Multi-Path Validation Dataset for ERA5-Derived Atmospheric Refraction Coefficient (κ): Path 4 — Karagöl Summit–Mount Elbrus

Overview This deposit is the fourth entry in a multi-path validation panel supporting Real-Time Atmospheric Refraction Coefficient Determination Using ERA5 Reanalysis Data for Line-of-Sight Visibility and Geodetic Applications (Alkalali, K.Z.A., under revision, Geodesy and Geodynamics, manuscript GEOG-D-26-00098R1), created in response to reviewer requests for validation across multiple paths, seasons, and climatic regions. Companion to Path 1 (Sağrak–Shkhara, DOI: 10.5281/zenodo.21413841), Path 2 (Pic de Finestrelles–Pic Gaspard, DOI: 10.5281/zenodo.21420699), and Path 3 (Łysa Góra–Warsaw Mokotów, DOI: 10.5281/zenodo.21429405). Path 4: Karagöl Summit → Mount Elbrus (474 km, 20 May 2025) On 20 May 2025, Richard Jezik — the same observer whose December 2024 Sağrak–Shkhara observation is the subject of Path 1 of this panel — photographed the West Summit of Mount Elbrus from the Karagöl relay station in Giresun Province, Turkey, a 474 km line of sight. This path is intentionally retained as a wide-margin ("comfortable") validation case, in contrast to the near-threshold character of Paths 1–3: the large observer–target elevation differential (2,534 m) means the target is geometrically close to visible even without significant refractive assistance. It is included specifically to demonstrate that the method correctly predicts visibility across the full range of margin conditions, not only in near-threshold cases — a working atmospheric refraction model should get the easy cases right as reliably as the hard ones. Observer: Karagöl summit, Giresun Province, Turkey (40.52234°N, 38.15395°E, 3,108 m). Target: Mount Elbrus, West Summit, Russia (43.355°N, 42.439°E, 5,642 m). Great-circle distance: 474 km. Date/time: 2025-05-20, ~02:00 UTC (sunrise-adjacent). Result: κ = 0.1555, required κ = 0.0294 — clear, margin +0.1261, consistent with the documented observation. Contents One JSON file containing the full path definition, κ result, atmospheric layer data, modified-refractivity M-profile, sensitivity analysis, and provenance/verification notes; and a README documenting method and data source provenance. Method Identical to Paths 1–3: refractivity N = 77.6·P/T + 3.73×10⁵·e/T² (Smith–Weintraub approximation to ITU-R P.453-14); ordinary least-squares regression of N against geometric altitude over the observer–target slice; κ = −R_Earth·(dN/dz)·10⁻⁶, R_Earth = 6,371,000 m. Full method detail in the main manuscript, §3.2–3.5. Provenance and verification Observer coordinates were provided directly by Richard Jezik from his own panorama-simulation-tool setup, cross-checked against Wikipedia's Karagöl location data. Elbrus's target elevation uses the standard West Summit reference value. This dataset was retrieved via the KAPPA frontend report generator rather than a direct API call; all reported N, N_avg, dN/dh, κ, and M-profile values were independently recomputed by hand from the raw atmospheric data and confirmed to match the reported summary statistics. A separate, unrelated report-generation bug affecting the frontend's display of per-level "local κ" values (duplicated boundary rows) was identified during this validation and does not affect any value reported here. Notes This deposit extends the multi-path validation panel begun with Paths 1–3. Along with Path 5 (Cerro Champaquí–Aconcagua), it provides the panel's wide-margin comparison cases, complementing the near-threshold Paths 1–3.