Inference of raindrop size distribution from attenuation and rain rate measurements
TL;DR: In this paper, a method to infer the raindrop size distribution from the measurements of point rain rate and rain attenuation at a frequency in centimeter or millimeter wave bands is proposed.
Abstract: A method to infer the raindrop size distribution from the measurements of point rain rate and rain attenuation at a frequency in centimeter or millimeter wave bands is proposed. This method is applied to the results of field propagation experiments at 81.8, 34.5, and 11.5 GHz through natural rain. It is shown that, if an appropriate frequency is employed, this method is effective as a frequency-scaling method for short terrestrial propagation paths.
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TL;DR: In this article, a physical-mathematical model of the dynamics of rain attenuation was developed and discussed, and the model was tested against the probability distributions of rain long-term 11.6GHz attenuation collected at the three Italian stations (Fucino, Gera Lario, and Spino d'Adda) during the SIRIO propagation experiment (13 years of data) for which concurrent rain rate time series are available.
Abstract: We have developed and discussed the theory and applications of a physical-mathematical model of the dynamics of rain attenuation and have tested it as a rain attenuation prediction model in slant paths. Other parameters, however, such as fade durations and rates of change of fades, can be calculated. The main physical input is the 1-min rain rate time series of a site, which is converted to a rain rate space series along horizontal or slant paths by using an estimate of the storm translation speed v method known as “synthetic storm technique.” However, the long-term predictions are found to be insensitive to v. The vertical structure of precipitation is modeled with two layers. The model was tested against the probability distributions of rain long-term 11.6-GHz attenuation collected at the three Italian stations (Fucino, Gera Lario, and Spino d'Adda) during the SIRIO propagation experiment (13 years of data) for which concurrent rain rate time series are available. In the outage probability range 10−1 to 5×10−3% defined the prediction error e = ( Ap − Am) / Am (where Am and Ap are respectively, the measured and predicted rain attenuations, dB), = −10.6%, σ=7.6% and rms=13%. Compared to nine other well-known prediction methods, the present model surmounts all of them in the three sites tested.
162 citations
Proceedings Article•
08 Apr 2013
TL;DR: In this article, the authors take advantage of the Weather Research and Forecasting (WRF) system, capable of providing reanalysis and forecasts at high resolution, to simulate the atmospheric conditions, to finally estimate the signal attenuation for slant path satellite links beyond 10 GHz.
Abstract: Next generations of satellite communication systems demand the use of high frequency bands and the effect of the troposphere at these frequencies has a major impact in the signal attenuation. In this context, the objective of the work presented in this paper is to take advantage of the Weather Research and Forecasting (WRF) system, capable of providing reanalysis and forecasts at high resolution, to be able to simulate the atmospheric conditions, to finally estimate the signal attenuation for slant path satellite links beyond 10 GHz. This is of paramount importance to effectively supplant the lack of measurements for the design of new satellite systems.
27 citations
TL;DR: A simple method is proposed that enables a quick and accurate estimation of the rain apparent extinction and highlights the influence of the link parameters.
Abstract: At optical wavelengths, geometrical optics holds that the extinction efficiency of raindrops is equal to two. This approximation yields a wavelength-independent extinction coefficient that, however, can hardly be used to predict accurately rain extinction measured in optical transmissions. Actually, in addition to the extinct direct incoming light, a significant part of the power scattered by the rain particles reaches the receiver. This leads to a reduced apparent extinction that depends on both rain characteristics and link parameters. A simple method is proposed to evaluate this apparent extinction. It accounts for the additional scattered power that enters the receiver when one considers the forward-scattering pattern of the raindrops as well as the multiple-scattering effects using, respectively, the Fraunhofer diffraction and Twersky theory. It results in a direct analytical formula that enables a quick and accurate estimation of the rain apparent extinction and highlights the influence of the link parameters. Predictions of apparent extinction through rain are found in excellent agreement with measurements in the visible and IR regions.
17 citations
01 Oct 1988
TL;DR: In this paper, the rain attenuation from 1 to 1000 GHz was calculated by using a Weibull distribution for raindrop-size using microwave experimental measurement data from 8 to 312.5 GHz.
Abstract: The rain attenuation from 1 to 1000 GHz was calculated by using a Weibull distribution for raindrop-size. The microwave experimental measurement data from 8 to 312.5 GHz were compared with our calculations. Especially, comparison between the submillimeter measurement and calculation at 312.5 GHz (0.96mm) was shown for the various rainfall rates. The empirical relation A = aRb between the specific attenuation A and the rainfall rate R was also found for a rain temperature of -10°C, 0°C and 20°C, and dependences of a and b on frequencies from 1 to 1000 GHz were tabulated.
