Nonlinear data assimilation in geosciences: an extremely efficient particle filter

Almost all research fields in geosciences use numerical models and observations and combine these using data-assimilation techniques. With ever-increasing resolution and complexity, the numerical models tend to be highly nonlinear and also observations become more complicated and their relation to the models more nonlinear. Standard data-assimilation techniques like (ensemble) Kalman filters and variational methods like 4D-Var rely on linearizations and are likely to fail in one way or another. Nonlinear data-assimilation techniques are available, but are only efficient for small-dimensional problems, hampered by the so-called ‘curse of dimensionality’. Here we present a fully nonlinear particle filter that can be applied to higher dimensional problems by exploiting the freedom of the proposal density inherent in particle filtering. The method is illustrated for the three-dimensional Lorenz model using three particles and the much more complex 40-dimensional Lorenz model using 20 particles. By also applying the method to the 1000-dimensional Lorenz model, again using only 20 particles, we demonstrate the strong scale-invariance of the method, leading to the optimistic conjecture that the method is applicable to realistic geophysical problems. Copyright c 2010 Royal Meteorological Society

State estimation using the particle filter with mode tracking

A particle filter is a data assimilation scheme that employs a fully nonlinear, non-Gaussian analysis step. Unfortunately as the size of the state grows the number of ensemble members required for the particle filter to converge to the true solution increases exponentially. To overcome this Vaswani [Vaswani N. 2008. IEEE Trans Signal Process 56:4583–97] proposed a new method known as mode tracking to improve the efficiency of the particle filter. When mode tracking, the state is split into two subspaces. One subspace is forecast using the particle filter, the other is treated so that its values are set equal to the mode of the marginal pdf. There are many ways to split the state. One hypothesis is that the best results should be obtained from the particle filter with mode tracking when we mode track the maximum number of unimodal dimensions. The aim of this paper is to test this hypothesis using the three dimensional stochastic Lorenz equations with direct observations. It is found that mode tracking the maximum number of unimodal dimensions does not always provide the best result. The best choice of states to mode track depends on the number of particles used and the accuracy and frequency of the observations.

Kinetic multi-layer model of gas-particle interactions in aerosols and clouds (KM-GAP): linking condensation, evaporation and chemical reactions of organics, oxidants and water

We present a novel kinetic multi-layer model for gas-particle interactions in aerosols and clouds (KM-GAP) that treats explicitly all steps of mass transport and chemical reaction of semi-volatile species partitioning between gas phase, particle surface and particle bulk. KM-GAP is based on the PRA model framework (Pöschl-Rudich-Ammann, 2007), and it includes gas phase diffusion, reversible adsorption, surface reactions, bulk diffusion and reaction, as well as condensation, evaporation and heat transfer. The size change of atmospheric particles and the temporal evolution and spatial profile of the concentration of individual chemical species can be modelled along with gas uptake and accommodation coefficients. Depending on the complexity of the investigated system, unlimited numbers of semi-volatile species, chemical reactions, and physical processes can be treated, and the model shall help to bridge gaps in the understanding and quantification of multiphase chemistry and microphysics in atmo- spheric aerosols and clouds. In this study we demonstrate how KM-GAP can be used to analyze, interpret and design experimental investigations of changes in particle size and chemical composition in response to condensation, evaporation, and chemical reaction. For the condensational growth of water droplets, our kinetic model results provide a direct link between laboratory observations and molecular dynamic simulations, confirming that the accommodation coefficient of water at 270 K is close to unity. Literature data on the evaporation of dioctyl phthalate as a function of particle size and time can be reproduced, and the model results suggest that changes in the experimental conditions like aerosol particle concentration and chamber geometry may influence the evaporation kinetics and can be optimized for eðcient probing of specific physical effects and parameters. With regard to oxidative aging of organic aerosol particles, we illustrate how the formation and evaporation of volatile reaction products like nonanal can cause a decrease in the size of oleic acid particles exposed to ozone.

