MMW propagation in warm water evaporation ducts

Atmospheric radio refractivity N ≡ (n − 1)10
⁶
, with n is the index of refraction, is conventionally expressed ( e.g. B. Bean and E. Dutton, Radio Meteorology, Dover, 1968) as a function of the atmospheric thermodynamic parameters of pressure p (mbar), temperature T (°K) and water vapor pressure e (mbar) as N = 77.6(p/T + 4807e/T
²
). To account for propagation over a spherical earth, the modified refractivity profile M(z) = N(z) + 0.157z is employed, where z is the vertical coordinate in meters. Over water bodies, there can be substantial near-surface vertical gradients in the water vapor pressure e(z), going from a high value at the air-water interface to a lower value at higher altitudes. This causes a positive curvature region in the M-profile: (M″ = d
²
M(z) over dz
²
> 0) at some altitude z = Z
d
, separating a negative M-gradient (M′ < 0) region for 0 < z < Z
d
from a positive M-gradient region (M′ > 0) for z > Z
d
. The part of the M-profile between 0 < z < Z
d
is termed an evaporation duct. Using bulk flux models for the temperature and humidity fluxes and Monin Obhukov stability theory (MOST), a commonly used analytic evaporation duct M-profile model is the ln-linear form: M(z) = M0 + g[z − (Z
d
+ z
o
) ln(Z
d
/z
o
+ 1)], where M0 is the surface modified refractivity, g is a gradient and z
o
is the aerodynamic roughness length. The significant parameters of the evaporation duct are the duct height Z
d
and the M-deficit ΔM = M
0
−M(Z
d
).