16 citations
01 Aug 2017
TL;DR: In this article, the use of a Numerical Weather Prediction (NWP) model to emulate site diversity statistics has been proposed, where the Weather Research and Forecasting (WRF) model coupled with an Electromagnetic Module (EMM) is used here to generate rain attenuation time series.
Abstract: This paper proposes the use of a Numerical Weather Prediction (NWP) model to emulate site diversity statistics. Particularly, the Weather Research and Forecasting (WRF) model coupled with an Electromagnetic Module (EMM) is used here to generate rain attenuation time series in four sites in south of France. Rain attenuation statistics derived from WRF simulations are then compared to experimental propagation data, collected in single site and site diversity configurations.
14 citations
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3,500 citations
TL;DR: In this article, the terminal velocities for distilled water droplets falling through stagnant air are accurately determined using a new method employing electronic techniques, and the over-all accuracy of the massterminal-velocity measurements is better than 0.7 per cent.
Abstract: The terminal velocities for distilled water droplets falling through stagnant air are accurately determined. More than 1500 droplets of mass from 0.2 to 100,000 micrograms, embracing droplets so small that Stokes' law is obeyed up to and including droplets so large that they are mechanically unstable, were measured by a new method employing electronic techniques. An apparatus for the production of electrically charged artificial water droplets at a controllable rate is described. The over-all accuracy of the mass-terminal-velocity measurements is better than 0.7 per cent.
1,465 citations
TL;DR: In this article, a compromise between maximum path-averaged rainfall rate sensitivity and minimum sensing errors may be achieved by the use of one-way methods between the transmitter and the receiver, with a wavelength of 1.5 to 2.0 cm.
Abstract: At a wavelength of about 0.9 cm, microwave attenuation is demonstrated to be linearly related to rainfall rate and independent of drop size distribution and temperature. In addition, practical methods for measuring path- and area-averaged rainfall rate are reviewed. A compromise between maximum path-averaged rainfall rate sensitivity and minimum sensing errors may be achieved by the use of one-way methods between the transmitter and the receiver, with a wavelength of 1.5 to 2.0 cm. Corrections for nonspherical drops and for multiple scattering are also discussed.
510 citations
TL;DR: In this paper, a multichannel microwave propagation experimental system whose frequencies are 1.7 GHz, 11.5 GHz and 34.8 GHz is introduced in order to measure not only attenuation and phase shift due to rain, but also to infer a path-averaged raindrop size distribution.
Abstract: A multichannel microwave propagation experimental system whose frequencies are 1.7 GHz, 11.5 GHz, 34.5 GHz, and 81.8 GHz is introduced in order to measure not only attenuation and phase shift due to rain, but also to infer a path-averaged raindrop size distribution \overline{N(D)} from the measurements, in addition to 11.5 GHz, 34.5 GHz, and 81.8 GHz copolar attenuation, phase variations between the frequencies of 34.5 GHz and 11.5 GHz (with reference to 34.5 GHz) due to heavy rain are measured. These measurements, i.e., propagation constants, constitute a Fredholm integral equation of the first kind with respect to \overline{N(D)} . This equation is solved numerically by several inversion techniques, and the results for \overline{N(D)} > are compared with each other. It is made clear that the remote sensing of \overline{N(D)} from the measurements of microwave scattering is a useful method.
26 citations
TL;DR: In this article, the applicability of several frequency scaling methods of rain attenuation is discussed based upon the cumulative distributions of RA attenuations at 81.8, 34.5, and 11.5 GHz measured in the same horizontal propagation path of 1.3 km for 1 year.
Abstract: The applicability of several frequency scaling methods of rain attenuation is discussed based upon the cumulative distributions of rain attenuations at 81.8, 34.5, and 11.5 GHz measured in the same horizontal propagation path of 1.3 km for 1 year. A frequency scaling method (MISD) based upon the concept of a path-averaged raindrop size distribution N−(D) is newly applied to statistical prediction of the attenuation and is shown to be effective at millimeter wave bands where attenuation changes remarkably depending upon the raindrop size distribution, although the usefulness of MISD has been verified for time-sequential data. The size distribution determined from the statistical data at the three frequencies is given by N−(D) = 26,000 R−(−0.294)exp [−(5.6 R−0.283D)], 10 ≤ R− ≤ 70 mm/h, where R− is the path-averaged rainfall rate in millimeters per hour and D is the diameter of a raindrop in millimeters. Frequency dependence of attenuation calculated by using this size distribution shows that the prediction of rain attenuation based upon the Laws and Parsons size distribution results in an underestimation at frequencies above 80 GHz.
6 citations