Estimating eddy diffusivities from noisy Lagrangian observations

TL;DR

This paper investigates methods to accurately estimate eddy diffusivity from noisy Lagrangian data, emphasizing the importance of optimal data sampling and data averaging to mitigate bias and measurement error.

Contribution

It provides a rigorous analysis and numerical validation of the necessity of subsampling and data averaging strategies for eddy diffusivity estimation in noisy environments.

Findings

Subsampling is essential for accurate estimation.

Optimal sampling rate depends on velocity field properties.

Averaging reduces observation error impact.

Abstract

The problem of estimating the eddy diffusivity from Lagrangian observations in the presence of measurement error is studied in this paper. We consider a class of incompressible velocity fields for which is can be rigorously proved that the small scale dynamics can be parameterised in terms of an eddy diffusivity tensor. We show, by means of analysis and numerical experiments, that subsampling of the data is necessary for the accurate estimation of the eddy diffusivity. The optimal sampling rate depends on the detailed properties of the velocity field. Furthermore, we show that averaging over the data only marginally reduces the bias of the estimator due to the multiscale structure of the problem, but that it does significantly reduce the effect of observation error.