Arbia's law of geography
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Arbia’s law of geography states, "Everything is related to everything else, but things observed at a coarse spatial resolution are more related than things observed at a finer resolution." Originally proposed as the 2nd law of
geography Geography (from Greek: , ''geographia''. Combination of Greek words ‘Geo’ (The Earth) and ‘Graphien’ (to describe), literally "earth description") is a field of science devoted to the study of the lands, features, inhabitants, and ...
, this is one of several laws competing for that title. Because of this, Arbia's law is sometimes referred to as the second law of geography, or Arbia's second law of geography.


Background

Since Tobler first invoked the first law in his 1970s paper, there have been many attempts at a second law, including Tobler's second law of geography, and Arbia's law is one such contender. Arbia's law builds on
Tobler's first law of geography The First Law of Geography, according to Waldo Tobler, is "everything is related to everything else, but near things are more related than distant things." This first law is the foundation of the fundamental concepts of spatial dependence and spatia ...
which states, "Everything is related to everything else, but near things tend to be more related than distant." While Tobler's first law relates to
spatial autocorrelation Spatial analysis or spatial statistics includes any of the formal techniques which studies entities using their topological, geometric, or geographic properties. Spatial analysis includes a variety of techniques, many still in their early dev ...
and
distance decay Distance decay is a geographical term which describes the effect of distance on cultural or spatial interactions. The distance decay effect states that the interaction between two locales declines as the distance between them increases. Once the di ...
, Arbia's law relates to the
modifiable areal unit problem __NOTOC__ The modifiable areal unit problem (MAUP) is a source of statistical bias that can significantly impact the results of statistical hypothesis tests. MAUP affects results when point-based measures of spatial phenomena are aggregated into ...
, or MAUP. Arbia's law was first invoked in a paper published by Giuseppe Arbia, R. Benedetti, and G. Espa titled "Effects of the MAUP on image classification," where it was presented as the second law of geography. It was later referenced by
Waldo Tobler Waldo Rudolph Tobler (November 16, 1930 – February 20, 2018) was an American-Swiss geographer and cartographer. Tobler's idea that "Everything is related to everything else, but near things are more related than distant things" is referred to ...
in his paper "On the first law of geography: A Reply" as a possible contender for the second law of geography (this is the same paper where Tobler first proposed his second law of geography). The laws of geography need not be numbered, however.


Foundation

In
spatial analysis Spatial analysis or spatial statistics includes any of the formal techniques which studies entities using their topological, geometric, or geographic properties. Spatial analysis includes a variety of techniques, many still in their early deve ...
with
geographic information systems A geographic information system (GIS) is a type of database containing geographic data (that is, descriptions of phenomena for which location is relevant), combined with software tools for managing, analyzing, and visualizing those data. In a br ...
, both
raster Raster may refer to: * Raster graphics, graphical techniques using arrays of pixel values * Raster graphics editor, a computer program * Raster scan, the pattern of image readout, transmission, storage, and reconstruction in television and compu ...
and
vector Vector most often refers to: *Euclidean vector, a quantity with a magnitude and a direction *Vector (epidemiology), an agent that carries and transmits an infectious pathogen into another living organism Vector may also refer to: Mathematic ...
data are used. Importantly, when working with spatially aggregate data (either in vector or raster) at a coarse resolution, it is impossible to make assumptions about what that data looks like at a finer resolution. Doing so would commit the
ecological fallacy An ecological fallacy (also ecological ''inference'' fallacy or population fallacy) is a formal fallacy in the interpretation of statistical data that occurs when inferences about the nature of individuals are deduced from inferences about the gr ...
.


