Conditioning of incremental variational data assimilation, with application to the Met Office system

Implementations of incremental variational data assimilation require the iterative minimization of a series of linear least-squares cost functions. The accuracy and speed with which these linear minimization problems can be solved is determined by the condition number of the Hessian of the problem. In this study, we examine how different components of the assimilation system influence this condition number. Theoretical bounds on the condition number for a single parameter system are presented and used to predict how the condition number is affected by the observation distribution and accuracy and by the specified lengthscales in the background error covariance matrix. The theoretical results are verified in the Met Office variational data assimilation system, using both pseudo-observations and real data.

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.

Quantitative genetic divergence and standing genetic (co)variance in thermal reaction norms along latitude

Although the potential to adapt to warmer climate is constrained by genetic trade-offs, our understanding of how selection and mutation shape genetic (co)variances in thermal reaction norms is poor. Using 71 isofemale lines of the fly Sepsis punctum, originating from northern, central, and southern European climates, we tested for divergence in juvenile development rate across latitude at five experimental temperatures. To investigate effects of evolutionary history in different climates on standing genetic variation in reaction norms, we further compared genetic (co)variances between regions. Flies were reared on either high or low food resources to explore the role of energy acquisition in determining genetic trade-offs between different temperatures. Although the latter had only weak effects on the strength and sign of genetic correlations, genetic architecture differed significantly between climatic regions, implying that evolution of reaction norms proceeds via different trajectories at high latitude versus low latitude in this system. Accordingly, regional genetic architecture was correlated to region-specific differentiation. Moreover, hot development temperatures were associated with low genetic variance and stronger genetic correlations compared to cooler temperatures. We discuss the evolutionary potential of thermal reaction norms in light of their underlying genetic architectures, evolutionary histories, and the materialization of trade-offs in natural environments.

A finite element method for nonlinear elliptic problems

We present a Galerkin method with piecewise polynomial continuous elements for fully nonlinear elliptic equations. A key tool is the discretization proposed in Lakkis and Pryer, 2011, allowing us to work directly on the strong form of a linear PDE. An added benefit to making use of this discretization method is that a recovered (finite element) Hessian is a byproduct of the solution process. We build on the linear method and ultimately construct two different methodologies for the solution of second order fully nonlinear PDEs. Benchmark numerical results illustrate the convergence properties of the scheme for some test problems as well as the Monge–Amp`ere equation and the Pucci equation.

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.

