Intercomparison of microwave radiative transfer models forprecipitating clouds

An intercomparison of microwave multiple scattering radiative transfer codes used in generating databases for satellite rainfall retrieval algorithms has been carried out to ensure that differences obtained from retrieval techniques do not originate from the underlying radiative transfer code employed for the forward modeling. A set of profiles containing liquid water and ice contents of cloud and rain water as well as snow, graupel and pristine ice were distributed to the participants together with a black box routine providing Mie single scattering, atmospheric background absorption and surface emissivity. Simulations were to be carried out for nadir and off-nadir (53.1°) observation angles at frequencies between 10 and 85 GHz. Among the radiative transfer models were two-stream, multiple stream and Monte Carlo models. The results showed that there were two major sources of differences between the codes. 1) If surface reflection/emission was considered isotropic, simulated brightness temperatures were significantly higher than for specular reflection and this effect was most pronounced at nadir observation and over ocean-type surfaces. 2) Flux-type models including delta-scaling could partially compensate for the errors introduced by the two-stream approximation. Largest discrepancies occurred at high frequencies where atmospheric scattering is most pronounced and at nadir observation. If the same surface boundary conditions, the same multiple-stream resolution and the same scaling procedures are used, the models were very close to each other with discrepancies below 1 K     

基于激光散射理论的微小颗粒测量的数值分析

根据算法的准确性、稳定性和快速性原则, 讨论了Mie散射和Rayleigh散射的数值算法。将Mie散射理论及Rayleigh散射理论的Matlab数值结果与Wiscombe结果对比分析, 证明了此Matlab程序的正确性。在此基础上, 确定了当颗粒粒径参量x0.3时采用Rayleigh散射理论来确定前向某一角度范围内散射光能分布, 从中求得颗粒的粒径大小和分布, 具有比Mie散射理论算法快速性的特点。该方法为某些测试对象(颗粒与分散介质相对折射率、颗粒种类等)确定、微小颗粒的在线测量提供了理论支持。     

Rayleigh-Mie approximation for line-of-sight propagation throughrain at 5-90 GHz

An earlier heuristic model of attenuation and phase changes through a layer of oblate spheroids is replaced by a new, simpler, model with much greater accuracy. The model is meant to cover propagation through rain at 5-90 GHz frequencies and at rain rates from 5-150 mm/hr. Accurate predictions of co and crosspolar attenuation, of co and crosspolar discrimination, and of the various phase changes associated with each polarization of the incident wave are now possible by means of calculations requiring no more than simple numerical extensions of Mie calculations superposed upon the Rayleigh forward-scattering cross sections. Some degree of canting-angle variations is included. Comparison of calculations by this approximation to a variety of empirical or simulated rain statistics available in the literature is presented     

Propagation constant and the velocity of the coherent wave in adense strongly scattering medium

Frequency- and time-domain experiments are conducted to study the effective propagation constant of the coherent wave in a dense strongly scattering medium. A wide-band microwave signal (10-40 GHz) is propagated through randomly distributed glass spheres with a 5.73 mm average diameter and separated into incoherent and coherent fields. The real and imaginary parts of the propagation constant are obtained from the coherent field. The narrow size distribution of the particles enables the authors to study scattering from the Rayleigh region through the Mie resonance scattering region. The results of the experiments are compared to independent scattering, effective-field approximation (Foldy's), and the higher order quasi-crystalline approximation (QCA) using Mie scattering coefficients and the Percus-Yevick approximation for the pair-distribution function. The phase and group velocities of the coherent wave are obtained from the effective propagation constant and compared with theory. In addition, the velocity of the coherent wave in random media is measured using the time-domain technique. It is shown that the velocity of the coherent wave in random media is neither phase nor group velocity     

