Improving Statistical Uncertainty Estimate of Satellite-Derived Bathymetry by Accounting for Depth-Dependent Uncertainty

Abstract

For mapping the near-shore seafloor bathymetry, retrieving depth information using multispectral satellite image is highly cost-effective. To effectively detect and characterize the bathymetry variation, accurate and reliable information about the uncertainty of the derived depths is critical. In estimating the uncertainty of the resulted satellite-derived bathymetry (SDB), the conventional homoscedasticity assumption states that the error variance of the observations is constant across different depth ranges. However, this assumption is violated due to the influence of various environmental factors inherently correlated with depth. In this article, we develop a data-driven approach to extract the depth-dependent pattern of observation error. The residual information of the regression is analyzed to model the influence of the depth on the uncertainty of retrieval bathymetry, while nonlinearity and outliers are also considered. This results in a more realistic estimate of SDB accuracy. Our experimental results reveal that the observation uncertainty is significantly correlated with the depth in the bathymetry retrieval process. It is also shown that the presented algorithm effectively captures the depth-dependent pattern of the observation uncertainty, and further provides a more realistic characterization of the uncertainty information of SDB.