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We consider the problem of propagating an ensemble of solutions and its characterization in terms of its mean and covariance matrix. We propose differential equations that lead to a continuous matrix factorization of the ensemble into a generalized singular value decomposition (SVD). The continuous factorization is applied to ensemble propagation under… (More)

Symmetry-breaking bifurcations have been studied for convection in a nonrotating spherical shell whose outer radius is twice the inner radius, under the influence of an externally applied central force field with a radial dependence proportional to 1/r(5). This work is motivated by the GeoFlow experiment, which is performed under microgravity condition at… (More)

Ensemble Kalman filter techniques are widely used to assimilate observations into dy-namical models. The dimension of phase is typically much larger than the number of ensemble members which leads to inaccurate results in the computed covariance matrices. These inaccuracies lead, among others, to spurious long range correlations which can be eliminated by… (More)

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