Backscattering Cross Section Research Articles

Rain effect on C-band scatterometer wind measurement and its correction

It is viewed traditionally that the attenuation and scattering of rain have no effect on C-band scatterometer because its wavelength is greater than the diameter of raindrops, so rain effects on C-band scatterometer wind measurement are often ignored. According to the attenuation and the volume backscatter of the scatterometer signal by raindrops and the perturbation of the water surface by rain, in this paper, we derive the radar equation of the rainfall, collect the data from ASCAT backscatter, rain data from PR and wind field from the European Centre for Medium-Rang Weather Foremasts in 2010, and quantitatively analyze the influence of rainfall on the normalized radar backscattering cross section of the C-band scatterometer. Our results show that the attenuation increases as the rain rate and the incidence angle increase, the volume backscatter and the perturbation of the water surface increase with the increase of rain rate and decrease with the increase of incidence angle, and the influence of the perturbation on the wind measurement of the scattermeter is greater than the volume backscatter. In addition, we establish the C-band active microwave radiative transfer model for the rainfall by the radar equation and the collected data. The experimental results indicate that the new model can improve the C-band scatterometer wind measurement accuracy under rainfall conditions.

Radar Backscattering from Snowflakes: Comparison of Fractal, Aggregate, and Soft Spheroid Models

Abstract The sensitivity of radar backscattering cross sections on different snowflake shapes is studied at C, Ku, Ka, and W bands. Snowflakes are simulated using two complex shape models, namely, fractal and aggregate, and a soft spheroid model. The models are tuned to emulate physical properties of real snowflakes, that is, the mass–size relation and aspect ratio. It is found that for particle sizes up to 5 mm and for frequencies from 5 to 35 GHz, there is a good agreement in the backscattering cross section for all models. For larger snowflakes at the Ka band, it is found that the spheroid model underestimates the backscattering cross sections by a factor of 10, and at W band by a factor of 50–100. Furthermore, there is a noticeable difference between spheroid and complex shape models in the linear depolarization ratios for all frequencies and particle sizes.

Single-scattering of preferentially oriented ice crystals at centimeter and millimeter wavelengths

The scattering properties of frozen cloud and precipitation particles at centimeter and millimeter wavelengths are fundamental for active and passive microwave remote sensing. So far the scattering parameters (scattering-, absorption-, and backscattering cross sections as well as asymmetry factor) have been calculated for randomly oriented particles only. However, some particle types, especially planar crystals, exhibit a preferred horizontal orientation. In this study the scattering and absorption parameters of four different planar ice crystal types have been modeled and exemplarily calculated from 1GHz to 300GHz with a freely available software code implementing the Discrete Dipole Approximation (DDA). It is presented how scattering and absorption of horizontally oriented ice crystals turn out for nadir-looking and inclined satellite sensors. The results show that small deviations around the horizontal orientation, as they are reported by relevant papers on cloud microphysics, have only marginal influence. Among all scattering parameters, the backscattering cross section of oriented crystals can differ most with respect to a random orientation. Especially if the incident wave direction is normal to the basal face, the parameter was found to be up to 20 times higher. Therefore the consideration of the orientation especially can be important for active microwave sensors. The more so if horizontally oriented particles and a nadir looking active sensor are involved. Furthermore the existing compilations for the index of refraction of ice at microwave frequencies have been reviewed.

The relative effects of particles and turbulence on acoustic scattering from deep-sea hydrothermal vent plumes

Acoustic methods are applied to the investigation and monitoring of a vigorous hydrothermal plume within the Main Endeavor vent field at the Endeavor segment of the Juan de Fuca Ridge. Forward propagation and scattering from suspended particulates using Rayleigh scattering theory is shown to be negligible (log-amplitude variance σ(χ) (2)~10(-7)) compared to turbulence induced by temperature fluctuations (σ(χ) (2)~0.1). The backscattering from turbulence is then quantified using the forward scattering derived turbulence level, which gives a volume backscattering strength of s(V)=6.5 × 10(-8) m(-1). The volume backscattering cross section from particulates can range from s(V)=3.3 × 10(-6) to 7.2 × 10(-10) m(-1) depending on the particle size. These results show that forward scatter acoustic methods in hydrothermal vent applications can be used to quantify turbulence and its effect on backscatter measurements, which can be a dominant factor depending on the particle size and its location within the plume.

