Computation of random errors in digital terrain models

Geostatistical methods make it possible to estimate the random errors in digital terrain models (DTMs) from one single set of measurements. After average interpolating trend removal, the error is derived from the variogram of the residual data set. This method is compared with a procedure that uses triangulation and resampling of two overlapping DTMs for extracting the error component. Eighteen small areas measured with a multibeam echo sounder are selected for the comparison. In the experiment the two methods come out with similar values for the random error. A by-product of the experiment is the development of a model for the average noise reduction caused by resampling of triangle models (TINs). The method we apply for the trend computation has time complexity O(n). Since the noise computation only requires the part of the variogram close to the origin, it is possible to formulate the computation of the random error in DTMs in O(n) time.