Variational approach in weighted Sobolev spaces to scattering by unbounded rough surfaces

We consider the problem of scattering of time harmonic acoustic waves by an unbounded sound soft surface which is assumed to lie within a finite distance of some plane. The paper is concerned with the study of an equivalent variational formulation of this problem set in a scale of weighted Sobolev spaces. We prove well-posedness of this variational formulation in an energy space with weights which extends previous results in the unweighted setting [S. Chandler-Wilde and P. Monk, SIAM J. Math. Anal., 37 (2005), pp. 598–618] to more general inhomogeneous terms in the Helmholtz equation. In particular, in the two-dimensional case, our approach covers the problem of plane wave incidence, whereas in the three-dimensional case, incident spherical and cylindrical waves can be treated. As a further application of our results, we analyze a finite section type approximation, whereby the variational problem posed on an infinite layer is approximated by a variational problem on a bounded region.

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.

Advancements in the estimation of ice particle fall speeds using laboratory and field measurements

Accurate estimates for the fall speed of natural hydrometeors are vital if their evolution in clouds is to be understood quantitatively. In this study, laboratory measurements of the terminal velocity vt for a variety of ice particle models settling in viscous fluids, along with wind-tunnel and field measurements of ice particles settling in air, have been analyzed and compared to common methods of computing vt from the literature. It is observed that while these methods work well for a number of particle types, they fail for particles with open geometries, specifically those particles for which the area ratio Ar is small (Ar is defined as the area of the particle projected normal to the flow divided by the area of a circumscribing disc). In particular, the fall speeds of stellar and dendritic crystals, needles, open bullet rosettes, and low-density aggregates are all overestimated. These particle types are important in many cloud types: aggregates in particular often dominate snow precipitation at the ground and vertically pointing Doppler radar measurements. Based on the laboratory data, a simple modification to previous computational methods is proposed, based on the area ratio. This new method collapses the available drag data onto an approximately universal curve, and the resulting errors in the computed fall speeds relative to the tank data are less than 25% in all cases. Comparison with the (much more scattered) measurements of ice particles falling in air show strong support for this new method, with the area ratio bias apparently eliminated.

A new frequency-uniform coercive boundary integral equation for acoustic scattering

A new boundary integral operator is introduced for the solution of the soundsoft acoustic scattering problem, i.e., for the exterior problem for the Helmholtz equation with Dirichlet boundary conditions. We prove that this integral operator is coercive in L2(Γ) (where Γ is the surface of the scatterer) for all Lipschitz star-shaped domains. Moreover, the coercivity is uniform in the wavenumber k = ω/c, where ω is the frequency and c is the speed of sound. The new boundary integral operator, which we call the “star-combined” potential operator, is a slight modification of the standard combined potential operator, and is shown to be as easy to implement as the standard one. Additionally, to the authors' knowledge, it is the only second-kind integral operator for which convergence of the Galerkin method in L2(Γ) is proved without smoothness assumptions on Γ except that it is Lipschitz. The coercivity of the star-combined operator implies frequency-explicit error bounds for the Galerkin method for any approximation space. In particular, these error estimates apply to several hybrid asymptoticnumerical methods developed recently that provide robust approximations in the high-frequency case. The proof of coercivity of the star-combined operator critically relies on an identity first introduced by Morawetz and Ludwig in 1968, supplemented further by more recent harmonic analysis techniques for Lipschitz domains.

Virtual reshaping and invisibility in obstacle scattering

We consider reshaping an obstacle virtually by using transformation optics in acoustic and electromagnetic scattering. Among the general virtual reshaping results, the virtual minification and virtual magnification in particular are studied. Stability estimates are derived for scattering amplitude in terms of the diameter of a small obstacle, which implies that the limiting case for minification corresponds to a perfect cloaking, i.e., the obstacle is invisible to detection.

Sea-ice anomalies in the Sea of Okhotsk and the relationship with storm tracks in the Northern Hemisphere during winter

Previous studies have shown that sea-ice in the Sea of Okhotsk can be affected by local storms; in turn, the resultant sea-ice changes can affect the downstream development of storm tracks in the Pacific and possibly dampen a pre-existing North Atlantic Oscillation (NAO) signal in late winter. In this paper, a storm tracking algorithm was applied to the six hourly horizontal winds from the National Centers for Environmental Prediction (NCEP) reanalysis data from 1978(9) to 2007 and output from the atmospheric general circulation model (AGCM) ECHAM5 forced by sea-ice anomalies in the Sea of Okhotsk. The life cycle response of storms to sea-ice anomalies is investigated using various aspects of storm activity—cyclone genesis, lysis, intensity and track density. Results show that, for enhanced positive sea-ice concentrations in the Sea of Okhotsk, there is a decrease in secondary cyclogenesis, a westward shift in cyclolysis and changes in the subtropical jet are seen in the North Pacific. In the Atlantic, a pattern resembling the negative phase of the NAO is observed. This pattern is confirmed by the AGCM ECHAM5 experiments driven with above normal sea-ice anomalies in the Sea of Okhotsk

