Field (geography)

Last updated August 14, 2023

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.^[1] 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) )^[2]

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:

Cartographic techniques for visualizing fields in thematic maps, including choropleth and isarithmic maps. In theoretical cartography, the concept of a "statistical surface" had gained wide acceptance by 1960, using the metaphor of a third dimension to conceptualize continuous quantitative variation in a variable.^[3] The statistical surface as a concept and term has persisted in cartography to the present.^[4]
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 and models of potential. Although they did not specifically used the term field, they were incorporating the mathematics of fields from physics.^[5]
The development of raster GIS models and software, starting with the Canadian Geographic Information System in the 1960s, which mapped fields such as land cover type.^[6]
The technique of cartographic modeling, pioneered by Ian McHarg in the 1960s^[7] and later formalized for digital implementation in raster GIS by Dana Tomlin as map algebra.^[8]
Geostatistics, which arose from mining geology starting in the 1950s, was originally developed around methods for interpolating the continuous variation in fields from finite point samples.^[9] Terms such as regionalized variable were often used in the literature rather than "field."^[10]

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,^[11] Helen Couclelis,^[12] 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.^[13] 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.^[14]

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."^[15] 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.^[16] 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.^[17] 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:

Natural fields, properties of matter that are formed at scales below that of human perception, and thus appear continuous at human scales, such as temperature or soil moisture.
Aggregate fields, statistically constructed properties of aggregate groups of individuals, such as Population density or tree canopy coverage.
Fields of potential or influence, 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 grocery store.

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,^[18] also known as a categorical coverage^[19] or area-class map,^[20] 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.^[21]

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 analytical and visualization tools such as GIS, statistics, and maps. Thus, several conceptual, mathematical and data models have emerged to approximate fields,^[22]^[23] including:

An irregular point sample, a finite set of sample locations, at either random or strategic locations. Examples include data from weather stations or Lidar point clouds.
Raster DEM of Earth's surface with elevations shaded such that lighter values indicate higher elevation
A lattice, or regular point sample, consisting of locations that are evenly spaced in each cartesian direction. These are typically stored in a Raster data structure. Examples include the Digital elevation model.
A Choropleth , an irregular a priori partition, in which space is partitioned into regions unrelated to the field itself, such as countries, and field values are summarized over each region. These are typically stored using vector polygons. Examples would include Population density by county, derived from census returns.
A Chorochromatic map or Area-class map, an irregular strategic partition usually used for discrete fields, in which space is partitioned into regions intended to match regions of homogeneous field value, typically stored as vector polygons. Examples include maps of geologic layers or vegetation stands.
A grid or regular partition, in which space is partitioned into equal regions (often squares), and field values are summarized over each region. These are also typically stored in a Raster data structure. Examples include the electromagnetic reflectance signature of land cover as represented in Remote sensing imagery.
A surface, in which the field is conceptualized as a third spatial dimension, and three dimensional data models are used for representation. Examples include the Triangulated irregular network (TIN).
Topographic map of Stowe, Vermont. The brown contour lines represent the elevation. The contour interval is 20 feet.
An isarithm or isopleth, in which lines are drawn connecting locations of equal field value, partitioning space into regions of similar value. An example is the Contour line of elevation, commonly found on topographic maps.

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.

Related Research Articles

A geographic information system (GIS) consists of integrated computer hardware and software that store, manage, analyze, edit, output, and visualize geographic data. Much of this often happens within a spatial database, however, this is not essential to meet the definition of a GIS. In a broader sense, one may consider such a system also to include human users and support staff, procedures and workflows, the body of knowledge of relevant concepts and methods, and institutional organizations.

Geostatistics is a branch of statistics focusing on spatial or spatiotemporal datasets. Developed originally to predict probability distributions of ore grades for mining operations, it is currently applied in diverse disciplines including petroleum geology, hydrogeology, hydrology, meteorology, oceanography, geochemistry, geometallurgy, geography, forestry, environmental control, landscape ecology, soil science, and agriculture. Geostatistics is applied in varied branches of geography, particularly those involving the spread of diseases (epidemiology), the practice of commerce and military planning (logistics), and the development of efficient spatial networks. Geostatistical algorithms are incorporated in many places, including geographic information systems (GIS).

