures superimposed on a mean westerly wind. The model is the inviscid, quasigeostrophic potential vorticity conservation equation with a mean zonal wind having vertical as well as horizontal shear. The used mean wind profile is typical of the atmosphere at midlatitude. The stationary, coherent solution is an antisymmetric dipole, with the anticyclone north of the cyclone; it has an equivalent barotropic vertical structure, is meridionally as well as zonally trapped and obeys a nonlinear dynamics in the zonal wave guide.
This pattern, even though idealized, exhibits a strong similarity and is consistent with observations of blocking patterns.
Abstract
Many recent theoretical and observational studies have been devoted to the understanding of atmospheric patterns that persist beyond the synoptic time scale. These patterns are known as blocking events.
Properties of blocking events emerging from the observational evidence are consistent with the properties of nonlinear, i.e., coherent, localized structures characterized by locking of phases and phase speeds which are amplitude dependent.
In the present paper we develop a nonlinear, analytical theory with solutions in the form of stationary, coherent structures superimposed on a mean westerly wind. The model is the inviscid, quasigeostrophic potential vorticity conservation equation with a mean zonal wind having vertical as well as horizontal shear. The used mean wind profile is typical of the atmosphere at midlatitude. The stationary, coherent solution is an antisymmetric dipole, with the anticyclone north of the cyclone; it has an equivalent barotropic vertical structure, is meridionally as well as zonally trapped and obeys a nonlinear dynamics in the zonal wave guide.
This pattern, even though idealized, exhibits a strong similarity and is consistent with observations of blocking patterns.
Abstract
In this paper we exploit a nonlinear baroclinic theory of atmospheric Rossby waves superimposed on westerly winds with meridional and vertical shear which was proposed in two earlier studies, Parts I and II. In Part I, nonlinear, stationary Rossby wave solutions were found consisting of a localized vortex pair and having an equivalent barotropic structure. These solutions, found in the context of an asymptotic theory for the quasigeostrophic baroclinic potential vorticity equation, were proposed as a model for atmospheric blocking. In Part II, the theory was extended to the timedependent, highly nonlinear case, removing the weakamplitude limitations of the asymptotic theory of Part I. The localized highly nonlinear dipole solution of Part II was found to be remarkably robust to different energetic perturbations, even with a baroclinically unstable mean zonal wind. A typical persistence (predictability) time for the solution of Part II was of the order 10 to 15 days, consistent with observations of blocking patterns.
In this paper we investigate two further aspects of the highamplitude solution of Part II. First, we study the formation of the coherent dipole starting from rather different initial conditions. We establish a necessary and sufficient criterion for the formation of the coherent structure. This criterion involves the preexistence of a zonal low wavenumber component (wavenumber one) in an antisymmetric meridional mode having a large enough amplitude. If this condition is satisfied, the evolution into the block configuration is assured by the model internal dynamics that is of the KortewegdeVries type.
Second, we study the effect of shortscale, transient eddies upon the blocking dipole. We include dissipative effects and find that the eddy forcing is such to maintain the coherent structure against both mean advection and dissipation. The eddy forcing pattern resulting from the numerical experiments compares well with the observational evidence, given the high truncation of the model used.
Abstract
In this paper we exploit a nonlinear baroclinic theory of atmospheric Rossby waves superimposed on westerly winds with meridional and vertical shear which was proposed in two earlier studies, Parts I and II. In Part I, nonlinear, stationary Rossby wave solutions were found consisting of a localized vortex pair and having an equivalent barotropic structure. These solutions, found in the context of an asymptotic theory for the quasigeostrophic baroclinic potential vorticity equation, were proposed as a model for atmospheric blocking. In Part II, the theory was extended to the timedependent, highly nonlinear case, removing the weakamplitude limitations of the asymptotic theory of Part I. The localized highly nonlinear dipole solution of Part II was found to be remarkably robust to different energetic perturbations, even with a baroclinically unstable mean zonal wind. A typical persistence (predictability) time for the solution of Part II was of the order 10 to 15 days, consistent with observations of blocking patterns.
In this paper we investigate two further aspects of the highamplitude solution of Part II. First, we study the formation of the coherent dipole starting from rather different initial conditions. We establish a necessary and sufficient criterion for the formation of the coherent structure. This criterion involves the preexistence of a zonal low wavenumber component (wavenumber one) in an antisymmetric meridional mode having a large enough amplitude. If this condition is satisfied, the evolution into the block configuration is assured by the model internal dynamics that is of the KortewegdeVries type.
