Criteria for Constructing Optimal Digital Terrain Models
Digital terrain models (DTMs) have applications in diverse fields of geomorphology, including land use inventories, land reclamation, engineering, floodplain zoning, teaching, and military uses. The objective of the model builder is to capture the variability of the landform while minimizing the extraneous data collection. Unfortunately, to date, no explicit criteria have been developed that allow the researcher to plan a sampling scheme that is optimal for his or her particular purposes. Such criteria should be specific for the area under investigation and thus will involve a feedback between the data and the sampling procedure.
In this paper, a criterion is suggested that measures the quality of the DTM, and a method is presented that will produce the best DTM for chosen levels of the criterion in any terrain. It is based on a measure of the degree of independence of the individual observations comprising the DTM given by the autocorrelation function (ACF). It is shown that the ACF of landforms typically displays an exponential decay at increasing sample spacings, converging to an ACF characteristic of independent observations.