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.

Sparse polynomial approximation in positive order Sobolev spaces with bounded mixed derivatives and applications to elliptic problems with random loading

In the present paper we study the approximation of functions with bounded mixed derivatives by sparse tensor product polynomials in positive order tensor product Sobolev spaces. We introduce a new sparse polynomial approximation operator which exhibits optimal convergence properties in L2 and tensorized View the MathML source simultaneously on a standard k-dimensional cube. In the special case k=2 the suggested approximation operator is also optimal in L2 and tensorized H1 (without essential boundary conditions). This allows to construct an optimal sparse p-version FEM with sparse piecewise continuous polynomial splines, reducing the number of unknowns from O(p2), needed for the full tensor product computation, to View the MathML source, required for the suggested sparse technique, preserving the same optimal convergence rate in terms of p. We apply this result to an elliptic differential equation and an elliptic integral equation with random loading and compute the covariances of the solutions with View the MathML source unknowns. Several numerical examples support the theoretical estimates.

Aerosol absorption over the clear-sky oceans deduced from POLDER-1 and AERONET observations

We estimate aerosol absorption over the clear-sky oceans using aerosol geophysical products from POLDER-1 space measurements and absorption properties from ground-based AERONET measurements. Our best estimate is 2.5 Wm-2 averaged over the 8-month lifetime of POLDER-1. Low and high absorption estimates are 2.2 and 3.1 Wm-2 based on the variability in aerosol single scattering albedo observed by AERONET. Main sources of uncertainties are the discrimation of the aerosol type from satellite measurements, and potential clear-sky bias induced by the cloud-screening procedure.

The integrated WRF/urban modelling system: development, evaluation, and applications to urban environmental problems

To bridge the gaps between traditional mesoscale modelling and microscale modelling, the National Center for Atmospheric Research, in collaboration with other agencies and research groups, has developed an integrated urban modelling system coupled to the weather research and forecasting (WRF) model as a community tool to address urban environmental issues. The core of this WRF/urban modelling system consists of the following: (1) three methods with different degrees of freedom to parameterize urban surface processes, ranging from a simple bulk parameterization to a sophisticated multi-layer urban canopy model with an indoor–outdoor exchange sub-model that directly interacts with the atmospheric boundary layer, (2) coupling to fine-scale computational fluid dynamic Reynolds-averaged Navier–Stokes and Large-Eddy simulation models for transport and dispersion (T&D) applications, (3) procedures to incorporate high-resolution urban land use, building morphology, and anthropogenic heating data using the National Urban Database and Access Portal Tool (NUDAPT), and (4) an urbanized high-resolution land data assimilation system. This paper provides an overview of this modelling system; addresses the daunting challenges of initializing the coupled WRF/urban model and of specifying the potentially vast number of parameters required to execute the WRF/urban model; explores the model sensitivity to these urban parameters; and evaluates the ability of WRF/urban to capture urban heat islands, complex boundary-layer structures aloft, and urban plume T&D for several major metropolitan regions. Recent applications of this modelling system illustrate its promising utility, as a regional climate-modelling tool, to investigate impacts of future urbanization on regional meteorological conditions and on air quality under future climate change scenarios. Copyright © 2010 Royal Meteorological Society

Problems with binary pattern measures for flood model evaluation

As the calibration and evaluation of flood inundation models are a prerequisite for their successful application, there is a clear need to ensure that the performance measures that quantify how well models match the available observations are fit for purpose. This paper evaluates the binary pattern performance measures that are frequently used to compare flood inundation models with observations of flood extent. This evaluation considers whether these measures are able to calibrate and evaluate model predictions in a credible and consistent way, i.e. identifying the underlying model behaviour for a number of different purposes such as comparing models of floods of different magnitudes or on different catchments. Through theoretical examples, it is shown that the binary pattern measures are not consistent for floods of different sizes, such that for the same vertical error in water level, a model of a flood of large magnitude appears to perform better than a model of a smaller magnitude flood. Further, the commonly used Critical Success Index (usually referred to as F<2 >) is biased in favour of overprediction of the flood extent, and is also biased towards correctly predicting areas of the domain with smaller topographic gradients. Consequently, it is recommended that future studies consider carefully the implications of reporting conclusions using these performance measures. Additionally, future research should consider whether a more robust and consistent analysis could be achieved by using elevation comparison methods instead.

PDFOS: PDF estimation based over-sampling for imbalanced two-class problems

This contribution proposes a novel probability density function (PDF) estimation based over-sampling (PDFOS) approach for two-class imbalanced classification problems. The classical Parzen-window kernel function is adopted to estimate the PDF of the positive class. Then according to the estimated PDF, synthetic instances are generated as the additional training data. The essential concept is to re-balance the class distribution of the original imbalanced data set under the principle that synthetic data sample follows the same statistical properties. Based on the over-sampled training data, the radial basis function (RBF) classifier is constructed by applying the orthogonal forward selection procedure, in which the classifier’s structure and the parameters of RBF kernels are determined using a particle swarm optimisation algorithm based on the criterion of minimising the leave-one-out misclassification rate. The effectiveness of the proposed PDFOS approach is demonstrated by the empirical study on several imbalanced data sets.

