Uncertainty Aware Probabilistic Modelling of Terrestrial Free Space Optical Links under South African Continental Fog

Abstract Fog is the dominant availability constraint for many terrestrial free-space optical (FSO) links, yet South African planning studies often report mean losses without distinguishing among visibility conventions, path lengths, and tail risk. This paper develops an uncertainty-aware, reproducible framework using peer-reviewed summaries derived from South African Weather Service observations rather than claiming access to station-level records. The model follows Recommendation ITU-R P.1814-1 (2025): meteorological optical range is converted to wavelength-dependent attenuation, propagated through Beer-Lambert loss, and transformed into fade-margin and outage quantities. A numerical audit of a published seven-location, three-wavelength South African table provides independent verification of implementation. The reported values are reproduced by a 0.23 km path calculation with a fixed wavelength exponent q = 1.3, giving R²=0.999998, root-mean-square error 2.52×10⁻⁴ dB, and mean absolute percentage error 0.133%. Back-calculated effective path lengths have a mean of 0.22997 km and a standard deviation of 0.00049 km. Accordingly, those values should be interpreted as approximately 230 m path losses rather than specific attenuation in dB/km. Scenario analysis then quantifies uncertainty from visibility error, wavelength exponent selection, and link length. Dense fog below 0.5 km suppresses the wavelength advantage in the ITU model; reducing span length therefore dominates wavelength selection for catastrophic events. Published exceedance probabilities above 80 dB/km imply approximately 33.3, 22.8, and 10.5 h year⁻¹ of severe exposure in Mbombela, Cape Town, and Polokwane, respectively, when treated as climatological frequencies. The framework provides auditable equations and conservative design rules while identifying that station-level validation is still required before site acceptance.