From a discrete to a continuum model of cell dynamics in one dimension

Multiscale modeling is emerging as one of the key challenges in mathematical biology. However, the recent rapid increase in the number of modeling methodologies being used to describe cell populations has raised a number of interesting questions. For example, at the cellular scale, how can the appropriate discrete cell-level model be identified in a given context? Additionally, how can the many phenomenological assumptions used in the derivation of models at the continuum scale be related to individual cell behavior? In order to begin to address such questions, we consider a discrete one-dimensional cell-based model in which cells are assumed to interact via linear springs. From the discrete equations of motion, the continuous Rouse [P. E. Rouse, J. Chem. Phys. 21, 1272 (1953)] model is obtained. This formalism readily allows the definition of a cell number density for which a nonlinear "fast" diffusion equation is derived. Excellent agreement is demonstrated between the continuum and discrete models. Subsequently, via the incorporation of cell division, we demonstrate that the derived nonlinear diffusion model is robust to the inclusion of more realistic biological detail. In the limit of stiff springs, where cells can be considered to be incompressible, we show that cell velocity can be directly related to cell production. This assumption is frequently made in the literature but our derivation places limits on its validity. Finally, the model is compared with a model of a similar form recently derived for a different discrete cell-based model and it is shown how the different diffusion coefficients can be understood in terms of the underlying assumptions about cell behavior in the respective discrete models.

Overview of mathematical approaches used to model bacterial chemotaxis I: the single cell

Mathematical modeling of bacterial chemotaxis systems has been influential and insightful in helping to understand experimental observations. We provide here a comprehensive overview of the range of mathematical approaches used for modeling, within a single bacterium, chemotactic processes caused by changes to external gradients in its environment. Specific areas of the bacterial system which have been studied and modeled are discussed in detail, including the modeling of adaptation in response to attractant gradients, the intracellular phosphorylation cascade, membrane receptor clustering, and spatial modeling of intracellular protein signal transduction. The importance of producing robust models that address adaptation, gain, and sensitivity are also discussed. This review highlights that while mathematical modeling has aided in understanding bacterial chemotaxis on the individual cell scale and guiding experimental design, no single model succeeds in robustly describing all of the basic elements of the cell. We conclude by discussing the importance of this and the future of modeling in this area.

Simulating the detailed chemical composition of secondary organic aerosol formed on a regional scale during the TORCH 2003 campaign in the southern UK

Following on from the companion study (Johnson et al., 2006), a photochemical trajectory model (PTM) has been used to simulate the chemical composition of organic aerosol for selected events during the 2003 TORCH (Tropospheric Organic Chemistry Experiment) field campaign. The PTM incorporates the speciated emissions of 124 nonmethane anthropogenic volatile organic compounds (VOC) and three representative biogenic VOC, a highly-detailed representation of the atmospheric degradation of these VOC, the emission of primary organic aerosol (POA) material and the formation of secondary organic aerosol (SOA) material. SOA formation was represented by the transfer of semi and non-volatile oxidation products from the gas-phase to a condensed organic aerosol-phase, according to estimated thermodynamic equilibrium phase-partitioning characteristics for around 2000 reaction products. After significantly scaling all phase-partitioning coefficients, and assuming a persistent background organic aerosol (both required in order to match the observed organic aerosol loadings), the detailed chemical composition of the simulated SOA has been investigated in terms of intermediate oxygenated species in the Master Chemical Mechanism, version 3.1 ( MCM v3.1). For the various case studies considered, 90% of the simulated SOA mass comprises between ca. 70 and 100 multifunctional oxygenated species derived, in varying amounts, from the photooxidation of VOC of anthropogenic and biogenic origin. The anthropogenic contribution is dominated by aromatic hydrocarbons and the biogenic contribution by alpha-and beta-pinene (which also constitute surrogates for other emitted monoterpene species). Sensitivity in the simulated mass of SOA to changes in the emission rates of anthropogenic and biogenic VOC has also been investigated for 11 case study events, and the results have been compared to the detailed chemical composition data. The role of accretion chemistry in SOA formation, and its implications for the results of the present investigation, is discussed.

