Journal of Atmospheric Electricity, Vol.34, No.1, 2014, pp.9-19.

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1 Journal of Atmospheric Electricity, Vol.34, No.1, 2014, pp Terahertz Radio Waves Specific Attenuation Due to Rain with Small Raindrops Yu. I. Malyshenko and A. N. Roenko Usikov Institute for Radiophysics and Electronics, National Academy of Sciences of Ukraine, Kharkov, Ukraine Abstract. It is pointed out, that raindrop size distributions widely used to estimate theoretically the radio waves specific attenuation due to rain in the microwave range, inadequately represent the quantity of small raindrops. According to eperimental data for some geographical regions (for eample, Japan) the quantity of these raindrops is too large. This fact restricts the use of well known distributions in the terahertz range. So, taking into account small raindrops, the new distribution is proposed and the radio waves specific attenuation due to rain is estimated more precisely for mentioned and some other geographical regions. Key words: raindrops, drop size distribution, specific attenuation, terahertz range 1. Introduction Nowadays, the radio wave attenuation due to rain has been investigated well enough in both microwave (1 300 GHz) (Medhurst, 1965; Usikov et al. 1961; Recommendation ITU-R, 2005) and optical (Bisyarin and Sokolov, 1977; Sokolov, 1970) ranges. Practically no reliable theoretical and eperimental data have been found among them, in the vast area of terahertz frequencies, including submillimeter (submm) wave range, until now. It is caused by poor technical developments for this wave range and inaccuracy of theoretical forecasts, occurred, in our opinion, due to inadequate raindrop size distribution (DSD) functions, used for these forecasts (Sokolov and Sukhonin, 1970; Rozenberg, 1970; Sekine and Lind, 1982; Sayama and Sekine, 2002; Ishii et al. 2010). DSD is an important factor in meteorology of the rain and cloud formations. DSD N( D ) is entered into epressions for rain intensity and rain and 3 R 6 DN( D) D 3 cloud water content per unit volume W 6 water DN( D) D, where D and water Copyright 2014 by the Society of Atmospheric Electricity of Japan.

2 10 Yu.I.Malyshenko, et al.: Terahertz Attenuation are drop diameter and water density correspondingly. DSD significance also becomes clear, when considering formulas for specific attenuation and scattering due to rains as 4 att( ) 10 lg e N( Di) Catt(, D i) Di (db/km) and ( ) N( Di) radar(, Di) Di (1/m), where C (, ) att D i and radar (, D i ) are attenuation and scattering cross sections of the rain drops with diameters D i at wavelength. DSD describes the probability density function (pdf) of raindrop sizes. In other words, the histogram of raindrop sizes (normalized with respect to the total number of observed raindrops) converges to the pdf of raindrop sizes. DSD variability results from a comple combination of dynamics, thermodynamics and microphysics processes. While some DSDs are generated purely in the liquid phase, others are related to the various grows habits of snow crystals, graupel, and hail. Interactions between drops and the collection of cloud liquid water also generate changes in DSDs. There are some reliable and tested DSD (Marshall-Palmer (М-Р), Laws-Parsons (L-P), lognormal and gamma distributions) (Marshall and Palmer, 1948; Laws and Parsons, 1943; Best, 1950; Cerro et al. 1997; Feingold and Levin, 1986), that are widely used in the microwave range (Fig.1). But their application in a submm range is already incorrect, as Fig.1. Raindrop size distributions used in the microwave range for different rain intensity values R (1 Best, 2 M-P, 3-6 L-P, lognormal and gamma distributions). they don t contain the data for small raindrops (with the diameters from 0,05 to 0,6 mm). The root cause is the absence of technical means to record and study such small raindrops at the time when these distributions were formulated. At microwave wavelengths, the inaccuracy of distributions mentioned above is not clear

