The raster data model is a widely used method of storing geographic data. The model most commonly takes the form of a grid-like structure that holds values at regularly spaced intervals over the extent of the raster. Rasters are especially well suited for storing continuous data such as temperature and elevation values, but can hold discrete and categorical data such as land use as well. The resolution of a raster is given in linear units (e.g., meters) or angular units (e.g., one arc second) and defines the extent along one side of the grid cell. High (or fine) resolution rasters have comparatively closer spacing and more grid cells than low (or coarse) resolution rasters, and require relatively more memory to store. Active research in the domain is oriented toward improving compression schemes and implementation for alternative cell shapes (such as hexagons), and better supporting multi-resolution raster storage and analysis functions.
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 interpolation methods use the measured values at given locations to estimate the values at unsampled locations, for example, in computing raster digital elevation models from scattered measured elevations. Since this problem does not have a unique solution, many approaches have been developed to accomplish this task. Methods based on linear superposition of radial basis functions (RBF) centered at the data points include multivariate splines that simultaneously minimize the sum of the deviations from the measured points and the smoothness seminorm referred to also as a roughness penalty. The thin plate spline minimizes the 2D surface curvature and mimics a thin steel plate forced to pass through the data points: its equilibrium shape minimizes the bending energy which is closely related to the surface curvature. There are many generalizations such as spline with tension that controls the plate stiffness, while regularized spline enables direct calculations of surface gradients and curvatures making it effective for terrain modeling with simultaneous topographic analysis. Trivariate splines are used to interpolate meteorological variables with influence of topography. The RBF splines are related to universal kriging with the choice of the covariance function determined by the smoothness seminorm. Multiquadric RBF methods are similar in formulation and performance to splines.