Optimal analysis of in situ data in the western Mediterranean using statistics and cross-validation

Abstract

To study the Mediterranean general circulation, there is a constant need for reliable interpretations of available hydrological observations. Optimal data analyses (in the probabilistic point of view of objective analysis) are fulfilled using an original finite-element technique to minimize the variational principle of the spline procedure. Anyway, a prior statistical knowledge of the problem is required to adapt the optimization criterion to the purpose of this study and to the particular features of the system. The main goal of this paper is to show how the cross-validation methodology can be used to deduce statistical estimators of this information only from the dataset. The authors also give theoretical and/or numerical evidence that modified estimators - using generalized cross-validation or sampling algorithms - are interesting in the analysis optimization process. Finally, results obtained by the application of these methods to a Mediterranean historical database and their comparison with those provided by other techniques show the usefulness and the reliability of the method.