Topography is the study of the forms and features of land surfaces. The topography of an area may refer to the land forms and features themselves, or a description or depiction in maps.

Ground truth is information that is known to be real or true, provided by direct observation and measurement as opposed to information provided by inference.

A GIS file format is a standard for encoding geographical information into a computer file, as a specialized type of file format for use in geographic information systems (GIS) and other geospatial applications. Since the 1970s, dozens of formats have been created based on various data models for various purposes. They have been created by government mapping agencies, GIS software vendors, standards bodies such as the Open Geospatial Consortium, informal user communities, and even individual developers.

A choropleth map is a type of statistical thematic map that uses pseudocolor, meaning color corresponding with an aggregate summary of a geographic characteristic within spatial enumeration units, such as population density or per-capita income.

Geographic information science or geoinformation science is a scientific discipline at the crossroads of computational science, social science, and natural science that studies geographic information, including how it represents phenomena in the real world, how it represents the way humans understand the world, and how it can be captured, organized, and analyzed. It is a sub-field of geography, specifically part of technical geography. It has applications to both physical geography and human geography, although its techniques can be applied to many other fields of study as well as many different industries.

Health geography is the application of geographical information, perspectives, and methods to the study of health, disease, and health care. Medical geography, a sub-discipline of or sister field of health geography, focuses on understanding spatial patterns of health and disease as related to the natural and social environment. Conventionally, there are two primary areas of research within medical geography: the first deals with the spatial distribution and determinants of morbidity and mortality, while the second deals with health planning, help-seeking behavior, and the provision of health services.

<span class="mw-page-title-main">Spatial analysis</span> Formal techniques which study entities using their topological, geometric, or geographic properties

Spatial analysis is any of the formal techniques which studies entities using their topological, geometric, or geographic properties. Spatial analysis includes a variety of techniques using different analytic approaches, especially spatial statistics. It may be applied in fields as diverse as astronomy, with its studies of the placement of galaxies in the cosmos, or to chip fabrication engineering, with its use of "place and route" algorithms to build complex wiring structures. In a more restricted sense, spatial analysis is geospatial analysis, the technique applied to structures at the human scale, most notably in the analysis of geographic data. It may also be applied to genomics, as in transcriptomics data.

Map algebra is an algebra for manipulating geographic data, primarily fields. Developed by Dr. Dana Tomlin and others in the late 1970s, it is a set of primitive operations in a geographic information system (GIS) which allows one or more raster layers ("maps") of similar dimensions to produce a new raster layer (map) using mathematical or other operations such as addition, subtraction etc.

A feature, in the context of geography and geographic information science, is a discrete phenomenon that exists at a location in the space and scale of relevance to geography; that is, at or near the surface of Earth, at a moderate to global scale. It is one of the primary types of phenomena represented in geographic information, such as that represented in maps, geographic information systems, remote sensing imagery, statistics, and other forms of geographic discourse. Such representations of features consists of descriptions of their inherent nature, their spatial form and location, and their characteristics or properties.

A geographic data model, geospatial data model, or simply data model in the context of geographic information systems, is a mathematical and digital structure for representing phenomena over the Earth. Generally, such data models represent various aspects of these phenomena by means of geographic data, including spatial locations, attributes, change over time, and identity. For example, the vector data model represents geography as collections of points, lines, and polygons, and the raster data model represent geography as cell matrices that store numeric values. Data models are implemented throughout the GIS ecosystem, including the software tools for data management and spatial analysis, data stored in a variety of GIS file formats, specifications and standards, and specific designs for GIS installations.

<span class="mw-page-title-main">Geography</span> Study of lands and inhabitants of Earth

Geography is a field of science devoted to the study of the lands, features, inhabitants, and phenomena of Earth. The first recorded use of the word γεωγραφία was as a title of a book by Greek scholar Eratosthenes. Geography is an all-encompassing discipline that seeks an understanding of Earth and its human and natural complexities—not merely where objects are, but also how they have changed and come to be. While geography is specific to Earth, many concepts can be applied more broadly to other celestial bodies in the field of planetary science. Geography has been called "a bridge between natural science and social science disciplines."

