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Over a hundred of experiments were realised between 1998 and 2022 in the Mediterranean Sea using surface Lagrangian drifters, at coastal and offshore level. Raw data were initially unified and pre-processed manually by eliminating spikes and wrong positions or date/time information. The integrity of the received data packages was checked, and incomplete ones were discarded. Deployment information was retrieved from an initial excel database and campaign notes for each drifter and integrated into the PostgreSQL database, realised and maintained by the National Institute of Oceanography and Applied Geophysics (OGS) in Trieste (IT). This database also collects a variety of metadata about the drifter model, project, owner and operator. Subsequently data were processed using standard procedures of editing and quality control developed for the OGS Mediterranean drifter dataset to remove spikes generated by malfunctioning of the sensors and obtain files with common characteristics. Drifter data and plots of each track were also visually checked to remove any point not identified by the automatic procedure and clearly erroneous. Drifters' trajectories were split into two or more segments that have been considered as different deployments, in case of specific drifters' behaviours. Data were interpolated at defined time intervals to temporarily unify tracks. From the original 138 experiments, a dataset of 204 tracks was obtained, available from the public open-access repository in SEANOE (SEA scieNtific Open data Edition) at https://doi.org/10.17882/90537 (Ribotti et al., 2022). [ABSTRACT FROM AUTHOR]

One way to analyze complicated non-autonomous flows is through trying to understand their transport behavior. In a quantitative, set-oriented approach to transport and mixing, finite time coherent sets play an important role. These are time-parametrized families of sets with unlikely transport to and from their surroundings under small or vanishing random perturbations of the dynamics. Here we propose, as a measure of transport and mixing for purely advective (i.e., deterministic) flows, (semi)distances that arise under vanishing perturbations in the sense of large deviations. Analogously, for given finite Lagrangian trajectory data we derive a discrete-time-and-space semidistance that comes from the “best” approximation of the randomly perturbed process conditioned on this limited information of the deterministic flow. It can be computed as shortest path in a graph with time-dependent weights. Furthermore, we argue that coherent sets are regions of maximal farness in terms of transport and mixing, and hence they occur as extremal regions on a spanning structure of the state space under this semidistance—in fact, under any distance measure arising from the physical notion of transport. Based on this notion, we develop a tool to analyze the state space (or the finite trajectory data at hand) and identify coherent regions. We validate our approach on idealized prototypical examples and well-studied standard cases. [ABSTRACT FROM AUTHOR]

We introduce a data assimilation method to estimate model parameters with observations of passive tracers by directly assimilating Lagrangian Coherent Structures. Our approach differs from the usual Lagrangian Data Assimilation approach, where parameters are estimated based on tracer trajectories. We employ the Approximate Bayesian Computation (ABC) framework to avoid computing the likelihood function of the coherent structure, which is usually unavailable. We solve the ABC by a Sequential Monte Carlo (SMC) method, and use Principal Component Analysis (PCA) to identify the coherent patterns from tracer trajectory data. Our new method shows remarkably improved results compared to the bootstrap particle filter when the physical model exhibits chaotic advection. [ABSTRACT FROM AUTHOR]

The ocean current predictability in the data limited Angola Basin was investigated using the Regional Ocean Modelling System (ROMS) with four-dimensional variational data assimilation. Six experiments were undertaken comprising a baseline case of the assimilation of salinity/temperature profiles and satellite sea surface temperature, with the subsequent addition of altimetry, OSCAR (satellite-derived sea surface currents), drifters, altimetry and drifters combined, and OSCAR and drifters combined. The addition of drifters significantly improves Lagrangian predictability in comparison to the baseline case as well as the addition of either altimetry or OSCAR. OSCAR assimilation only improves Lagrangian predictability as much as altimetry assimilation. On average the assimilation of either altimetry or OSCAR with drifter velocities does not significantly improve Lagrangian predictability compared to the drifter assimilation alone, even degrading predictability in some cases. When the forecast current speed is large, it is more likely that the combination improves trajectory forecasts. Conversely, when the currents are weaker, it is more likely that the combination degrades the trajectory forecast. [ABSTRACT FROM AUTHOR]

