Global and local magnitude and spatial pattern of uncertainty from geographically adaptive empirical and machine learning satellite-derived bathymetry models

Abstract

The spatial structure of local uncertainty of shallow-water satellite-derived bathymetry (SDB) relative to model type, imagery, and geographical adaptability was examined for an area near Key West, Florida (United States). The model types examined were a commonly used quasi-empirical linear regression model and a decision tree-based Categorical Boosting (CatBoost) machine learning (ML) model. Image types examined were (four) cloud-free Sentinel-2 images and a maximum blue band (Band 2) value image composite of the four Sentinel-2 images. Initial models fitted were based on band reflectances alone. Geographical adaptivity was added by including UTM coordinates and refitting the models. Major findings were: 1) The ML/CatBoost models provided substantially better depth estimates than the quasi-empirical models. 2) The geographically adaptive models outperformed the non-geographically adaptive models. 3) The ML/CatBoost models that included non-visible spectral bands including infra-red improved SDB accuracy compared to ML/CatBoost and quasi-empirical models based only on visible spectral bands. 4) Accuracies from ML/CatBoost models were comparable across all individual images and the composite suggesting that CatBoost models eliminate or at least minimize the need to find “the best” cloud-free image nor is it necessary to create a composite image. 5) Localized SDB inaccuracy was spatially random. 6) Significant spatial hotspots where SDB accuracy was consistently higher or lower across all images and models were present. Results suggest that image selection is less important for global and local SDB accuracy than using ML models that detect hidden interactions and non-linear relationships among pixel reflectance and geographic location. The spatially random local deviation from global accuracy suggests a weak ability to infer local accuracy from neighboring accuracies. This lack of spatial autocorrelation among errors is potentially problematic for the use of SDB maps for navigation since error at any location is generally inferred from known uncertainties at neighboring locations. Rigorous and robust uncertainty analysis is necessary in any effort to improve SDB, and the uncertainty analysis techniques employed that characterize SDB uncertainty in both statistical and geographical space could be an important part of quality assurance and continuous improvement.

Keywords

• Airborne LiDAR
• image composite
• categorical Boosting
• global moran’s i
• local moran’s i