3 Yu.I.Malyshenko, et al.: Terahertz Attenuation 11 enough. Here, small raindrops are considerably smaller than the wavelength and they can be ignored. At the same time at terahertz frequencies it is necessary to consider the small raindrops data, because their sizes coincide eactly with the wavelength, well-known Mie resonances appear and influence sufficiently on electromagnetic radiation. Evidently, this fact is confirmed by the Watson (1977) numeral eperiment for a hypothetical rain, consisting of small drops only, carried from the millimeter (mm) wave range into the submm one. It shows (Fig.2 Malyshenko and Roenko, 2009), that the contribution of small drops to a specific attenuation is comparable with the larger drops one. In particular, it emphasizes that the usage of the spherical raindrop model is more correct at submm wavelengths than at microwave ones. The contribution of a priori aspherical large drops into polydisperse specific cross section of rain is substantially smaller than the increasing contribution of small and middle raindrops, with the form tending to a sphere. 2. Method of Study and Calculation Results In the terahertz range, it is necessary to consider small raindrops. However, there is not enough such eperimental data. Mostly it is caused by the difficulties in recording and calculating small drops in cuvettes with a castor oil. This method, proposed by Polyakova and Shifrin (1953), was improved later in Japan (Ugai and Kato, 1977) and China (Huang and Wang, 1989). Ugai and Kato (1977) have measured more than 1000 size spectrums of small and middle raindrops at rain intensities up to 50 mm/h (Fig.2). Fig.2. Eperimental results and their approimations for different R values (Ugai and Kato, 1977). In the present study, these data were used as references. They were grouped in four

4 12 Yu.I.Malyshenko, et al.: Terahertz Attenuation rain intensity values R (50; 12,5; 2,5 and 1,25 mm/h) and approimated by power functions N( D ) 10, where is presented by the 5 th degree polynomials 5 0 i i. Approimation function coefficients for each rain intensity value are i 1 D shown in Table 1. Table 1. Approimation function coefficients for each rain intensity value. R, mm/h ,25 3, , , , , ,148 2,5 4, , , , , , ,5 5, , , , , , , , , , , ,06992 It is necessary to note that mentioned earlier distributions, widely used in the microwave range and supplemented by the small drop fractions from Ugai and Kato (1977), become essentially complete and self sufficient. Such complete distribution with lognormal DSD for large drops was proposed by Malyshenko and Roenko (2009). However, for obtaining the smoothest resulting curves for DSD, it was decided to use the L-P distribution instead of the lognormal one. In this work the L-P distribution epression is not taken in the de Wolf (2006) release, but was calculated on the base of the original data from Laws and Parsons (1943). For convenience in further use, the obtained dependences (L-P distribution) were approimated in the above mentioned manner with coefficients shown in Table 2 for each value of rain intensity R. Table 2. Approimation function coefficients for L-P distribution. R, mm/h ,25 3, ,1952-0, , , , ,5 3, , ,5565 0, , , ,5 3, , , , , , , , , ,3708 0, ,00285 Fig.3 illustrates the resulting DSD curve, with complete spectrum of drop sizes, consisting of Ugai and Kato (1977) data (up to the first intersection point) and L-P distribution approimation for middle and large drops at rain intensity value R = 50 mm/h.

5 Yu.I.Malyshenko, et al.: Terahertz Attenuation 13 Fig.3. L-P distribution (Laws and Parsons, 1943) (curve 1) and Ugai and Kato (1977) results approimation at rain intensity value R = 50 mm/h (curve 2). New curves for each value of rain intensity R (Fig.4) were approimated in the above mentioned manner with coefficients shown in Table 3. Fig.4. Proposed distributions approimations at different values of rain intensity R : 1 50 mm/h; 2 12,5 mm/h; 3 2,5 mm/h; 4 1,25 mm/h Now, using the obtained distributions (Fig.4) and the values of water comple permittivity in submm wave range presented earlier by Malyshenko et al. (2007), it becomes possible to specify the theoretical forecasts (Sokolov and Sukhonin, 1970; Rozenberg, 1970; Sekine and Lind, 1982; Sayama and Sekine, 2002), regarding the rain influence on submm radiation, more precisely.

