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.

Building a Globally Distributed Historical Sheet Map Set

This paper describes the procedures used to create a distributed collection of topographic maps of the Austro-Hungarian Empire, the Spezialkarte der Öesterriechisch-ungarnischen Monarchie, Masse. 1:75,000 der natur. This set of maps was published in Vienna over a period of years from 1877 to 1914. The part of the set used in this project includes 776 sheets; all sheets from all editions number over 3,665. The paper contains detailed information on how the maps were converted to digital images, how metadata were prepared, and how Web-browser access was created using ArcIMS Metadata Server. The project, funded by a 2004 National Leadership Grant from the Institute for Museums and Library Science (IMLS), was a joint project of the Homer Babbidge Library Map and Geographic Information Center at the University of Connecticut, the New York Public Library, and the American Geographical Society’s Map Library at the University of Wisconsin Milwaukee.