Duct propagation

Duct propagation is a form of space-wave propagation in which a microwave signal is trapped in a thin layer of the lower atmosphere (a duct) and guided along the earth's curvature, far beyond the normal line-of-sight range, like a wave in a waveguide.

Cause: abnormal refractive index profile

In a standard atmosphere the refractive index n falls slowly with height, so rays bend down slightly (effective earth radius = 4/3 R). Sometimes n falls much faster with height, due to:

• Temperature inversion (warm air over cold air), e.g. over cool sea, or after sunset over land;
• Sharp fall of humidity with height (moist air near sea surface, dry air above);
• Subsidence of air in high-pressure areas.

The modified refractive index is M = (n − 1 + h/R) × 10⁶. Normally M increases with height. Where dM/dh < 0 (n falls faster than 0.157 N-units per metre, i.e. dN/dh < −157 per km), the ray curvature becomes greater than the earth's curvature, and a duct forms.

   height          upper boundary (n jumps)
     |  ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
     |   /\    /\    /\    /\    /\
     |  /  \  /  \  /  \  /  \  /  \     trapped ray
     | /    \/    \/    \/    \/    \
  ===Tx==========================Rx===  earth / sea
        surface duct (few m to 100s m)

Mechanism

1. A ray launched at a low angle bends downward more strongly than the earth curves.
2. It returns to the earth (or the lower boundary of an elevated duct), reflects, goes up again, and is bent down again.
3. The wave keeps zig-zagging inside the layer and travels hundreds or even thousands of km with low loss.

Types

• Surface duct: lower boundary is the earth or sea surface (common over warm seas).
• Elevated duct: layer lies above the ground, between two heights.

Conditions

• Only wavelengths small compared with the duct thickness are trapped (like waveguide cut-off). A duct of thickness d supports roughly λ_max ≈ 2.5 d √(ΔM × 10⁻⁶); so mainly VHF high end, UHF and microwaves are ducted.
• Both antennas should be inside or near the duct, and the wave launched at a small angle.

Effects

• Very long, unexpected ranges for microwave and VHF/UHF signals (TV and radar "anomalous propagation").
• Interference between distant stations on the same frequency; false radar echoes.
• Not reliable for planned links, because ducts depend on weather.