Cartographic generalization, or map generalization, includes all changes in a map that are made when one derives a smaller-scale map from a larger-scale map or map data. It is a core part of cartographic design. Whether done manually by a cartographer or by a computer or set of algorithms, generalization seeks to abstract spatial information at a high level of detail to information that can be rendered on a map at a lower level of detail.

Quantitative geography is a subfield and methodological approach to geography that develops, tests, and uses mathematical and statistical methods to analyze and model geographic phenomena and patterns. It aims to explain and predict the distribution and dynamics of human and physical geography through the collection and analysis of quantifiable data. The approach quantitative geographers take is generally in line with the scientific method, where a falsifiable hypothesis is generated, and then tested through observational studies. This has received criticism, and in recent years, quantitative geography has moved to include systematic model creation and understanding the limits of their models. This approach is used to study a wide range of topics, including population demographics, urbanization, environmental patterns, and the spatial distribution of economic activity. The methods of quantitative geography are often contrasted by those employed by qualitative geography, which is more focused on observing and recording characteristics of geographic place. However, there is increasing interest in using combinations of both qualitative and quantitative methods through mixed-methods research to better understand and contextualize geographic phenomena.

An array database management system or array DBMS provides database services specifically for arrays, that is: homogeneous collections of data items, sitting on a regular grid of one, two, or more dimensions. Often arrays are used to represent sensor, simulation, image, or statistics data. Such arrays tend to be Big Data, with single objects frequently ranging into Terabyte and soon Petabyte sizes; for example, today's earth and space observation archives typically grow by Terabytes a day. Array databases aim at offering flexible, scalable storage and retrieval on this information category.

Geographic data and information is defined in the ISO/TC 211 series of standards as data and information having an implicit or explicit association with a location relative to Earth . It is also called geospatial data and information, georeferenced data and information, as well as geodata and geoinformation.

A Chorochromatic map, also known as an area-class, qualitative area, or mosaic map, is a type of thematic map that portray regions of categorical or nominal data using variations in color symbols. Chorochromatic maps are typically used to represent discrete fields, also known as categorical coverages. Chorochromatic maps differ from choropleth maps in that chorochromatic maps are mapped according to data-driven boundaries instead of trying to make the data fit within existing, sometimes arbitrary units such as political boundaries.

In spatial analysis and geographic information systems, cost distance analysis or cost path analysis is a method for determining one or more optimal routes of travel through unconstrained (two-dimensional) space. The optimal solution is that which minimizes the total cost of the route, based on a field of cost density that varies over space due to local factors. It is thus based on the fundamental geographic principle of Friction of distance. It is an optimization problem with multiple deterministic algorithm solutions, implemented in most GIS software.

Technical geography is the branch of geography that involves using, studying, and creating tools to obtain, analyze, interpret, understand, and communicate spatial information. The other branches, most commonly limited to human geography and physical geography, can usually apply the concepts and techniques of technical geography. However, the methods and theory are distinct, and a technical geographer may be more concerned with the technological and theoretical concepts than the nature of the data. Thus, the spatial data types a technical geographer employs may vary widely, including human and physical geography topics, with the common thread being the techniques and philosophies employed. To accomplish this, technical geographers often create their own software or scripts, which can then be applied more broadly by others. While technical geography mostly works with quantitative data, the techniques and technology can be applied to qualitative geography, differentiating it from quantitative geography. Within the branch of technical geography are the major and overlapping subbranches of geographic information science, geomatics, and geoinformatics.

