Abstract: In this paper,it is shown theoretically that the total variance of a meteorological field is composed of two parts: the variance of the signal field which represents the fundamental characteristics of the meteorological field and the variance of the noise field which represents the random turbulence. It is found that with the total van ance of the meteorological field given, the variance of the noise field will be weakl when the variance of the signal field is gstrong and vice versa. On this basis, the influencing factors of the convergence speed are demonstrated for Empirical Orthogonal Functions (EOFs). When the EOFs are applied to the meteorological field, it is noted that the speed of convergence in the original field depends upon the factors of both the joint entropies of the field and the individual entropies at the stations in the field. The former is proved to be the main factor.According to standardization, these factors are equivalent to the effects of both the correlation structure of the meteorological field and the variation of the spatial distribution in the field on the convergence speed. Several empirical criteria are presented for the estimation of the convergence speed when the EOFs are applied to any original field. Tests show that these criteria are very effective in meteorological field analysis.