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.

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 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.

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.

Airborne measurements of trace gases and aerosols over the London metropolitan region

The Emissions around the M25 motorway (EM25) campaign took place over the megacity of London in the United Kingdom in June 2009 with the aim of characterising trace gas and aerosol composition and properties entering and emitted from the urban region. It featured two mobile platforms, the UK BAe-146 Facility for Airborne Atmospheric Measurements (FAAM) research aircraft and a ground-based mobile lidar van, both travelling in circuits around London, roughly following the path of the M25 motorway circling the city. We present an overview of findings from the project, which took place during typical UK summertime pollution conditions. Emission ratios of volatile organic compounds (VOCs) to acetylene and carbon monoxide emitted from the London region were consistent with measurements in and downwind of other large urban areas and indicated traffic and associated fuel evaporation were major sources. Sub-micron aerosol composition was dominated by secondary species including sulphate (24% of sub-micron mass in the London plume and 29% in the non-plume regional aerosol), nitrate (24% plume; 20% regional) and organic aerosol (29% plume; 31% regional). The primary sub-micron aerosol emissions from London were minor compared to the larger regional background, with only limited increases in aerosol mass in the urban plume compared to the background (~12% mass increase on average). Black carbon mass was the major exception and more than doubled in the urban plume, leading to a decrease in the single scattering albedo from 0.91 in the regional aerosol to 0.86 in the London plume, on average. Our observations indicated that regional aerosol plays a major role on aerosol concentrations around London, at least during typical summertime conditions, meaning future efforts to reduce PM levels in London must account for regional as well as local aerosol sources.

The effects of springtime mid-latitude storms on trace gas composition determined from the MACC reanalysis

The relationship between springtime air pollution transport of ozone (O3) and carbon monoxide (CO) and mid-latitude cyclones is explored for the first time using the Monitoring Atmospheric Composition and Climate (MACC) reanalysis for the period 2003–2012. In this study, the most intense spring storms (95th percentile) are selected for two regions, the North Pacific (NP) and the North Atlantic (NA). These storms (∼60 storms over each region) often track over the major emission sources of East Asia and eastern North America. By compositing the storms, the distributions of O3 and CO within a "typical" intense storm are examined. We compare the storm-centered composite to background composites of "average conditions" created by sampling the reanalysis data of the previous year to the storm locations. Mid-latitude storms are found to redistribute concentrations of O3 and CO horizontally and vertically throughout the storm. This is clearly shown to occur through two main mechanisms: (1) vertical lifting of CO-rich and O3-poor air isentropically, from near the surface to the mid- to upper-troposphere in the region of the warm conveyor belt; and (2) descent of O3-rich and CO-poor air isentropically in the vicinity of the dry intrusion, from the stratosphere toward the mid-troposphere. This can be seen in the composite storm's life cycle as the storm intensifies, with area-averaged O3 (CO) increasing (decreasing) between 200 and 500 hPa. The influence of the storm dynamics compared to the background environment on the composition within an area around the storm center at the time of maximum intensity is as follows. Area-averaged O3 at 300 hPa is enhanced by 50 and 36% and by 11 and 7.6% at 500 hPa for the NP and NA regions, respectively. In contrast, area-averaged CO at 300 hPa decreases by 12% for NP and 5.5% for NA, and area-averaged CO at 500 hPa decreases by 2.4% for NP while there is little change over the NA region. From the mid-troposphere, O3-rich air is clearly seen to be transported toward the surface, but the downward transport of CO-poor air is not discernible due to the high levels of CO in the lower troposphere. Area-averaged O3 is slightly higher at 1000 hPa (3.5 and 1.8% for the NP and NA regions, respectively). There is an increase of CO at 1000 hPa for the NP region (3.3%) relative to the background composite and a~slight decrease in area-averaged CO for the NA region at 1000 hPa (-2.7%).

Advanced source apportionment of size-resolved trace elements at multiple sites in London during winter

