Notes and Correspondence on the Correlation Functions Associated with Polynomials of the Diffusion Operator.

摘要

Correlation functions (CFs) associated with the inverse background-error correlations (iBECs) represented by polynomials of the diffusion operator D are obtained analytically for the binomial approximations of the Gaussian BEC and in the general case of a quadratic polynomial of D . The respective analytical expressions for one-, two- and three-dimensional cases have two tuning parameters, which provide enough freedom in adjusting the CFs shape to experimental data. The polynomial coefficients of the corresponding iBEC operator are obtained in terms of these tun- ing parameters and may be useful in the design of the BEC models for variational data assimilation.