We present a new and fast method that blends altimetric and drifter positions data in order to predict the surface velocity in the Eastern Levantine Mediterranean. The method relies on a variational assimilation approach where a velocity correction is continuously obtained by matching observed drifter positions with those predicted by a simple advection model. The background velocity used in the advection of the drifters is the aggregate of a geostrophic and a wind-driven component and the velocity correction is constrained to be divergence free. The algorithm employs a sliding time window that assimilates at once and inside each frame, an entire trajectory of drifters. We show that with few drifters, our method improves the estimation of velocity in two typical situations: an eddy between the Lebanese coast and Cyprus, and velocities along the Lebanese coast. [ABSTRACT FROM AUTHOR]

This paper deals with numerical methods providing semi-analytic solutions to a wide class of macroscopic traffic flow models for piecewise affine initial and boundary conditions. In a very recent paper, a variational principle has been proved for models of the Generic Second Order Modeling (GSOM) family, yielding an adequate framework for effective numerical methods. Any model of the GSOM family can be recast into its Lagrangian form as a Hamilton–Jacobi equation (HJ) for which the solution is interpreted as the position of vehicles. This solution can be computed thanks to Lax–Hopf like formulas and a generalization of the inf-morphism property. The efficiency of this computational method is illustrated through a numerical example and finally a discussion about future developments is provided. [ABSTRACT FROM AUTHOR]

Phillips, R., Vincent, C.E., Bell, P.S., Dolphin, T., and Bacon, J., 2013. Use of GPS and X-Band Radar to track tidal currents around the shore parallel breakwaters at Sea Palling, Norfolk, UK Sea Palling on the East coast of the UK has a series of 9 shore parallel rock breakwaters. The numerical model TELEMAC2D has been used to simulate tidal currents around the system to assess the tidal contribution to sediment budgets and transport pathways. Numerical simulations are particularly useful for identifying the important processes involved in a complex system such as these breakwaters and understanding how the breakwaters might effect the local coastal region. Models are classically evaluated using a number of measurement stations to calibrate and then check it is giving realistic results. It is important to assess both the spatial and temporal performance of a model, but this is difficult with a model having tens of thousands of nodes, based on only a few discrete locations. This paper presents a method using Lagrangian data to assess confidence that can be applied to model performance. Measurements were made by deploying drogues tracked by X-band radar or GPS receivers throughout the breakwater system during calm 'no wave' and 'no wind' conditions to ensure that only tidal effects were measured. Modelled deployments were made at coincident times and locations for comparison and model performance statistics were calculated. Evidence of a number of features predicted by the model were found, giving confidence to its performance. Radar drogues are cheap to make and data capture onshore reduces the risk of data loss. GPS drogues can be used in a wider spatial area, however their onboard data storage requires drogue retrieval for data download. [ABSTRACT FROM AUTHOR]

Abstract: The ocean is a very complex medium with scales of motion that range from thousands of kilometers to the dissipation scales. Transport by ocean currents plays an important role in many practical applications ranging from climatic problems to coastal management and accident mitigation at sea. Understanding transport is challenging because of the chaotic nature of particle motion. In the last decade, new methods have been put forth to improve our understanding of transport. Powerful tools are provided by dynamical system theory, that allow the identification of the barriers to transport and their time variability for a given flow. A shortcoming of this approach, though, is that it is based on the assumption that the velocity field is known with good accuracy, which is not always the case in practical applications. Improving model performance in terms of transport can be addressed using another important methodology that has been recently developed, namely the assimilation of Lagrangian data provided by floating buoys. The two methodologies are technically different but in many ways complementary. In this paper, we review examples of applications of both methodologies performed by the authors in the last few years, considering flows at different scales and in various ocean basins. The results are among the very first examples of applications of the methodologies to the real ocean including testing with Lagrangian in-situ data. The results are discussed in the general framework of the extended fields related to these methodologies, pointing out to open questions and potential for improvements, with an outlook toward future strategies. [Copyright &y& Elsevier]