Farmers’ willingness to pay for a tuberculosis cattle vaccine

We use contingent valuation (CV) and choice experiment (CE) methods to assess cattle farmers’ attitudes to and willingness to pay (WTP) for a bovine tuberculosis (bTB) cattle vaccine, to help inform vaccine development and policy. A survey questionnaire was administered by means of telephone interviews to a stratified sample of 300 cattle farmers in annually bTB-tested areas in England and Wales. Farmers felt that bTB was a major risk for the cattle industry and that there was a high risk of their cattle getting the disease. The CE estimate produced a mean WTP of £35 per animal per single dose for a vaccine that is 90% effective at reducing the risk of a bTB breakdown and an estimated £55 for such a vaccine backed by 100% insurance of loss if a breakdown should occur. The CV estimate produced a mean WTP of nearly £17 per dose/per animal/per year for a vaccine (including 100% insurance) which, given the average lifespan of cattle, is comparable to the CE estimate. These WTP estimates are substantially higher than the expected cost of a vaccine which suggests that farmers in high risk bTB ‘hotspot’ areas perceive a substantial net benefit from buying the vaccine.

The system identification and control of Hammerstein system using non-uniform rational B-spline neural network and particle swarm optimization

In this paper a new system identification algorithm is introduced for Hammerstein systems based on observational input/output data. The nonlinear static function in the Hammerstein system is modelled using a non-uniform rational B-spline (NURB) neural network. The proposed system identification algorithm for this NURB network based Hammerstein system consists of two successive stages. First the shaping parameters in NURB network are estimated using a particle swarm optimization (PSO) procedure. Then the remaining parameters are estimated by the method of the singular value decomposition (SVD). Numerical examples including a model based controller are utilized to demonstrate the efficacy of the proposed approach. The controller consists of computing the inverse of the nonlinear static function approximated by NURB network, followed by a linear pole assignment controller.

Kinetic multi-layer model of gas-particle interactions in aerosols and clouds (KM-GAP): linking condensation, evaporation and chemical reactions of organics, oxidants and water

We present a novel kinetic multi-layer model for gas-particle interactions in aerosols and clouds (KMGAP) that treats explicitly all steps of mass transport and chemical reaction of semi-volatile species partitioning between gas phase, particle surface and particle bulk. KMGAP is based on the PRA model framework (P¨oschl-Rudich- Ammann, 2007), and it includes gas phase diffusion, reversible adsorption, surface reactions, bulk diffusion and reaction, as well as condensation, evaporation and heat transfer. The size change of atmospheric particles and the temporal evolution and spatial profile of the concentration of individual chemical species can be modeled along with gas uptake and accommodation coefficients. Depending on the complexity of the investigated system and the computational constraints, unlimited numbers of semi-volatile species, chemical reactions, and physical processes can be treated, and the model shall help to bridge gaps in the understanding and quantification of multiphase chemistry and microphysics in atmospheric aerosols and clouds. In this study we demonstrate how KM-GAP can be used to analyze, interpret and design experimental investigations of changes in particle size and chemical composition in response to condensation, evaporation, and chemical reaction. For the condensational growth of water droplets, our kinetic model results provide a direct link between laboratory observations and molecular dynamic simulations, confirming that the accommodation coefficient of water at 270K is close to unity (Winkler et al., 2006). Literature data on the evaporation of dioctyl phthalate as a function of particle size and time can be reproduced, and the model results suggest that changes in the experimental conditions like aerosol particle concentration and chamber geometry may influence the evaporation kinetics and can be optimized for efficient probing of specific physical effects and parameters. With regard to oxidative aging of organic aerosol particles, we illustrate how the formation and evaporation of volatile reaction products like nonanal can cause a decrease in the size of oleic acid particles exposed to ozone.

Modulation of vaccine response by concomitant probiotic administration

Evidence suggests that probiotic bacteria modulate both innate and adaptive immunity in the host, and in some situations can result in reduced severity of common illnesses, such as acute rotavirus infection and respiratory infections. Responses to vaccination are increasingly being used to provide high quality information on the immunomodulatory effects of dietary components in humans. The present review focuses on the effect of probiotic administration upon vaccination response. The majority of studies investigating the impact of probiotics on responses to vaccination have been conducted in healthy adults, and at best they show modest effects of probiotics on serum or salivary IgA titres. Studies in infants and in elderly subjects are very limited, and it is too early to draw any firm conclusions regarding the potential for probiotics to act as adjuvants in vaccination. Although some studies are comparable in terms of duration of the intervention and age and characteristics of the subjects, most differ in terms of the probiotic selected. Further well designed, randomized, placebo-controlled studies are needed to fully understand the immunomodulatory properties of probiotics, whether the effects exerted are strain-dependent and age-dependent, and their clinical relevance in enhancing immune protection following vaccination.

