Efficient calculation of two-dimensional periodic and waveguide acoustic Green’s functions

New representations and efficient calculation methods are derived for the problem of propagation from an infinite regularly spaced array of coherent line sources above a homogeneous impedance plane, and for the Green's function for sound propagation in the canyon formed by two infinitely high, parallel rigid or sound soft walls and an impedance ground surface. The infinite sum of source contributions is replaced by a finite sum and the remainder is expressed as a Laplace-type integral. A pole subtraction technique is used to remove poles in the integrand which lie near the path of integration, obtaining a smooth integrand, more suitable for numerical integration, and a specific numerical integration method is proposed. Numerical experiments show highly accurate results across the frequency spectrum for a range of ground surface types. It is expected that the methods proposed will prove useful in boundary element modeling of noise propagation in canyon streets and in ducts, and for problems of scattering by periodic surfaces.

A fast two-grid and finite section method for a class of integral equations on the real line with application to an acoustic scattering problem in the half-plane

We consider the numerical treatment of second kind integral equations on the real line of the form ∅(s) = ∫_(-∞)^(+∞)▒〖κ(s-t)z(t)ϕ(t)dt,s=R〗 (abbreviated ϕ= ψ+K_z ϕ) in which K ϵ L_1 (R), z ϵ L_∞ (R) and ψ ϵ BC(R), the space of bounded continuous functions on R, are assumed known and ϕ ϵ BC(R) is to be determined. We first derive sharp error estimates for the finite section approximation (reducing the range of integration to [-A, A]) via bounds on (1-K_z )^(-1)as an operator on spaces of weighted continuous functions. Numerical solution by a simple discrete collocation method on a uniform grid on R is then analysed: in the case when z is compactly supported this leads to a coefficient matrix which allows a rapid matrix-vector multiply via the FFT. To utilise this possibility we propose a modified two-grid iteration, a feature of which is that the coarse grid matrix is approximated by a banded matrix, and analyse convergence and computational cost. In cases where z is not compactly supported a combined finite section and two-grid algorithm can be applied and we extend the analysis to this case. As an application we consider acoustic scattering in the half-plane with a Robin or impedance boundary condition which we formulate as a boundary integral equation of the class studied. Our final result is that if z (related to the boundary impedance in the application) takes values in an appropriate compact subset Q of the complex plane, then the difference between ϕ(s)and its finite section approximation computed numerically using the iterative scheme proposed is ≤C_1 [kh log⁡〖(1⁄kh)+(1-Θ)^((-1)⁄2) (kA)^((-1)⁄2) 〗 ] in the interval [-ΘA,ΘA](Θ<1) for kh sufficiently small, where k is the wavenumber and h the grid spacing. Moreover this numerical approximation can be computed in ≤C_2 N log⁡N operations, where N = 2A/h is the number of degrees of freedom. The values of the constants C1 and C2 depend only on the set Q and not on the wavenumber k or the support of z.

Acoustic scattering by an inhomogeneous layer on a rigid plate

The problem of scattering of time-harmonic acoustic waves by an inhomogeneous fluid layer on a rigid plate in R2 is considered. The density is assumed to be unity in the media: within the layer the sound speed is assumed to be an arbitrary bounded measurable function. The problem is modelled by the reduced wave equation with variable wavenumber in the layer and a Neumann condition on the plate. To formulate the problem and prove uniqueness of solution a radiation condition appropriate for scattering by infinite rough surfaces is introduced, a generalization of the Rayleigh expansion condition for diffraction gratings. With the help of the radiation condition the problem is reformulated as a system of two second kind integral equations over the layer and the plate. Under additional assumptions on the wavenumber in the layer, uniqueness of solution is proved and the nonexistence of guided wave solutions of the homogeneous problem established. General results on the solvability of systems of integral equations on unbounded domains are used to establish existence and continuous dependence in a weighted norm of the solution on the given data.

