Multiscale Representations

The term multiscale representations refers to versions of a data set that are derived from the original compilation and designed for use at mapping scales other than the original compilation scale. Generally, the derived mapping scales are smaller scales than the compilation, but in current practice, it is accepted convention to derive multiscale representations for mapping at slightly larger scales as well. Taken as a group, the originally compiled version and the derived versions are stored in the database and make up the set of multiscale representations.

Creation of multiscale representations is a GIS process that relates mapping scale to data resolution in order to adjust data resolution to fit a particular mapping scale. Scale is defined here as the ratio between map distance and ground distance, or map area to ground area. For example, 1:10,000 means 1 map unit represents 10,000 units on the ground (e.g., 1 mm on the map represents 10 m). Resolution is not the same as scale and refers to the level of detail recorded in a data set. For example, in a 30 m digital terrain model, pixels are 30 m × 30 m, and so resolution is 30 m. For mapped data, Waldo Tobler's rule for converting between scale and resolution is to divide the denominator of the scale ratio by 1,000, to compute in meters the smallest detectable item one should expect to find in a data set, then divide this number by 2 to compute the resolution. Thus, in a 1:10,000 scale map, the smallest detectable item would be 10 m, and the resolution would be 5 m.

One might ask why multiscale representations are necessary, since GIS software provides many functions that adjust the viewing scale. This permits data from multiple sources to be incorporated into a single map or model, regardless of whether the data sets were compiled independently or at differing scales. One must remain aware, however, that changing the scale of a display does not change the amount of detail (the resolution) of what is displayed. Multiscale representations are not derived by simple zooming operations. Instead, the data geometry is altered in a systematic way so that the resolution is adjusted for appropriate display at a smaller scale (a coarser granularity).

In most cases, multiscale representations are generated in order to extend the range of display scales for which a data set is appropriate. If a display contains too much detail, features crowd together, roads appear to overrun buildings, stream braids are compressed into a messy knotted line, and geographic nonsense results. On a base map containing multiple data themes, the human eye quickly detects whether one theme contains too much or too little detail relative to other layers. At this point, it becomes necessary to adjust details by modifying geometry and/or eliminating features. Multiscale representations therefore play [Page 297]an important role in mobile GIS and on-demand Web mapping.

Another reason to generate multiscale representations is to avoid intensive computations. Consider that for a very large study area (such as the state of California) it would take a long time to interpolate 100 m contours from 30 m digital terrain models. Having done these computations once, however, the task of selecting every other contour or every fifth contour for display is relatively quick. The contours provide a multiscale representation of terrain because from a processing standpoint, contours are more efficient than the terrain model for some mapping purposes. It is much faster to create maps at multiple scales by contour selection than by having to reinterpolate the terrain over and over again. European national mapping agency cartographers refer to multiscale data sets such as described in this example as LoDs, or levels of detail data sets, because mapping agencies will generate these multiscale representations at scales intermediate to their originally compiled data. LoDs are stored permanently in a database to reduce computations and minimize workloads for subsequent data production.

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