A Galerkin boundary element method for high frequency scattering by convex polygons

In this paper we consider the problem of time-harmonic acoustic scattering in two dimensions by convex polygons. Standard boundary or finite element methods for acoustic scattering problems have a computational cost that grows at least linearly as a function of the frequency of the incident wave. Here we present a novel Galerkin boundary element method, which uses an approximation space consisting of the products of plane waves with piecewise polynomials supported on a graded mesh, with smaller elements closer to the corners of the polygon. We prove that the best approximation from the approximation space requires a number of degrees of freedom to achieve a prescribed level of accuracy that grows only logarithmically as a function of the frequency. Numerical results demonstrate the same logarithmic dependence on the frequency for the Galerkin method solution. Our boundary element method is a discretization of a well-known second kind combined-layer-potential integral equation. We provide a proof that this equation and its adjoint are well-posed and equivalent to the boundary value problem in a Sobolev space setting for general Lipschitz domains.

Boundary integral methods in high frequency scattering

In this article we review recent progress on the design, analysis and implementation of numerical-asymptotic boundary integral methods for the computation of frequency-domain acoustic scattering in a homogeneous unbounded medium by a bounded obstacle. The main aim of the methods is to allow computation of scattering at arbitrarily high frequency with finite computational resources.

A cost-effective high-throughput digital system for observation and acquisition of animal behavioral data

We have designed and implemented a low-cost digital system using closed-circuit television cameras coupled to a digital acquisition system for the recording of in vivo behavioral data in rodents and for allowing observation and recording of more than 10 animals simultaneously at a reduced cost, as compared with commercially available solutions. This system has been validated using two experimental rodent models: one involving chemically induced seizures and one assessing appetite and feeding. We present observational results showing comparable or improved levels of accuracy and observer consistency between this new system and traditional methods in these experimental models, discuss advantages of the presented system over conventional analog systems and commercially available digital systems, and propose possible extensions to the system and applications to nonrodent studies.

U.K. HiGEM: The New U.K. High-Resolution Global Environment Model—Model Description and Basic Evaluation

This article describes the development and evaluation of the U.K.’s new High-Resolution Global Environmental Model (HiGEM), which is based on the latest climate configuration of the Met Office Unified Model, known as the Hadley Centre Global Environmental Model, version 1 (HadGEM1). In HiGEM, the horizontal resolution has been increased to 0.83° latitude × 1.25° longitude for the atmosphere, and 1/3° × 1/3° globally for the ocean. Multidecadal integrations of HiGEM, and the lower-resolution HadGEM, are used to explore the impact of resolution on the fidelity of climate simulations. Generally, SST errors are reduced in HiGEM. Cold SST errors associated with the path of the North Atlantic drift improve, and warm SST errors are reduced in upwelling stratocumulus regions where the simulation of low-level cloud is better at higher resolution. The ocean model in HiGEM allows ocean eddies to be partially resolved, which dramatically improves the representation of sea surface height variability. In the Southern Ocean, most of the heat transports in HiGEM is achieved by resolved eddy motions, which replaces the parameterized eddy heat transport in the lower-resolution model. HiGEM is also able to more realistically simulate small-scale features in the wind stress curl around islands and oceanic SST fronts, which may have implications for oceanic upwelling and ocean biology. Higher resolution in both the atmosphere and the ocean allows coupling to occur on small spatial scales. In particular, the small-scale interaction recently seen in satellite imagery between the atmosphere and tropical instability waves in the tropical Pacific Ocean is realistically captured in HiGEM. Tropical instability waves play a role in improving the simulation of the mean state of the tropical Pacific, which has important implications for climate variability. In particular, all aspects of the simulation of ENSO (spatial patterns, the time scales at which ENSO occurs, and global teleconnections) are much improved in HiGEM.

Spatial and temporal scale issues in determining biomass burning regimes in Bolivia and Peru

ATSR-2 active fire data from 1996 to 2000, TRMM VIRS fire counts from 1998 to 2000 and burn scars derived from SPOT VEGETATION ( the Global Burnt Area 2000 product) were mapped for Peru and Bolivia to analyse the spatial distribution of burning and its intra- and inter-annual variability. The fire season in the region mainly occurs between May and October; though some variation was found between the six broad habitat types analysed: desert, grassland, savanna, dry forest, moist forest and yungas (the forested valleys on the eastern slope of the Andes). Increased levels of burning were generally recorded in ATSR-2 and TRMM VIRS fire data in response to the 1997/1998 El Nino, but in some areas the El Nino effect was masked by the more marked influences of socio-economic change on land use and land cover. There were differences between the three global datasets: ATSR-2 under-recorded fires in ecosystems with low net primary productivities. This was because fires are set during the day in this region and, when fuel loads are low, burn out before the ATSR-2 overpass in the region which is between 02.45 h and 03.30 h. TRMM VIRS was able to detect these fires because its overpasses cover the entire diurnal range on a monthly basis. The GBA2000 product has significant errors of commission (particularly areas of shadow in the well-dissected eastern Andes) and omission (in the agricultural zone around Santa Cruz, Bolivia and in north-west Peru). Particular attention was paid to biomass burning in high-altitude grasslands, where fire is an important pastoral management technique. Fires and burn scars from Landsat Thematic Mapper (TM) and Enhanced Thematic Mapper (ETM) data for a range of years between 1987 and 2000 were mapped for areas around Parque Nacional Rio Abiseo (Peru) and Parque Nacional Carrasco (Bolivia). Burn scars mapped in the grasslands of these two areas indicate far more burning had taken place than either the fires or the burn scars derived from global datasets. Mean scar sizes are smaller and have a smaller range in size between years the in the study area in Peru (6.6-7.1 ha) than Bolivia (16.9-162.5 ha). Trends in biomass burning in the two highland areas can be explained in terms of the changing socio-economic environments and impacts of conservation. The mismatch between the spatial scale of biomass burning in the high-altitude grasslands and the sensors used to derive global fire products means that an entire component of the fire regime in the region studied is omitted, despite its importance in the farming systems on the Andes.