Simulating regional scale secondary organic aerosol formation during the TORCH 2003 campaign in the southern UK

A photochemical trajectory model has been used to simulate the chemical evolution of air masses arriving at the TORCH field campaign site in the southern UK during late July and August 2003, a period which included a widespread and prolonged photochemical pollution episode. The model incorporates speciated emissions of 124 nonmethane anthropogenic VOC and three representative biogenic VOC, coupled with a comprehensive description of the chemistry of their degradation. A representation of the gas/aerosol absorptive partitioning of ca. 2000 oxygenated organic species generated in the Master Chemical Mechanism (MCM v3.1) has been implemented, allowing simulation of the contribution to organic aerosol (OA) made by semi- and non-volatile products of VOC oxidation; emissions of primary organic aerosol (POA) and elemental carbon (EC) are also represented. Simulations of total OA mass concentrations in nine case study events (optimised by comparison with observed hourly-mean mass loadings derived from aerosol mass spectrometry measurements) imply that the OA can be ascribed to three general sources: (i) POA emissions; (ii) a '' ubiquitous '' background concentration of 0.7 mu g m(-3); and (iii) gas-to-aerosol transfer of lower volatility products of VOC oxidation generated by the regional scale processing of emitted VOC, but with all partitioning coefficients increased by a species-independent factor of 500. The requirement to scale the partitioning coefficients, and the implied background concentration, are both indicative of the occurrence of chemical processes within the aerosol which allow the oxidised organic species to react by association and/or accretion reactions which generate even lower volatility products, leading to a persistent, non-volatile secondary organic aerosol (SOA). The contribution of secondary organic material to the simulated OA results in significant elevations in the simulated ratio of organic carbon (OC) to EC, compared with the ratio of 1.1 assigned to the emitted components. For the selected case study events, [OC]/[EC] is calculated to lie in the range 2.7-9.8, values which are comparable with the high end of the range reported in the literature.

State-space model identification of a wireless THz network

We model the large scale fading of wireless THz communications links deployed in a metropolitan area taking into account reception through direct line of sight, ground or wall reflection and diffraction. The movement of the receiver in the three dimensions is modelled by an autonomous dynamic linear system in state-space whereas the geometric relations involved in the attenuation and multi-path propagation of the electric field are described by a static non-linear mapping. A subspace algorithm in conjunction with polynomial regression is used to identify a Wiener model from time-domain measurements of the field intensity.

Robust background model for pixel based people counting using a single uncalibrated camera

Several pixel-based people counting methods have been developed over the years. Among these the product of scale-weighted pixel sums and a linear correlation coefficient is a popular people counting approach. However most approaches have paid little attention to resolving the true background and instead take all foreground pixels into account. With large crowds moving at varying speeds and with the presence of other moving objects such as vehicles this approach is prone to problems. In this paper we present a method which concentrates on determining the true-foreground, i.e. human-image pixels only. To do this we have proposed, implemented and comparatively evaluated a human detection layer to make people counting more robust in the presence of noise and lack of empty background sequences. We show the effect of combining human detection with a pixel-map based algorithm to i) count only human-classified pixels and ii) prevent foreground pixels belonging to humans from being absorbed into the background model. We evaluate the performance of this approach on the PETS 2009 dataset using various configurations of the proposed methods. Our evaluation demonstrates that the basic benchmark method we implemented can achieve an accuracy of up to 87% on sequence ¿S1.L1 13-57 View 001¿ and our proposed approach can achieve up to 82% on sequence ¿S1.L3 14-33 View 001¿ where the crowd stops and the benchmark accuracy falls to 64%.

Parallel implementation and one year experiments with the Danish Eulerian Model

Large scale air pollution models are powerful tools, designed to meet the increasing demand in different environmental studies. The atmosphere is the most dynamic component of the environment, where the pollutants can be moved quickly on far distnce. Therefore the air pollution modeling must be done in a large computational domain. Moreover, all relevant physical, chemical and photochemical processes must be taken into account. In such complex models operator splitting is very often applied in order to achieve sufficient accuracy as well as efficiency of the numerical solution. The Danish Eulerian Model (DEM) is one of the most advanced such models. Its space domain (4800 × 4800 km) covers Europe, most of the Mediterian and neighboring parts of Asia and the Atlantic Ocean. Efficient parallelization is crucial for the performance and practical capabilities of this huge computational model. Different splitting schemes, based on the main processes mentioned above, have been implemented and tested with respect to accuracy and performance in the new version of DEM. Some numerical results of these experiments are presented in this paper.

