Evaluation of Pogson and Kasten–Young Formulations for Near-Horizon Solar Photometry: Separating Geometrical and Atmospheric Contributions

Abstract. This paper evaluates the mathematical coupling and separability of the Pogson and Kasten–Young formulations for wideband solar photometry under extreme near-horizon airmass conditions, using the partial solar eclipse of 12 August 2026 as a methodological target event. Operating at exceptionally low solar altitudes from 5.4° down to 0° near Rzeszów, Poland, the observational line-of-sight encountered a rapid relative airmass transition from X ≈ 9.7 to X ≈ 38. At maximum eclipse, the geometrical flux reduction was constrained to a visible solar-disk fraction of f_vis ≈ 0.415, establishing a nominal geometry-based dimming reference of Δm = 0.955 mag. Through a systematic sensitivity analysis using the Bouguer–Beer–Lambert formulation, we map the severe mathematical degeneracy that arises when dynamic atmospheric extinction coefficients (k = 0.2–0.3 mag/airmass) scale concurrently with the geometric occultation signal at extreme airmasses. Due to the absence of independent collocated radiometric calibration, the atmospheric attenuation term cannot be uniquely decoupled from the geometrical signal, showcasing the boundary limits of uncalibrated optical monitoring. The results quantify the systematic uncertainties introduced by standard airmass models near the astronomical horizon and define the minimal calibration protocols—including concurrent aerosol optical depth (AOD) measurements and detector linearity characterization—required to break this signal degeneracy in future low-elevation transient solar photometry.