Granularities are integral to spatial and temporal data. A large number of applications require storage of facts along with their temporal and spatial context, which needs to be expressed in terms of appropriate granularities. For many real-world applications, a single granularity in the database is insufficient. In order to support any type of spatial or temporal reasoning, the semantics related to granularities needs to be embedded in the database. Specifying granularities related to facts is an important part of conceptual database design because under-specifying the granularity can restrict an application, affect the relative ordering of events and impact the topological relationships. Closely related to granularities is indeterminacy, i.e., an occurrence time or location associated with a fact that is not known exactly. In this paper, we present an ontology for spatial granularities that is a natural analog of temporal granularities. We propose an upward-compatible, annotation-based spatiotemporal conceptual model that can comprehensively capture the semantics related to spatial and temporal granularities, and indeterminacy without requiring new spatiotemporal constructs. We specify the formal semantics of this spatiotemporal conceptual model via translation to a conventional conceptual model. To underscore the practical focus of our approach, we describe an on-going case study. We apply our approach to a hydrogeologic application at the United States Geologic Survey and demonstrate that our proposed granularity-based spatiotemporal conceptual model is straightforward to use and is comprehensive.