Boundary problem (spatial analysis): Difference between revisions

Revision as of 10:51, 17 July 2025

Revision as of 10:53, 17 July 2025

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If a spatial process in an area occurs beyond a study area or has an interaction with neighbours outside artificial boundaries, the most common approach is to neglect the influence of the boundaries and assume that the process occurs at the internal area. However, such an approach leads to a significant model misspecification problem.<ref>{{cite book |last1=Upton |first1=Bernard Fingleton |title=Spatial data analysis by example: Volume 1: Point Pattern and Quantitative Data |date=1985 |publisher=Wiley |___location=Chichester, UK |isbn=978-0471905424}}</ref>

That is, for measurement or administrative purposes, geographic boundaries are drawn, but the boundaries ''per se'' can bring about different spatial patterns in geographic phenomena.<ref name=BESR02>{{cite book |title=Community and quality of life : data needs for informed decision making |date=2002 |publisher=Board on Earth Sciences and Resources, Division on Earth and Life Studies, National Research Council, National Academy Press |___location=Washington, DC |isbn=978-0309082600}}</ref> It has been reported that the difference in the way of drawing the boundary significantly affects identification of the spatial distribution and estimation of the statistical parameters of the spatial process.<ref>{{cite book |last1=Cressie |first1=Noel A. C. |title=Statistics for Spatial Data |url=https://archive.org/details/statisticsforsparevised0000cres_r7f4 |url-access=registration |date=1993 |publisher=Wiley |isbn=9781119115151 |language=en|doi=10.1002/9781119115151 |series=Wiley Series in Probability and Statistics }}</ref><ref name=Fotheringham93>{{cite journal |last1=Stewart Fotheringham |first1=A. |last2=Rogerson |first2=Peter A. |title=GIS and spatial analytical problems |journal=International Journal of Geographical Information Systems |date=January 1993 |volume=7 |issue=1 |pages=3–19 |doi=10.1080/02693799308901936}}</ref><ref name="Griffith83">{{cite journal |last1=Griffith |first1=DA |title=The boundary value problem in spatial statistical analysis. |journal=Journal of Regional Science |date=August 1983 |volume=23 |issue=3 |pages=377–87 |pmid=12279616|doi=10.1111/j.1467-9787.1983.tb00996.x }}</ref><ref>{{cite journal |last1=Martin |first1=R. J. |title=Some Comments on Correction Techniques for Boundary Effects and Missing Value Techniques |journal=Geographical Analysis |date=3 September 2010 |volume=19 |issue=3 |pages=273–282 |doi=10.1111/j.1538-4632.1987.tb00130.x|doi-access=free }}</ref> The difference is largely based on the fact that spatial processes are generally unbounded or fuzzy-bounded,<ref>{{cite journal |last1=Leung |first1=Yee |title=On the Imprecision of Boundaries |journal=Geographical Analysis |date=3 September 2010 |volume=19 |issue=2 |pages=125–151 |doi=10.1111/j.1538-4632.1987.tb00120.x|doi-access=free }}</ref> but the processes are expressed in data imposed within boundaries for analysis purposes.<ref>{{cite journal |last1=Miller |first1=Harvey J. |title=Potential Contributions of Spatial Analysis to Geographic Information Systems for Transportation (GIS-T) |journal=Geographical Analysis |date=3 September 2010 |volume=31 |issue=4 |pages=373–399 |doi=10.1111/j.1538-4632.1999.tb00991.x}}</ref> Although the boundary problem was discussed in relation to artificial and arbitrary boundaries, the effect of the boundaries also occurs according to natural boundaries as long as it is ignored that properties at sites on the natural boundary such as streams are likely to differ from those at sites within the boundary.<ref>{{cite book |last1=Martin |first1=R. J. |editor1-last=Griffith |editor1-first=D. A. |title=Spatial Statistics: Past, Present, and Future |date=1989 |publisher=Institute of Mathematical Geography |___location=Syracuse, NY |pages=107–129 |chapter-url=https://www.researchgate.net/publication/30858907 |chapter=The role of spatial statistical processes in geographic modeling}}</ref>

The boundary problem occurs with regard not only to horizontal boundaries but also to vertically drawn boundaries according to delineations of heights or depths (Pineda 1993). For example, biodiversity such as the density of species of plants and animals is high near the surface, so if the identically divided height or depth is used as a spatial unit, it is more likely to find fewer number of the plant and animal species as the height or depth increases.

== Types and examples ==