Multiple-scattering in radar systems: a review

Although extensively studied within the lidar community, the multiple scattering phenomenon has always been considered a rare curiosity by radar meteorologists. Up to few years ago its appearance has only been associated with two- or three-body-scattering features (e.g. hail flares and mirror images) involving highly reflective surfaces. Recent atmospheric research aimed at better understanding of the water cycle and the role played by clouds and precipitation in affecting the Earth's climate has driven the deployment of high frequency radars in space. Examples are the TRMM 13.5 GHz, the CloudSat 94 GHz, the upcoming EarthCARE 94 GHz, and the GPM dual 13-35 GHz radars. These systems are able to detect the vertical distribution of hydrometeors and thus provide crucial feedbacks for radiation and climate studies. The shift towards higher frequencies increases the sensitivity to hydrometeors, improves the spatial resolution and reduces the size and weight of the radar systems. On the other hand, higher frequency radars are affected by stronger extinction, especially in the presence of large precipitating particles (e.g. raindrops or hail particles), which may eventually drive the signal below the minimum detection threshold. In such circumstances the interpretation of the radar equation via the single scattering approximation may be problematic. Errors will be large when the radiation emitted from the radar after interacting more than once with the medium still contributes substantially to the received power. This is the case if the transport mean-free-path becomes comparable with the instrument footprint (determined by the antenna beam-width and the platform altitude). This situation resembles to what has already been experienced in lidar observations, but with a predominance of wide- versus small-angle scattering events. At millimeter wavelengths, hydrometeors diffuse radiation rather isotropically compared to the visible or near infrared region where scattering is predominantly in the forward direction. A complete understanding of radiation transport modeling and data analysis methods under wide-angle multiple scattering conditions is mandatory for a correct interpretation of echoes observed by space-borne millimeter radars. This paper reviews the status of research in this field. Different numerical techniques currently implemented to account for higher order scattering are reviewed and their weaknesses and strengths highlighted. Examples of simulated radar backscattering profiles are provided with particular emphasis given to situations in which the multiple scattering contributions become comparable or overwhelm the single scattering signal. We show evidences of multiple scattering effects from air-borne and from CloudSat observations, i.e. unique signatures which cannot be explained by single scattering theory. Ideas how to identify and tackle the multiple scattering effects are discussed. Finally perspectives and suggestions for future work are outlined. This work represents a reference-guide for studies focused at modeling the radiation transport and at interpreting data from high frequency space-borne radar systems that probe highly opaque scattering media such as thick ice clouds or precipitating clouds.

Influence of the solvent on the self-assembly of a modified amyloid beta peptide fragment. II. NMR and computer simulation investigation

The conformation of a model peptide AAKLVFF based on a fragment of the amyloid beta peptide A beta 16-20, KLVFF, is investigated in methanol and water via solution NMR experiments and Molecular dynamics computer simulations. In previous work, we have shown that AAKLVFF forms peptide nanotubes in methanol and twisted fibrils in water. Chemical shift measurements were used to investigate the solubility of the peptide as a function of concentration in methanol and water. This enabled the determination of critical aggregation concentrations, The Solubility was lower in water. In dilute solution, diffusion coefficients revealed the presence of intermediate aggregates in concentrated solution, coexisting with NMR-silent larger aggregates, presumed to be beta-sheets. In water, diffusion coefficients did not change appreciably with concentration, indicating the presence mainly of monomers, coexisting with larger aggregates in more concentrated solution. Concentration-dependent chemical shift measurements indicated a folded conformation for the monomers/intermediate aggregates in dilute methanol, with unfolding at higher concentration. In water, an antiparallel arrangement of strands was indicated by certain ROESY peak correlations. The temperature-dependent solubility of AAKLVFF in methanol was well described by a van't Hoff analysis, providing a solubilization enthalpy and entropy. This pointed to the importance of solvophobic interactions in the self-assembly process. Molecular dynamics Simulations constrained by NOE values from NMR suggested disordered reverse turn structures for the monomer, with an antiparallel twisted conformation for dimers. To model the beta-sheet structures formed at higher concentration, possible model arrangements of strands into beta-sheets with parallel and antiparallel configurations and different stacking sequences were used as the basis for MD simulations; two particular arrangements of antiparallel beta-sheets were found to be stable, one being linear and twisted and the other twisted in two directions. These structures Were used to simulate Circular dichroism spectra. The roles of aromatic stacking interactions and charge transfer effects were also examined. Simulated spectra were found to be similar to those observed experimentally.(in water or methanol) which show a maximum at 215 or 218 nm due to pi-pi* interactions, when allowance is made for a 15-18 nm red-shift that may be due to light scattering effects.

