KAPPA Arc — Physically Consistent Fusion Case Study: Optimal Interpolation Validation (Paper 3, Section 8.3)

Supporting data for Section 8.3 of Beyond ERA5: Data Source Limitations and Enhancement Pathways for Real-Time Geodetic Atmospheric Refraction Correction (Alkalali, K.Z.A., manuscript GEOG-D-26-00124, under review, Geodesy and Geodynamics). This deposit archives the full computational record behind a reviewer-requested case study testing Optimal Interpolation (OI) — the classical precursor to variational data assimilation — as a physically consistent alternative to direct surface-observation substitution. Four experimental cases are documented, all built from real values returned by the live KAPPA Arc V4 production endpoint (/api/compute/surface) combined with real NOAA ISD Lite surface observations (station OERK, identifier independently verified against NOAA's own official station registry): (1) the unmodified ERA5-Land background, which returns a physically implausible κ due to a real near-surface temperature inversion; (2) direct substitution of a real, complete surface observation, which corrects it; (3) a controlled reproduction of the specific failure mechanism documented in Section 3.2.1 of the manuscript — substitution with a deliberately degraded, synthetic pressure value — which produces an implausible result on the same grounds as the manuscript's OERK case; and (4) a field-wise OI treatment of the same degraded observation, independently weighting temperature and pressure by their genuine relative confidence, which recovers a result closely matching the complete-data case. Files: fusion_case_study_data.json (full experimental record, including raw API responses, observation provenance, all four cases with their inputs and results, and the exact formulas used) and README.md (full methodology, primary source citations, and scope/limitations). This is new, original computation performed specifically for this case study, distinct from the companion reproduction deposit at DOI 10.5281/zenodo.21931557.