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Lagrangian data assimilation in ocean general circulation models
Abstract
Written by a group of international experts in their field, this book is a review of Lagrangian observation, analysis and assimilation methods in physical and biological oceanography. This multidisciplinary text presents new results on nonlinear analysis of Lagrangian dynamics, the prediction of particle trajectories, and Lagrangian stochastic models. It includes historical information, up-to-date developments, and speculation on future developments in Lagrangian-based observations, analysis, and modeling of physical and biological systems. Containing contributions from experimentalists, theoreticians, and modellers in the fields of physical oceanography, marine biology, mathematics, and meteorology, this book will be of great interest to researchers and graduate students looking for both practical applications and information on the theory of transport and dispersion in physical systems, biological modelling, and data assimilation.
Precise measurements of ocean surface flow velocities are essential for refining forecasts in a coupled ocean–atmosphere system. While oceanic data are generally sparse, surface drifters present an opportunity by providing detailed and frequently observed sea surface currents, which are a critical component in the dynamics at air–sea interface. Such observations could potentially address the usual data gaps in a coupled ocean–atmosphere assimilation system. In this study, we investigate the implications of assimilating drifter data within a coupled system with intermediate complexity based on a quasigeostrophic model—Modular Arbitrary-Order Ocean–Atmosphere Model (MAOOAM)—using observing system simulation experiments (OSSEs). Two main strategies for assimilating surface drifter data include the Eulerian approach, which translates Lagrangian positions into Eulerian velocity, and the fully Lagrangian method, which integrates both original fluid states and augmented drifter state variables into the system state vector. We evaluated both Lagrangian and Eulerian drifter assimilation techniques using the ensemble transform Kalman filter (ETKF) across two different coupling intensities within MAOOAM between the atmosphere and the ocean: one featuring strong interaction and the other featuring weak interaction. Our findings indicate a clear advantage of the Lagrangian method over the Eulerian, especially in estimating ocean streamfunctions and temperature. When combined with a large ensemble size and a short data assimilation (DA) window, the Lagrangian ensemble method adeptly manages atmospheric state error propagation. Additionally, as a preliminary demonstration, we evaluated a hybrid particle filter/ensemble Kalman filter (PF/EnKF) approach for Lagrangian DA in the coupled system with long DA windows, which can outperform the EnKF under specific configurations.
We consider the time-sequential state estimation of a flow field given a stream of noisy measurements that are provided by instruments advected by the flow, known as Lagrangian tracers or drifters. Lagrangian drifters collect real-time data as they move through the velocity field and are an important data collection method for atmospheric and oceanic measurements. We quantify the recovery of the Eulerian energy spectra from observations of Lagrangian drifters. This is performed by utilizing special Lagrangian data assimilation algorithms, known as conditionally Gaussian nonlinear filters. We address the following questions: how much of the turbulent Eulerian energy spectra can be recovered from assimilation of Lagrangian trajectory data and how accurately are the various energetic scales recovered relative to the truth. These issues are primarily studied in the perfect model scenario, but we quantify recovery due to model error by reduced order models via spectral truncation of the forecast model. We demonstrate high recovery skill of the two-dimensional turbulent energy spectra for both an exact filter and an imperfect filter, based on extreme localization of the covariance matrix, which is vastly cheaper than the exact filter, for both an inverse cascade spectrum with slope k−5∕3 and a direct cascade spectrum with slope k−3. The dependence of the spectral energy recovery skill on the number of tracers and the spectral truncation grid size is also studied.
We study the Lagrangian statistics of passively advected particles in an elementary velocity model for turbulent shear. The stochastic velocity model is exactly solvable and includes features that highlight the important differences between Lagrangian and Eulerian velocity statistics, which are not equal in the present context. A major element of the velocity model is the presence of a random, spatially uniform background mean, which is superimposed on a turbulent shear with a spectrum that typically follows a power law. We directly solve for the Eulerian and Lagrangian statistics and show how the sweeping motion of the background mean affects the Lagrangian velocity statistics with faster decaying correlations that oscillate more rapidly compared to the Eulerian velocity. This arises due to interaction of the cross-sweeps of the mean flow with the shear component, which determines Lagrangian tracer transport rates. We derive explicit expressions for the tracer dispersion that demonstrate how the dispersion rate depends on model parameters. We validate the predictions with numerical experiments in various test regimes that also highlight the behavior of Lagrangian particles in space. The proposed exactly solvable model serves as a test problem for Eulerian spectral recovery via Lagrangian data assimilation and parameter estimation methods.
The long-term goal of this project is the development and application of new methods of investigation for the use of Lagrangian data and other emerging in-situ and remote instruments (drifters, gliders, HF radar and satellite) that provide information on upper ocean advection. Special attention is given to the development of new techniques for data fusion and assimilation of data in Eulerian numerical models.
A model/data comparison was performed between simulated drifters from a high-resolution numerical simulation of the North Atlantic and a data set from in situ surface drifters. The comparison makes use of pseudo-Eulerian statistics such as mean velocity and eddy kinetic energy, and Lagrangian statistics such as integral time scales. The space and time distribution of the two data sets differ in the sense that the in situ drifters were released inhomogeneously in space and time while the simulated drifters were homogeneously seeded at the same time over a regular 1° grid. Despite this difference, the total data distributions computed over the complete data sets show some similarities that are mostly related to the large-scale pattern of Ekman divergence/convergence.
A new compilation of Lagrangian velocity observations describes the state of the North Atlantic surface circulation during the 1990s. Gridded fields of velocity and eddy kinetic energy (EKE) are constructed from trajectories of more than 1500 15-m drogued satellite-tracked surface drifters in service between January 1990 and December 1999. This time period overlaps a coordinated field study of circulation and variability in the North Atlantic completed between 1996–2000 as part of the World Ocean Circulation Experiment. We describe the construction of a self-consistent drifter climatology, present decadal-mean quasi-Eulerian velocity and EKE fields computed on a 1° grid, and compare these results with contemporary satellite measurements. Detailed discussion of the inferred surface circulation is focused on three regions: (1) The Gulf Stream and North Atlantic Current, (2) the Labrador Sea and subpolar gyre, and (3) the Caribbean Sea. The swiftest drifter motions were found in the equatorial region and along the tropical, subtropical, and subpolar western boundaries. The maximum instantaneous speed determined from a single (quality-controlled and filtered) drifter observation was 273 cm s−1 in the Gulf Stream southeast of Cape Cod. The highest EKE value in the North Atlantic (2790 cm2 s−2) was found in the Gulf Stream just downstream of the New England Seamounts. Over most of the Atlantic basin, drifter-derived EKE values were found to be O(100 cm2 s−2) higher than corresponding values derived from satellite altimetry. In the Labrador Sea a region of sharply elevated EKE appears to be geographically related to the localized ejection of drifters (and by extension, mass and kinetic energy) from the energetic West Greenland Current between 60° and 62°N. When compared to drifter measurements made in the late 1970s our results suggest (but do not statistically confirm) an enhancement and slight northward shift of the zonal Gulf Stream extension. Such a shift is consistent in sign with expectations based on observed interdecadal variations in wind stress and subtropical gyre potential energy associated with the North Atlantic Oscillation.
