Model Uncertainty Quantification in Seafloor Topography from Satellite Altimetry-Derived Gravity

For mapping high-precision seafloor topography, inverting bathymetry from satellite altimetry-derived gravity data provides a very cost-effective method. To accurately assess the quality and dependability of a seafloor topographic map, it is essential to quantify the uncertainty in inverted bathymetry. Existing inversion methods for seafloor topography implicitly assume that errors follow a highly idealized white noise distribution. However, this assumption is often violated due to deep-sea topography's inherent complexity and variability, with inversion residuals exhibiting spatial heterogeneity that correlates with topographic undulations. Building on advancements in interval prediction, particularly the conformal prediction (CP), this study introduces a comprehensive inference framework for seafloor topography, incorporating locally weighted inductive conformal prediction (LWICP) for uncertainty quantification in inverted bathymetry. The proposed LWICP interval is designed to integrate with various inversion methods for seafloor topography seamlessly, demonstrated through the application of three primary inversion methods as representative examples. To address the spatial heterogeneity in inversion residuals, the LWICP method, as a data-driven approach, integrates a local weighting function into CP, thereby providing prediction intervals with distribution-free marginal coverage guarantees for bathymetric point predictions from any inversion model. This generalizability ensures the adaptability of the LWICP interval to other emerging inversion methods for seafloor topography. Additionally, this work also highlights CP\u2019s robust generalization capabilities with digital bathymetric model (DBM) data, marking a novel application. Extensive experiments within the Mariana Trench region confirm that the proposed LWICP interval significantly outperforms existing methods in interval prediction,  adaptively capturing the dependence pattern of topographic variability in inversion residuals.