# Deriving High Spatial-Resolution Coastal Topography From Sub-meter Satellite Stereo Imagery
## 1 Introduction  
Accurate topographic data are frequently needed for the assessment of rapid morphological changes and for the implementation of models that can predict coastal evolution. High spatial resolution coastal Digital Elevation Models (DEMs--defined here as the representation of the terrain surface elevations at regularly spaced intervals) are used to support vulnerability and risk assessment of a range of coastal hazards, such as beach erosion and sedimentation, storm surges, inundation, and sea level rise [1]. For such studies, the availability of a topographic dataset is fundamental, in particular for coastal systems characterized by a complex, rapidly evolving morphology. Among topographic survey methods of suitable quality, those based on Global Navigation Satellite Systems (GPS), such as Real Time Kinematic GPS (RTK-GPS), have been used extensively to map and monitor coastal morphology [2]. Beach topographic surveys using RTK-GPS method can be performed either by walking and carrying a GPS receiver, or driving a mobile unit (e.g., quad bike). In both cases, the vertical precision is approximately 0.05 to 0.1 m, depending on the terrain relief [2]. This method typically requires an intense human effort, which normally is optimized by reducing the number of measurements to a limited number of cross-shore sections of the beach. Nevertheless, this limited spatial coverage results in an incomplete representation of topographic spatial patterns and evolving features, especially in the case of complex topographies such as steep and unconsolidated slopes. In such cases, interpolation methods are typically required, introducing additional uncertainty into the DEM [3]. Remote sensing techniques, such as airborne LiDAR (Light Detection and Ranging) and Unmanned Aerial Vehicle (UAV), emerge in this context as a solution to overcome the limited spatial coverage of the RTK-GPS method [4; 5; 6; 7; 8; 9]. The use of airborne LiDAR to measure geomorphological changes in coastal areas is relatively new. This instrumentation acquires millions of x, y, z points per hour, with a horizontal spacing of typically 1 to 3 m. This high spatial resolution, together with the capacity to survey over large areas (from \(10^{1}\) to \(10^{5}\) m), allows overcoming traditional survey limitations found with RTK-GPS [2]. The vertical accuracy of LiDAR ranges from 0.05 m to 0.15 m [5], which is in the same order as RTK-GPS and appropriate for studying beach morphology. Nonetheless, LiDAR-based DEMs are costly [5; 6], which limits the frequent (e.g., monthly or-post-storm) acquisition of large-scale topographic data adequate for the evaluation of coastal changes. Airborne optical remote sensing and 3D-mapping have been serving the needs of regional-scale low-altitude imaging and geospatial information [10]. The enhanced usability of recent UAV equipment with onboard accurate positioning, such as off-the-shelf drones, has resulted in a large change in their practical application. The RTK-GPS positioning of the camera, combined with the large number of overlapping images, makes any additional ground surveys trivial. Moreover, the high degree of automation of UAVs and the absolute vertical precision, of approximately 0.2 m, achieved by the DEMs suggests possible uses in the fields of natural hazards, disaster response, and high-resolution terrain analysis [6]. Despite these advantages, a few disadvantages still remain such as the cost of the photogrammetric software and computer power that can be relatively high [7], the difficulty in removing dense vegetation to obtain bare earth elevation estimates [11], the need for electric batteries for longer flight duration, or the usage limitations related to weather conditions [12]. Sub-meter satellite imagery can potentially provide an alternative to these field-based techniques in order to collect high spatial resolution topographic data over large areas.