Conditioning and preconditioning of the variational data assimilation problem

Numerical weather prediction (NWP) centres use numerical models of the atmospheric flow to forecast future weather states from an estimate of the current state. Variational data assimilation (VAR) is used commonly to determine an optimal state estimate that miminizes the errors between observations of the dynamical system and model predictions of the flow. The rate of convergence of the VAR scheme and the sensitivity of the solution to errors in the data are dependent on the condition number of the Hessian of the variational least-squares objective function. The traditional formulation of VAR is ill-conditioned and hence leads to slow convergence and an inaccurate solution. In practice, operational NWP centres precondition the system via a control variable transform to reduce the condition number of the Hessian. In this paper we investigate the conditioning of VAR for a single, periodic, spatially-distributed state variable. We present theoretical bounds on the condition number of the original and preconditioned Hessians and hence demonstrate the improvement produced by the preconditioning. We also investigate theoretically the effect of observation position and error variance on the preconditioned system and show that the problem becomes more ill-conditioned with increasingly dense and accurate observations. Finally, we confirm the theoretical results in an operational setting by giving experimental results from the Met Office variational system.

Coverage-dependent molecular tilt of carbon monoxide chemisorbed on Pt{110}: A combined LEED and DFT structural analysis

The adsorption of carbon monoxide on the Pt{110} surface at coverages of 0.5 ML and 1.0 ML was investigated using quantitative low-energy electron diffraction (LEED IV) and density-functional theory (DFT). At 0.5 ML CO lifts the reconstruction of the clean surface but does not form an ordered overlayer. At the saturation coverage, 1.0 ML, a well-ordered p(2×1) superstructure with glide line symmetry is formed. It was confirmed that the CO molecules adsorb on top of the Pt atoms in the top-most substrate layer with the molecular axes tilted by ±22° with respect to the surface normal in alternating directions away from the close packed rows of Pt atoms. This is accompanied by significant lateral shifts of 0.55 Å away from the atop sites in the same direction as the tilt. The top-most substrate layer relaxes inwards by −4% with respect to the bulk-terminated atom positions, while the consecutive layers only show minor relaxations. Despite the lack of long-range order in the 0.5 ML CO layer it was possible to determine key structural parameters by LEED IV using only the intensities of the integer-order spots. At this coverage CO also adsorbs on atop sites with the molecular axis closer to the surface normal (b10°). The average substrate relaxations in each layer are similar for both coverages and consistent with DFT calculations performed for a variety of ordered structures with coverages of 1.0 ML and 0.5 ML.

A gene variation (rs12691) in the CCAT/enhancer building α modulates glucose metabolism in metabolic syndrome

Background and aims CCAAT/enhancer-binding protein alpha (CEBPA) is a transcription factor involved in adipogenesis and energy homeostasis. Caloric restriction reduces CEBPA protein expression in patients with metabolic syndrome (MetS). A previous report linked rs12691 SNP in CEBPA to altered concentration of fasting triglycerides. Our objective was to assess the effects of rs12691 in glucose metabolism in Metabolic Syndrome (MetS) patients. Methods and results Glucose metabolism was assessed by static (glucose, insulin, adiponectin, leptin and resistin plasma concentrations) and dynamic (disposition index, insulin sensitivity index, HOMA-IR and acute insulin response to glucose) indices, performed at baseline and after 12 weeks of 4 dietary interventions (high saturated fatty acid (SFA), high monounsaturated fatty acid (MUFA), low-fat and low-fat-high-n3 polyunsaturated fatty acid (PUFA)) in 486 subjects with MetS. Carriers of the minor A allele of rs12691 had altered disposition index (p = 0.0003), lower acute insulin response (p = 0.005) and a lower insulin sensitivity index (p = 0.025) indicating a lower insulin sensitivity and a lower insulin secretion, at baseline and at the end of the diets. Furthermore, A allele carriers displayed lower HDL concentration. Conclusion The presence of the A allele of rs12691 influences glucose metabolism of MetS patients. Clinical Trials Registry number NCT00429195.

