Satellite-based bathymetric modeling using a wavelet network model

Accurate bathymetric modeling is required for safe maritime navigation in shallow waters as well as for other marine operations. Traditionally, bathymetric modeling is commonly carried out using linear models, such as the Stumpf method. Linear methods are developed to derive bathymetry using the strong linear correlation between the grey values of satellite imagery visible bands and the water depth where the energy of these visible bands, received at the satellite sensor, is inversely proportional to the depth of water. However, without satisfying homogeneity of the seafloor topography, this linear method fails. The current state-of-the-art is represented by artificial neural network (ANN) models, which were developed using a non-linear, static modeling function. However, more accurate modeling can be achieved using a highly non-linear, dynamic modeling function. This paper investigates a highly non-linear wavelet network model for accurate satellite-based bathymetric modeling with dynamic non-linear wavelet activation function that has been proven to be a valuable modeling method for many applications. Freely available Level-1C satellite imagery from the Sentinel-2A satellite was employed to develop and justify the proposed wavelet network model. The top-of-atmosphere spectral reflectance values for the multispectral bands were employed to establish the wavelet network model. It is shown that the root-mean-squared (RMS) error of the developed wavelet network model was about 1.82 m, and the correlation between the wavelet network model depth estimate and "truth" nautical chart depths was about 95%, on average. To further justify the proposed model, a comparison was made among the developed, highly non-linear wavelet network method, the Stumpf log-ratio method, and the ANN method. It is concluded that the developed, highly non-linear wavelet network model is superior to the Stumpf log-ratio method by about 37% and outperforms the ANN model by about 21%, on average, on the basis of the RMS errors. Also, the accuracy of the bathymetry-derived wavelet network model was evaluated on the basis of the International Hydrographic Organization (IHO)'s standards for all survey orders. It is shown that the accuracy of the bathymetry derived from the wavelet network model does not meet the IHO's standards for all survey orders; however, the wavelet network model can still be employed as an accurate and powerful tool for survey planning when conducting hydrographic surveys for new, shallow water areas.