# A coherent structure approach for parameter estimation in Lagrangian Data Assimilation

## TL;DR

This paper presents a novel data assimilation method that estimates model parameters by directly assimilating Lagrangian Coherent Structures using ABC and SMC, outperforming traditional methods in chaotic advection scenarios.

## Contribution

The paper introduces a new approach combining Lagrangian Coherent Structures, ABC, and PCA for parameter estimation, avoiding likelihood computation and improving accuracy in chaotic flows.

## Key findings

- Significantly better parameter estimation results than bootstrap particle filter.
- Effective identification of coherent patterns using PCA from tracer data.
- Robust performance in chaotic advection conditions.

## 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.