Derivation of internal solitary wave amplitude in the South China Sea deep basin from satellite images

In the present study, theories based on the Korteweg–de Vries equation are extended to the Benjamin–Ono equation to allow the determination of internal solitary wave (ISW) amplitude from satellite images. The free surface flow induced by an ISW is derived for deep water. As a coherent structure, the amplitude of the ISW has a unique relation to the convergence/divergence of surface flow, such that the flow convergence/divergence will increase/decrease the backscattering cross section and generate bright/dark bands in satellite images. The distance between bright and dark bands can be related to the amplitude of ISW. To validate the theory, a multi-ship measurement made on 9–11 May 2005 during the spring tide period is used. A systematic approach to determine the thickness and density of the upper and lower layers is also included so that the free surface flow can be determined with a relatively high accuracy.

Millimeter wave scattering from ice crystals and their aggregates: Comparing cloud model simulations with X- and Ka-band radar measurements

[1] Arctic clouds are often mixed-phase, such that the radiative properties of the clouds are a strong function of the relative amounts of cloud liquid and ice. Modeling studies have shown that the poorly understood ice phase processes are the regulators of the liquid water fraction. However, evaluating the fidelity of the model ice parameterizations has proven to be a difficult task. This study evaluates results of different ice microphysics representations in a cloud resolving model (CRM) using cloud radar measurements. An algorithm is presented to generate realistic ice crystals and their aggregates from which radar backscattering cross sections may be calculated using a generalized solution for a cluster of spheres. The aggregate is composed of a collection of ice crystals, each of which is constructed from a cluster of tiny ice spheres. Each aggregate satisfies the constraints set by the component crystal type and the mass-dimensional relationship used in the cloud resolving model, but is free to adjust its aspect ratio. This model for calculating radar backscattering is compared to two spherical and two spheroidal (bulk model) representations for ice hydrometeors. It was found that a refined model for representing the ice hydrometeors, both pristine crystals and their aggregates, is required in order to obtain good comparisons between the CRM calculations and the radar measurements. The addition of the radar-CRM comparisons to CRM-in situ measurements comparisons allowed conclusions about the appropriateness of different CRM ice microphysics parameterizations.

Quantifying quagga mussel veliger abundance and distribution in Copper Basin Reservoir (California) using acoustic backscatter

Quagga mussels ( Dreissena bugensis) have been linked to oligotrophication of lakes, alteration of aquatic food webs, and fouling of infrastructure associated with water supply and power generation, causing potentially billions of dollars in direct and indirect damages. Understanding their abundance and distribution is key in slowing their advance, assessing their potential impacts, and evaluating effectiveness of control strategies. Volume backscatter strength (Sv) measurements at 201- and 430-kHz were compared with quagga mussel veliger and zooplankton abundances determined from samples collected using a Wisconsin closing net from the Copper Basin Reservoir on the Colorado River Aqueduct. The plankton within the lower portion of the water column (>18 m depth) was strongly dominated by d-shaped quagga mussel veligers, comprising up to 95–99% of the community, and allowed direct empirical measurement of their mean backscattering cross-section. The upper 0–18 m of the water column contained a smaller relative proportion of veligers based upon net sampling. The difference in mean volume backscatter strength at these two frequencies was found to decrease with decreasing zooplankton abundance ( r 2 = 0.94), allowing for correction of Sv due to the contribution of zooplankton and the determination of veliger abundance in the reservoir. Hydroacoustic measurements revealed veligers were often present at high abundances (up to 100–200 ind L −1) in a thin 1–2 m layer at the thermocline, with considerable patchiness in their distribution observed along a 700 m transect on the reservoir. Under suitable conditions, hydroacoustic measurements can rapidly provide detailed information on the abundance and distribution of quagga mussel veligers over large areas with high horizontal and vertical resolution.