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     

Ground-based multifrequency microwave radiometry for rainfallremote sensing

Inversion algorithms for ground-based microwave radiometric retrieval of surface rain-rate, integrated cloud parameters, and slant-path attenuation are proposed and tested. The estimation methods are trained by numerical simulations of a radiative transfer model applied to microphysically-consistent precipitating cloud structures, representative of stratiform and convective rainy clouds. The discrete-ordinate method is used to solve the radiative transfer equation for plane-parallel seven-layer structures, including liquid, melted, and ice spherical hydrometeors. Besides ordinary multiple regression, a variance-constrained regression algorithm is developed and applied to synthetic data in order to evaluate its robustness to noise and its potentiality. Selection of optimal frequency sets and polynomial retrieval algorithms for rainfall parameters is carried out and discussed. Ground-based radiometric measurements at 13.0, 23.8, and 31.7 GHz are used for experimentally testing the retrieval algorithms. Comparison with rain-gauge data and rain path-attenuation measurements, derived from the three ITALSAT satellite beacons at 18.7, 39.6, and 49.5 GHz acquired at Pomezia (Rome, Italy), are performed for two selected cases of moderate and intense rainfall during 1998     

A broadband microwave radiometer technique at X-band for rain and drop size distribution estimation

Radiometric brightness temperatures below about 12 GHz provide accurate estimates of path attenuation through precipitation and cloud water. Multiple brightness temperature measurements at X-band frequencies can be used to estimate rainfall rate and parameters of the drop size distribution once correction for cloud water attenuation is made. Employing a stratiform storm model, calculations of the brightness temperatures at 9.5, 10, and 12 GHz are used to simulate estimates of path-averaged median mass diameter, number concentration, and rainfall rate. The results indicate that reasonably accurate estimates of rainfall rate and information on the drop size distribution can be derived over ocean under low to moderate wind speed conditions.     

On the estimation of snow depth from microwave radiometricmeasurements

Multiple-channel microwave radiometric measurements made over Alaska at aircraft (near 90 and 183 GHz) and satellite (at 37 and 85 GHz) altitudes are used to study the effect of atmospheric absorption on the estimation of snow depth. The estimation is based on the radiative transfer calculations using an early theoretical model of Mie scattering of single-size particles. It is shown that the radiometric correction for the effect of atmospheric absorption is important even at 37 GHz for a reliable estimation of snow depth. Under a dry atmosphere and based on single-frequency radiometric measurements, the underestimation of snow depth could amount to 50% at 85 GHz and 20-30% at 37 GHz if the effect of atmospheric absorption is not taken into account. The snow depths estimated from the 90-GHz aircraft and 85-GHz satellite measurements are found to be in reasonable agreement. However, there is a discrepancy in the snow depth estimated from the 37-GHz (at both vertical and horizontal polarizations) and 85-GHz satellite measurements     

Bistatic scatter from rain

An experimental investigation of bistatic scatter from rain was conducted using a 143 km scatter path at frequencies of 4.5 and 7.7 GHz. The ratio of transmitted to received power (transmission loss) was measured for scattering angles ranging from6degto130deg. Simultaneous weather radar observations were made at a frequency of 1.3 GHz. Transmission loss estimates for the bistatic scatter path were computed using the weather radar data, the bistatic radar equation, and a model for the scattering cross section per unit volume of rain based upon Rayleigh scattering by an ensemble of water spheres. The measured and estimated transmission loss values were compared to test the use of the scattering model for the estimation of interference. The averaged ratio of measured-to-calculated transmission loss for the 4.5 GHz data is 1.2pm 0.4dB. The averaged ratio for the 7.7 GHz data is -1.6pm 0.5dB. Both these values are within the combined calibration uncertainties of each measurement system. The results show that the use of the simplified Rayleigh scattering cross section model for an ensemble of water spheres adequately describes bistatic scatter for a wide range of scattering angles and frequencies below 7.7 GHz for the hydrometeor types (rain, snow, and mixed rain and snow) encountered in New England.     

