Variables describing atmospheric circulation and other climate parameters derived from various GCMs and obtained from observations can be represented on a spatio-temporal grid (lattice) structure. The primary objective of this paper is to explore existing as well as new statistical methods to analyze such data structures for the purpose of model diagnostics and intercomparison from a statistical perspective. Among the several statistical methods considered here, a new method based on common principal components appears most promising for the purpose of intercomparison of spatiotemporal data structures arising in the task of model/model and model/data intercomparison. A strategy for such an intercomparison is outlined in two steps: first, the commonalty of spatial structures in two (or more) fields is captured in the common principal vectors, and second, the corresponding principal components obtained as time series are then compared on the basis of similarities in their temporal evolution.