Abstract: In this paper, the classical correlation coefficient formula is changed into some new forms which are denoted by some Fourier spectra coefficients. And the advantages of the formulas are discussed. The new formulas can be directly connected with the dynamical equations of atmosphere. Thus, the equations can be denoted by correlation coefficients. It is pointed out that it is of significance to use correlation fields to reveal the large scale dynamical processes in the atmosphere. And the relationships revealled by correlation fields can be physically interpretated by the dynamical equations denoted by correlation coefficients directly.