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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 quasi-geostrophic 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 high-amplitude 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 boundary-forced case, the weakly nonlinear problem is thoroughly analyzed and boundary-forced, 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, equilibrium-forced solutions obey a forced Korteweg-de 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 time-dependent 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 long-wave radiation, it can be shown analytically that the cross-channel structure of the interior field is very different from the structure allowed by the corresponding linear model. In the linear case, over an essentially northward-sloping relief, an eastward-moving 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 quasi-geostrophic 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 high-amplitude 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 boundary-forced case, the weakly nonlinear problem is thoroughly analyzed and boundary-forced, 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, equilibrium-forced solutions obey a forced Korteweg-de 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 time-dependent 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 long-wave radiation, it can be shown analytically that the cross-channel structure of the interior field is very different from the structure allowed by the corresponding linear model. In the linear case, over an essentially northward-sloping relief, an eastward-moving 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 time-dependent, highly nonlinear extension of our earlier analytical theory. In this theory, stationary coherent structures were found as asymptotic solutions of the inviscid, quasi-geostrophic 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 time-evolution 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 time-dependent, highly nonlinear extension of our earlier analytical theory. In this theory, stationary coherent structures were found as asymptotic solutions of the inviscid, quasi-geostrophic 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 time-evolution 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

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 large-scale 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 time-varying Ekman cell.

Comparison with previous steady-state optimizations of Yu and Malanotte-Rizzoli 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 steady-state 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 steady-state 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 large-scale 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 time-varying Ekman cell.

Comparison with previous steady-state optimizations of Yu and Malanotte-Rizzoli 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 steady-state 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 steady-state 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 wind-driven 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 wind-driven 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

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 quasi-geostrophic baroclinic potential vorticity equation, were proposed as a model for atmospheric blocking. In Part II, the theory was extended to the time-dependent, highly nonlinear case, removing the weak-amplitude 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 high-amplitude 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 Korteweg-deVries type.

Second, we study the effect of short-scale, 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 quasi-geostrophic baroclinic potential vorticity equation, were proposed as a model for atmospheric blocking. In Part II, the theory was extended to the time-dependent, highly nonlinear case, removing the weak-amplitude 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 high-amplitude 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 Korteweg-deVries type.

Second, we study the effect of short-scale, 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

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 new-coastal 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 multi-level 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 two-level 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 new-coastal strip, moreover, the total transport in alongshore direction is most often directed northward contrary to what occurs in winter. Dynamical considerations suggest that the near-coastal 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 new-coastal 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 multi-level 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 two-level 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 new-coastal strip, moreover, the total transport in alongshore direction is most often directed northward contrary to what occurs in winter. Dynamical considerations suggest that the near-coastal 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, quasi-geostrophic 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, quasi-geostrophic 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 Part I of the present work we performed assimilation experiments with a multilayer, quasi-geostrophic (QG) eddy-resolving model of the ocean general circulation. In Part I we studied the quasi-linear, 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 time-dependent, fully eddy-resolving 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, time-dependent 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 quasi-linear 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 rms-error DIFF2 is used to quantify the effectiveness of the different section as the “true” rms-error 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 stress-curl (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 rms-errors 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” rms-error 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, quasi-geostrophic (QG) eddy-resolving model of the ocean general circulation. In Part I we studied the quasi-linear, 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 time-dependent, fully eddy-resolving 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, time-dependent 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 quasi-linear 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 rms-error DIFF2 is used to quantify the effectiveness of the different section as the “true” rms-error 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 stress-curl (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 rms-errors 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” rms-error 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 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 quasi-geostrophic 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*, 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}*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 *V*-function 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 quasi-geostrophic 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*, 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}*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 *V*-function shows both northern and southern positive brriers at the latitudes of block confinement.