Skip to Main content Skip to Navigation
New interface
Documents associated with scientific events

Posterior Covariance vs. Analysis Error Covariance in Data Assimilation

François-Xavier Le Dimet 1, * Victor Shutyaev 2, * Igor Gejadze 3, * 
* Corresponding author
1 MOISE - Modelling, Observations, Identification for Environmental Sciences
Inria Grenoble - Rhône-Alpes, LJK - Laboratoire Jean Kuntzmann, Grenoble INP - Institut polytechnique de Grenoble - Grenoble Institute of Technology
Abstract : The problem of variational data assimilation for a nonlinear evolution model is formulated as an optimal control problem to find the initial condition function (analysis). The data contain errors (observation and background errors), hence there is an error in the analysis. For mildly nonlinear dynamics, the analysis error covariance can be approximated by the inverse Hessian of the cost functional in the auxiliary data assimilation problem, whereas for stronger nonlinearity - by the 'effective' inverse Hessian. However, it has been noticed that the analysis error covariance is not the posterior covariance from the Bayesian perspective. While these two are equivalent in the linear case, the difference may become significant in practical terms with the nonlinearity level rising. For the proper Bayesian posterior covariance a new approximation via the Hessian is derived and its 'effective' counterpart is introduced. An approach for computing the mentioned estimates in the matrix-free environment using Lanczos method with preconditioning is suggested. Numerical examples which validate the developed theory are presented for the model governed by Burgers equation with a nonlinear viscous term.
Complete list of metadata
Contributor : Eugene Kazantsev Connect in order to contact the contributor
Submitted on : Friday, January 17, 2014 - 1:14:51 PM
Last modification on : Thursday, January 20, 2022 - 5:28:13 PM
Long-term archiving on: : Friday, April 18, 2014 - 11:38:26 AM


Files produced by the author(s)


  • HAL Id : hal-00932577, version 1



François-Xavier Le Dimet, Victor Shutyaev, Igor Gejadze. Posterior Covariance vs. Analysis Error Covariance in Data Assimilation. 6th WMO Symposium on Data Assimilation, Oct 2013, College Park, United States. 2013. ⟨hal-00932577⟩



Record views


Files downloads