Trace element measurements in PM10–2.5, PM2.5–1.0 and PM1.0–0.3 aerosol were performed with 2 h time resolution at kerbside, urban background and rural sites during the ClearfLo winter 2012 campaign in London. The environment-dependent variability of emissions was characterized using the Multilinear Engine implementation of the positive matrix factorization model, conducted on data sets comprising all three sites but segregated by size. Combining the sites enabled separation of sources with high temporal covariance but significant spatial variability. Separation of sizes improved source resolution by preventing sources occurring in only a single size fraction from having too small a contribution for the model to resolve. Anchor profiles were retrieved internally by analysing data subsets, and these profiles were used in the analyses of the complete data sets of all sites for enhanced source apportionment. A total of nine different factors were resolved (notable elements in brackets): in PM10–2.5, brake wear (Cu, Zr, Sb, Ba), other traffic-related (Fe), resuspended dust (Si, Ca), sea/road salt (Cl), aged sea salt (Na, Mg) and industrial (Cr, Ni); in PM2.5–1.0, brake wear, other traffic-related, resuspended dust, sea/road salt, aged sea salt and S-rich (S); and in PM1.0–0.3, traffic-related (Fe, Cu, Zr, Sb, Ba), resuspended dust, sea/road salt, aged sea salt, reacted Cl (Cl), S-rich and solid fuel (K, Pb). Human activities enhance the kerb-to-rural concentration gradients of coarse aged sea salt, typically considered to have a natural source, by 1.7–2.2. These site-dependent concentration differences reflect the effect of local resuspension processes in London. The anthropogenically influenced factors traffic (brake wear and other traffic-related processes), dust and sea/road salt provide further kerb-to-rural concentration enhancements by direct source emissions by a factor of 3.5–12.7. The traffic and dust factors are mainly emitted in PM10–2.5 and show strong diurnal variations with concentrations up to 4 times higher during rush hour than during night-time. Regionally influenced S-rich and solid fuel factors, occurring primarily in PM1.0–0.3, have negligible resuspension influences, and concentrations are similar throughout the day and across the regions.

Climatology and variability of trace gases in extratropical double-tropopause regions from MLS, HIRDLS, and ACE-FTS measurements

Upper tropospheric and lower stratospheric measurements from the Aura Microwave Limb Sounder (MLS), the Aura High Resolution Dynamics Limb Sounder (HIRDLS), and the Atmospheric Chemistry Experiment-Fourier transform spectrometer (ACE-FTS) are used to present the first global climatological comparison of extratropical, nonpolar trace gas distributions in double-tropopause (DT) and single-tropopause (ST) regions. Stratospheric tracers, O3, HNO3, and HCl, have lower mixing ratios ∼2–8 km above the primary (lowermost) tropopause in DT than in ST regions in all seasons, with maximum Northern Hemisphere (NH) differences near 50% in winter and 30% in summer. Southern Hemisphere winter differences are somewhat smaller, but summer differences are similar in the two hemispheres. H2O in DT regions of both hemispheres shows strong negative anomalies in November through February and positive anomalies in July through October, reflecting the strong seasonal cycle in H2O near the tropical tropopause. CO and other tropospheric tracers examined have higher DT than ST values 2–7 km above the primary tropopause, with the largest differences in winter. Large DT-ST differences extend to high NH latitudes in fall and winter, with longitudinal maxima in regions associated with enhanced wave activity and subtropical jet variations. Results for O3 and HNO3 agree closely between MLS and HIRDLS, and differences from ACE-FTS are consistent with its sparse and irregular midlatitude sampling. Consistent signatures in climatological trace gas fields provide strong evidence that transport from the tropical upper troposphere into the layer between double tropopauses is an important pathway for stratosphere-troposphere exchange.

Kerb and urban increment of highly time-resolved trace elements in PM10, PM2.5 and PM1.0 winter aerosol in London during ClearfLo 2012

Ambient concentrations of trace elements with 2 h time resolution were measured in PM10–2.5, PM2.5–1.0 and PM1.0–0.3 size ranges at kerbside, urban background and rural sites in London during winter 2012. Samples were collected using rotating drum impactors (RDIs) and subsequently analysed with synchrotron radiation-induced X-ray fluorescence spectrometry (SR-XRF). Quantification of kerb and urban increments (defined as kerb-to-urban and urban-to-rural concentration ratios, respectively), and assessment of diurnal and weekly variability provided insight into sources governing urban air quality and the effects of urban micro-environments on human exposure. Traffic-related elements yielded the highest kerb increments, with values in the range of 10.4 to 16.6 for SW winds (3.3–6.9 for NE) observed for elements influenced by brake wear (e.g. Cu, Sb, Ba) and 5.7 to 8.2 for SW (2.6–3.0 for NE) for other traffic-related processes (e.g. Cr, Fe, Zn). Kerb increments for these elements were highest in the PM10–2.5 mass fraction, roughly twice that of the PM1.0–0.3 fraction. These elements also showed the highest urban increments (~ 3.0), although no difference was observed between brake wear and other traffic-related elements. All elements influenced by traffic exhibited higher concentrations during morning and evening rush hours, and on weekdays compared to weekends, with the strongest trends observed at the kerbside site, and additionally enhanced by winds coming directly from the road, consistent with street canyon effects. Elements related to mineral dust (e.g. Al, Si, Ca, Sr) showed significant influences from traffic-induced resuspension, as evidenced by moderate kerb (3.4–5.4 for SW, 1.7–2.3 for NE) and urban (~ 2) increments and increased concentrations during peak traffic flow. Elements related to regional transport showed no significant enhancement at kerb or urban sites, with the exception of PM10–2.5 sea salt (factor of up to 2), which may be influenced by traffic-induced resuspension of sea and/or road salt. Heavy-duty vehicles appeared to have a larger effect than passenger vehicles on the concentrations of all elements influenced by resuspension (including sea salt) and wearing processes. Trace element concentrations in London were influenced by both local and regional sources, with coarse and intermediate fractions dominated by traffic-induced resuspension and wearing processes and fine particles influenced by regional transport.