Evaluating the ability of a numerical weather prediction model to forecast tracer concentrations during ETEX 2

In this paper the meteorological processes responsible for transporting tracer during the second ETEX (European Tracer EXperiment) release are determined using the UK Met Office Unified Model (UM). The UM predicted distribution of tracer is also compared with observations from the ETEX campaign. The dominant meteorological process is a warm conveyor belt which transports large amounts of tracer away from the surface up to a height of 4 km over a 36 h period. Convection is also an important process, transporting tracer to heights of up to 8 km. Potential sources of error when using an operational numerical weather prediction model to forecast air quality are also investigated. These potential sources of error include model dynamics, model resolution and model physics. In the UM a semi-Lagrangian monotonic advection scheme is used with cubic polynomial interpolation. This can predict unrealistic negative values of tracer which are subsequently set to zero, and hence results in an overprediction of tracer concentrations. In order to conserve mass in the UM tracer simulations it was necessary to include a flux corrected transport method. Model resolution can also affect the accuracy of predicted tracer distributions. Low resolution simulations (50 km grid length) were unable to resolve a change in wind direction observed during ETEX 2, this led to an error in the transport direction and hence an error in tracer distribution. High resolution simulations (12 km grid length) captured the change in wind direction and hence produced a tracer distribution that compared better with the observations. The representation of convective mixing was found to have a large effect on the vertical transport of tracer. Turning off the convective mixing parameterisation in the UM significantly reduced the vertical transport of tracer. Finally, air quality forecasts were found to be sensitive to the timing of synoptic scale features. Errors in the position of the cold front relative to the tracer release location of only 1 h resulted in changes in the predicted tracer concentrations that were of the same order of magnitude as the absolute tracer concentrations.

Using Doppler radar with a simple explicit microphysics model to diagnose problems with ice sublimation depth-scales in forecast models

Several previous studies have attempted to assess the sublimation depth-scales of ice particles from clouds into clear air. Upon examining the sublimation depth-scales in the Met Office Unified Model (MetUM), it was found that the MetUM has evaporation depth-scales 2–3 times larger than radar observations. Similar results can be seen in the European Centre for Medium-Range Weather Forecasts (ECMWF), Regional Atmospheric Climate Model (RACMO) and Météo-France models. In this study, we use radar simulation (converting model variables into radar observations) and one-dimensional explicit microphysics numerical modelling to test and diagnose the cause of the deep sublimation depth-scales in the forecast model. The MetUM data and parametrization scheme are used to predict terminal velocity, which can be compared with the observed Doppler velocity. This can then be used to test the hypothesis as to why the sublimation depth-scale is too large within the MetUM. Turbulence could lead to dry air entrainment and higher evaporation rates; particle density may be wrong, particle capacitance may be too high and lead to incorrect evaporation rates or the humidity within the sublimating layer may be incorrectly represented. We show that the most likely cause of deep sublimation zones is an incorrect representation of model humidity in the layer. This is tested further by using a one-dimensional explicit microphysics model, which tests the sensitivity of ice sublimation to key atmospheric variables and is capable of including sonde and radar measurements to simulate real cases. Results suggest that the MetUM grid resolution at ice cloud altitudes is not sufficient enough to maintain the sharp drop in humidity that is observed in the sublimation zone.

Kinetic multi-layer model of aerosol surface and bulk chemistry (KM-SUB): the influence of interfacial transport and bulk diffusion on the oxidation of oleic acid by ozone