SAR SIMULATION STUDY OF STEEP SLOPE BOTTOM TOPOGRAPHY

A simulation model for the radar backscattering cross section of the sea surface was developed based on the synthetic aperture radar (SAR) imaging mechanism of sea bottom topography. With this model, steep slope bottom topography was simulated. The results show that the maximum depth of measurement can be 100～200 meters if the slope of bottom topography is steep enough. This is in agreement with the SAR observation of the Zengwenxi bottom topography in Taiwan.

On observing acoustic backscattering from salinity turbulence

It has been hypothesized that at sufficiently high levels of oceanic salinity turbulence it should be possible to observe acoustic backscattering. However, there have been limited in situ measurements to confirm this hypothesis. Using an autonomous underwater vehicle equipped with upward and downward looking 1.2 MHz acoustic Doppler current profilers and with turbulence and fine scale sensors, measurements were performed in a region of intense turbulence and a strong salinity gradient. The approach taken was to correlate variations in the backscattered acoustic intensity, I, with a theoretical acoustic backscattering cross section per volume for salinity turbulence, σ(s), to obtain an estimated scattering cross section per volume, σ(e). Results indicated that of order 50% of the observed region was characterized by salinity turbulence induced backscattering.

A new transducer receive transfer function calibration method: application to microbubble backscattering cross-section measurements at high frequency

When comparing acoustic scattering experiments with theory, the relationship between the pressure generated by a scatterer at the surface of a transducer and the induced voltage must be known. Methods have been previously proposed to measure the receive transfer function that rely on several assumptions. A new, experimental method for measuring the acoustic response of a spherically-focused transducer, using a hydrophone at twice the focal distance, is proposed that requires a minimum number of assumptions and calculations. The receive transfer function of a spherically-focused, high-frequency transducer was calculated, and found to be within 10% of the receive transfer function calculated assuming reciprocity. Further, using the receive transfer function, the effective backscattering cross-section of bound microbubbles interrogated at 30 MHz was measured to be, on average, 65% of the geometric backscattering cross-section, with significant size-independent variability. These results give insight into selecting the optimal microbubble size distribution for linear microbubble imaging at high frequencies.

CloudSat W-Band Radar Measurements of Surface Backscatter

The authors examine the characteristics of the W-band surface backscatter cross section using data from the 94-GHz cloud profiling radar on the CloudSat mission. These data from CloudSat represent the first global measurements of surface properties at 94 GHz. The authors use these data to investigate seasonal changes in surface backscatter over both land and ocean. The authors also make use of a limited set of off-nadir data to investigate behavior of W-band backscatter from the ocean versus wind speed for incidence angles up to 17°.

Measurement and analysis of the diffuse reflectance of powdered samples at terahertz frequencies using a quantum cascade laser

We report terahertz (THz) diffuse reflectance measurements of bulk powdered samples at a frequency of 2.83 THz using a narrowband quantum cascade laser. Samples studied comprise polydisperse powders with absorption coefficients extending over two orders of magnitude from ∼3 cm(-1) to >200 cm(-1). Diffuse reflectance measurements are used to obtain the effective absorption coefficient of these samples from the backscattering cross-section, predicted under the quasi-crystalline approximation (QCA) in the T-matrix formulation and in conjunction with the Percus-Yevick pair distribution function. Results are compared with effective absorption coefficients obtained from THz time-domain spectroscopy measurements on pressed pellet samples, and show good agreement over the range of effective absorption coefficients studied. We observe that the backscattering cross-section predicted under the QCA is strongly dependent on both the real and imaginary components of the complex permittivity of the sample, and we show that reliable determination of the absorption coefficient from diffuse reflectance measurements therefore requires knowledge of the sample's refractive index. This work demonstrates the applicability of diffuse reflectance measurements, using a THz frequency quantum cascade laser, to the high-resolution spectroscopic analysis of bulk powdered samples at THz frequencies.