Observed trends and teleconnections of the Siberian high: A recently declining center of action

This study investigates variability in the intensity of the wintertime Siberian high (SH) by defining a robust SH index (SHI) and correlating it with selected meteorological fields and teleconnection indices. A dramatic trend of -2.5 hPa decade(-1) has been found in the SHI between 1978 and 2001 with unprecedented (since 1871) low values of the SHI. The weakening of the SH has been confirmed by analyzing different historical gridded analyses and individual station observations of sea level pressure (SLP) and excluding possible effects from the conversion of surface pressure to SLP. SHI correlation maps with various meteorological fields show that SH impacts on circulation and temperature patterns extend far outside the SH source area extending from the Arctic to the tropical Pacific. Advection of warm air from eastern Europe has been identified as the main mechanism causing milder than normal conditions over the Kara and Laptev Seas in association with a strong SH. Despite the strong impacts of the variability in the SH on climatic variability across the Northern Hemisphere, correlations between the SHI and the main teleconnection indices of the Northern Hemisphere are weak. Regression analysis has shown that teleconnection indices are not able to reproduce the interannual variability and trends in the SH. The inclusion of regional surface temperature in the regression model provides closer agreement between the original and reconstructed SHI.

Convectively coupled equatorial waves in high resolution Hadley centre climate models

Current global atmospheric models fail to simulate well organised tropical phenomena in which convection interacts with dynamics and physics. A new methodology to identify convectively coupled equatorial waves, developed by NCAS-Climate, has been applied to output from the two latest models of the Met Office/Hadley Centre which have fundamental differences in dynamical formulation. Variability, horizontal and vertical structures, and propagation characteristics of tropical convection and equatorial waves, along with their coupled behaviour in the models are examined and evaluated against a previous comprehensive study of observations. It is shown that, in general, the models perform well for equatorial waves coupled with off-equatorial convection. However they perform poorly for waves coupled with equatorial convection. The vertical structure of the simulated wave is not conducive to energy conversion/growth and does not support the correct physical-dynamical coupling that occurs in the real world. The following figure shows an example of the Kelvin wave coupled with equatorial convection. It shows that the models fail to simulate a key feature of convectively coupled Kelvin wave in observations, namely near surface anomalous equatorial zonal winds together with intensified equatorial convection and westerly winds in phase with the convection. The models are also not able to capture the observed vertical tilt structure and the vertical propagation of the Kelvin wave into the lower stratosphere as well as the secondary peak in the mid-troposphere, particularly in HadAM3. These results can be used to provide a test-bed for experimentation to improve the coupling of physics and dynamics in climate and weather models.

Annular variability and eddy-zonal flow interactions in a simplified atmospheric GCM. Part 1: Characterization of high and low frequency behaviour

Experiments have been performed using a simplified, Newtonian forced, global circulation model to investigate how variability of the tropospheric jet can be characterized by examining the combined fluctuations of the two leading modes of annular variability. Eddy forcing of this variability is analyzed in the phase space of the leading modes using the vertically integrated momentum budget. The nature of the annular variability and eddy forcing depends on the time scale. At low frequencies the zonal flow and baroclinic eddies are in quasi equilibrium and anomalies propagate poleward. The eddies are shown primarily to reinforce the anomalous state and are closely balanced by the linear damping, leaving slow evolution as a residual. At high frequencies the flow is strongly evolving and anomalies are initiated on the poleward side of the tropospheric jet and propagate equatorward. The eddies are shown to drive this evolution strongly: eddy location and amplitude reflect the past baroclinicity, while eddy feedback on the zonal flow may be interpreted in terms of wave breaking associated with baroclinic life cycles in lateral shear.

