Field (geography)

In the context of spatial analysis, geographic information systems, and geographic information science, the term field has been adopted from physics, in which it denotes a quantity that can be theoretically assigned to any point of space, such as temperature or density. This use of field is synonymous with the spatially dependent variable that forms the foundation of geostatistics and crossbreeding between these disciplines is common. Both scalar and vector fields are found in geographic applications, although the former is more common. The simplest formal model for a field is the function, which yields a single value given a point in space (i.e., t = f(x, y, z) )

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).

Geographic fields can exist over a temporal domain as well as space. For example, temperature varies over time as well as location in space. In fact, many of the methods used in time geography and similar spatiotemporal models treat the location of an individual as a function or field over time.

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.

• Cartographic techniques for visualizing "statistical surfaces" (another synonym for fields), including choropleth and isarithmic maps.
• The quantitative revolution of geography, starting in the 1950s, and leading to the modern discipline of spatial analysis; especially techniques such as the gravity model.
• The development of raster GIS models and software, starting with the Canadian 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.

Each of these movements pushed geography towards a more refined, quantitative discipline and instigated the sub-discipline of Geographic Information Science. Doing so has required more explicit definitions of approaches that have long been used by geographers to produce maps. The most famous effort to elucidate a fundamental concept in geography was 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 an important part of understanding patterns in geographic fields. The first law of geography is essentially the same as the concept of spatial dependence or spatial autocorrelation, which underlies the method of geostatistics. A parallel concept that has received less publicity, but has underlain geographic theory since at least Alexander von Humboldt is spatial association, which describes how phenomena are similarly distributed. This concept is regularly used in the method of map algebra.

This use of field should not be confused with that of computer science and databases, which is also frequently used in geographic information systems.