A cell by cell anisotropic adaptive mesh ALE scheme for the numerical solution of the Euler equations

In this paper a cell by cell anisotropic adaptive mesh technique is added to an existing staggered mesh Lagrange plus remap finite element ALE code for the solution of the Euler equations. The quadrilateral finite elements may be subdivided isotropically or anisotropically and a hierarchical data structure is employed. An efficient computational method is proposed, which only solves on the finest level of resolution that exists for each part of the domain with disjoint or hanging nodes being used at resolution transitions. The Lagrangian, equipotential mesh relaxation and advection (solution remapping) steps are generalised so that they may be applied on the dynamic mesh. It is shown that for a radial Sod problem and a two-dimensional Riemann problem the anisotropic adaptive mesh method runs over eight times faster.

The influence of viscous and latent heating on crystal-rich magma flow in a conduit

The flow dynamics of crystal-rich high-viscosity magma is likely to be strongly influenced by viscous and latent heat release. Viscous heating is observed to play an important role in the dynamics of fluids with temperature-dependent viscosities. The growth of microlite crystals and the accompanying release of latent heat should play a similar role in raising fluid temperatures. Earlier models of viscous heating in magmas have shown the potential for unstable (thermal runaway) flow as described by a Gruntfest number, using an Arrhenius temperature dependence for the viscosity, but have not considered crystal growth or latent heating. We present a theoretical model for magma flow in an axisymmetric conduit and consider both heating effects using Finite Element Method techniques. We consider a constant mass flux in a 1-D infinitesimal conduit segment with isothermal and adiabatic boundary conditions and Newtonian and non-Newtonian magma flow properties. We find that the growth of crystals acts to stabilize the flow field and make the magma less likely to experience a thermal runaway. The additional heating influences crystal growth and can counteract supercooling from degassing-induced crystallization and drive the residual melt composition back towards the liquidus temperature. We illustrate the models with results generated using parameters appropriate for the andesite lava dome-forming eruption at Soufriere Hills Volcano, Montserrat. These results emphasize the radial variability of the magma. Both viscous and latent heating effects are shown to be capable of playing a significant role in the eruption dynamics of Soufriere Hills Volcano. Latent heating is a factor in the top two kilometres of the conduit and may be responsible for relatively short-term (days) transients. Viscous heating is less restricted spatially, but because thermal runaway requires periods of hundreds of days to be achieved, the process is likely to be interrupted. Our models show that thermal evolution of the conduit walls could lead to an increase in the effective diameter of flow and an increase in flux at constant magma pressure.

A collocation method for high frequency scattering by convex polygons

We consider the problem of scattering of a time-harmonic acoustic incident plane wave by a sound soft convex polygon. For standard boundary or finite element methods, with a piecewise polynomial approximation space, the computational cost required to achieve a prescribed level of accuracy grows linearly with respect to the frequency of the incident wave. Recently Chandler–Wilde and Langdon proposed a novel Galerkin boundary element method for this problem for which, by incorporating the products of plane wave basis functions with piecewise polynomials supported on a graded mesh into the approximation space, they were able to demonstrate that the number of degrees of freedom required to achieve a prescribed level of accuracy grows only logarithmically with respect to the frequency. Here we propose a related collocation method, using the same approximation space, for which we demonstrate via numerical experiments a convergence rate identical to that achieved with the Galerkin scheme, but with a substantially reduced computational cost.

A high-order arbitrarily unstructured finite-volume model of the global atmosphere: tests solving the shallow-water equations

Simulations of the global atmosphere for weather and climate forecasting require fast and accurate solutions and so operational models use high-order finite differences on regular structured grids. This precludes the use of local refinement; techniques allowing local refinement are either expensive (eg. high-order finite element techniques) or have reduced accuracy at changes in resolution (eg. unstructured finite-volume with linear differencing). We present solutions of the shallow-water equations for westerly flow over a mid-latitude mountain from a finite-volume model written using OpenFOAM. A second/third-order accurate differencing scheme is applied on arbitrarily unstructured meshes made up of various shapes and refinement patterns. The results are as accurate as equivalent resolution spectral methods. Using lower order differencing reduces accuracy at a refinement pattern which allows errors from refinement of the mountain to accumulate and reduces the global accuracy over a 15 day simulation. We have therefore introduced a scheme which fits a 2D cubic polynomial approximately on a stencil around each cell. Using this scheme means that refinement of the mountain improves the accuracy after a 15 day simulation. This is a more severe test of local mesh refinement for global simulations than has been presented but a realistic test if these techniques are to be used operationally. These efficient, high-order schemes may make it possible for local mesh refinement to be used by weather and climate forecast models.

