Optimal convergence estimates for the trace of the polynomial L2-projection operator on a simplex

In this paper we study convergence of the L2-projection onto the space of polynomials up to degree p on a simplex in Rd, d >= 2. Optimal error estimates are established in the case of Sobolev regularity and illustrated on several numerical examples. The proof is based on the collapsed coordinate transform and the expansion into various polynomial bases involving Jacobi polynomials and their antiderivatives. The results of the present paper generalize corresponding estimates for cubes in Rd from [P. Houston, C. Schwab, E. Süli, Discontinuous hp-finite element methods for advection-diffusion-reaction problems. SIAM J. Numer. Anal. 39 (2002), no. 6, 2133-2163].

Highly resolved observations of trace gases in the lowermost stratosphere and upper troposphere from the SPURT project: an overview

During SPURT (Spurenstofftransport in der Tropopausenregion, trace gas transport in the tropopause region) we performed measurements of a wide range of trace gases with different lifetimes and sink/source characteristics in the northern hemispheric upper troposphere (UT) and lowermost stratosphere (LMS). A large number of in-situ instruments were deployed on board a Learjet 35A, flying at altitudes up to 13.7 km, at times reaching to nearly 380 K potential temperature. Eight measurement campaigns (consisting of a total of 36 flights), distributed over all seasons and typically covering latitudes between 35° N and 75° N in the European longitude sector (10° W–20° E), were performed. Here we present an overview of the project, describing the instrumentation, the encountered meteorological situations during the campaigns and the data set available from SPURT. Measurements were obtained for N2O, CH4, CO, CO2, CFC12, H2, SF6, NO, NOy, O3 and H2O. We illustrate the strength of this new data set by showing mean distributions of the mixing ratios of selected trace gases, using a potential temperature-equivalent latitude coordinate system. The observations reveal that the LMS is most stratospheric in character during spring, with the highest mixing ratios of O3 and NOy and the lowest mixing ratios of N2O and SF6. The lowest mixing ratios of NOy and O3 are observed during autumn, together with the highest mixing ratios of N2O and SF6 indicating a strong tropospheric influence. For H2O, however, the maximum concentrations in the LMS are found during summer, suggesting unique (temperature- and convection-controlled) conditions for this molecule during transport across the tropopause. The SPURT data set is presently the most accurate and complete data set for many trace species in the LMS, and its main value is the simultaneous measurement of a suite of trace gases having different lifetimes and physical-chemical histories. It is thus very well suited for studies of atmospheric transport, for model validation, and for investigations of seasonal changes in the UT/LMS, as demonstrated in accompanying and elsewhere published studies.

Retrievals of sea surface temperature from infrared imagery: origin and form of systematic errors

We show that retrievals of sea surface temperature from satellite infrared imagery are prone to two forms of systematic error: prior error (familiar from the theory of atmospheric sounding) and error arising from nonlinearity. These errors have different complex geographical variations, related to the differing geographical distributions of the main geophysical variables that determine clear-sky brightness-temperatures over the oceans. We show that such errors arise as an intrinsic consequence of the form of the retrieval (rather than as a consequence of sub-optimally specified retrieval coefficients, as is often assumed) and that the pattern of observed errors can be simulated in detail using radiative-transfer modelling. The prior error has the linear form familiar from atmospheric sounding. A quadratic equation for nonlinearity error is derived, and it is verified that the nonlinearity error exhibits predominantly quadratic behaviour in this case.

Distribution and availability of trace elements in municipal solid waste composts

