Atmospheric Attenuation due to Humidity (Electromagnetic Waves) Part 2

Calculation of the specific cloud attenuation

The specific cloud attenuation is a function of clouds’ liquid water content and a coefficient, which is a function of frequency and temperature. In this case, the main problem is the value of clouds’ water content, because the direct measurements at a point in space are problematic. In cases when such data is unavailable, models that require only the meteorological parameters, measured at ground level, can be used. These models are based on the fact that the condensation is possible when the water vapour concentration exceeds the saturation density at the temperature, which is prevailing at that height. The water vapour density can be estimated from the humidity measurements carried out at ground level. The cloud’s water content value can be estimated as the difference between water vapour concentration and saturation density at cloud temperature. The specific cloud attenuation is, unlike the case of rain, independent of drop-size distribution (Freeman, 2007). Several cloud attenuation models were developed. In (Freeman, 2007), the specific cloud attenuation was expressed as the function of liquid water content M:

where KC is the attenuation constant.

The attenuation constant KC is the function of frequency f and temperature T. The values of KC for pure water droplets are presented in (Freeman, 2007). The values of KC for salt-water droplets (over the sea and ocean surfaces) are higher. The necessity to know M value is limiting the direct use of relationship (10).

Often there are no possibility to measure the liquid water content and temperature within the clouds. In such cases the methods that require only meteorological parameters measured at the ground level may be used. The basic idea of such models (Dintelmann &Ortgies, 1989) is that the water vapour in the atmosphere would lead to the formation of clouds whenever there would be a possibility for condensation at some height h above ground level. There is also mentioned that the condensation is possible when the water vapour density p exceeds the saturation density ps at temperature T prevailing at that height. It is assumed that the water vapour density p can be estimated from humidity measurements carried out at ground level.

The height at which cloud exists is very important for accurate determination of results of attenuation due to clouds (Sarkar et al., 2005). It was assumed in (Ito, 1989, as cited in Dintelmann &Ortgies, 1989) that clouds are created starting in the vicinity of the height h, and h [km] follows ground temperature T0 [K] as:

Relation (11) is based on analysis of temperature profiles in rain and on the Aerological Data of Japan and we have specified the applicability of this relation in the territory of Lithuania. The condensed water content M is estimated as the difference between p and saturation density ps at cloud temperature (Dintelmann & Ortgies, 1989):

where ps [g/m3] is the saturated vapour density.

It is assumed that clouds are formed when M >0. As mentioned above, the determination of the water content value M is complicated. Its values differ in each group of the clouds (the clouds are grouped according to their shape, height, and structure). In our calculations, the main problem was determination of M. According to (Dintelmann & Ortgies, 1989), the values of water vapour density p at the height h can be estimated from the equation of state, assuming an adiabatic process:

where p0 is the water vapour density at the ground level, T0 is the ground level temperature, T is the absolute temperature in the vicinity of h, denotes the specific heat ratio which is 4/3 for the water vapour molecule, p is the water molar mass, g is the acceleration due to gravity, h is the height, and R is the fundamental gas constant. The values of p0 can be determined by using known relations (Freeman, 2007).

We assume that the clouds are created starting in the vicinity of the height h. We determine the values of h by using relation (11) or the data of the dew point temperature, temperature at the ground level, and the temperature gradient of 6.5°C/km (Rec. ITU-R P. P.835-3, 2004). The values of h obtained here we compared to the cloud base height values measured at the weather stations (see Table 1). The analysis of the cloud cover over the localities of Lithuania data shows that the relationship (11) can be used only in the cases when the middle or high clouds are formed over those localities.

To [K]	Cloud base height (data of weather stations)	Cloud base height (equation 11)
280.1	0.6-1.0	2.06
280.1	2.0-2.5	2.06
280.4	2.0-2.5	2.11
281.5	2.0-2.5	2.29
281.6	2.0-2.5	2.31
282.6	2.0-2.5	2.47
284.4	2.0-2.5	2.77

Table 1. Temperature at the ground level and the values of the cloud base heights (data of weather station) in Vilnius in April 2007, as well as the height h determined using equation (8) (Tamosiunaite et al., 2008).