A combined BIE-FE method for the Stokes equations

A numerical algorithm for the biharmonic equation in domains with piecewise smooth boundaries is presented. It is intended for problems describing the Stokes flow in the situations where one has corners or cusps formed by parts of the domain boundary and, due to the nature of the boundary conditions on these parts of the boundary, these regions have a global effect on the shape of the whole domain and hence have to be resolved with sufficient accuracy. The algorithm combines the boundary integral equation method for the main part of the flow domain and the finite-element method which is used to resolve the corner/cusp regions. Two parts of the solution are matched along a numerical ‘internal interface’ or, as a variant, two interfaces, and they are determined simultaneously by inverting a combined matrix in the course of iterations. The algorithm is illustrated by considering the flow configuration of ‘curtain coating’, a flow where a sheet of liquid impinges onto a moving solid substrate, which is particularly sensitive to what happens in the corner region formed, physically, by the free surface and the solid boundary. The ‘moving contact line problem’ is addressed in the framework of an earlier developed interface formation model which treats the dynamic contact angle as part of the solution, as opposed to it being a prescribed function of the contact line speed, as in the so-called ‘slip models’. Keywords: Dynamic contact angle; finite elements; free surface flows; hybrid numerical technique; Stokes equations.

Impact of mass lumping on gravity and Rossby waves in 2D finite-element shallow-water models

The goal of this study is to evaluate the effect of mass lumping on the dispersion properties of four finite-element velocity/surface-elevation pairs that are used to approximate the linear shallow-water equations. For each pair, the dispersion relation, obtained using the mass lumping technique, is computed and analysed for both gravity and Rossby waves. The dispersion relations are compared with those obtained for the consistent schemes (without lumping) and the continuous case. The P0-P1, RT0 and P-P1 pairs are shown to preserve good dispersive properties when the mass matrix is lumped. Test problems to simulate fast gravity and slow Rossby waves are in good agreement with the analytical results.

A review of the theoretical basis for bulk mass flux convective parameterization

Most parameterizations for precipitating convection in use today are bulk schemes, in which an ensemble of cumulus elements with different properties is modelled as a single, representative entraining-detraining plume. We review the underpinning mathematical model for such parameterizations, in particular by comparing it with spectral models in which elements are not combined into the representative plume. The chief merit of a bulk model is that the representative plume can be described by an equation set with the same structure as that which describes each element in a spectral model. The equivalence relies on an ansatz for detrained condensate introduced by Yanai et al. (1973) and on a simplified microphysics. There are also conceptual differences in the closure of bulk and spectral parameterizations. In particular, we show that the convective quasi-equilibrium closure of Arakawa and Schubert (1974) for spectral parameterizations cannot be carried over to a bulk parameterization in a straightforward way. Quasi-equilibrium of the cloud work function assumes a timescale separation between a slow forcing process and a rapid convective response. But, for the natural bulk analogue to the cloud-work function (the dilute CAPE), the relevant forcing is characterised by a different timescale, and so its quasi-equilibrium entails a different physical constraint. Closures of bulk parameterization that use the non-entraining parcel value of CAPE do not suffer from this timescale issue. However, the Yanai et al. (1973) ansatz must be invoked as a necessary ingredient of those closures.

A simple model of convection with memory

There are at least three distinct time scales that are relevant for the evolution of atmospheric convection. These are the time scale of the forcing mechanism, the time scale governing the response to a steady forcing, and the time scale of the response to variations in the forcing. The last of these, tmem, is associated with convective life cycles, which provide an element of memory in the system. A highly simplified model of convection is introduced, which allows for investigation of the character of convection as a function of the three time scales. For short tmem, the convective response is strongly tied to the forcing as in conventional equilibrium parameterization. For long tmem, the convection responds only to the slowly evolving component of forcing, and any fluctuations in the forcing are essentially suppressed. At intermediate tmem, convection becomes less predictable: conventional equilibrium closure breaks down and current levels of convection modify the subsequent response.