Second, we study the effect of shortscale, transient eddies upon the blocking dipole. We include dissipative effects and find that the eddy forcing is such to maintain the coherent structure against both mean advection and dissipation. The eddy forcing pattern resulting from the numerical experiments compares well with the observational evidence, given the high truncation of the model used.
Abstract
In a series of previous papers, a local theory was formulated to model the persistent atmospheric patterns known as blocking events. The adopted model was the fully nonlinear, baroclinic quasigeostrophic potential vorticity equation with a mean zonal wind having vertical and horizontal shear. Solutions were found consisting of localized dipole structures with an equivalent barotropic vertical structure. The basic “recipe” provided by the theory was that, in order to form a block characterized by a split flow with an embedded vortex pair, the upstream mean zonal wind ū(y, z) must have a structure which allows for local confinement. Specifically, the function V = ¼ − q̄_{y} /ū, with q̄_{y} , the meridional gradient of mean potential vorticity, must have the shape of a potential well. The bound states of this potential well are structures localized in the (y, z) plane and trapped by the well's positive barriers.
The data analysis carried out here and the results presented are designed to establish whether such a trapping structure exists for the positive blocking cases when compared with the winter climatological mean or other patterns such as the negative anomaly cases of Dole. The unambiguous and robust results emerging from the data analysis are: (i) the composite of the positive anomaly cases shows a strong northern barrier centered in the latitude band 62° to 72°N, in agreement with the northern confinement of the block. The southern barrier, if present, is not covered by the available data. The northern, positive barrier is not present in the climatology. Its presence and significance are doubtful and debatable for the negative anomaly composite. (ii) For the individual positive cases of blocking in which the vortex pair is sufficiently north to be fully covered by the analysis and for which a smooth and zonal upstream wind can be defined, the Vfunction shows both northern and southern positive brriers at the latitudes of block confinement.
Abstract
In a series of previous papers, a local theory was formulated to model the persistent atmospheric patterns known as blocking events. The adopted model was the fully nonlinear, baroclinic quasigeostrophic potential vorticity equation with a mean zonal wind having vertical and horizontal shear. Solutions were found consisting of localized dipole structures with an equivalent barotropic vertical structure. The basic “recipe” provided by the theory was that, in order to form a block characterized by a split flow with an embedded vortex pair, the upstream mean zonal wind ū(y, z) must have a structure which allows for local confinement. Specifically, the function V = ¼ − q̄_{y} /ū, with q̄_{y} , the meridional gradient of mean potential vorticity, must have the shape of a potential well. The bound states of this potential well are structures localized in the (y, z) plane and trapped by the well's positive barriers.
The data analysis carried out here and the results presented are designed to establish whether such a trapping structure exists for the positive blocking cases when compared with the winter climatological mean or other patterns such as the negative anomaly cases of Dole. The unambiguous and robust results emerging from the data analysis are: (i) the composite of the positive anomaly cases shows a strong northern barrier centered in the latitude band 62° to 72°N, in agreement with the northern confinement of the block. The southern barrier, if present, is not covered by the available data. The northern, positive barrier is not present in the climatology. Its presence and significance are doubtful and debatable for the negative anomaly composite. (ii) For the individual positive cases of blocking in which the vortex pair is sufficiently north to be fully covered by the analysis and for which a smooth and zonal upstream wind can be defined, the Vfunction shows both northern and southern positive brriers at the latitudes of block confinement.
Abstract
The major objective of oceanic data assimilation studies has been thus far to obtain a fourdimensional realization (space plus time) of the oceanic flow simultaneously consistent with the observations and the model dynamics. In these latest years, however, the forecasting of oceanic motions has emerged as a legitimate and important goal per se. In particular, the operational prediction of mesoscale flows and frontal systems has been the objective of recent assimilation applications in various regional systems of the World Ocean. One such effort focused on the shortterm prediction of the Gulf Stream system in the DAMEE GSR (Data Assimilation and Model Evaluation Experiments Gulf Stream Region) sponsored by the U.S. Navy. The objective of DAMEE GSR phases I and II was 1–2week forecast experiments. Phase III extended the suite of case studies by adding a 2monthlong assimilation experiment to assess the impact of longterm assimilations on model performance and forecasting skill.
