Lagrangian Time Series Models for Ocean Surface Drifter Trajectories

This paper proposes stochastic models for the analysis of ocean surface trajectories obtained from freely-drifting satellite-tracked instruments. The proposed time series models are used to summarise large multivariate datasets and infer important physical parameters of inertial oscillations and other ocean processes. Nonstationary time series methods are employed to account for the spatiotemporal variability of each trajectory. Because the datasets are large, we construct computationally efficient methods through the use of frequency-domain modelling and estimation, with the data expressed as complex-valued time series. We detail how practical issues related to sampling and model misspecification may be addressed using semi-parametric techniques for time series, and we demonstrate the effectiveness of our stochastic models through application to both real-world data and to numerical model output.Comment: 21 pages, 10 figure

Particle energization in space plasmas : towards a multi-point, multi-scale plasma observatory

This White Paper outlines the importance of addressing the fundamental science theme "How are charged particles energized in space plasmas" through a future ESA mission. The White Paper presents five compelling science questions related to particle energization by shocks, reconnection, waves and turbulence, jets and their combinations. Answering these questions requires resolving scale coupling, nonlinearity, and nonstationarity, which cannot be done with existing multi-point observations. In situ measurements from a multi-point, multi-scale L-class Plasma Observatory consisting of at least seven spacecraft covering fluid, ion, and electron scales are needed. The Plasma Observatory will enable a paradigm shift in our comprehension of particle energization and space plasma physics in general, with a very important impact on solar and astrophysical plasmas. It will be the next logical step following Cluster, THEMIS, and MMS for the very large and active European space plasmas community. Being one of the cornerstone missions of the future ESA Voyage 2050 science programme, it would further strengthen the European scientific and technical leadership in this important field.Peer reviewe

An Ensemble-Proper Orthogonal Decomposition Method for the Nonstationary Navier-Stokes Equations

The definition of partial differential equation (PDE) models usually involves a set of parameters whose values may vary over a wide range. The solution of even a single set of parameter values may be quite expensive. In many cases, e.g., optimization, control, uncertainty quantification, and other settings, solutions are needed for many sets of parameter values. We consider the case of the time-dependent Navier-Stokes equations for which a recently developed ensemble-based method allows for the efficient determination of the multiple solutions corresponding to many parameter sets. The method uses the average of the multiple solutions at any time step to define a linear set of equations that determines the solutions at the next time step. To significantly further reduce the costs of determining multiple solutions of the Navier-Stokes equations, we incorporate a proper orthogonal decomposition (POD) reduced-order model into the ensemble-based method. The stability and convergence results for the ensemble-based method are extended to the ensemble-POD approach. Numerical experiments are provided that illustrate the accuracy and efficiency of computations determined using the new approach