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Jim Kompanek
Kriging
In numerous fields, it is impractical and unnecessary to collect all possible information regarding a study area. It is often possible to infer information or attributes of the unknown based on observations made at nearby sample points. For example, an entomologist studying the distribution of a particular insect may choose to examine only a few trees per acre and infer the surrounding distribution based on the sample points. In the case of archaeology, this inference, or interpolation is used on virtually every excavation and survey.
Kriging is an interpolation method used to determine the spatial distribution of a phenomenon based on data collected at sample points (Gruver 2007). This interpolation method is considered both local and stochastic. A local interpolator uses only nearby sample points to determine the unknown value of an unsampled location, versus a global interpolator which uses data derived from all available sample points in an area of interest. A stochastic interpolatator, such as kriging, predicts values of unsampled locations, and the "spatial arrangement of values over a range of unsampled locations" (Gruver 2007) based on the statistical analysis of the spatial structure and observed values collected at sample points.
In the case of archaeology, interpolation methods such as kriging can be used during every step of the investigative process. The first stage of examining a site typically involves first finding the site and this is often done during an archaeological survey. This typically involves the excavation of test probes on an assigned grid or by examining the ground surface in areas of high visibility along transects. The purpose of these test probes or walked transects, is not solely to determine the presence of artifacts at these specific points but to determine site boundaries, artifact densities, etc. An interpolation method, such as kriging, may be used to interpolate the potential value, in this case artifact density, of the area between the control points. If further investigation was deemed necessary, the areas identified with the highest artifact density may be more intensively investigated. Ultimately, if a site is intensively excavated, artifact distribution based on interpolation may be used to examine potential activity areas based on recovered cultural materials.
There are numerous advantages to kriging interpolation. Primarily, a map produced by this method not only creates the desired surface based on control points but also maps the errors of estimation (Thurston et al. 2003). These errors are ultimately dependent on the distribution of observation points and are of primary interest to sampling where every observation point counts. According to Thurston et al. (2003), an interpolated surface based on kriging also indicates areas where more information is needed.
According to Gruver (2007), the values of a surface are divided into three components. The first component includes a drift, which indicates an overall trend of a surface. For example, if the elevation of the state of Kentucky was examined, outside of isolated features, the overall drift would be increasing elevation from the Mississippi floodplain to the west and the Appalachian Mountains to the east. The second component is that of local spatial autocorrelation, which assumes nearby points are more likely to have similar values than more distant points. Local spatial autocorrelation takes this variation into account through semivariance, which is a statistical measure of the degree of variation between the unknown region between two points. The reliability of the semivariance for control points is largely dependent on how representative the attributes of the control points are for the area in between; for example, if the elevation of two nearby hilltops was taken, the resulting semivariance of the adjoining valley will not be accurately reflected through interpolation. Generally, the more observation points taken, including outside of a given study area, the higher quality of the interpolation. Ultimately, this allows for the calculation of distance lag "to group sets of points that are similar distances apart and calculate an average semivariance" (Gruver 2007) based on a mathematical function or equation. It is possible to plot the spatial structure of the data in a semivariogram; once plotted, it is possible to examine the random stochastic variation in the data. This noise may take the form of variations in the observations taken at the same control point. According to Gruver (2007), once a mathematical function is applied to a semivariogram, it can be used to "calculate weights for estimating the values of [an] attribute of interest at an unknown location".
References
Gruver, Adrienne
2007 Cartography and Visualization (Spring 2007). Lesson 5, Representing Volume and Surfaces, Penn State World Campus GIS Program. Accessed May 12, 2007.
Thurston, Jeff, Thomas K. Poiker, and J. Patrick Moore
Integrated Geospatial Technologies: A Guide to GPS, GIS, and Data Logging. John Wiley & Sons, Inc., Hoboken, New Jersey.
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This document is published in fulfillment of an assignment by a student enrolled in an educational offering of The Pennsylvania State University. The student, named above, retains all rights to the document and responsibility for its accuracy and originality.