A finite element method for second order nonvariational elliptic problems

We propose a numerical method to approximate the solution of second order elliptic problems in nonvariational form. The method is of Galerkin type using conforming finite elements and applied directly to the nonvariational (nondivergence) form of a second order linear elliptic problem. The key tools are an appropriate concept of “finite element Hessian” and a Schur complement approach to solving the resulting linear algebra problem. The method is illustrated with computational experiments on three linear and one quasi-linear PDE, all in nonvariational form.

The mysterious presence of a 5-methylcytosine oxidase in the Drosophila genome: Possible explanations

5-methylcytosine is an important epigenetic modification involved in gene control in vertebrates and many other complex living organisms. Its presence in Drosophila has been a matter of debate and recent bisulfite sequencing studies of early-stage fly embryos have concluded that the genome of Drosophila is essentially unmethylated. However, as we outline here, the Drosophila genome harbors a well-conserved homolog of the TET protein family. The mammalian orthologs TET1/2/3 are known to convert 5-methylcytosine into 5-hydroxymethylcytosine. We discuss several possible explanations for these seemingly contradictory findings. One possibility is that the 2 modified cytosine bases are generated in Drosophila only at certain developmental stages and in a cell type-specific manner during neurogenesis. Alternatively, Drosophila Tet and its mammalian homologs may carry out catalytic activity-independent functions, and the possibility that these proteins may oxidize 5-methylcytosine in RNA created by the methyltransferase Dnmt2 should also be strongly considered.

An “A-train” strategy for quantifying direct climate forcing by anthropogenic aerosols

This document outlines a practical strategy for achieving an observationally based quantification of direct climate forcing by anthropogenic aerosols. The strategy involves a four-step program for shifting the current assumption-laden estimates to an increasingly empirical basis using satellite observations coordinated with suborbital remote and in situ measurements and with chemical transport models. Conceptually, the problem is framed as a need for complete global mapping of four parameters: clear-sky aerosol optical depth δ, radiative efficiency per unit optical depth E, fine-mode fraction of optical depth ff, and the anthropogenic fraction of the fine mode faf. The first three parameters can be retrieved from satellites, but correlative, suborbital measurements are required for quantifying the aerosol properties that control E, for validating the retrieval of ff, and for partitioning fine-mode δ between natural and anthropogenic components. The satellite focus is on the “A-Train,” a constellation of six spacecraft that will fly in formation from about 2005 to 2008. Key satellite instruments for this report are the Moderate Resolution Imaging Spectroradiometer (MODIS) and Clouds and the Earth's Radiant Energy System (CERES) radiometers on Aqua, the Ozone Monitoring Instrument (OMI) radiometer on Aura, the Polarization and Directionality of Earth's Reflectances (POLDER) polarimeter on the Polarization and Anistropy of Reflectances for Atmospheric Sciences Coupled with Observations from a Lidar (PARASOL), and the Cloud and Aerosol Lider with Orthogonal Polarization (CALIOP) lidar on the Cloud–Aerosol Lidar and Infrared Pathfinder Satellite Observations (CALIPSO). This strategy is offered as an initial framework—subject to improvement over time—for scientists around the world to participate in the A-Train opportunity. It is a specific implementation of the Progressive Aerosol Retrieval and Assimilation Global Observing Network (PARAGON) program, presented earlier in this journal, which identified the integration of diverse data as the central challenge to progress in quantifying global-scale aerosol effects. By designing a strategy around this need for integration, we develop recommendations for both satellite data interpretation and correlative suborbital activities that represent, in many respects, departures from current practice

General circulation model estimates of aerosol transport and radiative forcing during the Indian Ocean Experiment

