Communications in Mathematical Sciences

Estimating eddy diffusivities from noisy Lagrangian observations

C.J. Cotter and G. A. Pavliotis

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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 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.

Article information

Source
Commun. Math. Sci., Volume 7, Number 4 (2009), 805-838.

Dates
First available in Project Euclid: 25 January 2010

Permanent link to this document
https://projecteuclid.org/euclid.cms/1264434134

Mathematical Reviews number (MathSciNet)
MR2604621

Zentralblatt MATH identifier
1183.62143

Subjects
Primary: 62M05: Markov processes: estimation 86A05: Hydrology, hydrography, oceanography [See also 76Bxx, 76E20, 76Q05, 76Rxx, 76U05] 86A10: Meteorology and atmospheric physics [See also 76Bxx, 76E20, 76N15, 76Q05, 76Rxx, 76U05] 60H10: Stochastic ordinary differential equations [See also 34F05] 60H30: Applications of stochastic analysis (to PDE, etc.) 62F12: Asymptotic properties of estimators

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

Citation

Cotter, C.J.; Pavliotis, G. A. Estimating eddy diffusivities from noisy Lagrangian observations. Commun. Math. Sci. 7 (2009), no. 4, 805--838. https://projecteuclid.org/euclid.cms/1264434134


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