How does co-registration affect geomorphic change estimates in multi-temporal surveys?

High-Resolution Topography (HRT) data sets are becoming increasingly available, improving our ability and opportunities to monitor geomorphic changes through multi-temporal Digital Terrain Models (DTMs). The use of repeated topographic surveys enables inferring the sediment dynamics of hazardous geomorphic processes such as floods, debris flows, and landslides, and allows us to derive important information on the risks often associated with these processes. The topographic surveying platforms, georeferencing systems, and processing tools have seen important developments in the last two decades, in particular Light Detection And Ranging (LiDAR) technology used in Airborne Laser Scanning (ALS) and Terrestrial Laser Scanning (TLS). Moreover, HRT data, produced through these techniques, changed a lot in terms of point cloud density, accuracy and precision over time. Therefore, old "legacy" data sets and recent surveys can often show comparison problems, especially when multi-temporal data are not homogeneous in terms of quality and uncertainties. In this context, data co-registration should be used to guarantee the coherence among multi-temporal surveys, minimizing, on stable areas, the distance between corresponding points acquired at different epochs. Although several studies highlight that this process is fundamental to properly compare multi-temporal DTMs, it is often not addressed in LiDAR post-processing workflows. In this paper we focus on the alignment of multi-temporal surveys in a topographically complex and rugged environment as the Moscardo debris-flow catchment (Eastern Italian Alps), testing various co-registration methods to align multi-temporal ALS point clouds (i.e. years 2003, 2009 and 2013) and the derived DTMs. In particular, we tested the pairwise registration with manual correspondences, the Iterative Closest Point (ICP) algorithm and a mathematical model that allows aligning simultaneously a generic number of point clouds, the so-called Generalized Procrustes Analysis (GPA), also in its GPA-ICP variant. Then, to correct the possible small inaccuracies generated from the gridding interpolation process, a custom-developed DTM co-registration tool (GRD-CoReg) was used to align gridded data. Both alignment phases (i.e. at point cloud and DTM level) proved to be fundamental and allowed us to obtain proper and reliable DTMs of Difference (DoDs), useful to quantify the debris mobilized and to detect the spatial and temporal patterns of catchment-scale erosion and deposition. The consistency of DoDs data was verified through the comparison between the erosion estimate of DoDs and the volumes of debris-flow events measured by the monitoring station close to the Moscardo torrent catchment outlet. The GPA-ICP algorithm followed by the GRD-CoReg tool proved to be the most effective solution for improving DoDs results with a decrease of systematic trend due to vertical and horizontal uncertainties between surveys, especially at steep slopes. The net volume difference (i.e. the sediment output from the catchment) of the 2003-2013 period changed from 3,237,896 m to 135,902 m in DoDs obtained from not co-registered and co-registered DTMs. The volume of debris flows measured at the catchment outlet during the same time interval amounts to 169,660 m. The comparison with debris-flow volume measures at the monitoring station shows, therefore, that the DTMs obtained from the co-registration processes generate more reliable DoDs than those obtained from the raw DTMs (without the alignment).