The Influence of the Climatic Peculiarities on the Electromagnetic Waves Attenuation in the Baltic Sea Region

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1 PIERS ONLINE, VOL. 4, NO. 3, The Influence of the Climatic Peculiarities on the Electromagnetic Waves Attenuation in the Baltic Sea Region M. Zilinskas 1,2, M. Tamosiunaite 2,3, S. Tamosiunas 2,3, and M. Tamosiuniene 4 1 Communications Regulatory Authority of the Republic of Lithuania Department of Radio Communication, Algirdo 27, LT Vilnius, Lithuania 2 Faculty of Physics, Vilnius University, Sauletekio 9, LT Vilnius, Lithuania 3 Institute of Materials Science and Applied Research, Vilnius University Sauletekio 9, LT Vilnius, Lithuania 4 Semiconductor Physics Institute, A. Gostauto 11, LT Vilnius, Lithuania Abstract The peculiarities of the climatic conditions in the Baltic Sea Region are reviewed. According to the values of rain rates measured in the Lithuanian Weather Stations with the 10- minute s integration time, a relation between the rain rate and the annual precipitation has been derived. The model for one-minute rain rate calculation on the months starting from May up to September in Lithuania has been presented. The values of the electromagnetic waves attenuation due to the rain have been determined. The cloud attenuation has been computed by using the meteorological data measured at the ground level. The semi empirical method has been used. The values of the specific attenuation under conditions of cloud cover have been determined. 1. INTRODUCTION Knowledge of the electromagnetic waves attenuation due to rain and clouds is desirable while planning the communication systems, especially at frequencies of 10 GHz and above. Most of the methodologies for the prediction of rain attenuation on radio waves paths require the knowledge of the rain rate R-value. Rain rate data is presented in units of length per unit time (in millimeters per hour), but in practice it is measured over intervals of typically one minute, five minutes, hour or yearlong. In [1], it was mentioned that the integration time t (time between the readings of the values of rainfall amount) is important parameter and it can change the R-value. Most of the rain attenuation prediction methods require one-minute rain rate value. One-minute rain rate (mm/h) is the rainfall for one minute (mm/min) multiplied by 60. Rainfall rate is highly variable. Therefore, the rain rate and rain attenuation are analyzed for concrete climatic conditions. However, the electromagnetic waves attenuation due to rain under the Baltic Sea Region climatic conditions has been analyzed not enough [2, 3]. The electromagnetic waves attenuation due the clouds, as far as we know, has been not analyzed under Lithuanian climatic conditions. The main goals of this paper were to determine the one-minute value of rain rate by using ten-minutes rainfall amount data measured in the Lithuanian Weather Stations and to estimate the values of the electromagnetic waves attenuation due to the rain and the clouds. 2. THE PECULIARITIES OF THE CLIMATIC CONDITIONS IN THE BALTIC SEA REGION The climate of Baltic Sea Region (BSR) is specific. BSR, being in the transition geography zone from Baltic Sea climate to Atlantic and continentals East Europe climate, may be distinguished for its variable climate. The average amount of precipitation in the BSR is 679 mm. The average nebulosity in the region is 50%. The minimal nebulosity (46%) occurs in spring [4]. The increase of nebulosity is going from north to south. In this paper we analyze Lithuanian climate more particularly. The climate of Lithuania is definable as middling cold, with the snowy winters. There are thaw days even in mid-winter. In Lithuania, humid weathers predominate all over the year. The annual precipitation in rainy wet year is almost twice higher than in dry year. The values of annual rainfall measured in the localities of Lithuania are presented in Table 1. The showers are observed in the warm period of the year. Such climate is typical climate of the middle part of the East Europe. The climate of the west part of Lithuania (for example, of Klaipeda) is specified as the moderate warm climate. The average temperature of the coldest month is more than 3 C. Such type of the climate is dominating in the West Europe. Vilnius is one of the cloudiest localities of Lithuania. There are about 100 overcast days in the year.

