The Inverse Distance Weighted interpolation method and error propagation mechanism – creating a DEM from an analogue topographical map

Abstract

Interpolation procedures are widely used in science, especially in sciences that involve spatial data and continuous phenomena that can be depicted on a continuous spatial surface. Interpolation makes use of accurate and qualitative sampling data in order to produce a continuous representation of the phenomenon in question. The accuracy of the data used for interpolation directly affects the results. This research examines error propagation within the Inverse Distance Weighted (IDW) method, applied as a means of representing the earth's relief. Interpolation of a DEM within contours on a topographical map is considered to be a three-stage procedure. The first stage is the digitising of the contours depicted on the analogue map. Errors involved in this stage are propagated to the second stage, the geometric transformation of coordinates of these digitised contours. Additional errors due to the application of the transformation model are embedded within the results thus obtained. Finally, the errors are propagated to the third stage. Errors are magnified due to the application of an interpolation method, in our case, the IDW method. Any stage of the procedure can be considered separately. The procedure aims to cover the situation where a DEM is created using an analogue topographical map in conjunction with the IDW interpolation method.