Horizontal divergence and vertical velocity in the surface mixed layer of the equatorial Pacific between 90° and 150°W are estimated from current measurements obtained from trajectories of freely drifting buoys during 1979-1990. The 12-year averaged horizontal divergence is predominantly meridional and has a maximum magnitude of 3-4 (×10-6 s-1) in a 20-km-wide latitude band centered on the equator. Using the equation of continuity, this divergence corresponds to an upwelling velocity of 1.5-2 (× 10-4 m s-1) at 50-m depth. The seasonal variations of equatorial divergence are in good agreement with the local zonal wind stress. -Author
The annual buildup and obliteration of the seasonal thermocline and the associated ventilation of the permanent thermocline in a wind- and thermally driven ocean basin are simulated numerically. The model developed for this purpose is a combination of a single-layer model of the oceanic mixed layer, based on a simple closure of the turbulence kinetic energy equation, and a three-dimensional isopycnic coordinate model of the stratified oceanic interior. The joint model, set in a rectangular ocean basin, is forced by annually varying wind stress and radiative plus turbulent heal fluxes approximating zonnaly averaged conditions over the North Atlantic. Special emphasis is placed on the description of the mixed-layer detrainment process, which requires distributing mixed-layer water of continuously variable density among constant-density interior layers. The truncation errors associated with this process are found to be numerically tolerable.
The quasi-Lagrangian character of the model's vertical coordinate permits easy tracking of water masses left behind during the annual retreat of the mixed layer to form the seasonal thermocline. Likewise, the subduction of ventilated water into the permanent thermocline by the horizontal gyre motion is explicitly simulated.
While a comparison of simulated mixed-layer characteristics with actual observations is problematic due to the idealized basin configuration, the model appears to be reasonably successful in duplicating the seasonal cycle of the zonally averaged conditions over the North Atlantic.
The historical dataset provided by 700-m acoustically tracked floats is analyzed in different regions of the northwestern Atlantic Ocean. The goal is to characterize the main properties of the mesoscale turbulence and to explore Lagrangian stochastic models capable of describing them. The data analysis is carried out mostly in terms of Lagrangian velocity autocovariance and cross-covariance functions. In the Gulf Stream recirculation and extension regions, the autocovariances and cross covariances exhibit significant oscillatory patterns on time scales comparable to the Lagrangian decorrelation time scale. They are indicative of sub- and superdiffusive behaviors in the mean spreading of water particles. The main result of the paper is that the properties of Lagrangian data can be considered as a superposition of two different regimes associated with looping and nonlooping trajectories and that both regimes can be parameterized using a simple first-order Lagrangian stochastic model with spin parameter Ω. The spin couples the zonal and meridional velocity components, reproducing the effects of rotating coherent structures such as vortices and mesoscale eddies. It is considered as a random parameter whose probability distribution is approximately bimodal, reflecting the distribution of loopers (finite Ω) and nonloopers (zero Ω). This simple model is found to be very effective in reproducing the statistical properties of the data.
A single-layer, reduced-gravity, double-gyre primitive equation model in a 2000 km x 2000 km square domain is used to test the accuracy and sensitivity of time-dependent Eulerian velocity fields reconstructed from numerically generated drifter trajectories and climatology. The goal is to determine how much Lagrangian data is needed to capture the Eulerian velocity field within a specified accuracy. The Eulerian fields are found by projecting, on an analytic set of divergence-free basis functions, drifter data launched in the active western half of the basin supplemented by climatology in the eastern domain. The time-dependent coefficients are evaluated by least squares minimization and the reconstructed fields are compared to the original model output. The authors find that the accuracy of the reconstructed fields depends critically on the spatial coverage of the drifter observations. With good spatial coverage, the technique allows accurate Eulerian reconstructions with under 200 drifters deployed in the 1000 km X 1400 km energetic western region. The base reconstruction error, achieved with full observation of the velocity field, ranges from 5% (with 191 basis functions) to 30% (with 65 basis functions). Specific analysis of the relation between spatial coverage and reconstruction error is presented using 180 drifters deployed in 100 different initial configurations that maximize coverage extremes. The simulated drifter data is projected on 107 basis functions for a 50-day period. The base reconstruction error of 15% is achieved when drifters occupy approximately 110 (out of 285) 70-km cells in the western region. Reconstructions from simulated mooring data located at the initial positions of representative good and poor coverage drifter deployments show the effect drifter dispersion has on data voids. The authors conclude that with appropriate coverage, drifter data could provide accurate basin-scale reconstruction of Eulerian velocity fields.
A reduced-order information filter (ROIF) for the Miami Isopycnal Coordinate Ocean Model (MICOM) is implemented for assimilation of the TOPEX/Poseidon sea surface height (SSH) data. ROIF is an approximate Kalman filter that compactly parameterizes the covariance matrix using a Gaussian-Markov random field. Performance of the assimilation system is investigated through observation system simulation experiments in an identical twin scenario. An adiabatic and eddy-resolving (20-km horizontal resolution) configuration for double-gyre simulation, as well as a more realistic North Atlantic model with thermodynamics, are considered. In each case, a 180-day assimilation window is found sufficient to reconstruct the surface layer topography by assimilating the SSH data sampled under the satellite tracks. The reconstructed geometric features, such as jet meanders, are found to be qualitatively accurate. A subsequent forecast run (without data assimilation) has also remained stable and accurate. An important profiling parameter in SSH assimilation is a strong positive correlation between SSH and the surface pressure (layer thickness).
Satellite-tracked drifting buoy data are being collected by numerous investigators and agencies in several countries for the World Ocean Circulation Experiment-Tropical Oceans Global Atmosphere (WOCE-TOGA) Surface Velocity Program. By the end of the century, and thereafter, this global dataset will provide the best available climatology and chronology of the surface currents of the World Ocean. To expedite completion of research quality datasets for archival and dissemination, a data acquisition activity is being conducted at NOAA Atlantic Oceanographic and Meteorological Laboratory (AOML), Miami, Florida. At AOML, data from drifting buoys of cooperating operators are quality controlled and optimally interpolated to uniform 6-h interval trajectories for archival at the Marine Environmental Data Service (Canada). This report describes in detail the procedures used in preparing these data for the benefit of second- or third-party users, or future buoy operators who may wish to process data in a consistent way. Particular attention is given to provide quantitative estimates for uncertainty of interpolation.
