Diagnosis and adaptive tuning of observation-error parameters in a variational assimilation

Following the a posteriori diagnosis approach proposed by some authors, a p ractical computation of the expectation of sub-parts of the value of a cost function at the minimum is shown to be feasible by using a randomization t echnique based on a perturbation of observations or background fields. Thes e computations allow the tuning of observation-error weighting parameters b y applying a simple iterative fixed-point procedure. The procedure is first tested in a simplified variational scheme on a circular domain and then in a similar scheme but with the addition of the vertical coordinate. The rel ationship between the proposed approach and the Generalized Cross Validatio n is also shown. A test in the French Action de Recherche Petite Echelle Gr ande Echelle (ARPEGE) three-dimensional variational framework with both sim ulated observations and background fields is finally performed. It shows th at a complete description of observation-error parameters can be retrieved with only a few iterations and, thus, at a reasonable cost.