Backscattering Cross Section Research Articles

Relation between Raman backscattering from droplets and bulk water: Effect of refractive index dispersion

A theoretical framework is presented that permits investigations of the relation between inelastic backscattering from microparticles and bulk samples of Raman-active materials. It is based on the Lorentz reciprocity theorem and no fundamental restrictions concerning the microparticle shape apply. The approach provides a simple and intuitive explanation for the enhancement of the differential backscattering cross-section in particles in comparison to bulk. The enhancement factor for scattering of water droplets in the diameter range from 0 to 60 µm (vitally important for the a priori measurement of liquid water content of warm clouds with spectroscopic Raman lidars) is about a factor of 1.2–1.6 larger (depending on the size of the sphere) than an earlier study has shown. The numerical calculations are extended to 1000 µm and demonstrate that dispersion of the refractive index of water becomes an important factor for spheres larger than 100 µm. The physics of the oscillatory phenomena predicted by the simulations is explained.

Study of sea-surface slope distribution and its effect on radar backscatter based on Global Precipitation Measurement Ku-band precipitation radar measurements

The collocated normalized radar backscattering cross-section measurements from the Global Precipitation Measurement (GPM) Ku-band precipitation radar (KuPR) and the winds from the moored buoys are used to study the effect of different sea-surface slope probability density functions (PDFs), including the Gaussian PDF, the Gram–Charlier PDF, and the Liu PDF, on the geometrical optics (GO) model predictions of the radar backscatter at low incidence angles (0 deg to 18 deg) at different sea states. First, the peakedness coefficient in the Liu distribution is determined using the collocations at the normal incidence angle, and the results indicate that the peakedness coefficient is a nonlinear function of the wind speed. Then, the performance of the modified Liu distribution, i.e., Liu distribution using the obtained peakedness coefficient estimate; the Gaussian distribution; and the Gram–Charlier distribution is analyzed. The results show that the GO model predictions with the modified Liu distribution agree best with the KuPR measurements, followed by the predictions with the Gaussian distribution, while the predictions with the Gram–Charlier distribution have larger differences as the total or the slick filtered, not the radar filtered, probability density is included in the distribution. The best-performing distribution changes with incidence angle and changes with wind speed.

The Ecology, Biogeochemistry, and Optical Properties of Coccolithophores.

Coccolithophores are major contributors to phytoplankton communities and ocean biogeochemistry and are strong modulators of the optical field in the sea. New discoveries are changing paradigms about these calcifiers. A new role for silicon in coccolithophore calcification is coupling carbonate and silicon cycles. Phosphorus and iron play key roles in regulating coccolithophore growth. Comparing molecular phylogenies with coccolith morphometrics is forcing the reconciliation of biological and geological observations. Mixotrophy may be a possible life strategy for deep-dwelling species, which has ramifications for biological pump and alkalinity pump paradigms. Climate, ocean temperatures, and pH appear to be affecting coccolithophores in unexpected ways. Global calcification is approximately 1-3% of primary productivity and affects CO2 budgets. New measurements of the backscattering cross section of coccolithophores have improved satellite-based algorithms and their application in case I and case II optical waters. Remote sensing has allowed the detection of basin-scale coccolithophore features in the Southern Ocean.

A fast convolution based waveform model for conventional and unfocused SAR altimetry

