Analysis error covariance versus posterior covariance in variational data assimilation

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, and 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 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

Transport of nucleosides in Bacillus subtilis: the effect of purine nucleosides on the cytidine-uptake

The structural effects of chemical modifications upon the affinity of purine nucleosides to cytidine-transport system in Bacillus subtilis were investigated using a series of modified derivatives. The interaction involves protein molecule(s) which require the presence and proper orientation of the sugar residue and its hydroxylic functions. Moreover, a specific interaction with the heterocyclic ring system is involved in the process which results in a requirement for an aromatic π -electron system and an absence of a polarizable function at position 6 of the purine heterocycle. The region in the protein responsible for the latter interaction is rather limited and, consequently, a proper nucleoside conformation is required