A numerically efficient data analysis method with error map generation

The variational inverse model (VIM) for data analysis was already shown to be statistically equivalent to objective analysis (OA) provided the covariance function for the OA and the VIM reproducing kernel are identical. The VIM, however does not allow a direct derivation of the error field associated with the analysis. The purpose of the paper is to extend the one to one correspondance between the two analysis shemes by proposing a heuristic statistical error expression for the VIM. The numerical efficiency on analysis and error map generation of both methods is compared on quasi-synoptic and climatological data sets. It is shown that the VIM analysis and error map generation offers interesting numerical skills in both case studies.