One-dimensional variational retrieval algorithm of temperature, water vapor, and cloud water profiles from advanced microwave sounding unit (AMSU)

The measurements from satellite microwave imaging and sounding channels are simultaneously utilized through a one-dimensional (1-D) variation method (1D-var) to retrieve the profiles of atmospheric temperature, water vapor and cloud water. Since the radiative transfer model in this 1D-var procedure includes scattering and emission from the earth's atmosphere, the retrieval can perform well under all weather conditions. The iterative procedure is optimized to minimize computational demands and to achieve better accuracy. At first, the profiles of temperature, water vapor, and cloud liquid water are derived using only the AMSU-A measurements at frequencies less than 60 GHz. The second step is to retrieve rain and ice water using the AMSU-B measurements at 89 and 150 GHz. Finally, all AMSU-A/B sounding channels at 50-60 and 183 GHz are utilized to further refine the profiles of temperature and water vapor while the profiles of cloud, rain, and ice water contents are constrained to those previously derived. It is shown that the radiative transfer model including multiple scattering from clouds and precipitation can significantly improve the accuracy for retrieving temperature, moisture and cloud water. In hurricane conditions, an emission-based radiative transfer model tends to produce unrealistic temperature anomalies throughout the atmosphere. With a scattering-based radiative transfer model, the derived temperature profiles agree well with those observed from aircraft dropsondes.     

Cloud Liquid Water Content and Cloud Attenuation Studies with Radiosonde Data at a Tropical Location

The profile of cloud liquid water density and the total liquid water content (LWC) are obtained from the radiosonde data using the Salonen model at Kolkata, India, a tropical location. The cumulative distribution LWC shows a departure from the ITU-R model at this location, exhibiting a significantly enhanced occurrence during the monsoon months. The cloud attenuation, derived by integrating the profile of specific attenuation obtained from the radiosonde data, is related to LWC at different frequencies in the range 10-100 GHz. A comparison indicates that the cloud attenuation at frequencies below 50 GHz is somewhat overestimated by the ITU-R model generated values and significantly underestimated by the ITU-R model at frequencies above 70 GHz at the present location.     

A More Precise Empirical Formula for Estimating Normalized Fog Attenuation in the Millimeter-Wave Frequency Range 30 ~ 100 GHz

At millimeter wavelengths, normalized fog attenuation (NFA) in units of (dB/km)/ (g/m³) is generally calculated by the Rayleigh approximation when working wavelengths are much larger than the average diameter of fog droplets. The calculations of the Rayleigh approximation are much less than those of Mie scattering theory, but still complex and heavy. To solve the above problem and facilitate the engineering applications of the Rayleigh approximation, a new empirical formula is discussed to estimate NFA in the frequency range 30?~?100 GHz and the fog common temperature range ?8?~?20 °C. The simulation results of the new formula are compared with those got by other three empirical formulae: the Altshuler empirical formula, the Liebe empirical formula and the Zhao empirical formula. Maximal absolute value of the relative errors (MAVRE) and Pearson correlation coefficient (PCC) indicate the largest deviation of estimated results and the fitting performance of an empirical formula, respectively. Comparisons show that the MAVRE of the new formula is only 4.482 %, which is much smaller than those of the other three formulae. The mean value of the Pearson correlation coefficients (PCCs) of the proposed formula is 0.999943, larger than those of other methods. Additionally, relative error (RE) curves of the four empirical formulae are given at four certain temperatures ?8 °C, 0 °C, 10 °C and 20 °C.     

Q-switched semiconductor diode lasers

Diode lasers with an intracavity electroabsorption modulator have been operated with full on/off modulation at rates of 3 GHz. In addition, modulation of the lasers has been shown up to a detector-limited frequency of 6 GHz. A new model of these devices, which includes amplified spontaneous emission and high gain is developed in this paper. A quasi-static gain approximation is introduced and the dynamics of the electron and photon population are modeled by three coupled nonlinear difference equations which can be numerically solved with very little computation time. The model predicts the possibility of a new mode ofQ-switched operation with the capacity for repetition rates of tens of gigahertz and binary pulse position modulation at rates of the order of 10 Gbits/s.     

