Condition number estimates for combined potential boundary integral operators in acoustic scattering

We study the classical combined field integral equation formulations for time-harmonic acoustic scattering by a sound soft bounded obstacle, namely the indirect formulation due to Brakhage-Werner/Leis/Panic, and the direct formulation associated with the names of Burton and Miller. We obtain lower and upper bounds on the condition numbers for these formulations, emphasising dependence on the frequency, the geometry of the scatterer, and the coupling parameter. Of independent interest we also obtain upper and lower bounds on the norms of two oscillatory integral operators, namely the classical acoustic single- and double-layer potential operators.

Simulating the spatial variation of soil mineral N within fields using the model SUNDIAL

Variable rate applications of nitrogen (N) are of environmental and economic interest. Regular measurements of soil N supply are difficult to achieve practically. Therefore accurate model simulations of soil N supply might provide a practical solution for site-specific management of N. Mineral N, an estimate of N supply, was simulated by the model SUNDIAL (Simulation of Nitrogen Dynamics In Arable Land) at more than 100 locations within three arable fields in Bedfordshire, UK. The results were compared with actual measurements. The outcomes showed that the spatial patterns of the simulations of mineral N corresponded to the measurements but the range of values was underestimated.

Exploring the spatial relations between soil properties and electro-magnetic induction (EMI) and the implications for management

The relations between soil electrical conductivity (ECa) and top- and sub-soil physical properties were examined for an arable field in England. The correlation coefficients between ECa and the soil particle size fractions were large and their cross variograms showed that the coregionalization was also strong. The coregionalization was stronger for the subsoil properties than for the topsoil, the reverse to the correlation coefficients. The relations between ECa and some soil properties, such as clay and water content, appear complex and emphasize that a map of ECa cannot substitute for sampling the soil.

Co-kriging when the soil and ancillary data are not co-located

Data such as digitized aerial photographs, electrical conductivity and yield are intensive and relatively inexpensive to obtain compared with collecting soil data by sampling. If such ancillary data are co-regionalized with the soil data they should be suitable for co-kriging. The latter requires that information for both variables is co-located at several locations; this is rarely so for soil and ancillary data. To solve this problem, we have derived values for the ancillary variable at the soil sampling locations by averaging the values within a radius of 15 m, taking the nearest-neighbour value, kriging over 5 m blocks, and punctual kriging. The cross-variograms from these data with clay content and also the pseudo cross-variogram were used to co-krige to validation points and the root mean squared errors (RMSEs) were calculated. In general, the data averaged within 15m and the punctually kriged values resulted in more accurate predictions.

Exploring the spatial variation of take-all (Gaeumannomyces graminis var. tritici) for site-specific management

The fungus Gaeumannomyces graminis var. tritici (Ggt), commonly known as the take-all fungus, causes damage to roots of wheat and barley that limits crop growth and causes loss of yield. There was little knowledge on the within-field spatial variation of take-all and relations with features in the growing crop, selected soil properties and spectral information from remotely sensed imagery. Geostatistical analyses showed that take-all, chlorosis and leaf area index had similar patchy distributions. Many of the spectral bands from a hyperspectral image also had similar spatial patterns to take-all and chlorosis. Relations between take-all and mineral nitrogen, elevation and pH were generally weaker.

A well-posed integral equation formulation for three-dimensional rough surface scattering

We consider the problem of scattering of time-harmonic acoustic waves by an unbounded sound-soft rough surface. Recently, a Brakhage Werner type integral equation formulation of this problem has been proposed, based on an ansatz as a combined single- and double-layer potential, but replacing the usual fundamental solution of the Helmholtz equation with an appropriate half-space Green's function. Moreover, it has been shown in the three-dimensional case that this integral equation is uniquely solvable in the space L-2 (Gamma) when the scattering surface G does not differ too much from a plane. In this paper, we show that this integral equation is uniquely solvable with no restriction on the surface elevation or slope. Moreover, we construct explicit bounds on the inverse of the associated boundary integral operator, as a function of the wave number, the parameter coupling the single- and double-layer potentials, and the maximum surface slope. These bounds show that the norm of the inverse operator is bounded uniformly in the wave number, kappa, for kappa > 0, if the coupling parameter h is chosen proportional to the wave number. In the case when G is a plane, we show that the choice eta = kappa/2 is nearly optimal in terms of minimizing the condition number.