Aerosol sources, transport, and sinks are simulated, and aerosol direct radiative effects are assessed over the Indian Ocean for the Indian Ocean Experiment (INDOEX) Intensive Field Phase during January to March 1999 using the Laboratoire de Me´te´orologie Dynamique (LMDZT) general circulation model. The model reproduces the latitudinal gradient in aerosol mass concentration and optical depth (AOD). The model-predicted aerosol concentrations and AODs agree reasonably well with measurements but are systematically underestimated during high-pollution episodes, especially in the month of March. The largest aerosol loads are found over southwestern China, the Bay of Bengal, and the Indian subcontinent. Aerosol emissions from the Indian subcontinent are transported into the Indian Ocean through either the west coast or the east coast of India. Over the INDOEX region, carbonaceous aerosols are the largest contributor to the estimated AOD, followed by sulfate, dust, sea salt, and fly ash. During the northeast winter monsoon, natural and anthropogenic aerosols reduce the solar flux reaching the surface by 25 W m�2, leading to 10–15% less insolation at the surface. A doubling of black carbon (BC) emissions from Asia results in an aerosol single-scattering albedo that is much smaller than in situ measurements, reflecting the fact that BC emissions are not underestimated in proportion to other (mostly scattering) aerosol types. South Asia is the dominant contributor to sulfate aerosols over the INDOEX region and accounts for 60–70% of the AOD by sulfate. It is also an important but not the dominant contributor to carbonaceous aerosols over the INDOEX region with a contribution of less than 40% to the AOD by this aerosol species. The presence of elevated plumes brings significant quantities of aerosols to the Indian Ocean that are generated over Africa and Southeast and east Asia.

A simple framework for assessing the trade-off between the climate impact of aviation carbon dioxide emissions and contrails for a single flight

Persistent contrails are an important climate impact of aviation which could potentially be reduced by re-routing aircraft to avoid contrailing; however this generally increases both the flight length and its corresponding CO emissions. Here, we provide a simple framework to assess the trade-off between the climate impact of CO emissions and contrails for a single flight, in terms of the absolute global warming potential and absolute global temperature potential metrics for time horizons of 20, 50 and 100 years. We use the framework to illustrate the maximum extra distance (with no altitude changes) that can be added to a flight and still reduce its overall climate impact. Small aircraft can fly up to four times further to avoid contrailing than large aircraft. The results have a strong dependence on the applied metric and time horizon. Applying a conservative estimate of the uncertainty in the contrail radiative forcing and climate efficacy leads to a factor of 20 difference in the maximum extra distance that could be flown to avoid a contrail. The impact of re-routing on other climatically-important aviation emissions could also be considered in this framework.

Using an individual-based model to select among alternative foraging strategies of woodpigeons: data support a memory-based model with a flocking mechanism

Population modelling is increasingly recognised as a useful tool for pesticide risk assessment. For vertebrates that may ingest pesticides with their food, such as woodpigeon (Columba palumbus), population models that simulate foraging behaviour explicitly can help predicting both exposure and population-level impact. Optimal foraging theory is often assumed to explain the individual-level decisions driving distributions of individuals in the field, but it may not adequately predict spatial and temporal characteristics of woodpigeon foraging because of the woodpigeons’ excellent memory, ability to fly long distances, and distinctive flocking behaviour. Here we present an individual-based model (IBM) of the woodpigeon. We used the model to predict distributions of foraging woodpigeons that use one of six alternative foraging strategies: optimal foraging, memory-based foraging and random foraging, each with or without flocking mechanisms. We used pattern-oriented modelling to determine which of the foraging strategies is best able to reproduce observed data patterns. Data used for model evaluation were gathered during a long-term woodpigeon study conducted between 1961 and 2004 and a radiotracking study conducted in 2003 and 2004, both in the UK, and are summarised here as three complex patterns: the distributions of foraging birds between vegetation types during the year, the number of fields visited daily by individuals, and the proportion of fields revisited by them on subsequent days. The model with a memory-based foraging strategy and a flocking mechanism was the only one to reproduce these three data patterns, and the optimal foraging model produced poor matches to all of them. The random foraging strategy reproduced two of the three patterns but was not able to guarantee population persistence. We conclude that with the memory-based foraging strategy including a flocking mechanism our model is realistic enough to estimate the potential exposure of woodpigeons to pesticides. We discuss how exposure can be linked to our model, and how the model could be used for risk assessment of pesticides, for example predicting exposure and effects in heterogeneous landscapes planted seasonally with a variety of crops, while accounting for differences in land use between landscapes.