Efficient calculation of the green function for acoustic propagation above a homogeneous impedance plane

This paper is concerned with the problem of propagation from a monofrequency coherent line source above a plane of homogeneous surface impedance. The solution of this problem occurs in the kernel of certain boundary integral equation formulations of acoustic propagation above an impedance boundary, and the discussion of the paper is motivated by this application. The paper starts by deriving representations, as Laplace-type integrals, of the solution and its first partial derivatives. The evaluation of these integral representations by Gauss-Laguerre quadrature is discussed, and theoretical bounds on the truncation error are obtained. Specific approximations are proposed which are shown to be accurate except in the very near field, for all angles of incidence and a wide range of values of surface impedance. The paper finishes with derivations of partial results and analogous Laplace-type integral representations for the case of a point source.

Comments on 'Balance and the slow quasimanifold: some explicit results'

The concept of slow vortical dynamics and its role in theoretical understanding is central to geophysical fluid dynamics. It leads, for example, to “potential vorticity thinking” (Hoskins et al. 1985). Mathematically, one imagines an invariant manifold within the phase space of solutions, called the slow manifold (Leith 1980; Lorenz 1980), to which the dynamics are constrained. Whether this slow manifold truly exists has been a major subject of inquiry over the past 20 years. It has become clear that an exact slow manifold is an exceptional case, restricted to steady or perhaps temporally periodic flows (Warn 1997). Thus the concept of a “fuzzy slow manifold” (Warn and Ménard 1986) has been suggested. The idea is that nearly slow dynamics will occur in a stochastic layer about the putative slow manifold. The natural question then is, how thick is this layer? In a recent paper, Ford et al. (2000) argue that Lighthill emission—the spontaneous emission of freely propagating acoustic waves by unsteady vortical flows—is applicable to the problem of balance, with the Mach number Ma replaced by the Froude number F, and that it is a fundamental mechanism for this fuzziness. They consider the rotating shallow-water equations and find emission of inertia–gravity waves at O(F2). This is rather surprising at first sight, because several studies of balanced dynamics with the rotating shallow-water equations have gone beyond second order in F, and found only an exponentially small unbalanced component (Warn and Ménard 1986; Lorenz and Krishnamurthy 1987; Bokhove and Shepherd 1996; Wirosoetisno and Shepherd 2000). We have no technical objection to the analysis of Ford et al. (2000), but wish to point out that it depends crucially on R 1, where R is the Rossby number. This condition requires the ratio of the characteristic length scale of the flow L to the Rossby deformation radius LR to go to zero in the limit F → 0. This is the low Froude number scaling of Charney (1963), which, while originally designed for the Tropics, has been argued to be also relevant to mesoscale dynamics (Riley et al. 1981). If L/LR is fixed, however, then F → 0 implies R → 0, which is the standard quasigeostrophic scaling of Charney (1948; see, e.g., Pedlosky 1987). In this limit there is reason to expect the fuzziness of the slow manifold to be “exponentially thin,” and balance to be much more accurate than is consistent with (algebraic) Lighthill emission.

Further evidence for variable synchrotron emission in XTE J1118+480 in outburst

We present simultaneous multicolor infrared and optical photometry of the black hole X-ray transient XTE J1118+480 during its short 2005 January outburst, supported by simultaneous X-ray observations. The variability is dominated by short timescales, ~10 s, although a weak superhump also appears to be present in the optical. The optical rapid variations, at least, are well correlated with those in X-rays. Infrared JHKs photometry, as in the previous outburst, exhibits especially large-amplitude variability. The spectral energy distribution (SED) of the variable infrared component can be fitted with a power law of slope α=-0.78+/-0.07, where F_ν~ν^α. There is no compelling evidence for evolution in the slope over five nights, during which time the source brightness decayed along almost the same track as seen in variations within the nights. We conclude that both short-term variability and longer timescale fading are dominated by a single component of constant spectral shape. We cannot fit the SED of the IR variability with a credible thermal component, either optically thick or thin. This IR SED is, however, approximately consistent with optically thin synchrotron emission from a jet. These observations therefore provide indirect evidence to support jet-dominated models for XTE J1118+480 and also provide a direct measurement of the slope of the optically thin emission, which is impossible, based on the average spectral energy distribution alone.

