A coherent structure approach for parameter estimation in Lagrangian Data Assimilation

Abstract

We introduce a data assimilation method to estimate model parameters with observations of passive tracers by directly assimilating Lagrangian Coherent Structures. Our approach differs from the usual Lagrangian Data Assimilation approach, where parameters are estimated based on tracer trajectories. We employ the Approximate Bayesian Computation (ABC) framework to avoid computing the likelihood function of the coherent structure, which is usually unavailable. We solve the ABC by a Sequential Monte Carlo (SMC) method, and use Principal Component Analysis (PCA) to identify the coherent patterns from tracer trajectory data. Our new method shows remarkably improved results compared to the bootstrap particle filter when the physical model exhibits chaotic advection.

20 pages, 5 figures, submitted to Physica D: Nonlinear Phenomena

References in corpus (11)

• Approximate Bayesian computation scheme for parameter inference and model selection in dynamical systems
• On Dynamic Mode Decomposition: Theory and Applications
• Adaptive approximate Bayesian computation
• Transport in time-dependent dynamical systems: Finite-time coherent sets
• Data Assimilation: A Mathematical Introduction
• On adaptive resampling strategies for sequential Monte Carlo methods
• Coherent sets for nonautonomous dynamical systems
• Understanding the geometry of transport: diffusion maps for Lagrangian trajectory data unravel coherent sets
• Estimating long term behavior of flows without trajectory integration: the infinitesimal generator approach
• Optimally coherent sets in geophysical flows: A new approach to delimiting the stratospheric polar vortex
• Two-state filtering for joint state-parameter estimation

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• Model and Data Reduction for Data Assimilation: Particle Filters Employing Projected Forecasts and Data with Application to a Shallow Water Model
• Simultaneous Coherent Structure Coloring facilitates interpretable clustering of scientific data by amplifying dissimilarity
• Uncertainty Quantification of Nonlinear Lagrangian Data Assimilation Using Linear Stochastic Forecast Models
• The convergence of stochastic differential equations to their linearisation in small noise limits