Landscape change in central Latvia since the Iron Age: multi-proxy analysis of the vegetation impact of conflict, colonization and economic expansion during the last 2000 years

This study represents the first detailed multi-proxy palaeoenvironmental investigation associated with a Late Iron Age lake-dwelling site in the eastern Baltic. The main objective was to reconstruct the environmental and vegetation dynamics associated with the establishment of the lake-dwelling and land-use during the last 2,000 years. A lacustrine sediment core located adjacent to a Late Iron Age lake-dwelling, medieval castle and Post-medieval manor was sampled in Lake Āraiši. The core was dated using spheroidal fly-ash particles and radiocarbon dating, and analysed in terms of pollen, non-pollen palynomorphs, diatoms, loss-on-ignition, magnetic susceptibility and element geochemistry. Associations between pollen and other proxies were statistically tested. During ad 1–700, the vicinity of Lake Āraiši was covered by forests and human activities were only small-scale with the first appearance of cereal pollen (Triticum and Secale cereale) after ad 400. The most significant changes in vegetation and environment occurred with the establishment of the lake-dwelling around ad 780 when the immediate surroundings of the lake were cleared for agriculture, and within the lake there were increased nutrient levels. The highest accumulation rates of coprophilous fungi coincide with the occupation of the lake-dwelling from ad 780–1050, indicating that parts of the dwelling functioned as byres for livestock. The conquest of tribal lands during the crusades resulted in changes to the ownership, administration and organisation of the land, but our results indicate that the form and type of agriculture and land-use continued much as it had during the preceding Late Iron Age.

Experimental evolution for generalists and specialists reveals multivariate genetic constraints on thermal reaction norms

Theory predicts the emergence of generalists in variable environments and antagonistic pleiotropy to favour specialists in constant environments, but empirical data seldom support such generalist–specialist trade-offs. We selected for generalists and specialists in the dung fly Sepsis punctum (Diptera: Sepsidae) under conditions that we predicted would reveal antagonistic pleiotropy and multivariate trade-offs underlying thermal reaction norms for juvenile development. We performed replicated laboratory evolution using four treatments: adaptation at a hot (31 °C) or a cold (15 °C) temperature, or under regimes fluctuating between these temperatures, either within or between generations. After 20 generations, we assessed parental effects and genetic responses of thermal reaction norms for three correlated life-history traits: size at maturity, juvenile growth rate and juvenile survival. We find evidence for antagonistic pleiotropy for performance at hot and cold temperatures, and a temperature-mediated trade-off between juvenile survival and size at maturity, suggesting that trade-offs associated with environmental tolerance can arise via intensified evolutionary compromises between genetically correlated traits. However, despite this antagonistic pleiotropy, we found no support for the evolution of increased thermal tolerance breadth at the expense of reduced maximal performance, suggesting low genetic variance in the generalist–specialist dimension.

Discontinuous Galerkin methods for the p-biharmonic equation from a discrete variational perspective

We study discontinuous Galerkin approximations of the p-biharmonic equation for p∈(1,∞) from a variational perspective. We propose a discrete variational formulation of the problem based on an appropriate definition of a finite element Hessian and study convergence of the method (without rates) using a semicontinuity argument. We also present numerical experiments aimed at testing the robustness of the method.

Fast adaptive real-time classification for data streams with concept drift

An important application of Big Data Analytics is the real-time analysis of streaming data. Streaming data imposes unique challenges to data mining algorithms, such as concept drifts, the need to analyse the data on the fly due to unbounded data streams and scalable algorithms due to potentially high throughput of data. Real-time classification algorithms that are adaptive to concept drifts and fast exist, however, most approaches are not naturally parallel and are thus limited in their scalability. This paper presents work on the Micro-Cluster Nearest Neighbour (MC-NN) classifier. MC-NN is based on an adaptive statistical data summary based on Micro-Clusters. MC-NN is very fast and adaptive to concept drift whilst maintaining the parallel properties of the base KNN classifier. Also MC-NN is competitive compared with existing data stream classifiers in terms of accuracy and speed.