Observations of ice multiplication in a weakly convective cell embedded in supercooled mid-level stratus

Simultaneous observations of cloud microphysical properties were obtained by in-situ aircraft measurements and ground based Radar/Lidar. Widespread mid-level stratus cloud was present below a temperature inversion (~5 °C magnitude) at 3.6 km altitude. Localised convection (peak updraft 1.5 m s−1) was observed 20 km west of the Radar station. This was associated with convergence at 2.5 km altitude. The convection was unable to penetrate the inversion capping the mid-level stratus. The mid-level stratus cloud was vertically thin (~400 m), horizontally extensive (covering 100 s of km) and persisted for more than 24 h. The cloud consisted of supercooled water droplets and small concentrations of large (~1 mm) stellar/plate like ice which slowly precipitated out. This ice was nucleated at temperatures greater than −12.2 °C and less than −10.0 °C, (cloud top and cloud base temperatures, respectively). No ice seeding from above the cloud layer was observed. This ice was formed by primary nucleation, either through the entrainment of efficient ice nuclei from above/below cloud, or by the slow stochastic activation of immersion freezing ice nuclei contained within the supercooled drops. Above cloud top significant concentrations of sub-micron aerosol were observed and consisted of a mixture of sulphate and carbonaceous material, a potential source of ice nuclei. Particle number concentrations (in the size range 0.1Ice crystal concentrations in the cloud were constant at around 0.2 L−1. It is estimated that entrainment of aerosol particles into cloud cannot replenish the loss of ice nuclei from the cloud layer via precipitation. Precipitation from the mid-level stratus evaporated before reaching the surface, whereas rates of up to 1 mm h−1 were observed below the convective feature. There is strong evidence for the Hallett-Mossop (HM) process of secondary ice particle production leading to the formation of the precipitation observed. This includes (1) Ice concentrations in the convective feature were more than an order of magnitude greater than the concentration of primary ice in the overlaying stratus, (2) Large concentrations of small pristine columns were observed at the ~−5 °C level together with liquid water droplets and a few rimed ice particles, (3) Columns were larger and increasingly rimed at colder temperatures. Calculated ice splinter production rates are consistent with observed concentrations if the condition that only droplets greater than 24 μm are capable of generating secondary ice splinters is relaxed. This case demonstrates the importance of understanding the formation of ice at slightly supercooled temperatures, as it can lead to secondary ice production and the formation of precipitation in clouds which may not otherwise be considered as significant precipitation sources.

Evidence that ice forms primarily in supercooled liquid clouds at temperatures > -27C

Using 4 years of radar and lidar observations of layer clouds from the Chilbolton Observatory in the UK, we show that almost all (95%) ice particles formed at temperatures >-20°C appear to originate from supercooled liquid clouds. At colder temperatures, there is a monotonic decline in the fraction of liquid-topped ice clouds: 50% at -27°C, falling to zero at -37°C (where homogeneous freezing of water droplets occurs). This strongly suggests that deposition nucleation plays a relatively minor role in the initiation of ice in mid-level clouds. It also means that the initial growth of the ice particles occurs predominantly within a liquid cloud, a situation which promotes rapid production of precipitation via the Bergeron-Findeison mechanism.

A review on Northern Hemisphere sea-ice, storminess and the North Atlantic Oscillation: observations and projected changes

The Arctic has undergone substantial changes over the last few decades in various cryospheric and derivative systems and processes. Of these, the Arctic sea ice regime has seen some of the most rapid change and is one of the most visible markers of Arctic change outside the scientific community. This has drawn considerable attention not only from the natural sciences, but increasingly, from the political and commercial sectors as they begin to grapple with the problems and opportunities that are being presented. The possible impacts of past and projected changes in Arctic sea ice, especially as it relates to climatic response, are of particular interest and have been the subject of increasing research activity. A review of the current knowledge of the role of sea ice in the climate system is therefore timely. We present a review that examines both the current state of understanding, as regards the impacts of sea-ice loss observed to date, and climate model projections, to highlight hypothesised future changes and impacts on storm tracks and the North Atlantic Oscillation. Within the broad climate-system perspective, the topics of storminess and large-scale variability will be specifically considered. We then consider larger-scale impacts on the climatic system by reviewing studies that have focused on the interaction between sea-ice extent and the North Atlantic Oscillation. Finally, an overview of the representation of these topics in the literature in the context of IPCC climate projections is presented. While most agree on the direction of Arctic sea-ice change, the rates amongst the various projections vary greatly. Similarly, the response of storm tracks and climate variability are uncertain, exacerbated possibly by the influence of other factors. A variety of scientific papers on the relationship between sea-ice changes and atmospheric variability have brought to light important aspects of this complex topic. Examples are an overall reduction in the number of Arctic winter storms, a northward shift of mid-latitude winter storms in the Pacific and a delayed negative NAO-like response in autumn/winter to a reduced Arctic sea-ice cover (at least in some months). This review paper discusses this research and the disagreements, bringing about a fresh perspective on this issue.