Why the western Pacific subtropical high has extended westward since the late 1970s

The western Pacific subtropical high (WPSH) is closely related to Asian climate. Previous examination of changes in the WPSH found a westward extension since the late 1970s, which has contributed to the inter-decadal transition of East Asian climate. The reason for the westward extension is unknown, however. The present study suggests that this significant change of WPSH is partly due to the atmosphere's response to the observed Indian Ocean-western Pacific (IWP) warming. Coordinated by a European Union's Sixth Framework Programme, Understanding the Dynamics of the Coupled Climate System (DYNAMITE), five AGCMs were forced by identical idealized sea surface temperature patterns representative of the IWP warming and cooling. The results of these numerical experiments suggest that the negative heating in the central and eastern tropical Pacific and increased convective heating in the equatorial Indian Ocean/ Maritime Continent associated with IWP warming are in favor of the westward extension of WPSH. The SST changes in IWP influences the Walker circulation, with a subsequent reduction of convections in the tropical central and eastern Pacific, which then forces an ENSO/Gill-type response that modulates the WPSH. The monsoon diabatic heating mechanism proposed by Rodwell and Hoskins plays a secondary reinforcing role in the westward extension of WPSH. The low-level equatorial flank of WPSH is interpreted as a Kelvin response to monsoon condensational heating, while the intensified poleward flow along the western flank of WPSH is in accord with Sverdrup vorticity balance. The IWP warming has led to an expansion of the South Asian high in the upper troposphere, as seen in the reanalysis.

Tolerance of ruminant animals to high dose in-feed administration of a selenium-enriched yeast

The objective of the study was to determine if there were adverse effects on animal health and performance when a range of ruminant animals species were fed at least 10 times the maximum permitted European Union (EU) selenium (Se) dietary inclusion rate (0.568 mg Se/kg DM) in the form of selenium enriched yeast (SY) derived from a specific strain of Saccharomyces cerevisiae CNCM I-3060. In a series of studies, dairy cows, beef cattle, calves and lambs were offered either a control diet which contained no Se supplement or a treatment diet which contained the same basal feed ingredients plus a SY supplement which increased total dietary Se from 0.15 to 6.25, 0.20 to 6.74, 0.15 to 5.86 and 0.14 to 6.63 mg Se/kg DM, respectively. The inclusion of the SY supplement (P < 0.001) increased whole blood Se concentrations, reaching maximum mean values of 716, 1,505, 1,377, and 724 ng Se/mL for dairy cattle, beef cattle, calves and lambs, respectively. Selenomethionine accounted for 10% of total whole blood Se in control animals whereas the proportion in SY animals ranged between 40 and 75%. Glutathione peroxidase (EC 1.11.1.9) activity was higher (P < 0.05) in SY animals when compared with controls. A range of other biochemical and hematological parameters were assessed, but few differences of biological significance were established between treatments groups. There were no differences between treatment groups within each species with regard to animal physical performance or overall animal health. It was concluded that there were no adverse effects on animal health, performance and voluntary feed intake to the administration of at least ten times the EU maximum, or approximately twenty times the US FDA permitted concentration of dietary Se in the form of SY derived from a specific strain of Saccharomyces cerevisiae CNCM I-3060.

Do High-Frequency Eddies Contribute to Low-Frequency Teleconnection Tendencies?*

An isentropic potential vorticity (PV) budget analysis is employed to examine the role of synoptic transients, advection, and nonconservative processes as forcings for the evolution of the low-frequency PV anomalies locally and those associated with the North Atlantic Oscillation (NAO) and the Pacific–North American (PNA) pattern. Specifically, the rate of change of the low-frequency PV is expressed as a sum of tendencies due to divergence of eddy transport, advection by the low-frequency flow (hereafter referred to as advection), and the residual nonconservative processes. The balance between the variances and covariances of these terms is illustrated using a novel vector representation. It is shown that for most locations, as well as for the PNA pattern, the PV variability is dominantly driven by advection. The eddy forcing explains a small amount of the tendency variance. For the NAO, the role of synoptic eddy fluxes is found to be stronger, explaining on average 15% of the NAO tendency variance. Previous studies have not assessed quantitively how the various forcings balance the tendency. Thus, such studies may have overestimated the role of eddy fluxes for the evolution of teleconnections by examining, for example, composites and regressions that indicate maintenance, rather than evolution driven by the eddies. The authors confirm this contrasting view by showing that during persistent blocking (negative NAO) episodes the eddy driving is relatively stronger.

A high-wavenumber boundary-element method for an acoustic scattering problem

In this paper we show stability and convergence for a novel Galerkin boundary element method approach to the impedance boundary value problem for the Helmholtz equation in a half-plane with piecewise constant boundary data. This problem models, for example, outdoor sound propagation over inhomogeneous flat terrain. To achieve a good approximation with a relatively low number of degrees of freedom we employ a graded mesh with smaller elements adjacent to discontinuities in impedance, and a special set of basis functions for the Galerkin method so that, on each element, the approximation space consists of polynomials (of degree $\nu$) multiplied by traces of plane waves on the boundary. In the case where the impedance is constant outside an interval $[a,b]$, which only requires the discretization of $[a,b]$, we show theoretically and experimentally that the $L_2$ error in computing the acoustic field on $[a,b]$ is ${\cal O}(\log^{\nu+3/2}|k(b-a)| M^{-(\nu+1)})$, where $M$ is the number of degrees of freedom and $k$ is the wavenumber. This indicates that the proposed method is especially commendable for large intervals or a high wavenumber. In a final section we sketch how the same methodology extends to more general scattering problems.