Abstract: We present a suite of algorithms for migrating Lagrangian data between processors in a parallel environment when the underlying mesh is Eulerian. The collection of algorithms applies to both uniform and adaptive meshes. The algorithms are implemented in, and distributed with, FLASH, a publicly available multiphysics simulation code. Migrating Lagrangian data on an Eulerian mesh is non-trivial because the Eulerian grid points are spatially fixed whereas Lagrangian entities move with the flow of a simulation. Thus, the movement of Lagrangian data cannot use the data migration methods associated with the Eulerian mesh. Additionally, when the mesh is adaptive, as the simulation progresses the grid resolution changes. The resulting regridding process can cause complex Lagrangian data migration. The algorithms presented in this paper describe Lagrangian data movement on a static uniform mesh and on an adaptive octree based block-structured mesh. Some of the algorithms are general enough to be applicable to any block structured mesh, while some others exploit the meta-data and structure of PARAMESH, the adaptive mesh refinement (AMR) package used in FLASH. We also present an analysis of the algorithms’ comparative performances in different parallel environments, and different flow characteristics. [Copyright &y& Elsevier]

Lagrangian data of surfzone flows are scarce, but important for understanding the spatial variability of currents. Surfzone drifters capable of collecting high frequency, accurate, Lagrangian data in the surfzone have been developed. The main issues of a robust design capable of autonomous positioning fixing, the dynamic response of the drifters, position fixing accuracy and field validation are addressed. A simple, low-cost drifter design using non-differential Global Positioning System (GPS) position fixing is described. A drogue consisting of a series of small parachutes prevents the drifter surfing in breaking waves. The methodology and results of simulations of drifter response in idealised surfzone waves are presented and predict that the drifter will perform well in low to medium energy surfzones. An analysis of positioning errors shows that only surfzone motions with frequencies of less than 0.05 Hz can be reliably resolved without differential correction. A field validation of the drifters shows that although there is significant scatter in the data, the best-fit correspondence of the drifter velocity and depth-averaged Acoustic Doppler Current Profiler (ADCP) measurements is good. [Copyright &y& Elsevier]

An improved estimation of the surface currents in the Levantine Basin of the Mediterranean sea is crucial for a wide range of applications, including pollutants transport and nutrients distribution. This estimation remains challenging due to the scarcity or shortcomings of various data types used for this purpose. In this paper, we present an objective validation of a variational assimilation algorithm that blends geostrophic velocities derived from altimetry, wind-induced velocities, and drifter positions, to continuously obtain velocity corrections. The assessment of the validation impact was based on available independent in-situ data (current meters, gliders, and independent drifters) and satellite ocean color images. In all cases, the improvement was shown either qualitatively (position of the eddies) or quantitatively. • We validate an assimilation algorithm blending drifters and altimetry. • The algorithm is extensively applied in the Levantine Mediterranean. • The validation is done with independent current meters, gliders and Chl-a images. • Significant improvement is shown qualitatively and quantitatively. [ABSTRACT FROM AUTHOR]

Abstract: The reconstruction of currents at 50 m depth was performed in the Gulf of Lions, merging Lagrangian data with outputs from a numerical ocean model. The Lagrangian data set consists of trajectories obtained from 12 satellite-tracked drifters released in the Northern Current in June 2005. The low-pass filtered trajectories revealed the well-known mean patterns of along-slope circulation and sampled its mesoscale activity, showing meandering pathways over the slope and closed pathways trapped over the shelf. They were used to reorganise the model eddy activity by refining the location and shape of meanders and eddies. The impacts of the reconstruction procedure were assessed by comparing the simulated and reconstructed fields with simultaneous SST images. Finally, the reconstructed fields were used to study some of the observed mesoscale structures. They provide a realistic scenario for diagnostics of the shelf-slope transports in the Gulf of Lions. [Copyright &y& Elsevier]