Spectral analysis of diffusions with jump boundary

In this paper we consider one-dimensional diffusions with constant coefficients in a finite interval with jump boundary and a certain deterministic jump distribution. We use coupling methods in order to identify the spectral gap in the case of a large drift and prove that there is a threshold drift above which the bottom of the spectrum no longer depends on the drift. As a corollary to our result we are able to answer two questions concerning elliptic eigenvalue problems with non-local boundary conditions formulated previously by Iddo Ben-Ari and Ross Pinsky.

Progressive palaeoenvironmental change during the Late Barremian-Early Aptian as prelude to Oceanic Anoxic Event 1a: Evidence from the Gorgo a Cerbara section (Umbria-Marche basin, central Italy)

During Oceanic Anoxic Event 1a (OAE 1a, 120 Ma; Li et al., 2008), organic carbon-rich layers were deposited in marine environments under anoxic conditions on a global scale. In this study, palaeoenvironmental conditions leading to this event are characterised by studying the Upper Barremian to the Lower Aptian succession of the Gorgo a Cerbara section (central Italy). For this, an integrated multi-proxy approach (δ13Ccarb; δ13Corg; δ18O; phosphorus; Total Organic Carbon, TOC; bulk-rock mineralogy, as well as redox-sensitive trace elements — RSTEs) has been applied. During the LateBarremian, thin organic-rich layers occur episodically, and associated Corg:Ptot ratios indicate the presence of intermittent dysoxic to anoxic conditions. Coarse correlations are observed between TOC, P and biogenic silica contents, indicating links between P availability, productivity, and TOC preservation. However, the corresponding δ13Ccarb and δ18O records remain quite stable, indicating that these brief periods of enhanced TOC preservation did not have sufficient impact on the marine carbon reservoir to deviate δ13C records. Around the Barremian–Aptian boundary, TOC-enriched layers become more frequent. These layers correlate with negative excursions in the δ13Ccarb and δ13Corg records, possibly due to a warming period as indicated by the δ18O record. During the earliest Aptian, this warming trend is reverted into a cooling trend, which is then followed by an important warming step near the onset of Oceanic Anoxic Event 1a (OAE 1a). During this time period, organic-rich intervals occur, which are characterised by the progressive increase in RSTE. The warming step prior the onset of OAE 1a is associated with the well-known negative spike in δ13Ccarb and δ13Corg records, an important peak in P accumulation, RSTE enrichments and Corg:Ptot ratios indicating the prevalence of anoxic conditions. The Selli Level itself may document a cooling phase. RSTE enrichments and Corg:Ptot ratios confirm the importance of anoxic conditions during OAE 1a at this site. The Gorgo a Cerbara section is interpreted to reflect the progressive impact of palaeoenvironmental change related to the formation of the Ontong-Java plate-basalt plateau, which started already around the Barremian–Aptian boundary and culminated into OAE 1a.

Seasonality and the valuation of commodity options

Price movements in many commodity markets exhibit significant seasonal patterns. However, given an observed futures price, a deterministic seasonal component at the price level is not relevant for the pricing of commodity options. In contrast, this is not true for the seasonal pattern observed in the volatility of the commodity price. Analyzing an extensive sample of soybean, corn, heating oil and natural gas options, we find that seasonality in volatility is an important aspect to consider when valuing these contracts. The inclusion of an appropriate seasonality adjustment significantly reduces pricing errors in these markets and yields more improvement in valuation accuracy than increasing the number of stochastic factors.

Assessment of a 1 hour gridded precipitation dataset to drive a hydrological model: a case study of the summer 2007 floods in the Upper Severn, UK

In this study a gridded hourly 1-km precipitation dataset for a meso-scale catchment (4,062 km2) of the Upper Severn River, UK was constructed using rainfall radar data to disaggregate a daily precipitation (rain gauge) dataset. The dataset was compared to an hourly precipitation dataset created entirely from rainfall radar data. Results found that when assessed against gauge readings and as input to the Lisflood-RR hydrological model, the rain gauge/radar disaggregated dataset performed the best suggesting that this simple method of combining rainfall radar data with rain gauge readings can provide temporally detailed precipitation datasets for calibrating hydrological models.