“Pussy cat, pussy cat where have you been..?” Evaluating the use of stable isotopes, radiogenic isotopes and trace elements for investigating the ecology of Panthera leo

1. Understanding the behaviour and ecology of large carnivores is becoming increasingly important as the list of endangered species grows, with felids such as Panthera leo in some locations heading dangerously close to extinction in the wild. In order to have more reliable and effective tools to understand animal behaviour, movement and diet, we need to develop novel, integrated approaches and effective techniques to capture a detailed profile of animal foraging and movement patterns. 2. Ecological studies have shown considerable interest in using stable isotope methods, both to investigate the nature of animal feeding habits, and to map their geographical location. However, recent work has suggested that stable isotope analyses of felid fur and bone is very complex and does not correlate directly with the isotopic composition of precipitation (and hence geographical location). 3. We present new data that suggest these previous findings may be atypical, and demonstrate that isotope analyses of Felidae are suitable for both evaluating dietary inputs and establishing geo-location as they have strong environmental referents to both food and water. These data provide new evidence of an important methodology that can be applied to the family Felidae for future research in ecology, conservation, wildlife forensics and archaeological science.

Characterization of Metal and Trace Element Contents of Particulate Matter (PM10) Emitted by Vehicles Running on Brazilian FuelsHydrated Ethanol and Gasoline with 22% of Anhydrous Ethanol

Emission of fine particles by mobile sources has been a matter of great concern due to its potential risk both to human health and the environment. Although there is no evidence that one sole component may be responsible for the adverse health outcomes, it is postulated that the metal particle content is one of the most important factors, mainly in relation to oxidative stress. Data concerning the amount and type of metal particles emitted by automotive vehicles using Brazilian fuels are limited. The aim of this study was to identify inhalable particles (PM10) and their trace metal content in two light-duty vehicles where one was fueled with ethanol while the other was fueled with gasoline mixed with 22% of anhydrous ethanol (gasohol); these engines were tested on a chassis dynamometer. The elementary composition of the samples was evaluated by the particle-induced x-ray emission technique. The experiment showed that total emission factors ranged from 2.5 to 11.8 mg/km in the gasohol vehicle, and from 1.2 to 3 mg/km in the ethanol vehicle. The majority of particles emitted were in the fine fraction (PM2.5), in which Al, Si, Ca, and Fe corresponded to 80% of the total weight. PM10 emissions from the ethanol vehicle were about threefold lower than those of gasohol. The elevated amount of fine particulate matter is an aggravating factor, considering that these particles, and consequently associated metals, readily penetrate deeply into the respiratory tract, producing damage to lungs and other tissues.

A general Trotter-Kato formula for a class of evolution operators

In this article we prove new results concerning the existence and various properties of an evolution system U(A+B)(t, s)0 <= s <= t <= T generated by the sum -(A(t) + B(t)) of two linear, time-dependent, and generally unbounded operators defined on time-dependent domains in a complex and separable Banach space B. In particular, writing L(B) for the algebra of all linear bounded operators on B, we can express U(A+B)(t, s)0 <= s <= t <= T as the strong limit in C(8) of a product of the holomorphic contraction semigroups generated by -A (t) and - B(t), respectively, thereby proving a product formula of the Trotter-Kato type under very general conditions which allow the domain D(A(t) + B(t)) to evolve with time provided there exists a fixed set D subset of boolean AND(t is an element of)[0,T] D(A(t) + B(t)) everywhere dense in B. We obtain a special case of our formula when B(t) = 0, which, in effect, allows us to reconstruct U(A)(t, s)0 <=(s)<=(t)<=(T) very simply in terms of the semigroup generated by -A(t). We then illustrate our results by considering various examples of nonautonomous parabolic initial-boundary value problems, including one related to the theory of timedependent singular perturbations of self-adjoint operators. We finally mention what we think remains an open problem for the corresponding equations of Schrodinger type in quantum mechanics.