In this paper we derive a closed-form solution to generate a backscatter power representation for both unfocused synthetic aperture radar altimetry and conventional altimetry signals in the frequency/slow-time domain. This new approach involves fast convolutions and leads to a fast numerical computational model which uses very few approximations. The transform back to the range-time/doppler frequency domain is then made numerically.Two retrackers based on this Signal Model Involving Numerical Convolution (SINC) are constructed for conventional and synthetic aperture radar altimetry and are named SINC2 and SINCS respectively. Output from retracking are the epoch t0 with respect to the tracking reference point, the significant wave height and the backscattering cross section at normal incidence σ0.Main benefits of the SINC model are its flexibility, the possibility to use the real point target response (PTR) or more complex representations of the height probability density function of scattering sea surface elements (PDF), and its fast computation speed to retrack the waveforms.The retrackers are applied to CryoSat-2 reduced SAR (RDSAR) and unfocused SAR waveforms. The RDSAR SINC2 retracker is only ten percent slower than the commonly used MLE3 retracker, which is a minor slowdown compared to the benefits of the SINC model. The SAR processing including the SINCS retracking procedure is three times slower than the RDSAR processing including retracking with SINC2.Model and algorithms are validated on both synthetic data generated by Monte-Carlo simulations and on real datasets. SAR SAMOSA+ results accessible through the ESA G-POD SARvatore service serve as a reference. Cross-validation shows higher agreement between SAR SAMOSA+ and SAR SINCS sea level anomaly and lower agreement between SAR SAMOSA+ and RDSAR SINC2, with accuracy of −0.1 cm for SAR SINCS and 1.7 cm for RDSAR SINC2. Instead, the accuracy of significant wave height, 4.9 cm and 3.9 cm for SAR and RDSAR and of backscatter coefficient, 0.16 and 0.12 dB in SAR and RDSAR, are comparable.Cross-validation results shows for sea level anomaly and significant wave height a higher precision of SAR SINCS and a lower precision of RDSAR SINC2, with precision of 0.92 cm and 6.6 cm for SAR SINCS and 1.96 cm and 12.6 cm for RDSAR SINC2 in sea level anomaly and significant wave height respectively. Instead, the precision of the backscatter coefficient is higher in RDSAR SINC2 than in SAR SINCS, and is 0.014 and 0.016 dB.In summary the new open ocean retrackers are a viable alternative recommended for both reduced and unfocused SAR processing in open ocean.

Lidar cross-sections of soot fractal aggregates: Assessment of equivalent-sphere models

This work assesses the ability of equivalent-sphere models to reproduce the optical properties of soot aggregates relevant for lidar remote sensing, i.e. the backscattering and extinction cross sections. Lidar cross-sections are computed with a spectral discrete dipole approximation model over the visible-to-infrared (400–5000 nm) spectrum and compared with equivalent-sphere approximations. It is shown that the equivalent-sphere approximation, applied to fractal aggregates, has a limited ability to calculate such cross-sections well. The approximation should thus be used with caution for the computation of broadband lidar cross-sections, especially backscattering, at small and intermediate wavelengths (e.g. UV to visible).

Differential Raman backscattering cross sections of black carbon nanoparticles

We report the measurements of the differential Raman backscattering cross sections for several carbonaceous ultrafine particles of environmental relevances. These were obtained by dispersing the target particles in liquid water which was used as the internal standard reference. The optical collection was performed in a configuration to ensure a detection as close as possible to the backward direction. These are the first cross sections on black carbon-type particles although Raman spectroscopy is widely used in Carbon science. The high values of the cross sections, few 10−28 cm2.sr−1.atom−1, reflect resonance effects that take advantages of the disordered polyaromatic structures. Because they were measured in conditions intended to mimic the aerosol phase, these measurements provide a crucial step to move toward quantitative Raman spectroscopy and enable development of dedicated teledetection of black carbon in the atmosphere and in combustion chambers.

The First Results of Monitoring the Formation and Destruction of the Ice Cover in Winter 2014–2015 on Ilmen Lake according to the Measurements of Dual-Frequency Precipitation Radar