Biological and chemical assessment of zinc ageing in field soils

As zinc (Zn) is both an essential trace element and potential toxicant, the effects of Zn fixation in soil are of practical significance. Soil samples from four field sites amended with ZnSO4 were used to investigate ageing of soluble Zn under field conditions over a 2-year period. Lability of Zn measured using 65Zn radioisotope dilution showed a significant decrease over time and hence evidence of Zn fixation in three of the four soils. However, 0.01 M CaCl2 extractions and toxicity measurements using a genetically modified lux-marked bacterial biosensor did not indicate a decrease in soluble/bioavailable Zn over time. This was attributed to the strong regulatory effect of abiotic properties such as pH on these latter measurements. These results also showed that Zn ageing occurred immediately after Zn spiking, emphasising the need to incubate freshly spiked soils before ecotoxicity assessments. Ageing effects were detected in Zn-amended field soils using 65Zn isotopic dilution as a measure of lability, but not with either CaCl2 extractions or a lux-marked bacterial biosensor.

The GlobMODEL demonstrator: assimilation of new satellite products in an operational meteorological center

As part of its Data User Element programme, the European Space Agency funded the GlobMODEL project which aimed at investigating the scientific, technical, and organizational issues associated with the use and exploitation of remotely-sensed observations, particularly from new sounders. A pilot study was performed as a "demonstrator" of the GlobMODEL idea, based on the use of new data, with a strong European heritage, not yet assimilated operationally. Two parallel assimilation experiments were performed, using either total column ozone or ozone profiles retrieved at the Royal Netherlands Meteorological Institute (KNMI) from the Ozone Monitoring Instrument (OMI). In both cases, the impact of assimilating OMI data in addition to the total ozone columns from the SCanning Imaging Absorption spectroMeter for Atmospheric CartograpHY (SCIAMACHY) on the European Centre for Medium Range Weather Forecasts (ECMWF) ozone analyses was assessed by means of independent measurements. We found that the impact of OMI total columns is mainly limited to the region between 20 and 80 hPa, and is particularly important at high latitudes in the Southern hemisphere where the stratospheric ozone transport and chemical depletion are generally difficult to model with accuracy. Furthermore, the assimilation experiments carried out in this work suggest that OMI DOAS (Differential Optical Absorption Spectroscopy) total ozone columns are on average larger than SCIAMACHY total columns by up to 3 DU, while OMI total columns derived from OMI ozone profiles are on average about 8 DU larger than SCIAMACHY total columns. At the same time, the demonstrator brought to light a number of issues related to the assimilation of atmospheric composition profiles, such as the shortcomings arising when the vertical resolution of the instrument is not properly accounted for in the assimilation. The GlobMODEL demonstrator accelerated scientific and operational utilization of new observations and its results - prompted ECMWF to start the operational assimilation of OMI total column ozone data.

Annual textural banding in Holocene estuarine silts, Severn Estuary Levels (SW Britain): patterns, cause and implications

A high-resolution textural study has been made of laminated and banded estuarine silts exposed intertidally at representative localities and horizons in the Holocene deposits of the Severn Estuary Levels. The laminae, on a submillimetre to millimetre scale, are sharp-based, graded couplets formed of a lower silty part overlain by a finer-textured clayey element. The centimetre- to decimetre-scale banding is formed of laminae in alternating, gradually intergrading sets of relatively coarse and relative fine-grained examples. At outcrop in the field, the banding is recognizable because the coarse sets prove to be recessive to varying degrees under the influence of weathering and current action. Independent evidence at two localities points toward an annual origin for the banding; at a third it arose during part of what appears to have been a relatively short period. Quantified physical arguments suggest that the textural banding is a response of suspended fine sediment to marked seasonal changes in sea temperature and windiness. The banded silts occur in four distinct stratigraphical contexts and record high deposition rates (order 0.01-0.1 m/yr). Because physical factors determine their textures, the silts potentially afford insights in all contexts into aspects of changing Holocene climatic conditions. In one context, the thickness of the bands points to high (order 0.01-0.1 m/yr) but comparatively short-lived (order 10s-100s yrs) rates of relative water-level rise. In the others, however, the banding has no implications for sea-level behaviour, and simply records gross environmental disequilibrium, for example, the recovery of mudflats/marshes after an erosional episode. Similarly, because on account of their rapid accumulation the banded silts preserve animal and human tracks and trackways especially well, they provide an archive of animal and human behaviour in the area during the Holocene.

