The Discontinuous Nature of Kriging Interpolation for Digital Terrain Modeling

Kriging is a widely employed method for interpolating and estimating elevations from digital elevation data. Its place of prominence is due to its elegant theoretical foundation and its convenient practical implementation. From an interpolation point of view, kriging is equivalent to a thin-plate spline and is one species among the many in the genus of weighted inverse distance methods, albeit with attractive properties. However, from a statistical point of view, kriging is a best linear unbiased estimator and, consequently, has a place of distinction among all spatial estimators because any other linear estimator that performs as well as kriging (in the least squares sense) must be equivalent to kriging, assuming that the parameters of the semivariogram are known. Therefore, kriging is often held to be the gold standard of digital terrain model elevation estimation. However, I prove that, when used with local support, kriging creates discontinuous digital terrain models, which is to say, surfaces with “rips” and “tears” throughout them. This result is general; it is true for ordinary kriging, kriging with a trend, and other forms. A U.S. Geological Survey (USGS) digital elevation model was analyzed to characterize the distribution of the discontinuities. I show that the magnitude of the discontinuity does not depend on surface gradient but is strongly dependent on the size of the kriging neighborhood.

Community Trails in Community Context: GIS Analysis of Associations between Trail and Neighborhood Characteristics

This research examines the site and situation characteristics of community trails as landscapes promoting physical activity. Trail segment and neighborhood characteristics for six trails in urban, suburban, and exurban towns in northeastern Massachusetts were assessed from primary Global Positioning System (GPS) data and from secondary Census and land use data integrated in a geographic information system (GIS). Correlations between neighborhood street and housing density, land use mix, and sociodemographic characteristics and trail segment characteristics and amenities measure the degree to which trail segment attributes are associated with the surrounding neighborhood characteristics.

Two Perspectives on GIS/LIS Education in the United States

Education in Geographic information science (GIS/LIS) happens in the United States both within surveying-related academic programs and in other academic programs that use spatially oriented data and information. This article presents an overview of two such programs. The first is a four-year Bachelor of Science degree program in Geographic Information Science at Texas A&M University-Corpus Christi. The second is a concentration with a four-year Bachelor of Science degree program in Natural Resources at the University of Connecticut (UConn). Geographic information science is the primary focus of the Texas A&M program, whereas GIS/LIS is an emphasis of the UConn program. Both approaches are presented for comparison.