Multi-Path Validation Dataset for ERA5-Derived Atmospheric Refraction Coefficient (κ): Path 3 — Łysa Góra–Warsaw Mokotów

Overview This deposit is the third 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) and Path 2 (Pic de Finestrelles–Pic Gaspard, DOI: 10.5281/zenodo.21420699). Path 3: Łysa Góra → Warsaw Mokotów (144.9 km, 28/29 April 2025) On the night of 28/29 April 2025, Paweł Kłak photographed lights of the Mokotów district of Warsaw from Łysa Góra in the Świętokrzyskie Mountains — a documented, minute-precision observation attributed to a strong nocturnal radiative temperature inversion. Visibility of the specific Mokotów buildings held for a two-minute window (00:27–00:29 local CEST) during a longer observation session. This path is distinct from Paths 1–2 in three respects: a much shorter baseline (144.9 km vs. 443–493 km for the other two paths), a nighttime radiative-inversion atmospheric regime rather than a standard daytime lapse profile, and the availability of an independent, previously published local refraction-coefficient estimate against which KAPPA's path-averaged result can be directly compared. Observer: Łysa Góra scree field, Świętokrzyskie Mountains (50.86097°N, 21.04751°E, 578 m). Target: TDT headquarters, Puławska 125, Mokotów, Warsaw (52.164377°N, 21.017320°E, 169.5 m — light position). Great-circle distance: 144.9 km. Date/time: 2025-04-28, 22:28 UTC. Result: κ = 0.2235, required κ = 0.1670 — clear, margin +0.0565, consistent with the documented observation. Contents One JSON file containing the full path definition, κ result, sliced atmospheric layer data, an independent local-κ comparison and its reconciliation, and provenance/verification notes; and a README documenting method and data source provenance. Method Identical to Paths 1–2: 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. Independent comparison — a note on interpretation The original observers (DalekieWidoki.PL / DalekieHoryzonty.pl) separately derived a local refraction coefficient of κ≈0.65 for this line of sight, using a Legionowo radiosonde sounding (WMO 12374, 00 UTC 29 April 2025) and their own published methodology. This is not directly comparable to KAPPA's path-averaged result: their estimate is concentrated in a thin near-surface layer (approximately 95–145 m altitude, where local κ was reported to briefly exceed 1.0), while KAPPA's regression spans the full 170–578 m geometric slice — a range that does not sample the 95–145 m band at all, since the target elevation itself sits above it. KAPPA's computed κ (0.2235), roughly 1.7× the standard ICAO/mid-latitude value, correctly reflects a genuinely enhanced but diluted path-averaged gradient rather than the extreme, thin-layer core of the inversion. Both analyses agree refraction was substantially enhanced that night, and both are consistent with the documented successful observation. Provenance and verification Data retrieved directly from the KAPPA backend API rather than the arc.kappasuite.com frontend, using a verified, source-code-confirmed replica of the client-side κ computation. ERA5 L137 data for this date/time was already present in the operational archive and required no manual backfill. Primary source Kłak, P. (2025). Warszawski Mokotów widziany z Łysej Góry. DalekieWidoki.PL, 13 May 2025. https://dalekiewidoki.pl/2025/05/warszawski-mokotow-widziany-z-lysej-gory.html Notes This deposit extends the multi-path validation panel begun with Paths 1–2. Further paths will be added as separate, cross-referenced Zenodo deposits.