Question E3A07:
Atmospheric ducts capable of propagating microwave signals often form over what geographic feature?  

Choices:  
A: Mountain ranges  
B: Stratocumulus clouds  
C: Large bodies of water  
D: Nimbus clouds    

Correct Answer is  C: Large bodies of water  

Correct answer: C — Large bodies of water

Why this is correct:
- Over oceans and large lakes, a strong humidity and temperature gradient forms just above the surface (the marine boundary layer). This creates an evaporation duct where the refractive index decreases rapidly with height, bending microwave rays back toward the surface and trapping them.
- This “duct” can guide microwave and UHF/VHF signals far beyond the normal line-of-sight, often for hundreds of miles.

Why the other choices are incorrect:
- A: Mountain ranges — While terrain can influence local temperature inversions, mountains tend to disrupt the smooth, layered structure needed for stable ducts. Ducting is far more common and persistent over flat, uniform water surfaces.
- B and D: Stratocumulus clouds, Nimbus clouds — Clouds are not geographic features and are not the primary cause of ducting. Microwave propagation is governed by refractive index gradients in the clear-air troposphere; clouds/rain usually increase attenuation (especially above about 10 GHz) rather than promote ducting.

Useful formulas and rules of thumb:
- Refractivity (N-units) of air:
  $$N = (n - 1)\times 10^6 \approx 77.6\frac{P}{T} + 3.73\times 10^5\frac{e}{T^2}$$
  where:
  - $n$ = refractive index
  - $P$ = pressure (hPa)
  - $T$ = temperature (K)
  - $e$ = water vapor pressure (hPa)

- Ducting (trapping) occurs when the vertical gradient is sufficiently negative:
  $$\frac{dN}{dh} < -157\ \text{N-units/km}$$
  Superrefraction (enhanced bending) occurs for:
  $$-157 < \frac{dN}{dh} < -79\ \text{N-units/km}$$

- Standard atmosphere gives $k \approx 4/3$ effective Earth radius and extends the radio horizon. Strong ducting can far exceed this, especially over water.

- Practical cue: Evaporation ducts are common when warm, humid air overlies cooler water—often overnight and in the early morning—favoring microwave paths parallel to the water surface.