Meteorological data are collected over space and time. Techniques for modeling the temporal characteristics of meteorological data are well known and accepted. While methods for accommodating the spatial character of meteorological variables have been available for over 30 years, they are far less frequently used. In part, this is because many theoretical and computational issues remain to be resolved concerning the application of spatial modeling methods to meteorological data. One of these issues is the fitting of spatial-correlation functions. In this paper, it is shown that temporal correlations can seriously bias fitted covariance functions that are used in optimal interpolation and optimal spatial-averaging methods. A result of this bias is that the fitting of correlation functions to temporal correlations can result in overestimates of spatial correlations. In contrast, the fitting of structure function models from data for fixed time periods does not suffer from the temporal biases of correlation function fitting and should be the preferred method for estimating spatial correlations. Structure function modeling must, however, accommodate anisotropy in the data.