We review the celebrated Johnson Lindenstrauss Lemma and some recent advances in the understanding of probability measures with geometric characteristics on R, for large d. These advances include the central limit theorem for convex sets, according to which the uniform measure on a high dimensional convex body1 has marginals that are approximately Gaussian. We try to combine these two results t...

In this chapter we give an introduction to different types of Ensemble Kalman filter, describe the Local Ensemble Transform Kalman Filter (LETKF) as a representative prototype of these methods, and several examples of how advanced properties and applications that have been developed and explored for 4D-Var (four-dimensional variational assimilation) can be adapted to the LETKF without requiring...

A modification scheme to the ensemble Kalman filter (EnKF) is introduced based on the concept of the unscented transform (Julier et al., 2000; Julier and Uhlmann, 2004), which therefore will be called the ensemble unscented Kalman filter (EnUKF) in this work. When the error distribution of the analysis is symmetric (not necessarily Gaussian), it can be shown that, compared to the ordinary EnKF,...

The ensemble Kalman filter (EnKF) is nowadays recognized as an excellent inverse method for hydraulic conductivity characterization using transient piezometric head data. Its implementation is well suited for a parallel computing environment. A parallel code has been designed that uses parallelization both in the forecast step and in the analysis step. In the forecast step, each member of the e...

This paper designs an Image-based Ensemble Kalman Filter (IEnKF), whose components are defined only from image properties, to estimate motion on image sequences. The key elements of this filter are, first, the construction of the initial ensemble, and second, the propagation in time of this ensemble on the studied temporal interval. Both are analyzed in the paper and their impact on results is ...

In this paper, we propose and develop a methodology for nonlinear systems health monitoring by modeling the damage and degradation mechanism dynamics as ”slow” states that are augmented with the system ”fast” dynamical states. This augmentation results in a two-time scale nonlinear system that is utilized for development of health estimation and prediction modules within a health monitoring fra...

In the last decade, ensemble-based methods have been widely investigated and applied for data assimilation of flow problems associated with atmospheric physics and petroleum reservoir history matching. This paper focuses entirely on the reservoir history-matching problem. Among the ensemble-based methods, the ensemble Kalman filter (EnKF) is the most popular for history-matching applications. H...

Data assimilation experiments are performed using an ensemble Kalman filter (EnKF) implemented for a twolayer spectral shallow water model at triangular truncation T100 representing an abstract planet covered by a strongly stratified fluid. Advantage is taken of the inherent parallelism in the EnKF by running each ensemble member on a different processor of a parallel computer. The Kalman filte...

A Global Carbon Assimilation System based on the ensemble Kalman filter (GCAS-EK) is developed for assimilating atmospheric CO2 data into an ecosystem model to simultaneously estimate the surface carbon fluxes and atmospheric CO2 distribution. This assimilation approach is similar to CarbonTracker, but with several new developments, including inclusion of atmospheric CO2 concentration in state ...