References

↑ Peuquet, Donna J., Barry Smith, Berit Brogaard, ed. The Ontology of Fields, Report of a Specialist Meeting Held under the Auspices of the Varenius Project, June 11–13, 1998, 1999
↑ Kemp, Karen K.; Vckovsky, Andrej (1998). "Towards an ontology of fields". Proceedings of the 3rd International Conference on GeoComputation.
↑ Robinson, Arthur H. (1960). Elements of Cartography (2nd ed.). Wiley. pp. 181–184.
↑ Golebiowska, I.; Korycka-Skorupa, J.; Slomska-Przech, K. (2021). "CV-11 Common Thematic Map Types". GIS&T Body of Knowledge. UCGIS. doi: 10.22224/gistbok/2021.2.7 . S2CID 237963029.
↑ Harvey, David (1967). "Models of the Evolution of Spatial Patterns in Human Geography". In Chorley, Richard J.; Haggett, Peter (eds.). Models in Geography. Methuen. pp. 549–608.
↑ Fisher, Terry & Connie MacDonald, An Overview of the Canada Geographic Information System (CGIS), Proceedings of Auto-Carto IV, Cartography and Geographic Information Society, 1979
↑ McHarg, Ian, Design with Nature, American Museum of Natural History, 1969
↑ Tomlin, C. Dana, Geographic information systems and cartographic modelling Prentice-Hall 1990.
↑ Griffith, Daniel A., Spatial Statistics: A quantitative geographer's perspective, Spatial Statistics, 1:3–15, DOI: 10.1016/j.spasta.2012.03.005
↑ Journel, A.G.; Huijbregts, Ch. J. (1978). Mining Geostatistics. Academic Press. pp. 10–11. ISBN 0-12-391050-1.
↑ Peuquet, Donna J. (1988). "Representations of Geographic Space: Toward a Conceptual Synthesis". Annals of the Association of American Geographers. 78 (3): 375–394. doi:10.1111/j.1467-8306.1988.tb00214.x.
↑ Couclelis, Helen (1992). "People manipulate objects (but cultivate fields): Beyond the raster-vector debate in GIS". In Frank, Andrew U.; Campari, Irene; Formentini, Ubaldo (eds.). Theories and Methods of Spatio-Temporal Reasoning in Geographic Space: International Conference GIS – From Space to Territory. Lecture Notes in Computer Science. Vol. 639. Springer-Verlag. pp. 65–77. doi:10.1007/3-540-55966-3_3. ISBN 978-3-540-55966-5.
↑ Goodchild, Michael F. (1992). "Geographical data modeling". Computers and Geosciences. 18 (4): 401–408. doi:10.1016/0098-3004(92)90069-4.
↑ Liu, Y.; Goodchild, M.F.; Guo, Q.; Tian, Y.; Wu, L. (2008). "Towards a General Field model and its order in GIS". International Journal of Geographical Information Science. 22 (6): 623–643. doi:10.1080/13658810701587727. S2CID 1603188.
↑ Tobler W., (1970) "A computer movie simulating urban growth in the Detroit region". Economic Geography, 46(Supplement): 234–240.
↑ Cliff, A. and J. Ord, Spatial Autocorrelation, Pion, 1973
↑ Bradley Miller Fundamentals of Spatial Prediction Archived 2017-06-17 at the Wayback Machine www.geographer-miller.com, 2014.
↑ Huisman, Otto; de By, Rolf A. (2009). Principles of Geographic Information Systems (PDF). Enschede, The Netherlands: ITC. p. 64. Retrieved 1 November 2021.
↑ Chrisman, Nicholas R. (1982). Methods of Spatial Analysis Based on Error in Categorical Maps. PhD Dissertation, U. Bristol.
↑ Bunge, W. (1966). Theoretical Geography. Lund, Sweden: C.W.K. Gleerup. pp. 14–23.
↑ Miller, H. J.; Bridwell, S. A (2009). "A field-based theory for time geography". Annals of the Association of American Geographers. 99 (1): 49–75. doi:10.1080/00045600802471049. S2CID 128893534.
↑ O'Sullivan, David O.; Unwin, David J. (2003). Geographic Information Analysis. Wiley. pp. 213–220. ISBN 0-471-21176-1.
↑ Longley, Paul A.; Goodchild, Michael F.; Maguire, David J.; Rhind, David W. (2011). Geographic Information Systems & Science. Wiley. pp. 89–90.

This page is based on this Wikipedia article
Text is available under the CC BY-SA 4.0 license; additional terms may apply.
Images, videos and audio are available under their respective licenses.

[1] Peuquet, Donna J., Barry Smith, Berit Brogaard, ed. The Ontology of Fields, Report of a Specialist Meeting Held under the Auspices of the Varenius Project, June 11–13, 1998, 1999

[Kemp1998-2] Kemp, Karen K.; Vckovsky, Andrej (1998). "Towards an ontology of fields". Proceedings of the 3rd International Conference on GeoComputation.

[robinson1960-3] Robinson, Arthur H. (1960). Elements of Cartography (2nd ed.). Wiley. pp. 181–184.

