Objective analysis combining observation errors in physical space and observation space

A generalization of the traditional observation-error model in objective analysis is presented. It is suggested that for observations with nonlinear observation operators, the observation errors should be split up into one contribution in the measurement domain and one contribution in the domain of the model physical quantities interpolated to the measurement locations (physical space). In particular, errors of representativeness are better modelled in physical space. Analysis equations are derived for this generalized problem. The approach suggested has important applications in the assimilation of satellite observations. For special cases with a wide application this generalization does not introduce an inhibiting computational complexity.