Analysis of wheat SAGE tags reveals evidence for widespread antisense transcription

BACKGROUND: Serial Analysis of Gene Expression (SAGE) is a powerful tool for genome-wide transcription studies. Unlike microarrays, it has the ability to detect novel forms of RNA such as alternatively spliced and antisense transcripts, without the need for prior knowledge of their existence. One limitation of using SAGE on an organism with a complex genome and lacking detailed sequence information, such as the hexaploid bread wheat Triticum aestivum, is accurate annotation of the tags generated. Without accurate annotation it is impossible to fully understand the dynamic processes involved in such complex polyploid organisms. Hence we have developed and utilised novel procedures to characterise, in detail, SAGE tags generated from the whole grain transcriptome of hexaploid wheat. RESULTS: Examination of 71,930 Long SAGE tags generated from six libraries derived from two wheat genotypes grown under two different conditions suggested that SAGE is a reliable and reproducible technique for use in studying the hexaploid wheat transcriptome. However, our results also showed that in poorly annotated and/or poorly sequenced genomes, such as hexaploid wheat, considerably more information can be extracted from SAGE data by carrying out a systematic analysis of both perfect and "fuzzy" (partially matched) tags. This detailed analysis of the SAGE data shows first that while there is evidence of alternative polyadenylation this appears to occur exclusively within the 3' untranslated regions. Secondly, we found no strong evidence for widespread alternative splicing in the developing wheat grain transcriptome. However, analysis of our SAGE data shows that antisense transcripts are probably widespread within the transcriptome and appear to be derived from numerous locations within the genome. Examination of antisense transcripts showing sequence similarity to the Puroindoline a and Puroindoline b genes suggests that such antisense transcripts might have a role in the regulation of gene expression. CONCLUSION: Our results indicate that the detailed analysis of transcriptome data, such as SAGE tags, is essential to understand fully the factors that regulate gene expression and that such analysis of the wheat grain transcriptome reveals that antisense transcripts maybe widespread and hence probably play a significant role in the regulation of gene expression during grain development.

Strongly nucleophilic RhI centre in square-planar complexes with terdentate (κ3) 2,2′:6′,2′′-terpyridine ligands: crystallographic, electrochemical and density functional theoretical studies

Rh-I-terpyridine complexes have been unambiguously formed for the first time. The 2,21:6',2"-terpyridine (tpy), 4'-chloro-2,2':6',2"-terpyridine (4'-Cl-tpy) and 4'-(tert-butyldimethylsilyl-ortho-carboranyl)-2,2':6',2"-terpyridine (carboranyl-tpy) ligands were used for successful syntheses and characterisation of the corresponding Rh-I complexes with halide coligands, [Rh(X)(4'-Y-terpyridine)] (X = Cl, Y = H, Cl, carboranyl; X = Br, Y = H). All four neutral Rh-tpy complexes are square planar, with Rh-X bonds in the plane of the 4'-Y-terpyridine ligands. Full characterisation of these dark blue, highly air-sensitive compounds was hampered by their poor solubility in various organic solvents. This is mainly due to the formation of pi-stacked aggregates, as evidenced by the crystal structure of [Rh(Cl)(tpy)]; in addition, [Rh(Cl)(carboranyl-tpy)] merely forms discrete dimers. The (bonding) properties of the novel Rh-I-terpyridine complexes have been studied with single-crystal X-ray diffraction, (time-dependent) density functional theoretical (DFT) calculations, far-infrared spectroscopy, electronic absorption spectroscopy and cyclic voltammetry. From DFT calculations, the HOMO of the studied Rh-I-terpyridine complexes involves predominantly the metal centre, while the LUMO resides on the terpyridine ligand. Absorption bands of the studied complexes in the visible region (400-900 nm) can be assigned to MLCT and MLCT/XLCT transitions. The relatively low oxidation potentials of [Rh(X)(tpy)] (X = Cl, Br) point to a high electron density on the metal centre. This makes the Rh-I-terpyridine complexes strongly nucleophilic and (potentially) highly reactive towards various (small) substrate molecules containing carbon-halide bonds.