We present a new method for assimilating observations of sea surface height (SSH) into a high-resolution primitive equation model. The method is based on the concept of reinitialization. First, the surface velocity increments necessary to adjust the model forecast to the observed geostrophic surface currents are projected onto deep velocity increments by a linear regression method. Second, changes in the density field required to balance the changes in the velocity field geostrophically are obtained from an inversion of the thermal wind equation. A unique partition of the density increments into corresponding temperature and salinity changes is realized by conserving the local theta-S relation of the model forecast. In contrast to pure statistical methods that infer temperature and salinity changes from correlations with SSH anomalies, our approach explicitly conserves water mass properties on isopycnals. For the assimilation experiment we use optimally interpolated maps of Geosat SSH anomalies (the mean topography is taken from the model), which are assimilated into the World Ocean Circulation Experiment (WOCE) Community Modeling Effort (CME) model of the North Atlantic Ocean at 5-day intervals covering the year 1987. It is shown that the assimilation significantly improves the model's representation of eddy activity, with the hydrographic structure of individual eddies agreeing well with independent hydrographic observations. The importance of a careful treatment of water mass properties in the assimilation process is discussed and further illustrated by comparing different assimilation schemes.
A basin-scale, reduced-gravity model is used to study how drifter launch strategies affect the accuracy of Eulerian velocity fields reconstructed from limited Lagrangian data. Optimal dispersion launch sites are found by tracking strongly hyperbolic singular points in the flow field. Lagrangian data from drifters launched from such locations are found to provide significant improvement in the reconstruction accuracy over similar but randomly located initial deployments. The eigenvalues of the hyperbolic singular points in the flow field determine the intensity of the local particle dispersion and thereby provide a natural timescale for initializing subsequent launches. Aligning the initial drifter launch in each site along an outflowing manifold ensures both high initial particle dispersion and the eventual sampling of regions of high kinetic energy, two factors that substantially affect the accuracy of the Eulerian reconstruction. Reconstruction error is reduced by a factor of ~2.5 by using a continual launch strategy based on both the local stretching rates and the outflowing directions of two strong saddles located in the dynamically active region south of the central jet. Notably, a majority of those randomly chosen launch sites that produced the most accurate reconstructions also sampled the local manifold structure.
An isopycnic-coordinate oceanic circulation model formulated with the aim of simulating thermodynamically and mechanically driven flow in realistic basins is presented. Special emphasis is placed on the handling of diabatic surface processes and on thermocline ventilation. The model performance is illustrated by a 30-year spinup run with coarse horizontal resolution (2° mesh) in a domain with North Atlantic topography extending from 10° to 60°N latitude. The vertical structure encompasses 10 isopycnic layers in steps of 0.2 σ units, capped by a thermodynamically active mixed layer. From an initially isohaline state with isopycnals prescribed by zonally averaged climatology, the model is forced by seasonally varying wind stress, radiative and freshwater fluxes, and by a thermal relaxation process at the surface. After a mechanical spinup time of about 15 years, a quasi-stationary pattern of mean circulation and annual variability ensues, characterized by pronounced subtropical mode-water formation...
Because of the increases in the realism of OGCMs and in the coverage of Lagrangian datasets in most of the world's oceans, assimilation of Lagrangian data in OGCMs emerges as a natural avenue to improve ocean state forecast with many potential practical applications, such as environmental pollutant transport, biological, and naval-related problems.
In this study, a Lagrangian data assimilation method, which was introduced in prior studies in the context of single-layer quasigeostrophic and primitive equation models, is extended for use in multilayer OGCMs using statistical correlation coefficients between velocity fields in order to project the information from the data-containing layer to the other model layers. The efficiency of the assimilation scheme is tested using a set of twin experiments with a three-layer model, as a function of the layer in which the floats are launched and of the assimilation sampling period normalized by the Lagrangian time scale of motion.
It is found that the assimilation scheme is effective provided that the correlation coefficient between the layer that contains the data and the others is high, and the data sampling period Δt is smaller than the Lagrangian time scale TL. When the assimilated data are taken in the first layer, which is the most energetic and is characterized by the fastest time scale, the assimilation is very efficient and gives relatively low errors also in the other layers (≈ 40% in the first 120 days) provided that Δt is small enough, Δt << TL. The assimilation is also efficient for data released in the third layer (errors < 60%), while the dependence on Δt is distinctively less marked for the same range of values, since the time scales of the deeper layer are significantly longer. Results for the intermediate layer show a similar insensitivity to Δt, but the errors are higher (exceeding 70%), because of the lower correlation with the other layers. These results suggest that the assimilation of deep-layer data with low energetics can be very effective, but it is strongly dependent on layer correlation. The methodology also remains quite robust to large deviations from geostrophy.
An experiment design problem–-that of drifter cast strategy–-is discussed. Different optimization techniques used as part of preparations for the Semaphore-93 air-sea experiment, during which drifters were deployed, are examined. The oceanographic experiment objective was to sample a 500-km-square zone cantered at 33°N, 22°W in the Azores current area, using an average of 25 surface drifters for at least one month. We investigate different “orders of merit” for determining the performance of a particular cast strategy, as well as the method of genetic algorithms for optimizing the strategy. Our technique uses dynamic reference knowledge of the area where the simulation takes place. Two reference sets were used: a steady-state field calculated with data collected from the Kiel University April 1982 hydrographic experiment, and data output from a regional quasigeostrophic model assimilating two years of Geosat altimetric data. The strategies obtained via the genetic algorithm method were compared w...
Evolution of the Loop Current and the adjacent mesoscale rings was investigated over a 20-day period, starting June 1, 1998. Model sea-surface height and near-surface velocity fields from the Colorado University Princeton Ocean Model of the Gulf of Mexico were used along with drifter data in the study. A Lagrangian analysis provided detailed information about ring interaction and revealed features that were not apparent in the Eulerian picture. During the observation period, a new ring was formed in the meander of the Loop Current and a large anticyclonic ring to the west was cleaved by a cyclonic eddy. The coherent structures were identified in the Lagrangian framework by means of material curves (manifolds) that act as their boundaries. Concurrent drifter trajectories were in qualitative agreement with the results of the Lagrangian analysis.
This chapter provides a review of current operational practice and of advanced data assimilation techniques in meteorology. Numerical models can be used to assimilate meteorological and oceanographic data, creating a dynamically consistent, complete and accurate “movie” of the two geofluids, atmosphere, and ocean in motion. The ocean's strong stratification helps determine the most energetic scales and processes for the global ocean circulation. Active research on data assimilation is burgeoning rapidly in both meteorology and oceanography. Operational NWP requirements have produced a mature data-assimilation technology in meteorology, from which climatic research has benefitted as well. Ocean is characterized by transient, energetic motions with a broad spectrum in frequency and wave number. A steady component of the circulation may not even exist, and be only a model resulting from the analysis of data sets sparse in space and time, like hydrographic data sets, for which steadiness is assumed a priori. Thus, in oceanic data-assimilation problems, the choice of a model and related data assimilation scheme and the definition of success of the assimilation process itself depend crucially on the scientific issue of interest as the starting point.
