Weibull Raindrop-Size Distribution and its Application to Rain Attenuation from 30 GHz to 1000 GHz
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Weibull Raindrop-Size Distribution and its Application to Rain Attenuation from 30 GHz to 1000 GHz M. Sekine & S. Ishii & S. I. Hwang & S. Sayama
Received: 15 January 2007 / Accepted: 19 March 2007 / Published online: 31 March 2007 # Springer Science + Business Media, LLC 2007
Abstract A weibull raindrop-size distribution is fitted to the measurements of rainfall observed using a distrometer in Tokyo. A propagation experiment at 103 GHz is also introduced. The rain attenuation is calculated by considering the Mie scattering for the Marshall-Palmer, Best, Joss-Thomas-Waldvogel, Gamma and Weibull raindrop-size distributions. The results of frequency characteristics from the Weibull raindrop-size distribution agrees well with some experimental data for the millimeter and submillimeter waves above 30 GHz. The quick read table is calculated for the rain attenuation from 30 GHz to 1000 GHz.
Keywords Raindrop-size distribution . Rain attenuation . Weibull distribution
1 Introduction In the design of terrestrial and satellite communications links that operate at frequencies above 10 GHz, rain attenuation is a major obstacle. For radar in the millimeter and submillimeter ranges, rain attenuation is also a most important characteristic, because of its masking action. In monitoring rainfall and predicting the rain attenuation, the raindrop-size distribution has in recent years been found to play an important role. Especially, in millimeter and submillimeter wave links, rain attenuation is severe and greatly dependent on the various models of raindrop-size distribution.
M. Sekine : S. Ishii (*) : S. I. Hwang : S. Sayama Department of Communications Engineering, National Defense Academy, Yokosuka, Japan e-mail: [email protected]
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Int J Infrared Milli Waves (2007) 28:383–392
Fig. 1 System of distrometer.
Marshall and Palmer [1] proposed the following famous empirical expression by fitting their data and data of Laws and Parsons, N ð DÞ ¼ N0 eLD N0 ¼ 8000 m3 mm1 L ¼ 4:1 R0:21 mm1
ð1Þ
where D is the diameter in mm and R is the precipitation rate in mm/hr. Their data were taken in Ottawa, Canada in 1946 using the filter paper method. The fit of this distribution to the experimental points is not very good for drops less than D=1 mm. Best [2] proposed a drop-size distribution model by analyzing a large number of experimental data by 1950. This is written in the form D 1:75 ð D Þ2:25 e a N ðDÞ ¼ 13:5W πa4 a W ¼ 67R0:846 m3 mm3 a ¼ 1:3R0:232 mm1
ð2Þ
Joss, Thams and Waldvogel [3] measured the raindrop-size distribution using a distrometer at Locarno in Switzerland and obtained a similar experimental form of Eq. (1). The constants N0 and Λ differ for drizzle, widespread and thunderstorm rain cases as follows: N ð DÞ ¼ N0 eLD
ð3Þ
Type of Rain
N0 m-3mm−1
Λ mm−1
Drizzle [J-D] Widespread [J-W] Thunderstorm [J-T]
N0 =30000 N0 =7000 N0 =1400
Λ=5.7R−0.21 Λ=4.1R−0.21 Λ=3.0R−0.21
Thus, N0 and Λ vary with the rain type.
Int J Infrared Milli Waves (2007) 28:383–392
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Atlas and Ulbrich[4] proposed the followi
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