Nonparametric Empirical Depth Regression for Bathymetric Mapping in Coastal Waters

Existing empirical methods for estimation of bathymetry from multispectal satellite imagery are based on simplified radiative transfer models that assume that transformed radiance values will have a linear relationship with depth. However, application of these methods in temperate coastal waters of New Zealand demonstrates that this assumption does not always hold true and consequently existing methods perform poorly. A new purely empirical method based on a nonparametric nearest-neighbor regression is proposed and applied to WorldView-2 and WorldView-3 imagery of temperate reefs dominated by submerged kelp forests interspersed with other bottom types of varying albedo including reef devoid of kelp and large patches of sand. Multibeam sonar data are used to train and validate the model and results are compared with those from a widely used linear empirical method. Free and open source Python code was developed for the implementation of both methods and is presented for use. Given sufficient training data, the proposed method provided greater accuracy (0.8 m RMSE) than the linear empirical method (2.2 m RMSE) and depth errors were less dependent on bottom type. The proposed method has great potential as an efficient and inexpensive method for the estimation of high spatial resolution bathymetry over large areas in a wide range of coastal environments.