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.
Spatial data are often encoded within a set of spatial units that exhaustively partition a region, where individual level data are aggregated, or continuous data are summarized, over a set of spatial units. Such is the case with census data aggregated to enumeration units for public dissemination. Partitioning schemes can vary by scale, where one partitioning scheme spatially nests within another, or by zoning, where two partitioning schemes have the same number of units but the unit shapes and boundaries differ. The Modifiable Areal Unit Problem (MAUP) refers to the fact the nature of spatial partitioning can affect the interpretation and results of visualization and statistical analysis. Generally, coarser scales of data aggregation tend to have stronger observed statistical associations among variables. The ecological fallacy refers to the assumption that an individual has the same attributes as the aggregate group to which it belongs. Combining spatial data with different partitioning schemes to facilitate analysis is often problematic. Areal interpolation may be used to estimate data over small areas or ecological inference may be used to infer individual behaviors from aggregate data. Researchers may also perform analyses at multiple scales as a point of comparison.