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

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

Seasonal Variability of Near-Inertial Internal Waves in the Deep Central Part of the Black Sea

This observational study is concerned with the seasonal variability of near-inertial internal waves (NIWs) in the central part of the Black Sea. Rotary spectral analysis of the nearly year-long time series of the sea current velocity measurements at 100 m and 1700 m revealed the prevailing anticyclonic component of the motions near the local inertial frequency f. Both the rotary spectra and the visual exploration of the time series showed that the peaks of NIWs were blue-shifted to higher frequencies. The monthly average blue-shift was stronger up to 1.038f in the summer. It was found that the minimum intensification of the NIWs occurred in summertime and the maximum intensification was characteristic of the autumn-winter period when the NIW packets included up to 16 waves with pronounced clockwise rotation of the velocity vectors

Seasonal Variability of Near-Inertial Internal Waves in the Deep Central Part of the Black Sea

This observational study is concerned with the seasonal variability of near-inertial internal waves (NIWs) in the central part of the Black Sea. Rotary spectral analysis of the nearly year-long time series of the sea current velocity measurements at 100 m and 1700 m revealed the prevailing anticyclonic component of the motions near the local inertial frequency f. Both the rotary spectra and the visual exploration of the time series showed that the peaks of NIWs were blue-shifted to higher frequencies. The monthly average blue-shift was stronger up to 1.038f in the summer. It was found that the minimum intensification of the NIWs occurred in summertime and the maximum intensification was characteristic of the autumn-winter period when the NIW packets included up to 16 waves with pronounced clockwise rotation of the velocity vectors