The Influence of Fog on the Propagation of the Electromagnetic Waves under Lithuanian Climate Conditions

PIERS ONLINE, VOL. 5, NO. 6, 2009 576 The Influence of Fog on the Propagation of the Electromagnetic Waves under Lithuanian Climate Conditions S. Tamosiunas 1, 2, M. Tamosiunaite 1, 2, M. Zilinskas 1, 3, and M. Tamosiuniene 4 1 Faculty of Physics, Vilnius University, Sauletekio 9, LT-10222 Vilnius, Lithuania 2 Institute of Materials Science and Applied Research, Vilnius University Sauletekio 9, LT-10222 Vilnius, Lithuania 3 Department of Radio Communication Communications Regulatory Authority of the Republic of Lithuania Algirdo 27, LT-03219 Vilnius, Lithuania 4 Semiconductor Physics Institute, A. Gostauto 11, LT-01108 Vilnius, Lithuania Abstract The types of fog and the existing methods of calculation of the electromagnetic waves attenuation due to fog are reviewed. The meteorological data, which was measured in the localities of Lithuania, has been analyzed. According to this data, the specific attenuation due to fog has been computed under the Lithuanian climatic conditions. The models that have been used in calculations of fog attenuation are based on the liquid water content and optical visibility. 1. INTRODUCTION Moist fog frequently appears over the localities of Lithuania. The influence of fog on the attenuation of the electromagnetic waves can lead to the perturbation of the wireless communication. In [1], it was mentioned that fog may be one of dominant factors in determining 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 vapor into water droplets that remain suspended in air [2]. Fog can be characterized by water content, optical visibility, drop size distribution and temperature [1, 3]. Several meteorological mechanisms will determine whether fog will form and degree of its intensity. There were observed a strong influence of wind, turbulence, radiation, surface configuration and wetness on the fog formation. 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; all three processes can occur, although one meteorological mechanism may dominate [4]. This circumstance leads to the different types of the fog. There are several types of fog. The main types of fog are the advection fog and the radiation one [3, 5]. Both types of fog differ in the location and in the methods of formation. In [6], the fog is classified in four types: strong advection fog, light advection fog, strong radiation fog, and light radiation fog. Radiation fog forms when the ground becomes cold at night and cools the adjacent air mass until it becomes supersaturated. Advection fog forms when warm moist air moves across a cooler surface [5, 7]. The influence of the local factors in the formation of radiation fog was studied in [3, 5]. In [7], it was mentioned that average drop size of an advection fog is usually larger than that of a radiation fog. The advection fog is coastal fog, and the radiation fog is inland fog. The advection fog may cover the hundred thousands of kilometers. The advection fog has no cleared away even by day. The water vapor content of fog varies from less than 0.4 up to as much as 1 g/m 3 ; typical liquid water content values for the fog vary from 0.1 to 0.2 g/m 3 [2]. There are many foggy days in a year in Lithuania. In the year 1958, there were 100 122 foggy days in the North and in the East Lithuania, and there were 130 141 foggy days in Samogitian Hill. There were 107 113 foggy days in Samogitian Hill in the year 1964. There were 20 foggy days in July of 1977 year in Vilnius. This month was the foggiest month from the year 1875 in Vilnius. The visibility was only 100 meters on 15 17 October 1991. Even on 18 hours the moist fog covers Varena in 2 3 November 1984. On 15 hours the moist fog covers the Airport of Vilnius in 9 10 March 1994. In light of these facts, it is necessary to analyze the influence of the fog on the attenuation of electromagnetic waves when the telecommunication systems are planning in Lithuania. In [8], the values of the electromagnetic waves attenuation due to the rain and clouds have been determined by using the meteorological data measured at the ground level in the localities