Attenuation due to fog

The influence of the fog on the attenuation of the electromagnetic waves can to lead to the perturbation of the wireless communication. In (Chen et al., 2004), it was mentioned that fog may be one of dominant factors in determination of the reliability of millimeter wave systems, especially in coastal areas, where dense moist fog with high liquid water content happen frequently. Fog results from the condensation of atmospheric water vapour into water droplets that remain suspended in air (Freeman, 2007). Moist fog frequently appears over the localities of Lithuania (Tamosiunas et al., 2009). There are several meteorological mechanisms for determination whether fog will form and of degree of its intensity. The physical mechanism of the formation of the fog can be reduced to three processes: cooling, moistening, and vertical mixing of air parcels with different temperatures and humidity (Duynkerke et al., 1991). All three processes can occur, although one meteorological mechanism may dominate. This circumstance leads to the different types of the fog. In (Galati et. al., 2006), the fog is classified in four types: strong advection fog, light advection fog, strong radiation fog, and light radiation fog.

The calculation methods for determination of fog attenuation are used in many cases. The propagation properties for microwave and millimeter-wave frequencies at the foggy air conditions were examined in (Liebe et. al, 1989). The values of the specific attenuation were derived from a complex refractivity based on the Rayleigh absorption approximation of Mie’s scattering theory. In (Liebe et. al, 1989), the particle mass content and permittivity, which depends on the frequency and the temperature, were key variables. Attenuation due to fog is a complex function of the particle size distribution, density, extent, index of refraction, and wavelength (Altshuler, 1984). Normalized fog attenuation directly, given only the wavelength and fog temperature is presented in (Altshuler, 1984):

where A is attenuation in [(dB/km)/(g/m3)], X is wavelength in [mm], t is temperature in [°C]; the relation (14) is valid only for 3 mm< X <3 cm and -8°C< T < 25°C. It was mentioned in (Altshuler, 1984], that the total fog attenuation could be obtained by multiplying the normalized attenuation by the fog density in [g/m3] and the fog extent in [km]. In (Zhao &Wu, 2000), it was mentioned that fog is often characterized by the visibility and the visibility is defined as the greatest distance at which it is just possible for an observer to see a prominent dark object against the sky at the horizon.

Attenuation due to fog can be expressed in terms of the water content M, and the microstructure of the fog can be ignored (Galati et al., 2000). In (Altshuler, 1984), the empirical formula for fog visibility as a function of fog density was derived:

where V is the visibility in [km] and M is the liquid water content in [g/ m3]. It was mentioned in (Altshuler, 1984), that the empirical formula (15) is valid for drop diameter between 0.3 ^m and 10 ^m. For the case of dense haze or other special type fogs, it is recommended to replace the coefficient 0.024 with 0.017 (Altshuler, 1984). If the visibility data are available, but the fog density data are not available, the following expression may be used (Altshuler, 1984):

In (Chen et al., 2004; Galati et al., 2006; Recommendation ITU-R PN 840-4, 2009), based on the Rayleigh approximation, the specific attenuation due to the fog afog has been written as:

where K is specific attenuation coefficient.

where d =300/T, f is frequency, and T is temperature [K].

V, km	M, g/m3
0.1	0.111
0.2	0.038
0.3	0.020
0.5	0.010
1.0	0.003

Table 2. The values of visibility V measured in the localities of Lithuania and the values of fog water content M (Tamosiunas et al., 2009).

The values of the visibility measured in the localities of Lithuania and the values of fog water content M determined using (16) are presented in Table 2. The highest value of the specific fog attenuation determined using M-data presented in Table 2 was 0.59 dB/km. In (Naveen Kumar Chaudhary et al., 2011), it was concluded, that the link reliability can be improved by increasing the transmission power or using high gain directional antennas in the cases when the foggy conditions occur and the visibility is less than 500 meters. For the same value of visibility, the fog attenuation decreases when the temperature increases (Naveen Kumar Chaudhary et al., 2011).

Radio refractive index and its variability

The atmospheric refractive index is the ratio of the velocity of propagating electromagnetic wave in free space and its velocity in a specific medium (Freeman, 2007). The value of the atmosphere’s refractive index is very close to the unit. Furthermore, changes of the refractive index value are very small in time and space. In the aim to make those changes more noticeable, the term of refractivity is used. It is a function of temperature, atmospheric pressure and partial vapour pressure. The value of the refractivity is about million times greater than the value of refractive index.

