Raindrop size distribution profiling by laser distrometer and rain attenuation of centimeter radio waves

Transcription

1 Indian Journal of Radio & Space Physics Vol. 38, April 2009, pp Raindrop size distribution profiling by laser distrometer and rain attenuation of centimeter radio waves M Saikia $,*, M Devi, A K Barbara & H K Sarmah Department of Physics, Gauhati University, Guwahati, Assam $ manojksaikia@gmail.com Received 10 August 2007; revised 21 September 2008; accepted 10 December 2008 The paper describes system design of laser distrometer, its calibration process and profiling of raindrop size distribution (RSD). Here, raindrop signature is extracted by allowing the drops to pass through a controlled field of view of a sensor. A laser beam works as signal source, phototransistor as detector-cum-amplifier and optical fibers as trans-receiving ports. RSD profiles and rain rate at different weather conditions have been presented. Specific raindrop attenuation of line of sight radio signals at GHz of various drop diameters is then calculated by using standard attenuation equations and model values of scattering functions. Finally, the rain attenuation magnitudes are compared with those given by a model framed earlier [Timothy K I, Sharma S, Devi M & Barbara A K, Model for estimating rain attenuation in frequencies range 5-30 GHz, Electron Lett (UK), 31 (17) (1995)]. Keywords: Raindrop size distribution (RSD), Rain attenuation, Rain rate, Centimeter radio wave PACS No.: eg 1 Introduction Electromagnetic waves above 10 GHz suffer attenuation due to rain and in situations signal may be totally lost 1,2. It is important to measure real time raindrop size distribution to evaluate depth of attenuation by rain as model RSD profiles give rain rate over a zonal location only 3-5. For profiling of RSD and to measure size and shape of raindrops, one of the most reliable systems is the Distrometer. Jones 6 in 1959 measured the rain drop size by illuminating a volume of space with rain drops. The system consists of two short exposure cameras receiving photographs of the rain drops in the space from two different perpendicular angles. But calculations necessary for correction of measured image sizes to the tuned drop sizes are enormous. In 1967, Joss & Waldovgel 7 have introduced an electromechanical sensor which converts momentum of rain drops into electrical pulses. Since then, progressive improvement of the system has been incorporated for obtaining reliable output A laboratory model 12 of a distrometer was developed in 1990 and here the field version of this system is discussed. In the distrometer 12, a laser beam illuminates the detector. The detector is kept inside a black box to minimize the ambient noise. Rain drops, while passing through the beam, intercept some amount of light thereby making a shadow representing its size and shape. The laser beam, therefore, falling on the detector gives rise to a representative pulse. The height and width of the pulse are proportional to the raindrop size and the time a raindrop takes to cross the beam. A calibration is done by allowing simulated rain drops from known nozzle diameters to fall on the field of view of the receiver. The pulse characteristics are processed at various stages for determination of raindrop size and shape. But this laboratory model distrometer had inherent problems in using it in fields mainly because the sensor unit was not immune to even slight changes in background light intensity. A variation in background light off sets its zero level settings. Therefore, the instrument had to be manually adjusted at frequent intervals. Further, in this model the source was kept in-house and the detector over an adjustable open air rail outside the laboratory, thereby making the system potentially unusable as field equipment. The system is, therefore, modified for field use; a brief description is given here. 2 Basic circuits and system The main drawback in the earlier model, as stated above, was variation of system output with background light intensity which undergoes rapid changes particularly at rainy conditions. Thus, the