Species 2000 & ITIS Catalogue of Life, 2013 Annual Checklist

This release of the Catalogue of Life contains contributions from 132 databases with information on 1,352,112 species, 114,069 infraspecific taxa and also includes 928,147 synonyms and 408,689 common names covering the following groups: Viruses • Viruses and Subviral agents from ICTV_MSL UPDATED! Bacteria and Archaea from BIOS Chromista • Chromistan fungi from Species Fungorum Protozoa • Major groups from ITIS Regional, • Ciliates from CilCat, • Polycystines from WoRMS Polycystina UPDATED!, • Protozoan fungi from Species Fungorum and Trichomycetes database • Slime moulds from Nomen.eumycetozoa.com Fungi • Various taxa in whole or in part from CABI Bioservices databases (Species Fungorum, Phyllachorales, Rhytismatales, Saccharomycetes and Zygomycetes databases) and from three other databases covering Xylariaceae, Glomeromycota, Trichomycetes, Dothideomycetes • Lichens from LIAS UPDATED! Plantae (Plants) • Mosses from MOST • Liverworts and hornworts from ELPT • Conifers from Conifer Database • Cycads and 6 flowering plant families from IOPI-GPC, and 99 families from WCSP • Plus individual flowering plants families from AnnonBase, Brassicaceae, ChenoBase, Droseraceae Database, EbenaBase, GCC UPDATED!, ILDIS UPDATED!, LecyPages, LHD, MELnet UPDATED!, RJB Geranium, Solanaceae Source, Umbellifers. Animalia (Animals) • Marine groups from URMO, ITIS Global, Hexacorals, ETI WBD (Euphausiacea), WoRMS: WoRMS Asteroidea UPDATED!, WoRMS Bochusacea UPDATED!, WoRMS Brachiopoda UPDATED!, WoRMS Brachypoda UPDATED!, WoRMS Brachyura UPDATED!, WoRMS Bryozoa UPDATED!, WoRMS Cestoda NEW!, WoRMS Chaetognatha UPDATED!, WoRMS Cumacea UPDATED!, WoRMS Echinoidea UPDATED!, WoRMS Gastrotricha NEW!, WoRMS Gnathostomulida NEW!, WoRMS Holothuroidea UPDATED!, WoRMS Hydrozoa UPDATED!, WoRMS Isopoda UPDATED!, WoRMS Leptostraca UPDATED!, WoRMS Monogenea NEW!, WoRMS Mystacocarida UPDATED!, WoRMS Myxozoa NEW!, WoRMS Nemertea UPDATED!, WoRMS Oligochaeta UPDATED!, WoRMS Ophiuroidea UPDATED!, WoRMS Phoronida UPDATED!, WoRMS Placozoa NEW!, WoRMS Polychaeta UPDATED!, WoRMS Polycystina UPDATED!, WoRMS Porifera UPDATED!, WoRMS Priapulida NEW!, WoRMS Proseriata and Kalyptorhynchia UPDATED!, WoRMS Remipedia UPDATED!, WoRMS Scaphopoda UPDATED!, WoRMS Tanaidacea UPDATED!, WoRMS Tantulocarida UPDATED!, WoRMS Thermosbaenacea UPDATED!, WoRMS Trematoda NEW!, WoRMS Xenoturbellida UPDATED! • Rotifers, mayflies, freshwater hairworms, planarians from FADA databases: FADA Rotifera UPDATED!, FADA Ephemeroptera NEW!, FADA Nematomorpha NEW! & FADA Turbellaria NEW! • Entoprocts, water bears from ITIS Global • Spiders, scorpions, ticks & mites from SpidCat via ITIS UPDATED!, SalticidDB , ITIS Global, TicksBase, SpmWeb BdelloideaBase UPDATED! & Mites GSDs: OlogamasidBase, PhytoseiidBase, RhodacaridBase & TenuipalpidBase • Diplopods, centipedes, pauropods and symphylans from SysMyr UPDATED! & ChiloBase • Dragonflies and damselflies from Odonata database • Stoneflies from PlecopteraSF UPDATED! • Cockroaches from BlattodeaSF UPDATED! • Praying mantids from MantodeaSF UPDATED! • Stick and leaf insects from PhasmidaSF UPDATED! • Grasshoppers, locusts, katydids and crickets from OrthopteraSF UPDATED! • Webspinners from EmbiopteraSF UPDATED! • Bark & parasitic lices from PsocodeaSF NEW! • Some groups of true bugs from ScaleNet, FLOW, COOL, Psyllist, AphidSF UPDATED! , MBB, 3i Cicadellinae, 3i Typhlocybinae, MOWD & CoreoideaSF NEW!• Twisted-wing parasites from Strepsiptera Database UPDATED! • Lacewings, antlions, owlflies, fishflies, dobsonflies & snakeflies from LDL Neuropterida • Some beetle groups from the Scarabs UPDATED!, TITAN, WTaxa & ITIS Global • Fleas from Parhost • Flies, mosquitoes, bots, midges and gnats from Systema Dipterorum, CCW & CIPA • Butterflies and moths from LepIndex UPDATED!, GloBIS (GART) UPDATED!, Tineidae NHM, World Gracillariidae • Bees & wasps from ITIS Bees, Taxapad Ichneumonoidea, UCD, ZOBODAT Vespoidea & HymIS Rhopalosomatidae NEW!• Molluscs from WoRMS Mollusca NEW!, FADA Bivalvia NEW!, MolluscaFW NEW! & AFD (Pulmonata) • Fishes from FishBase UPDATED! • Reptiles from TIGR Reptiles • Amphibians, birds and mammals from ITIS Global PLUS additional species of many groups from ITIS Regional, NZIB and CoL China NEW!

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.

Cadaver decomposition in terrestrial ecosystems

A dead mammal (i.e. cadaver) is a high quality resource (narrow carbon:nitrogen ratio, high water content) that releases an intense, localised pulse of carbon and nutrients into the soil upon decomposition. Despite the fact that as much as 5,000 kg of cadaver can be introduced to a square kilometre of terrestrial ecosystem each year, cadaver decomposition remains a neglected microsere. Here we review the processes associated with the introduction of cadaver-derived carbon and nutrients into soil from forensic and ecological settings to show that cadaver decomposition can have a greater, albeit localised, effect on belowground ecology than plant and faecal resources. Cadaveric materials are rapidly introduced to belowground floral and faunal communities, which results in the formation of a highly concentrated island of fertility, or cadaver decomposition island (CDI). CDIs are associated with increased soil microbial biomass, microbial activity (C mineralisation) and nematode abundance. Each CDI is an ephemeral natural disturbance that, in addition to releasing energy and nutrients to the wider ecosystem, acts as a hub by receiving these materials in the form of dead insects, exuvia and puparia, faecal matter (from scavengers, grazers and predators) and feathers (from avian scavengers and predators). As such, CDIs contribute to landscape heterogeneity. Furthermore, CDIs are a specialised habitat for a number of flies, beetles and pioneer vegetation, which enhances biodiversity in terrestrial ecosystems.

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.

