Representations of space and time are central to GIScience. Field-based representations conceptualize space and time as continuous surfaces where each location is associated with measurable attribute values. Traditional models, such as raster grids and Triangulated Irregular Networks (TINs), discretize continuous fields for computational efficiency. However, these models often rely on rigid pixel assumptions and linear interpolations that fail to capture subtle curvatures and variations in real-world phenomena. To address these shortcomings, surface adjustment methods refine spatial measurements by constructing local terrain models that better represent spatial variations. Beyond static spatial fields, higher-dimensional models integrate space, time, and scale into a unified framework. Time-geography introduces the space-time cube, where space and time are integrated into a 3D field. Additionally, the Triangle Model (TM) and Pyramid Model (PM) incorporate scale into temporal and spatial analysis, respectively. These models allow for more nuanced analysis, such as tracking objects, assessing interaction probabilities, and exploring cross-scale relationships in space and time. Taken together, these models form a multi-scale spatio-temporal framework with four key dimensions: spatial location (s), spatial scale (s′), temporal location (t) and temporal scale (t′), providing a systematic approach to analyze dynamic geographic phenomena across multiple dimensions.
Volumes in Geographic Information Science (GIScience) represent three-dimensional (3D) spatial phenomena that are often dynamic and have hard-to-determine boundaries. Studying their temporal evolution and dynamics is crucial for understanding and managing complex spatial systems such as atmospheric layers, aquatic systems, and subsurface structures. This chapter introduces a comprehensive framework for analyzing 3D volumes, including voxel-based models, Triangulated Irregular Networks (TIN), and boundary representation techniques. Additionally, it explores space-time volume representation, integrating temporal dynamics into 3D models to capture the evolution of phenomena over time through a graph-based spatiotemporal data framework. Practical applications in climate change detection and disaster management are highlighted, showcasing the potential of this framework to enhance predictive accuracy and support strategic decision-making.