6 14 Yu.I.Malyshenko, et al.: Terahertz Attenuation Table 3. Approimation function coefficients for new distributions. R, mm/h ,25 3, , , , , , ,5 3, , , , ,0221-0, ,5 4, ,4707 1, , , , , ,1273 3, , , ,00716 Calculation results of attenuation factors due to rain at 20 С temperature are presented in the Tables 4 and 5. Table 4. Calculated and eperimental values of attenuation factors at rain intensity values R = 1,25 mm/h and R = 2,5 mm/h. F, GHz Attenuation, db/km, at R = 1,25 mm/h Attenuation, db/km, at R = 2,5 mm/h Calculation Eperiment Calculation Eperiment 37,5 0,30 0,32 0,36 Asen and Tjelta, 2003) 0,60 0,65 0,72 Sekine et al. 2007) 1,5 1,7 0,85 0, ,75 1,37 (Asen and Tjelta, 2003) Asen and Tjelta, 2003) 100 1,30 1,1 1,4 Zhao and Li, 2006) 2,18 1,9 2,3 (Zhao and Li, 2006; Ho, 1978) 200 1,67 1,4 1,65 2,2 2,6 2,73 (Sekine et al. 2007) (Sekine et al. 2007) 300 1,69 1,3 1,6 2,0 2,5 2,77 (Babkin et al. 1970) (Babkin et al. 1970) 360 1,65 2, ,59 2, ,49 1,6 (Zlewellyn-Jones and Zavody, 1971) 2,47 2,6 (Zlewellyn-Jones and Zavody, 1971) ,35 2,25 The figures 5 and 6 show the dependences of specific attenuation due to rain of submm

7 Yu.I.Malyshenko, et al.: Terahertz Attenuation 15 radiation at rain intensity values R = 12,5 mm/h and R = 50 mm/h. The curves 1, 2 and 3 were taken from Sekine and Lind (1982), Sukhonin (2002) and Recommendation ITU-R (2005) correspondingly, the curve 4 is calculated by the authors for L-P distribution added with data on small drops from Ugai and Kato (1977). Points ( ) in Fig.5 and Fig.6 represent the eperimental data from the references. Table 5. Calculated and eperimental values of attenuation factors at rain intensity values R = 12,5 mm/h and R = 50 mm/h. Attenuation, db/km, at R = 12,5 mm/h Attenuation, db/km, at R = 50 mm/h F, GHz Calculation Eperiment Calculation Eperiment 37,5 3, , , , ,92 2,9 3, ,5 (Babkin et al. 1970; 11,75 Norbury and White, 1972; Gibbins and Carter, 1987; Watson, 1976) Norbury and White, 1972) 5,8 6, ,48 Asen and Tjelta, 2003) 6,5 8 19,95 Zhao and Li, 2006; [35] 7,8 8,8 (Vakser and Malyshenko, 23, ) 6,5 8,0 24,97 (Babkin et al. 1970) 360 8,81 24, ,67 25, ,25 9,1 (Zlewellyn-Jones and Zavody, 1971) 24, ,51 22,13 Asen and Tjelta, 2003) Utsunomiya and Sekine, 2005; Zhao and Li, 2006;) (Babkin et al. 1970) (Babkin et al. 1970) 23,5 (Zlewellyn-Jones and Zavody, 1971)

8 16 Yu.I.Malyshenko, et al.: Terahertz Attenuation Fig.5. Specific attenuation due to rain of submm radiation at rain intensity value R =12,5 mm/h Fig.6. Specific attenuation due to rain of submm radiation at rain intensity value R =50 mm/h 3. Summary For terahertz range, a new raindrop size distribution N( D ) is proposed. This distribution is based on the published eperimental data of Ugai and Kato (1977) in the area of small drops and is represented by the original L-P distribution (Laws and Parsons, 1943) in the area of middle and large drops. Taking into account the small drops leads to increasing of the attenuation factors in terahertz and short millimeter wave ranges. The calculations conducted gave a satisfactory coincidence with the eisted eperimental data at different values of rain intensity R.

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