Small- and waiting-time behaviour of the thin-film-equation

We consider the small-time behavior of interfaces of zero contact angle solutions to the thin-film equation. For a certain class of initial data, through asymptotic analyses, we deduce a wide variety of behavior for the free boundary point. These are supported by extensive numerical simulations. © 2007 Society for Industrial and Applied Mathematics

Stratosphere-troposphere transport in a numerical simulation of midlatitude convection

The transport of stratospheric air deep into the troposphere via convection is investigated numerically using the UK Met Office Unified Model. A convective system that formed on 27 June 2004 near southeast England, in the vicinity an upper level potential vorticity anomaly and a lowered tropopause, provides the basis for analysis. Transport is diagnosed using a stratospheric tracer that can either be passed through or withheld from the model’s convective parameterization scheme. Three simulations are performed at increasingly finer resolutions, with horizontal grid lengths of 12, 4, and 1 km. In the 12 and 4 km simulations, tracer is transported deeply into the troposphere by the parameterized convection. In the 1 km simulation, for which the convective parameterization is disengaged, deep transport is still accomplished but with a much smaller magnitude. However, the 1 km simulation resolves stirring along the tropopause that does not exist in the coarser simulations. In all three simulations, the concentration of the deeply transported tracer is small, three orders of magnitude less than that of the shallow transport near the tropopause, most likely because of the efficient dilution of parcels in the lower troposphere.

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.

Can the dynamical impact of the stratosphere on the troposphere be described by large-scale adjustment to the stratospheric PV distribution?

Recent numerical experiments have demonstrated that the state of the stratosphere has a dynamical impact on the state of the troposphere. To account for such an effect, a number of mechanisms have been proposed in the literature, all of which amount to a large-scale adjustment of the troposphere to potential vorticity (PV) anomalies in the stratosphere. This paper analyses whether a simple PV adjustment suffices to explain the actual dynamical response of the troposphere to the state of the stratosphere, the actual response being determined by ensembles of numerical experiments run with an atmospheric general-circulation model. For this purpose, a new PV inverter is developed. It is shown that the simple PV adjustment hypothesis is inadequate. PV anomalies in the stratosphere induce, by inversion, flow anomalies in the troposphere that do not coincide spatially with the tropospheric changes determined by the numerical experiments. Moreover, the tropospheric anomalies induced by PV inversion are on a larger scale than the changes found in the numerical experiments, which are linked to the Atlantic and Pacific storm-tracks. These findings imply that the impact of the stratospheric state on the troposphere is manifested through the impact on individual synoptic-scale systems and their self-organization in the storm-tracks. Changes in these weather systems in the troposphere are not merely synoptic-scale noise on a larger scale tropospheric response, but an integral part of the mechanism by which the state of the stratosphere impacts that of the troposphere.

Climate entropy budget of the HadCM3 atmosphere-ocean general circulation model and of FAMOUS, its low resolution version

The entropy budget is calculated of the coupled atmosphere–ocean general circulation model HadCM3. Estimates of the different entropy sources and sinks of the climate system are obtained directly from the diabatic heating terms, and an approximate estimate of the planetary entropy production is also provided. The rate of material entropy production of the climate system is found to be ∼50 mW m−2 K−1, a value intermediate in the range 30–70 mW m−2 K−1 previously reported from different models. The largest part of this is due to sensible and latent heat transport (∼38 mW m−2 K−1). Another 13 mW m−2 K−1 is due to dissipation of kinetic energy in the atmosphere by friction and Reynolds stresses. Numerical entropy production in the atmosphere dynamical core is found to be about 0.7 mW m−2 K−1. The material entropy production within the ocean due to turbulent mixing is ∼1 mW m−2 K−1, a very small contribution to the material entropy production of the climate system. The rate of change of entropy of the model climate system is about 1 mW m−2 K−1 or less, which is comparable with the typical size of the fluctuations of the entropy sources due to interannual variability, and a more accurate closure of the budget than achieved by previous analyses. Results are similar for FAMOUS, which has a lower spatial resolution but similar formulation to HadCM3, while more substantial differences are found with respect to other models, suggesting that the formulation of the model has an important influence on the climate entropy budget. Since this is the first diagnosis of the entropy budget in a climate model of the type and complexity used for projection of twenty-first century climate change, it would be valuable if similar analyses were carried out for other such models.

How well do high resolution models reproduce tropical convection?

Cascade is a multi-institution project studying the temporal and spatial organization of tropical convective systems. While cloud resolving numerical models can reproduce the observed diurnal cycle of such systems they are sensitive to the chosen resolution. As part of this effort, we are comparing results from the Met. Office Unified Model to data from the Global Earth Radiation Budget satellite instrument over the African Monsoon Interdisciplinary Analyses region of North Africa. We use a variety of mathematical techniques to study the outgoing radiation and the evolution of properties such as the cloud size distribution. The effectiveness of various model resolutions is tested with a view to determining the optimum balance between resolution and the need to reproduce the observations.

Accumulated metal speciation in earthworm populations with multi-generational exposure to metalliferous soils: cell fractionation and high energy synchrotron analyses

Predicting metal bioaccumulation and toxicity in soil organisms is complicated by site-specific biotic and abiotic parameters. In this study we exploited tissue fractionation and digestion techniques, combined with X-ray absorption spectroscopy (XAS), to investigate the whole-body and subcellular distributions, ligand affinities, and coordination chemistry of accumulated Pb and Zn in field populations of the epigeic earthworm Lumbricus rubellus inhabiting three contrasting metalliferous and two unpolluted soils. Our main findings were (i) earthworms were resident in soils with concentrations of Pb and Zn ranging from 1200 to 27 000 mg kg(-1) and 200 to 34 000 mg kg(-1), respectively; (ii) Pb and Zn primarily accumulated in the posterior alimentary canal in nonsoluble subcellular fractions of earthworms; (iii) site-specific differences in the tissue and subcellular partitioning profiles of populations were observed, with earthworms from a calcareous site partitioning proportionally more Pb to their anterior body segments and Zn to the chloragosome-rich subcellular fraction than their acidic-soil inhabiting counterparts; (iv) XAS indicated that the interpopulation differences in metal partitioning between organs were not accompanied by qualitative differences in ligand-binding speciation, because crystalline phosphate-containing pyromorphite was a predominant chemical species in the whole-worm tissues of all mine soil residents. Differences in metal (Pb, Zn) partitioning at both organ and cellular levels displayed by field populations with protracted histories of metal exposures may reflect their innate ecophysiological responses to essential edaphic variables, such as Ca2+ status. These observations are highly significant in the challenging exercise of interpreting holistic biomarker data delivered by "omic" technologies.

Soil geochemical analyses as an indication of metal working at the excavation of a house in the Roman City at Silchester (UK)

Silchester is the site of a major late Iron Age and Roman town (Calleva Atrebatum), situated in northern Hampshire (England (UK)) and occupied between the late first century BC and the fifth or sixth century AD. Extensive evidence of the nature of the buildings and the plan of the town was obtained from excavations undertaken between 1890 and 1909. The purpose of this study was to use soil geochemical analyses to reinforce the archaeological evidence particularly with reference to potential metal working at the site. Soil analysis has been used previously to distinguish different functions or land use activity over a site and to aid identification and interpretation of settlement features (Entwistle et al., 2000). Samples were taken from two areas of the excavation on a 1-metre grid. Firstly from an area of some 500 square metres from contexts of late first/early second century AD date throughout the entirety of a large 'town house' (House 1) from which there was prima facie evidence of metalworking.