Modeling of a tropical raindrop size distribution for microwave and millimeter wave applications
TL;DR: In this article, the authors describe the modeling of the average raindrop size distribution measured at Ile-Ife, a tropical station in South Western Nigeria, using a method of moment regression, which allows a single lognormal function to be accurately fitted over the entire range of rain rates measured, a convenient result for rain attenuation and scattering applications.
Abstract: The paper describes the modeling of the average raindrop size distribution measured at Ile-Ife, a tropical station in South Western Nigeria. The new “method of moment regression” employed is a systematic one that has allowed a single lognormal function to be accurately fitted over the entire range of rain rates measured, a convenient result for rain attenuation and scattering applications. The Marshall and Palmer law, frequently used for such calculations, has been shown to be inadequate as a model for this tropical station, especially at the high rain rates important for communications systems design. This result suggests that the similar Laws and Parsons dropsize distribution currently adopted by the International Radio Consultative Committee for estimating rain attenuation from 1 to 1000 GHz may not be adequate over such a large frequency range in such tropical locations. Some comparisons are also made with the lognormal models and modeling approaches of other workers. The results confirm the utility of the rain rate parameterization used in the model for Ile-Ife, while giving further support to the accuracy of the lognormal distribution.
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TL;DR: In this article, a framework based on measured raindrop size distribution (DSD) data has been developed to assess uncertainties in DSD models employed in Ku-and Ka-band dual-wavelength radar retrievals.
Abstract: A framework based on measured raindrop size distribution (DSD) data has been developed to assess uncertainties in DSD models employed in Ku- and Ka-band dual-wavelength radar retrievals. In this study, the rain rates and attenuation coefficients from DSD parameters derived by dual-wavelength algorithms are compared with those directly obtained from measured DSD spectra. The impact of the DSD gamma parameterizations on rain estimation from the Global Precipitation Measurement mission (GPM) Dual-Frequency Precipitation Radar (DPR) is examined for the cases of a fixed shape factor μ as well as for a constrained μ—that is, a μ–Λ relation (a relationship between the shape parameter and slope parameter Λ of the gamma DSD)—by using 11 Particle Size and Velocity (Parsivel) disdrometer measurements with a total number of about 50 000 one-minute spectra that were collected during the Iowa Flood Studies (IFloodS) experiment. It is found that the DPR-like dual-wavelength techniques provide fairly accurate est...
76 citations
TL;DR: In this article, a review of the deficiencies and their likely impact on system performance is presented, highlighting difficulties and encouraging realistic expectations and examining the question of whether costly, application-specific measurement programs might now be avoided by mining increasingly sophisticated national meteorological records.
Abstract: Due to pressures in the commercial sphere for increased information transfer rates or from the military to further miniaturize equipment to improve its portability, there has been a steady move toward higher carrier frequencies. For more than a decade now, increasing numbers of satellite communications systems have been in operation at millimeter wavelengths. Even where there is a clear view of the satellite from the ground station, a range of meteorological phenomena still combine to make propagation impairment a serious problem. Because of their complexity, difficulties in modeling them, and deficiencies in basic physical understanding, progress in engineering such systems has involved a large dose of empiricism. Ideally, this means a solid database of propagation measurements, made as nearly as possible in the intended geographical area of operations. Because of the time and cost of their accumulation, attempts have been made to use classification into climate zones on a worldwide basis to extend existing data to a wider range of situations. However, most of the measurements in the databases have been made in northern hemisphere temperate zones. Much evidence suggests that in tropical and equatorial zones, the factors that make important contributions to propagation impairment are different, putting a strong question mark over the use of existing design methods. This review looks at those deficiencies and their likely impact on system performance. At this time, rather than providing definitive answers - which must wait on further work - the best that can be done is to highlight difficulties and encourage realistic expectations. In a final section, the review examines the question of whether costly, application-specific measurement programs might now be avoided by mining increasingly sophisticated national meteorological records.
71 citations
TL;DR: In this article, the results of the modeling of drop size distributions (DSD) observed during a 2-yr study in Barcelona are presented. But the results are limited to three standard distribution functions: exponential, gamma, and lognormal.
Abstract: This study shows the results of the modeling of drop size distributions (DSD) observed during a 2-yr study in Barcelona. Thirty-second individual sample collections of drop sizes and velocities were measured with an optical disdrometer and grouped into different classes according to their rain rate. Using the moments method, the entire experimental dataset was fitted to three standard distribution functions: exponential, gamma, and lognormal. Relationships were found between rain rate R and other moments of the DSD, such as optical attenuation Σ, liquid water content W, and reflectivity Z. Although gamma distribution generally reproduced experimental measurements more accurately, the Z(R) relationship, which is particularly relevant in radar meteorology, yielded the best results when calculated from fitted exponential distribution.
57 citations
Cites methods from "Modeling of a tropical raindrop siz..."
