SMART-SDB: Sample-specific multiple band ratio technique for satellite-derived bathymetry

Spectrally-based retrieval of bathymetry is challenging in inland/coastal waters due to variations in factors other than water depth across a water body, including bottom type, optically significant constituents, water surface roughness, and others. Optimal band ratio analysis (OBRA) is the most widely used method to deal with these confounding effects to retrieve water depth. OBRA identifies the pair of bands that provides the highest accuracy among all possible pairs when using a log-transformed band ratio model. However, this approach fits a single ratio model to all training samples without fully accounting for the heterogeneity of the aforementioned complicating factors. To deal with this problem, we introduce a novel method called Sample-specific Multiple bAnd Ratio Technique for Satellite-Derived Bathymetry (SMART-SDB). The proposed SMART-SDB technique partitions the feature space of the spectral data and creates for every subspace a different band ratio model that performs better than the other models within that subspace. Bathymetry is then predicted based on the closest model/s in the feature space by performing a sample-specific k-nearest neighbor (K−NN) analysis. The depth estimates provided by the neighboring models are averaged with weights proportional to their inverse distance in the feature space. The proposed method can be used in both inland and coastal waters. Here, we thoroughly examine its effectiveness in the challenging and heterogenous environments of fluvial systems using a wide range of spectral data including radiative transfer simulations, an airborne hyperspectral image of the Snake River (USA), and a WorldView-3 satellite image of the Sarca River (Italy). The results of this study indicate a significant improvement in depth retrieval for estimations based on the SMART-SDB method relative to standard OBRA, either when a single model or multiple models are employed.