Testing 3D landform quantification methods with synthetic drumlins in a real digital elevation model

Metrics such as height and volume quantifying the 3D morphology of landforms are important observations that reflect and constrain Earth surface processes. Errors in such measurements are, however, poorly understood. A novel approach, using statistically valid ‘synthetic’ landscapes to quantify the errors is presented. The utility of the approach is illustrated using a case study of 184 drumlins observed in Scotland as quantified from a Digital Elevation Model (DEM) by the ‘cookie cutter’ extraction method. To create the synthetic DEMs, observed drumlins were removed from the measured DEM and replaced by elongate 3D Gaussian ones of equivalent dimensions positioned randomly with respect to the ‘noise’ (e.g. trees) and regional trends (e.g. hills) that cause the errors. Then, errors in the cookie cutter extraction method were investigated by using it to quantify these ‘synthetic’ drumlins, whose location and size is known. Thus, the approach determines which key metrics are recovered accurately. For example, mean height of 6.8 m is recovered poorly at 12.5 ± 0.6 (2σ) m, but mean volume is recovered correctly. Additionally, quantification methods can be compared: A variant on the cookie cutter using an un-tensioned spline induced about twice (× 1.79) as much error. Finally, a previously reportedly statistically significant (p = 0.007) difference in mean volume between sub-populations of different ages, which may reflect formational processes, is demonstrated to be only 30–50% likely to exist in reality. Critically, the synthetic DEMs are demonstrated to realistically model parameter recovery, primarily because they are still almost entirely the original landscape. Results are insensitive to the exact method used to create the synthetic DEMs, and the approach could be readily adapted to assess a variety of landforms (e.g. craters, dunes and volcanoes).