Conditioning of the weak-constraint variational data assimilation problem for numerical weather prediction

4-Dimensional Variational Data Assimilation (4DVAR) assimilates observations through the minimisation of a least-squares objective function, which is constrained by the model flow. We refer to 4DVAR as strong-constraint 4DVAR (sc4DVAR) in this thesis as it assumes the model is perfect. Relaxing this assumption gives rise to weak-constraint 4DVAR (wc4DVAR), leading to a different minimisation problem with more degrees of freedom. We consider two wc4DVAR formulations in this thesis, the model error formulation and state estimation formulation. The 4DVAR objective function is traditionally solved using gradient-based iterative methods. The principle method used in Numerical Weather Prediction today is the Gauss-Newton approach. This method introduces a linearised `inner-loop' objective function, which upon convergence, updates the solution of the non-linear `outer-loop' objective function. This requires many evaluations of the objective function and its gradient, which emphasises the importance of the Hessian. The eigenvalues and eigenvectors of the Hessian provide insight into the degree of convexity of the objective function, while also indicating the difficulty one may encounter while iterative solving 4DVAR. The condition number of the Hessian is an appropriate measure for the sensitivity of the problem to input data. The condition number can also indicate the rate of convergence and solution accuracy of the minimisation algorithm. This thesis investigates the sensitivity of the solution process minimising both wc4DVAR objective functions to the internal assimilation parameters composing the problem. We gain insight into these sensitivities by bounding the condition number of the Hessians of both objective functions. We also precondition the model error objective function and show improved convergence. We show that both formulations' sensitivities are related to error variance balance, assimilation window length and correlation length-scales using the bounds. We further demonstrate this through numerical experiments on the condition number and data assimilation experiments using linear and non-linear chaotic toy models.

Mesh adaptation on the sphere using optimal transport and the numerical solution of a Monge-Ampère type equation

An equation of Monge-Ampère type has, for the first time, been solved numerically on the surface of the sphere in order to generate optimally transported (OT) meshes, equidistributed with respect to a monitor function. Optimal transport generates meshes that keep the same connectivity as the original mesh, making them suitable for r-adaptive simulations, in which the equations of motion can be solved in a moving frame of reference in order to avoid mapping the solution between old and new meshes and to avoid load balancing problems on parallel computers. The semi-implicit solution of the Monge-Ampère type equation involves a new linearisation of the Hessian term, and exponential maps are used to map from old to new meshes on the sphere. The determinant of the Hessian is evaluated as the change in volume between old and new mesh cells, rather than using numerical approximations to the gradients. OT meshes are generated to compare with centroidal Voronoi tesselations on the sphere and are found to have advantages and disadvantages; OT equidistribution is more accurate, the number of iterations to convergence is independent of the mesh size, face skewness is reduced and the connectivity does not change. However anisotropy is higher and the OT meshes are non-orthogonal. It is shown that optimal transport on the sphere leads to meshes that do not tangle. However, tangling can be introduced by numerical errors in calculating the gradient of the mesh potential. Methods for alleviating this problem are explored. Finally, OT meshes are generated using observed precipitation as a monitor function, in order to demonstrate the potential power of the technique.