Trace element contamination is one of the main problems linked to the quality of compost, especially when it is produced from urban wastes, which can lead to high levels of some potentially toxic elements such as Cu, Pb or Zn. In this work, the distribution and bioavailability of five elements (Cu, Zn, Pb, Cr and Ni) were studied in five Spanish composts obtained from different feedstocks (municipal solid waste, garden trimmings, sewage sludge and mixed manure). The five composts showed high total concentrations of these elements, which in some cases limited their commercialization due to legal imperatives. First, a physical fractionation of the composts was performed, and the five elements were determined in each size fraction. Their availability was assessed by several methods of extraction (water, CaCl2–DTPA, the PBET extract, the TCLP extract, and sodium pyrophosphate), and their chemical distribution was assessed using the BCR sequential extraction procedure. The results showed that the finer fractions were enriched with the elements studied, and that Cu, Pb and Zn were the most potentially problematic ones, due to both their high total concentrations and availability. The partition into the BCR fractions was different for each element, but the differences between composts were scarce. Pb was evenly distributed among the four fractions defined in the BCR (soluble, oxidizable, reducible and residual); Cu was mainly found in the oxidizable fraction, linked to organic matter, and Zn was mainly associated to the reducible fraction (iron oxides), while Ni and Cr were mainly present almost exclusively in the residual fraction. It was not possible to establish a univocal relation between trace elements availability and their BCR fractionation. Given the differences existing for the availability and distribution of these elements, which not always were related to their total concentrations, we think that legal limits should consider availability, in order to achieve a more realistic assessment of the risks linked to compost use.

The aluminium content of breast tissue taken from women with breast cancer

The aetiology of breast cancer is multifactorial. While there are known genetic predispositions to the disease it is probable that environmental factors are also involved. Recent research has demonstrated a regionally specific distribution of aluminium in breast tissue mastectomies while other work has suggested mechanisms whereby breast tissue aluminium might contribute towards the aetiology of breast cancer. We have looked to develop microwave digestion combined with a new form of graphite furnace atomic absorption spectrometry as a precise, accurate and reproducible method for the measurement of aluminium in breast tissue biopsies. We have used this method to test the thesis that there is a regional distribution of aluminium across the breast in women with breast cancer. Microwave digestion of whole breast tissue samples resulted in clear homogenous digests perfectly suitable for the determination of aluminium by graphite furnace atomic absorption spectrometry. The instrument detection limit for the method was 0.48 μg/L. Method blanks were used to estimate background levels of contamination of 14.80 μg/L. The mean concentration of aluminium across all tissues was 0.39 μg Al/g tissue dry wt. There were no statistically significant regionally specific differences in the content of aluminium. We have developed a robust method for the precise and accurate measurement of aluminium in human breast tissue. There are very few such data currently available in the scientific literature and they will add substantially to our understanding of any putative role of aluminium in breast cancer. While we did not observe any statistically significant differences in aluminium content across the breast it has to be emphasised that herein we measured whole breast tissue and not defatted tissue where such a distribution was previously noted. We are very confident that the method developed herein could now be used to provide accurate and reproducible data on the aluminium content in defatted tissue and oil from such tissues and thereby contribute towards our knowledge on aluminium and any role in breast cancer.

The influence of vegetation, fire spread and fire behaviour on biomass burning and trace gas emissions: results from a process-based model

A process-based fire regime model (SPITFIRE) has been developed, coupled with ecosystem dynamics in the LPJ Dynamic Global Vegetation Model, and used to explore fire regimes and the current impact of fire on the terrestrial carbon cycle and associated emissions of trace atmospheric constituents. The model estimates an average release of 2.24 Pg C yr−1 as CO2 from biomass burning during the 1980s and 1990s. Comparison with observed active fire counts shows that the model reproduces where fire occurs and can mimic broad geographic patterns in the peak fire season, although the predicted peak is 1–2 months late in some regions. Modelled fire season length is generally overestimated by about one month, but shows a realistic pattern of differences among biomes. Comparisons with remotely sensed burnt-area products indicate that the model reproduces broad geographic patterns of annual fractional burnt area over most regions, including the boreal forest, although interannual variability in the boreal zone is underestimated.

Impact of variable atmospheric and oceanic form drag on simulations of Arctic sea ice

Over Arctic sea ice, pressure ridges and floe andmelt pond edges all introduce discrete obstructions to the flow of air or water past the ice and are a source of form drag. In current climate models form drag is only accounted for by tuning the air–ice and ice–ocean drag coefficients, that is, by effectively altering the roughness length in a surface drag parameterization. The existing approach of the skin drag parameter tuning is poorly constrained by observations and fails to describe correctly the physics associated with the air–ice and ocean–ice drag. Here, the authors combine recent theoretical developments to deduce the total neutral form drag coefficients from properties of the ice cover such as ice concentration, vertical extent and area of the ridges, freeboard and floe draft, and the size of floes and melt ponds. The drag coefficients are incorporated into the Los Alamos Sea Ice Model (CICE) and show the influence of the new drag parameterization on the motion and state of the ice cover, with the most noticeable being a depletion of sea ice over the west boundary of the Arctic Ocean and over the Beaufort Sea. The new parameterization allows the drag coefficients to be coupled to the sea ice state and therefore to evolve spatially and temporally. It is found that the range of values predicted for the drag coefficients agree with the range of values measured in several regions of the Arctic. Finally, the implications of the new form drag formulation for the spinup or spindown of the Arctic Ocean are discussed.

