Estimation of Rain Attenuation From Experimental Drop ... - IEEE Xplore

IEEE ANTENNAS AND WIRELESS PROPAGATION LETTERS, VOL. 10, 2011

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Estimation of Rain Attenuation From Experimental Drop Size Distributions José Miguel García-Rubia, Member, IEEE, José Manuel Riera, Member, IEEE, Ana Benarroch, and Pedro García-del-Pino

Abstract—Detailed measurements of the rain phenomena can be obtained from modern equipment that provides experimental drop size distributions (DSDs), which can be used to analyze the effects of past rain events or to predict their influence on colocated radio links. In this letter, the use of experimental DSDs to predict rain effects on millimeter-wave propagation is discussed from a practical point of view, taking advantage of the availability of measurements from various instruments. The derived results show that predictions can be calculated with reasonable accuracy, provided that some practical considerations are taken into account. Index Terms—Attenuation measurement, millimeter-wave propagation, rain attenuation, satellite applications, tropospheric propagation.

I. INTRODUCTION

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HE PREDICTION and analysis of rain attenuation has become of increasing interest in recent years because of the wider use of millimeter-wave radio communication systems. In this context, improvements in the analysis of both rain phenomena and their effects on propagation can lead to enhancements in future systems, through a better design and operation of fade mitigation techniques (FMTs) [1]. Modern meteorological equipment, which can be available in radio-communication sites at an affordable cost, provides rain drop size distributions (DSDs) both at surface level and in height. Rain attenuation time series can be estimated from the DSDs, provided that several conditions are met: 1) the availability of meteorological data of this kind, either real-time or recorded from past events, depending on the intended use; 2) the existence of models that allow the calculation of attenuation from the DSDs and the development of procedures to apply these models; 3) the validation of the whole procedures in order to check the accuracy and reliability of the estimations. The second condition is partially met by the existence of physical

Manuscript received April 06, 2011; revised May 13, 2011 and June 22, 2011; accepted July 20, 2011. Date of publication August 04, 2011; date of current version August 29, 2011. This work was supported in part by the Spanish Ministry of Science and Innovation, Spanish National Program of R&D, under Projects TEC2010-19241-C02-01 and CONSOLIDER—Ingenio 2010 CSD-2008-00068. J. M. García-Rubia is with the Escuela Politécnica Superior, Universidad de Jaén, 23700 Linares, Jaén, Spain (e-mail: [email protected]). J. M. Riera and A. Benarroch are with ETSI Telecomunicación, Universidad Politécnica de Madrid, Madrid 28040, Spain (e-mail: [email protected]; [email protected]). P. García-del-Pino is with EUIT Telecomunicación, Universidad Politécnica de Madrid, Madrid 28031, Spain (e-mail: [email protected]). Color versions of one or more of the figures in this letter are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/LAWP.2011.2163609

models of scattering by raindrops. However, the development of practical procedures and their validation need experimental data consisting of both rain DSDs and attenuation measurements. A propagation experiment is being carried out at Universidad Politécnica de Madrid, Madrid, Spain. The experiment makes use of both advanced meteorological equipment and experimental transmitters and receivers that operate at millimeter-wave frequencies in terrestrial and slant paths [2]. This combination of propagation and meteorological data brings about the opportunity to develop practical procedures to estimate link attenuation from the DSDs and to validate those procedures through the comparison of predictions with measured attenuation values. The experimental equipment is presented in Section II, whereas Section III is dedicated to the estimation of rain attenuation from drop size distributions, as obtained from the instruments. These estimations are compared in Section IV to propagation measurements. Wet antenna effects, discussed in Section V, provide a reasonable explanation for the differences observed between predictions and measurements. Section VI concludes the letter with a summary of the main results and their possible applications. II. EQUIPMENT The equipment for propagation measurements includes a satellite receiver at 19.7 GHz, with integrated radiometer in the same band, and three horizontal links at 38, 75, and 85 GHz. This letter is focused on the results concerning the 19.7-GHz receiver and the 38-GHz microwave link. The satellite receiver, which has been designed and built at the university [3], measures the Eutelsat HB-6 Ka-band beacon at 19.7 GHz, with a path elevation of 40.2 . The horizontal links are installed between two buildings at the university campus in Madrid, with a path length of 0.84 km. Madrid is located in the central area of the Iberian Peninsula (40.27 N, 3.43 W) at an altitude of 630 m above sea level. It has a continental climate, with hot and dry summers and cold winters. Rain occurs mainly in spring and autumn, with the average rainfall being about 440 mm per year. A conventional meteorological station is installed, with a tipping-bucket rain gauge. Its measurements are used as a reference for the rain rate data, its derivation being more straightforward with this instrument. Experimental DSDs are provided by two instruments. A 24-GHz vertical-pointing Doppler radar (METEK Micro Rain Radar MRR-2) provides drop size and velocity distributions at 30 different heights. These measurements are not independent: The terminal fall velocity of a drop is a primary measurement, and its size is calculated using the well-known Gunn–Kinzer

