Ensemble Variational Assimilation as a Probabilistic Estimator. Part I: The linear and weak non-linear case

Abstract

Abstract.Data assimilation is considered as a problem in Bayesian estimation, viz. determine the probability distribution for the state of the observed system, conditioned by the available data. In the linear and additive Gaussian case, a Monte-Carlo sample of the Bayesian probability distribution (which is Gaussian and known explicitly) can be obtained by a simple procedure : perturb the data according to the probability 5 distribution of their own errors, and perform an assimilation on the perturbed data. The performance of that approach, called Ensemble Variational Assimilation (EnsVAR), is studied in the two parts of the paper on the non-linear low-dimensional Lorenz-96 chaotic system, the assimilation being performed by the standard variational procedure. In Part I, EnsVAR is implemented first, for reference, in a linear and Gaussian case, and then in a weakly non-linear case (assimilation over 5 days of the system). The perfor-10 mances of the algorithm, considered as a statistical estimator, are very similar in the two cases. Additional comparison shows that the performance of EnsVAR is better, both in the assimilation and forecast phases, than that of standard algorithms for Ensemble Kalman Filter and Particle Filter (although at a higher cost). Globally similar results are obtained with the Kuramoto-Sivashinsky equation.

Data assimilation in the geosciences: An overview of methods, issues, and perspectives

“…This is rather close to the idea of the hybrid EnKF‐3DVar, but with a 4DVar scheme. It is worth to note that, in the linear case and Gaussian case, EDA is exactly Bayesian, in the sense that it produces an ensemble of independent realizations of the conditional PDF, though not necessarily in the nonlinear or non‐Gaussian case (Jardak & Talagrand, ; Liu et al, , and references therein). The method has been implemented at Météo‐France (Berre, Varella, & Desroziers, ; Raynaud, Berre, & Desroziers, , ) and at the ECMWF (Bonavita, Isaksen, & Hólm, ; Bonavita, Raynaud, & Isaksen, ).…”