Implementation of position assimilation for ARGO floats in a realistic Mediterranean Sea OPA model and twin experiment testing

In this paper, a Lagrangian assimilation method is presented and implemented in a realistic OPA OGCM with the goal of providing an assessment of the assimilation of realistic Argo float position data. We focus on an application in the Mediterranean Sea, where in the framework of the MFSTEP project an array of Argo floats have been deployed with parking depth at 350 m and sampling interval of 5 days. In order to quantitatively test the method, the "twin experiment" approach is followed and synthetic trajectories are considered. The method is first tested using "perfect" data, i.e. without shear drift errors and with relatively high coverage. Results show that the assimilation is effective, correcting the velocity field at the parking depth, as well as the velocity profiles and the geostrophically adjusted mass field. We then consider the impact of realistic datasets, which are spatially sparse and characterized by shear drift errors. Such data provide a limited global correction of the model state, but they efficiently act on the location, intensity and shape of the described mesoscale structures of the intermediate circulation

Wind-driven ocean circulation and equilibrium statistical mechanics

In this paper, we show that numerical solutions of the single-layer quasigeostrophic equation in a beta-plane basin approach the state predicted by equilibrium statistical mechanics when the forcing and dissipation are (unrealistically) zero. This equilibrium state, which we call Fofonoff flow, consists of a quasi-steady uniform westward interior flow closed by inertial boundary layers. When wind stress and bottom drag are switched on, we find that the nonlinear terms in the quasigeostrophic equation still try to drive the flow toward Fofonoff flow, but their success at this depends strongly on the geometry of the wind stress. If the prescribed wind stress exerts a torque with the right sign to balance the bottom-drag torque around every closed streamline of the Fofonoff flow, then solutions to the wind-driven quasigeostrophic equation are energetic, Fofonoff-like, and nearly steady. If, on the other hand, the wind opposes Fofonoff flow, the wind-driven solutions are turbulent, with small mean flows, and much less energy. Our results suggest that integral conservation laws (on which the equilibrium statistical mechanics is solely based) largely define the role of the nonlinearities in the quasigeostrophic equation. To support this viewpoint, we demonstrate a resemblance between the solutions of the quasigeostrophic equation and the solutions of a stochastic model equation. The stochastic model equation, in which the advected vorticity is replaced by a random variable, has only gross conservation laws in common with the quasigeostrophic equation

Nonlinear general circulation of an ocean model driven by wind with a stochastic component

The effects of the stochastic component of the large-scale wind on the climatological mean of the nonlinear ocean circulation are studied, using a set of numerical solutions for the single-layer, quasi-geostrophic equation in a closed basin with a flat bottom. In the absence of a steady wind, the purely stochastic wind is found to drive the solutions toward a nonlinear mean flow similar to that of the free system (i.e. without forcing and dissipation). This equilibrium mean flow (Fofonoff flow), is predicted by statistical mechanics and is characterized by a westward interior closed by inertial boundary layers along the coast. When a steady component of the wind is present, the effects of the stochastic wind depend on the geometry of the steady wind. If the steady wind is compatible with Fofonoff flow, the stochastic wind tends to reinforce the Fofonoff-like mean solution obtained with the steady wind alone. When the steady wind opposes Fofonoff flow, the contribution of the stochastic wind does not increase the energy of the mean solution, but instead tends to change the spatial structure of the mean flow. An example of steady wind opposing Fofonoff flow is the classical double-gyre wind, often used to represent the realistic mean wind in mid-latitude ocean regions. We study the double-gyre wind case in detail. The stochastic wind is found to weaken the recirculating regions and the meandering jet between the two gyres, and the homogenization of potential vorticity in the recirculations is inhibited. These changes are explained in terms of increased mixing of the probability density in phase space due to the stochastic wind, causing an increased tendency toward the equilibrium state predicted by statistical mechanics

Predictability of Lagrangian particle trajectories: Effects of smoothing of the underlying Eulerian flow

