A mutual assessment of the uncertainties of digital elevation models using the triple collocation technique

This study investigates the uncertainties of digital elevation models (DEMs) using the triple collocation (TC) method. DEMs from satellite missions are important for many geoscience disciplines and for economic benefits and are freely available. Validating DEMs is necessary to select an appropriate model for a given region and application. Provided certain assumptions about the error structure of any three data sets - measuring the same phenomenon - can be made, the TC approach can be used to provide an unbiased and scaled estimate of the error variances of the data sets, without requiring a reference data. We compared the TC approach to the traditional approach of using a reference data set using the Shuttle Radar Topography Mission version 4.1 (SRTM v4.1) DEM, ASTER (the Advanced Spaceborne Thermal Emission and Reflection Radiometer) GDEM (Global DEM) version 2, the 1 arc-minute global relief model (ETOPO1), a DEM compiled by the Survey and Mapping Division of Ghana (SMD DEM), and 545 ground control stations (GCSs). The error estimates for the DEMs via TC were considerably smaller than those obtained from the reference-based approach. As an example, the best performing DEM (SRTM v4.1) recorded a root-mean-square error (RMSE) of 15.601 m using the GCSs as reference, while its TC-derived accuracy was 6.517 m. We note that based on the results of the TC, the estimated error of the GCSs is approximately 14 m. Using a data set with an error of 14 m to validate other data sets is certainly bound to result in unfavorable results. Thus, we have demonstrated in this work that the TC approach is able to provide an unbiased error of DEMs. The approach is important even for regions where GCSs are highly accurate, but more so for regions with low-quality GCSs.