The launch of the Dual-frequency Precipitation Radar (DPR) opens up new opportunities for studying and monitoring the land and inland waters. It is the first time radar with a swath (±65°) covering regions with cold climate where waters are covered with ice and land with snow for prolonged periods of time has been used. It is also the first time that the remote sensing is carried out at small incidence angles (less than 19°) at two frequencies (13.6 and 35.5 GHz). The high spatial resolution (4–5 km) significantly increases the number of objects that can be studied using the new radar. Ilmen Lake is chosen as the first test object for the development of complex programs for processing and analyzing data obtained by the DPR. The problem of diagnostics of ice-cover formation and destruction according to DPR data has been considered. It is shown that the dependence of the radar backscatter cross section on the incidence angle for autumn ice is different from that of spring ice, and can be used for classification. A comparison with scattering on the water surface has shown that, at incidence angles exceeding 10°, it is possible to discern all three types of reflecting surfaces: open water, autumn ice, and spring ice, under the condition of making repeated measurements to avoid possible ambiguity caused by wind.

Electromagnetic retroreflection augmented by spherical and conical metasurfaces

The focus of this paper is on phase gradient metasurfaces conformal to spherical and conical bodies of revolution, with an aim of engineering retroreflections and therefore augmenting backscattering cross-sections of those three-dimensional geometries under the illumination of a plane electromagnetic wave. Based on the conducting sphere and cone, the effect of the geometric revolution property on the selection of the unit inclusion of metasurfaces is considered. The procedure for using the selected unit inclusion to implement the proper reflection phase gradient onto the illuminated surfaces of those objects is formulated in detail. Retroreflections resembling conducting plates under normal incidence are observed for both the conducting sphere and cone coated with conformal metasurfaces. As a result, the redirection-induced retroreflection effectively contributes to the backscattering cross-section enhancement. A good agreement between full-wave simulations and measurements demonstrates the validity and effectiveness of backscattering cross-section enhancement using spherical and conical metasurfaces.

Bulk-Density Representations of Branched Planar Ice Crystals: Errors in the Polarimetric Radar Variables

AbstractRecent interest in interpreting polarimetric radar observations of ice and evaluating microphysical model output with these observations has highlighted the importance of accurately computing the scattering of microwave radiation by branched planar ice crystals. These particles are often represented as spheroids with uniform bulk density, reduced from that of solid ice to account for the complex, nonuniform structure of natural branched crystals. In this study, the potential errors that arise from this assumption are examined by comparing scattering calculations of branched planar crystals with those of homogeneous, reduced-density plate crystals and spheroids with the same mass, aspect ratio, and maximum dimension. The results show that this assumption leads to significant errors in backscatter cross sections at horizontal and vertical polarization, specific differential phase (KDP), and differential reflectivity (ZDR), with the largest ZDR errors for ice crystals with the most extreme aspect ratios (<0.01) and effective densities < 250 kg m−3. For example, the maximum errors in X-band ZDR are 4.5 dB for 5.6-mm branched planar crystals. However, substantial errors are present at all weather radar frequencies, with resonance scattering effects at Ka and W band amplifying the low-frequency errors. The implications of these results on the interpretation of polarimetric radar observations and forward modeling of the polarimetric radar variables from microphysical model output are discussed.

Using snowflake surface-area-to-volume ratio to model and interpret snowfall triple-frequency radar signatures

Abstract. The snowflake microstructure determines the microwave scattering properties of individual snowflakes and has a strong impact on snowfall radar signatures. In this study, individual snowflakes are represented by collections of randomly distributed ice spheres where the size and number of the constituent ice spheres are specified by the snowflake mass and surface-area-to-volume ratio (SAV) and the bounding volume of each ice sphere collection is given by the snowflake maximum dimension. Radar backscatter cross sections for the ice sphere collections are calculated at X-, Ku-, Ka-, and W-band frequencies and then used to model triple-frequency radar signatures for exponential snowflake size distributions (SSDs). Additionally, snowflake complexity values obtained from high-resolution multi-view snowflake images are used as an indicator of snowflake SAV to derive snowfall triple-frequency radar signatures. The modeled snowfall triple-frequency radar signatures cover a wide range of triple-frequency signatures that were previously determined from radar reflectivity measurements and illustrate characteristic differences related to snow type, quantified through snowflake SAV, and snowflake size. The results show high sensitivity to snowflake SAV and SSD maximum size but are generally less affected by uncertainties in the parameterization of snowflake mass, indicating the importance of snowflake SAV for the interpretation of snowfall triple-frequency radar signatures.