A multimodel assessment of the influence of regional anthropogenic emission reductions on aerosol direct radiative forcing and the role of intercontinental transport

In this study, we assess changes of aerosol optical depth (AOD) and direct radiative forcing (DRF) in response to the reduction of anthropogenic emissions in four major pollution regions in the Northern Hemisphere by using results from nine global models in the framework of the Hemispheric Transport of Air Pollution (HTAP). DRF at top of atmosphere (TOA) and surface is estimated based on AOD results from the HTAP models and AOD-normalized DRF (NDRF) from a chemical transport model. The multimodel results show that, on average, a 20% reduction of anthropogenic emissions in North America, Europe, East Asia, and South Asia lowers the global mean AOD (all-sky TOA DRF) by 9.2% (9.0%), 3.5% (3.0%), and 9.4% (10.0%) for sulfate, particulate organic matter (POM), and black carbon (BC), respectively. Global annual average TOA all-sky forcing efficiency relative to particle or gaseous precursor emissions from the four regions (expressed as multimodel mean ± one standard deviation) is  ±3.5 ±0.8,  ±4.0 ±1.7, and 29.5 ±18.1mWm ±2 per Tg for sulfate (relative to SO2), POM, and BC, respectively. The impacts of the regional emission reductions on AOD and DRF extend well beyond the source regions because of intercontinental transport (ICT). On an annual basis, ICT accounts for 11 ±5% to 31 ±9% of AOD and DRF in a receptor region at continental or subcontinental scale, with domestic emissions accounting for the remainder, depending on regions and species. For sulfate AOD, the largest ICT contribution of 31 ±9% occurs in South Asia, which is dominated by the emissions from Europe. For BC AOD, the largest ICT contribution of 28 ±18% occurs in North America, which is dominated by the emissions from East Asia. The large spreads among models highlight the need to improve aerosol processes in models, and evaluate and constrain models with observations.

Modelling of urban sensible heat flux at multiple spatial scales : a demonstration using airborne hyperspectral imagery of Shanghai and a temperature–emissivity separation approach

Urbanization related alterations to the surface energy balance impact urban warming (‘heat islands’), the growth of the boundary layer, and many other biophysical processes. Traditionally, in situ heat flux measures have been used to quantify such processes, but these typically represent only a small local-scale area within the heterogeneous urban environment. For this reason, remote sensing approaches are very attractive for elucidating more spatially representative information. Here we use hyperspectral imagery from a new airborne sensor, the Operative Modular Imaging Spectrometer (OMIS), along with a survey map and meteorological data, to derive the land cover information and surface parameters required to map spatial variations in turbulent sensible heat flux (QH). The results from two spatially-explicit flux retrieval methods which use contrasting approaches and, to a large degree, different input data are compared for a central urban area of Shanghai, China: (1) the Local-scale Urban Meteorological Parameterization Scheme (LUMPS) and (2) an Aerodynamic Resistance Method (ARM). Sensible heat fluxes are determined at the full 6 m spatial resolution of the OMIS sensor, and at lower resolutions via pixel aggregation and spatial averaging. At the 6 m spatial resolution, the sensible heat flux of rooftop dominated pixels exceeds that of roads, water and vegetated areas, with values peaking at ∼ 350 W m− 2, whilst the storage heat flux is greatest for road dominated pixels (peaking at around 420 W m− 2). We investigate the use of both OMIS-derived land surface temperatures made using a Temperature–Emissivity Separation (TES) approach, and land surface temperatures estimated from air temperature measures. Sensible heat flux differences from the two approaches over the entire 2 × 2 km study area are less than 30 W m− 2, suggesting that methods employing either strategy maybe practica1 when operated using low spatial resolution (e.g. 1 km) data. Due to the differing methodologies, direct comparisons between results obtained with the LUMPS and ARM methods are most sensibly made at reduced spatial scales. At 30 m spatial resolution, both approaches produce similar results, with the smallest difference being less than 15 W m− 2 in mean QH averaged over the entire study area. This is encouraging given the differing architecture and data requirements of the LUMPS and ARM methods. Furthermore, in terms of mean study QH, the results obtained by averaging the original 6 m spatial resolution LUMPS-derived QH values to 30 and 90 m spatial resolution are within ∼ 5 W m− 2 of those derived from averaging the original surface parameter maps prior to input into LUMPS, suggesting that that use of much lower spatial resolution spaceborne imagery data, for example from Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER) is likely to be a practical solution for heat flux determination in urban areas.