Vaccine glycoproteins tagged with the human Fc domain as second generation vaccine candidates

Traditional vaccines such as inactivated or live attenuated vaccines, are gradually giving way to more biochemically defined vaccines that are most often based on a recombinant antigen known to possess neutralizing epitopes. Such vaccines can offer improvements in speed, safety and manufacturing process but an inevitable consequence of their high degree of purification is that immunogenicity is reduced through the lack of the innate triggering molecules present in more complex preparations. Targeting recombinant vaccines to antigen presenting cells (APCs) such as dendritic cells however can improve immunogenicity by ensuring that antigen processing is as efficient as possible. Immune complexes, one of a number of routes of APC targeting, are mimicked by a recombinant approach, crystallizable fragment (Fc) fusion proteins, in which the target immunogen is linked directly to an antibody effector domain capable of interaction with receptors, FcR, on the APC cell surface. A number of virus Fc fusion proteins have been expressed in insect cells using the baculovirus expression system and shown to be efficiently produced and purified. Their use for immunization next to non-Fc tagged equivalents shows that they are powerfully immunogenic in the absence of added adjuvant and that immune stimulation is the result of the Fc-FcR interaction.

A laboratory study of an inactivated bivalent iron restricted Salmonella enterica serovars Enteritidis and Typhimurium dual vaccine against Typhimurium challenge in chickens

A commercial inactivated iron restricted Salmonella Typhimurium and Salmonella Enterifidis vaccine was used to vaccinate chicks at I day and again at 4 weeks of age, with challenge by a high and a low dose of S. Typhimurium given either orally or by contact with seeder birds inoculated orally with a high dose of S. Typhimurium. In all three challenge regimes, the shedding of challenge strain was reduced significantly (p < 0.05) in vaccinated birds compared with unvaccinated controls. Vaccination reduced colonisation of internal organs after challenge by contact seeder birds. However, no effect of vaccination upon colonisation of internal organs after either high or low oral challenge was apparent. In conclusion, the data indicate that the vaccine should be a useful tool in the control of S. Typhimurium infection in chickens. (C) 2002 Elsevier Science B.V. All rights reserved.

The efficacy of Salenvac, a Salmonella enterica subsp. Enterica serotype Enteritidis iron-restricted bacterin vaccine, in laying chickens

The protective effect of two vaccination regimes using Salenvac, a commercially available iron-restricted Salmonella enterica subsp. Enterica serotype Enteritidis PT4 bacterin vaccine, was verified in laying birds. Immunization was intramuscular at 1 day old and again at 4 weeks of age (V2), or at 1 day and 4 weeks with a third dose at 18 weeks of age (V3). Challenge S. Enteritidis (5 to 7.5) x 10(7) colony forming units) was given intravenously at 8, 17, 23, 30 and 59 weeks of age. For all age groups, both vaccination regimes reduced significantly the number of tissues and faecal samples that were culture positive for the challenge strain. For laying birds, fewer eggs (P < 0.001) were culture positive for S. Enteritidis after challenge from vaccinated laying birds ( 56/439 batches of eggs) than unvaccinated birds (99/252 batches). The data give compelling evidence that the vaccine is efficacious and may contribute to the reduction of layer infection and egg contamination.

What have dendritic cells ever done for adjuvant design? Cellular and molecular methods for the rational development of vaccine adjuvants

Our new molecular understanding of immune priming states that dendritic cell activation is absolutely pivotal for expansion and differentiation of naïve T lymphocytes, and it follows that understanding DC activation is essential to understand and design vaccine adjuvants. This chapter describes how dendritic cells can be used as a core tool to provide detailed quantitative and predictive immunomics information about how adjuvants function. The role of distinct antigen, costimulation, and differentiation signals from activated DC in priming is explained. Four categories of input signals which control DC activation – direct pathogen detection, sensing of injury or cell death, indirect activation via endogenous proinflammatory mediators, and feedback from activated T cells – are compared and contrasted. Practical methods for studying adjuvants using DC are summarised and the importance of DC subset choice, simulating T cell feedback, and use of knockout cells is highlighted. Finally, five case studies are examined that illustrate the benefit of DC activation analysis for understanding vaccine adjuvant function.