Observing the evolution and fate of free methane in the ocean

Free methane gas is increasingly observed escaping the seabed in the world’s oceans from sources that are either biogenic, typically in shallow sediments, or from deeper geologic reservoirs. Methane gas bubbles undergo a complicated journey as they rise toward the sea surface. Some or all of the methane may pass through the gas-liquid boundary, into aqueous solution, where it is eventually oxidized and can impact ocean chemistry. Some of the methane, particularly in shallow environments, may reach the atmosphere where it acts as a strong greenhouse gas. One of the key questions regarding the transport of methane upward from the seabed is how much goes where, and this question is being increasingly addressed using acoustic remote sensing techniques. Answering this question begins with seep detection and localization, now routinely performed on data collected with split-beam and multibeam echo sounders. Once located, observations of the bubble-plume backscattering cross section can be used to address questions of flux and vertical gas transport. Both narrow- and broad-band techniques and some of the associated challenges, including wobbly bubbles and multiple scattering in dense plumes, will be discussed.

Backscattering Effects in Media with Strongly Elongated Scattering Indicatrices

We consider the weak localization and the backscattering halo in media with strongly elongated scattering indicatrices. The earlier theory is generalized to the case of a nonuniform backscattering cross section in the rear hemisphere. Asymptotic formulas for the backscattering intensities are obtained in the low-angle diffusion approximation.

Gold nanoshells: Contrast agents for cell imaging by cardiovascular optical coherence tomography

Optical coherence tomography (OCT) has gained considerable attention in interventional cardiovascular medicine and is currently used in clinical settings to assess atherosclerotic lesions and to optimize stent placement. Artery imaging at the cellular level constitutes the first step towards cardiovascular molecular imaging, which represents a major advance in the development of personalized noninvasive therapies. In this work, we demonstrate that cardiovascular OCT can be used to detect individual cells suspended in biocompatible fluids. Importantly, the combination of this catheter-based clinical technique with gold nanoshells (GNSs) as intracellular contrast agents led to a substantial enhancement in the backscattered signal produced by individual cells. This cellular contrast enhancement was attributed to the large backscattering cross-section of GNSs at the OCT laser wavelength (1,300 nm). A simple intensity analysis of OCT cross-sectional images of suspended cells makes it possible to identify the sub-population of living cells that successfully incorporated GNSs. The generalizability of this method was demonstrated using two different cell lines (HeLa and Jurkat cells). This work provides novel insights into cardiovascular molecular imaging using specifically modified GNSs.

Exponential Decomposition with Implicit Deconvolution of Lidar Backscatter from the Water Column

Bathymetric laser scanning is a powerful tool to obtain information about the morphology of coastal, river, and inland waters. Laser scanning in general is a method to sense the shape of remote objects by sweeping a laser beam across the objects while measuring the distance to every surface point. In bathymetric applications, the electromagnetic light wave also needs to penetrate the water column resulting in a spread reflection from below the surface of the water body complicating the interpretation of the received wave. As the signal seen by the sensor’s receiver is the result of a convolution of the system waveform with the differential backscatter cross section, one approach is to use a deconvolution method to recover the object shape. An alternative approach is to fit a parameterised model to the measured receiver signal. While deconvolution methods are not capable to directly deliver object parameters such as distance to water surface or bottom, modelling methods suffer from neglecting the system waveform. We present a new waveform decomposition method that avoids current shortcomings. The proposed method uses a model composed of segments of exponential functions, which is motivated by the physics of the backscatter process in the water column, and a record of the system waveform which is stored as part of the sensor’s calibration data. The method further consists of an algorithm which evaluates the parameters of the exponential model while, at the same time, performing a deconvolution from the system waveform in an implicit manner. The effectiveness of the method is exemplified using real data from a nearshore airborne LIDAR data acquisition.

