Field (geography)
In the context of spatial analysis, geographic information systems, and geographic information science, a field is a property that fills space, and varies over space, such as temperature or density. This use of the term has been adopted from physics and mathematics, due to their similarity to physical fields (vector or scalar) such as the electromagnetic field or gravitational field. Synonymous terms include spatially dependent variable (geostatistics), statistical surface (thematic mapping), and intensive property (physics and chemistry) and crossbreeding between these disciplines is 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") ) History. The modeling and analysis of fields in geographic applications was developed in five essentially separate movements, all of which arose during the 1950s and 1960s: While all of these incorporated similar concepts, none of them used the term "field" consistently, and the integration of the underlying conceptual models of these applications has only occurred since 1990 as part of the emergence of Geographic information science. During the 1980s, the maturation of the core technologies of GIS enabled academics to begin to theorize about the fundamental concepts of  geographic space upon which the software seemed to be based. Donna Peuquet, Helen Couclelis, and others began to recognize that the competing vector and raster data models were based on a duality between a view of the world as filled with objects and a "location-based" or "image-based" view of the world filled with properties of location. Michael F. Goodchild introduced the term "field" from physics by 1992 to formalize the location-property conceptual model. During the 1990s, the raster-vector debate transformed into a debate over whether the "object view" or the "field view" was dominant, whether one  reflected the nature of the real world and the other was merely an conceptual abstraction. The nature and types of fields. Fields are useful in geographic thought and analysis because when properties vary over space, they tend to do so in spatial patterns due to underlying spatial structures and processes. A common pattern is, according to Tobler's first law of geography: "Everything is related to everything else, but near things are more related than distant things." That is, fields (especially those found in nature) tend to vary gradually, with nearby locations having similar values. This concept has been formalized  as 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. 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 although geographic fields may show patterns similar to gravity and magnetism, they can have a very different underlying nature , and be created by very different processes. Geographic fields can be classified by their ontology or fundamental nature as: Geographic fields can also be categorized according to the type of domain of the measured variable, which determines the pattern of spatial change. A "continuous field" has a continuous (real number) domain, and typically shows gradual change over space, such as temperature or soil moisture; a "discrete field," also known as a "categorical coverage" or "area-class map", has a discrete (often qualitative) domain, such as land cover type, soil class, or surface geologic formation, and typically has a pattern of  regions of homogeneous value with boundaries (or transition zones) where the value changes. Both scalar (having a single value for any location) and vector (having multiple values for any location representing different but related properties) fields are found in geographic applications, although the former is more common. 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. Representation models . Because, in theory, a field consists of an infinite number of values at an infinite number of locations, exhibiting a non-parametric pattern, only finite sample-based representations can be used in analyical and visualization tools such as GIS, statistics, and maps. Thus, several conceptual, mathematical and data models have emerged to approximate fields, including: The choice of representation model typically depends on a variety of factors, including the analyst's conceptual model of the phenomenon, the devices or methods available to measure the field, the tools and techniques available to analyze or visualize the field, and the models being  used for other phenomena with which the field in question will be integrated. It is common to transform data from one model to another; for example, an isarithmic weather map of temperature is often generated from a raster grid, which was created from raw weather station data (an irregular point sample). Every such transformation requires Interpolation to estimate field values between or within the sample locations, which can lead to a number of forms of uncertainty, or misinterpretation traps such as the Ecological fallacy and the Modifiable areal unit problem. This also means that when data is transformed from one  model to another, the result will always be less certain than the source.