The evaluation of CloudSat and CALIPSO ice microphysical products using ground-based cloud radar and lidar observations

In this paper, the statistical properties of tropical ice clouds (ice water content, visible extinction, effective radius, and total number concentration) derived from 3 yr of ground-based radar–lidar retrievals from the U.S. Department of Energy Atmospheric Radiation Measurement Climate Research Facility in Darwin, Australia, are compared with the same properties derived using the official CloudSat microphysical retrieval methods and from a simpler statistical method using radar reflectivity and air temperature. It is shown that the two official CloudSat microphysical products (2B-CWC-RO and 2B-CWC-RVOD) are statistically virtually identical. The comparison with the ground-based radar–lidar retrievals shows that all satellite methods produce ice water contents and extinctions in a much narrower range than the ground-based method and overestimate the mean vertical profiles of microphysical parameters below 10-km height by over a factor of 2. Better agreements are obtained above 10-km height. Ways to improve these estimates are suggested in this study. Effective radii retrievals from the standard CloudSat algorithms are characterized by a large positive bias of 8–12 μm. A sensitivity test shows that in response to such a bias the cloud longwave forcing is increased from 44.6 to 46.9 W m−2 (implying an error of about 5%), whereas the negative cloud shortwave forcing is increased from −81.6 to −82.8 W m−2. Further analysis reveals that these modest effects (although not insignificant) can be much larger for optically thick clouds. The statistical method using CloudSat reflectivities and air temperature was found to produce inaccurate mean vertical profiles and probability distribution functions of effective radius. This study also shows that the retrieval of the total number concentration needs to be improved in the official CloudSat microphysical methods prior to a quantitative use for the characterization of tropical ice clouds. Finally, the statistical relationship used to produce ice water content from extinction and air temperature obtained by the Cloud-Aerosol Lidar and Infrared Pathfinder Satellite Observation (CALIPSO) satellite is evaluated for tropical ice clouds. It is suggested that the CALIPSO ice water content retrieval is robust for tropical ice clouds, but that the temperature dependence of the statistical relationship used should be slightly refined to better reproduce the radar–lidar retrievals.

The statistical properties of tropical ice clouds generated by the West-African and Australian monsoons from ground-based radar-lidar observations

In the present paper we characterize the statistical properties of non-precipitating tropical ice clouds (deep ice anvils resulting from deep convection and cirrus clouds) over Niamey, Niger, West Africa, and Darwin, northern Australia, using ground-based radar–lidar observations from the Atmospheric Radiation Measurement (ARM) programme. The ice cloud properties analysed in this paper are the frequency of ice cloud occurrence, cloud fraction, the morphological properties (cloud-top height, base height, and thickness), the microphysical and radiative properties (ice water content, visible extinction, effective radius, terminal fall speed, and concentration), and the internal cloud dynamics (in-cloud vertical air velocity). The main highlight of the paper is that it characterizes for the first time the probability density functions of the tropical ice cloud properties, their vertical variability and their diurnal variability at the same time. This is particularly important over West Africa, since the ARM deployment in Niamey provides the first vertically resolved observations of non-precipitating ice clouds in this crucial area in terms of redistribution of water and energy in the troposphere. The comparison between the two sites also provides an additional observational basis for the evaluation of the parametrization of clouds in large-scale models, which should be able to reproduce both the statistical properties at each site and the differences between the two sites. The frequency of ice cloud occurrence is found to be much larger over Darwin when compared to Niamey, and with a much larger diurnal variability, which is well correlated with the diurnal cycle of deep convective activity. The diurnal cycle of the ice cloud occurrence over Niamey is also much less correlated with that of deep convective activity than over Darwin, probably owing to the fact that Niamey is further away from the deep convective sources of the region. The frequency distributions of cloud fraction are strongly bimodal and broadly similar over the two sites, with a predominance of clouds characterized either by a very small cloud fraction (less than 0.3) or a very large cloud fraction (larger than 0.9). The ice clouds over Darwin are also much thicker (by 1 km or more statistically) and are characterized by a much larger diurnal variability than ice clouds over Niamey. Ice clouds over Niamey are also characterized by smaller particle sizes and fall speeds but in much larger concentrations, thereby carrying more ice water and producing more visible extinction than the ice clouds over Darwin. It is also found that there is a much larger occurrence of downward in-cloud air motions less than 1 m s−1 over Darwin, which together with the larger fall speeds retrieved over Darwin indicates that the life cycle of ice clouds is probably shorter over Darwin than over Niamey.