Raster

Arbia's law was for invoked when working with raster datasets. Arbia's law is important to remember when working with raster data, particularly
remote sensing Remote sensing is the acquisition of information about an object or phenomenon without making physical contact with the object, in contrast to in situ or on-site observation. The term is applied especially to acquiring information about Earth ...
, where the electromagnetic spectrum is sampled at a pixel level.
Spatial resolution In physics and geosciences, the term spatial resolution refers to distance between independent measurements, or the physical dimension that represents a pixel of the image. While in some instruments, like cameras and telescopes, spatial resolutio ...
in remote sensing is related to the smallest pixel size within an image, and one value is returned for the area within a pixel. The coarser the
image resolution Image resolution is the detail an image holds. The term applies to digital images, film images, and other types of images. "Higher resolution" means more image detail. Image resolution can be measured in various ways. Resolution quantifies how ...
(the larger the pixel) in a remotely sensed image, the larger the area that will be represented with the same value. Thus, a coarse resolution has a soothing effect on the image, making land cover appear more homogenous than an image with a fine spatial resolution.


Vector

When working with vector datasets, the same effect is present as in Raster. With Vector datasets in GIS, it is often necessary to aggregate data into discreet spatial enumeration units (often referred to as aerial units), such as county boundaries or national borders. The
Modifiable Areal Unit Problem __NOTOC__ The modifiable areal unit problem (MAUP) is a source of statistical bias that can significantly impact the results of statistical hypothesis tests. MAUP affects results when point-based measures of spatial phenomena are aggregated into ...
, or MAUP, arises from the countless possible ways to divide up the same area of land. Dividing the land differently may produce different statistical results from the same underlying dataset, an example of which can be found in
Simpson's paradox Simpson's paradox is a phenomenon in probability and statistics in which a trend appears in several groups of data but disappears or reverses when the groups are combined. This result is often encountered in social-science and medical-science st ...
. How land is aggregated can affect the results or analysis, an effect that has been exploited by politicians through the process of
gerrymandering In representative democracies, gerrymandering (, originally ) is the political manipulation of electoral district boundaries with the intent to create undue advantage for a party, group, or socioeconomic class within the constituency. The m ...
. Arbia's law applies not just to how data are aggregated spatially but to the size of the aerial units. The larger these aerial units, the more homogenous the underlying data will appear. The same area may not appear very homogenous when the aerial units are smaller.


Controversy

In general, some dispute the entire concept of laws in geography and the social sciences. These criticisms have been addressed by Tobler and others. However, this is an ongoing source of debate in geography and unlikely to be resolved anytime soon.


Other Proposed Second Laws of Geography

Some have argued that geographic laws do not need to be numbered. However, the existence of a first invites the creation of a second. In addition to Arbia, several scholars have proposed candidates for a second. *
Tobler's second law of geography The second law of geography, according to Waldo Tobler, is "the phenomenon external to a geographic area of interest affects what goes on inside." Background Tobler's second law of geography, "the phenomenon external to a geographic area of inte ...
, "the phenomenon external to a geographic area of interest affects what goes on inside," is probably the most widely accepted. * Tim Foresman and Ruth Luscombe's Second law of geography: "Things that know where they are can act on their locational knowledge. Spatially enabled things have increased financial and functional utility." * the uncertainty principle: "that the geographic world is infinitely complex and that any representation must therefore contain elements of uncertainty, that many definitions used in acquiring geographic data contain elements of vagueness, and that it is impossible to measure location on the Earth's surface exactly." * It has been proposed that Tobler's first law of geography should be moved to the second and replaced with another.