We present a novel kinetic multi-layer model that explicitly resolves mass transport and chemical reaction at the surface and in the bulk of aerosol particles (KM-SUB). The model is based on the PRA framework of gas-particle interactions (Poschl-Rudich-Ammann, 2007), and it includes reversible adsorption, surface reactions and surface-bulk exchange as well as bulk diffusion and reaction. Unlike earlier models, KM-SUB does not require simplifying assumptions about steady-state conditions and radial mixing. The temporal evolution and concentration profiles of volatile and non-volatile species at the gas-particle interface and in the particle bulk can be modeled along with surface concentrations and gas uptake coefficients. In this study we explore and exemplify the effects of bulk diffusion on the rate of reactive gas uptake for a simple reference system, the ozonolysis of oleic acid particles, in comparison to experimental data and earlier model studies. We demonstrate how KM-SUB can be used to interpret and analyze experimental data from laboratory studies, and how the results can be extrapolated to atmospheric conditions. In particular, we show how interfacial and bulk transport, i.e., surface accommodation, bulk accommodation and bulk diffusion, influence the kinetics of the chemical reaction. Sensitivity studies suggest that in fine air particulate matter oleic acid and compounds with similar reactivity against ozone (carbon-carbon double bonds) can reach chemical lifetimes of many hours only if they are embedded in a (semi-)solid matrix with very low diffusion coefficients (< 10(-10) cm(2) s(-1)). Depending on the complexity of the investigated system, unlimited numbers of volatile and non-volatile species and chemical reactions can be flexibly added and treated with KM-SUB. We propose and intend to pursue the application of KM-SUB as a basis for the development of a detailed master mechanism of aerosol chemistry as well as for the derivation of simplified but realistic parameterizations for large-scale atmospheric and climate models.

Kinetic multi-layer model of aerosol surface and bulk chemistry (KM-SUB): the influence of interfacial transport and bulk diffusion on the oxidation of oleic acid by ozone

We present a novel kinetic multi-layer model that explicitly resolves mass transport and chemical reaction at the surface and in the bulk of aerosol particles (KM-SUB). The model is based on the PRA framework of gas–particle interactions (P¨oschl et al., 5 2007), and it includes reversible adsorption, surface reactions and surface-bulk exchange as well as bulk diffusion and reaction. Unlike earlier models, KM-SUB does not require simplifying assumptions about steady-state conditions and radial mixing. The temporal evolution and concentration profiles of volatile and non-volatile species at the gas-particle interface and in the particle bulk can be modeled along with surface 10 concentrations and gas uptake coefficients. In this study we explore and exemplify the effects of bulk diffusion on the rate of reactive gas uptake for a simple reference system, the ozonolysis of oleic acid particles, in comparison to experimental data and earlier model studies. We demonstrate how KM-SUB can be used to interpret and analyze experimental data from laboratory stud15 ies, and how the results can be extrapolated to atmospheric conditions. In particular, we show how interfacial transport and bulk transport, i.e., surface accommodation, bulk accommodation and bulk diffusion, influence the kinetics of the chemical reaction. Sensitivity studies suggest that in fine air particulate matter oleic acid and compounds with similar reactivity against ozone (C=C double bonds) can reach chemical lifetimes of 20 multiple hours only if they are embedded in a (semi-)solid matrix with very low diffusion coefficients (10−10 cm2 s−1). Depending on the complexity of the investigated system, unlimited numbers of volatile and non-volatile species and chemical reactions can be flexibly added and treated with KM-SUB. We propose and intend to pursue the application of KM-SUB 25 as a basis for the development of a detailed master mechanism of aerosol chemistry as well as for the derivation of simplified but realistic parameterizations for large-scale atmospheric and climate models.

Assessment of a climate model to reproduce rainfall variability and extremes over Southern Africa

It is increasingly accepted that any possible climate change will not only have an influence on mean climate but may also significantly alter climatic variability. A change in the distribution and magnitude of extreme rainfall events (associated with changing variability), such as droughts or flooding, may have a far greater impact on human and natural systems than a changing mean. This issue is of particular importance for environmentally vulnerable regions such as southern Africa. The sub-continent is considered especially vulnerable to and ill-equipped (in terms of adaptation) for extreme events, due to a number of factors including extensive poverty, famine, disease and political instability. Rainfall variability and the identification of rainfall extremes is a function of scale, so high spatial and temporal resolution data are preferred to identify extreme events and accurately predict future variability. The majority of previous climate model verification studies have compared model output with observational data at monthly timescales. In this research, the assessment of ability of a state of the art climate model to simulate climate at daily timescales is carried out using satellite-derived rainfall data from the Microwave Infrared Rainfall Algorithm (MIRA). This dataset covers the period from 1993 to 2002 and the whole of southern Africa at a spatial resolution of 0.1° longitude/latitude. This paper concentrates primarily on the ability of the model to simulate the spatial and temporal patterns of present-day rainfall variability over southern Africa and is not intended to discuss possible future changes in climate as these have been documented elsewhere. Simulations of current climate from the UKMeteorological Office Hadley Centre’s climate model, in both regional and global mode, are firstly compared to the MIRA dataset at daily timescales. Secondly, the ability of the model to reproduce daily rainfall extremes is assessed, again by a comparison with extremes from the MIRA dataset. The results suggest that the model reproduces the number and spatial distribution of rainfall extremes with some accuracy, but that mean rainfall and rainfall variability is underestimated (over-estimated) over wet (dry) regions of southern Africa.

