Correlation functions for atmospheric data analysis

Atmospheric data assimilation techniques rely on parametric models for spatial correlation functions. This article proposes and discusses various families of homogeneous and isotropic correlation models on Euclidean spaces and on the sphere. In particular, three simply parametrized classes of compactly supported, smooth, and analytically simple correlation functions are proposed. the first two classes approximate standard second‐ and third‐order autoregressive functions, and a member of the third family approximates the Gaussian function within a maximal error of 0.0056. Furthermore, correlation models suggested previously for meteorological applications are checked for permissibility, with both positive and negative results.