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A. R. Robinson and A. Gangopadhyay

Abstract

A multiparameter kinematic synthesis of multiscale feature models for the circulation of the western North Atlantic was developed in Part I of this study. The dispersion characteristics and dynamical behavior of this circulation model are presented here in detail. Insertion of the kinematically synthesized features into a numerical dynamical model dynamically adjust the features and provide the basis for a multiparameter sensitivity study with respect to the reasonable range of parameter variation consistent with observations. Two primary characteristics of the Gulf Stream meandering behavior, namely, the wave-growth characteristics and the ring formation and absorption statistics are studied via both quasigeostrophic and primitive equation dynamics. In achieving realistic dispersion characteristics, a comprehensive methodology for dynamical model tuning and validation in this limited region ocean is developed. The realistic regimes of parameter variation are identified on the basis of observational growth rate and phase speed of the Gulf Stream meanders. Long-term simulations within these realistic regimes provide statistics of ring production and interaction behavior. The observed range of transport variability of the Gulf Stream system further constrains the parameter selection. Final tuning of parameters is obtained through an extensive study of the response from the dynamical models to the changes of parameters of the circulation model. Usefulness of the circulation model for initializing, forecasting, and updating in real synoptic cases will be the focus of Part III of this series of studies.

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A. Gangopadhyay and A. R. Robinson

Abstract

The multiscale feature models (MSFMs) developed for the circulation of the western North Atlantic (Part I) have been used for initialization in this study to forecast the Gulf Stream meanders and rings. The Harvard primitive equation model, which was calibrated and verified for the statistics of the synoptical dynamics in this region (Part II), provides the basis for these simulations. Three 2-week-long synoptical dynamical hindcasts are presented. These hindcasts are carried out in a forecast mode without assimilating any future information. In general, when compared against SST-derived frontal location and ring–stream interactions, 2-week-long forecasts are found to be statistically superior than persistence and dynamically consistent. These forecasts are also compared against similar forecasts based on the U.S. Navy’s Optimum Thermal Interpolation System (OTIS) initializations. It is found that the MSFM-initialized simulations provide a better predictive capability than OTIS-initialized simulations over 2 weeks. Quantitatively, in terms of a statistical measure called the average offset of the axis of the stream, the former did better than persistence in all three cases over the 2-week periods. However, OTIS has two inherent characteristics, namely, a longitudinal distribution of temperature–salinity from climatology, and a warm pool at the core of the stream, which should be incorporated in the MSFM scheme to further enhance its predictive capability. The usefulness of multiscale kinematic synthesis in the initialization of the calibrated primitive equation dynamical model for forecasting the region over a 2-week period brings a closure to this three-part study of circulation and dynamics of the western North Atlantic.

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J. R. Luyten and A. R. Robinson

Abstract

Simultaneous path and bottom velocity measurements made during the Transient Meander Experiment, reported in Part I, are analyzed in terms of a quasi-geostrophic thin jet model of the meandering Gulf Stream. The theory gives an explicit representation of the velocity field which may be used to decompose the observed velocities. This representation is shown to be consistent with the observations. The dynamics of this model provides an equation of the path of the Stream, a cross-sectional average of the vorticity equation. A linearized form of this equation is used to examine the relations between the space and time scales of the variability. The historical data on the space and time scales of the meandering are shown to be consistent with those implicit in the linearized form of the path equation. The contributions to the local vorticity balance are estimated from the observations reported in Part I. The data, although complicated by observational errors, suggest a balance between the local rate of change of vorticity and the advection of vorticity. The contributions from vortex stretching due to variable topography appear to be unimportant for the scales of the meandering. The local dynamics appears to be fully time-dependent.

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A. R. Robinson and D. B. Haidvogel

Abstract

The initial/boundary value problem for the barotropic version of a quasi-geostrophic open ocean model which requires normal flow everywhere on the boundary and vorticity on the inflow is studied. Parameter dependencies and sensitivities are determined for dynamical forecast experiments carried out over a 500 square kilometer domain with data simulated to represent the mid-ocean eddy field at 1500 m. The computational rms forecast error due to open boundary conditions is kept to 5% after one year of integration. Errors, gaps and noise are then introduced into the boundary and initial condition data. Objective analysis is introduced for mapping coarsely-distributed data onto the computational grid, and vorticity is derived from the streamfunction by several methods. Forecast error is sensitive to the frequency of updating of boundary data, but generally insensitive to vorticity errors. A simulated forecast experiment with composite error sources representative of feasible oceanic conditions is carried out for four months duration with rms error maintained to about 10%.

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A. R. Robinson and J. C. McWilliams

Abstract

Baroclinic instability is examined in a two-layer, quasi-geostrophic model for linearized mesoscale waves (i.e., with periods of a few months and length scales near the internal deformation radius). The mid-ocean wave environment includes the, β-effect, bottom topography and mean currents, all presumed to vary only on scales much greater than those of the wave. An optimization of the local rate of unstable growth shows the process to be potentially important for mesoscale generation: typically, a vertical velocity shear of 5 cm sec−1 permits an e-folding time of two months. The many processes included in the model allow a great variety of behavior; for example, although both β and topography are generally stabilizing by themselves, their combination can be destabilizing.

