RT-ProtoNet: radiative-transfer-guided few-shot prototype networks for cross-region bathymetry in optically clear reef environments

Satellite-derived bathymetry faces two coupled obstacles: labels are scarce, and models transfer poorly across regions. We propose RT-ProtoNet, a radiative-transfer-guided few-shot prototype network, which takes patches from three penetrating Sentinel-2 bands and treats ICESat-2 depths, aggregated to the 10 m grid, as sparse supervision; cross-region episodic meta-training then yields a transferable metric representation. Rather than embedding the radiative transfer relation as an analytic formula, we use it as a comparability criterion between support and query pixels, entering the attention as a learnable additive distance penalty. The prediction sums a convex combination over support depths and a base regression head trained on source domains only and frozen at deployment, so no target-domain parameters are estimated. We evaluate on five optically clear shallow reef regions by leave-one-region-out cross-validation against airborne laser bathymetry, against nine baselines, where K is the total number of support pixels (3, 5, 10, 20, 50). For K ≤ 20, RT-ProtoNet attains the lowest cross-region macro-mean RMSE (2.79–2.48 m), with a run-to-run standard deviation 0.67 times the runner-up’s; at K = 50, pre-training with head fine-tuning overtakes it. Ablation shows the residual head’s gain scales with support depth coverage (correlation 0.991) and that the two physical priors are largely substitutable; twelve perturbations to the attenuation input change RMSE by only 0.66%. The method suits depths of roughly 2–20 m and budgets of K ≤ 20, and does not extrapolate to turbid or optically complex waters. Independent evaluation at two external optical-domain sites, a moderately turbid embayment (Tampa Bay) and a clear-to-moderately-turbid transition site (Boquerón Bay), further delineates the method’s applicability across contrasting optical conditions, showing reliable transfer within the clear-water regime but substantial degradation under stronger optical attenuation.