Abstract
Shallow water depth is one of the important factors in science and coastal environmental management. However, in-situ measurement is quite costly and time-consuming. Past research efforts have provided a number of optically-based methods to estimate shallow water depth distribution from satellite image, but they cannot properly handle with the heterogeneity in bottom sediment distribution because they require image-specific assumptions or additional information on bottom reflectivity. It is therefore indispensable to develop a method that can be applied more generally to water areas with inhomogeneous bottom material.
In any application of depth prediction methods, we need depth data for some points to validate the results. A leave-one-out cross validation technique enables us to use the data for predictive model building without degrading the reliability of prediction error evaluation. From this standpoint, we present a new generalized method over the previous methodologies by utilizing depth measurement data.
In the new method, the bottom reflection term of the optical model is assumed to be a nonparametric function of the depth-independent variables (bottom indexes), which can be calculated from the brightness values of the pixels. In this way, the water depth is explained by a semiparametric regression model. The ratios of the diffuse attenuation coefficients, which are needed to calculate the bottom index, are optimized to minimize Generalized Cross-Validation(GCV).
The new method is applied to 3 coral reef areas and artificially generated situations, and the prediction accuracy is compared with those of the methods proposed by Paredes et al., Stumpf et al., and Kanno et al. As a result, the new method is found to have the highest accuracy in cases that enough depth-known pixels are available and that the optical model apply well.
