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