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D. E. Harrison and A. R. Robinson

Abstract

A simple linear model of the barotropic basin response to forcing imposed along the northern boundary is described. The dependence on latitude of the response may include oscillatory behavior or not, depending on whether the forcing frequency is smaller or greater than the fundamental free basin mode frequency. When oscillatory behavior is found, the forced solution may resemble oceanic mesoscale eddies. The relevance of this simple model to a description of the eddy fields of several mesoscale resolution general ocean circulation numerical experiments is examined. It is found that a single term of the analytical solution can very well describe the numerically produced eddy fields, away from the regions of strong currents. The possibility that this general mechanism might account for the existence of mesoscale eddies in the ocean is briefly discussed.

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E. F. Carter and A. R. Robinson

Abstract

A general model for statistically optimal estimates is presented for dealing with scalar, vector and multivariale datasets. The method deals with anisotropic fields and treats space and time dependence equivalently. Problems addressed include the analysis, or the production of synoptic lime series of regularly gridded fields from irregular and gappy datasets, and the estimate of fields by compositing observations from several different instruments and sampling schemes. Technical issues are discussed, including the convergence of statistical estimates, the choice of representation of the correlations, the influential domain of an observation, and the efficiency of numerical computations.

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Michael A. Spall and Allan R. Robinson

Abstract

Primitive equation and quasi-geostrophic eddy resolving, open ocean models are used for hindcast studies in the Gulf Stream meander and ring formation region. A feature model approach is used to initialize the models, based on one month of observations during November to December 1984. Flat bottom and topographic calculations are carried out using an initial Gulf Stream velocity profile based on the Pegasus dataset. All of the major events observed in the upper thermocline are reproduced by both numerical models. The addition of bottom topography is shown to significantly alter the character of the deep velocity fields. Large, basin scale circulations found near the bottom in both flat bottom calculations were replaced by energetic jets and eddies associated with the dominant spatial scales of the bottom topography. Use of the quasi-geostrophic model to dynamically adjust the initial conditions for the primitive equation model is shown to reduce the growth of large scale meanders on time scales of one month. A local primitive equation energy and vorticity analysis (PRE-EVA) routine is used to determine the dominant processes of simulated warm and cold ring formation events. The warm ring formation is achieved by differential horizontal advection of a developed meander system. The cold ring formation involves geostrophic and ageostrophic horizontal advection, vertical advection, and baroclinic conversion. Ageostrophic horizontal and vertical advections and stronger baroclinic conversion are believed to be responsible for the more realistic structure of the rings produced by the primitive equation model.

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P. F. J. Lermusiaux and A. R. Robinson

Abstract

A rational approach is used to identify efficient schemes for data assimilation in nonlinear ocean–atmosphere models. The conditional mean, a minimum of several cost functionals, is chosen for an optimal estimate. After stating the present goals and describing some of the existing schemes, the constraints and issues particular to ocean–atmosphere data assimilation are emphasized. An approximation to the optimal criterion satisfying the goals and addressing the issues is obtained using heuristic characteristics of geophysical measurements and models. This leads to the notion of an evolving error subspace, of variable size, that spans and tracks the scales and processes where the dominant errors occur. The concept of error subspace statistical estimation (ESSE) is defined. In the present minimum error variance approach, the suboptimal criterion is based on a continued and energetically optimal reduction of the dimension of error covariance matrices. The evolving error subspace is characterized by error singular vectors and values, or in other words, the error principal components and coefficients.

Schemes for filtering and smoothing via ESSE are derived. The data–forecast melding minimizes variance in the error subspace. Nonlinear Monte Carlo forecasts integrate the error subspace in time. The smoothing is based on a statistical approximation approach. Comparisons with existing filtering and smoothing procedures are made. The theoretical and practical advantages of ESSE are discussed. The concepts introduced by the subspace approach are as useful as the practical benefits. The formalism forms a theoretical basis for the intercomparison of reduced dimension assimilation methods and for the validation of specific assumptions for tailored applications. The subspace approach is useful for a wide range of purposes, including nonlinear field and error forecasting, predictability and stability studies, objective analyses, data-driven simulations, model improvements, adaptive sampling, and parameter estimation.

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A. R. Robinson, J. R. Luyten, and F. C. Fuglister

Abstract

The results from an observational experiment on the mesoscale space-time variability of the Gulf Stream are reported. Various techniques, including aerial surveys, ship trackings of the 15C isotherm at 200 m, drogues and moored current meters were used and are compared, to give estimates of the variability of the motion over a wide range of scales. A two-week time series of daily tracks of the Stream near 70W are used to interpolate instantaneous paths over 2° of longitude. These paths provide the first detailed information on the small-scale variability of the path indicator of the Gulf Stream northeast of Cape Hatteras. Similarly, the long time series of triweekly aerial surveys provides a detailed picture of the evolution of a large-scale meander.

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