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Anne Molcard, Annalisa Griffa, and Tamay M. Özgökmen

Abstract

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.

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Milena Veneziani, Annalisa Griffa, and Pierre-Marie Poulain

Abstract

In this paper, a method to analyze historical surface drifter data is presented that is aimed at investigating particle evolution as a function of initial conditions. Maps of drifter concentration at different times are built and interpreted as maps of the probability of finding a particle at a given time in the neighborhood of a given point in the domain. A case study is considered in a coastal area of the middle Adriatic Sea (a subbasin of the Mediterranean Sea) around the Gargano Cape, which is the focus of a newly planned experiment, the Dynamics of the Adriatic in Real Time (DART). A specific application is considered that seeks to improve the DART Lagrangian sampling planning.

The results indicate that the analysis of historical drifters can provide very valuable information on statistical particle prediction to be used in experiment design. In the DART region, particle dynamics appear mostly controlled by the upstream properties of the boundary current as well as by the presence of a stagnation point located offshore of the tip of Gargano and separating two cross-basin recirculations. A significant seasonal dependence is observed, with drifters being more likely to leave the boundary current in winter and fall, when the current is wider and more connected to the cross-basin recirculations. Future developments are discussed, including joint analyses with numerical model results.

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Arthur J. Mariano, Annalisa Griffa, Tamay M. Özgökmen, and Enrico Zambianchi

Abstract

The first Lagrangian Analysis and Predictability of Coastal and Ocean Dynamics (LAPCOD) meeting took place in Ischia, Italy, 2–6 October 2000. The material presented at LAPCOD 2000 indicated both a maturing of Lagrangian-based observing systems and the development of new analysis and assimilation techniques for Lagrangian data. This summary presents a review of the state-of-the-art technology in Lagrangian exploration of oceanic and coastal waters that was presented at the meeting.

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Pierpaolo Falco, Annalisa Griffa, Pierre-Marie Poulain, and Enrico Zambianchi

Abstract

The surface transport properties in the Adriatic Sea, a semienclosed subbasin of the Mediterranean Sea, have been studied using a drifter dataset in the period December 1994–March 1996. Three main points have been addressed. First, the exchange between southern and northern regions and between deep and coastal areas have been studied, focusing on the role of topography. A significant cross-topography or cross-shelf exchange has been found, probably due to the direct wind forcing and to the influence of stratification that isolates the surface flow from bottom effects, especially in the open sea. Second, a Lagrangian transport model with parameters derived from the data has been implemented. Simulated particles have been compared with drifter data with positive results. The model is found to be able to reproduce reality with good approximation, except for a specific advective event during the late summer season. Finally, the residence timescale T, that is, the average time spent by a surface particle in the basin, has been estimated. Direct estimates from the data suggest T ≈ 70–90 days, but these values are biased due to the finite lifetime of the drifters. Model results have been used to estimate the bias, and they suggest a “true” value of T ≈ 200 days.

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Milena Veneziani, Annalisa Griffa, Zulema Garraffo, and Jean A. Mensa

Abstract

Barrier layers are generated when the surface mixed layer is shallower than the layer where temperature is well mixed, in geographical regions where salinity plays a key role in setting up upper-ocean density stratification. In the tropical oceans, thick barrier layers are also found in a latitude range where spiraling trajectories from surface in situ drifters suggest the presence of predominantly cyclonic submesoscale-like vortices. The authors explore these dynamical processes and their interplay in the present paper, focusing on the tropical South Atlantic Ocean and using a high-resolution modeling approach. The objective is threefold: to investigate the mean dynamics contributing to barrier-layer formation in this region, to study the distribution and seasonality of submesoscale features, and to verify whether and how the submesoscale impacts barrier-layer thickness. The model used is the Regional Ocean Modeling System (ROMS) in its Adaptive Grid Refinement in Fortran (AGRIF) online-nested configuration with a horizontal resolution ranging between 9 and 1 km. The simulated circulation is first described in terms of mean and submesoscale dynamics, and the associated seasonal cycle. Mechanisms for barrier-layer formation are then investigated. The results confirm previous hypotheses by Mignot et al. on the relevance of enhanced winter mixing deepening the isothermal layer, whereas the salinity stratification is sustained by advection of surface fresh waters and subsurface salinity maxima. Finally, submesoscale effects on barrier-layer thickness are studied, quantifying their contribution to vertical fluxes of temperature and salinity. Submesoscale vortices associated with salinity fronts are found to have a significant effect, producing thicker barrier layers (by ~20%–35%) and a shallower mixed layer because of their restratifying effect on salinity.

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Milena Veneziani, Annalisa Griffa, Andy M. Reynolds, and Arthur J. Mariano

Abstract

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.

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Tamay M. Özgökmen, Annalisa Griffa, Arthur J. Mariano, and Leonid I. Piterbarg

Abstract

The predictability of particle trajectories in oceanic flows is investigated in the context of a primitive equation, idealized, double-gyre ocean model. This study is motivated not only by the fact that this is an important conceptual problem but also by practical applications, such as searching for objects lost at sea, and ecological problems, such as the spreading of pollutants or fish larvae. The original aspect of this study is the use of Lagrangian drifter data to improve the accuracy of predicted trajectories. The prediction is performed by assimilating velocity data from the surrounding drifters into a Gauss–Markov model for particle motion. The assimilation is carried out using a simplified Kalman filter.

