Consistent Dirichlet Boundary Conditions for Numerical Solution of Moving Boundary Problems

We consider the imposition of Dirichlet boundary conditions in the finite element modelling of moving boundary problems in one and two dimensions for which the total mass is prescribed. A modification of the standard linear finite element test space allows the boundary conditions to be imposed strongly whilst simultaneously conserving a discrete mass. The validity of the technique is assessed for a specific moving mesh finite element method, although the approach is more general. Numerical comparisons are carried out for mass-conserving solutions of the porous medium equation with Dirichlet boundary conditions and for a moving boundary problem with a source term and time-varying mass.

A comparison of stratosphere-troposphere transport in convection-permitting and convection-parameterizing simulations of three mesoscale convective systems

The transport of stratospheric air into the troposphere within deep convection was investigated using the Met Office Unified Model version 6.1. Three cases were simulated in which convective systems formed over the UK in the summer of 2005. For each of these three cases, simulations were performed on a grid having 4 km horizontal grid spacing in which the convection was parameterized and on a grid having 1 km horizontal grid spacing, which permitted explicit representation of the largest energy-containing scales of deep convection. Cross-tropopause transport was diagnosed using passive tracers that were initialized above the dynamically defined tropopause (2 potential vorticity unit surface) with a mixing ratio of 1. Although the synoptic-scale environment and triggering mechanisms varied between the cases, the total simulated transport was similar in all three cases. The total stratosphere-to-troposphere transport over the lifetime of the convective systems ranged from 25 to 100 kg/m2 across the simulated convective systems and resolutions, which corresponds to ∼5–20% of the total mass located within a stratospheric column extending 2 km above the tropopause. In all simulations, the transport into the lower troposphere (defined as below 3.5 km elevation) accounted for ∼1% of the total transport across the tropopause. In the 4 km runs most of the transport was due to parameterized convection, whereas in the 1 km runs the transport was due to explicitly resolved convection. The largest difference between the simulations with different resolutions occurred in the one case of midlevel convection considered, in which the total transport in the 1 km grid spacing simulation with explicit convection was 4 times that in the 4 km grid spacing simulation with parameterized convection. Although the total cross-tropopause transport was similar, stratospheric tracer was deposited more deeply to near-surface elevations in the convection-parameterizing simulations than in convection-permitting simulations.

The ecology of lizard reproductive output

Aim  We provide a new quantitative analysis of lizard reproductive ecology. Comparative studies of lizard reproduction to date have usually considered life-history components separately. Instead, we examine the rate of production (productivity hereafter) calculated as the total mass of offspring produced in a year. We test whether productivity is influenced by proxies of adult mortality rates such as insularity and fossorial habits, by measures of temperature such as environmental and body temperatures, mode of reproduction and activity times, and by environmental productivity and diet. We further examine whether low productivity is linked to high extinction risk. Location  World-wide. Methods  We assembled a database containing 551 lizard species, their phylogenetic relationships and multiple life history and ecological variables from the literature. We use phylogenetically informed statistical models to estimate the factors related to lizard productivity. Results  Some, but not all, predictions of metabolic and life-history theories are supported. When analysed separately, clutch size, relative clutch mass and brood frequency are poorly correlated with body mass, but their product – productivity – is well correlated with mass. The allometry of productivity scales similarly to metabolic rate, suggesting that a constant fraction of assimilated energy is allocated to production irrespective of body size. Island species were less productive than continental species. Mass-specific productivity was positively correlated with environmental temperature, but not with body temperature. Viviparous lizards were less productive than egg-laying species. Diet and primary productivity were not associated with productivity in any model. Other effects, including lower productivity of fossorial, nocturnal and active foraging species were confounded with phylogeny. Productivity was not lower in species at risk of extinction. Main conclusions  Our analyses show the value of focusing on the rate of annual biomass production (productivity), and generally supported associations between productivity and environmental temperature, factors that affect mortality and the number of broods a lizard can produce in a year, but not with measures of body temperature, environmental productivity or diet.

Effects of parylene-C photooxidation on serum-assisted glial and neuronal patterning

The increasing use of patterned neural networks in multielectrode arrays and similar devices drives the constant development and evaluation of new biomaterials. Recently, we presented a promising technique to guide neurons and glia reliably and effectively. Parylene-C, a common hydrophobic polymer, was photolithographically patterned on silicon oxide (SiO2) and subsequently activated via immersion in serum. In this article, we explore the effects of ultraviolet (UV)-induced oxidation on parylene's ability to pattern neurons and glia. We exposed parylene-C stripe patterns to increasing levels of UV radiation and found a dose-dependent reduction in the total mass of patterned cells, as well as a gradual loss of glial and neuronal conformity to the patterns. In contrast, nonirradiated patterns had superior patterning results and increased presence of cells. The reduced cell adhesion and patterning after the formation of aldehyde and carboxyl groups on UV-radiated parylene-C supports our hypothesis that cell adhesion and growth on parylene is facilitated by hydrophobic adsorption of serum proteins. We conclude that unlike other cell patterning schemes, our technique does not rely on photooxidation of the polymer. Nonetheless, the precise control of oxygenated groups on parylene could pave the way for the differential binding of proteins and other molecules on the surface, aiding in the adhesion of alternative cell types. © 2010 Wiley Periodicals, Inc. J Biomed Mater Res, 2010

