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International audience; 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.

The major environmental challenges to society, for example, climate change, environmental degradation and the extreme weather effects, require comprehensive information for a resourceful response, including informed decision making related to future actions. Estuaries are especially exposed to the footprints of climate change because alterations in climatic variables that impact freshwater and marine systems will also influence estuaries. While this knowledge is useful, scientists currently lack detailed information on the impact of global change in a diverse range of morphological estuary types across continental and global regions (Scanes et al., 2020). By identifying the processes and attributes responsible for estuary change, the dynamics of estuaries is more accurately predictable around the globe. However, to achieve this goal, two remaining components are needed: (1) a tool for collecting information; and (2) a robust method to elaborate this information. In other words, observations (measurements) support the first component, and the latter component is provided by models. The mechanisms to secure these two avenues of investigation are distinct: observations are directly connected with the system under investigation through measurement devices, while models have an indirect connection with the system, being an expression of measurements and represent an abstraction of reality. To make use of the information incorporated in observations and models, it is essential to understand the characteristics of this information. In particular, the errors and limitations associated with both observations and models. Errors in models are generated through incomplete implementation of the model as well as their imperfect simulation of real world processes. Another basic attribute of observations is that they are spatially and temporally discrete, which results in gaps in the information provided by them. To fill these gaps, it is important to first make observations more complete, with better spatial coverage, and hence more useful; secondly, use observation on the behaviour of the system to extend the observations for the purpose of reflecting the reality (e.g., using a model) (W. Lahoz et al., 2010). The model can then propagate the information from observations and better represent the real state of the system under investigation. The idea behind choosing a model for a particular environment is that the model provides a set of consistent principles which when registered, makes the most efficient use of observations.

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, 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., Comment: J Nonlinear Sci, 2018

The Sacramento-San Joaquin River Delta in California becomes inadequate in fresh water resources, while the water demand in California keeps increasing. Large-scale numerical flow models, for example Delta Simulation Model II (DSM2) and River, Estuary, And Land Model (REALM), used as crucial water resources management tools, are capable of providing critical information about tidal forcing and salinity transport in the bays and channels of the Delta. Reliable flow estimation and prediction of these models, however, largely depend on an accurate representation of open boundary conditions and initial conditions, which are usually calibrated against historical data sets acquired from Eulerian measurements near the boundaries. In large watershed, unfortunately, these measurements have demonstrated many intrinsic limitations, for example small spatial coverage and sparse temporal sampling. Also, existing Eulerian sensors have many recorded failures, such as broken gauges, sensor drifts, process leaks, improper measuring devices, and many other random sources. More importantly, if the hydraulic system is radically altered, as in the case of extensive levee failures, the historical data sets can be of limited usage.In this dissertation, a sensing-modeling system featuring rapidly deployed Lagrangian drifters is developed. The system is capable of predicting regional flows and transport in the Delta in a real-time mode, without dependence on historical data. Lagrangian data is obtained when floating drifters move along with the flow and report their locations. The data provides instant information about the flow, including flow advections and eddy dispersions, and is further assimilated into underlying shallow water equation (SWE) models to characterize the flow state. Different approaches to facilitate the flow estimation have been investigated in this dissertation. First, a variational assimilation method (Quadratic Programming) is applied to a 1D SWE model (Linearized Saint-Venant equations). The assimilation method poses the problem of estimating the flow state in a channel network as a quadratic programming by minimizing a quadratic cost function -- the norm of the difference between the drifter observations and the model velocity predictions -- and expressing the constraints in terms of linearized equalities and inequalities. The problem is then efficiently solved using a fast and robust algorithm. The approach is easy to implement and low in computation costs.Later, a sequential assimilation method (Ensemble Kalman Filtering) is implemented to a 2D SWE model (depth-integrated Navier-Stokes equations). The assimilation method involves a series of state analysis and updates, where the observed Lagrangian data is incorporated into the state one step at a time to incrementally correct the model prediction. The implementation of this method demands powerful computation ability, and is achieved on high-performance computing clusters at NERSC. To assess the performance of the proposed data assimilation methods, we investigated a distributed network of channels, subject to quasi-periodic tidal forcing, in the Sacramento-San Joaquin River Delta. Field operational experiments were carried out with a fleet of over 70 floating drifters, deployed within approximately 0.55 km2 of the river network. During the experiments, more than 325,000 GPS readings were taken from the floating drifters and collected, in real time, onto a central server. It is the first experiment of this kind conducted at such scale, where high-density Lagrangian data have been collected in a real river environment and successfully assimilated over a full tidal cycle. It is demonstrated that both of the proposed assimilation methods (i.e., QP in 1D SWE model and EnKF in 2D SWE model) can handle the Lagrangian data with sufficiently accurate estimations. In many practical cases, the 1D flow estimation is adequate for water resource management to retrieve critical flow characteristics in a prompt and efficient manner. In the case of complex channel geometry, however, the 2D flow estimation is vital to describe the hydraulic system.