GridRM: a resource monitoring architecture for the grid

Monitoring resources is an important aspect of the overall efficient usage and control of any distributed system. In this paper, we describe a generic open-source resource monitoring architecture that has been specifically designed for the Grid. The paper consists of three main sections. In the first section, we outline our motivation and briefly detail similar work in the area. In the second section, we describe the general monitoring architecture and its components. In the final section of the paper, we summarise the experiences so far and outline our future work.

The water quality of the River Enborne, UK: observations from high-frequency Monitoring in a rural, lowland river system

This paper reports the results of a 2-year study of water quality in the River Enborne, a rural river in lowland England. Concentrations of nitrogen and phosphorus species and other chemical determinands were monitored both at high-frequency (hourly), using automated in situ instrumentation, and by manual weekly sampling and laboratory analysis. The catchment land use is largely agricultural, with a population density of 123 persons km−2. The river water is largely derived from calcareous groundwater, and there are high nitrogen and phosphorus concentrations. Agricultural fertiliser is the dominant source of annual loads of both nitrogen and phosphorus. However, the data show that sewage effluent discharges have a disproportionate effect on the river nitrogen and phosphorus dynamics. At least 38% of the catchment population use septic tank systems, but the effects are hard to quantify as only 6% are officially registered, and the characteristics of the others are unknown. Only 4% of the phosphorus input and 9% of the nitrogen input is exported from the catchment by the river, highlighting the importance of catchment process understanding in predicting nutrient concentrations. High-frequency monitoring will be a key to developing this vital process understanding.

Effects of 3-nitrooxypropanol on methane emission,digestion, and energy and nitrogen balance of lactating dairy cows

The objective was to measure effects of 3-nitrooxypropanol (3NP) on methane production of lactating dairy cows and any associated changes in digestion and energy and nitrogen metabolism. Six Holstein-Friesian dairy cows in mid-lactation were fed twice daily a total mixed ration with maize silage as the primary forage source. Cows received 1 of 3 treatments using an experimental design based on two 3 × 3 Latin squares with 5-wk periods. Treatments were a control placebo or 500 or 2,500 mg/d of 3NP delivered directly into the rumen, via the rumen fistula, in equal doses before each feeding. Measurements of methane production and energy and nitrogen balance were obtained during wk 5 of each period using respiration calorimeters and digestion trials. Measurements of rumen pH (48 h) and postprandial volatile fatty acid and ammonia concentrations were made at the end of wk 4. Daily methane production was reduced by 3NP, but the effects were not dose dependent (reductions of 6.6 and 9.8% for 500 and 2,500 mg/d, respectively). Dosing 3NP had a transitory inhibitory effect on methane production, which may have been due to the product leaving the rumen in liquid outflow or through absorption or metabolism. Changes in rumen concentrations of volatile fatty acids indicated that the pattern of rumen fermentation was affected by both doses of the product, with a decrease in acetate:propionate ratio observed, but that acetate production was inhibited by the higher dose. Dry matter, organic matter, acid detergent fiber, N, and energy digestibility were reduced at the higher dose of the product. The decrease in digestible energy supply was not completely countered by the decrease in methane excretion such that metabolizable energy supply, metabolizable energy concentration of the diet, and net energy balance (milk plus tissue energy) were reduced by the highest dose of 3NP. Similarly, the decrease in nitrogen digestibility at the higher dose of the product was associated with a decrease in body nitrogen balance that was not observed for the lower dose. Milk yield and milk fat concentration and fatty acid composition were not affected but milk protein concentration was greater for the higher dose of 3NP. Twice-daily rumen dosing of 3NP reduced methane production by lactating dairy cows, but the dose of 2,500 mg/d reduced rumen acetate concentration, diet digestibility, and energy supply. Further research is warranted to determine the optimal dose and delivery method of the product. Key words: 3-nitrooxypropanol, methane, digestion, rumen, dairy cow

