Solar power variability is a concern to grid operators as unanticipated changes in PV plant power output can strain the electric grid. The main cause of solar variability is clouds passing over PV modules. However, geographic diversity across a region leads to a reduction in the cloud-induced variability. In this paper, spatio-temporal correlations of irradiance data are analyzed and spatial and spatiotemporal ordinary Kriging methods are applied to model irradiation at an arbitrary point based on the given time series of irradiation at some observed locations. The correlations among the irradiances at observed locations are modeled by general parametric covariance functions. Besides the isotropic covariance function (which is independent of direction), a new non-separable anisotropic parametric covariance function is proposed to model the transient clouds. Also, a new approach is proposed to estimate the spatial and temporal decorrelation distances analytically using the applied parametric covariance functions, which reduce the size of the computations without loss in accuracy (parameter shrinkage). The analysis has been performed and the Kriging method is first validated by using two spatially and temporally resolved artificial irradiance datasets generated from Large Eddy Simulation. Then, the spatiotemporal Kriging method is applied on real irradiance and output power data in California (Sacramento and San Diego areas) where the cloud motion had to be estimated during the process using cross-correlation method (CCM). Results confirm that the anisotropic model is most accurate with an average normalized root mean squared error (nRMSE) of 7.92% representing a 66% relative improvement over the persistence model.