The effect of chosen extraterrestrial solar spectrum on clear-sky atmospheric absorption and heating rates in the near infrared

The extraterrestrial solar spectrum (ESS) is an important component in near infrared (near-IR) radiative transfer calculations. However, the impact of a particular choice of the ESS in these regions has been given very little attention. A line-by-line (LBL) transfer model has been used to calculate the absorbed solar irradiance and solar heating rates in the near-IR from 2000-10000 cm−1(1-5 μm) using different ESS. For overhead sun conditions in a mid-latitude summer atmosphere, the absorbed irradiances could differ by up to about 11 Wm−2 (8.2%) while the tropospheric and stratospheric heating rates could differ by up to about 0.13 K day−1 (8.1%) and 0.19 K day−1 (7.6%). The spectral shape of the ESS also has a small but non-negligible impact on these factors in the near-IR.

Infrared absorption spectra, radiative efficiencies, and global warming potentials of newly-detected halogenated compounds: CFC-113a, CFC-112 and HCFC-133a

CFC-113a (CF3CCl3), CFC-112 (CFCl2CFCl2) and HCFC-133a (CF3CH2Cl) are three newly detected molecules in the atmosphere that are almost certainly emitted as a result of human activity. It is important to characterise the possible contribution of these gases to radiative forcing of climate change and also to provide information on the CO2-equivalence of their emissions. We report new laboratory measurements of absorption cross-sections of these three compounds at a resolution of 0.01 cm−1 for two temperatures 250 K and 295 K in the spectral range of 600–1730 cm−1. These spectra are then used to calculate the radiative efficiencies and global warming potentials (GWP). The radiative efficiencies are found to be between 0.15 and 0.3 W∙m−2∙ppbv−1. The GWP for a 100 year time horizon, relative to carbon dioxide, ranges from 340 for the relatively short-lived HCFC-133a to 3840 for the longer-lived CFC-112. At current (2012) concentrations, these gases make a trivial contribution to total radiative forcing; however, the concentrations of CFC-113a and HCFC-133a are continuing to increase. The 2012 CO2-equivalent emissions, using the GWP (100), are estimated to be about 4% of the current global CO2-equivalent emissions of HFC-134a

Emotional and behavioural problems in children with language impairments and children with autism spectrum disorders

Background: Although it is well-established that children with language impairment (LI) and children with autism spectrum disorders (ASD) both show elevated levels of emotional and behavioural problems, the level and types of difficulties across the two groups have not previously been directly compared. Aims: To compare levels of emotional and behavioural problems in children with LI and children with ASD recruited from the same mainstream schools. Methods & Procedures: We measured teacher-reported emotional and behavioural problems using the Strengths and Difficulties Questionnaire (SDQ) in a sample of 5-to-13-year old children with LI (N=62) and children with ASD (N=42) attending mainstream school but with identified special educational needs. Outcomes & Results: Both groups showed similarly elevated levels of emotional, conduct and hyperactivity problems. The only differences between the LI and ASD groups were on subscales assessing peer problems (which were higher in the ASD group) and prosocial behaviours (which were higher in the LI group). Overall, there were few associations between emotional and behavioural problems and child characteristics, reflecting the pervasive nature of these difficulties in children with LI and children with ASD, although levels of problems were higher in children with ASD with lower language ability. However, in the ASD group only, a measure of family social economic status was associated with language ability and attenuated the association between language ability and emotional and behavioural problems. Conclusions & Implications: Children with LI and children with ASD in mainstream school show similarly elevated levels of emotional and behavioural problems, which require monitoring and may benefit from intervention. Further work is required to identify the child, family and situational factors that place children with LI and children with ASD at risk of emotional and behavioural problems, and whether these differ between the two groups. This work can then guide the application of evidence-based interventions to these children.

Drug permeability in 16HBE14o- airway cell layers correlates with absorption from the isolated perfused rat lung

The permeability of the lung is critical in determining the disposition of inhaled drugs and the respiratory epithelium provides the main physical barrier to drug absorption. The 16HBE14o- human bronchial epithelial cell line has been developed recently as a model of the airway epithelium. In this study, the transport of 10 low molecular weight compounds was measured in the 16HBE14o- cell layers, with apical to basolateral (absorptive) apparent permeability coefficients (P(app)) ranging from 0.4 x 10(-6)cms(-1) for Tyr-D-Arg-Phe-Phe-NH(2) to 25.2x10(-6)cms(-1) for metoprolol. Permeability in 16HBE14o- cells was found to correlate with previously reported P(app) in Caco-2 cells and absorption rates in the isolated perfused rat lung (k(a,lung)) and the rat lung in vivo (k(a,in vivo)). Log linear relationships were established between P(app) in 16HBE14o- cells and P(app) in Caco-2 cells (r(2)=0.82), k(a,lung) (r(2)=0.78) and k(a,in vivo) (r(2)=0.68). The findings suggest that permeability in 16HBE14o- cells may be useful to predict the permeability of compounds in the lung, although no advantage of using the organ-specific cell line 16HBE14o- compared to Caco-2 cells was found in this study.