*2.1. Atmospheric Duct Model*

The atmospheric duct structure is described by a modified refractive index that varies with height. When the modified refractive index has a negative gradient, the atmospheric duct phenomenon appears [21].

$$M = N + \frac{h}{r\_{\varepsilon}} \times 10^6\tag{1}$$

$$N = \frac{77.6}{T} \times (P + \frac{4810c}{T}) \tag{2}$$

where *re*, *P*, *T*, and *e* are the average Earth radius, the atmospheric pressure, absolute temperature, and water vapor partial pressure at height *h* from the ground. The units for *P*, *T*, and *e* are kPa, K and kPa.

The surface duct model is a two-parameter model:

$$M(z) = \begin{cases} M\_0 - \frac{M\_d}{\tilde{z}\_t} z & 0 \le z \le z\_t \\ M\_0 - \frac{M\_d}{\tilde{z}\_t} z + 0.118z & z \ge z\_t \end{cases} \tag{3}$$

where *zt* is surface duct height, *Md* is surface duct strength, and *M*0 is the modified refractive index of surface or sea surface. The elevated duct model is a four-parameter model [22] expressed in Equation (4) as shown below:

$$M(z) = M\_0 + \begin{cases} kz & 0 \le z \le z\_b \\ kz\_b - \frac{M\_d}{z\_l}(z - z\_b) & z\_b \le z \le z\_b + z\_l \\ kz\_b - M\_d + 0.118(z - z\_b - z\_l) & z \ge z\_b + z\_l \end{cases} \tag{4}$$

where *k* is the foundation layer slope, *<sup>M</sup>*(*z*) is the modified refractive index at height *z*, *zb* is the trapped layer bottom height, *zt* is the trapped layer thickness, and *Md* is elevated duct strength. The structure diagram of the surface duct and elevated duct is shown in Figure 2.

**Figure 2.** Elevated duct and surface duct structure diagram ((**a**) is the elevated duct structure diagram; (**b**) is the surface duct structure diagram).
