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Concept
Arbia's law of geography
Résumé
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, 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.
Since Tobler first invoked the first law of geography 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 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 and distance decay, Arbia's law relates to the modifiable areal unit problem, or MAUP and scale dependence of correlation. 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 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.
In spatial analysis with geographic information systems, both raster and vector 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. Aggregating data spatially has a statistical smoothing effect due to the scale effect.
Arbia's law was first invoked when working with raster datasets. Arbia's law is important to remember when working with raster data, particularly remote sensing, where the electromagnetic spectrum is sampled at a pixel level.
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