Pressure effects revealed by small angle neutron scattering on block copolymer gels

We study the effects of hydrostatic pressure (P) on aqueous solutions and gels of the block copolymer B20E610 (E, oxyethylene; B, oxybutylene; subscripts, number of repeats), by performing simultaneous small angle neutron scattering/pressure experiments. Micellar cubic gels were studied for 9.5 and 4.5 wt% B20E610 at T = 20-80 and 35-55 degrees C, respectively, while micellar isotropic solutions where Studied for 4.5 wt% B20E610 at T > 55 degrees C. We observed that the interplanar distance d(110) (cubic unit cell parameter a = root 2d(110)) decreases while the correlation length of the Cubic order (delta) increases, upon increasing P at a fixed T for 9.5 wt% B20E610. The construction of master Curves for d(110) and delta corresponding to 9.5 wt% B20E610 proved the correlation between changes in T and P. Neither d(110) and delta nor the cubic-isotropic phase transition temperature was affected by the applied pressure for 4.5 wt% B20E610. The dramatic contrast between the pressure-induced behavior observed for 9.5 and 4.5 wt% B20E610 suggests that pressure induced effects might be more effectively transmitted through samples that present wider domains of cubic structure order (9.5 wt% compared to 4.5 wt% B20E610).

Effects of Thomson-scattering geometry on white-light imaging of an interplanetary shock: synthetic observations from forward magnetohydrodynamic modelling

Stereoscopic white-light imaging of a large portion of the inner heliosphere has been used to track interplanetary coronal mass ejections. At large elongations from the Sun, the white-light brightness depends on both the local electron density and the efficiency of the Thomson-scattering process. To quantify the effects of the Thomson-scattering geometry, we study an interplanetary shock using forward magnetohydrodynamic simulation and synthetic white-light imaging. Identifiable as an inclined streak of enhanced brightness in a time–elongation map, the travelling shock can be readily imaged by an observer located within a wide range of longitudes in the ecliptic. Different parts of the shock front contribute to the imaged brightness pattern viewed by observers at different longitudes. Moreover, even for an observer located at a fixed longitude, a different part of the shock front will contribute to the imaged brightness at any given time. The observed brightness within each imaging pixel results from a weighted integral along its corresponding ray-path. It is possible to infer the longitudinal location of the shock from the brightness pattern in an optical sky map, based on the east–west asymmetry in its brightness and degree of polarisation. Therefore, measurement of the interplanetary polarised brightness could significantly reduce the ambiguity in performing three-dimensional reconstruction of local electron density from white-light imaging.

Water wave scattering by finite arrays of circular structures

The scattering of small amplitude water waves by a finite array of locally axisymmetric structures is considered. Regions of varying quiescent depth are included and their axisymmetric nature, together with a mild-slope approximation, permits an adaptation of well-known interaction theory which ultimately reduces the problem to a simple numerical calculation. Numerical results are given and effects due to regions of varying depth on wave loading and free-surface elevation are presented.

LDA or GGA? A combined experimental inelastic neutron scattering and ab initio lattice dynamics study of alkali metal hydrides

In a previous work, we carried out inelastic neutron scattering (INS) spectroscopy experiments and preliminary first principles calculations on alkali metal hydrides. The complete series of alkali metal hydrides, LiH, NaH, KH, RbH and CsH was measured in the high-resolution TOSCA INS spectrometer at ISIS. Here, we present the results of ab initio electronic structure calculations of the properties of the alkali metal hydrides using both the local density approximation (LDA) and the generalized gradient approximation (GGA), using the Perdew–Burke–Ernzerhof (PBE) parameterization. Properties calculated were lattice parameters, bulk moduli, dielectric constants, effective charges, electronic densities and inelastic neutron scattering (INS) spectra. We took advantage of the currently available computer power to use full lattice dynamics theory to calculate thermodynamic properties for these materials. For the alkali metal hydrides (LiH, NaH, KH, RbH and CsH) using lattice dynamics, we found that the INS spectra calculated using LDA agreed better with the experimental data than the spectra calculated using GGA. Both zero-point effects and thermal contributions to free energies had an important effect on INS and several thermodynamic properties.

Phase separated structures in tethered dPS–PMMA copolymer films revealed using X-ray scattering with a novel contrast enhancement agent

Tethered deuterated polystyrene-block-polymethyl methacrylate films have been examined by X-ray scattering both in their native state and following treatment with ruthenium tetroxide. The use of the stain, while increasing the thickness of the films, does not significantly alter the lateral structure or periodicity of the films and provides contrast between the two blocks. Both the periodicity of the films and the structure normal to the surface have been identified following staining. Experiments were also performed on films treated by a solvent exchange process, and the effects of staining on these films are discussed.

