Data assimilation

Chin T M, Turmon M J, Jewell J B, Ghil M. An Ensemble-Based Smoother with Retrospectively Updated Weights for Highly Nonlinear Systems. Monthly Weather Review. 2007;135 :186–202.Abstract

Monte Carlo computational methods have been introduced into data assimilation for nonlinear systems in order to alleviate the computational burden of updating and propagating the full probability distribution. By propagating an ensemble of representative states, algorithms like the ensemble Kalman filter (EnKF) and the resampled particle filter (RPF) rely on the existing modeling infrastructure to approximate the distribution based on the evolution of this ensemble. This work presents an ensemble-based smoother that is applicable to the Monte Carlo filtering schemes like EnKF and RPF. At the minor cost of retrospectively updating a set of weights for ensemble members, this smoother has demonstrated superior capabilities in state tracking for two highly nonlinear problems: the double-well potential and trivariate Lorenz systems. The algorithm does not require retrospective adaptation of the ensemble members themselves, and it is thus suited to a streaming operational mode. The accuracy of the proposed backward-update scheme in estimating non-Gaussian distributions is evaluated by comparison to the more accurate estimates provided by a Markov chain Monte Carlo algorithm.

Carrassi A, Ghil M, Trevisan A, Uboldi F. Data assimilation as a nonlinear dynamical systems problem: Stability and convergence of the prediction-assimilation system. Chaos. 2008;18 (2) :023112.Abstract

We study prediction-assimilation systems, which have become routine in meteorology and oceanography and are rapidly spreading to other areas of the geosciences and of continuum physics. The long-term, nonlinear stability of such a system leads to the uniqueness of its sequentially estimated solutions and is required for the convergence of these solutions to the system's true, chaotic evolution. The key ideas of our approach are illustrated for a linearized Lorenz system. Stability of two nonlinear prediction-assimilation systems from dynamic meteorology is studied next via the complete spectrum of their Lyapunov exponents; these two systems are governed by a large set of ordinary and of partial differential equations, respectively. The degree of data-induced stabilization is crucial for the performance of such a system. This degree, in turn, depends on two key ingredients: (i) the observational network, either fixed or data-adaptive, and (ii) the assimilation method.

Ghil M, S. Coho JT, Bube K, Isaacson E. Dynamic Meteorology: Data Assimilation Methods. In: Bengtsson L, Ghil M, Källén E Applied Mathematical Sciences. Vol. 36. Dynamic Meteorology - Data Assimilation Methods. Springer-Verlag ; 1981. pp. 139–224.