In design of the radio communication networks, it is important to know the atmospheric radio refractive index. The path of a radio ray becomes curved when the radio wave propagates through the Earth’s atmosphere due to the variations in the atmospheric refractivity index along its trajectory (Freeman, 2007). Refractivity of the atmosphere affects not only the curvature of the radio ray path but also gives some insight into the fading phenomenon. The anomalous electromagnetic wave propagation can be a problem for radars because the variation of the refractive index can induce loss of radar coverage (Norland, 2006). In practice, the propagation conditions are more complicated in comparison with the conditions predictable in design of radio system in most cases. The anomalous propagation is due to the variations of the humidity, temperature and pressure at the atmosphere that cause variations in the refractive index (Norland, 2006). The climatic conditions are very changeable and unstable in Lithuania (Pankauskas & Bukantis, 2006). The territory of Lithuania belongs to the area where there is the excess of moisture. The relative humidity is about 70% in spring and summer while in winter it is as high as 85 – 90% (Bagdonas & Karaleviciene, 1987). Lithuanian climate is also characterized by large temperature fluctuations. Difference between the warmest and coldest months is 21.8°C (Pankauskas & Bukantis, 2006). It was noted in (Priestley & Hill, 1985; Kablak, 2007) that even small changes of temperature, humidity and partial water vapour pressure lead to changes in the atmospheric refractive index. In (Zilinskas et al., 2008), the measurements of these meteorological parameters were analyzed in the different time of year and different time of day. The values of the refractive index have been determined by using measured meteorological data. In (Zilinskas et al., 2010), it was mentioned that seasonal variation of refractivity gradient could cause microwave systems unavailability.

Calculation of radio refractivity

As mentioned above, the value of the radio refractive index, n, is very close to the unit and changes in this value are very small in the time and in the space. With the aim to make those changes more noticeable, the term of radio refractivity, N, is used (Freeman, 2007; Rec. ITU-R P. 453-9, 2003):

According to the recommendation of ITU -R (Rec. ITU-R P. 453-9, 2003):

where T [K] is a temperature; p [hPa] is the atmospheric pressure; e [hPa] is partial water vapour pressure. The refractivity is expressed in N – units.

It was mentioned in (Freeman, 2007; Rec. ITU-R P. 453-9, 2003), that expression (21) may be used for all radio frequencies; for frequencies up to 100 GHz, the error is less than 0.5%. There are two terms (the "dry term" and the "wet term") in relationship (21). The values of the refractivity N in Lithuania were determined by using (21). The data of temperature, humidity, and atmospheric pressure were taken from a meteorological data website (http://rp5.ru).

Fig. 3. The dependences of average N- values on the time of day in cities of Lithuania: Vilnius (curve 1), Mazeikiai (curve 2), Kaunas (curve 3), and Klaipeda (curve 4) in July 2008 (Valma, et al., 2010).

The dependences of average N-values on the time of day in cities of Lithuania are presented in Fig. 3. As can be seen, the behaviours of those dependences at the diurnal time are similar in all localities that are situated in the Continental part of Lithuania (Vilnius, Kaunas and Mazeikiai) and slightly different in Seacoast (Klaipeda). The climate of Klaipeda is moderate and warm (Pankauskas &Bukantis, 2006; Zilinskas et al., 2008). The climate of Continental part of Lithuania is typical climate of the middle part of the Eastern Europe. This may explain the difference between the daily variations of N in Klaipeda and in other localities analyzed here. In Lithuania, the highest N-values were in July.

Conclusions

The main models for calculation of electromagnetic wave attenuation due to atmosphere humidity were revised. In Lithuania, when the reliability of the radio system of 99,99% is required, the R(1 min)-value is R(1 min) = 60.23 mm/h. It is twice the ITU-R recommended value. The dependency of the average specific electromagnetic wave attenuation due to rain on the operating frequency (0-100 GHz) was determined. The attenuation of horizontally polarized electromagnetic waves is greater than the attenuation of vertically polarized electromagnetic waves. In cases when the required reliability of the radio system is other than 99,99%, the "Worst-month" model can be used. However, for small R(1 min)-values the parameters of that model should be corrected. In Vilnius, the city of Lithuania, when R(1 min) > 34mm/h, ITU-R recommended values Q1 = 2.82 and P = 0.15 could be used. In cases when R(1 min) < 34mm/h, the corrected values Q1 = 2 and P = 0.03 are more appropriate.

The main problem of models for calculation of electromagnetic wave attenuation due to clouds and fog is the required value of liquid water content. In Lithuania it is impossible to gather such meteorological information. Therefore, models excluding or calculating the liquid water content were revised. The variations of the atmospheric humidity, temperature and pressure can cause the fluctuations of the atmospheric refractive index. In Lithuania, the atmosphere refractive index fluctuates most in July. The variations of N in diurnal time are similar in all localities that are situated in the Continental part of Lithuania and slightly different in Seacoast.