...(9)eff Ly eff A third model, used by Levin (1971), Bradley and Stow (1974), Markowitz (1976), Ajayi and Olsen (1985), and Feingold and Levin (1986) is the threeparameter lognormal distribution model, which reflects the observed behavior of small drops....
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...A third model, used by Levin (1971), Bradley and Stow (1974), Markowitz (1976), Ajayi and Olsen (1985), and Feingold and Levin (1986) is the threeparameter lognormal distribution model, which reflects the observed behavior of small drops....
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TL;DR: In this paper, the authors used the method of moments to estimate the parameters of lognormal DSD and optimized the modeled DSD parameters by examining the root mean square (RMS) error and the average probability ratio (APR) in estimation of the rain rate, rain attenuation, and radar reflectivity factor simultaneously.
Abstract: As communication services using higher frequencies are growing rapidly in the tropics, there is an increasing need for a finer model to predict the attenuation due to rain. The raindrop size distribution (DSD) is one of the major sources of error in any prediction model, mainly because of its variability in both space and time. The DSD parameters are computed from distrometer data that are classified into stratiform and convective types using S-band radar data. The method of moments is employed to estimate the parameters of lognormal DSD. The modeled DSD parameters are optimized by examining the root mean square (RMS) error and the average probability ratio (APR) in estimation of the rain rate, rain attenuation, and radar reflectivity factor simultaneously. The proposed model gives maximum (close to unity) APR and minimum RMS error when compared to any other set of DSD parameters.
53 citations
TL;DR: In this article, the distribution of pluies in trois lieux of Nigeria (Calabar, Ile-Ife, and Zaria) has been investigated, i.e., bruine, averse, pluie etendue, orage.
Abstract: Les distributions des tailles des gouttes de pluie ont ete mesurees en trois lieux du Nigeria (Calabar, Ile-Ife et Zaria). Les donnees collectees pendant trois ans ont servi a obtenir des modeles de ces distributions pour divers types de pluie : bruine, averse, pluie etendue, orage. La distribution lognormale constitue un bon ajustement pour tous les types de pluie en des lieux tropicaux, sauf pour la bruine ou le modele exponentiel convient. On discute aussi les consequences de ces modeles pour des calculs de l’affaiblissement lineique du aux pluies tropicales.
42 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: The applicability of such results to conditions of natural rainfall has been thrown in doubt as discussed by the authors, and the results have been found to be affected by the drop-size and velocity of the artificial rains applied.
Abstract: Curiosity concerning the drop-size composition of natural rain has arisen from attempts to measure erodibility and infiltration-capacity by sprinkling small areas of land with artificial rain. The results have been found to be affected by the drop-size and velocity of the artificial rains applied, and the applicability of such results to conditions of natural rainfall has been thrown in doubt.
921 citations
TL;DR: In this paper, the empirical relation A = aR^{b} between the specific attenuation A and the rain rate R is used in the calculation of rain attenuation statistics.
Abstract: Because of its simplicity, the empirical relation A = aR^{b} between the specific attenuation A and the rainrate R is often used in the calculation of rain attenuation statistics. Values for the frequency-dependent parameters a and b are available, however, for only a limited number of frequencies. Some of these values, furthermore, were obtained experimentally, and may contain errors due to limitations in the experimental techniques employed. The aR^{b} relation is shown to be an approximation to a more general relation, except in the low-frequency and optical limits. Because the approximation is a good one, however, a comprehensive and self-consistent set of values for a and b is presented in both tabular and graphical form for the frequency range f = 1-1000 GHz. These values were computed by applying logarithmic regression to Mie scattering calculations. The dropsize distributions of Laws and Parsons, Marshall and Palmer, and Joss et al., were employed to provide calculations applicable to "widespread" and "convective" rain. Empirical equations for some of the curves of a(f) and b(f) are presented for use in systems studies requiring calculations at many frequencies. Some comparison is also made with experimental results, and suggestions are given regarding application of the various calculations.
674 citations
TL;DR: In this article, the authors measured raindrop spectra by two parameters, N0 and A, the intercept and slope respectively of an exponential distribution having the same water content and radar reflectivity factor as the observed sample.
Abstract: Raindrop spectra are measured with an electromechanical raindrop spectrometer, responding to drops >0.3 mm in diameter. The radar reflectivity profile is measured simultaneously with a 5-cm vertically pointing radar. Measured raindrop spectra are described by two parameters, N0 and A, the intercept and slope respectively of an exponential distribution having the same water content and radar reflectivity factor as the observed sample. Sudden variations in the raindrop spectra and in the reflectivity profile during widespread rain situations were observed. Due to the parameterization used, these sudden variations of the spectra can be recognized easily as N0 jumps. It seems that the N0 jumps indicate the transition from one mesoscale area within the precipitation field to another. The characteristics of the N0 jumps and the related cloud physics are discussed. An empirical model is proposed for the relation between the type of raindrop spectra and the convective activity of the precipitating air mass.
317 citations