# Field (geography)

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) ).

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

## 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).

While the prototypical field represents a quantitative variable that varies continuously over space, other kinds of field variables are possible. Fields of nominal variables also occur, in which the value being measured is a category, such as "the surface geologic formation at x,y" or "the dominant vegetation type at x,y." These Nominal or Discrete fields tend to have large areas of constant value, bounded by more or less abrupt transitions. They are often modeled in GIS as categorical coverages in GIS using either raster or vector data models, and are typically visualized using chorochromatic maps.

## 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 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.

## Recognizing Fields

While some phenomena are unambiguously recognizable as fields, others are more problematic. A simple method for determining whether a property is a spatially intensive field or a spatially extensive value is the "addition test." Imagine you have two neighboring districts with a value of 50 in the chosen variable. Next, suppose you realign the districts so that these two become a single district. If you would expect the new district to have a value of 50 (e.g., population per square mile, percent Hispanic, annual precipitation), then it is a continuous field or intensive variable. If you expect it to have a value of 100 (e.g., total population, acres of farmland), then it is extensive.

A similar test can be used for nominal variables. Again, imagine you have two districts, each with a value of X, and you put them together. If the aggregate district still has a value of X, then it is a nominal field. If it is more appropriate to say that "there are two Xs," or the question becomes meaningless, then it is something else. For example, surficial geological formation, soil order, and climate type all fall into the former group, while attributes like county name or mayor's political party would be in the latter.