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relation [4], [5]. Additionally, the fall velocity changes with increasing height as the air pressure decreases. These changes are modeled by the Foote and duToit relation [6]. For each of the 30 heights, the drops are classified into 46 size bins. More details can be found in [7]. In this experiment, the DSDs and other derived calculations are recorded each minute. A laser optical disdrometer (THIES Laser precipitation monitor [8]) is also available. Diameter and velocity of the detected particles are independently measured with this instrument, which also provides accurate observations of the amount, intensity, and type of precipitation. The DSD spectrum is obtained every minute, with 22 bins in diameter and 20 bins in velocity so that the relationship between terminal fall velocity and diameter can be measured in a direct way. III. ESTIMATION OF RAIN ATTENUATION Assuming spherical raindrops, Mie theory [9], [10] is used to calculate the extinction coefficient of a single particle at millimeter wave frequencies. Apart from size information, the application of the Mie theory needs the complex refractive index. The dielectric function of Liebe et al. [11], covering the frequency range from 1 to 1000 GHz, is used. Therefore, the specific rain attenuation is calculated by integrating the extinction term over all the range of drop sizes as (1) (m mm ) is the drop size distribution value where at the diameter (mm) and is the Mie extinction cross section for the diameter , which depends on frequency and temperature. For the horizontal 38-GHz link, is obtained both from the disdrometer data and the MRR-2 measurements corresponding to the lowest atmospheric layer (200 m). Attenuation for this link is calculated as the product of the specific attenuation by the effective propagation path length. The path reduction factor is assumed to be unity since rain rate is considered uniform for the entire path length of 0.84 km. To compare to the satellite link measurements, the specific attenuation at 19.7 GHz is derived for each height level, using the profiles provided by the MRR-2. Zenith attenuation is calculated by integration from the surface level up to the melting layer. Attenuation in the slant path is estimated by dividing this zenith attenuation by , being the elevation angle. The aforementioned procedures are derived from well-known theoretical considerations on the influence of rain on propagation. In order to obtain useful estimations, the following practical considerations must be taken into account. 1) It was found that the MRR-2 measurements underestimate the rain rate by a ratio varying between 2 and 4, depending on the events. Other researchers have also found significant differences between the measurements obtained with this radar and with rain gauges [12]. Following the manufacturer indications, an attempt was made to calculate an updated value for an internal calibration constant of the equipment, but that was not successful. Apparently, the optimal value of this constant, calculated from the comparison to rain gauge measurements, is not

sufficiently stable. The problem is solved by calculating an adjustment factor, as the result of dividing the average rain rates derived from the MRR-2 and the rain gauge. This factor is then applied to the measured DSDs. In this research, the adjustment factor was refreshed for every day of measurements, from daily average rain rates, though factors calculated on a longer-term basis (weekly or monthly) could also be useful. 2) It was also found that the disdrometer measurements occasionally include particles with large diameter and low velocity, which cannot be liquid raindrops. Because of their large diameter, these particles cause unrealistic peaks in the estimated attenuation. A filter was implemented to discard them, as they may arise from spurious responses of the equipment or from solid particles of different origin (insects, vegetation, or dust). This filter is based on the classification of precipitation particles presented in [13] and basically discards very isolated particles in the velocity/size histograms as well as any particle whose size is in excess of 1 mm and whose terminal velocity is below 1.5 m/s, which is not realistic for liquid rain particles. 3) The proposed calculation of attenuation in the slant path is sensitive to the melting-layer altitude under consideration, as the integration is performed from the ground up to this height level. In order to separate the different problems, the melting-layer altitude has been obtained so far by visual inspection of radar profiles. Additionally, a small correction is applied to account for the attenuation excess in the melting layer [14] (2) is the mean attenuation excess at the frequency , estimated from the surface rain rate . For GHz, and are proposed [14]. Future versions of the procedures should ideally automatically determine a melting-layer altitude from the radar data, at least in those cases when the melting layer is more clearly defined. Radio-sounding data can also be used to estimate the rain height altitude for non-real-time applications. IV. COMPARISON TO PROPAGATION MEASUREMENTS An example of attenuation time series for the 38-GHz link is shown in Fig. 1. This corresponds to a 5-h event with maximum rain rate of 4 mm/h. Measurements are compared to the attenuation estimations produced from the experimental DSDs. Predictions and measurements follow similar trends, but a systematic difference of about 0.5–1 dB appears most of the time. This is not particular of this event, but more general for this link. From a detailed analysis, it was found that these differences do not grow indefinitely, but reach a saturation value, around 2 dB, when attenuation increases. A likely explanation for these differences is presented in Section V. The results for the satellite link for the same event are shown in Fig. 2. The melting-layer altitude for this event is estimated at 1200 m above ground. The maximum attenuation values, integrated from the MRR-2 measurements, show a fair correlation in time and magnitude with the satellite link

GARCÍA-RUBIA et al.: ESTIMATION OF RAIN ATTENUATION FROM EXPERIMENTAL DROP SIZE DISTRIBUTIONS

Fig. 1. Measured and estimated total attenuation time series at 38 GHz.