Conditioning and preconditioning of the optimal state estimation problem

Optimal state estimation is a method that requires minimising a weighted, nonlinear, least-squares objective function in order to obtain the best estimate of the current state of a dynamical system. Often the minimisation is non-trivial due to the large scale of the problem, the relative sparsity of the observations and the nonlinearity of the objective function. To simplify the problem the solution is often found via a sequence of linearised objective functions. The condition number of the Hessian of the linearised problem is an important indicator of the convergence rate of the minimisation and the expected accuracy of the solution. In the standard formulation the convergence is slow, indicating an ill-conditioned objective function. A transformation to different variables is often used to ameliorate the conditioning of the Hessian by changing, or preconditioning, the Hessian. There is only sparse information in the literature for describing the causes of ill-conditioning of the optimal state estimation problem and explaining the effect of preconditioning on the condition number. This paper derives descriptive theoretical bounds on the condition number of both the unpreconditioned and preconditioned system in order to better understand the conditioning of the problem. We use these bounds to explain why the standard objective function is often ill-conditioned and why a standard preconditioning reduces the condition number. We also use the bounds on the preconditioned Hessian to understand the main factors that affect the conditioning of the system. We illustrate the results with simple numerical experiments.

Transatlantic flight times and climate change

Aircraft do not fly through a vacuum, but through an atmosphere whose meteorological characteristics are changing because of global warming. The impacts of aviation on climate change have long been recognised, but the impacts of climate change on aviation have only recently begun to emerge. These impacts include intensified turbulence and increased take-off weight restrictions. Here we investigate the influence of climate change on flight routes and journey times. We feed synthetic atmospheric wind fields generated from climate model simulations into a routing algorithm of the type used operationally by flight planners. We focus on transatlantic flights between London and New York, and how they change when the atmospheric concentration of carbon dioxide is doubled. We find that a strengthening of the prevailing jet-stream winds causes eastbound flights to significantly shorten and westbound flights to significantly lengthen in all seasons. Eastbound and westbound crossings in winter become approximately twice as likely to take under 5 h 20 min and over 7 h 00 min, respectively. For reasons that are explained using a conceptual model, the eastbound shortening and westbound lengthening do not cancel out, causing round-trip journey times to increase. Even assuming no future growth in aviation, the extrapolation of our results to all transatlantic traffic suggests that aircraft will collectively be airborne for an extra 2000 h each year, burning an extra 7.2 million gallons of jet fuel at a cost of US$ 22 million, and emitting an extra 70 million kg of carbon dioxide, which is equivalent to the annual emissions of 7100 average British homes. Our results provide further evidence of the two-way interaction between aviation and climate change.

Ecuador Paraiso Escondido virus, a new flavivirus isolated from New World sand flies in Ecuador, is the first representative of a novel clade in the genus flavivirus

A new flavivirus, Ecuador Paraiso Escondido virus (EPEV), named after the village where it was discovered, was isolated from sand flies (Psathyromyia abonnenci, formerly Lutzomyia abonnenci) that are unique to the New World. This represents the first sand fly-borne flavivirus identified in the New World. EPEV exhibited a typical flavivirus genome organization. Nevertheless, the maximum pairwise amino acid sequence identity with currently recognized flaviviruses was 52.8%. Phylogenetic analysis of the complete coding sequence showed that EPEV represents a distinct clade which diverged from a lineage that was ancestral to the nonvectored flaviviruses Entebbe bat virus, Yokose virus, and Sokoluk virus and also the Aedes-associated mosquito-borne flaviviruses, which include yellow fever virus, Sepik virus, Saboya virus, and others. EPEV replicated in C6/36 mosquito cells, yielding high infectious titers, but failed to reproduce either in vertebrate cell lines (Vero, BHK, SW13, and XTC cells) or in suckling mouse brains. This surprising result, which appears to eliminate an association with vertebrate hosts in the life cycle of EPEV, is discussed in the context of the evolutionary origins of EPEV in the New World.The flaviviruses are rarely (if ever) vectored by sand fly species, at least in the Old World. We have identified the first representative of a sand fly-associated flavivirus, Ecuador Paraiso Escondido virus (EPEV), in the New World. EPEV constitutes a novel clade according to current knowledge of the flaviviruses. Phylogenetic analysis of the virus genome showed that EPEV roots the Aedes-associated mosquito-borne flaviviruses, including yellow fever virus. In light of this new discovery, the New World origin of EPEV is discussed together with that of the other flaviviruses.