The Mathematical Institute, University of Oxford, Eprints Archive

Variational data assimilation using targetted random walks

Cotter, S. L. and Dashti, M. and Robinson, J. C. and Stuart, A. M. (2010) Variational data assimilation using targetted random walks. International Journal for Numerical Methods in Fluids . (Submitted)

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Abstract

The variational approach to data assimilation is a widely used methodology for both online prediction and for reanalysis (offline hindcasting). In either of these scenarios it can be important to assess uncertainties in the assimilated state. Ideally it would be desirable to have complete information concerning the Bayesian posterior distribution for unknown state, given data. The purpose of this paper is to show that complete computational probing of this posterior distribution is now within reach in the offline situation. In this paper we will introduce an MCMC method which enables us to directly sample from the Bayesian
posterior distribution on the unknown functions of interest, given observations. Since we are aware that these
methods are currently too computationally expensive to consider using in an online filtering scenario, we frame this in the context of offline reanalysis. Using a simple random walk-type MCMC method, we are able to characterize the posterior distribution using only evaluations of the forward model of the problem, and of the model and data mismatch. No adjoint model is required for the method we use; however more sophisticated MCMC methods are available
which do exploit derivative information. For simplicity of exposition we consider the problem of assimilating data, either Eulerian or Lagrangian, into a low Reynolds number (Stokes flow) scenario in a two dimensional periodic geometry. We will show that in many cases it is possible to recover the initial condition and model error (which we describe as unknown forcing to the model) from data, and that with increasing amounts of informative data, the uncertainty in our estimations reduces.

Item Type:Article
Subjects:D - G > General
Research Groups:Oxford Centre for Collaborative Applied Mathematics
ID Code:1026
Deposited By:Peter Hudston
Deposited On:06 Jan 2011 08:23
Last Modified:09 Feb 2012 15:52

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