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Fig. 3. Measured and estimated total attenuation time series at 38 GHz, with ). the corrections for wet antenna (

layer that attaches to the radome surfaces. As they are nearly vertical planes, made of hydrophobic materials, it is likely that the amount of water attached to the radome surfaces has a maximum value, which would lead to a saturation value of the attenuation that it provokes. After reviewing the literature on this effect, a single-frequency model was found [15] that proposes an exponential relationship between the attenuation measurements and the wet antenna attenuation . Considering that , where is the path attenuation, a similar exponential relationship can be proposed relating the attenuation caused by the two wet antennas, , to the predicted path attenuation (3) Fig. 2. Measured and estimated total attenuation time series at 19.7 GHz.

measurements, though the peaks are not strictly coincident in time. This may be attributed to the fact that the experimental paths are different—vertical for the MRR-2 and slanted for the satellite—and rain rate is not homogeneous in space. For this reason, temporal correlation between both curves is not so marked as in Fig. 1. After visualizing a large number of events, it is concluded that the shapes of the predicted curves are realistic and their values are similar to the measurements. There does not appear to be a systematic difference as in the horizontal link; if present, it would amount only to a few tenths of a decibel. V. WET ANTENNA EFFECTS After discarding other hypotheses, wet antenna effects are the most likely cause for the observed differences between predictions and measurements in the horizontal link. Water layers that attach to the surfaces of reflectors, radomes, and horn caps in the presence of rain are known to cause significant attenuation in some cases. Parabolic antennas of 0.3 m diameter are used in the 38-GHz link. Their aperture surfaces are covered with flat radomes. Hence, the attenuation is attributed to the water

and are model parameters. This approach can be where more convenient, as we start from the predicted values of , obtained from the DSDs, as has been previously discussed. These empirical relationships can be proposed as a consequence of the common dependence on rain (rainfall rate, type of precipitation) of , , and their sum . This model has been tested yielding satisfactory results. Both the original model and the proposed correction predict that wet antenna attenuation increases with path attenuation and rain rate for their lowest values, but later it reaches a saturation value of dB. In this case, dB was chosen as representative of the maximum differences between predictions and measurements observed both in the time series, as pointed out in Section IV, and in the cumulative distributions of attenuation, as is shown in Fig. 4. Then, dB was obtained from numerical tuning of the model for the observation period considered throughout this letter, which corresponds to the fairly rainy months of April and May 2008. Higher values of (6 and 8 for 20 and 27 GHz) are reported in [15], while is smaller (1/6 and 1/8). The maximum attenuation by the wet antennas depends on their physical characteristics and frequency. Parameter quantifies how rapidly this saturation value is reached. In our case, the calculated value implies that the maximum attenuation, which is lower than in other

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given the different pointing of the radar and satellite antennas. For a short horizontal 38-GHz link, systematic differences have been found between predictions and measurements. These differences have been qualitatively explained by considering the effects of wet antennas. Preliminary work carried out so far with higher frequency measurements (75 and 85 GHz) leads to similar conclusions. The presented procedures find different applications. Attenuation due to current rain events can be estimated in real time allowing for the optimization of system operation. On the other hand, DSD data stored for long periods can be used to synthesize realistic time series of attenuation and to derive statistics of the expected attenuation for a given link. REFERENCES Fig. 4. Cumulative distributions of rain attenuation at 38 GHz.

experiments, is reached earlier, i.e., for smaller values of . This is physically sound and is coherent with the observed differences between predictions and measurements. Fig. 3 represents the effect of applying this correction to the results already presented in Fig. 1. If the wet antenna attenuation is added to the predictions, a qualitative agreement between measurements and predictions is obtained. Similar results have been obtained for a large number of events analyzed. The cumulative distributions of attenuation for the observation period have been calculated and are plotted in Fig. 4. The distributions based on the predictions are in good agreement with the measured one when the corrections for wet antenna effects are included. These results support the hypothesis that the differences found between predictions and measurements can be attributed to the fact that experimental values include the attenuation caused by the wet antennas. Although this attenuation may also be present in the satellite link measurements, its value is probably much smaller because of the lower frequency, the different antenna geometry (Cassegrain, 1.2 m diameter) and materials (horn cap instead of radome), and the fact that there is only one antenna exposed to rain. VI. CONCLUSION The use of modern meteorological equipment (Doppler radar and laser disdrometer), which provides experimental DSDs, has been investigated with a view to its application in the field of millimeter-wave propagation. Attenuation time series have been calculated and compared to experimental measurements in two links. In the case of the satellite link, realistic attenuation series are obtained, though a perfect time coincidence is not feasible,

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