A GCSS model intercomparison for a tropical squall line observed during toga-coare. II: Intercomparison of single-column models and a cloud-resolving model

This paper presents single-column model (SCM) simulations of a tropical squall-line case observed during the Coupled Ocean-Atmosphere Response Experiment of the Tropical Ocean/Global Atmosphere Programme. This case-study was part of an international model intercomparison project organized by Working Group 4 ‘Precipitating Convective Cloud Systems’ of the GEWEX (Global Energy and Water-cycle Experiment) Cloud System Study. Eight SCM groups using different deep-convection parametrizations participated in this project. The SCMs were forced by temperature and moisture tendencies that had been computed from a reference cloud-resolving model (CRM) simulation using open boundary conditions. The comparison of the SCM results with the reference CRM simulation provided insight into the ability of current convection and cloud schemes to represent organized convection. The CRM results enabled a detailed evaluation of the SCMs in terms of the thermodynamic structure and the convective mass flux of the system, the latter being closely related to the surface convective precipitation. It is shown that the SCMs could reproduce reasonably well the time evolution of the surface convective and stratiform precipitation, the convective mass flux, and the thermodynamic structure of the squall-line system. The thermodynamic structure simulated by the SCMs depended on how the models partitioned the precipitation between convective and stratiform. However, structural differences persisted in the thermodynamic profiles simulated by the SCMs and the CRM. These differences could be attributed to the fact that the total mass flux used to compute the SCM forcing differed from the convective mass flux. The SCMs could not adequately represent these organized mesoscale circulations and the microphysicallradiative forcing associated with the stratiform region. This issue is generally known as the ‘scale-interaction’ problem that can only be properly addressed in fully three-dimensional simulations. Sensitivity simulations run by several groups showed that the time evolution of the surface convective precipitation was considerably smoothed when the convective closure was based on convective available potential energy instead of moisture convergence. Finally, additional SCM simulations without using a convection parametrization indicated that the impact of a convection parametrization in forced SCM runs was more visible in the moisture profiles than in the temperature profiles because convective transport was particularly important in the moisture budget.

Horizontal and vertical structure of the Eyjafjallajökull ash cloud over the UK: a comparison of airborne lidar observations and simulations

During April and May 2010 the ash cloud from the eruption of the Icelandic volcano Eyjafjallajökull caused widespread disruption to aviation over northern Europe. The location and impact of the eruption led to a wealth of observations of the ash cloud were being obtained which can be used to assess modelling of the long range transport of ash in the troposphere. The UK FAAM (Facility for Airborne Atmospheric Measurements) BAe-146-301 research aircraft overflew the ash cloud on a number of days during May. The aircraft carries a downward looking lidar which detected the ash layer through the backscatter of the laser light. In this study ash concentrations derived from the lidar are compared with simulations of the ash cloud made with NAME (Numerical Atmospheric-dispersion Modelling Environment), a general purpose atmospheric transport and dispersion model. The simulated ash clouds are compared to the lidar data to determine how well NAME simulates the horizontal and vertical structure of the ash clouds. Comparison between the ash concentrations derived from the lidar and those from NAME is used to define the fraction of ash emitted in the eruption that is transported over long distances compared to the total emission of tephra. In making these comparisons possible position errors in the simulated ash clouds are identified and accounted for. The ash layers seen by the lidar considered in this study were thin, with typical depths of 550–750 m. The vertical structure of the ash cloud simulated by NAME was generally consistent with the observed ash layers, although the layers in the simulated ash clouds that are identified with observed ash layers are about twice the depth of the observed layers. The structure of the simulated ash clouds were sensitive to the profile of ash emissions that was assumed. In terms of horizontal and vertical structure the best results were obtained by assuming that the emission occurred at the top of the eruption plume, consistent with the observed structure of eruption plumes. However, early in the period when the intensity of the eruption was low, assuming that the emission of ash was uniform with height gives better guidance on the horizontal and vertical structure of the ash cloud. Comparison of the lidar concentrations with those from NAME show that 2–5% of the total mass erupted by the volcano remained in the ash cloud over the United Kingdom.