Field-Based Spatial Modeling

Definition

A field (or continuous field) is defined as a mapping from location x to a function f. In modeling geographic phenomena the domain of x is most often the two dimensions of geographic space, but may include the third spatial dimension for applications that extend above or below the Earth’s surface, and may include time for dynamic phenomena. Fields can also be defined on one-dimensional networks embedded in two- or three-dimensional space. Moreover, most applications are limited to a specified sub-domain of geographic space, such as the limits of a country or county, or of a map sheet or arbitrarily defined study area. The domain of fincludes scalar measurements on interval and ratio scales, nominal and ordinal classifications, and vectors describing such directional phenomena as wind or topographic gradient. Field-based spatial modeling can in principle be employed in the representation of any space, including the spaces of the human brain, the surfaces of other planets,...