Attenuation in melting snow on microwave- and millimetre-wave terrestrial radio links

The scattering properties of melting snow on microwave and millimetre-wave terrestrial radio links are predicted using a new model for melting which includes coalescence. Attenuation, differential attenuation and differential phase are calculated for a horizontal path, with results at 36.25 GHz presented. Peak specific attenuation in the range 8?13 dB/km is expected for underspread rain with 10?15 mm/h rain rates.     

Backward and forward scattering by the melting layer composed ofspheroidal hydrometeors at 5-100 GHz

This paper addresses the behavior of the differential reflectivity, specific attenuation, and specific phase shift due to a melting layer composed of oblate-spheroidal hydrometeors. The results are based on a melting layer model and scattering computations derived from the point-matching technique with the truncation and recurrence adjusted. Computations at 5-100 GHz for five raindrop size distributions at rain rates below 12.5 mm/h are presented. In general, the reflectivity factor and differential reflectivity features with height at centimeter wavelengths agree with available radar measurements. At millimeter wavelengths, contributions to the radar backscatter from smaller hydrometeors become more and more important as the frequency increases and approaches 100 GHz. This should be instructive for utilizing millimeter wavelength radar techniques in radar remote sensing studies of the melting layer. Corresponding vertical profiles of the specific attenuation and phase shift are also presented at 5-100 GHz. The differential attenuation and phase shift indicate the particle shape effects. These attenuation and phase shift become more and more considerable as the frequency increases. Such forward scattering calculations should prove useful for studying propagation effects caused by the melting layer for satellite-earth communications, including depolarizations     

Scattering of radiowaves by a melting layer of precipitation inbackward and forward directions

A melting layer of precipitation is composed of melting snowflakes (snow particles); the assumption of spherical particles along with mass conservation is used. The melting layer is studied by deriving the size distribution of the melting snow particles, the thickness of a melting layer, the density of a dry snow particle, and the average dielectric constant of a melting snow particle. Vertical profiles of radar reflectivity and specific attenuation are computed at 1-100 GHz by using the Mie theory for five raindrop size distributions at rain rates below 12.5 mm/h. The radar bright band is explained with computed radar reflectivities at 3-10 GHz. It is shown that the radar bright band can be absent in the melting layer at frequencies above 20 GHz. This agrees with radar observations at 35 and 94 GHz. The specific attenuation, as well as the average specific attenuation of the melting layer, is divided into absorption part and scattering part. The latter is increasingly significant with the increase of frequency. The total zenith attenuation due to stratiform rain is divided into the rain zenith attenuation and the additional zenith attenuation, which is the difference between zenith attenuation, due to the melting layer, and attenuation, due to the same path length of the resulting rain. The additional zenith attenuation increases with the increase of rain rate even at frequencies above 20 GHz. This should be taken into account in radar remote sensing and satellite-Earth communications     

Calculations of millimeter wave depolarization due to melting layer and rain

A model for calculating the total depolarization due to the melting layer and rain is proposed under the assumption that oblate spheroidal melting particles and raindrops have the same orientation. The melting layer is composed of the melting particles which are made up from the mixture of ice, air and water. The specific attenuation and the specific phase shift both for the melting layer and for rain are given in the power lawaR ^b form for the rain rates 0≤R≤12.5 mm/h and the parameters are tabled over the frequency range of 1–100 GHz. Using the model, the numerical calculation of the depolarization is possible for three drop size distributions.     

不同类型降水对毫米波传播特性的影响研究

为了提高复杂降水条件下毫米波传播衰减的评估精度,通过分析多个地区的降水谱特征,得出具有代表性的层状云降雨、积层混合云降雨、积雨云降雨以及干雪、湿雪的谱分布参数,然后结合降水粒子的形状、相态、介电模型,计算降水体目标在毫米波波段的散射特性.结果表明,降水强度不是唯一影响毫米波传播衰减的因素; 降水粒子相态、谱分布、入射波频率和温度等对毫米波传播特性均有不同程度的影响,其中谱分布和数密度是影响降雨对毫米波衰减的主要因素; 冰水构成比例是影响降雪对毫米波衰减的主要因素; 不同相态的降水,尤其是干雪、湿雪和雨对毫米波传播影响的差异较大; 而温度的影响较小.并建立了考虑谱分布和温度的降水衰减模型.     