The increasing realism of ocean circulation models is leading to an increasing use of Eulerian models as a basis to compute transport properties and to predict the fate of Lagrangian quantities. There exists, however, a significant gap between the spatial scales of model resolution and that of forces acting on Lagrangian particles. These scales may contain high vorticity coherent structures that are not resolved due to computational issues and/or missing dynamics and are typically suppressed by smoothing operators. In this study, the impact of smoothing of the Eulerian fields on the predictability of Lagrangian particles is first investigated by conducting twin experiments that involve release of clusters of synthetic Lagrangian particles into true (unmodified) and model (smoothed) Eulerian fields, which are generated by a QG model with a flow field consisting of many turbulent coherent structures. The Lagrangian errors induced by Eulerian smoothing errors are quantified by using two metrics, the difference between the centers of mass (CM) of particle clusters, ρ, and the difference between scattering of particles around the center of mass, s. The results show that the smoothing has a strong effect on the CM behavior, while the scatter around it is only partially affected. The QG results are then compared to results obtained from a multi-particle Lagrangian Stochastic Model (LSM) which parameterizes turbulent flow using main flow characteristics such as mean flow, velocity variance and Lagrangian time scale. In addition to numerical results, theoretical results based on the LSM are also considered, providing asymptotics of ρ, s and predictability time. It is shown that both numerical and theoretical LSM results for the center of mass error (ρ) provide a good qualitative description, and a quantitatively satisfactory estimate of results from QG experiments. The scatter error (s) results, on the other hand, are only qualitatively reproduced by the LSM

Estimates of turbulence parameters from Lagrangian data using a stochastic particle model

A new parametric approach for the study of Lagrangian data is presented. It provides parameter estimates for velocity and transport components and is based on a stochastic model for single particle motion. The main advantage of this approach is that it provides more accurate parameter estimates than existing methods by using the a-priori knowledge of the model. Also, it provides a complete error analysis of the estimates and is valid in presence of observation errors. Unlike nonparametric methods (e.g. Davis, 1991b), our technique depends on a-priori assumptions which require that the model validity be checked in order to obtain reliable estimates. The model used here is the simplest one in a hierarchy of “random flight” models (e.g. Thomson, 1987), and it describes the turbulent velocity as a linear Markov process, characterized by an exponential autocorrelation. Experimental and numerical estimates show that the model is appropriate for mesoscale turbulent flows in homogeneous regions of the upper ocean. More complex models, valid under more general conditions, are presently under study. Estimates of the mean flow, variance, turbulent time scale and diffusivity are obtained. The properties of the estimates are discussed in terms of biases and sampling errors, both analytically and using numerical experiments. Optimal sampling for the measurements is studied and an example application to drifter data from the Brazil/Malvinas extension is presented

Inertial gyre solutions from a primitive equation ocean model

A numerical exploration of inertial equilibrium states obtained with a primitive equation ocean model suggests that they can be described using statistical mechanics theory developed in the framework of quasi-geostrophy. The performance of the numerical model is first assessed with respect to the quasi-geostrophic model considering a series of experiments in the quasi-geostrophic range, in a closed basin with flat bottom and varying Rossby numbers. The results show that our model is consistent with the quasi-geostrophic model even in terms of dependence from boundary conditions and eddy viscosity values, and that the free surface contribution is negligible. As in the quasi-geostrophic experiments, a tendency toward Fofonoff flows is observed. This tendency remains in a second series of experiments performed outside the quasi-geostrophic range, namely with flows with higher Rossby numbers and with steep topography, characterized by sloping boundaries with an order one fractional change in the depth. It is only close to the boundaries that ageostrophic effects modify the flows. In conclusion, the fact that statistical mechanics theory, initially developed in the framework of quasi-geostrophy, holds for more realistic flows with steep topography supports development of subgrid scale parameterizations based on statistical mechanics theory, to be used in realistic general circulation models

Lagrangian spin parameter and coherent structures from trajectories released in a high-resolution ocean model

