Autocorrelation, Spatial
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Autocorrelation, Spatial C HANDANA G ANGODAGAMAGE 1, X IAOBO Z HOU 2 , H ENRY L IN 2 1 Saint Anthony Falls Laboratory, Department of Civil Engineering, University of Minnesota, Minneapolis, MN, USA 2 Department of Crop and Soil Sciences, The Pennsylvania State University, University Park, PA, USA Synonyms Spatial correlation; Spatial dependence; Spatial inter-dependence
Definition In many spatial data applications, the events at a location are highly influenced by the events at neighboring locations. In fact, this natural inclination of a variable to exhibit similar values as a function of distance between the spatial locations at which it is being measured is known as spatial dependence. Spatial autocorrelation is used to measure this spatial dependence. If the variable exhibits a systematic pattern in its spatial distribution, it is said to be spatially autocorrelated. The existence and strength of such interdependence among values of a specific variable with reference to a spatial location can be quantified as a positive, zero, or negative spatial autocorrelation. Positive spatial autocorrelation indicates that similar values or properties tend to be collocated, while negative spatial autocorrelation indicates that dissimilar values or properties tend to be near each other. Random patterns indicate zero spatial autocorrelation since independent, identically distributed random data are invariant with regard to their spatial location. Historical Background The idea of spatial autocorrelation is not new in the literature and was conceptualized as early as 1854, when nebula-like spatial clusters with distance-decay effects were readily apparent in mapped cholera cases in the city of London [1]. This led to the hypothesis that the systematic spatial pattern of Cholera outbreak decayed smoothly with distance from a particular water supply which acted as the source for the disease. This concept of spatial autocorrelation was also documented in the first law of geography in 1970 which states: “Everything is related to everything else, but near things are more related than distant things” [11]. Scientific Fundamentals Spatial autocorrelation is a property of a variable that is often distributed over space [9]. For example, land surface elevation values of adjacent locations are generally quite similar. Similarly, temperature, pressure, slopes, and rainfall vary gradually over space, thus forming a smooth gradient of a variable between two locations in space. The propensity of a variable to show a smooth gradient across space aggregates
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