1] Close to 1800 surface drifters are used to investigate the 15 m circulation of the North Atlantic Ocean. The data are used to describe structures of the average Eulerian circulation and of the associated eddy variability. The data resolve scales on the order of 50 km, which have hitherto not been systematically described, in particular, near shelf breaks and near the most intense currents, the Gulf Stream, the North Atlantic Current (NAC), and the frontal currents of the subpolar gyre. This reveals a complex series of quasi-permanent eddies, meanders, and recirculation patterns. Gulf Stream intensity is portrayed as changing abruptly near 54°W, east of which, it is identified as two current branches centered near 39° and 41.5°N, the northern one connecting more directly with the NAC, and the southern one with the recirculation gyre and the Azores Current (AC). Many features of the currents are controlled by topography, in particular, currents are often intensified near shelf breaks or parallel to ridges in the subpolar gyre. However, the largest northward branch of the NAC in the Icelandic basin is located near the deepest bathymetry, not near steep bathymetry. Other currents, in particular, in the subtropical gyre, are less clearly related to topography: for instance, the AC is featured as a zonal eastward current extending far west of the Mid-Atlantic Ridge (MAR) to at least 55°W and possibly 63°W. In the interior and away from topographic features the eddy kinetic energy (EKE) is the largest where the mean currents are the largest. In the subpolar gyre, there are striking differences in EKE between southward flowing currents (the Labrador and east Greenland Current) and the northward flowing currents (west Greenland Current and branches of the NAC), which have higher EKE. The areas of weakest variability are located in the southwest part of the subpolar gyre, northeast of Iceland, and in the eastern Atlantic south of 45°N. The AC eddies and the mesoscales south of the Canary Islands transect this eastern eddy desert. Drifter trajectories are used as realizations of Lagrangian particles in the vicinity of current cores. These illustrate the variety of paths or connections between different current systems and demonstrate cross-stream dispersions.
Point-vortex systems with both regular and chaotic motion can be tracked by a combination of Lagrangian observations of vortex position and of Eulerian observations of fluid velocity at a few fixed points. If only Eulerian observations are available, singularities in the tracking can develop due to nonlinearity in the observing functions on two occasions: when point vortices pass very close to an observing station, and when the observed speed is small. In Part II of this two-part paper, the vorticity concentrations are approximated by Rankine vortices with finite core in solid-body rotation, while a cut-off criterion is imposed on the Eulerian observations; this removes the singularities and hence results in satisfactory tracking when the observations are judiciously chosen.The main result is that a number of observations comparable to that of the distinct vorticity concentrations suffices for very accurate tracking. The key elements for successful tracking of Rankine-vortex systems using nonlinear, Eulerian observations are: distribution of available stations, threshold criteria for the selection of stations used in each update, and the observing frequency. Simple analysis provides the optimal estimate for these key elements, together with the optimal size of the estimated Rankine vortices.
Planetary flows-atmospheric and oceanic-are approximately two-dimensional and dominated by coherent concentrations of vorticity. Data assimilation attempts to determine optimally the current state of a fluid system from a limited number of current and past observations. In this two-part paper, an advanced method of data assimilation, the extended Kalman filter, is applied to the Lagrangian representation of a two-dimensional flow in terms of vortex systems. Smaller scales of motion are approximated here by stochastic forcing of the vortices.In Part I, the systems studied have either two point vortices, leading to regular motion or four point vortices and chaotic motion, in the absence of stochastic forcing. Numerical experiments are performed in the presence or absence of stochastic forcing. Point-vortex systems with both regular and chaotic motion can be tracked by a combination of Lagrangian observations of vortex positions and of Eulerian observations of fluid velocity at a few fixed points. Dynamically, the usual extended Kalman filter tends to yield insufficient gain if stochastic forcing is absent, whether the underlying system is regular or chaotic. Statistically, the type and accuracy of observations are the key factors in achieving a sufficiently accurate flow description. A simple analysis of the update mechanism supports the numerical results and also provides geometrical insight into them. In Part II, tracking of Rankine vortices with a finite core area is investigated and the results are used for observing-system design.
The motion of fluid parcels in a two-dimensional kinematic model of a meandering jet is investigated using Melnikov's method. The study is motivated by a recent analysis of float trajectories in the Gulf Stream. The results indicate that the efficiency of cross-jet exchange induced by fluctuating meander amplitudes depends strongly on the frequency of the fluctuations. For high frequencies (= or 0.04 cpd), exchange between the core of the jet and regions of 'trapped' fluid moving with the meander is preferred, while for low frequencies (= or 0.04 cpd), exchange between the 'trapped' fluid and the slow-moving fluid surrounding the jet is preferred. Propagating waves superimposed on the meandering jet can efficiently cause exchange between regimes when their phase speeds roughly match the basic flow velocities along the regime boundaries. Numerical results suggest that exchange across the center of the jet is less efficient than exchange between adjacent regimes so that the meandering jet will tend to stir fluid along each of its sides but preserve gradients across the jet core. (A)
In light of the increasing number of drifting buoys in the ocean and recent advances in the realism of ocean general circulation models toward oceanic forecasting, the problem of assimilation of Lagrangian observations data in Eulerian models is investigated. A new and general rigorous approach is developed based on optimal interpolation (OI) methods, which takes into account directly the Lagrangian nature of the observations. An idealized version of this general formulation is tested in the framework of identical twin experiments using a reduced gravity, quasi-geostrophic model. An extensive study is conducted to quantify the effectiveness of Lagrangian data assimilation as a function of the number of drifters, the frequency of assimilation, and the uncertainties associated with the forcing functions driving the ocean model. The performance of the Lagrangian assimilation technique is also compared to that of conventional methods of assimilating drifters as moving current meters, and assimilation of Eulerian data, such as fixed-point velocities. Overall, the results are very favorable for the assimilation of Lagrangian observations to improve the Eulerian velocity field in ocean models. The results of our assimilation twin experiments imply an optimal sampling frequency for oceanic Lagrangian instruments in the range of 20–50% of the Lagrangian integral timescale of the flow field.
Motivated by increases in the realism of OGCMs and the number of
drifting buoys in the ocean observing system, a new Lagrangian
assimilation technique is implemented in an idealized, reduced-gravity
configuration of the layered primitive equation model MICOM. Using an
extensive set of twin experiments, the effectiveness of the Lagrangian
observation operator and of a dynamical balancing technique for
corrected model variables, which is based on geostrophy and mass
conservation, are explored in comparison to a conventional
Pseudo-Lagrangian observation operator and an implementation of the
Kalman filter method. The results clearly illustrate that the Lagrangian
observation operator is superior to the Pseudo-Lagrangian in the
parameter range that is relevant for typical oceanic drifter
observations, and that the simple dynamical balancing technique works
well for midlatitude ocean circulation.
