Communications in Mathematical Sciences

Volume 7 (2009)

Number 4

Estimating eddy diffusivities from noisy Lagrangian observations

Pages: 805 – 838



C.J. Cotter

G. A. Pavliotis


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 it can be rigorously proved that the small scale dynamics can be parameterized 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.


Parameter estimation; stochastic differential equations; multiscale analysis; Lagrangian observations; subsampling; oceanic transport

2010 Mathematics Subject Classification

60H10, 60H30, 62F12, 62M05, 86A05, 86A10

Full Text (PDF format)