## 1 Introduction
In [22], random forests are used to analyze several Landsat 8 surface reflectance products over a specific site in order to create a map of the bathymetry in shallow waters (0 to 20 m). Recently, numerous Earth observation and remote sensing applications have adopted deep learning (DL) methods using convolutional neural networks (CNN), due to their image processing and feature analysis abilities [30; 31; 32; 33]. The use of DL for bathymetry estimation is a recent and growing application; Ref. [34] estimate river bed topography from depth-averaged flow velocity observations. Both [35; 36] use aerial imagery to estimate water depth, on the surf zone of Duck, North Carolina (NC) and the floodplain of the Lech river, respectively. The use of DL on satellite products for bathymetry estimation is relatively unexplored but presents an opportunity for global, low-cost bathymetry estimation. In [37], DL is used to estimate seabed depth based on the radiative transfer of light in water in multispectral images from the Orbview-3 satellite. In [38], a CNN is used to estimate depths of the Devils Lake Area (ND, USA), casting estimation as a classification problem with classes at each foot of depth. The most convincing application of deep learning to coastal SDB currently appears to be from [39], which uses reflectance values from Sentinel-2 Level 2A images to estimate coastal water depth with high precision in clear waters (1.48 m RMSE). While machine learning and deep learning applications for satellite-derived bathymetry have--until now--mainly been applied to color-based approaches, great expectations come from the combination of different methods, in particular, based on wave information [40; 41]. To our knowledge, this work's contribution of DL for satellite-derived coastal bathymmetry based on wave kinematics from real satellite products is novel. In this work, we apply the previously developed Deep Single-Point Estimation of Bathymetry (DSPEB) method [42] and showcase its ability to reconstruct bathymetry using real-world data. We create a supervised dataset for bathymetry inversion using publicly available Sentinel-2 imagery [12] and a number of bathymetry surveys obtained from the French Naval Hydrographic and Oceanographic Service (SHOM). We present two different satellite image pre-processing techniques to augment wave kinematics and color information as inputs to two DSPEB models. We train our models in two different sites and compare the performance of color-based and wave kinematics-based DSPEB to one of the current state-of-the-art bathymetry inversion models based on wave kinematics, Satellite to Shores (S2 Shores) [24; 43]. The layout of this article is as follows. In Section 2, we present the DSPEB and S2 Shores approaches for SDB. We then describe our dataset creation methodology and the datasets used in our experiments. In Section 3, we present our results and compare our DSPEB models to the physical method's performances in two application sites. Section 4 concludes the work with a discussion of the results presented, highlighting possible further research paths. In the appendices, we include additional supporting results from the different models presented in the article, our first steps towards a hybrid approach to SDB using deep learning that makes use of the physical characteristics of surface waves in addition to water color to estimate depth, in addition to a full list of the Sentinel-2 images used in order to facilitate reproducibility.