A dual band algorithm for shallow water depth retrieval from high spatial resolution imagery with no ground truth

For shallow water depth retrieval from high spatial resolution satellite images, although numerous empirical models have been developed, it remains impossible to estimate shallow water depths without collection of required ground truth depth. To address this limitation, a new physically based dual band algorithm is developed to estimate shallow water depths using blue and green bands from high spatial resolution multispectral image with no ground truth. The dual band log-linear model is first analytically formulated, which then is used for shallow water depths retrieval by solving all unknown model parameters based on different types of sampling pixels directly extracted from the multispectral image. The adjacent pixel pairs from the intersecting edges of different bottom types across various depths over shallow water area, are employed to calculate the optimal band rotation coefficient unit vector by minimization method. On the basis, the bottom parameter is estimated through the pixels from the coastline. Additionally, the pixels from various depths of same bottom type are also employed to achieve the blue to green band ratio of diffused attenuation coefficient. The sum of the diffuse attenuation coefficients of green band for upwelling and downwelling light is estimated by QAA and Kd algorithms. To evaluate the performance of the proposed algorithm, the GeoEye-1 image covered Jinqing Island and the Chinese Gaofen-2 image across Kaneohe Bay are chosen to achieve shallow water depth by using the proposed algorithm after geo-rectification and atmospheric correction. The validations using the actual water depths show the overall root mean square errors (RMSEs) for the derived water depths are 1.18 m for Jinqing Island and 1.34 m for Kaneohe Bay respectively. Compared to the Lyzenga empirical model, the developed approach can generally achieve slightly better results for shallow water depths with no ground truth data. Finally, the effects of the variation in the model parameters to water depth retrieval are discussed and analyzed.