Soil management in relation to sustainable agriculture and ecosystem services

Requirements for research, practices and policies affecting soil management in relation to global food security are reviewed. Managing soil organic carbon (C) is central because soil organic matter influences numerous soil properties relevant to ecosystem functioning and crop growth. Even small changes in total C content can have disproportionately large impacts on key soil physical properties. Practices to encourage maintenance of soil C are important for ensuring sustainability of all soil functions. Soil is a major store of C within the biosphere – increases or decreases in this large stock can either mitigate or worsen climate change. Deforestation, conversion of grasslands to arable cropping and drainage of wetlands all cause emission of C; policies and international action to minimise these changes are urgently required. Sequestration of C in soil can contribute to climate change mitigation but the real impact of different options is often misunderstood. Some changes in management that are beneficial for soil C, increase emissions of nitrous oxide (a powerful greenhouse gas) thus cancelling the benefit. Research on soil physical processes and their interactions with roots can lead to improved and novel practices to improve crop access to water and nutrients. Increased understanding of root function has implications for selection and breeding of crops to maximise capture of water and nutrients. Roots are also a means of delivering natural plant-produced chemicals into soil with potentially beneficial impacts. These include biocontrol of soil-borne pests and diseases and inhibition of the nitrification process in soil (conversion of ammonium to nitrate) with possible benefits for improved nitrogen use efficiency and decreased nitrous oxide emission. The application of molecular methods to studies of soil organisms, and their interactions with roots, is providing new understanding of soil ecology and the basis for novel practical applications. Policy makers and those concerned with development of management approaches need to keep a watching brief on emerging possibilities from this fast-moving area of science. Nutrient management is a key challenge for global food production: there is an urgent need to increase nutrient availability to crops grown by smallholder farmers in developing countries. Many changes in practices including inter-cropping, inclusion of nitrogen-fixing crops, agroforestry and improved recycling have been clearly demonstrated to be beneficial: facilitating policies and practical strategies are needed to make these widely available, taking account of local economic and social conditions. In the longer term fertilizers will be essential for food security: policies and actions are needed to make these available and affordable to small farmers. In developed regions, and those developing rapidly such as China, strategies and policies to manage more precisely the necessarily large flows of nutrients in ways that minimise environmental damage are essential. A specific issue is to minimise emissions of nitrous oxide whilst ensuring sufficient nitrogen is available for adequate food production. Application of known strategies (through either regulation or education), technological developments, and continued research to improve understanding of basic processes will all play a part. Decreasing soil erosion is essential, both to maintain the soil resource and to minimise downstream damage such as sedimentation of rivers with adverse impacts on fisheries. Practical strategies are well known but often have financial implications for farmers. Examples of systems for paying one group of land users for ecosystem services affecting others exist in several parts of the world and serve as a model.

Corynebacterium uterequi sp. nov., a non-lipophilic bacterium isolated from urogenital samples from horses

Three strains of a Gram-positive, catalase-positive, fermentative, non-lipophilic, previously unknown bacterium were isolated from urogenital samples taken from mares in Scotland (M401624/00/1) and Sweden (VM 2074 and VM 2298T). All were deposited with the CCUG with tentative identifications as Corynebacterium spp. The strains were characterized using a polyphasic taxonomic approach. Biochemically, the strains were very similar to each other, but phylogenetically distinct from Corynebacterium species with validly published names (≤95% sequence similarity). rpoB gene sequence data confirmed the strains belonged to the same species (>99% sequence similarity) and were distinct from species with validly published names (>13% sequence divergence). On the basis of phenotypic and sequence data, the strains represent a novel species within the genus Corynebacterium, for which the name Corynebacterium uterequi is proposed. The type strain is VM 2298T (=CCUG 61235T = DSM 45634T), isolated from equine uterus.

