Optimal exploitation of measurements and remote sensing retrievals are an enduring problem in data assimilation. A special task to foster efficiency consists in spreading local data information over an embedding irregular region, while statistical optimality characteristics of the data assimilation algorithms remain unaffected. Frontal and filamental structures of the the polar vortex require markedly dynamic anisotropic and inhomogeneous covariance modelling, where symmetrical and positive definite properties must be granted in a high dimensional phase space. The presentation addresses this issue for chemistry data assimilation by replacing the covariance matrix with a statistically corresponding self-adjoint operator. This concept has been generalized for irregular patterns in other areas of data assimilation, like for soil parameters. Examples of other challenges and approaches are given, especially for cases where non-Gaussian error characteristics prevail.