[GISTBOK-4] Golebiowska, I.; Korycka-Skorupa, J.; Slomska-Przech, K. (2021). "CV-11 Common Thematic Map Types". GIS&T Body of Knowledge. UCGIS. doi: 10.22224/gistbok/2021.2.7 . S2CID 237963029.

[5] Harvey, David (1967). "Models of the Evolution of Spatial Patterns in Human Geography". In Chorley, Richard J.; Haggett, Peter (eds.). Models in Geography. Methuen. pp. 549–608.

[6] Fisher, Terry & Connie MacDonald, An Overview of the Canada Geographic Information System (CGIS), Proceedings of Auto-Carto IV, Cartography and Geographic Information Society, 1979

[7] McHarg, Ian, Design with Nature, American Museum of Natural History, 1969

[8] Tomlin, C. Dana, Geographic information systems and cartographic modelling Prentice-Hall 1990.

[9] Griffith, Daniel A., Spatial Statistics: A quantitative geographer's perspective, Spatial Statistics, 1:3–15, DOI: 10.1016/j.spasta.2012.03.005

[Journel-10] Journel, A.G.; Huijbregts, Ch. J. (1978). Mining Geostatistics. Academic Press. pp. 10–11. ISBN 0-12-391050-1.

[peuquet1988-11] Peuquet, Donna J. (1988). "Representations of Geographic Space: Toward a Conceptual Synthesis". Annals of the Association of American Geographers. 78 (3): 375–394. doi:10.1111/j.1467-8306.1988.tb00214.x.

[12] Couclelis, Helen (1992). "People manipulate objects (but cultivate fields): Beyond the raster-vector debate in GIS". In Frank, Andrew U.; Campari, Irene; Formentini, Ubaldo (eds.). Theories and Methods of Spatio-Temporal Reasoning in Geographic Space: International Conference GIS – From Space to Territory. Lecture Notes in Computer Science. Vol. 639. Springer-Verlag. pp. 65–77. doi:10.1007/3-540-55966-3_3. ISBN 978-3-540-55966-5.

[goodchild1992-13] Goodchild, Michael F. (1992). "Geographical data modeling". Computers and Geosciences. 18 (4): 401–408. doi:10.1016/0098-3004(92)90069-4.

[Liu2008-14] Liu, Y.; Goodchild, M.F.; Guo, Q.; Tian, Y.; Wu, L. (2008). "Towards a General Field model and its order in GIS". International Journal of Geographical Information Science. 22 (6): 623–643. doi:10.1080/13658810701587727. S2CID 1603188.

[15] Tobler W., (1970) "A computer movie simulating urban growth in the Detroit region". Economic Geography, 46(Supplement): 234–240.

[16] Cliff, A. and J. Ord, Spatial Autocorrelation, Pion, 1973

[17] Bradley Miller Fundamentals of Spatial Prediction Archived 2017-06-17 at the Wayback Machine www.geographer-miller.com, 2014.

[huisman-18] Huisman, Otto; de By, Rolf A. (2009). Principles of Geographic Information Systems (PDF). Enschede, The Netherlands: ITC. p. 64. Retrieved 1 November 2021.

[chrisman1982-19] Chrisman, Nicholas R. (1982). Methods of Spatial Analysis Based on Error in Categorical Maps. PhD Dissertation, U. Bristol.

[bunge1966-20] Bunge, W. (1966). Theoretical Geography. Lund, Sweden: C.W.K. Gleerup. pp. 14–23.

[21] Miller, H. J.; Bridwell, S. A (2009). "A field-based theory for time geography". Annals of the Association of American Geographers. 99 (1): 49–75. doi:10.1080/00045600802471049. S2CID 128893534.

[osullivan-22] O'Sullivan, David O.; Unwin, David J. (2003). Geographic Information Analysis. Wiley. pp. 213–220. ISBN 0-471-21176-1.

[Longley2011-23] Longley, Paul A.; Goodchild, Michael F.; Maguire, David J.; Rhind, David W. (2011). Geographic Information Systems & Science. Wiley. pp. 89–90.

[1]

[2]

[3]

[4]

[5]

[6]

[7]

[8]

[9]

[10]

[11]

[12]

[13]

[14]

[15]

[16]

[17]

[18]

[19]

[20]

[21]

[22]

[23]