Accurate radiometry from space: an essential tool for climate studies

The Earth's climate is undoubtedly changing; however, the time scale, consequences and causal attribution remain the subject of significant debate and uncertainty. Detection of subtle indicators from a background of natural variability requires measurements over a time base of decades. This places severe demands on the instrumentation used, requiring measurements of sufficient accuracy and sensitivity that can allow reliable judgements to be made decades apart. The International System of Units (SI) and the network of National Metrology Institutes were developed to address such requirements. However, ensuring and maintaining SI traceability of sufficient accuracy in instruments orbiting the Earth presents a significant new challenge to the metrology community. This paper highlights some key measurands and applications driving the uncertainty demand of the climate community in the solar reflective domain, e.g. solar irradiances and reflectances/radiances of the Earth. It discusses how meeting these uncertainties facilitate significant improvement in the forecasting abilities of climate models. After discussing the current state of the art, it describes a new satellite mission, called TRUTHS, which enables, for the first time, high-accuracy SI traceability to be established in orbit. The direct use of a ‘primary standard’ and replication of the terrestrial traceability chain extends the SI into space, in effect realizing a ‘metrology laboratory in space’.

Land-atmosphere energy exchange in Arctic tundra and boreal forest: available data and feedbacks to climate

This paper summarizes and analyses available data on the surface energy balance of Arctic tundra and boreal forest. The complex interactions between ecosystems and their surface energy balance are also examined, including climatically induced shifts in ecosystem type that might amplify or reduce the effects of potential climatic change. High latitudes are characterized by large annual changes in solar input. Albedo decreases strongly from winter, when the surface is snow-covered, to summer, especially in nonforested regions such as Arctic tundra and boreal wetlands. Evapotranspiration (QE) of high-latitude ecosystems is less than from a freely evaporating surface and decreases late in the season, when soil moisture declines, indicating stomatal control over QE, particularly in evergreen forests. Evergreen conifer forests have a canopy conductance half that of deciduous forests and consequently lower QE and higher sensible heat flux (QH). There is a broad overlap in energy partitioning between Arctic and boreal ecosystems, although Arctic ecosystems and light taiga generally have higher ground heat flux because there is less leaf and stem area to shade the ground surface, and the thermal gradient from the surface to permafrost is steeper. Permafrost creates a strong heat sink in summer that reduces surface temperature and therefore heat flux to the atmosphere. Loss of permafrost would therefore amplify climatic warming. If warming caused an increase in productivity and leaf area, or fire caused a shift from evergreen to deciduous forest, this would increase QE and reduce QH. Potential future shifts in vegetation would have varying climate feedbacks, with largest effects caused by shifts from boreal conifer to shrubland or deciduous forest (or vice versa) and from Arctic coastal to wet tundra. An increase of logging activity in the boreal forests appears to reduce QE by roughly 50% with little change in QH, while the ground heat flux is strongly enhanced.

Towards global drought early warning capability: expanding international cooperation for the development of a framework for global drought monitoring and forecasting

Drought is a global problem that has far-reaching impacts and especially 47 on vulnerable populations in developing regions. This paper highlights the need for a Global Drought Early Warning System (GDEWS), the elements that constitute its underlying framework (GDEWF) and the recent progress made towards its development. Many countries lack drought monitoring systems, as well as the capacity to respond via appropriate political, institutional and technological frameworks, and these have inhibited the development of integrated drought management plans or early warning systems. The GDEWS will provide a source of drought tools and products via the GDEWF for countries and regions to develop tailored drought early warning systems for their own users. A key goal of a GDEWS is to maximize the lead time for early warning, allowing drought managers and disaster coordinators more time to put mitigation measures in place to reduce the vulnerability to drought. To address this, the GDEWF will take both a top-down approach to provide global real-time drought monitoring and seasonal forecasting, and a bottom-up approach that builds upon existing national and regional systems to provide continental to global coverage. A number of challenges must be overcome, however, before a GDEWS can become a reality, including the lack of in-situ measurement networks and modest seasonal forecast skill in many regions, and the lack of infrastructure to translate data into useable information. A set of international partners, through a series of recent workshops and evolving collaborations, has made progress towards meeting these challenges and developing a global system.