Machine Learning Approaches for Tidal Data Interpolation in Satellite-Derived Bathymetry Applications

Satellite-derived bathymetry (SDB) has been developed since the 1970s and has grown exponentially with the popularization of remote sensing technologies. Over the years, several authors have proposed various methods to perform bathymetric inversion from the information contained in the pixels of satellite images, aiming to improve the accuracy and reliability of non-direct methods for estimating depth data in shallow waters. 

Despite the potential of remote sensing-based algorithms and global models to monitor multiple parameters of the planet's surface, few studies correlate SDB with water level in satellite images, obtained for the same region under different tidal conditions. Most recent efforts are limited to cluster analyses, separating the images into high-tide and low-tide groups to perform SDB with empirical models in a segmented approach, adjusting the linear coefficients of the regression models, partly for high-tide conditions and partly for low-tide conditions. The present study seeks to integrate tidal variation data with SDB techniques through Machine Learning (ML), particularly through the input channels of a Convolutional Neural Network (CNN). 

Previous research employing a simpler ML model, the Multi-Layer Perceptron (MLP), in Babitonga Bay, a microtidal region situated along the southern coast of Santa Catarina, Brazil, was compared to empirical SDB models that rely on the linear interaction of electromagnetic spectrum bands with the water column. The findings demonstrated that the nonlinear inferences generated by deep neural networks can enhance the accuracy of SDB data by more than 100% in optically complex environments, influenced by high concentrations of Colored Dissolved Organic Matter (CDOM) and Suspended Particulate Matter (SPM), such as Babitonga Bay. 

The application of more complex neural networks, such as CNN combined with additional input layers incorporating tidal data, has great potential for enhancing the performance of SDB, since CNN models utilize kernels that analyze multiple pixels surrounding a target point, enabling a more robust and context-aware approach, unlike MLP models, which infer depth on a pixel-by-pixel basis. The introduction of tide level variables as input channels in these deep learning neural networks makes these models suitable for universal application across micro-, meso-, and macrotidal environments. 

The CNN model applied to Babitonga Bay yielded substantial improvements in SDB accuracy, reducing the mean absolute error (MAE) from 2.9 m (traditional SDB methods) and 1.3 m (MLP) to 0.1 m. These results were obtained using field data collected in 2018 through single-beam echo sounder surveys for training, testing, and validation for both cases, the traditional empirical SBD models, and the machine learning models (MLP and CNN).