A study of the mesoscale eddy field in the presence of coherent vortices, by means of Lagrangian trajectories released in a high-resolution ocean model, is presented in this paper. The investigation confirms previous results drawn from real float data statistics (Veneziani et al., 2004) that the eddy field characteristics are due to the superposition of two distinct regimes associated with strong coherent vortices and with a typically more quiescent background eddy flow. The former gives rise to looping trajectories characterized by subdiffusivity properties due to the trapping effect of the vortices, while the latter produces nonlooping floats characterized by simple diffusivity features. Moreover, the present work completes the study by Veneziani et al. (2004) in regard to the nature of the spin parameter Ω, which was used in the Lagrangian stochastic model that best described the observed eddy statistics.The main result is that the spin obtained from the looping trajectories not only represents a good estimate of the relative vorticity of the vortex core in which the loopers are embedded, but it is also able to follow the vortex temporal evolution. The Lagrangian parameter Ω is then directly connected to the underlying Eulerian structure and could be used as a proxy for the relative vorticity field of coherent vortices

Oceanic Turbulence and Stochastic Models from Subsurface Lagrangian Data for the Northwest Atlantic Ocean

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 V. 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 V) and nonloopers (zero V). This simple model is found to be very effective in reproducing the statistical properties of the data. 1

Combining Litter Observations with a Regional Ocean Model to Identify Sources and Sinks of Floating Debris in a Semi-enclosed Basin: The Adriatic Sea

Visual ship transect surveys provide crucial information about the density, and spatial distribution of floating anthropogenic litter in a basin. However, such observations provide a ‘snapshot’ of local conditions at a given time and cannot be used to deduce the provenance of the litter or to predict its fate, crucial information for management and mitigation policies. Particle tracking techniques have seen extensive use in these roles, however, most previous studies have used simplistic initial conditions based on bulk average inputs of debris to the system. Here, observations of floating anthropogenic macro debris in the Adriatic Sea are used to define initial conditions (number of particles, location, and time) in a Lagrangian particle tracking model. Particles are advected backward and forward in time for 60 days (120 days total) using surface velocities from an operational regional ocean model. Sources and sinks for debris observed in the central and southern Adriatic in May 2013 and March 2015 included the Italian coastline from Pescara to Brindisi, the Croatian island of Mljet, and the coastline from Dubrovnik through Montenegro to Albania. Debris observed in the northern Adriatic originated from the Istrian peninsula to the Italian city of Termoli, as well as the Croatian island of Cres and the Kornati archipelago. Particles spent a total of roughly 47 days afloat. Coastal currents, notably the eastern and western Adriatic currents, resulted in large alongshore displacements. Our results indicate that anthropogenic macro debris originates largely from coastal sources near population centers and is advected by the cyclonic surface circulation until it strands on the southwest (Italian) coast, exits the Adriatic, or recirculates in the southern gyreVersión del edito

Submesoscale dispersion in the vicinity of the Deepwater Horizon spill

Reliable forecasts for the dispersion of oceanic contamination are important for coastal ecosystems, society and the economy as evidenced by the Deepwater Horizon oil spill in the Gulf of Mexico in 2010 and the Fukushima nuclear plant incident in the Pacific Ocean in 2011. Accurate prediction of pollutant pathways and concentrations at the ocean surface requires understanding ocean dynamics over a broad range of spatial scales. Fundamental questions concerning the structure of the velocity field at the submesoscales (100 meters to tens of kilometers, hours to days) remain unresolved due to a lack of synoptic measurements at these scales. \textcolor{black} {Using high-frequency position data provided by the near-simultaneous release of hundreds of accurately tracked surface drifters, we study the structure of submesoscale surface velocity fluctuations in the Northern Gulf Mexico. Observed two-point statistics confirm the accuracy of classic turbulence scaling laws at 200m$-$50km scales and clearly indicate that dispersion at the submesoscales is \textit{local}, driven predominantly by energetic submesoscale fluctuations.} The results demonstrate the feasibility and utility of deploying large clusters of drifting instruments to provide synoptic observations of spatial variability of the ocean surface velocity field. Our findings allow quantification of the submesoscale-driven dispersion missing in current operational circulation models and satellite altimeter-derived velocity fields.Comment: 9 pages, 6 figure