Runge-Kutta IMEX schemes for the Horizontally Explicit/Vertically Implicit (HEVI) solution of wave equations

Many operational weather forecasting centres use semi-implicit time-stepping schemes because of their good efficiency. However, as computers become ever more parallel, horizontally explicit solutions of the equations of atmospheric motion might become an attractive alternative due to the additional inter-processor communication of implicit methods. Implicit and explicit (IMEX) time-stepping schemes have long been combined in models of the atmosphere using semi-implicit, split-explicit or HEVI splitting. However, most studies of the accuracy and stability of IMEX schemes have been limited to the parabolic case of advection–diffusion equations. We demonstrate how a number of Runge–Kutta IMEX schemes can be used to solve hyperbolic wave equations either semi-implicitly or HEVI. A new form of HEVI splitting is proposed, UfPreb, which dramatically improves accuracy and stability of simulations of gravity waves in stratified flow. As a consequence it is found that there are HEVI schemes that do not lose accuracy in comparison to semi-implicit ones. The stability limits of a number of variations of trapezoidal implicit and some Runge–Kutta IMEX schemes are found and the schemes are tested on two vertical slice cases using the compressible Boussinesq equations split into various combinations of implicit and explicit terms. Some of the Runge–Kutta schemes are found to be beneficial over trapezoidal, especially since they damp high frequencies without dropping to first-order accuracy. We test schemes that are not formally accurate for stiff systems but in stiff limits (nearly incompressible) and find that they can perform well. The scheme ARK2(2,3,2) performs the best in the tests.

Tackling regional climate change by leaf albedo bio-geoengineering

The likelihood that continuing greenhouse-gas emissions will lead to an unmanageable degree of climate change [1] has stimulated the search for planetary-scale technological solutions for reducing global warming [2] (“geoengineering”), typically characterized by the necessity for costly new infrastructures and industries [3]. We suggest that the existing global infrastructure associated with arable agriculture can help, given that crop plants exert an important influence over the climatic energy budget 4 and 5 because of differences in their albedo (solar reflectivity) compared to soils and to natural vegetation [6]. Specifically, we propose a “bio-geoengineering” approach to mitigate surface warming, in which crop varieties having specific leaf glossiness and/or canopy morphological traits are specifically chosen to maximize solar reflectivity. We quantify this by modifying the canopy albedo of vegetation in prescribed cropland areas in a global-climate model, and thereby estimate the near-term potential for bio-geoengineering to be a summertime cooling of more than 1°C throughout much of central North America and midlatitude Eurasia, equivalent to seasonally offsetting approximately one-fifth of regional warming due to doubling of atmospheric CO2[7]. Ultimately, genetic modification of plant leaf waxes or canopy structure could achieve greater temperature reductions, although better characterization of existing intraspecies variability is needed first.

Non-pain goal pursuit inhibits attentional bias to pain

Although dealing with pain is a vital goal to pursue, most individuals are also engaged in the pursuit of other goals. The aim of the present experiment was to investigate whether attentional bias to pain signals is inhibited when one is pursuing a concurrent salient but nonpain task goal. Attentional bias to pain signals was measured in pain-free volunteers (n=63) using a spatial cueing task with pain cues and neutral cues. The pursuit of a concurrent goal was manipulated by including additional trials in which a digit appeared at the middle of the screen. Half of the participants (goal group) were instructed to name these additional stimuli aloud. In order to increase the affective-motivational value of this non-pain-related goal, monetary reward and punishment were made contingent upon the performance of this task. Participants of the control group did not perform the additional task. As predicted, the results show attentional bias to pain signals in the control group, but not in the goal group. This indicates that attentional bias to signals of impending pain is inhibited when one is engaged in the pursuit of another salient but nonpain goal. The results of this study underscore a motivational view on attention to pain, in which the pursuit of multiple goals, including nonpain goals, is taken into account.

Spectra of a class of non-self-adjoint matrices

We consider a new class of non-self-adjoint matrices that arise from an indefinite self- adjoint linear pencil of matrices, and obtain the spectral asymptotics of the spectra as the size of the matrices diverges to infinity. We prove that the spectrum is qualitatively different when a certain parameter c equals 0, and when it is non-zero, and that certain features of the spectrum depend on Diophantine properties of c.