Copyrighted by American Geophysical Union. The well-known fact that tropical sea level can be usefully simulated by linear wind driven models recommends it as a realistic test problem for data assimilation schemes. Here we report on an assimilation of monthly data for the period 1975-1992 from 34 tropical Pacific tide gauges into such a model using a Kalman filter. We present an approach to the Kalman filter that uses a reduced state space representation for the required error covariance matrices. This reduction makes the calculation highly feasible. We argue that a more complete representation will be of no value in typical oceanographic practice, that in principle it is unlikely to be helpful, and that it may even be harmful if the data coverage is sparse, the usual case in oceanography. This is in part a consequence of ignorance of the correct error statistics for the data and model, but only in part. The reduced state space is obtained from a truncated set of multivariate empirical orthogonal functions (EOFs) derived from a long model run without assimilation. The reduced state space filter is compared with a full grid point Kalman filter using the same dynamical model for the period 1979-1985, assimilating eight tide gauge stations and using an additional seven for verification [Miller et al., 1995]. Results are not inferior to the full grid point filter, even when the reduced filter retains only nine EOFs. Five sets of reduced space filter assimilations are run with all tide gauge data for the period 1975-1992. In each set a different number of EOFs is retained: 5, 9, 17, 32, and 93, accounting for 60, 70, 80, 90, and 99% of the model variance, respectively. Each set consists of 34 runs, in each of which one station is withheld for verification. Comparing each set to the nonassimilation run, the average rms error at the withheld stations decreases by more than 1 cm. The improvement is generally larger for the stations at lowest latitudes. Increasing the number of EOFs increases agreement with data at locations where data are assimilated; the added structures allow better fits locally. In contrast, results at withheld stations are almost insensitive to the number of EOFs retained. We also compare the Kalman filter theoretical error estimates with the actual errors of the assimilations. Features agree on average, but not in detail, a reminder of the fact that the quality of theoretical estimates is limited by the quality of error models they assume. We briefly discuss the implications of our work for future studies, including the application of the method to full ocean general circulation models and coupled models.
The realism of large scale numerical ocean models has improved dra matically in recent years, in part because modern computers permit a more faithful representation of the differential equations by their algebraic analogs. Equally significant, if not more so, has been the improved under standing of physical processes on space and time scales smaller than those that can be represented in such models. Today, some of the most challeng ing issues remaining in ocean modeling are associated with parameterizing the effects of these high-frequency, small-space scale processes. Accurate parameterizations are especially needed in long term integrations of coarse resolution ocean models that are designed to understand the ocean vari ability within the climate system on seasonal to decadal time scales. Traditionally, parameterizations of subgrid-scale, high-frequency mo tions in ocean modeling have been based on simple formulations, such as the Reynolds decomposition with constant diffusivity values. Until recently, modelers were concerned with first order issues such as a correct represen tation of the basic features of the ocean circulation. As the numerical simu lations become better and less dependent on the discretization choices, the focus is turning to the physics of the needed parameterizations and their numerical implementation. At the present time, the success of any large scale numerical simulation is directly dependent upon the choices that are made for the parameterization of various subgrid processes.
The study of the ocean is almost as old as the history of mankind itself. When the first seafarers set out in their primitive ships they had to understand, as best they could, tides and currents, eddies and vortices, for lack of understanding often led to loss of live. These primitive oceanographers were, of course, primarily statisticians. They collected what empirical data they could, and passed it down, ini tially by word of mouth, to their descendants. Data collection continued throughout the millenia, and although data bases became larger, more re liable, and better codified, it was not really until surprisingly recently that mankind began to try to understand the physics behind these data, and, shortly afterwards, to attempt to model it. The basic modelling tool of physical oceanography is, today, the partial differential equation. Somehow, we all 'know" that if only we could find the right set of equations, with the right initial and boundary conditions, then we could solve the mysteries of ocean dynamics once and for all.
Observations of ocean circulation have increased as a result of international field programmes and of remote sensing systems on artificial earth satellites. Oceanographers are increasingly turning to inverse methods for combining these observations with numerical models of ocean circulation. Professor Bennett's work explores the potential for inverse theory, emphasizing possibilities rather than expedient or rudimentary applications. In addition to interpolating the data and adding realism to the model solutions, the methods can yield estimates for unobserved flow variables, forcing fields, and model parameters. Inverse formulations can resolve ill-posed modelling problems, lead to design criteria for oceanic observing systems, and enable the testing of models as scientific hypothesis. Exercises of varying difficulty rehearse technical skills and supplement the central theoretical development. Thus this book will be invaluable for environmental scientists and engineers, advanced undergraduates in applied mathematics, and graduate students in physical oceanography.
The motions of eight Autonomous Lagrangian Circulation Explorer (ALACE)
floats released near 750 m depth in Drake Passage and followed through
the South Atlantic are described and compared with emulations made by
advecting model floats through 12 monthly snapshots of velocity from the
fine resolution Antarctic model (FRAM). Both ALACEs and FRAM reproduce
the major features of the general circulation as follows: strong
intermediate depth flow in Drake Passage, bifurcation of the Antarctic
Circumpolar Current (ACC) passing over the Falkland Plateau, a strong
Falkland Current, its confluence with the Brazil Current, and moderate
zonal flow across the South Atlantic. FRAM versus ALACE comparisons are
made in both the Eulerian frame and using observed and modeled
trajectories. In Drake Passage, where float velocities agree with
earlier observations, FRAM velocities are about twice too big. Both FRAM
and ALACE velocities are consistent with an O(100 Sv) Falkland Current.
In the central South Atlantic the few available float observations
indicate the ACC and South Atlantic Current (SAC) to be more localized
than in the model. Eddy kinetic energy is much stronger in the
observations than in FRAM. Float dispersion in both the model and
observations is due primarily to mean shear. Initial RMS particle
separation of 100 km grows to nearly 1000 km after 1 year, but most of
this is associated with floats that take different paths of the general
circulation. The observations indicate that eddy effects are
particularly important near the Falkland-Brazil Current confluence in
allowing Antarctic Intermediate Water to transfer from the ACC to the
SAC, from which they may enter the subtropical gyre.
The prospect for describing advection and eddy transport of tracers in the general circulation using floats is examined. This is done within the context of a recently proposed generalization of the advection-diffusion equation for passive scalars in which eddy transport is governed by a time-dependent eddy diffusivity tensor κ(t) which at large t approaches the constant κ(∞) appropriate to pure advection-diffusion models. A minimal description of the general circulation would include the Eulerian mean velocity U(x) and the diffusivity κ(t). Given sufficient numbers of current-followers which adequately follow ideal fluid particles, both the horizontal components of U and the purely horizontal components of K could be measured.
During 1983 and 1984, approximately 40 neutrally buoyant (isopycnal) floats were released into the Gulf Stream. These floats, which were released at approximately weekly intervals, measured their location and depth three times a day for 30–45 days. The basic statistics of these floats are briefly described. This float data set has been applied to the important problem of assimilation of Lagrangian information into a numerical model of the oceanic mesoscale. The assimilation method is a Kalman-filter type technique. Since the processed float data consists of a time series of position, velocity and depth it is natural to use a dynamical model that uses these variables directly. For this purpose a simple shallow-water model utilizing a Lax-Wendroff numerical scheme is used. This type of numerical model has been successfully used in meteorological data assimilation studies. Some results using both one- and two-dimensional versions of this model are described.