Characterization of Surface Radar Cross Sections at W-Band at Moderate Incidence Angles

This paper presents the results of a recent flight campaign conducted over the Great Lakes region and reports the first observations of the W-band normalized backscattered cross section ( $\sigma _{0}$ ) for V and H polarization and the linear depolarization ratios (LDRs) from different types of surfaces at moderate incidence angles ( $\sigma _{0}$ behaves as previously reported at small incidence angles, it features a marked decrease with increasing incidence angles between 20° and 50°. There is a strong dependence of normalized backscattered cross sections both on the wind speed and on the wind direction, with larger values found in the presence of higher wind speeds and when the radar antenna is looking upwind. This is in line with theoretical models (though models tend to overpredict the range of variability at a given incidence angle) and with observations at lower frequencies. The LDRs are steadily increasing from values certainly lower than −30 dB, at vertical incidence, to the values of about −10 dB, at the incidence angles of about 60°–70°, with a good matching between observations and theoretical predictions. On the other hand, land surface backscattering properties are not characterized by a strong angular dependence: $\sigma _{0}$ and LDR values typically range between −20 and 0 dB and between −15 and −5 dB, respectively. This paper is relevant for spaceborne concepts of W-band radars, which envisage moderate incidence angles to achieve a broad swath needed for global coverage.

Impacts of oil spills on altimeter waveforms and radar backscatter cross section

AbstractOcean surface films can damp short capillary‐gravity waves, reduce the surface mean square slope, and induce “sigma0 blooms” in satellite altimeter data. No study has ascertained the effect of such film on altimeter measurements due to lack of film data. The availability of Environmental Response Management Application (ERMA) oil cover, daily oil spill extent, and thickness data acquired during the Deepwater Horizon (DWH) oil spill accident provides a unique opportunity to evaluate the impact of surface film on altimeter data. In this study, the Jason‐1/2 passes nearest to the DWH platform are analyzed to understand the waveform distortion caused by the spill as well as the variation of σ0 as a function of oil thickness, wind speed, and radar band. Jason‐1/2 Ku‐band σ0 increased by 10 dB at low wind speed (<3 m s−1) in the oil‐covered area. The mean σ0 in Ku and C bands increased by 1.0–3.5 dB for thick oil and 0.9–2.9 dB for thin oil while the waveforms are strongly distorted. As the wind increases up to 6 m s−1, the mean σ0 bloom and waveform distortion in both Ku and C bands weakened for both thick and thin oil. When wind exceeds 6 m s−1, only does the σ0 in Ku band slightly increase by 0.2–0.5 dB for thick oil. The study shows that high‐resolution altimeter data can certainly help better evaluate the thickness of oil spill, particularly at low wind speeds.

Surface Echo Characteristics Derived From the Wide Swath Experiment of the Precipitation Radar Onboard TRMM Satellite During Its End-of-Mission Operation

The purpose of this paper is to assess the height and strength of the surface echo clutter from the wide swath operation of a future spaceborne precipitation radar (PR) using the wide swath observation data during the end-of-mission experiment of the PR onboard the Tropical Rainfall Measuring Mission (TRMM) satellite. In this experiment, the maximum incident angle was expanded up to 32.5° from nadir, while the maximum incident angle is 18° for normal observation of the TRMM/PR. Although the results show that the clutter height monotonically increases with the incident angle as expected, the clutter height is suppressed for wide angles because of the weakening of the surface echo strength. As a result, the clutter height is less than 2 km if the rain echo is 15 dB higher than the noise level (i.e., about 34 dBZ echo for the TRMM/PR). The clutter height and the normalized backscattering cross section ( $\sigma ^{\mathrm {\mathbf {0}}}$ ) are compared between ocean and land. Suppression of the clutter height is significant over ocean because of the relatively smaller $\sigma ^{\mathrm {\mathbf {0}}}$ (smoother surface) and flat surface (no topography). The impact of the $\sigma ^{\mathrm {\mathbf {0}}}$ for wide swath observation on the rain retrieval algorithm, especially on the surface reference technique, is also examined. The operation with a swath width almost twice the current TRMM/PR is achievable if relatively intense echoes are targeted; however, relatively weak and shallow precipitation will be masked by the clutter.

