Snow Attenuation
Specific and total attenuation of a free-space optical link in dry or wet snow from the water-equivalent snowfall rate and wavelength, with the Koschmieder-equivalent visibility.
Specific attenuation γ
5.58 dB/km
a = 5.5799, b = 1.38
Path attenuation
5.58 dB
over 1 km
Transmittance
27.67 %
Koschmieder-equivalent visibility
3.04 km
3.912/V = this extinction; not a forecast
Specific attenuation at 1550 nm
Model
γ = a·S^b [dB/km]; dry: a = 5.42×10⁻⁵ λ + 5.4958776, b = 1.38; wet: a = 1.023×10⁻⁴ λ + 3.7855466, b = 0.72
An empirical law from the TU Graz FSO group (Sheikh Muhammad et al., ICTON 2005; Awan, PhD thesis 2010, eq. 3.29), λ in nm; Awan applies wet snow below 500 m elevation and dry snow above. The source calls S the precipitation rate recorded at weather stations without saying more; it is read here as mm/h of melted water, which matches observed snow visibilities better than snow depth. Snowflakes are much larger than the wavelength, so λ changes a by under 3 % across 780–1600 nm. Dry snow attenuates more than wet snow above 0.59 mm/h; below that the wet-snow law is the higher one.
Snowflake density, size and wetness vary widely, so a single rate can give a factor of several either way. Snow on the windows of the terminals, a common cause of outages, is not modelled.
Model and references
Textbook approximation. A standard approximation from the literature (for example paraxial, plane-wave or Gaussian-beam), valid within the range the page states. About the tiers
Empirical γ = a·S^b (dry/wet snow) from TU Graz FSO work; S read as liquid-water-equivalent rate (the source is not explicit). Flake type and density scatter real attenuation by a factor of several.
- Sheikh Muhammad S., Köhldorfer P., Leitgeb E. (2005). Channel modeling for terrestrial free space optical links. Proc. ICTON 2005, Tu.B3.5, 407–410. Eqs. (6)–(8): the snow law, S in mm/h (earliest print found). doi:10.1109/ICTON.2005.1505832
- Awan M. S., Leitgeb E., Nebuloni R., Nadeem F., Khan M. S. (2009). Optical wireless ground-link attenuation statistics of fog and snow conditions. Proc. IFIP WOCN 2009, 1–5. doi:10.1109/WOCN.2009.5010571
- Awan M. S. (2010). Statistical-dynamical channel modeling of outdoor optical wireless links. PhD thesis, Graz University of Technology, eq. (3.29): a and b with λ in nm. theses.eurasip.org