Spatiotemporal data, in particular fuzzy and complex spatial objects representing geographic entities and relations, is a topic of great importance in geographic information systems and environmental data management systems. For database researchers, modeling and designing a database of fuzzy spatiotemporal data and querying such a database efficiently have been challenging issues due to complex spatial features and uncertainty involved. This paper presents an integrated approach to modeling, indexing, and efficiently querying spatiotemporal data related to fuzzy spatial and complex objects and spatial relations. As our case study, we design and implement a meteorological database application that involves fuzzy spatial and complex objects, and a spatiotemporal index structure, and supports various types of spatial queries including fuzzy spatiotemporal queries. Our implementation is based on an intelligent database system architecture that combines a fuzzy object-oriented database with a fuzzy knowledge base.