As part of the World Ocean Circulation Experiment, 300 Autonomous Lagrangian Circulation Explorer floats were deployed in the tropical and South Pacific to measure the general circulation at 900 m depth. Most floats measured average currents over 25 submerged days between ascents to the surface for locating and data relay. By the end of 1997, over 12,500 observations spanning 840 float years were obtained. Accuracy of the average velocity is limited by variability, some of which is found to arise from steady flows with spatial variations smaller than averaging scales. Observed 25-day velocities are serially uncorrelated except near the equator where energetic zonal variability has seasonal timescales and appears to be described by a data-assimilating ocean circulation model run by the National Centers for Environmental Prediction. Space-time averages of float velocities disclose a general pattern of middepth flow that resembles the surface circulation with the strongest flows of O (3 cm/s) in the deep Antarctic Circumpolar Current and East Australian Current. The weaker elements of the flow, including an interior subtropical circulation with O (millimeters per second) flows, are described by an objective analysis whose accuracy is limited by sampling noise rather than uncertainty of the analysis parameters. The subtropical circulation has a gyres-within-a-gyre structure including boundary currents along Australia and east of New Zealand and a concentrated equatorial limb with surprising strength in the western basin. This current is also involved in a tropical gyre with generally eastward flow along the equator in the western basin at least. Because of strong seasonal-scale variability, the equatorial zonal currents are not well measured yet but data are still being accumulated. Comparison with Reid's [1997] absolute circulation shows more areas of agreement than of disagreement.
ABSTRACT Eulerian and Lagrangian statistics were calculated from the North Atlantic surface drifter dataset for the years 1993‐97 and a high-resolution eddy-resolving configuration,of the Los Alamos National Laboratory (LANL) Parallel Ocean Program (POP) model. The main purpose of the study was to statistically quantify the state of the surface circulation in the North Atlantic Ocean for this period and compare,it with the equivalent modeled state. Diffusivities and time and length scales are anisotropic over most of the ocean basin, except in most of the subpolar regions. Typical time and length scales are 2‐4 days and 20‐50 km. Longest timescales are found in the energetically quiescent regions in the south and southeast sectors of the basin. The longest length scales are found in the energetic western boundary current system, the most dispersive region of the domain. In many respects the eddy-resolving model reproduced a surface circulation in good statistical agreement,with that depicted by the drifters. Model time and length scales were also anisotropic, with typical timescales of 2‐4 days and length scales of 20‐50 km in the zonal direction, and 30‐50 km in the meridional direction. An eddy-permitting POP simulation produced,unrealistic time and length scales that were,too long and too short relative to the drifter scales; these were attributed to the model being too stable hydrodynamically.
Lagrangian data from 657 SVP drifters, CNES/Aviso (Archiving, Validation, and Interpretation of Satellite Oceanographic data) time variable satellite altimeter sea level anomaly and Levitus 98 hydrographic data are used to develop 0.25° spatial resolution maps of the mean and eddy circulations in the northwestern Pacific during the 1990s. Drifter velocities at 15 m depth and 200 m temperature data clearly indicate in the Kuroshio Extension (KE) jet two prominent meanders that culminate in a 300 km northward deflection east of the Shatsky Rise at 160°E. The interannual trends of Aviso mesoscale variance are absent along the path of the meandering KE jet. Three anticyclonic recirculations can be identified south or southeast of the Kuroshio, the southernmost around Daito Island being a new discovery. About 3% of the drifters with drogues attached crossed the Kuroshio front. The Aviso currents are correlated at 0.8 with drifter geostrophic velocity. The Aviso geostrophic currents are adjusted in amplitude to the contemporaneous drifter observations and are further used to compute an unbiased mean geostrophic circulation and the quasi-geostrophic Reynolds' stresses in the KE region. The principal axes of the eddy Reynolds' stresses are oriented along the unbiased mean velocity vectors within the meandering KE jet. The time-mean horizontal momentum balance that includes both the mean and eddy momentum convergences is used to compute absolute sea level map and its uncertainty. At 145°E the 2000 m depth absolute dynamic height referenced to the sea level reveals a heretofore unknown 70 dynamic cm drop from 25° to 42°N.
A hierarchy or inhomogeneous, nonstationary stochastic models of material transport is formulated, and its properties are described. The transport models from the hierarchy sequence provide progressively more skillful simulations of the subgrid-scale transport by mesoscale eddies, which are typically not resolved in coarse-grid representations of the ocean circulation. The stochastic transport models yield random motion of individual passive particles, and the probability density function of the particle population can be interpreted as the concentration of a passive tracer. Performance of the models is evaluated by (a) estimating their parameters from Eulerian and Lagrangian statistics of a fluid-dynamic reference solution, (b) solving for the transport, and (c) comparing the stochastic and fluid-dynamic transports. The reference solution represents midlatitude oceanic gyres, and it is found by solving steadily forced, quasigeostrophic equations of motion at large Reynolds number. The gyres are characterized by abundant coherent structures, such as swift, meandering currents, strong vortices, eddies, and planetary waves. The common, nondiffusive spreading of material (i.e., single-particle dispersion that is a nonlinear function of time) is induced by all these structures on intermediate times and by inhomogeneity and lateral boundaries on longer times. The higher-order members of the hierarchy are developed specially for simulating nondiffusive transports by turbulence in the presence of organized fluid patterns. The simplest, but least skillful, member of the hierarchy is the commonly used diffusion model. In terms of the random particle motion, the diffusion is equivalent to the random walk (Markov-O) process for particle positions. The higher-order members of the hierarchy are the Markov-1 (a.k.a. Langevin or random acceleration), Markov-2, and Markov-3 models, which are jointly Markovian for particle position and its time derivatives. Each model in the hierarchy incorporates all features of the models below it. The Markov-1 model simulates short-time ballistic behavior associated with exponentially decaying Lagrangian velocity correlations, but on large times it is overly dispersive because it does not account for trapping of material by the coherent structures. The Markov-2 model brings in the capability to simulate intermediate-time, subdiffusive (slow) spreading associated with such trappings and with both decaying and oscillating Lagrangian velocity correlations. The Markov-3 model is also capable of simulating intermediate-time, superdiffusive (fast) spreading associated with sustained particle drifts combined with the trapping phenomenon and with the related asymmetry of the decaying and oscillating Lagrangian velocity correlations.