Accurate absolute measurements of the Raman backscattering differential cross-section of water and ice and its dependence on the temperature and excitation wavelength

Measurements of Raman backscattering spectra between −15°C and 22°C in liquid water (including its supercooled state) and in polycrystalline ice (−35°C to 0°C) at two excitation wavelengths (407 and 532nm) are presented. It is found that the spectrum-integrated backscattering cross-section of the 3400cm−1 band is about 1.2 times larger for ice in comparison to liquid water. The excitation-wavelength dependence of the cross-section in ice is very close to that in water. A discontinuous change of the spectrum is observed upon phase transition at 0°C. The results are applicable to preliminary calibration of lidar systems designed for water content surveys in the atmosphere.

Quantifying uncertainties in radar forward models through a comparison between CloudSat and SPartICus reflectivity factors

AbstractInterpretations of remote sensing measurements collected in sample volumes containing ice‐phase hydrometeors are very sensitive to assumptions regarding the distributions of mass with ice crystal dimension, otherwise known as mass‐dimensional or m‐D relationships. How these microphysical characteristics vary in nature is highly uncertain, resulting in significant uncertainty in algorithms that attempt to derive bulk microphysical properties from remote sensing measurements. This uncertainty extends to radar reflectivity factors forward calculated from model output because the statistics of the actual m‐D in nature is not known. To investigate the variability in m‐D relationships in cirrus clouds, reflectivity factors measured by CloudSat are combined with particle size distributions (PSDs) collected by coincident in situ aircraft by using an optimal estimation‐based (OE) retrieval of the m‐D power law. The PSDs were collected by 12 flights of the Stratton Park Engineering Company Learjet during the Small Particles in Cirrus campaign. We find that no specific habit emerges as preferred, and instead, we find that the microphysical characteristics of ice crystal populations tend to be distributed over a continuum‐defying simple categorization. With the uncertainties derived from the OE algorithm, the uncertainties in forward‐modeled backscatter cross section and, in turn, radar reflectivity is calculated by using a bootstrapping technique, allowing us to infer the uncertainties in forward‐modeled radar reflectivity that would be appropriately applied to remote sensing simulator algorithms.

An Approach to Determining Turbidity and Correcting for Signal Attenuation in Airborne Lidar Bathymetry

Airborne lidar bathymetry is an efficient technique for measuring the bottom of shallow water bodies. A characteristical feature of lidar bathymetry beam propagation is given by scattering and absorption effects in the water column, both leading to a loss of received signal intensity. This loss of signal intensity depends on the turbidity of the water body. Inversely, an analysis of the decay of the recorded waveform signal allows for deriving statements on the local degree of turbidity in the water. The paper shows a first approach on the determination of one turbidity measure per laser pulse by analysing the recorded waveform and fitting an exponential function, wherein the decay coefficient depicts an integral measure describing turbidity. The technique was applied to a shallow inland water, and the results were validated by conventional point-wise turbidity measurement techniques. An obvious consequence of attenuation and loss of signal intensity in lidar bathymetry is the fact that the bottom returns become rather weak. In many cases, conventional ground pulse echo detection techniques fail in detecting water bottom points, leading to a reduced number of water body bottom points and thus limiting the application range of the technique. To partly compensate for this effect, a differential backscatter cross section determination based signal attenuation correction method has been developed, which allows for a signal-derived re-amplification of the ground signal. Although the technique also amplifies noise, it could be shown that it is capable of delivering a higher number of additional ground points and thus extending the applicability of the technique.