The ship as symbol in the prehistory of Scandinavia and south-east Asia

The ship is the dominant element in the visual culture of the South Scandinavian Bronze Age, appearing in several different media, including rock carvings, decorated metalwork and above-ground monuments. Discussion has divided between those scholars who interpret this imagery in terms of long-distance exchange networks and those who emphasize its more local significance, including its deployment in mortuary ritual. A strikingly similar system is identified in Southeast Asia and part of Melanesia and can be interpreted through archaeological and ethnographic sources, but in this case there is no need to distinguish between 'practical' and 'symbolic' interpretations of the depictions of ships. This paper summarizes the evidence from this region and suggests that it can offer a fruitful source of comparison for archaeologists working in northern Europe.

Geochemical precursors to volcanic activity at Mount St. Helens, USA

The importance of the interplay between degassing and crystallization before and after the eruption of Mount St. Helens (Washington, USA) in 1980 is well established. Here, we show that degassing occurred over a period of decades to days before eruptions and that the manner of degassing, as deduced from geochemicai signatures within the magma, was characteristic of the eruptive style. Trace element (lithium) and short-lived radioactive isotope (lead-210 and radium-226) data show that ascending magma stalled within the conduit, leading to the accumulation of volatiles and the formation of lead-210 excesses, which signals the presence of degassing magma at depth.

Trace element partitioning and soil particle characterisation around mining and smelting areas at Tharsis, Riotinto and Huelva, SW Spain

Trace elements may present an environmental hazard in the vicinity of mining and smelting activities. However, the factors controlling trace element distribution in soils around ancient and modem mining and smelting areas are not always clear. Tharsis, Riotinto and Huelva are located in the Iberian Pyrite Belt in SW Spain. Tharsis and Riotinto mines have been exploited since 2500 B.C., with intensive smelting taking place. Huelva, established in 1970 and using the Flash Furnace Outokumpu process, is currently one of the largest smelter in the world. Pyrite and chalcopyrite ore have been intensively smelted for Cu. However, unusually for smelters and mines of a similar size, the elevated trace element concentrations in soils were found to be restricted to the immediate vicinity of the mines and smelters, being found up to a maximum of 2 kin from the mines and smelters at Tharsis, Riotinto and Huelva. Trace element partitioning (over 2/3 of trace elements found in the residual immobile fraction of soils at Tharsis) and soil particles examination by SEM-EDX showed that trace elements were not adsorbed onto soil particles, but were included within the matrix of large trace element-rich Fe silicate slag particles (i.e. 1 min circle divide at least 1 wt.% As, Cu and Zn, and 2 wt.% Pb). Slag particle large size (I mm 0) was found to control the geographically restricted trace element distribution in soils at Tharsis, Riotinto and Huelva, since large heavy particles could not have been transported long distances. Distribution and partitioning indicated that impacts to the environment as a result of mining and smelting should remain minimal in the region. (c) 2006 Elsevier B.V. All rights reserved.

Land degradation and vegetation distribution in Chott El Beida wetland, Algeria

The aim of this study is to explore the environmental factors that determine plant Community distribution in northeast Algeria. This paper provides a quantitative analysis of the vegetation-environment relationships for a study site in the Cholt El Beida wetland, a RAMSAR site in Setif, Algeria. Sixty vegetation plots were sampled and analysed using TWINSPAN and Detrended Correspondence Analysis (DCA) in order to identify the principal vegetation communities and determine the environmental gradients associated with these. 127 species belonging to 41 families and 114 genera were recorded. Six of the recorded species were endemic representing 4.7% of the total species. The richest families were Compositae, Gramineae, Cruciferae and Chenopodiaceae. Therophytes and hemicryptophytes were the most frequent life forms. the Mediterranean floristic element is dominant and is represented by 39 species. The samples were classified into four main community types. The principal DCA axes represent gradients of soil salinity, moisture and anthropogenic pressure. The use of classification in combination with ordination techniques resulted in a good discrimination between plant communities and a greater understanding of controlling environmental factors. The methodology adopted can be employed for improving baseline information on plant community ecology and distribution in often critically endangered Mediterranean wetland areas. (C) 2008 Elsevier Ltd. All rights reserved.