An efficient shock capturing algorithm for compressible flows in a duct of variable cross-section

A numerical scheme is presented for the solution of the Euler equations of compressible flow of a gas in a single spatial co-ordinate. This includes flow in a duct of variable cross-section as well as flow with slab, cylindrical or spherical symmetry and can prove useful when testing codes for the two-dimensional equations governing compressible flow of a gas. The resulting scheme requires an average of the flow variables across the interface between cells and for computational efficiency this average is chosen to be the arithmetic mean, which is in contrast to the usual ‘square root’ averages found in this type of scheme. The scheme is applied with success to five problems with either slab or cylindrical symmetry and a comparison is made in the cylindrical case with results from a two-dimensional problem with no sources.

Acoustic trapped modes in a three-dimensional waveguide of slowly varying cross section

In this paper we develop an asymptotic scheme to approximate the trapped mode solutions to the time harmonic wave equation in a three-dimensional waveguide with a smooth but otherwise arbitrarily shaped cross section and a single, slowly varying `bulge', symmetric in the longitudinal direction. Extending the work in Biggs (2012), we first employ a WKBJ-type ansatz to identify the possible quasi-mode solutions which propagate only in the thicker region, and hence find a finite cut-on region of oscillatory behaviour and asymptotic decay elsewhere. The WKBJ expansions are used to identify a turning point between the cut-on and cut-on regions. We note that the expansions are nonuniform in an interior layer centred on this point, and we use the method of matched asymptotic expansions to connect the cut-on and cut-on regions within this layer. The behaviour of the expansions within the interior layer then motivates the construction of a uniformly valid asymptotic expansion. Finally, we use this expansion and the symmetry of the waveguide around the longitudinal centre, x = 0, to extract trapped mode wavenumbers, which are compared with those found using a numerical scheme and seen to be extremely accurate, even to relatively large values of the small parameter.

Noise propagation from a cutting of arbitrary cross-section and impedance

A boundary integral equation is described for the prediction of acoustic propagation from a monofrequency coherent line source in a cutting with impedance boundary conditions onto surrounding flat impedance ground. The problem is stated as a boundary value problem for the Helmholtz equation and is subsequently reformulated as a system of boundary integral equations via Green's theorem. It is shown that the integral equation formulation has a unique solution at all wavenumbers. The numerical solution of the coupled boundary integral equations by a simple boundary element method is then described. The convergence of the numerical scheme is demonstrated experimentally. Predictions of A-weighted excess attenuation for a traffic noise spectrum are made illustrating the effects of varying the depth of the cutting and the absorbency of the surrounding ground surface.

Efficient incorporation of channel cross-section geometry uncertainty into regional and global scale flood inundation models

This paper investigates the challenge of representing structural differences in river channel cross-section geometry for regional to global scale river hydraulic models and the effect this can have on simulations of wave dynamics. Classically, channel geometry is defined using data, yet at larger scales the necessary information and model structures do not exist to take this approach. We therefore propose a fundamentally different approach where the structural uncertainty in channel geometry is represented using a simple parameterization, which could then be estimated through calibration or data assimilation. This paper first outlines the development of a computationally efficient numerical scheme to represent generalised channel shapes using a single parameter, which is then validated using a simple straight channel test case and shown to predict wetted perimeter to within 2% for the channels tested. An application to the River Severn, UK is also presented, along with an analysis of model sensitivity to channel shape, depth and friction. The channel shape parameter was shown to improve model simulations of river level, particularly for more physically plausible channel roughness and depth parameter ranges. Calibrating channel Manning’s coefficient in a rectangular channel provided similar water level simulation accuracy in terms of Nash-Sutcliffe efficiency to a model where friction and shape or depth were calibrated. However, the calibrated Manning coefficient in the rectangular channel model was ~2/3 greater than the likely physically realistic value for this reach and this erroneously slowed wave propagation times through the reach by several hours. Therefore, for large scale models applied in data sparse areas, calibrating channel depth and/or shape may be preferable to assuming a rectangular geometry and calibrating friction alone.

Equation for the microwave backscatter cross section of aggregate snowflakes using the self-similar Rayleigh–Gans approximation

In this paper an equation is derived for the mean backscatter cross section of an ensemble of snowflakes at centimeter and millimeter wavelengths. It uses the Rayleigh–Gans approximation, which has previously been found to be applicable at these wavelengths due to the low density of snow aggregates. Although the internal structure of an individual snowflake is random and unpredictable, the authors find from simulations of the aggregation process that their structure is “self-similar” and can be described by a power law. This enables an analytic expression to be derived for the backscatter cross section of an ensemble of particles as a function of their maximum dimension in the direction of propagation of the radiation, the volume of ice they contain, a variable describing their mean shape, and two variables describing the shape of the power spectrum. The exponent of the power law is found to be −. In the case of 1-cm snowflakes observed by a 3.2-mm-wavelength radar, the backscatter is 40–100 times larger than that of a homogeneous ice–air spheroid with the same mass, size, and aspect ratio.

