Combinatorial Selection of Multi-Pass ICESat-2 ATL24 Calibration Tracks for Sentinel-2 Satellite-Derived Bathymetry

ICESat-2 ATL24 data provide along-track shallow-water depths that can serve as spaceborne calibration information for satellite-derived bathymetry (SDB). A study area is usually crossed by multiple passes, but the tracks differ in quality, depth coverage, and spatial coverage. Existing studies still mainly pool all tracks, use a single pass, or refine the data point by point, and no systematic method yet exists for selecting among large numbers of candidate-track combinations. We formulate ATL24 track selection as a combinatorial optimization problem whose objective is the bathymetric retrieval error, measured against independent airborne lidar bathymetry (ALB) reference depths within the study area so that selection requires local survey data, and test it in three coral-reef areas whose depth ranges and track-quality structures complement one another, using two retrieval models of different flexibility, XGBoost and the Stumpf band-ratio model. On a 16-track controlled pool small enough to enumerate, with the exhaustive global optimum as ground truth, a genetic algorithm (GA) reproduced the global optimum exactly in three of the six cases formed by the three study areas and two models and came within 1.28% of it in the other three, while evaluating fewer than 1% of all possible subsets; on randomly composed pools the GA approached the optimum equally reliably, whereas random search with the same number of evaluations found it with a probability below 1%. The GA was then extended to full candidate pools of 42–70 tracks, corresponding to 1012–1021 subsets, and compared with four conventional practices under spatial-block five-fold cross-validation. Relative to pooling all tracks, the root-mean-square error (RMSE) fell by 9.2–63.3% for XGBoost and by 2.2–30.5% for Stumpf (a magnitude sensitive to the Stumpf fitting settings), and all of these gains kept their sign under strict spatial isolation, in which the calibration points inside the test blocks were also withheld. The gains were concentrated in the deepest water, and some shallower depth bands deteriorated. These results show that the value of an ATL24 calibration track is determined jointly by track quality, coverage complementarity, and the downstream model, and that, where local reference depths are available, task-oriented combinatorial selection is better suited than the per-track thresholds and rankings tested here to the quality control of multi-pass calibration data.