Dominant Source Identification in the Propagation of Ocean Observation Uncertainty to Underwater Detection Performance: A Differentiable End-To-End Framework

Underwater detection performance is constrained by ocean observation uncertainties that propagate nonlinearly through sound speed profile (SSP) inversion, acoustic transmission-loss (TL) prediction, and sonar performance estimation. We develop a differentiable end-to-end framework that traces observation uncertainty through SSP inversion, acoustic propagation, and passive sonar detection probability (Pd), enabling a quantitative ranking of the dominant uncertainty sources. The framework comprises a Bayesian deep ensemble for SSP inversion, a physics-constrained Fourier neural operator for acoustic propagation, and an analytic sonar-equation module, all implemented in PyTorch with automatic differentiation. Applied to the eddy-active northern South China Sea using the SCSORA reanalysis and validated against independent glider observations, bias-corrected Sobol' first-order indices show that satellite SST observation uncertainty dominates detection-performance uncertainty in deep water (S1 ≈ 0.38–0.52, conditional on the upper-200 m water column), exceeding the acoustic model structural error (S1 ≈ 0.10–0.19). The ranking is robust to a factor-of-two variation in the assigned acoustic structural-error variance and to the choice of attribution scheme (Sobol' vs. Shapley). A paired bootstrap test of a cross-training experiment indicates a small but significant sensitivity of the SST index to the training configuration (ΔS1 = 0.052; 95% CI [0.018, 0.086]), which does not alter the qualitative ranking. In shallow-shelf environments, seabed geoacoustic uncertainty prevails (S1 ≈ 0.41). The framework operates entirely on publicly available data and provides a quantitative basis for prioritizing environmental-observation resources in naval environmental support. Limitations include the absence of independent winter glider observations and the use of a 200-m SSP truncation in deep-water regimes; both are discussed in the paper.