Commodity risks and the cross-section of equity returns

The article examines whether commodity risk is priced in the cross-section of global equity returns. We employ a long-only equally-weighted portfolio of commodity futures and a term structure portfolio that captures phases of backwardation and contango as mimicking portfolios for commodity risk. We find that equity-sorted portfolios with greater sensitivities to the excess returns of the backwardation and contango portfolio command higher average excess returns, suggesting that when measured appropriately, commodity risk is pervasive in stocks. Our conclusions are robust to the addition to the pricing model of financial, macroeconomic and business cycle-based risk factors.

A study by high energy transfer inelastic neutron scattering spectroscopy of the mineral fraction of ox femur bone

We have used high energy transfer (HET) inelastic neutron scattering spectroscopy to measure the vibrational modes in the spectra of hydroxyapatite, bone and brushite to confirm our earlier work that only a fraction of the hydroxyl groups in bone mineral are substituted. The HET spectra are better observed due to the higher scattering cross section of hydrogen compared with the other elements in the calcium phosphate compounds. (C) 2003 Elsevier Science B.V. All rights reserved.

A study by high energy transfer inelastic neutron scattering spectroscopy of the mineral fraction of ox femur bone

We have used high energy transfer (HET) inelastic neutron scattering spectroscopy to measure the vibrational modes in the spectra of hydroxyapatite, bone and brushite to confirm our earlier work that only a fraction of the hydroxyl groups in bone mineral are substituted. The HET spectra are better observed due to the higher scattering cross section of hydrogen compared with the other elements in the calcium phosphate compounds. (C) 2003 Elsevier Science B.V. All rights reserved.

A study of the atmospherically relevant reaction between molecular chlorine and dimethylsulfide (DMS): establishing the reaction intermediate and measurement of absolute photoionization cross-sections

In a study using UV photoelectron spectroscopy (PES) of the atmospherically relevant reaction CH3SCH3 + Cl2 → CH3SCH2Cl + HCl bands associated with a reaction intermediate have been observed. These have been assigned to ionization of the covalently bound molecule (CH3)2SCl2 on the basis of the intensity of the observed bands as a function of reaction time, molecular orbital calculations of vertical ionization energies and evidence from infrared spectroscopy. A method has also been developed, with the flow-tube/PE spectrometer combination used, to measure photoionization cross-sections of the reagents and products at the photon energy utilized and this has allowed the photoionization cross-section of the intermediate to be estimated. This work augments an earlier study in which the rate constant of the reaction between CH3SCH3 (DMS) and Cl2 has been measured at room temperature.

Resolution of the uncertainties in the radiative forcing of HFC-134a

HFC-134a (CF3CH2F) is the most rapidly growing hydrofluorocarbon in terms of atmospheric abundance. It is currently used in a large number of household refrigerators and air-conditioning systems and its concentration in the atmosphere is forecast to increase substantially over the next 50–100 years. Previous estimates of its radiative forcing per unit concentration have differed significantly 25%. This paper uses a two-step approach to resolve this discrepancy. In the first step six independent absorption cross section datasets are analysed. We find that, for the integrated cross section in the spectral bands that contribute most to the radiative forcing, the differences between the various datasets are typically smaller than 5% and that the dependence on pressure and temperature is not significant. A “recommended'' HFC-134a infrared absorption spectrum was obtained based on the average band intensities of the strongest bands. In the second step, the “recommended'' HFC-134a spectrum was used in six different radiative transfer models to calculate the HFC-134a radiative forcing efficiency. The clear-sky instantaneous radiative forcing, using a single global and annual mean profile, differed by 8%, between the 6 models, and the latitudinally-resolved adjusted cloudy sky radiative forcing estimates differed by a similar amount.

A 3D cloud-construction algorithm for the EarthCARE satellite mission

This article presents and assesses an algorithm that constructs 3D distributions of cloud from passive satellite imagery and collocated 2D nadir profiles of cloud properties inferred synergistically from lidar, cloud radar and imager data. It effectively widens the active–passive retrieved cross-section (RXS) of cloud properties, thereby enabling computation of radiative fluxes and radiances that can be compared with measured values in an attempt to perform radiative closure experiments that aim to assess the RXS. For this introductory study, A-train data were used to verify the scene-construction algorithm and only 1D radiative transfer calculations were performed. The construction algorithm fills off-RXS recipient pixels by computing sums of squared differences (a cost function F) between their spectral radiances and those of potential donor pixels/columns on the RXS. Of the RXS pixels with F lower than a certain value, the one with the smallest Euclidean distance to the recipient pixel is designated as the donor, and its retrieved cloud properties and other attributes such as 1D radiative heating rates are consigned to the recipient. It is shown that both the RXS itself and Moderate Resolution Imaging Spectroradiometer (MODIS) imagery can be reconstructed extremely well using just visible and thermal infrared channels. Suitable donors usually lie within 10 km of the recipient. RXSs and their associated radiative heating profiles are reconstructed best for extensive planar clouds and less reliably for broken convective clouds. Domain-average 1D broadband radiative fluxes at the top of theatmosphere(TOA)for (21 km)2 domains constructed from MODIS, CloudSat andCloud–Aerosol Lidar and Infrared Pathfinder Satellite Observations (CALIPSO) data agree well with coincidental values derived from Clouds and the Earth’s Radiant Energy System (CERES) radiances: differences betweenmodelled and measured reflected shortwave fluxes are within±10Wm−2 for∼35% of the several hundred domains constructed for eight orbits. Correspondingly, for outgoing longwave radiation∼65% are within ±10Wm−2.

