## 1 Introduction  
Coastal areas are under a constant multitude of pressures resulting from different natural forces. The ability to reliably track and measure the nearshore bathymetry over time is critical for a wide array of applications including coastal development and management, coastal risk monitoring and mitigation, coastal science studies, among others [1, 2]. Traditional in situ bathymetric measurements using echo-sounding or Light Detection and Ranging (LiDAR) are time-consuming and expensive [3] and are preconditioned on a number of environmental factors such as the navigability of the site to be surveyed [4], in addition to a multitude of logistical constraints [5, 6]. Remote sensing tools have recently become an important tool to collect different types of data that allows the monitoring of coastal areas [7, 8]. These tools differ in their temporal frequency and spatial coverage. Shore-based or drone-mounted video cameras provide high-resolution imagery frequently with a spatially limited coverage [9; 10; 11]. On the other hand, satellite constellations such as the European Space Agency's (ESA) Sentinel-2 satellite constellation provide high resolution (10 m) imagery with global coverage at a relatively high revisit frequency (every 5 days with Sentinel-2) [12; 13]. These remotely sensed satellite products have been shown to be a valuable resource in a wide variety of coastal science studies and applications. For example, a large body of work exists on the use of ocean color data to quantify water quality parameters [14; 15; 16]. Methods making use of satellite imagery to estimate water depth can be divided into two categories based on the target phenomena studied. Namely, the effect of bathymetry on the propagation and dispersion of surface waves (wave kinematics), as well as the relation between water depth and light penetration and reflectance in water (water color). Methods based on the radiative transfer of light in water as a function of depth and wavelength (i.e., color-based methods) can be used to estimate depth in optically shallow waters [17; 18; 19; 20; 21; 22]. Such methods are sensitive to the optical properties of seawater and are generally limited to clear and non-turbid waters [1; 23]. Other methods based on wave kinematics extract wave features from satellite imagery such as the wave phase shift and wave number to estimate depth using the linear dispersion relation [24] (described in more detail in Section 2). Both approaches offer different advantages. Methods based on the radiative transfer of light in water are more accurate in shallow waters (up to 15 m depth) and are able to detect smaller-scale bathymetric features, with an absolute error order of 10-20% of the target value, and an average RMSE of 1.5 m [25; 26; 27]. On the other hand, wave kinematics-based approaches are preconditioned on the observability of wave patterns in the input imagery, however, their detectable depth range is significantly larger than the typical range of color-based methods [20] but with less accuracy when applied globally (RMSE between 6-9 m, [23]). The task of constructing a depth estimation function applicable to satellite data is non-trivial and remains a topic of ongoing research due to the great potential it offers to in-expensively monitor coastal morphodynamics at a large scale. Machine learning has been applied to satellite-derived bathymetry to automatically learn an estimation function, bringing great expectations to solve satellite-based bathymetry issues in areas of complex physics and environmental parameters. Early works made use of multi-layered perceptrons to estimate water depth as a function of spectral radiance in input satellite imagery [28]. Other works that make use of more traditional machine learning algorithms include [29], where support vector machines are used to estimate depth based on a transformed ratio between the blue and green bands of the National Aeronautics and Space Administration's (NASA) EO-1 satellite imagery.