Discrete versus Continuous Phenomena

Scale

The term scale has at least three meanings in geographic information science: representative fraction, spatial resolution, and geographic extent. Representative fraction (RF), or map scale, indicates the ratio between distance represented on the map and the distance measured on the ground. Drafting or printing technology for map production determines the smallest feature that can be distinguished on a map. For example, the smallest feature that can be drawn on a [Page 112]1:24,000 scaled map using a pen size of 0.1 mm is of 2.4 m (~ 8 feet) on the ground. Similarly, spatial resolution also determines the smallest feature that can be captured in an image or a GIS database. Spatial resolution indicates the finest unit of measurement and the smallest features discernible from an observation. In contrast, geographic extent bounds a spatial domain in which the phenomenon of interest operates. In general, phenomena operating at a large scale are observed at a coarse resolution and displayed on a small-scale map.

Scale can be a factor in determining discrete or continuous geographic phenomena because spatial discreteness or continuity can be influenced by the smallest unit of observation (resolution), the domain of consideration (geographic extent), and the representative fraction. Since the three meanings of scale are interrelated, the meaning of geographic extent is used here for ease of discussion. A geographic phenomenon may be considered discrete at one scale, but continuous at another. In some cases, a continuous phenomenon operating at a large process scale may be considered as discrete at a smaller scale. For example, a forest is considered a continuous phenomenon at a regional scale within the domain of the forest. The discrete nature of the forest may become apparent if one zooms into a local scale and observes gaps among stand patches. In other circumstances, however, a discrete phenomenon at a larger scale of operation may become continuous at a smaller scale. Desertified areas may be considered as a discrete phenomenon at the global scale, where pockets of desertification processes transform arid and semi-arid lands to deserts, while desertification is a spatially continuous process at a regional scale. Fundamentally, geography is of infinite complexity, and therefore the spatial discreteness or continuity of a geographic phenomenon can be ambiguous until the scale of processes and observations is determined.

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