A simultaneous assimilation model of drifting buoy and altimetric data is proposed to determine the mean sea surface height (SSH) as well as the temporal evolution of the surface circulation on synoptic scales. To demonstrate the efficiency of our assimilation model, several identical twin experiments for the double-gyre circulation system are performed using a 11/2-layer primitive equation model. An optimal interpolation for the multivariate is used for the assimilation scheme that assumes the geostrophic relationship between the error fields of the velocity and the interface depth. To identify the nature of the assimilation of the buoy-derived velocities into the dynamical ocean model, the authors first conduct the assimilation experiment using the drifting buoy data alone. The result shows that realistic buoy deployment (32 in a 40° square) can effectively constrain the model variables; that is, both the absolute (mean plus time varying) velocity and SSH (interface depth) fields are significantly improved by this buoy data assimilation. Moreover, in the case of denser buoy deployment in the energetic western boundary current regions, where the mean SSH is comparable to the time-varying part and the geoid error is relatively large, the assimilation provides a better determination of the absolute velocity and SSH. This is because significant changes in the mean SSH lead to an improvement along the extensive buoy trajectories associated with the strong current. It is worth noting that the assimilation of drifting buoy data is more effective than that of moored velocity data, thanks to the Lagrangian information content of the drifting buoys. Successive correction of the mean SSH is made with simultaneous assimilation of drifting buoy and altimetric data. Consequently, a better correction of the mean SSH is obtained: The initial error of the mean SSH is reduced by approximately 40% after the 1-year experiment. In contrast, the assimilation experiment of altimetric data alone corrects only the time-varying part, but yields little error reduction for the mean SSH in our model. These results clearly show that the simultaneous assimilation of drifting buoy and altimetric data into the dynamical model is a very useful tool for improving the model's realism.
One hundred isopycnal floats were tracked on the 27.2 and 2.75 sigmatheta surfaces in the Newfoundland Basin (NFB) from July 1993 to July 1995 to study the current structure and exchanges of waters between the subtropical and subpolar gyres. The float-mapped mean flow consists of weak flows in the NFB and a strong boundary current (the North Atlantic Current (NAC)), which separates from the boundary at the Northwest Corner, becoming a diffusive zonal drift. The NAC meanders are linked to topography and have similar patterns on the two isopycnals despite the fact that the upper layer velocities are twice as fast as the lower layer ones. Perturbation velocity from the mean is used to compute isopycnal turbulent dispersion and diffusivity. This large data set allows us to resolve a narrow mean NAC and results in a Gaussian turbulence. The turbulence approximately follows the classic Taylor dispersion theory. Integral timescales and length scales and turbulent isopycnal diffusivity are of 1.5-2.5 days, 20-30 km, and (1-7)×103m2s-1, respectively. The timescale increases with depth and decreases with latitude, the length scale decreases with depth and longitude, and the diffusivity decreases with depth and from NAC to NFB. Compared to previous results from surface drifters and isobaric floats, our isopycnal statistics are more isotropic and agree better with the Taylor dispersion theory because (1) the mean velocity has a better resolution and (2) the isopycnal floats are better Lagrangian followers. The diffusivity scales better with the rms velocity and length scale than with the velocity variance and timescale.
Wind-driven spin-up of the four-layer, quasi-isopycnic, eddy-resolving primitive equation model of Bleck and Boudra (1981) is compared with that obtained with a (numerically dissimilar) ``pure'' isopycnic coordinate model and an isobaric (i.e., quasi-Cartesian) coordinate model. In particular, the onset of hydrodynamic instabilities in the flow forced by a double-gyre wind stress pattern is studied. The spin-up processes associated with the isopycnic and quasi-isopycnic model are found to be similar, whereas the flow pattern produced by the quasi-Cartesian model deviates in the direction of Holland's (1978) and Holland and Lin's (1975a,b) two-layer solutions.
Eddy diffusivity of the surface velocity field in the tropical Pacific Ocean was estimated using satellite‐tracked drifting buoys (1979 through mid‐1996). The tropical Pacific surface current system is characterized by nonstationarity, strong meridional shear, and an energetic mesoscale velocity field. Eddy diffusivity may be defined as the integral of the autocovariance of Lagrangian eddy velocities, requiring both stationary and homogeneous statistics of the eddy field. Eddy velocities were obtained by removing a splined mean field to eliminate mean shear from observations binned (1) spatially to group data that have similar dispersion characteristics and (2) temporally to create stationary eddy statistics. Zonal diffusivity estimates are up to ≈7 times larger than meridional diffusivity estimates in the high eddy energy regions. This anisotropy is associated with the meridional mesoscale wave motion (i.e., by equatorial and tropical instability waves) that increases eddy variance but does not lead to a proportional increase in water parcel diffusion because of the coherent character of the trajectory motion, at least for initial time lags. Simple autoregressive models of first and second order are used to describe and classify the resulting eddy statistics. An independent confirmation of the diffusivity estimate in the central/eastern Pacific was obtained by comparing tracer flux divergence computed from a parameterization using diffusivity estimates of our analysis with that from direct eddy Reynolds stress flux divergence. Our results show that diffusivity can be estimated for regions not considered previously either because of sparse data or the complexities of the velocity field.
Observations from satellite-tracked drifting buoys, expendable bathythermograph and conductivity-temperature-depth data, and Geosat altimeter data are used to describe anticyclonic eddies that occur in small numbers off the Pacific coast of Central America. These eddies are similar in many respects to the well-known warm-core rings that are observed north of the Gulf Stream off the Atlantic coast of North America, except that they occur in an environment that also is warm, and they contain considerably greater kinetic energy. It is hypothesized that the are formed as a result of conservation of potential vorticity when the North Equatorial Countercurrent (NECC) turns northward upon approaching the eastern boundary during its autumnal maximum. The rings so formed have a strongly nonlinear character which causes them to propagate westward between 9°N and 14°N with a speed in excess of that of long Rossby waves. Due to relatively small available potential energy content, these rings have a dissipation time scale of about 6 months and perhaps end by collision with an reabsorbtion into the NECC. The rings account for the observed enhancement of surface kinetic energy, and probably for the seaward transport of waters enriched in copper.
A new method for directly assimilating Lagrangian tracer observations for flow state estimation is presented. It is developed in the context of point vortex systems. With tracer advection equations augmenting the point vortex model, the correlations between the vortex and tracer positions allow one to use the observed tracer positions to update the non-observed vortex positions. The method works efficiently when the observations are accurate and frequent enough. Low-quality data and large intervals between observations can lead to divergence of the scheme. Nonlinear effects, responsible for the failure of the extended Kalman filter, are triggered by the exponential rate of separation of tracer trajectories in the neighbourhoods of the saddle points of the velocity field.
This article was chosen from Selected Proceedings of the 4th International Workshop on Vortex Flows and Related Numerical Methods (UC Santa-Barbara, 17-20 March 2002) ed E Meiburg, G H Cottet, A Ghoniem and P Koumoutsakos.
