Rain Attenuation
Specific and path attenuation of a free-space optical link in rain with the ITU-R P.1814-1 model: γ = k·R^α for a gamma drop-size distribution, path reduction factor and multiple-scattering gain.
Specific attenuation γ
10.3 dB/km
k = 1.2924, α = 0.6436
Path attenuation A
10.1 dB
over 1 km
Transmittance
9.797 %
Path reduction F
0.9929
A′ = γ L F = 10.2 dB
Multiple-scattering gain
0.0972 dB
A = A′ − G_ms
Path attenuation over 1 km
Model (Rec. ITU-R P.1814-1, 2025)
γ = k·R^α [dB/km], F = 1 / (1 + L(R − 6.2)/2623), A = γ·L·F − a_ms·L^b_ms
Raindrops (radius 0.1–4 mm) are far larger than the wavelength, so rain attenuation is the same in the 780–850 nm and 1520–1600 nm bands. k and α come from Mie theory over a gamma drop-size distribution whose shape µ measurements put between −2 and 2. F accounts for rain cells being smaller than the link, and the multiple-scattering gain G_ms = a_ms·L^b_ms (a_ms, b_ms quadratic in ln R) for light scattered forward into the receiver. R in mm/h, L in km (the Recommendation states the path model for L ≤ 5 km, so the link length is limited to 5 km).
Below 1 mm/h the G_ms fit misbehaves (it turns negative, or grows as the rain stops), so there the gain is taken proportional to A′, matching the fit at 1 mm/h. Not modelled: rain-rate statistics along the path (the Recommendation combines them with fog via CCDFs), wet windows, and turbulence.
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
ITU-R P.1814-1: γ = k·R^α (Mie, gamma DSD, µ = −2…2), path reduction and multiple-scattering gain for L ≤ 5 km; flat over 780–850 and 1520–1600 nm. Gain fit tapered below 1 mm/h. No rain-rate statistics.
- Recommendation ITU-R P.1814-1 (09/2025), Prediction methods required for the design of terrestrial free-space optical links. §4.1.2.2, Table 4 (k, α); §4.2.3, eqs. (14)–(19), Table 5. itu.int