See also

*
Concepts and Techniques in Modern Geography ''Concepts and Techniques in Modern Geography'', abbreviated CATMOG, is a series of 59 short publications, each focused on an individual method or theory in geography. Background and impact ''Concepts and Techniques in Modern Geography'' were p ...
*
boundary problem A boundary problem in analysis is a phenomenon in which geographical patterns are differentiated by the shape and arrangement of boundaries that are drawn for administrative or measurement purposes. The boundary problem occurs because of the loss o ...
*
Biogeography Biogeography is the study of the distribution of species and ecosystems in geographic space and through geological time. Organisms and biological communities often vary in a regular fashion along geographic gradients of latitude, elevation, ...
*
Cartography Cartography (; from grc, χάρτης , "papyrus, sheet of paper, map"; and , "write") is the study and practice of making and using maps. Combining science, aesthetics and technique, cartography builds on the premise that reality (or an im ...
*
distance decay Distance decay is a geographical term which describes the effect of distance on cultural or spatial interactions. The distance decay effect states that the interaction between two locales declines as the distance between them increases. Once the di ...
*
ecological fallacy An ecological fallacy (also ecological ''inference'' fallacy or population fallacy) is a formal fallacy in the interpretation of statistical data that occurs when inferences about the nature of individuals are deduced from inferences about the gr ...
*
geography Geography (from Greek: , ''geographia''. Combination of Greek words ‘Geo’ (The Earth) and ‘Graphien’ (to describe), literally "earth description") is a field of science devoted to the study of the lands, features, inhabitants, and ...
*
geographic information systems A geographic information system (GIS) is a type of database containing geographic data (that is, descriptions of phenomena for which location is relevant), combined with software tools for managing, analyzing, and visualizing those data. In a br ...
*
geographic information science Geographic information science or geographical information science (GIScience or GISc) is the scientific discipline that studies geographic information, including how it represents phenomena in the real world, how it represents the way humans unders ...
* Giuseppe Arbia *
Indicators of spatial association Indicators of spatial association are statistics that evaluate the existence of clusters in the spatial arrangement of a given variable. For instance, if we are studying cancer rates among census tracts in a given city local clusters in the rates ...
*
Level of analysis The term "level of analysis" is used in the social sciences to point to the location, size, or scale of a research target. "Level of analysis" is distinct from the term "unit of observation" in that the former refers to a more or less integrated s ...
* Moran's ''I'' *
modifiable areal unit problem __NOTOC__ The modifiable areal unit problem (MAUP) is a source of statistical bias that can significantly impact the results of statistical hypothesis tests. MAUP affects results when point-based measures of spatial phenomena are aggregated into ...
*
spatial analysis Spatial analysis or spatial statistics includes any of the formal techniques which studies entities using their topological, geometric, or geographic properties. Spatial analysis includes a variety of techniques, many still in their early deve ...
*
spatial autocorrelation Spatial analysis or spatial statistics includes any of the formal techniques which studies entities using their topological, geometric, or geographic properties. Spatial analysis includes a variety of techniques, many still in their early dev ...
*
Spatial heterogeneity Spatial heterogeneity is a property generally ascribed to a landscape or to a population. It refers to the uneven distribution of various concentrations of each species within an area. A landscape with spatial heterogeneity has a mix of concentra ...
*
Scientific law Scientific laws or laws of science are statements, based on repeated experiments or observations, that describe or predict a range of natural phenomena. The term ''law'' has diverse usage in many cases (approximate, accurate, broad, or narrow) ...
*
Time geography Time geography or time-space geography is an evolving transdisciplinary perspective on spatial and temporal processes and events such as social interaction, ecological interaction, social and environmental change, and biographies of individuals. T ...
*
Tobler's first law of geography The First Law of Geography, according to Waldo Tobler, is "everything is related to everything else, but near things are more related than distant things." This first law is the foundation of the fundamental concepts of spatial dependence and spatia ...
*
Tobler's second law of geography The second law of geography, according to Waldo Tobler, is "the phenomenon external to a geographic area of interest affects what goes on inside." Background Tobler's second law of geography, "the phenomenon external to a geographic area of inte ...
*
Transportation geography Transport geography or transportation geography is a branch of geography that investigates the movement and connections between people, goods and information on the Earth's surface. Aims and scope Transportation geography detects, describes, and e ...
*
Urban geography Urban geography is the subdiscipline of geography that derives from a study of cities and urban processes. Urban geographers and urbanists examine various aspects of urban life and the built environment. Scholars, activists, and the public have ...
*
Waldo Tobler Waldo Rudolph Tobler (November 16, 1930 – February 20, 2018) was an American-Swiss geographer and cartographer. Tobler's idea that "Everything is related to everything else, but near things are more related than distant things" is referred to ...


References

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