Incremental frequency, amplitude and phase tracker (IFAPT) forcoherent demodulation over fast flat fading channels

The incremental frequency amplitude and phase tracker (IFAPT) is a recursive algorithm that estimates the parameters of piecewise-linear approximation to assumed continuous narrow-band signals. The parameters are amplitude, phase, and their respective slopes. The simple, recursive nature of IFAPT enables its direct interaction with recursive algorithms, such as the Viterbi and the BCJR in the APP SISO module, used for iteratively decoding concatenated codes. An augmented APP (A ²P²)-module, containing IFAPT and BCJR algorithms, is here applied to iterative decoding serial concatenated convolutional codes under Rayleigh fading conditions with diversity reception. The bit-error rate under Rayleigh fading with dual diversity reception at E _bT/N₀=6 dB and f_dT_s=10^-2 is 10^-4, where E _bT is the total mean energy per bit in both diversity branches, f_d is the Doppler frequency, and T_s the symbol time     

The role of circular polarization in bistatic radar for mitigation of interference due to rain

Based on the existing theories on scattering from a volume of rain and empirical models on rain drop size distribution and Mie solution of the problem of diffraction by a sphere, it is shown that for radar frequencies below 10 GHz one can realize 10 dB rain rejection by using circular polarization as opposed to linear polarization for bistatic angles of up to90deg.     

Millimeter-wave attenuation and delay rates due to frog/cloudconditions

Propagation properties of suspended water and ice particles which make up atmospheric haze, fog, and clouds were examined for microwave and millimeter-wave frequencies. Rates of attenuation α (dB/km) and delay τ (ps/km) are derived from a complex refractivity based on the Rayleigh absorption approximation of Mie's scattering theory. Key variables are particle mass content and permittivity, which depends on frequency and temperature both for liquid and ice states. Water droplet attenuation can be estimated within a restricted (10±10°C) temperature range using a simple two-coefficient approximation. Experimental data on signal loss and phase delay caused by fog at four frequencies (50, 82, 141, and 246 GHz) over a 0.81-km line-of-sight path were found to be consistent with the model     

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     

The GSMaP Precipitation Retrieval Algorithm for Microwave Sounders—Part I: Over-Ocean Algorithm

We develop an over-ocean rainfall retrieval algorithm for the Advanced Microwave Sounding Unit (AMSU) based on the Global Satellite Mapping of Precipitation (GSMaP) microwave radiometer algorithm. This algorithm combines an emission-based estimate from brightness temperature (Tb) at 23 GHz and a scattering-based estimate from Tb at 89 GHz, depending on a scattering index (SI) computed from Tb at both 89 and 150 GHz. Precipitation inhomogeneities are also taken into account. The GSMaP-retrieved rainfall from the AMSU (GSMaP_AMSU) is compared with the National Oceanic and Atmospheric Administration (NOAA) standard algorithm (NOAA_AMSU)-retrieved data using Tropical Rainfall Measuring Mission (TRMM) data as a reference. Rain rates retrieved by GSMaP_AMSU have better agreement with TRMM estimates over midlatitudes during winter. Better estimates over multitudes over winter are given by the use of Tb at 23 GHz in the GSMaP_AMSU algorithm. It was also shown that GSMaP_AMSU has higher rain detection than NOAA_AMSU.      

三波段超材料吸波体及其优化*

基于超材料的电磁谐振原理设计了一种三波段的超材料吸波体.该吸波体由电环谐振器和金属线组成.仿真结果显示,该谐振器有3个明显的吸收峰.在8.06GHz时,吸收率达到了94.02％;在4.76GHz时,吸收率为79.02％;而12.3GHz时,吸收率则是73％.在此基础上,利用一种结合了连续蚁群算法和差分进化算法的新型优化算法对该结构进行优化,使得该结构在4.9GHz和11.85GHz附近吸收率达到95％以上,可以灵活地实现特定频率处的高吸收率.     

Radar reflectivity in snowfall

Backscattering properties of dry snowflakes at different microwave frequencies are examined. It is shown that the Rayleigh approximation does not often provide the necessary accuracy for snowflake reflectivity calculations for radar wavelengths used in meteorology; however, another simple approximation, the Rayleigh-Gans approximation, can be safely used for such calculations. Reflectivity-snowfall rate relationships are derived for different snow densities and different radar frequencies. It is shown that dual-wavelength radar measurements can be used for estimating the effective sizes of snowflakes. Experimental data obtained during radar snowfall measurements in the WISP project of 1991 with the NOAA X- and Ka-band radars are found to be consistent with the described theoretical results