Comparative analysis of the Copernicus, TanDEM-X, and UAV-SfM digital elevation models to estimate lavaka (gully) volumes and mobilization rates in the Lake Alaotra region (Madagascar)

Over the past few decades, developments in remote sensing have resulted in an ever-growing availability of topographic information on a global scale. A recent development is TanDEM-X (TerraSAR-X add-on for digital elevation measurements), an interferometric synthetic aperture radar (SAR) mission of the Deutsche Zentrum fiir Luft- and Raumfahrt, providing near-global coverage and 12 m resolution digital elevation models (DEMs). Moreover, ongoing developments in uncrewed aerial vehicle (UAV) technology have enabled acquisitions of topographic information at a sub-meter resolution. Although UAV products are generally preferred for volume assessments of geomorphic features, their acquisition remains a time-consuming task and is spatially constrained. However, some applications in geomorphology, such as the estimation of regional or national erosion quantities of specific landforms, require data over large areas. TanDEM-X data can be applied at such scales, but this raises the question of how much accuracy is lost because of the lower spatial resolution. Here, we evaluated the performance of the 12 m TanDEM-X DEM to (i) estimate gully volume, (ii) establish an area-volume relationship, and (iii) determine mobilization rates through comparison with a higher-resolution (0.2 m) UAV structure-from-motion (SfM) DEM and a lower resolution (30 m) Copernicus DEM. We did this for six study areas in the Lake Alaotra region (central Madagascar), where lavaka (gullies) are omnipresent and surface area changes over the period 1949-2010s are available for 699 lavaka. Copernicus-derived lavaka volume estimates were systematically too low, indicating that the Copernicus DEM is too coarse to accurately estimate volumes of geomorphic features at the lavaka scale (100-10(5) m(2)). Lavaka volumes obtained from TanDEM-X were similar to UAV-SfM volumes for the largest features, whereas the volumes of smaller features were generally underestimated. To deal with this bias we introduce a breakpoint analysis to eliminate volume reconstructions that suffer from processing errors as evidenced by significant fractions of negative volumes. This elimination allowed the establishment of an area-volume relationship for the TanDEM-X data with fitted coefficients within the 95 % confidence interval of the UAV-SfM relationship. Our calibrated area-volume relationship enabled us to obtain large-scale lavaka mobilization rates ranging between 18 +/- 3 and 311 +/- 82 tha(-1) yr(-1) for the six different study areas, with an average of 108 +/- 26 t ha(-1) yr(-1) for the full dataset. These results indicate that current lavaka mobilization rates are 2 orders of magnitude higher than long-term erosion rates. With this study we demonstrate that the global TanDEM-X 12 m DEM can be used to accurately estimate volumes of gully-shaped features at the lavaka scale (100-10(5) m(2)), where the proposed breakpoint method can be applied without requiring the availability of a higher-resolution DEM. Furthermore, we use this information to make a first assessment of regional lavaka erosion rates in the central highlands of Madagascar.