A comparison of extreme European daily precipitation simulated by a global and a regional climate model for present and future climates

The intensity and distribution of daily precipitation is predicted to change under scenarios of increased greenhouse gases (GHGs). In this paper, we analyse the ability of HadCM2, a general circulation model (GCM), and a high-resolution regional climate model (RCM), both developed at the Met Office's Hadley Centre, to simulate extreme daily precipitation by reference to observations. A detailed analysis of daily precipitation is made at two UK grid boxes, where probabilities of reaching daily thresholds in the GCM and RCM are compared with observations. We find that the RCM generally overpredicts probabilities of extreme daily precipitation but that, when the GCM and RCM simulated values are scaled to have the same mean as the observations, the RCM captures the upper-tail distribution more realistically. To compare regional changes in daily precipitation in the GHG-forced period 2080-2100 in the GCM and the RCM, we develop two methods. The first considers the fractional changes in probability of local daily precipitation reaching or exceeding a fixed 15 mm threshold in the anomaly climate compared with the control. The second method uses the upper one-percentile of the control at each point as the threshold. Agreement between the models is better in both seasons with the latter method, which we suggest may be more useful when considering larger scale spatial changes. On average, the probability of precipitation exceeding the 1% threshold increases by a factor of 2.5 (GCM and RCM) in winter and by I .7 (GCM) or 1.3 (RCM) in summer.

The impact of large scale atmospheric circulation patterns on wind power generation and its potential predictability: a case study over the UK

Over recent years there has been an increasing deployment of renewable energy generation technologies, particularly large-scale wind farms. As wind farm deployment increases, it is vital to gain a good understanding of how the energy produced is affected by climate variations, over a wide range of time-scales, from short (hours to weeks) to long (months to decades) periods. By relating wind speed at specific sites in the UK to a large-scale climate pattern (the North Atlantic Oscillation or "NAO"), the power generated by a modelled wind turbine under three different NAO states is calculated. It was found that the wind conditions under these NAO states may yield a difference in the mean wind power output of up to 10%. A simple model is used to demonstrate that forecasts of future NAO states can potentially be used to improve month-ahead statistical forecasts of monthly-mean wind power generation. The results confirm that the NAO has a significant impact on the hourly-, daily- and monthly-mean power output distributions from the turbine with important implications for (a) the use of meteorological data (e.g. their relationship to large scale climate patterns) in wind farm site assessment and, (b) the utilisation of seasonal-to-decadal climate forecasts to estimate future wind farm power output. This suggests that further research into the links between large-scale climate variability and wind power generation is both necessary and valuable.

Ensemble prediction for nowcasting with a convection-permitting model - II: forecast error statistics

A 24-member ensemble of 1-h high-resolution forecasts over the Southern United Kingdom is used to study short-range forecast error statistics. The initial conditions are found from perturbations from an ensemble transform Kalman filter. Forecasts from this system are assumed to lie within the bounds of forecast error of an operational forecast system. Although noisy, this system is capable of producing physically reasonable statistics which are analysed and compared to statistics implied from a variational assimilation system. The variances for temperature errors for instance show structures that reflect convective activity. Some variables, notably potential temperature and specific humidity perturbations, have autocorrelation functions that deviate from 3-D isotropy at the convective-scale (horizontal scales less than 10 km). Other variables, notably the velocity potential for horizontal divergence perturbations, maintain 3-D isotropy at all scales. Geostrophic and hydrostatic balances are studied by examining correlations between terms in the divergence and vertical momentum equations respectively. Both balances are found to decay as the horizontal scale decreases. It is estimated that geostrophic balance becomes less important at scales smaller than 75 km, and hydrostatic balance becomes less important at scales smaller than 35 km, although more work is required to validate these findings. The implications of these results for high-resolution data assimilation are discussed.