Predictabilities and uncertainties of tracer trajectories and Lagrangian Coherent Structures with ensemble system

The US Navy's regional ensemble system is run with 32 members of NCOM and NCODA 3D-Var DA. The predictability and uncertainty are studied using ensemble systems with various resolutions in conventional Eulerian formulation. However, in many practical applications, the predictabilities and uncertainties of tracers such as the oils spills in ocean and pollutants in air are better studied in the Lagrangian framework by following the movements of tracer particles. One of the fundamental measurements of the predictabilities and uncertainties for tracer particles is the finite-time Lyapunov exponent (FTLE). The FTLEs, which are used to capture the stable and unstable manifolds in a dynamical system, are employed to infer the Lagrangian Coherent Structures (LCSs) in this work.

With ensemble, not only the repelling and attracting LCSs, but also their respective uncertainties can be computed at the same time. It is shown that the Absolute Dispersion (AD) and its uncertainties in km for tracer particles can be easily computed within the ensemble. The Lagrangian Spread provided by ensemble is directly related to the Relative Dispersion (RD). It is known that the AD and RD play critical roles in studying mixing and transport of particles in meso/submeso-scale dynamics. We demonstrate that both of them can be calculated efficiently as by-products in an ensemble system. The predictability and uncertainty are discussed and compared the both Eulerian and Lagrangian frameworks.