Change of spatiotemporal scale in dynamic models

Spatiotemporal processes show complicated and different patterns across different space-time scales. Each process that we attempt to model must be considered in the context of its own spatial and temporal resolution. Both scientific understanding and observed data vary in form and content across scale. Such information sources can be combined through Bayesian hierarchical framework. This approach restricts a few essential scales. However, it is common in the trade-off view between simple modeling and analysis strategy with complicate modeling. Wikle and Berliner (2005) suggested a specialized, though useful, approach to the change of support (COS) problem within hierarchical framework. We extended their strategy by adding temporal modeling in their style and allowing discretized time-varying parameters. We apply a Bayesian inference based on combining information across spatiotemporal scale to some climate temperature data, which are point-referenced data and areal unit data. The inference focuses on the temperature process on specific prediction grid scale and maybe different time scale.