At frequencies of the order of 100 GHz and above, attenuation due to fog may be significant. Typical water content for different fog types are listed in table 6.5. Table 6.4: Typical liquid water density of fog types [5.5] Fog type Typical liquid water density in g/m3 medium fog (visibility of the order of 0.05 300 m) thick fog (visibility of the order of 0.5 50 m) A mathematical model based on Rayleigh scattering, which uses a double-Debye model for the dielectric permittivity ( ) of water, can be used to calculate the value of for frequencies up to f Kl 1 000 GHz: (dB/km)/(g/m3) (5.13) is the frequency (GHz), and: f (5.14) The complex dielectric permittivity of is given by: (5.15) (5.16) where: = 77.66 + 103.3 ( 1) (5.17) – 0 = 0.0671 (5.18) 1 = 3.52 (5.19) 2 = 300 / (5.20) T with being the temperature (K). The principal and secondary relaxation frequencies are: T = 20.20 146 ( 1) + 316 ( 1)2 GHz (5.21) fp – – – = 39.8fp GHz (5.22) fs In [5.6] some values for the average liquid content of clouds are given, see table 6.5 Table 6.5: Liquid water content of cloud types [5.6] Cloud type Average content in g/m3 large cumulus 2.5 fair weather cumulus 0.5 Stratocumulus 0.2 Stratus 0.2-0.3 Altostratus 0.2
At frequencies of the order of 100 GHz and above, attenuation due to fog may be significant. Typical water content for different fog types are listed in table 6.5. Table 6.4: Typical liquid water density of fog types [5.5] Fog type Typical liquid water density in g/m3 medium fog (visibility of the order of 300 m) 0.05 thick fog (visibility of the order of 50 m) 0.5 A mathematical model based on Rayleigh scattering, which uses a double-Debye model for the dielectric permittivity ( f ) of water, can be used to calculate the value of Kl for frequencies up to 1 000 GHz: (dB/km)/(g/m3) (5.13) f is the frequency (GHz), and: (5.14) The complex dielectric permittivity of is given by: (5.15) (5.16) where: 0 = 77.66 + 103.3 ( – 1) (5.17) 1 = 0.0671 (5.18) 2 = 3.52 (5.19) = 300 / T (5.20) with T being the temperature (K). The principal and secondary relaxation frequencies are: fp = 20.20 – 146 ( – 1) + 316 ( – 1)2 GHz (5.21) fs = 39.8fp GHz (5.22) In [5.6] some values for the average liquid content of clouds are given, see table 6.5 Table 6.5: Liquid water content of cloud types [5.6] Cloud type Average content in g/m3 large cumulus 2.5 fair weather cumulus 0.5 Stratocumulus 0.2 Stratus 0.2-0.3 Altostratus 0.2