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Correlation functions for atmospheric data analysis
Author(s) -
Gneiting Tilmann
Publication year - 1999
Publication title -
quarterly journal of the royal meteorological society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.744
H-Index - 143
eISSN - 1477-870X
pISSN - 0035-9009
DOI - 10.1002/qj.49712555906
Subject(s) - autoregressive model , mathematics , correlation , gaussian , isotropy , correlation function (quantum field theory) , homogeneous , spatial correlation , parametric statistics , statistical physics , function (biology) , mathematical analysis , statistics , geometry , physics , combinatorics , spectral density , quantum mechanics , evolutionary biology , biology
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.