An empirical formula for the prediction of rain attenuation infrequency range 0.6 - 100 GHz

An empirical formula for calculating the extinction cross section (ECS) by raindrops over a broad frequency range is first derived based on extensive calculations made on a widely varying in mean radius of modified Pruppacher and Pitter (MPP) raindrop models ranging from 0.25 to 3.5 mm. The expansion coefficients in the empirical formula are determined by least-squares curve fitting of numerical data obtained by the volume integral equation formulation (VIEF). The formula satisfies the frequency and raindrop size dependence. Numerical results obtained from the empirical formula for calculating the ECS are generally in good agreement with those calculated by the VIEF for raindrops with mean radius varying from 0.25 to 3.5 mm in the frequency range from 0.6 to 100 GHz. The average error in the ECS is less than 10%. The formula thus provides a simple and inexpensive method for calculating the ECS of raindrops, which otherwise requires complicated and expensive methods of calculation. By implementing this empirical formula of ECS into the rain attenuation equation, a new numerically empirical formula for calculating the specific rain attenuation is also proposed. The validity of the empirical formula for calculating the specific rain attenuation is also checked by comparing the obtained results of specific rain attenuation with those obtained from Li et al.'s (1995) solution, Yeo et al.'s (1993) measurement, and Olsen et al.'s (1978) power-law equation     

A dual-polarization rain profiling algorithm

A new attenuation correction algorithm based on profiles of reflectivity, differential reflectivity, and differential propagation phase shift is presented. A solution for specific attenuation retrieval in rain medium is proposed, which solves the integral equations for reflectivity and differential reflectivity with cumulative differential propagation phase shift constraint. The conventional rain profiling algorithms that connect reflectivity and specific attenuation can retrieve specific attenuation values along the radar path assuming a constant intercept parameter of the normalized drop size distribution. However, in convective storms, the drop size distribution parameters can have significant variation along the path. This paper presents a dual-polarization rain profiling algorithm for horizontal looking radars incorporating reflectivity as well as differential reflectivity profiles. The dual-polarization rain profiling algorithm has been evaluated with X-band radar observations simulated from drop size distribution derived from high-resolution S-band measurements collected by the Colorado Statue University CHILL radar. The analysis shows that the retrieved specific attenuation, differential attenuation, reflectivity, and differential reflectivity from the dual-polarization rain profiling algorithm provide significant improvement over the current algorithms.     

广州地区33．5GHz和93GHz降雨传播特性测量

本文给出了１９９２年７—９月份广州地区Ｏ．４ｋｍ地面电路３３．５ＧＨｚ和９３ＧＨｚ雨衰减测量结果及雨衰减和降雨率短期统计结果之间的关系，并利用这一结果和长期降雨率统计对雨衰减预报作了初步探讨。同时分析了３３．５ＧＨＺ和９３ＧＨＺ雨衰减频率换算关系。文中还导出了雨致交叉极化鉴别度（ＸＰＤ）与实测差分衰减和差分相移之间的理论关系。在８ｍｍ波段可忽略差分相移的情况下，给出了利用３３．５ＧＨｚ部分实测差分衰减计算的ＸＰＤ结果，并与理论模式预测值作了比较。     

Characteristics of rain induced attenuation and phase shift at cm and mm waves using a tropical raindrop size distribution model

The tropical raindrop size distribution model developed by Ajayi and Olsen has been employed to study some characteristics of rain induced attenuation and phase shift for a tropical location for spherical, oblate spheroidal and Pruppacher-Pitter drop shapes. Parameters such as the a and b values for the power law relation between the specific attenuation and rainfall rate as well as differential attenuation and phase shift and their normalized values, were computed. A single power law between the specific phase shift and the rain rate was found to be adequate for vertical polarization, whilst a two-segment power law fitting is required for horizontal polarization between 1GHz and about 100GHz. The results were compared in many cases with those obtained with the Laws and Parsons drop size distribution, currently adopted by the CCIR for scattering applications.     

Analytical models for cross-polarization on earth-space radio paths for frequency range 9–30 GHz

Depolarization and attenuation of radiowaves along earth-space paths due to rain storms are characterised. Frequency-dependent expressions for specific attenuation and phase shift at (PC and 20°C and for Laws-Parsons raindrop size distribution are given. Using small amplitude and phase approximations, a simple relation for cross-polar discrimination due to rain in terms of co-polar attenuation, frequency, angle of elevation and polarization angle is derived. Expressions for depolarization due to ice crystals are given, treating them as Rayleigh scatterers of spheroidal shape. For both rain and ice the relationship between linear and circular crosspolar ratio can be shown to be simply sin 2 θ, where θ is the polarization angle.     