Radiative forcing and global warming potentials of 11 halogenated compounds

Radiative forcing values have been calculated for 11 halogenated compounds which are in current use or which have been suggested as possible replacements for the chlorofluorocarbons. Absorption cross-sections measured over a range of atmospheric temperature and pressure conditions as part of a multi-laboratory programme have been used together with a narrow band radiative transfer model. We provide a “best estimate” radiative forcing taking into account the likely vertical profile of the gas in each case. The Global Warming Potential over a variety of time horizons has also been calculated where the lifetime is available. We present the first such information for 1,2-dichloroethane. For chloroform our radiative forcing is 5 times higher than the value used in previous assessments, possibly because these ignored the effect of absorption outside the 800–1200 cm−1 “window”. For several of the other compounds considered here, our forcing is between 10 and 30% lower than previous assessments. The perfluorocarbons have been found to have large global warming potentials, many times that of CFC-11, due to both strong absorption and long lifetimes. The importance of absorption features at wavenumbers below 800 cm−1 and the effect of temperature variations in absorption cross-section on the radiative forcing are also investigated.

Further considerations of cosmic ray modulation of infra-red radiation in the atmosphere

Understanding effects of ionisation in the lower atmosphere is a new interdisciplinary area, crossing the traditionally distinct scientific boundaries between astro-particle and atmospheric physics and also requiring understanding of both heliospheric and magnetospheric influences on cosmic rays. Following the paper of Erlykin et al. (2014) we develop further the interpretation of our observed changes in long-wave (LW) radiation, Aplin and Lockwood (2013) by taking account of both cosmic ray ionisation yields and atmospheric radiative transfer. To demonstrate this, we show that the thermal structure of the whole atmosphere needs to be considered along with the vertical profile of ionisation. Allowing for, in particular, ionisation by all components of a cosmic ray shower and not just by the muons, reveals that the effect we have detected is certainly not inconsistent with laboratory observations of the LW absorption cross section. The analysis presented here, although very different from that of Erlykin et al., does come to the same conclusion that the events detected by AL were not caused by individual cosmic ray primaries – not because it is impossible on energetic grounds, but because events of the required energy are too infrequent for the 12 h_1 rate at which they were seen by the AL experiment. The present paper numerically models the effect of three different scenario changes to the primary GCR spectrum which all reproduce the required magnitude of the effect observed by AL. However, they cannot solely explain the observed delay in the peak effect which, if confirmed, would appear to open up a whole new and interesting area in the study of water oligomers and their effects on LW radiation. We argue that a technical artefact in the AL experiment is highly unlikely and that our initial observations merit both a wide-ranging follow-up experiment and more rigorous, self-consistent, three-dimensional radiative transfer modelling

The EarthCARE satellite: the next step forward in global measurements of clouds, aerosols, precipitation, and radiation

The collective representation within global models of aerosol, cloud, precipitation, and their radiative properties remains unsatisfactory. They constitute the largest source of uncertainty in predictions of climatic change and hamper the ability of numerical weather prediction models to forecast high-impact weather events. The joint European Space Agency (ESA)–Japan Aerospace Exploration Agency (JAXA) Earth Clouds, Aerosol and Radiation Explorer (EarthCARE) satellite mission, scheduled for launch in 2018, will help to resolve these weaknesses by providing global profiles of cloud, aerosol, precipitation, and associated radiative properties inferred from a combination of measurements made by its collocated active and passive sensors. EarthCARE will improve our understanding of cloud and aerosol processes by extending the invaluable dataset acquired by the A-Train satellites CloudSat, Cloud–Aerosol Lidar and Infrared Pathfinder Satellite Observations (CALIPSO), and Aqua. Specifically, EarthCARE’s cloud profiling radar, with 7 dB more sensitivity than CloudSat, will detect more thin clouds and its Doppler capability will provide novel information on convection, precipitating ice particle, and raindrop fall speeds. EarthCARE’s 355-nm high-spectral-resolution lidar will measure directly and accurately cloud and aerosol extinction and optical depth. Combining this with backscatter and polarization information should lead to an unprecedented ability to identify aerosol type. The multispectral imager will provide a context for, and the ability to construct, the cloud and aerosol distribution in 3D domains around the narrow 2D retrieved cross section. The consistency of the retrievals will be assessed to within a target of ±10 W m–2 on the (10 km)2 scale by comparing the multiview broadband radiometer observations to the top-of-atmosphere fluxes estimated by 3D radiative transfer models acting on retrieved 3D domains.