Backscattering of light by hexagonal ice crystals: A numerical study

The characteristics of backscattering of light by hexagonal crystals, namely, the depolarization ratio and backscattering cross section, are numerically studied. The dependence of the microphysical characteristics of backscattering on the particle shape in the case of chaotic particle orientation is investigated. The numerical study is performed using a computer code, developed by the author; it combines two approaches: the ray-tracing technique and the physical-optics method.

Backscattering from a pressure-release rough surface.

The backscattering of an incident Gaussian-tapered acoustic plane wave is modeled using finite elements, the Kirchhoff approximation, and perturbation theory, with the aim of quantifying the validity of the approximate models. von Karman-type power spectra describing the bottom roughness are sampled from the literature with rms roughness from 3–15% of the acoustic wavelength. Realizations of each type of spectrum are made assuming a Gaussian surface height distribution, and an average backscattering cross section is obtained by ensemble averaging. The pressure-release bottom is used instead of a penetrable sediment, as the focus in this study is to quantify the differences between finite elements and the approximate models due to roughness. [Work supported by ONR.]

An ultra‐wideband fractal slot antenna with low backscattering cross section

AbstractIn this article, an ultra‐wide modified Koch fractal antenna is proposed.Simulated and measured results show that the bandwidth of −10 dB return loss is from 2.7 GHz to more than 15 GHz. The radiation patterns are comparatively symmetrical at both 3 and 8 GHz. Moreover, this novel antenna has low backscattering cross section compared with the initial square slot antenna. The backscattering cross section values of the two antennas with different load are also presented to make the achievement of the RCS values with arbitrary load possible. © 2011 Wiley Periodicals, Inc. Microwave Opt Technol Lett 53:1150–1154, 2011; View this article online at wileyonlinelibrary.com. DOI 10.1002/mop.25915

Improving the rainfall rate estimation in the midstream of the Heihe River Basin using raindrop size distribution

Abstract. During the intensive observation period of the Watershed Allied Telemetry Experimental Research (WATER), a total of 1074 raindrop size distribution were measured by the Parsivel disdrometer, the latest state-of-the-art optical laser instrument. Because of the limited observation data in Qinghai-Tibet Plateau, the modelling behaviour was not well done. We used raindrop size distributions to improve the rain rate estimator of meteorological radar in order to obtain many accurate rain rate data in this area. We got the relationship between the terminal velocity of the raindrop and the diameter (mm) of a raindrop: v(D) = 4.67D0.53. Then four types of estimators for X-band polarimetric radar are examined. The simulation results show that the classical estimator R (ZH) is most sensitive to variations in DSD and the estimator R (KDP, ZH, ZDR) is the best estimator for estimating the rain rate. An X-band polarimetric radar (714XDP) is used for verifying these estimators. The lowest sensitivity of the rain rate estimator R (KDP, ZH, ZDR) to variations in DSD can be explained by the following facts. The difference in the forward-scattering amplitudes at horizontal and vertical polarizations, which contributes KDP, is proportional to the 3rd power of the drop diameter. On the other hand, the exponent of the backscatter cross-section, which contributes to ZH, is proportional to the 6th power of the drop diameter. Because the rain rate R is proportional to the 3.57th power of the drop diameter, KDP is less sensitive to DSD variations than ZH.

