Adaptive Tuning of Numerical Weather Prediction Models: Randomized GCV in Three- and Four-Dimensional Data Assimilation

In variational data assimilation, optimal ingestion of the observational data and optimal use of prior physical and statistical information involve the choice of numerous weighting, smoothing and tuning parameters which control the filtering and merging of divers sources of information. Generally these weights must be obtained from a partial and imperfect understanding of various sources of errors, and are frequently chosen by a combination of historical information, physical reasoning and trial and error. Generalized Cross Validation (GCV) has long been one of the methods of choice for choosing certain tuning, smoothing, regularization parameters in ill-posed inverse problems, smoothing and filtering problems. In theory, it is well suited for the adaptive choice of certain parameters that occur in variational objective analysis, and data assimilation problems that are mathematically equivalent to variational problems. The main drawback of the use of GCV in data assimilation...