A field (in the context of Spatial Analysis, Geographic Information Systems, and Geographic Information Science) is a property that can be theoretically assigned to any point or area of space, such as temperature or population density, to represent a characteristic or property associated with that point or area. The property being described is not discrete such as the extent of a body of water, rather a field would be a representation of a characteristic of the body of water such as its temperature. This use of the term is synonymous with the spatially dependent variable that forms the foundation of geostatistics, the statistical surface often described in thematic cartography, and continuous data as opposed to discrete data. The concept of fields was originally adopted from the fields of potential (especially electromagnetism) in physics. The simplest formal model for a field is the function, which yields a single value given a point in space (i.e., v = f(x, y) ).
Types of Fields
The most common form of field used in geography is a two dimensional scalar field, in which the independent variable is a location in two dimensional space, and the dependent variable is a simple value: v = f(x, y). However, there are extensions of this. In a vector field, the dependent variable is a tuple of two or more numbers ( <a, b> = f(x, y)), such as the magnitude and direction of the wind. Fields can be three dimensional if the value depends on height (v = f(x, y, z) ), or four dimensional if time is added as an independent variable ( v = f(x, y, z, t) ). In fact, many of the methods used in Time Geography and similar spatiotemporal models treat the location or a property of an individual as a function or field over time but not space ( v = f(t) ).
Even though the basic concept of a field came from physics, geographers have developed independent theories, data models, and analytical methods. One reason for this apparent disconnect is that "geographic fields" tend to have a different fundamental nature than physical fields; that is, they have patterns similar to gravity and magnetism, but are in reality very different. Common types of geographic fields include:
- Natural fields, properties of matter that are formed at scales below that of human perception, such as temperature or soil moisture.
- Artificial or aggregate fields, statistically constructed properties of aggregate groups of individuals, such as population density.
- Fields of potential, which measure conceptual, non-material quantities (and are thus most closely related to the fields of physics), such as the probability that a person at any given location will prefer to use a particular facility (e.g. a grocery store).
History and Methods
The modeling and analysis of fields in geographic applications was developed in five essentially separate movements, which have gradually been integrated in recent years.
- The quantitative revolution of geography, starting in the 1950s, and leading to the modern discipline of spatial analysis; especially continuous models such as the gravity model.
- The development of raster GIS models and software, starting with the Canada Geographic Information System in the 1960s.
- The technique of cartographic modeling, pioneered by Ian McHarg in the 1960s and later formalized in a field-centric form by Dana Tomlin as Map algebra.
- Geostatistics, which arose from geology starting in the 1950s.
- Cartographic techniques for visualizing "statistical surfaces," including choropleth and isarithmic maps.
The single concept that underlies each of these methods is the concept of spatial dependence or spatial autocorrelation, probably most succinctly expressed as Tobler's first law of geography: "Everything is related to everything else, but near things are more related than distant things." Although it is more of a general tendency than a universal law, Tobler's Law (and the frequent exceptions to it) forms the basic language for understanding patterns in geographic fields.