Non-bee insects are important contributors to global crop pollination

Wild and managed bees are well documented as effective pollinators of global crops of economic importance. However, the contributions by pollinators other than bees have been little explored despite their potential to contribute to crop production and stability in the face of environmental change. Non-bee pollinators include flies, beetles, moths, butterflies, wasps, ants, birds, and bats, among others. Here we focus on non-bee insects and synthesize 39 field studies from five continents that directly measured the crop pollination services provided by non-bees, honey bees, and other bees to compare the relative contributions of these taxa. Non-bees performed 25–50% of the total number of flower visits. Although non-bees were less effective pollinators than bees per flower visit, they made more visits; thus these two factors compensated for each other, resulting in pollination services rendered by non-bees that were similar to those provided by bees. In the subset of studies that measured fruit set, fruit set increased with non-bee insect visits independently of bee visitation rates, indicating that non-bee insects provide a unique benefit that is not provided by bees. We also show that non-bee insects are not as reliant as bees on the presence of remnant natural or seminatural habitat in the surrounding landscape. These results strongly suggest that non-bee insect pollinators play a significant role in global crop production and respond differently than bees to landscape structure, probably making their crop pollination services more robust to changes in land use. Non-bee insects provide a valuable service and provide potential insurance against bee population declines.

Plastic and evolutionary responses to heat stress in a temperate dung fly: negative correlation between basal and induced heat tolerance?

Extreme weather events such as heat waves are becoming more frequent and intense. Populations can cope with elevated heat stress by evolving higher basal heat tolerance (evolutionary response) and/or stronger induced heat tolerance (plastic response). However, there is ongoing debate about whether basal and induced heat tolerance are negatively correlated and whether adaptive potential in heat tolerance is sufficient under ongoing climate warming. To evaluate the evolutionary potential of basal and induced heat tolerance, we performed experimental evolution on a temperate source 4 population of the dung fly Sepsis punctum. Offspring of flies adapted to three thermal selection regimes (Hot, Cold and Reference) were subjected to acute heat stress after having been exposed to either a hot-acclimation or non-acclimation pretreatment. As different traits may respond differently to temperature stress, several physiological and life history traits were assessed. Condition dependence of the response was evaluated by exposing juveniles to different levels of developmental (food restriction/rearing density) stress. Heat knockdown times were highest, whereas acclimation effects were lowest in the Hot selection regime, indicating a negative association between basal and induced heat tolerance. However, survival, adult longevity, fecundity and fertility did not show such a pattern. Acclimation had positive effects in heat-shocked flies, but in the absence of heat stress hot-acclimated flies had reduced life spans relative to nonacclimated ones, thereby revealing a potential cost of acclimation. Moreover, body size positively affected heat tolerance and unstressed individuals were less prone to heat stress than stressed flies, offering support for energetic costs associated with heat tolerance. Overall, our results indicate that heat tolerance of temperate insects can evolve under rising temperatures, but this response could be limited by a negative relationship between basal and induced thermotolerance, and may involve some but not other fitness-related traits.

Detection of Leishmania (Leishmania) infantum RNA in fleas and ticks collected from naturally infected dogs

The occurrence of the insect vector (sand flies) with low rates of Leishmania infection, as well as autochthonous transmission in the absence of the natural vector in dogs, have been reported. These unexpected data suggest a hypothesis of other arthropods as a possible way of Leishmania transmission. The prevalence of Leishmania (Leishmania) infantum in fleas and ticks collected from dogs with canine visceral leishmaniasis (CVL), as well as parasite viability, were evaluated herein. The presence of L. (L.) infantum was assayed by PCR and ELISA in ectoparasites and biological samples from 73 dogs living in a Brazilian endemic area. As the occurrence of Leishmania DNA in ticks and fleas is expected given their blood-feeding habits, we next investigated whether parasites can remain viable inside ticks. PCR and ELISA confirmed that 83% of the dogs had CVL. Fleas and ticks (nymphs, male and female adults) were collected in 55% and 63% of the 73 dogs, respectively. Out of the 60 dogs with CVL, 80% harbored ectoparasites infected with L. (L.) infantum. The infection rates of the ectoparasites were 23% and 50% for fleas and ticks, respectively. The RNA analysis of the extract from ticks left in laboratory conditions during 7 to 10 days after removal from CVL dogs showed that parasites were alive. In addition, live parasites were also detected inside adult ticks recently molted in laboratory conditions. These findings indicate a higher infection rate of L. (L.) infantum in ticks and fleas, but they do not conclusively demonstrate whether these ticks can act as vectors of CVL, despite the fact that their rates were higher than those previously described in Lutzomyia longipalpis. The presence of viable L. (L.) infantum in ticks suggests the possible importance of dog ectoparasites in CVL dissemination.

Bilateral anomaly in the style of Sciopemyia sordellii (Shannon & Del Ponte) (Diptera, Psychodidae)

This paper presents a male specimen of Sciopemyia sordellii with a rare bilateral anomaly, consisting in eight spines in a style and five in the other. This species has four spines in each style as its normal number. The specimen was captured using a CDC light trap, in a forested area in the State Park ""Floresta Estadual Edmundo Navarro de Andrade"", in May 2004, located in the city of Rio Claro, Sao Paulo State, Brazil. Similar anomaly was once described but this is the first specimen found with a bilateral alteration. It may cause confusion in taxonomic identification and even lead to description of new species, increasing the number of synonymies.