Predictions of radiowave attenuations due to a melting layer ofprecipitation

A melting layer model related to the physical constants and meteorological parameters is employed in this investigation. The specific phase shift, together with the specific attenuation, is computed at 1-100 GHz by using the Mie theory. The additional zenith attenuation, which is the difference between zenith attenuation due to the melting layer and attenuation due to the same thickness of the resulting rain, is comprehensively studied. The ratio of the difference to rain zenith attenuation may be over 1 at 1-5 GHz although the difference is much less than 1 dB. The difference can be over 1 dB at frequencies above 20 GHz. A minimum of the ratio is below 0.05 at frequencies about 40-60 GHz but the ratio can become a value of about 0.1 at 100 GHz. The additional attenuation should be taken into account in satellite-Earth communications and radar remote sensing. The power law parameters of the average specific attenuation of the melting layer and rain specific attenuation are tabulated for three raindrop size distributions at rain rates of below 25 mm/h. The power law method could be utilized in the additional attenuation calculation. It is a good approximation of the Mie theory results at 1-50 GHz and a useful estimate at 50-100 GHz     

Rain induced depolarization from 1 GHz to 300 GHz in a tropical environment

The rain induced depolarization in a tropical environment has been studied using a tropical raindrop size distribution developed by Ajayi and Olsen (A-O). The differential attenuation, differential phase shift and cross polarization discrimination, XPD, were computed over a frequency range of 1GHz to 300GHz for spheroidal drops and up to 33GHz for Pruppacher-Pitter drops. The variations of XPD with frequency, rainfall rate and copolar attenuation, CPA, were investigated. A mathematical relationship was established between the XPD and the CPA, canting angle and frequency of propagation from 5GHz to 300 GHz for spheroidal drops and up to 33 GHz for Pruppacher-Pitter drops. The results obtained using the A-O drop size distribution have been compared with those assuming the Laws and Parsons (L-P) distribution. The Pruppacher-Pitter drop shape has been found to give rise to higher XPD, especially at low CPA and high frequencies.     

Frequency dependence of rain attenuation measurements at microwave frequencies

The values of attenuation versus frequency for 10 mm/h, 25 mm/h, and 40 mm/h rain rates for frequencies of 11, 18, and 22.2 GHz are presented. On the basis of these observations the attenuation at frequencies below 10 GHz and above 22.2 GHz have been obtained. The values obtained at various frequencies show an agreement with those calculated on the basis of Oguchi's work. Comparison of the above values in dB/km (assuming a path length of 2.5 km) have been made and they show an agreement with International Radio Consultative Committee (CCIR) values. Also cumulative distributions of attenuation at various frequencies have been given taking 11 GHz results as the reference point.     

Retrieval of Snow and Rain From Combined X- and W-Band Airborne Radar Measurements

Two independent airborne dual-wavelength techniques, based on nadir measurements of radar reflectivity factors and Doppler velocities, respectively, are investigated with respect to their capability of estimating microphysical properties of hydrometeors. The data used to investigate the methods are taken from the ER-2 Doppler radar (X-band) and cloud radar system (W-band) airborne Doppler radars during the Cirrus Regional Study of Tropical Anvils and Cirrus Layers-Florida Area Cirrus Experiment campaign in 2002. Validity is assessed by the degree to which the methods produce consistent retrievals of the microphysics. For deriving snow parameters, the reflectivity-based technique has a clear advantage over the Doppler-velocity-based approach because of the large dynamic range in the dual- frequency ratio (DFR) with respect to the median diameter D₀ and the fact that the difference in mean Doppler velocity at the two frequencies, i.e., the differential Doppler velocity (DDV), in snow is small relative to the measurement errors and is often not uniquely related to D₀. The DFR and DDV can also be used to independently derive D₀ in rain. At W-band, the DFR-based algorithms are highly sensitive to attenuation from rain, cloud water, and water vapor. Thus, the retrieval algorithms depend on various assumptions regarding these components, whereas the DDV-based approach is unaffected by attenuation. In view of the difficulties and ambiguities associated with the attenuation correction at W-band, the DDV approach in rain is more straightforward and potentially more accurate than the DFR method.     