2 PIERS ONLINE, VOL. 4, NO. 3, Table 1: The values of annual rainfall (mm) measured in the Localities of Lithuania in the period of years Year Locality Vilnius Klaipeda ELECTROMAGNETIC WAVES ATTENUATION DUE TO RAIN One of the most accepted methods for prediction of rain attenuation is an empirical procedure based on the approximate relation between specific attenuation α (db/km) and the rain rate R (mm/h) [5]: α = ar b (1) where a and b are the functions of frequency f and rain temperature T. According to the ITU-R (the Radiocommunication Sector of the International Union) Recommendation, the rain rate R = 22 mm/h when the rain attenuation is determined in Lithuania and Latvia can be used. In [1] it was mentioned that the ITU-R value R = 22 mm/h is too low for prediction of the rain attenuation in Latvia. The events when the rain rate exceeds the value mentioned above were observed in Lithuania as well. We analyze the intense rain events in Vilnius in more detail (see Table 2). The values of very intense rain rates measured in Vilnius Weather Station in the period of years [6], the integration time and the percent of the time of the year are presented. The values of 10-minutes rain rates R 10 min 0.01% (mm/h), determined by using the data measured in Lithuanian Weather Station in Vilnius in the period of years , and the values converted to one-minute rain rate using method [7] R 1 min 0.01%.are presented in Table 3. About 60% of the annual rainfall amount falls in the warm period of the year in Lithuania. This fact must be taken into account when the rain attenuation is predicted in the localities of Lithuania. The review of results measured at the Weather Station in Vilnius shows that relation between the ten-minutes rain rate for 0.01% of time and the annual precipitation can be written as: R 10 min 0.01 = 3.23(γM r ) (2) where M r is the annual precipitation (mm) and γ is the coefficient of the warm period (γ = 0.6 in our case). The average value of the one-minute rain rate for 0.01% is 35.2 mm/h in Vilnius (in the period of years ) and it is by 1.6 times higher than the ITU-R value R = 22 mm/h. Table 2: The values of very intense rain rates R measured in Vilnius in the period of years [6]. R (mm/h) t (min) % of time Table 3: The values of R 10 min 0.01% (mm/h) and ones converted to one-minute rain rate R 1 min 0.01% using (3). Year R 10 min 0.01% (mm/h) R 10 min 0.01%, (mm/h) In [7], the relationship between one-minute rain rate for 0.01% of time and τ-minutes rain rate for 0.01% of time R (τ min) 0.01% is expressed as: R 1 min 0.01% = (R(τ min) 0.01% ) d (3)

3 PIERS ONLINE, VOL. 4, NO. 3, with d = 0987 (τ min) 0.061, where R (τ min) 0.01% exceeded during 0.01 percent of time for τ-minute integration time. Analysis of rainfall data in the localities of Lithuania shows that the events of heavy rainfall and showers happen frequently in the months of May September. During the warm period, the part of convectional precipitation in the general precipitation amount is 0.48 [4]. In light of these facts, the relationship presented in [8] under Lithuanian climatic conditions, may be written as: R(1 min) = [ln (0, 03 0, 48 M w/t)] 0, 03 (4) where M w is amount of rainfall during the months of May September, and t is the number of hours in a year when the value of rain rate exceeds the value R. The value of R 0.01% measured with 10-minute s integration time and the value of R 0.01% measured with 20-minute s integration time [4] were used in our calculations. The R (20 min)-value is maximum value of the rain rate on the event of 20 minutes duration when such event is recurring by one time in a year [4]. The values of R 1 min 0.01% determined using relations (3) and (4), and the values of α (for horizontal polarization) determined by using relationship (1), and the values of R 1 min 0.01%, mentioned above, are presented in Table 4. It was obtained, that the value of R (1 min) = 58.9 mm/h are by 67% higher than the average value of R (10 min) = 35.2 mm/h. Table 4: The values of R (1 min) obtained by using relations (3) and (4) and the values of α (f = 20 GHz). t (min) Relation (4) (3) (3) R (mm/h) α (db/km) ELECTROMAGNETIC WAVES ATTENUATION DUE TO CLOUDS In [5], the specific cloud attenuation α (db/km) was expressed as a function of the liquid water content M: α c = K c M. (5) The attenuation constant K c is the function of the frequency f and temperature T. The values of K c for pure water droplets are presented in [5]. M describes the mass of water drops in the volume units. In the cloud, M varies in the wide range. The knowledge of the liquid water content M is the main problem when using (5). The direct measurements of M at a point in space or averaged over the radio path are problematic. We have been determinating the attenuation due to clouds under Lithuanian climatic conditions for the first time. There was no possibility to measure the specific cloud attenuation as well as the liquid water content and temperature within the clouds. Considering these facts, the method, which required only the meteorological parameters measured at the ground level, was chosen. We used the basic idea of a model [9]: the water vapour in the atmosphere will lead to the formation of clouds whenever there is a possibility for condensation at some height h above ground level. It is mentioned in [9], that the condensation is possible when the water vapour concentration exceeds the saturation density ρ s at temperature T prevailing at that height. It is assumed in [9], that the water vapour density ρ(h) can be estimated from humidity measurements carried out at ground level. M is estimated as the difference between ρ and saturation density ρ s at cloud temperature. It is assumed that clouds are formed when M > 0. In [9, 10], it was considered that clouds are created starting in the vicinity of the height h of the 0 C isotherm and h (km). Relationship between the ground temperature T 0 (K) and the height h was presented in [9, 10]. The analysis of the cloud cover under the localities of Lithuania data shows that the [10] model can be used only in cases when the middle or high clouds will be formed. The cloud cover data in Vilnius on the April 2007 is presented in Table 5. According the Data of the Weather Station, in most cases the cloud base heights were of km (19 events). It is worth to mention that [10] model was suitable in almost all of the 19 cases mentioned above (h = km) whenever temperature at the ground level was t 10 C. When t 10 C, the values of h determined by using model [10] are over high. However, according to the Weather Station Data (see Table 6),