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.

26 pages; International audience; 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.

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.

The problem of estimating the drift of a stochastic flow given Lagrangian observations is an estimation problem for a multidimensional diffusion with a degenerate diffusion matrix. The maximum-likelihood estimator of the constant drift is considered. A long-time asymptotic of its mean-square error (MSE) is computed. It is shown that the time-space average of the observed Lagrangian velocities has the same asymptotic. These estimators are compared to the least-squares estimator based on Eulerian data. In the most important, for applications, two-dimensional case the Lagrangian estimator is typically preferable for incompressible flows, while for flows close to potential the Eulerian estimator is better.

We investigate the assimilation of data that are collected while Lagrangian ocean instruments are in transit between surfacings. We introduce an observation operator that takes these data into account in addition to the data that are typically assimilated. A key point is that the subsurface, en-route paths of these ocean instruments are estimated as part of the assimilation scheme. We present a twin experiment model scenario that lets us compare the improvement by assimilating en-route data over traditional data alone. We make this comparison and present results for both sequential filtering and smoothing. Keywords: data assimilation, underwater sampling, Lagrangian instruments, Eulerian data (Published: 6 November 2013) Citation: Tellus A 2013, 65 , 20319, http://dx.doi.org/10.3402/tellusa.v65i0.20319

This work concerns the variational assimilation of lagrangian data in river hydraulics, for the identification of parameters in a numerical model relying on the shallow water equations. We propose to take into account Lagrangian data such as trajectories of particles transported on the surface of the flow, in addition to classical eulerian observations which are sometimes not sufficient. The advantages of this approach to improve the identification of parameters are demonstrated through a series of numerical experiments using synthetic data as well as real data from an open channel flow where trajectories are extracted from a video., Ce travail porte sur l'assimilation variationnelle de données lagrangiennes en hydraulique fluviale, pour l'identification de paramètres dans un modèle numérique de rivière basé sur les équations de Saint-Venant, mise oeuvre dans le logiciel Dassflow. Nous proposons de prendre en compte des observations de nature Lagrangienne, comme des trajectoires de particules transportées à la surface de l'écoulement, en plus des observations classiquement disponibles, parfois insuffisantes. L'intérêt de cette approche pour améliorer l'identification de certains paramètres est mis en évidence à travers une série d'expériences numériques utilisant soit des données synthétiques, soit des données réelles issues d'un écoulement en canal, où des trajectoires sont extraites d'une séquence vidéo.

A method for the reconstruction of the mesoscale Eulerian velocity field based on Lagrangian data at given sampling period is presented. A variational approach is used, where information on the float positions are combined with a simple model constraint describing the motion of particles advected in a velocity field. The velocity field of a priori specified space scale is estimated minimizing a cost function which measures the distance between the observed float positions and the model predicted ones for each sampling period. The method is first implemented considering the time-independent approximation of the velocity correction during a time interval shorter than the typical time scale of the mesoscale field. In a second step, this approximation is relaxed to consider inertial oscillations superimposed on the mesoscale field. The method is tested on a numerical regional circulation on the Northwestern Mediterranean Sea, characterized by an Eulerian time scale significantly longer than the inertial period. The observational coverage of the region varies between 80% and 16% and the corresponding error in the velocity reconstruction varies from less than 10% to approximately 50%, with a sampling period of the day. For smaller sampling intervals, the reconstruction is further improved in the time-dependent approximation. Finally, the method is used to combine information from Lagrangian data and General Circulation Models. The results suggest the useful application of the method for assimilation studies.