Wave scattering by an axisymmetric ice floe of varying thickness

The problem of water wave scattering by a circular ice floe, floating in fluid of finite depth, is formulated and solved numerically. Unlike previous investigations of such situations, here we allow the thickness of the floe (and the fluid depth) to vary axisymmetrically and also incorporate a realistic non-zero draught. A numerical approximation to the solution of this problem is obtained to an arbitrary degree of accuracy by combining a Rayleigh–Ritz approximation of the vertical motion with an appropriate variational principle. This numerical solution procedure builds upon the work of Bennets et al. (2007, J. Fluid Mech., 579, 413–443). As part of the numerical formulation, we utilize a Fourier cosine expansion of the azimuthal motion, resulting in a system of ordinary differential equations to solve in the radial coordinate for each azimuthal mode. The displayed results concentrate on the response of the floe rather than the scattered wave field and show that the effects of introducing the new features of varying floe thickness and a realistic draught are significant.

Memory effects in liquid crystal elastomers

Free-standing monodomain liquid crystal elastomer samples are shown to have a complete memory of the orientational configuration at the time of cross-linking. This memory is demonstrated through samples in which the parent polymer system is first aligned in a magnetic field prior to cross-linking. These films show reversible nematic-isotropic phase transitions and x-ray scattering patterns characteristic of nematic phases. The liquid crystal elastomer films exhibit a remarkable memory effect, in that the sample may be held at temperatures well above the nematic-isotropic transition for extended periods ( > 2 weeks), but on cooling into the liquid crystal phase region, both the original director alignment and the degree of preferred orientation are recovered. It is demonstrated that these novel memory effects are equilibrium in nature. The origins of this phenomena in terms of coupling between the mesogenic side-chains and the polymer network are discussed.

Effects of absorbing aerosols in cloudy skies: a satellite study over the Atlantic Ocean

We present a method for deriving the radiative effects of absorbing aerosols in cloudy scenes from satellite retrievals only. We use data of 2005–2007 from various passive sensors aboard satellites of the “A-Train” constellation. The study area is restricted to the tropical- and subtropical Atlantic Ocean. To identify the dependence of the local planetary albedo in cloudy scenes on cloud liquid water path and aerosol optical depth (AOD), we perform a multiple linear regression. The OMI UV-Aerosolindex serves as an indicator for absorbing-aerosol presence. In our method, the aerosol influences the local planetary albedo through direct- (scattering and absorption) and indirect (Twomey) aerosol effects. We find an increase of the local planetary albedo (LPA) with increasing AOD of mostly scattering aerosol and a decrease of the LPA with increasing AOD of mostly absorbing aerosol. These results allow us to derive the direct aerosol effect of absorbing aerosols in cloudy scenes, with the effect of cloudy-scene aerosol absorption in the tropical- and subtropical Atlantic contributing (+21.2±11.1)×10−3 Wm−2 to the global top of the atmosphere radiative forcing.

Simulating the effects of mid- to upper-tropospheric clouds on microwave emissions in EC-Earth using COSP

In this work, the Cloud Feedback Model Intercomparison (CFMIP) Observation Simulation Package (COSP) is expanded to include scattering and emission effects of clouds and precipitation at passive microwave frequencies. This represents an advancement over the official version of COSP (version 1.4.0) in which only clear-sky brightness temperatures are simulated. To highlight the potential utility of this new microwave simulator, COSP results generated using the climate model EC-Earth's version 3 atmosphere as input are compared with Microwave Humidity Sounder (MHS) channel (190.311 GHz) observations. Specifically, simulated seasonal brightness temperatures (TB) are contrasted with MHS observations for the period December 2005 to November 2006 to identify possible biases in EC-Earth's cloud and atmosphere fields. The EC-Earth's atmosphere closely reproduces the microwave signature of many of the major large-scale and regional scale features of the atmosphere and surface. Moreover, greater than 60 % of the simulated TB are within 3 K of the NOAA-18 observations. However, COSP is unable to simulate sufficiently low TB in areas of frequent deep convection. Within the Tropics, the model's atmosphere can yield an underestimation of TB by nearly 30 K for cloudy areas in the ITCZ. Possible reasons for this discrepancy include both incorrect amount of cloud ice water in the model simulations and incorrect ice particle scattering assumptions used in the COSP microwave forward model. These multiple sources of error highlight the non-unique nature of the simulated satellite measurements, a problem exacerbated by the fact that EC-Earth lacks detailed micro-physical parameters necessary for accurate forward model calculations. Such issues limit the robustness of our evaluation and suggest a general note of caution when making COSP-satellite observation evaluations.