Rational engineering of recombinant picornavirus capsids to produce safe, protective vaccine antigen

Foot-and-mouth disease remains a major plague of livestock and outbreaks are often economically catastrophic. Current inactivated virus vaccines require expensive high containment facilities for their production and maintenance of a cold-chain for their activity. We have addressed both of these major drawbacks. Firstly we have developed methods to efficiently express recombinant empty capsids. Expression constructs aimed at lowering the levels and activity of the viral protease required for the cleavage of the capsid protein precursor were used; this enabled the synthesis of empty A-serotype capsids in eukaryotic cells at levels potentially attractive to industry using both vaccinia virus and baculovirus driven expression. Secondly we have enhanced capsid stability by incorporating a rationally designed mutation, and shown by X-ray crystallography that stabilised and wild-type empty capsids have essentially the same structure as intact virus. Cattle vaccinated with recombinant capsids showed sustained virus neutralisation titres and protection from challenge 34 weeks after immunization. This approach to vaccine antigen production has several potential advantages over current technologies by reducing production costs, eliminating the risk of infectivity and enhancing the temperature stability of the product. Similar strategies that will optimize host cell viability during expression of a foreign toxic gene and/or improve capsid stability could allow the production of safe vaccines for other pathogenic picornaviruses of humans and animals.

Particle swarm optimisation assisted classification using elastic net prefiltering

A novel two-stage construction algorithm for linear-in-the-parameters classifier is proposed, aiming at noisy two-class classification problems. The purpose of the first stage is to produce a prefiltered signal that is used as the desired output for the second stage to construct a sparse linear-in-the-parameters classifier. For the first stage learning of generating the prefiltered signal, a two-level algorithm is introduced to maximise the model's generalisation capability, in which an elastic net model identification algorithm using singular value decomposition is employed at the lower level while the two regularisation parameters are selected by maximising the Bayesian evidence using a particle swarm optimization algorithm. Analysis is provided to demonstrate how “Occam's razor” is embodied in this approach. The second stage of sparse classifier construction is based on an orthogonal forward regression with the D-optimality algorithm. Extensive experimental results demonstrate that the proposed approach is effective and yields competitive results for noisy data sets.

Aircraft observations and model simulations of concentration and particle size distribution in the Eyjafjallajökull volcanic ash cloud

The Eyjafjallajökull volcano in Iceland emitted a cloud of ash into the atmosphere during April and May 2010. Over the UK the ash cloud was observed by the FAAM BAe-146 Atmospheric Research Aircraft which was equipped with in-situ probes measuring the concentration of volcanic ash carried by particles of varying sizes. The UK Met Office Numerical Atmospheric-dispersion Modelling Environment (NAME) has been used to simulate the evolution of the ash cloud emitted by the Eyjafjallajökull volcano during the period 4–18 May 2010. In the NAME simulations the processes controlling the evolution of the concentration and particle size distribution include sedimentation and deposition of particles, horizontal dispersion and vertical wind shear. For travel times between 24 and 72 h, a 1/t relationship describes the evolution of the concentration at the centre of the ash cloud and the particle size distribution remains fairly constant. Although NAME does not represent the effects of microphysical processes, it can capture the observed decrease in concentration with travel time in this period. This suggests that, for this eruption, microphysical processes play a small role in determining the evolution of the distal ash cloud. Quantitative comparison with observations shows that NAME can simulate the observed column-integrated mass if around 4% of the total emitted mass is assumed to be transported as far as the UK by small particles (< 30 μm diameter). NAME can also simulate the observed particle size distribution if a distal particle size distribution that contains a large fraction of < 10 μm diameter particles is used, consistent with the idea that phraetomagmatic volcanoes, such as Eyjafjallajökull, emit very fine particles.