Analysis error covariance versus posterior covariance in variational data assimilation

作者：Gejadze I Yu^*; Shutyaev V; Le Dimet F X

来源：Quarterly Journal of the Royal Meteorological Society, 2013, 139(676): 1826-1841.

DOI：10.1002/qj.2070

• large-scale flow models
• nonlinear dynamics
• data assimilation
• optimal control
• analysis error covariance
• Bayesian posterior covariance
• Hessian

The problem of variational data assimilation for a nonlinear evolution model is formulated as an optimal control problem to find the initial condition 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, and for stronger nonlinearity by the effective%26apos; 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%26apos; counterpart is introduced. An approach for computing the mentioned estimates in the matrix-free environment using the 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.

• 出版日期2013-10