2 SAIKIA et al.: RAINDROP SIZE DISTRIBUTION PROFILING 81 principle of this model is to make its response free from albedo states and also to adopt it for field use. The problem was removed by using optical fibers as transmission-reception medium and source and detectors are housed in the same platform placed within a room. Here, one optical fiber is used to transmit the laser beam that illuminates a 1.5 cm wide optical window where raindrops leave their imprints as they pass through. Another optical fiber collects and carries the characteristic raindrop signals to sensor (housed in the same platform as the source), which is connected with a buffer unit before reaching subsequent stages. The signal after amplification goes to the processing device. After a raindrop passes through field of view of the sensor, detector converts its optical signature into an electric pulse. The amplitude and width of such pulses vary with size and shape of drops; pulse height gives their horizontal diameter and pulse width gives vertical diameter. Use of optical fiber (core diameter 1 mm), thus, drastically reduces the background noise intensity. Further, for elimination of small changes in background light a comparator was used to null the ambient effect. For this purpose, an error signal is fed to a comparator through a feedback loop so that the output level remains invariant irrespective of background light. The comparator output is fed to an amplifier of gain and adjusted for obtaining distortion less pulse, which is then stored and analysed through a digital storage oscilloscope and logged into computer for analysis. 3 Calibration For calibration, drops are made by using nozzles of diameter mm. These drops are allowed to pass through the optical window and intercept the light beam as they cross it. The height, rise time and fall time of pulses generated by the passing drops are calibrated in terms of nozzle diameter. For this purpose, a large number of drops from a nozzle are taken and pulse parameters are noted for each pass. Further, as pulse patterns are controlled by terminal velocity of drops, to minimize velocity errors, drops from different nozzle heights (height of the nozzle from the window) are allowed till pulse patterns are independent of drop (nozzle) height. Figure 1 presents pulse amplitude variation with fall distance of drops for nozzle diameter of 0.7 mm and it is noted that the pulse height magnitude remains constant at 250 mv beyond 3 m range. This exercise has been carried out for all nozzle diameters. The calibration curve is then drawn associating nozzle diameter with pulse height, rise time and fall time [Figs 2 (a)-(c)]. For spherical drops, the rise time and fall time of pulses are almost equal but for larger drops, the rise and fall times are not symmetric and raindrop shapes come out as Fig. 2(a) Nozzle diameter-pulse height graph and solid line Fig. 1 Variation of pulse height with nozzle height and solid line Fig. 2(b) Nozzle diameter-pulse rise time graph and solid line

3 82 INDIAN J RADIO & SPACE PHYS, APRIL 2009 spheroid, oblate spheroid or in other forms as shown in Fig Measurement of RSD and comparison of rain rates for different weather condition Once the calibration is done, raindrop size is measured in conditions of thunderstorm, shower, and Fig. 2(c) Nozzle diameter-pulse fall time graph and solid line drizzle. The RSD profiles are drawn by using Eq. (1) (ref. 4). N (D)=N/VA D N m -3 mm (1) where, N, is number of drops of diameter D observed in a minute interval; V, the terminal velocity in m/s; A, area of the optical window in m2; and D, drop diameter interval in mm. Analysis shows that RSD profile for drizzle follows a negative exponential relation following Eq. (2) N ( D ) = N ex p 0 λ D (2) where, λ, is function of rain fall rate, and D, drop diameter. In Fig. 4, RSD for two cases during drizzle observed in June 2006 are shown. Here the profile 1 ( mark) is for 2 June 2006 and profile 2 ( mark) represents a drizzle on 9 June The corresponding rain rate for two events is 30 and 45 mmh -1, respectively and the negative exponential distribution followed by two profiles is apparent from Fig. 3 Raindrop size and shape

4 SAIKIA et al.: RAINDROP SIZE DISTRIBUTION PROFILING 83 the figure. It was also observed that for shower and thunderstorm, rain drop size distribution follows lognormal pattern, two profiles for such rains are presented in Fig. 5, one for rain event in May 1993 and another for the same pre monsoon month of May in Next, using N (D), i.e. drop number density from RSD, rain rate (R) is calculated by Eq. (3) (ref. 4): R = 6π Di N ( Di ) V ( D ) i D i... (3) where, N(D), is number density in m -3 mm -1, and V(D), terminal velocity in msec -1. Fig. 4 RSD of drizzles and solid line during June 2006 Fig. 5 Comparison of RSD of thunderstorm during May 1993 and May 2006, solid line The equation shows that rain rate depends on RSD which is controlled by the type of rain. On calculation of rain rate for the two events of Fig. 4, it is observed that raindrops are reduced by 50% in the rain event of 2006 where rain-rate was 35 mmh -1, a four fold decrease in this value compared to May 1993 event when rain rate was 142 mmh Specific rain attenuation and comparison with existing model For meaningful interpretation of experimentally observed rain rate, it is worthwhile to asses the rain contribution on microwave signal. There are a number of models defining rain attenuation in terms of rainfall rate and drop size distribution. The specific rain attenuation is calculated by adopting the following relation1: 3 A λ 10 Im f ( D ) N ( D ) dd = 0 db/km... (4) where, A, is specific rain attenuation; f, complex scattering function; D, rain drop diameter; N(D), number density of drops; and λ, signal wavelength. The complex scattering function (f) is strongly dependent on λ, the signal wavelength. Imaginary part of scattering function is directly proportional to specific rain attenuation. To study the influence of scattering function, Fiser 1 has plotted its imaginary part Im f(d) in the frequency range GHz in Mie scattering process. Using this function from Fiser, rain attenuation is calculated for frequency range GHz. from Eq. (3) with N(D) received from distrometer observation. The calculated result is presented in Fig. 6 showing attenuation variation with drop diameter. Rain attenuation is calculated for rain rate of 20 mmh -1. It is found that specific attenuation increases with drop diameter but after a threshold the attenuation decreases. At higher frequencies, threshold moves towards smaller raindrops. It is observed that contribution to specific attenuation is formed by drops of diameter not exceeding 2 mm. Now to calculate total attenuation contributed by drops of all sizes, a polynomial equation is derived for each curve of Fig. 6 and taking this polynomial equation, the curve area is integrated for each case. As an example, the best fit polynomial for profile 1 (for 20 mmh -1 rain rate) of Fig. 6 is: y = x x x x x x

