## 1 Introduction
### Related Work  
Over the past decades, remotely sensed data have been employed for bathymetric applications. Airborne Light Detection and Ranging (LiDAR) Bathymetry (ALB) systems have been developed to measure water depth in coastal zones [12]. ALB systems typically operate at dual-wavelengths, namely near infrared (1064 nm) and green (532 nm), in order to detect water surfaces and benthic layers. [PERSON] et al. [13] presented a combination of mathematical and heuristic methods to estimate the water depth in very shallow water areas. The LiDAR waveforms, recorded at the near infrared and green wavelengths, were first synchronized, and the peak of the waveform at near infrared wavelength was amplified. The approximate positions of the water surface and benthic layer were then performed by simple maxima detection algorithm. After that, a non-linear least square fitting of a sum of two Gaussian functions on the green signal were conducted. Finally, the water depth was calculated from the accurate estimation of the water surface and benthic layer positions, and the minimum detectable depth was around 1 m. This approach is found to be computationally expensive and requires many processing steps, as well, the delineation of land/water interface was not reported in that study. When the green laser contacts water molecules, a small portion of energy is returned at a wavelength of 647 nm, which is called the red (Raman) channel [14]. [PERSON] and [PERSON] [15] analyzed the recorded waveform at the Raman channel, which represents the received intensity (digital number) relative to time (in nanoseconds), and divided it into 41 bins. Then, a normalized difference index (NDI) was created between bin 11 and bin 27 to discriminate water from land by applying a threshold value to the NDI. The LiDAR measurements were manually classified into land, water, and suspected as water. Despite the good achieved results (97%), there is a transition class \"suspected as water\" that cannot be identified as land or water. In addition, the manual processing of the waveform is required for each tested dataset. Over the past years, land/water discrimination has been investigated using LiDAR data collected by monochromatic-wavelength airborne LiDAR systems. LiDAR point features such as point density [16; 17; 18], roughness [18; 19], and intensity variation [19] were extracted and used in the discrimination process. However, data-driven threshold values were manually selected to make those point features fit the tested data, which means the existing methods are ad hoc. In addition, the existing methods require prior knowledge of the land/water interface to aid in the supervised discrimination process. [PERSON] et al. [20] introduced a supervised object-orientated approach to separate the water bodies from land objects in urban areas. The water surfaces were assumed to have low elevation and intensity values so that the LiDAR points within a specific height range and average intensity values of less than specific threshold values were classified as water points. The manual setting of such threshold values leads to more than a 95% accuracy index for water class. [PERSON] et al. [17] used a set of features to train a Support Vector Machine (SVM) algorithm in order to classify water areas. The results were then refined by incorporating contextual knowledge to remove pixel-wise misclassification. Their proposed work achieved an overall accuracy of more than 95% in coastal areas. [PERSON] et al. [18] developed a decision tree to classify water areas based on point density, elevation standard deviation, and intensity standard deviation of the LiDAR data. The results revealed that the water areas were classified with more than 95% accuracy compared to manually interpreted data. [PERSON] et al. [16] classified the water surface in the Wadden Sea using a supervised fuzzy classifier based on height, intensity, and 2D point density.