The relationship between the transport of scalar properties and the statistics of material particle motion is examined. It is shown that evolution of the mean concentration field is determined by the statistics of single particles while two particle statistics describe the typical dispersal of individual property clouds. It is argued that oceanic observations of quasi-Lagrangian floats provide a useful and direct description of lateral advection and eddy dispersal. A simple model for predicting statistics of particle dispersal from Eulerian statistics of velocity is advanced. This model is tested against simulations of particle motion in random two-dimensional velocity fields with prescribed Eulerian statistics in which there is no mean velocity. The model is found to provide satisfactory description of the one and two particle statistics in statistically stationary, homogeneous, and joint normally distributed velocity fields. Adequately predicted are (i) mean particle velocity and mean square particle speed, (ii) the Lagrangian frequency spectrum of single particles from which the single particle diffusivity can be computed, and (iii) the mean square separation between particles from which the two particle diffusivity can be computed. A simple generalization of the theory to velocity fields with weakly inhomogeneous statistics describes the evolution of the single particle density, or equivalently the mean concentration field of a conserved scalar property, and describes particle migration induced by spatial variation of dispersion.
In the Lagrangian representation, the problem of advection of a passive marker particle by a prescribed flow defines a dynamical system. For two-dimensional incompressible flow this system is Hamiltonian and has just one degree of freedom. For unsteady flow the system is non-autonomous and one must in general expect to observe chaotic particle motion. These ideas are developed and subsequently corroborated through the study of a very simple model which provides an idealization of a stirred tank. In the model the fluid is assumed incompressible and inviscid and its motion wholly two-dimensional. The agitator is modelled as a point vortex, which, together with its image(s) in the bounding contour, provides a source of unsteady potential flow. The motion of a particle in this model device is computed numerically. It is shown that the deciding factor for integrable or chaotic particle motion is the nature of the motion of the agitator. With the agitator held at a fixed position, integrable marker motion ensues, and the model device does not stir very efficiently. If, on the other hand, the agitator is moved in such a way that the potential flow is unsteady, chaotic marker motion can be produced. This leads to efficient stirring. A certain case of the general model, for which the differential equations can be integrated for a finite time to produce an explicitly given, invertible, area-preserving mapping, is used for the calculations. The paper contains discussion of several issues that put this regime of chaoticadvection in perspective relative to both the subject of turbulent advection and to recent work on critical points in the advection patterns of steady laminar flows. Extensions of the model, and the notion of chaotic advection, to more realistic flow situations are commented upon.
In this paper an initial analysis of an 0.1°simulation of the North Atlantic Ocean using a level-coordinate ocean general circulation model forced with realistic winds covering the period 1985-96 is presented. Results are compared to the North Atlantic sector of a global 0.28°simulation with similar surface forcing and to a variety of satellite and in situ observations. The simulation shows substantial improvements in both the eddy variability and the time-mean circulation compared to previous eddy-permitting simulations with resolutions in the range of 1/2°-1/6°. The resolution is finer than the zonal-mean first baroclinic mode Rossby radius at all latitudes, and the model appears to be capturing the bulk of the spectrum of mesoscale energy. The eddy kinetic energy constitutes 70% of the total basin-averaged kinetic energy. Model results agree well with observations of the magnitude and geographical distribution of eddy kinetic energy and sea-surface height variability, with the wavenumber-frequency spectrum of surface height anomalies in the Gulf Stream, with estimates of the eddy length scale as a function of latitude, and with measurements of eddy kinetic energy as a function of depth in the eastern basin. The mean circulation also shows significant improvements compared to previous models, although there are notable remaining discrepancies with observations in some areas. The Gulf Stream separates at Cape Hatteras, and its speed and cross-stream structure are in good agreement with current meter data; however, its path is somewhat too far south and its meander envelope too broad to the west of the New England Seamounts. The North Atlantic Current is remarkably well simulated in the model: it is exhibits meanders and troughs in its time-mean path that agree with similar structures seen in float data, although the separation of this current in the region of the 'Northwest Corner' is displaced somewhat too far to the northwest. The Azores Current appears in the simulation, perhaps for the first time in a basin-scale model, and its position, total transport, and eddy variability are consistent with observational estimates.
Velocity data obtained from trajectories of SOFAR floats launched as part of several experiments carried out in the Northwest Atlantic during the last two decades are used to give a statistical description of the mean Gulf Stream and its recirculation. The distribution of eddy variability in the region is also presented. A mean Gulf Stream which bifurcates between 55° and 45°W to feed the North Atlantic Current and a southern recirculation can be clearly identified. A weak interior Sverdrup flow is also suggested. The spatial distribution of eddy variability is consistent with previous descriptions, showing a maximum near the Gulf Stream.
A variational adjoint method is developed to assimilate the trajectories of drifting buoys into a simple ocean model. The method is applied to the equatorial Pacific Ocean. In the variational formalism a cost function measuring the distance between the trajectories of the model simulated buoys and of the observed buoys is minimized. Adjoint equations are forced by the model-data misfit that is proportional to the difference of model simulated and observed buoy positions. A hypothetical mean upper layer thickness of the model is used as a control parameter. The optimal spatial structure giving the best fit of the model to the observations is determined, and it is used as the initial condition of the model. Model simulated data are used first in several experiments and later experiments with real observations are discussed. Assimilation periods and regional effects with relations of buoy trajectory and wave propagation on the assimilation processes are examined. Upper layer thickness in the western equatorial region is improved relatively better than in the eastern region for the assimilation period of three months, because the western equatorial region acts as a special “caustic” region in the adjoint system. This east-west inhomogeneity vanishes using a one-year period. The upper layer thickness optimized with real buoy data is compared with independently observed sea level data.
SOFAR floats that looped in discrete eddies were studied in order to map and describe the distribution and characteristics of eddies in the North Atlantic. One hundred eighteen individual looping float trajectories (loopers) were identified, each consisting of two or more consecutive loops. Each looper was interpreted to be in a discrete eddy, and its characteristics were estimated from the float trajectory. The highest percentage of loopers occured at 700m in the Newfoundland Basin, where roughly half of the float data were in loopers, mostly cyclones. In the Gulf Stream region, approximately 20% of the float data recorded at 700m were in loopers, again mostly cyclones. Overall, 21% of 700m data and 6% of 2000m data were in loopers.
Two techniques were developed for estimating statistics of inertial oscillations from satellite-tracked drifters that overcome the difficulties inherent in estimating such statistics from data dependent upon space coordinates that are a function of time. Application of these techniques to tropical surface drifter data collected during the NORPAX, EPOCS, and TOGA programs reveals a latitude-dependent, statistically significant 'blue shift' of inertial wave frequency. The latitudinal dependence of the blue shift is similar to predictions based on 'global' internal-wave spectral models, with a superposition of frequency shifting due to modification of the effective local inertial frequency by the presence of strongly sheared zonal mean currents within 12 deg of the equator.
Spatial regression with Markov Random Fields for Kalman filter approximation in least-squares solution of oceanic data assimilation problems
- Chin
A Bayesian approach to observation quality control in variational and statistical assimilation
- Lorenc