5 84 INDIAN J RADIO & SPACE PHYS, APRIL 2009 Fig. 6 Specific attenuation with drop diameter and solid line represents the best fit curve Table 1 Comparison of rain attenuation for 10 GHz signal Rain rate (R) (mm/hr) Attenuation from our approach (db/km) Attenuation using relation A=aR b (db/km) * *Here, a= f 2.42 and b= ln(f) for 10 to 20 mm/hr rain rate and a= f and b = ln(f) for 35 to 140 mm/hr rain rate. This exercise is repeated for rain rate in the range mmh -1 only for 10 GHz signal and attenuation values are shown in Table 1 (column 2). The signal of 10 GHz is selected for attenuation estimation because in present study attenuation measurement data are taken at 11 GHz P&T link of 3.2 km length and also that a semi empirical model has been framed based on this observation where the relevant parameters are given in Table 1. As a test of working of this approach, the rain attenuation values were compared with those derived from the semi empirical model. It is seen that rain attenuation through the scattering function is well applicable up to 80 mmh -1. However, for higher rain rate, it gives a larger value. 6 Conclusions Disdrometer circuit is simple and the cost is low. By use of optical fiber, the problem of open space distance between source and sensor is avoided and trans-receiver system could be housed in a single platform where only the window is exposed for raindrops. So the system is suitable for field use. The analysis shows that thunder associated RSD always follows lognormal pattern irrespective of rain rate condition but number density of larger drops drastically go down in drought like situation. It is found that number of larger diameter drops goes down by 50% and then rain rate declines by four folds compared to high rain situation of The main drawback of this system lies with the window area limited by the use of a single optical fiber. This has resulted to inaccuracy in the drizzle measurement if the rain lasts for less than two minutes and also for windy situation. To overcome this problem, the single optical fiber is replaced by an array of optical fiber at the optical window so that the effective field of view increases and good signal to noise ratio is achieved. It is found that rain attenuations calculated by using imaginary part of scattering function [Im f(d)] match with values of the existing model for rain rate < 100 mmh -1. So both the approaches may be used for calculating rain attenuation (<100 mmh -1 ) in the frequency range GHz. It is also found that contribution to specific attenuation is mainly limited to drops of diameter not exceeding 2 mm within the observed frequency range. Acknowledgement The authors acknowledge with thanks the financial support received from ISRO, Govt. of India, for carrying out this work. The authors also thank the referees for their helpful comments and suggestions. References 1 Fiser O, The role of particular rain drop size classes on specific rain attenuation at various frequencies with Czech data example, Proceedings of ERAD, (Copernicus GmbH), 2002, Tokay A, Kruger A & Krajewki W F, Comparison of drop size distribution measurements by Impact and Optical Disdrometers, J Appl Meteorol (USA), 40 (2001) Campos E F, On measurements of drop size distribution, Top Meteorol Oceanog (Costa Rica), 6 (1999) Zainal A R, Glover I A & Watson P A, Rain rate and drop size distribution measurements in Malaysia, International Geo-science and Remote Sensing Symposium 93, 1 (1993) Reddy K K & Kozu T, Measurements of raindrop size distribution over Gadanki during south-west and north-east monsoon, Indian J Radio Space Phy, 32 (5) (2003) pp Jones D M A, The shape of raindrops, J Meteorol (USA), 16 (1959) pp

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