Modified Lyzenga's Method for Estimating Generalized Coefficients of Satellite-Based Predictor of Shallow Water Depth

The multispectral method for the remote sensing of water depth proposed by Lyzenga has been widely applied to shallow-water bathymetry by researchers. The predictor of water depth used in this method is a linear function of image-derived variables for each visible band. The coefficients of the predictor are estimated by using a number of pixels with known depth as training data; this depth information is usually obtained by performing in situ depth measurements. Theoretically, if an appropriate set of coefficients is chosen, the predictor can be insensitive to some variations in the optical properties of the bottom material and water. However, it is sensitive to variations in atmospheric and water surface transmittance and sun and satellite elevations. Consequently, a single set of coefficients cannot always be applied to multiple images. In this letter, we propose a simple method to estimate a general set of coefficients for Lyzenga's predictor that is relatively less affected by the aforementioned factors. We derive and utilize the theoretical fact that these factors affect only the intercept (constant term) of the predictor function. We demonstrate the effectiveness of the proposed method using WorldView-2 images of coral reefs. The proposed method will enable the application of a single set of coefficients (except for the intercept) to a broad range of images. This will significantly reduce the number of pixels with known depth required for the prediction of an image and thereby improve the feasibility of remote sensing of water depth.