Exhaustive feature-subset search for data-driven post-correction of satellite atmospheric processors: a case study on...

Satellite retrieval of chlorophyll-a (Chl-a) is central to monitoring eutrophication in inland reservoirs, yet the atmospheric-correction processors it depends on, trained on oceanic and large-lake conditions, are systematically biased over small water bodies. A data-driven post-correction layer is increasingly used to reduce this bias; for such a layer over the joint output of the C2-Net processors (C2RCC, C2X, and C2XC), we ask which engineered features robustly carry the corrective signal rather than chasing an accuracy headline. Enumerating all 2¹⁷-1 = 131, 071 subsets of a symmetric 17-feature pool exposes a broad performance plateau on which three mainstream heuristics pick inequivalent "best" subsets at near-identical error, so any single optimum is an artifact of selection on the cross-validated statistic. Stability selection instead isolates a small robust core (led by $\sqrt{\left|\text{C}2\text{X}{\text{C}}_r\right|}$ , chosen in 98% of subsamples at k = 6), the transformations that dominate the lowest-error subset being selected near chance. On 252 satellite-in-situ pairs from five Guadiana-Basin reservoirs (Spain), the correction improves pooled RMSE over raw C2RCC modestly but, for the Huber model, significantly (~10-16%, p = 0.047 under a cross-validation-corrected test), with the three estimators statistically indistinguishable from one another; under Leave-One-Reservoir-Out validation the degradation runs from ~15% (pooled) to ~34% (per-reservoir mean), both within the wide bootstrap intervals and thus approximate rather than precise. We distill a compact reporting template: an RMSE-vs.-k curve with variance bands, stability selection in place of a single "best" subset, a relative-error metric (MdAPE) alongside RMSE, and LORO as a minimum transferability check. All code, data, and models are released openly.