PIERS ONLINE, VOL. 5, NO. 6, 2009 577 of Lithuania. However, the influence of fog on the propagation properties of the electromagnetic waves at the Lithuanian climatic conditions as far, as we know, has been no examined yet. The main goals of the paper were to analyze the fog events in Lithuania, to review the methods for determining fog attenuation, and to apply them for the calculation of the fog attenuation under the Lithuanian climatic conditions. 2. CALCULATION METHODS FOR DETERMINING OF FOG ATTENUATION The calculation methods for determining of fog attenuation are frequently used. In [9], a onedimensional radiation fog model, which includes a detail description of the interaction between atmospheric radiative transfer and the microphysical structure of the fog was presented. In [10] model, attenuation due to clouds and fog was expressed in terms of the water content, and was mentioned that microstructure of the fog can be ignored for fog consisting entirely of small droplets at frequencies below 200 GHz. The parameters of gamma drop size distribution model of fog and clouds are derived based on the liquid water content and optical visibility in [6] and [10]. The propagation properties for microwave and millimeter-wave frequencies at the foggy air conditions were examined in [11]. The values of the specific attenuation were derived from a complex refractivity based on the Rayleigh absorption approximation of Mie s scattering theory. In [11], 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 density, extent, index of refraction, and wavelength. Normalized fog attenuation directly, given only the wavelength and fog temperature is presented in [7]: A = 1.347 + 0.0372λ + 18.0/λ 0.022t (1) where A is attenuation in (db/km)/(g/m 3 ), λ is wavelength in mm, t is temperature in C. The relation (1) is valid only if 3 mm < λ < 3 cm and 8 C < T < 25 C. It was mentioned in [7], that the total fog attenuation could be obtained by multiplying the normalized attenuation by the fog density in g/m 3 and the fog extent in km. Fog is often characterized by the visibility. 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 in [7]. In [3], the visibility is defined as that distance from an observer at which a minimum contract ratio C between a black target and a bright background is equal to C = 0.02. It was noted in [12], that within each fog classification the liquid water content decreases as the visibility increases. The relation of visibility V (km) and optical attenuation α (db/km) was presented in [3]: V = 4.343/α ln 1/C = 16.99/α (2) In [7], the empirical formula for fog visibility as a function of fog density was derived: V = 0.024M 0.65 (3) where V is the visibility in km and M is the liquid water content in g/m 3. It was mentioned in [7], that the empirical formula (3) is valid for drop diameter between 0.3 µ and 10 µ. For the case of dense haze or other special type fogs, the coefficient 0.024 recommends be replaced by 0.017 in [11]. If the visibility data are available, but the fog density data are not available, the following expression may be used for fog [7, 12]: M = (0.024/V ) 1.54 (4) In [1, 6], and [10] based on the Rayleigh approximation, the specific attenuation due to the fog α fog has been written as: α fog = KM (db/km) (5) where K is specific attenuation coefficient expressed in db/km/g/m 3 : K = 6.0826 10 4 f 1.8963 θ γ (6) where γ = (7.8087 0.01565 f 3.0730 10 4 f 2 ), θ = 300/T, f is frequency (GHz), and T is temperature (K).

PIERS ONLINE, VOL. 5, NO. 6, 2009 578 3. RESULTS AND DISCUSSION Analysis of meteorological data measured in Lithuanian weather stations show, that the climate of Lithuania is variable and contrasting. Depending on the relief of locality, there are differences in the distribution of the foggy days. In average, there are 90 105 foggy days a year in the west slant of Samogitian Hill and there are 60 80 ones in the west slant of Baltic Hill [5]. Only 38 51 foggy days a year were registered in Lowland of Lithuania Mid. In Lithuania, November March are the foggiest months in a year. March May are the foggiest months in a year in Seacoast of Lithuania. However, there are least of all foggy days in May July in the other part of territory. In average, there are 350 650 foggy hours a year in Lithuania (most of them were observed in Samogitian Hill and in East of Lithuania) [5]. According to the data measured in Lithuanian weather stations, in average, there are 41 105 foggy days a year in Lithuania. 4 6 hours is the average duration of a fog event. However, the maximum duration of the fog event is several days. In Lithuania, according to the data of Lithuanian Hydrometeorological Service, the advection fog events consist 50 60% of all the fog events and the radiation ones consist 20 30% of all the fog events. By using (4) we determined M values in the cases when the values of visibility V (the data of visibility was taken from the website http://www.rp5.ru) were starting from 0.1 km up to 1 km (see Table 1). It is seen, that the M values various from 0.003 g/m 3 up to 0.111 g/m 3 in the localities of Lithuania. In March 2008 and February 2009, the Values of Visibility V Varied from 0.5 km up to 10 km in Klaipeda. Table 1: The values of fog water content M. V, km M (g/m 3 ) 0.1 0.111 0.2 0.038 0.3 0.020 0.5 0.010 1.0 0.003 Table 2: The duration τ of the periods with the different V in February 