# Unmanned Aerial Vehicle Depth Inversion to Monitor River-Mouth Bar Dynamics
## 1 Introduction  
The coastal zone is a valuable space for marine species and various human activities. Many coastal areas face erosion problems, which will worsen due to climate change [1, 2]. Monitoring coastal bathymetry is essential for coastal erosion management. However, we cannot frequently conduct bathymetric surveys with costly vessel operations. From practical and scientific viewpoints, it is crucial to monitor dynamic bathymetry around a river mouth as a relay point of fluvial sediment supply to coastal zones. During an extreme event of fluvial sediment discharge, a large amount of sediment accumulates on the deltaic bar in front of a river mouth, some of which is later transported to surrounding coasts mainly by wave action [3, 4]. The morphological change of a river-mouth bar is also linked to littoral drift across the river mouth [5]. Without understanding the morphodynamics of a river mouth during an extreme event, we cannot estimate the sediment budget in a coastal zone and conduct proper erosion management in the long term. As such, there is an urgent need for a low-cost method to monitor highly two-dimensional coastal bathymetry. Water depth estimation from video-sensed waves has gained popularity as a low-cost alternative to obtain two-dimensional coastal bathymetry. Different algorithms have been proposed for the depth inversion, which commonly estimates water depth using the dispersion relation from linear wave theory. There are two main approaches to extract wave parameters from the video imagery: spectral and temporal methods. Both methods assume that the pixel intensity time series is closely related to water surface variation [6]. On the one hand, the spectral method estimates wavenumber and frequency pairs by decomposing intensity signals with empirical orthogonal function analysis [7, 8, 9]. The water depth isestimated from the dispersion relation using the multiple wave components. On the other hand, the temporal method determines wave celerity by a cross-correlation analysis of the intensity time series [10; 11]. Video-based depth inversion has recently been applied to monitor beach profiles in a wide range of environmental conditions [12; 13; 14] and nearshore currents via data assimilation into numerical models [15]. The root-mean-square error (RMSE) of the estimated bathymetry in these studies is commonly around 0.5 m. However, monitoring a broad coastal area requires a camera fixed at a high elevation point. As such, it is often difficult to find a suitable place to install a camera to monitor the bathymetry of a river mouth. Recent advancements in unmanned aerial vehicle (UAV) technology have expanded the possibility of video-based depth inversion. UAVs enable us to obtain aerial footage of a broad area from an arbitrary location and angle under preferable wave and weather conditions. Still, they are not without their limitations. One shortcoming is that UAV oscillations by wind generate noise in the sea-surface intensity signals. Recent studies overcome the issue by automatic rectification to realize the same accuracy as a fixed camera [16; 17; 18; 19]. However, most previous studies conducted the depth inversion in coastal areas with nearly uniform bathymetry in the longshore direction. It is still uncertain whether the UAV depth inversion applies to highly two-dimensional bathymetry in front of a river mouth. Depth contours around a river mouth are convex seaward due to the presence of a river-mouth bar. Hence, incoming waves cause refraction over the convex topography and produce a non-uniform vector field of wave celerity. The bathymetry estimation requires a robust algorithm that can extract wave parameters from intensity signals generated by the non-uniform wave field. This research aims to construct a UAV-based depth inversion method that works for highly two-dimensional bathymetry in front of a river mouth. Our strategy is to utilize video signals of swells that have a high dependency on coastal bathymetry.