4 PIERS ONLINE, VOL. 4, NO. 3, in January 2007, in most cases, the low clouds with the cloud base height of m were formed over the localities of Lithuania (16 events); in one case, the humidity of 100% was at the ground level. It is evident that the relation between the h and the ground temperature T 0 presented in [10] is not suitable in the cases mentioned above. If a dew point and the temperature at the ground level are known, the value of h can be obtained by using a temperature lapse rate. Table 5: The values of the clouds base heights measured on April 2007 in Vilnius. Cloud base heigh, km N Table 6: The values of the clouds base heights measured on January 2007 in Vilnius. Cloud base heigh, km N Analysis of the cover data over the Lithuania shows, that the low clouds base height is near the height determined from the difference between the temperature at the ground level and the dew point temperature divided by the lapse of temperature (6.5 C). In the frequent events, the cumulonimbus clouds have been formed at the height of m; the cumulus clouds occur at the height of m. The review of data measured in the Weather Station shows that the use of the ITU-R vertical profiles of the atmosphere proposed in Recommendation ITU-R P for calculation of the clouds temperature must be revised before using under the Lithuanian climatic conditions. In our calculations, it was assumed, that the temperature within the cloud is near the dew point temperature. The temperature at height h is the temperature of the cloud in our study. The equation of state, assuming an adiabatic process [9] has been used for determination of the water vapour density ρ (h) at the height h. Using the values of the relative humidity H and the temperature at the ground level we have determined the water vapour density at the ground level. For example, in Vilnius, on 1 October 2007, there was the daily temperature of 3.9 C. The relative humidity at the ground level was H 0 = 90% on that day. The dew point temperature was t d = 2.4 C. The clouds have been formed at the height of 0.23 km. We obtained, that M = 0.9 g/m 3. According to data of Meteorological Weather Station, recorded when the stratocumulus clouds were formed over Vilnius, the cloud base height was about m. It is known, that the values of M for stratocumulus clouds varied starting from 0.3 up to 1.3 g/m 3 and the value of M = 0.9 g/m 3 is from the range mentioned above. The values of the α c, determined using the value M = 0.9 g/m 3 and relation (5), are presented in Table 7. Table 7: The values of specific cloud attenuation α c. f, GHz α c, db/km CONCLUSIONS It is a necessity to take the peculiarities of the Baltic Sea Region climate into account, when determining he values of the specific rain attenuation and cloud attenuation in this region. The ITU-R-value R = 22 mm/h is too low for prediction of the rain attenuation in Lithuania. The review of cloud data shows that relationship presented in [10] can be used for determination of the middle and high clouds base height under the Lithuanian climatic conditions. ACKNOWLEDGMENT The authors are grateful to the Direction of the Lithuanian Weather-Station for possibility to have a use of the data of the Archives of the Weather Stations.

5 PIERS ONLINE, VOL. 4, NO. 3, REFERENCES 1. Ivanovs, G. and D. Serdega, Rain intensity influence on to microwave line payback terms, Electronics and Electrical Engineering, No. 6 (70), 60 64, Tamosiunas, S., M. Zilinskas, M. Sileika, and M. Tamosiuniene, Revised model of attenuation of electromagnetic waves due to rain, Lithuanian Journal of Physics, Vol. 46, No. 4, , Zilinskas, M., S. Tamosiunas, and M. Tamosiuniene, Calculation of radio signal attenuation using annual precipitation and heavy rainfall data, Proceedings of 18th International Wroclaw Symposium and Exhibition on Electromagnetic Compatibility, , Wroclaw, Poland, June Pankauskas, M. and A. Bukantis, The dynamics of the Baltic Sea Region climate humidity in , Annales Geographicae, Vol. 39, No. 1, 5 14, Freeman, R. L., Radio System Design for Telecommunications, John Wiley & Sons, Inc., NewYork, Chichester, Weinheim, Brisbane, Singapore, Toronto, Bukantis, A., The Unusual Natural Phenomena in the Territory of Lithuania in the 11th 20th Centuries, Vilnius, 1998 (in Lithuanian). 7. Moupfouma, F. and L. Martin, Modelling of the rainfall rate cumulative distribution for the design of satellite and terrestrial communication systems, International J. of Satellite Comm., Vol. 13, No. 2, , Rice, P. L. and N. R. Holmberg, Cumulative time of surface-point rainfall rates, IEEE Trans. on Communications, Vol. 21, No. 10, , Dintelmann, F. and G. Ortgies, Semiempirical model for cloud attenuation prediction, Electronics Letters, Vol. 25, No. 22, , Ito, S., Dependence of 0 C isotherm height on temperature at ground level in rain, Trans. IEICE, Vol. E72, No. 2, , 1989.

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