Characterizing sampling bias in the trace gas climatologies of the SPARC Data Initiative

Monthly zonal mean climatologies of atmospheric measurements from satellite instruments can have biases due to the nonuniform sampling of the atmosphere by the instruments. We characterize potential sampling biases in stratospheric trace gas climatologies of the Stratospheric Processes and Their Role in Climate (SPARC) Data Initiative using chemical fields from a chemistry climate model simulation and sampling patterns from 16 satellite-borne instruments. The exercise is performed for the long-lived stratospheric trace gases O3 and H2O. Monthly sampling biases for O3 exceed 10% for many instruments in the high-latitude stratosphere and in the upper troposphere/lower stratosphere, while annual mean sampling biases reach values of up to 20% in the same regions for some instruments. Sampling biases for H2O are generally smaller than for O3, although still notable in the upper troposphere/lower stratosphere and Southern Hemisphere high latitudes. The most important mechanism leading to monthly sampling bias is nonuniform temporal sampling, i.e., the fact that for many instruments, monthly means are produced from measurements which span less than the full month in question. Similarly, annual mean sampling biases are well explained by nonuniformity in the month-to-month sampling by different instruments. Nonuniform sampling in latitude and longitude are shown to also lead to nonnegligible sampling biases, which are most relevant for climatologies which are otherwise free of biases due to nonuniform temporal sampling.

Does form meet function in the coronavirus replicative organelle?

If we use the analogy of a virus as a living entity, then the replicative organelle is the body where its metabolic and reproductive activities are concentrated. Recent studies have illuminated the intricately complex replicative organelles of coronaviruses, a group that includes the largest known RNA virus genomes. This review takes a virus-centric look at the coronavirus replication transcription complex organelle in the context of the wider world of positive sense RNA viruses, examining how the mechanisms of protein expression and function act to produce the factories that power the viral replication cycle.

How do atmospheric rivers form?

Identifying the source of atmospheric rivers: Are they rivers of moisture exported from the subtropics or footprints left behind by poleward travelling storms? The term atmospheric river is used to describe corridors of strong water vapor transport in the troposphere. Filaments of enhanced water vapor, commonly observed in satellite imagery extending from the subtropics to the extratropics, are routinely used as a proxy for identifying these regions of strong water vapor transport. The precipitation associated with these filaments of enhanced water vapor can lead to high impact flooding events. However, there remains some debate as to how these filaments form. In this paper we analyse the transport of water vapor within a climatology of wintertime North Atlantic extratropical cyclones. Results show that atmospheric rivers are formed by the cold front which sweeps up water vapor in the warm sector as it catches up with the warm front. This causes a narrow band of high water vapor content to form ahead of the cold front at the base of the warm conveyor belt airflow. Thus, water vapor in the cyclone's warm sector, and not long-distance transport of water vapor from the subtropics, is responsible for the generation of filaments of high water vapor content. A continuous cycle of evaporation and moisture convergence within the cyclone replenishes water vapor lost via precipitation. Thus, rather than representing a direct and continuous feed of moist air from the subtropics into the centre of a cyclone (as suggested by the term atmospheric river), these filaments are, in-fact, the result of water vapor exported from the cyclone and thus they represent the footprints left behind as cyclones travel polewards from subtropics.

Revolution blues: the reconstruction of Health and Safety as a ‘common-sense’ form of regulation

This paper provides a review of the last five years of policymaking in the area of health and safety law; this includes multiple reviews, legislative reform, and the reframing of rhetoric around the issue. It characterises this as a process of social construction of a new ‘universe of meaning’ around health and safety regulation, which provides a basis for a particular, narrow, neoliberal conception of regulation and responsibility to permeate the mainstream. Deliberative and public-facing policymaking processes have been utilised as a key element of this process.