Impact of vegetation and preferential source areas on global dust aerosol: results from a model study

[1] We present a model of the dust cycle that successfully predicts dust emissions as determined by land surface properties, monthly vegetation and snow cover, and 6-hourly surface wind speeds for the years 1982–1993. The model takes account of the role of dry lake beds as preferential source areas for dust emission. The occurrence of these preferential sources is determined by a water routing and storage model. The dust source scheme also explicitly takes into account the role of vegetation type as well as monthly vegetation cover. Dust transport is computed using assimilated winds for the years 1987–1990. Deposition of dust occurs through dry and wet deposition, where subcloud scavenging is calculated using assimilated precipitation fields. Comparison of simulated patterns of atmospheric dust loading with the Total Ozone Mapping Spectrometer satellite absorbing aerosol index shows that the model produces realistic results from daily to interannual timescales. The magnitude of dust deposition agrees well with sediment flux data from marine sites. Emission of submicron dust from preferential source areas are required for the computation of a realistic dust optical thickness. Sensitivity studies show that Asian dust source strengths are particularly sensitive to the seasonality of vegetation cover.

Implementation of an interior point source in the ultra weak variational formulation through source extraction

The Ultra Weak Variational Formulation (UWVF) is a powerful numerical method for the approximation of acoustic, elastic and electromagnetic waves in the time-harmonic regime. The use of Trefftz-type basis functions incorporates the known wave-like behaviour of the solution in the discrete space, allowing large reductions in the required number of degrees of freedom for a given accuracy, when compared to standard finite element methods. However, the UWVF is not well disposed to the accurate approximation of singular sources in the interior of the computational domain. We propose an adjustment to the UWVF for seismic imaging applications, which we call the Source Extraction UWVF. Differing fields are solved for in subdomains around the source, and matched on the inter-domain boundaries. Numerical results are presented for a domain of constant wavenumber and for a domain of varying sound speed in a model used for seismic imaging.

Curl free pressure gradients over orography in a solution of the fully compressible Euler equations with implicit treatment of acoustic and gravity waves

Steep orography can cause noisy solutions and instability in models of the atmosphere. A new technique for modelling flow over orography is introduced which guarantees curl free gradients on arbitrary grids, implying that the pressure gradient term is not a spurious source of vorticity. This mimetic property leads to better hydrostatic balance and better energy conservation on test cases using terrain following grids. Curl-free gradients are achieved by using the co-variant components of velocity over orography rather than the usual horizontal and vertical components. In addition, gravity and acoustic waves are treated implicitly without the need for mean and perturbation variables or a hydrostatic reference profile. This enables a straightforward description of the implicit treatment of gravity waves. Results are presented of a resting atmosphere over orography and the curl-free pressure gradient formulation is advantageous. Results of gravity waves over orography are insensitive to the placement of terrain-following layers. The model with implicit gravity waves is stable in strongly stratified conditions, with N∆t up to at least 10 (where N is the Brunt-V ̈ais ̈al ̈a frequency). A warm bubble rising over orography is simulated and the curl free pressure gradient formulation gives much more accurate results for this test case than a model without this mimetic property.

The impact of cognitive control on children's goal monitoring in a time-based prospective memory task

The present study investigated whether developmental changes in cognitive control may underlie improvements of time-based prospective memory. Five-, 7-, 9-, and 11-year-olds (N = 166) completed a driving simulation task (ongoing task) in which they had to refuel their vehicle at specific points in time (PM task). The availability of cognitive control resources was experimentally manipulated by imposing a secondary task that required divided attention. Children completed the driving simulation task both in a full attention condition and a divided attention condition where they had to carry out a secondary task. Results revealed that older children performed better than younger children on the ongoing task and PM task. Children performed worse on the ongoing and PM tasks in the divided attention condition compared to the full attention condition. With respect to time monitoring in the final interval prior to the PM target, divided attention interacted with age such that older children’s time monitoring was more negatively affected by the secondary task compared to younger children. Results are discussed in terms of developmental shifts from reactive to proactive monitoring strategies.