The performance of the prediction scheme is quantified as a function of a number of factors: 1) dynamically different flow regimes, such as interior gyre, western boundary current, and midlatitude jet regions; 2) density of drifter data used in assimilation; and 3) uncertainties in the knowledge of the mean flow field and the initial conditions. The data density is quantified by the number of data per degrees of freedom N R, defined as the number of drifters within the typical Eulerian space scale from the prediction particle. The simulations indicate that the actual World Ocean Circulation Experiment sampling (1 particle/[5° × 5°] or N R ≪ 1) does not improve particle prediction, but predictions improve significantly when N R ≫ 1. For instance, a coverage of 1 particle/[1° × 1°] or N RO(1) is already able to reduce the errors of about one-third or one-half. If the sampling resolution is increased to 1 particle/[0.5° × 0.5°] or 1 particle/[0.25° × 0.25°] or N R ≫ 1, reasonably accurate predictions (rms errors of less than 50 km) can be obtained for periods ranging from one week (western boundary current and midlatitude jet regions) to three months (interior gyre region). Even when the mean flow field and initial turbulent velocities are not known accurately, the information derived from the surrounding drifter data is shown to compensate when N R > 1. Theoretical error estimates are derived that are based on the main statistical parameters of the flow field. Theoretical formulas show good agreement with the numerical results, and hence, they may serve as useful a priori estimates of Lagrangian prediction error for practical applications.

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Angelique C. Haza, Tamay M. Özgökmen, Annalisa Griffa, Andrew C. Poje, and M.-Pascale Lelong

Abstract

To develop methodologies to maximize the information content of Lagrangian data subject to position errors, synthetic trajectories produced by both a large-eddy simulation (LES) of an idealized submesoscale flow field and a high-resolution Hybrid Coordinate Ocean Model simulation of the North Atlantic circulation are analyzed. Scale-dependent Lagrangian measures of two-particle dispersion, mainly the finite-scale Lyapunov exponent [FSLE; λ(δ)], are used as metrics to determine the effects of position uncertainty on the observed dispersion regimes. It is found that the cumulative effect of position uncertainty on λ(δ) may extend to scales 20–60 times larger than the position uncertainty. The range of separation scales affected by a given level of position uncertainty depends upon the slope of the true FSLE distribution at the scale of the uncertainty. Low-pass filtering or temporal subsampling of the trajectories reduces the effective noise amplitudes at the smallest spatial scales at the expense of limiting the maximum computable value of λ. An adaptive time-filtering approach is proposed as a means of extracting the true FSLE signal from data with uncertain position measurements. Application of this filtering process to the drifters with the Argos positioning system released during the LatMix: Studies of Submesoscale Stirring and Mixing (2011) indicates that the measurement noise dominates the dispersion regime in λ for separation scales δ < 3 km. An expression is provided to estimate position errors that can be afforded depending on the expected maximum λ in the submesoscale regime.

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Helga S. Huntley, Maristella Berta, Giovanni Esposito, Annalisa Griffa, Baptiste Mourre, and Luca Centurioni

Abstract

Horizontal velocity gradients of a flow field and the related kinematic properties (KPs) of divergence, vorticity, and strain rate can be estimated from dense drifter deployments. E.g., the spatio-temporal average divergence (and other KPs) over a triangular area defined by three drifters and over a given time interval can be computed from the initial and final areas of said triangle. Unfortunately, this computation can be subject to large errors, especially when the triangle shape is far from equilateral. Therefore, samples with small aspect ratios are generally discarded. Here we derive the thresholds on two shape metrics that optimize the balance between retention of good and removal of bad divergence estimates. The primary tool is a high-resolution regional ocean model simulation, where a baseline for the average divergence can be established, so that actual errors are available. A value of 0.2 for the scaled aspect ratio Λ and a value of 0.86π for the largest interior angle θ are found to be equally effective thresholds, especially at scales of 5 km and below. While discarding samples with low Λ or high θ values necessarily biases the distribution of divergence estimates slightly toward positive values, this bias is small compared to (and in the opposite direction of) the Lagrangian sampling bias due to drifters preferably sampling convergence regions. Errors due to position uncertainty are suppressed by the shape-based subsampling. The subsampling also improves the identification of the areas of extreme divergence or convergence. An application to an observational dataset demonstrates that these model-derived thresholds can be effectively used on actual drifter data.

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Daoxun Sun, Annalisa Bracco, Roy Barkan, Maristella Berta, Daniel Dauhajre, M. Jeroen Molemaker, Jun Choi, Guangpeng Liu, Annalisa Griffa, and James C. McWilliams

Abstract

The diurnal cycling of submesoscale circulations in vorticity, divergence, and strain is investigated using drifter data collected as part of the Lagrangian Submesoscale Experiment (LASER) experiment, which took place in the northern Gulf of Mexico during winter 2016, and ROMS simulations at different resolutions and degree of realism. The first observational evidence of a submesoscale diurnal cycle is presented. The cycling is detected in the LASER data during periods of weak winds, whereas the signal is obscured during strong wind events. Results from ROMS in the most realistic setup and in sensitivity runs with idealized wind patterns demonstrate that wind bursts disrupt the submesoscale diurnal cycle, independently of the time of day at which they happen. The observed and simulated submesoscale diurnal cycle supports the existence of a shift of approximately 1–3 h between the occurrence of divergence and vorticity maxima, broadly in agreement with theoretical predictions. The amplitude of the modeled signal, on the other hand, always underestimates the observed one, suggesting that even a horizontal resolution of 500 m is insufficient to capture the strength of the observed variability in submesoscale circulations. The paper also presents an evaluation of how well the diurnal cycle can be detected as function of the number of Lagrangian particles. If more than 2000 particle triplets are considered, the diurnal cycle is well captured, but for a number of triplets comparable to that of the LASER analysis, the reconstructed diurnal cycling displays high levels of noise both in the model and in the observations.

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