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IEEE ANTENNAS AND WIRELESS PROPAGATION LETTERS, VOL. 3, 2004
Rain Attenuation Modeling From Measurements of Rain Drop Size Distribution in the Indian Region A. Maitra, Member, IEEE
Abstract—The rain attenuation and attenuation distribution have been obtained using the measured rain drop size distribution (DSD) and the ITU-R model of rain rate distribution over the frequency range of 10–200 GHz at three locations in the Indian region, to indicate the variability in the rain attenuation pattern in the tropical region. The prevailing DSD in the tropical region can cause very significant variability in the rain attenuation distribution indicating the need of long term and extensive measurement of DSD in the tropical region. Index Terms—Attenuation, distribution, drop size, drop size distribution (DSD), rain, tropical region.
I. INTRODUCTION
senting the number of drops, is given as
, of diameter
in unit volume,
(1) where , and are considered rain rate dependent distribution parameters, is in mm. In [1], the path averaged DSD values were reported from the rain attenuation measurements at 94 GHz and 0.63 m at Calcutta (22 34 N, 88 29 E), for a year yielding the following models for the distribution parameters:
V
ARIABILITY of rain drop size distribution (DSD) in different climatic zones, particularly in the tropical region, has been a major concern in developing the models of rain attenuation on a global basis. A comprehensive description of DSD in the tropical region is hindered by a lack of adequate experimental observations that will cover the prominent regional and seasonal variability of average air motion and turbulence responsible for the development of precipitation and subsequent coalescence and breakup of rain drops. Upcoming satellite communications at Ku and Ka bands and a number of communication systems at millimeter wave bands have the pressing need of modeling the rain attenuation at frequencies above 10 GHz, particularly in the tropical regions where measured attenuation data are insufficient for having a reliable model. However, measurements of DSD from a number of tropical locations have been reported. To model the rain attenuation on the basis of DSD measurements, it is necessary to assess the variability of attenuation that can occur due to a difference in DSD in a particular region. In this letter, the rain attenuation values are derived from the experimentally observed DSD in the Indian region, as published in the open literature, to indicate the variability in the rain attenuation within this region.
where is the rain rate in mm/h. DSD measurements over a two-year period with an optical distrometer from Guwahati (26 12 N, 91 45 E) generated the following distribution parameters [2]:
The third DSD model considered is for the location of Dehradun (30 18 N, 78 6 E) from which the distribution parameters obtained from observations over a year with an impact type of disdrometer are expressed as [3]
For Calcutta and Dehradun, no classification of rain types was made and the DSD models are supposed to be average models for shower to thunderstorm rains whereas for Guwahati the DSD model is mentioned to be appropriate for thunderstorms.
II. RAIN DROP SIZE DISTRIBUTIONS
III. RAIN ATTENUATION MODELING
Rain DSD measurements have been carried out and modeled at a number of locations in the Indian region. Three models in terms of a lognormal function pertaining to three locations are published in the open literature. The lognormal function repre-
The specific attenuation due to rain using the DSD is obtained from the relation
Manuscript received January 28, 2004; revised June 15, 2004. This work was supported by a project on “Radio remote sensing of the tropical atmosphere,” sponsored by the Indian Space Research Organization under the S. K. Mitra Center for Research in Space Environment, University of Calcutta, Calcutta, India. The author is with the Institute of Radio Physics and Electronics, University of Calcutta, Calcutta 700 009, India (e-mail:
[email protected]). Digital Object Identifier 10.1109/LAWP.2004.833979
(2) is the total extinction cross section in mm . Fig. 1 where shows the specific attenuation values with the three DSD models pertaining to three locations over the frequency range 10–200 GHz at three rain rates 10, 50, and 100 mm/h, along with the attenuation values obtained from the ITU-R model which is based on the Laws–Parsons size distribution [4]. At Calcutta the devi-
1536-1225/04$20.00 © 2004 IEEE
MAITRA: RAIN ATTENUATION MODELING FROM MEASUREMENTS OF RAIN
Fig. 1. Specific rain attenuation at Guwahati, Calcutta, Dehradun, compared with the ITU-R model at different rain rates. TABLE I ANNUAL RAIN RATE DISTRIBUTION
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Fig. 2. Specific rain attenuations exceeded for different percentages of time over a year at Guwahati, Calcutta, and Dehradun.
are obtained with this model for the three locations and are shown in Fig. 2. The attenuation distributions indicate that a particular attenuation value at a given frequency will be exceeded for the longest duration at Guwahati and for the shortest time at Dehradun. The occurrence of intense rain rate is higher at Calcutta than at Guwahati while the latter location has a higher occurrence of intense attenuation compared to Calcutta. This is due to a difference in DSDs at Calcutta and Guwahati. However, the occurrence of least intense attenuation at Dehradun is commensurate with the least occurrence of rain. IV. CONCLUSION
ation from the ITU-R value is not very serious up to 50 GHz, within 1 dB, and the attenuation can be up to 6.5 dB/km higher at 100 GHz for a rain rate 100 mm/h. At Dehradun, the deviation from the ITU-R values can be quite substantial below 50 GHz, up to 4 dB/km at rain rate 50 mm/h, which is rather serious since at low frequencies the attenuation is comparatively low. At higher frequencies the ITU-R value can be significantly greater than the attentuation at Dehradun at high rain rates. The attenuation at Guwahati is again substantially higher than the ITU-R value over the entire frequency range, up to 16 dB/km at rain rate 50 mm/h. The annual distributions of rain attenuation are derived at the three locations from the rain rate distributions over a year at these locations obtained from Recommendation ITU-R P.837-3 [5] as given in Table I. According to the ITU-R model, the rain occurs most intensely at Calcutta and least intensely at Dehradun; Guwahati exhibiting an intermediate behavior. Rain attenuations exceeding different percentages of time over a year, from 0.001% to 3%, over the frequency range of 10–200 GHz
Based on DSD measurements at the three locations, though obtained over limited periods and with different techniques, it is found that the rain attenuation can significantly vary and be considerably different from the ITU-R model [4] in the Indian region. The DSD can play an important role in determining the rain attenuation occurrences and mere rain rate distribution may not reveal a true picture of the occurrence pattern of rain attenuation in the tropical region. There is a continuing need of long term observation on rain DSD to obtain a reliable rain attenuation model and also actual attenuation measurements to support the model. REFERENCES [1] A. Maitra, “Three parameter raindrop size distribution modeling at a tropical location,” Electron. Lett., vol. 36, pp. 906–907, 2000. [2] K. I. Timothi, S. Sharma, M. Devi, and A. K. Barbara, “Model for estimating rain attenuation at frequencies in range 6–30 GHz,” Electron. Lett., vol. 31, pp. 1505–1506, 1995. [3] A. K. Verma and K. K. Jha, “Rain drop size distribution model for Indian climate,” Indian J. Radio Space Phys., vol. 25, pp. 15–21, 1996. [4] Specific Attenuation Model for Rain for Use in Prediction Methods, Recommendation ITU-R P.838, 1992. [5] Characteristics of Precipitation for Propagation Modeling, Recommendation ITU-R P.837-3, 2001.