2009 in Klaipeda. V, km τ, hr % 0.5 27 4.0 2.0 3 0.5 4.0 222 33.0 10.0 351 52.3 Table 3: The duration τ of the periods with different V in March 2008 in Klaipeda. V, km τ, hr % 0.5 24 3.5 2.0 30 4.5 4.0 87 12.0 10.0 593 80.0 It is worth to mention, that the fog events with the visibility V 1 km were observed in afternoon and night in most cases in the localities of Lithuania. The values of visibility V on the 8th of October 2008 in Kaunas, Klaipeda, and Laukuva (Laukuva is the dampest locality of Lithuania; the average annual amount of precipitation is 820 mm) are presented in Table 4. It is clearly seen the difference in these values. The data of visibility observed in Lithuanian weather stations in that day show, that the strong fog (with the visibility of V = 0.1 km) was in Kaunas, Lazdijai, and in the vicinities of Vilnius. Almost all the territory of Lithuania swims in fog in most part of the night on 8th of October 2008. The visibility of 1 km or above was only over the Seacoasts and over the pinewood of Dzukija. The ideal conditions for formation of fog (high pressure, anticyclone (Indian summer) the bright sky at days, and high humidity) there were at days. When the sun was down, the water vapour condensed into the water drops. Such type of fog is a radiation one. The fog event with V = 0.5 km was observed in Laukuva on the 16th 18th of November 2006. The duration of this fog event was 45 hours (6.25% of the month time). Almost all the time the humidity was about 100% in this period. The average temperature of the period mentioned above was 6.2 C. There is the Geographical Centre of Europe near the city of Lithuania Vilnius and it was interesting to analyse the conditions of radio wave propagation in this locality. Analysis of meteorological data measured in Vilnius shows, that there were 267 foggy hours in the year 2008 (approximately 3% of the year time) when the visibilities V were of 0.3 1 km. The middle fog (the values of visibility were of 0.3 0.5 km) hovers over Vilnius 147 hours in the year 2008 (approximately 1.7% of the year time). February was the foggiest month in 2008 in Vilnius (63 hours). There were no foggy days in June of 2008 in Vilnius. Only 3 foggy hours were in March and August. The foggiest months were October February. It corresponds to the general tendency of weather in Lithuania.

PIERS ONLINE, VOL. 5, NO. 6, 2009 579 Table 4: The values of visibility V on 8th October 2008 in Kaunas, Klaipeda, and Laukuva. Locality Kaunas Klaipeda Laukuva Time V, km V, km V, km 21.00 0.2 10.0 10.0 18.00 20.0 10.0 10.0 15.00 10.0 10.0 10.0 12.00 0.2 10.0 10.0 09.00 0.2 4.0 10.0 06.00 0.1 4.0 0.5 03.00 0.5 4.0 0.5 00.00 0.5 4.0 4.0 Even 60 63 foggy hours there were in January, February, and November in Vilnius. There were often the foggy days a year with visibilities of 1 10 km in Vilnius (7173 hours); even 735 hours with visibilities from the range mentioned above were in December. In the morning of the 7th of November 2006, the moist fog covers Kaunas. The visibility V was only 0.2 km. The value of M = 0.038 g/m 3 was determined by using Eq. (4). As already was mentioned above, the data of visibility V varies in location. In Laukuva, there were 99 foggy hours in December 2008 when V = 0.5 km (13.3% of month time) and 3 hours when V = 1.0 km (in the other time, the visibility was above the value of V = 1.0 km). As already was mentioned above, the visibility varies in time. The data of visibility measured in December of 2008 in Siauliai confirms this proposition. The duration of the events with V = 20 km was 426 hours in this month. However, there were 15 hours with V = 0.5 km and even 27 hours with V = 0.2 km. On the 6th of December 2008, there was fog event with visibility of V = 0.2 km in Siauliai. The duration of this event was 18 hours except 3 hours within this period when the visibility value was of V = 0.5 km. Table 5: The number of hours with visibilities of V = 0.5 km in Laukuva. Year Jan Feb Mar April May Jun Jul Aug Sep Oct Nov Dec 2006 42 30 27 39 12 18 6 24 18 33 105 36 2007 6 9 132 12 9 9 12 24 24 147 60 2008 33 66 30 27 6 12 12 3 18 30 27 99 The visibility data shows that the visibility of V 0.5 km was on 366 hours a year (4.2% of time) in Laukuva and on 150 hours per year (1.7% of time) hours in Vilnius in 2008. The duration of fog events with visibilities V 1 km was of 273 hours (3.1% of year time) and total duration fog and mist events with V 10 km was of 507 hours (5.8% of year time) in the year 2008 in Vilnius. As far as we have been collected and analysed the visibility data in different localities of Lithuania, the least value of the visibility V = 0.1 km has been observed. The value M = 0.111,g/m 3 was obtained by using the relationship (4). By using relationship (1) and the meteorological