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

Advection and diffusion in random media: implications for sea surface temperature anomalies

The book presents the foundations of the theory of turbulent transport within the context of stochastic partial differential equations. It serves to establish a firm connection between rigorous and non-rigorous results concerning turbulent diffusion. Mathematically all of the issues addressed in this book are concentrated around a single linear equation: stochastic advection-diffusion (transport) equation. There is no attempt made to derive universal statistics for turbulent flow. Instead emphasis is placed on a statistical description of a passive scalar (tracer) under given velocity statistics. An application concerning transport of sea surface temperature anomalies reconciles the developed theory and a highly practical issue of modern physical oceanography by using the newly designed inversion techniques which take advantage of powerful maximum likelihood and autoregressive estimators. Audience: Graduate students and researchers in mathematics, fluid dynamics, and physical oceanography

A Simple Prediction Algorithm for the Lagrangian Motion in Two-Dimensional Turbulent Flows

Abstract. A new algorithm is suggested for prediction of a Lagrangian particle position in a stochastic flow, given observations of other particles. The algorithm is based on linearization of the motion equations and appears to be efficient for an initial tight cluster and small prediction time. A theoretical error analysis is given for the Brownian flow and a stochastic flow with memory. The asymptotic formulas are compared with simulation results to establish their applicability limits. Monte Carlo simulations are carried out to compare the new algorithm with two others: the centerof-mass prediction and a Kalman filter–type method. The algorithm is also tested on real data in the tropical Pacific

Parameterization of Submesoscale Eddy-Rich Flows Using a Stochastic Velocity Model

Abstract In light of the recent high-resolution radar data of surface velocity, which have revealed submesoscale eddies between the Florida Current and the coast, an objective method of detecting eddies and estimating their parameters such as center coordinates, size, and intensity is suggested. The obtained statistics are used to parametrically represent the birth–death process of eddies filling up the observation area via a model stochastic velocity field known as Çinlar flow. It appears that the suggested approach leads to a reasonable parameterization of this process for potential future use in OGCMs or coastal models

Assimilation of drifter observations for the reconstruction of the Eulerian circulation field

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