A New Prediction Model of Rain Attenuation That Separately Accounts for Stratiform and Convective Rain

An improved version of the exponential cell (EXCELL) rain attenuation model is presented here. Analogously to the original one, it predicts attenuation through a cellular representation of precipitation, but, in addition, is able to discriminate between stratiform and convective rain by means of an embedded algorithm. Accordingly, two separate physical rain heights, derived from the ERA-15 database, are used to calculate stratiform and convective rain attenuation and, when considering stratiform precipitation, the melting layer contribution to attenuation is added. Eventually, the predicted cumulative distribution function (CDF) of excess attenuation is the combination of the contributions due to stratiform and convective precipitation types. Some input parameters of the prediction model, such as those defining the melting layer process or the rain plateau embedding rain cells, can be modified in order to account for the local meteorological characteristics.      

Melting layer attenuation at 28.6 GHz from simultaneous comstar beacon and polarisation diversity radar data

Attenuation data at 28.6 GHz obtained from measurements of the Comstar beacon show that, for moderate rain, slant path attenuation may significantly exceed that calculated from simultaneous radar reflectivity measurements. Polarisation diversity radar data were used for positive identification of the rain and the melting layer, and for estimating the rain attenuation along the path. These results indicate that the melting layer attenuation is significant.     

Backscatter and attenuation by falling snow and rain at 96, 140,and 225 GHz

The results of measurements are presented for backscatter cross section per unit volume and attenuation for falling snow and rain at 96, 140, and 225 GHz. The attenuation due to rain is almost independent of the measurement frequency, but for snow the attenuation is considerably greater at 225 GHz than at 96 GHz. The rain attenuation generally varies with the rain accumulation rate in accordance with an aR^b relationship for a Laws and Parsons drop-size distribution where R is the rain rate and a and b are constants. The attenuation at all three frequencies is about 3 dB/km for a rain rate of 4 mm/h. The attenuation due to snow varies with airborne snow-mass concentration, with the average rates of increase being 0.9, 2.5, and 8.7 (dB/km)(g/m³) at 96, 140, and 225 GHz, respectively. Generally the attenuation for snow is lower than that for rain. The backscatter cross section per unit volume for rain at 96 GHz is about -35 dB m²/m³ for a rain rate of 4 mm/h. The backscatter from snow at 96 GHz is much lower than that from rain under equivalent accumulation rates or airborne mass concentrations. Snow backscatter at 140 GHz is comparable but higher than that at 96 GHz     

广州地区1—400GHz降雨传播特性的计算

本文利用广州地区滴尺寸分布模型计算了１－４００ＧＨｚ线极化波雨 致特征衰减和相移，并利用计算的雨衰减和相移值回是了其与降雨率之间的指数关系。     

A method to estimate statistics of rain depolarization

This paper is concerned with depolarization caused by rain due to nonsphericity of drops and the distribution of their axes orientations. The drops are assumed to be oblate spheroids having canting angles distribution obtained by Saunders. Differential phase shift as well as differential attenuation is important in the calculation of depolarization and the values proposed by Oguchi and Hosoya are utilized. In the first part expression to calculate depolarization amount for a uniform precipitation rate are presented. But communication engineers are usually interested on statistical variations of depolarization amount, so the second part of this paper is concerned with statistical distribution of depolarization. The rain cell proposed by Misme and Fimbel is used to describe the rain model over a path. If the precipitation rate distribution is known in one point of the path, the depolarization distribution is obtained by assuming only one rain cell along the path where, for a long time observation, the precipitation rate distribution for all points is the same.     

Ice-crystal depolarisation measurements at 28.6 GHz with simultaneous 16.5 GHz polarisation diversity radar observations

Simultaneous measurements with a 16.5 GHz polarisation diversity radar and the 28.56 GHz Comstar beacon are reported. Radar measurements of the differential propagation constant during a severe depolarisation event established that the depolarisation was due primarily to lossless scatterers above the melting layer, with little contribution from rain or the melting layer. Differential phase shifts as high as 1.7°/km at 16.5 GHz, corresponding to 2.9°/km at 28.56 GHz, were observed. Good agreement between radar derived and beacon measurements of differential phase shift was obtained.