data measured on 8th of October 2008 in Kaunas, we determined normalized fog attenuation A. The value of A = 5.31 db/km/g/m 3 was obtained when f = 90 GHz and t = 0.5 C. Since the visibility V = 0.1 km was in that night, we by using the value of A = 5.31 db/km/g/m 3 and the value of M = 0.111 (g/m 3 ) determined the specific fog attenuation A s. The value of A s = 0.589 db/km was obtained and it is the highest A s -value determined by using the visibility data analysed here. The least value of water content within fog is M = 0.003 g/m 3 and the minimum value A s = 0.0159 db/km has been determined. Fog is a cloudbank that is in contact with the ground [13]. Therefore, we determined the water content M at the height h = 5 m by using the semi empirical cloud attenuation model presented in [14, 15] and relationships proposed in [2]. We consider the fog event on 8th October 2008 in Kaunas (t = 0.5 C, H = 100%, V = 0.1 km). The value of M = 0.051 g/m 3 has been determined and it is lower than one determined using relationship (4). However, it is more near the value of 0.065 g/m 3 determined when the coefficient 0.024 in (4) was replaced by coefficient 0.017. It

PIERS ONLINE, VOL. 5, NO. 6, 2009 580 is worth to mention, that value of M = 0.051 g/m 3 was determined in that case when the height above the ground was 5 m and this value may be lower than one at the ground surface. 4. CONCLUSIONS The meteorological data measured in the localities of Lithuania have been analyzed. It was obtained, that the values of visibility varied starting from 0.1 km up to 1 km when fog has been formed under the localities of Lithuania. The differences in the values of visibility have been observed both in the locations and time. The total duration of strong and middle fog events with visibilities of V 0.5 km was 366 hours a year (4.2% of time) in 2008 in Laukuva and 150 hours a year (1.7% of time) in Vilnius. In Vilnius, the total duration of fog events with visibilities V 1 km was of 507 hours (5.8% of time). The least value of water content is M = 0.003 g/m 3 and the maximum one is 0.111 g/m 3. The highest A s -value determined by using the visibility data analysed here is A s = 0.589 db/km. The least value of water content is M = 0.003 g/m 3 and the minimum value A s = 0.0159 db/km has been determined. The value of the coefficient in relationship (4) will be specifying according the Lithuanian climate conditions when more meteorological data would be collected. REFERENCES 1. Chen, H., J. Dai and Y. Liu, Effect of fog and clouds on the image quality in millimeter communications, Int. J. of Infrared and Millimeter Waves, Vol. 25, No. 5, 749 757, 2004. 2. Freeman, R. L., Radio System Design for Telecommunications, John Wiley & Sons, Inc., New York, 2009. 3. Zhao, Z. and Z. Wu, Millimeter-wave attenuation due to fog and clouds, Int. J. of Infrared and Millimeter Waves, Vol. 21, No. 10, 1607 1615, 2000. 4. Duynkerke, P. G., Radiation fog: A comparison of model simulation with detailed observations, Monthly Weather Review, Vol. 119, 324 341, 1991. 5. Bukantis, A., The Unusual Natural Phenomena in the Territory of Lithuania in the 11th 20th centuries, Geography Institute, Vilnius, 1998 (in Lithuanian). 6. Galati, G., I. Dalmasso, G. Pavan, and G. Brogi, Fog detection using airport radar, Proceedings of International Radar Symposium IRS 2006, 209 212, Krakow, Poland, May 24 26, 2006. 7. Altshuler, E. E., A simple expression for estimating attenuation by fog at millimeter wavelengths, IEEE Trans. on Antennas and Propagation, Vol. 32, No. 7, 757 758, 1984. 8. Zilinskas, M., M. Tamosiunaite, S. Tamosiunas, and M. Tamosiuniene, The influence of the climatic peculiarities on the electromagnetic waves attenuation in the Baltic Sea region, PIERS ONLINE, Vol. 4, No. 3, 321 325, 2008. 9. Bott, A., U. Sievers, and W. Zdunkowski, A radiation fog model with a detailed treatment of the interaction between radiative transfer and fog microphysic, J. Atmospheric Sciences, Vol. 47, No. 18, 2153 2166, 1990. 10. Attenuation due to clouds and fog, ITU-R Recommendation PN 840 3, 1 7, 1999. 11. Liebe, H. J., T. Manabe, G. A. Liebe, and G. A. Hufford, Millimeter-wave attenuation and delay rates due to fog/cloud conditions, IEEE Trans. on Antennas and Propagation, Vol. 37, No. 12, 1617 1623 1989. 12. Eldridge, R. G., Haze and fog aerosol distributions, J. Atmospheric Sciences, Vol. 23, No. 5, 605 613, 1996. 13. http://en.wikipedia.org/wiki/fog. 14. Dintelmann, F. and G. Ortgies, Semiempirical model for cloud attenuation prediction, Electronics Letters, Vol. 25, No. 22, 1487 1488, 1989. 15. Tamosiunaite, M., S. Tamosiunas, M. Tamosiuniene, and M. Zilinskas, Influence of clouds on attenuation of electromagnetic waves, Lithuanian Journal of Physics, Vol. 48, No. 1, 65 72, 2008.