Altimeter-Derived Ocean Wave Period Using Genetic Algorithm

It is known that wave period can be estimated from altimeter measurements of wave height, wind speed, radar backscatter cross section, etc., using empirical relationship. Of late, the data adaptive approach of neural networks has been used to derive wave period from altimeter data, and it has been shown that the technique appears to be superior compared to the empirical approaches. Another powerful data adaptive approach of genetic algorithm has been advocated more recently in oceanographic studies. Although primarily used for forecasting time series, the algorithm can be tuned to find a relationship between input and output variables. In the present work, this algorithm has been used to find estimates of wave period from altimeter-observed parameters, and the performance of the algorithm has been found to be quite satisfactory. It has been also found that the introduction of wave age leads to significant enhancement of the accuracy of the estimate.

Reducing backscattering cross section of an electrically large sphere with metamaterial coating

In this paper, we present a method for hiding large spheres. Our proposed coating can make a significant reduction in backscattering cross section of an electrically large sphere. Since the monostatic radar cross section (RCS) is based on backscatter waves, such a coated sphere cannot be detected by this kind of radars. Also the effect of loss is considered in coating and we prove that even with a lossy coating, transparency is achievable in front of monostatic radars.

On the impact of non-sphericity and small-scale surface roughness on the optical properties of hematite aerosols

We perform a comparative modelling study to investigate how different morphological features influence the optical properties of hematite aerosols. We consider high-order Chebyshev particles as a proxy for aerosol with a small-scale surface roughness, and spheroids as a model for nonspherical aerosols with a smooth boundary surface. The modelling results are compared to those obtained for homogeneous spherical particles. It is found that for hematite particles with an absorption efficiency of order unity the difference in optical properties between spheres and spheroids disappears. For optically softer particles, such as ice particles at far-infrared wavelengths, this effect can be observed for absorption efficiencies lower than unity. The convergence of the optical properties of spheres and spheroids is caused by absorption and quenching of internal resonances inside the particles, which depend both on the imaginary part of the refractive index and on the size parameter, and to some extent on the real part of the refractive index. By contrast, small-scale surface roughness becomes the dominant morphological feature for large particles. This effect is likely to depend on the amplitude of the surface roughness, the relative significance of internal resonances, and possibly on the real part of the refractive index. The extinction cross section is rather insensitive to surface roughness, while the single-scattering albedo, asymmetry parameter, and the Mueller matrix are strongly influenced. Small-scale surface roughness reduces the backscattering cross section by up to a factor of 2–3 as compared to size-equivalent particles with a smooth boundary surface. This can have important implications for the interpretation of lidar backscattering observations.

Modeling radar scattering from icy lunar regoliths at 13 cm and 4 cm wavelengths

[1] Two orbital synthetic aperture radars (SARs), the Chandrayaan-1 Mini-SAR (13 cm wavelength) and the Lunar Reconnaissance Orbiter (LRO) Mini-RF (13 and 4.2 cm wavelengths), have been imaging the lunar surface searching for ice deposits in the polar permanently shadowed areas. To understand the radar signatures of lunar polar ices, an empirical two-component model with parametric variations of the specular and diffuse components was developed and validated. This model estimates scattering differences associated with slopes, surface roughness, thin regolith over ice, and patches of ice. Lunar radar backscatter cross sections for the average surface for the Chandrayaan-1 and LRO instruments are estimated from the radar cross sections from the Moon at 3.8, 23, and 68 cm wavelengths measured in the 1960s at the Massachusetts Institute of Technology. This modeling predicts that enhanced diffuse scattering from near-surface ice can be separated from rocks if the scattering is characterized by both the high reflectivity and circular polarization ratios (CPRs) like those observed on Mercury, Mars, and the Galilean satellites. Scattering from near-surface ices covered by a thin regolith can be separated from rocks if the enhancement is twice the average or more. If, however, the lunar ice is dispersed throughout the regolith as ice-filling pores, then scattering differences might be too small to detect. Preliminary validation using LRO radar data for a few polar and midlatitude craters indicate that the observed CPRs are consistent with our models for different regolith ice and roughness conditions.