In this paper the authors report the results of DAMEE GSR phase III but broaden the perspective by addressing two further issues, namely, the model sensitivity to the choice of the initial fields and the frequency of intermittent data assimilation. Two versions of the OTIS3 (Optimum Thermal Interpolation System) of the U.S. Navy Fleet Numerical Oceanography Center were available, providing slightly different distributions of temperature and salinity over the entire Gulf Stream system. They are referred to as OTIS3a, available with biweekly frequency from 4 May 1988 through 28 December 1988, in the context of a different assimilation work; and OTIS3b, provided by the DAMEE GSR phase III effort, for the 2month period 4 May–4 July 1988, with a slightly irregular frequency, weekly on the average. The main results can be summarized as follows.
The intermittent assimilation of the OTIS3b datasets with average weekly frequency profoundly improves the model forecasting skill. Without assimilation the model never beats persistence. With the assimilation, the modelpredicted Gulf Stream north wall is in excellent agreement with the verification infrared (IR) north wall, remaining always within the error bar of the IR north wall estimate, ±15km.
Two types of sensitivity experiments to the initial conditions were carried out: first, reconstruction of the initial fields with the two different OTIS3a and OTIS3b datasets but with the same initialization method; second, reconstruction of the initial fields with the same OTIS3a dataset but with two different initialization methods. The results show that the initial velocity field is much more crucial in affecting the model evolution and hence its predictive skill as it determines the stability properties of the Gulf Stream jet. Hence, it is very important to use the same dynamical initialization for velocity when starting from different distributions of temperature and salinity, as the jet profiles thus obtained will be very similar in structure and strength. This identical dynamical initialization will allow meaningful comparisons of experiments that start from slightly different density distributions.
Finally, we compare weekly assimilations of OTIS3b with biweekly and monthly assimilations of OTIS3a, initialized with the same procedure. The authors conclude that a weekly assimilation of the global OTIS3 dataset is not necessary and that a biweekly assimilation is equally effective in improving the model predictive skill.
Abstract
The major objective of oceanic data assimilation studies has been thus far to obtain a fourdimensional realization (space plus time) of the oceanic flow simultaneously consistent with the observations and the model dynamics. In these latest years, however, the forecasting of oceanic motions has emerged as a legitimate and important goal per se. In particular, the operational prediction of mesoscale flows and frontal systems has been the objective of recent assimilation applications in various regional systems of the World Ocean. One such effort focused on the shortterm prediction of the Gulf Stream system in the DAMEE GSR (Data Assimilation and Model Evaluation Experiments Gulf Stream Region) sponsored by the U.S. Navy. The objective of DAMEE GSR phases I and II was 1–2week forecast experiments. Phase III extended the suite of case studies by adding a 2monthlong assimilation experiment to assess the impact of longterm assimilations on model performance and forecasting skill.
In this paper the authors report the results of DAMEE GSR phase III but broaden the perspective by addressing two further issues, namely, the model sensitivity to the choice of the initial fields and the frequency of intermittent data assimilation. Two versions of the OTIS3 (Optimum Thermal Interpolation System) of the U.S. Navy Fleet Numerical Oceanography Center were available, providing slightly different distributions of temperature and salinity over the entire Gulf Stream system. They are referred to as OTIS3a, available with biweekly frequency from 4 May 1988 through 28 December 1988, in the context of a different assimilation work; and OTIS3b, provided by the DAMEE GSR phase III effort, for the 2month period 4 May–4 July 1988, with a slightly irregular frequency, weekly on the average. The main results can be summarized as follows.
The intermittent assimilation of the OTIS3b datasets with average weekly frequency profoundly improves the model forecasting skill. Without assimilation the model never beats persistence. With the assimilation, the modelpredicted Gulf Stream north wall is in excellent agreement with the verification infrared (IR) north wall, remaining always within the error bar of the IR north wall estimate, ±15km.
Two types of sensitivity experiments to the initial conditions were carried out: first, reconstruction of the initial fields with the two different OTIS3a and OTIS3b datasets but with the same initialization method; second, reconstruction of the initial fields with the same OTIS3a dataset but with two different initialization methods. The results show that the initial velocity field is much more crucial in affecting the model evolution and hence its predictive skill as it determines the stability properties of the Gulf Stream jet. Hence, it is very important to use the same dynamical initialization for velocity when starting from different distributions of temperature and salinity, as the jet profiles thus obtained will be very similar in structure and strength. This identical dynamical initialization will allow meaningful comparisons of experiments that start from slightly different density distributions.
Finally, we compare weekly assimilations of OTIS3b with biweekly and monthly assimilations of OTIS3a, initialized with the same procedure. The authors conclude that a weekly assimilation of the global OTIS3 dataset is not necessary and that a biweekly assimilation is equally effective in improving the model predictive skill.
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.
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
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.