Ensemble KF with Statistical Orthogonality

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XVI International Conference on Computational Methods in Water Resources (CMWR-XVI) Ingeniørhuset

Ensemble KF with Statistical Orthogonality
Author:Dimitri Treebushny <dima@env.com.ua> (UCEWP)
Presenter:Dimitri Treebushny <dima@env.com.ua> (UCEWP)
Date: 2006-06-18     Track: Special Sessions     Session: Data assimilation in water resources modelling

Correct propagation of uncertainty is of primary importance for a model when the assimilation of data is to be utilized. The most popular choice is a Monte Carlo approach within the Ensemble Kalman filter framework. In the filter independent realizations of the unofirm random noise should be generated each model time step. Additionally it has to be noted, that stochastic independency is one of the important assumptions in the classical Kalman filter derivation. The paper suggests a notion of statistical white noise and statistical independency rather than stochastic ones. The new system noise and measurement noises are generated and then modified to be statistically white and independent with the fixed number of previously generated noises. One part of the idea - measurement noise "purification" - was presented in (Wei et al. 2004) with the name "Breeding with orthogonalization", so the paper can be seen as an extension of this approach. The performance test results of the Ensemble KF with Statistical Orthogonality vs the classical Ensemble KF are presented for the transport Advection-Dispersion equation.