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Effect of reactive intermediates on the propagation of turbulent premixed flames

The most simple version of the Bray and Libby model of turbulent flame propagation has been extended to include a two-step reaction mechanism in which reactants decompose into reactive intermediates which then form products. A transport equation for the joint pdf of intermediate and product concentrations was derived, the pdf parameterized, and transport equations for the parameters obtained. The one-dimensional concentration equations were then solved for the parameters of the pdf and the turbulent kinetic energy. Flame speed and angle are recovered as eigenvalues of the problem. The results show the essential features observed in experiments. The product pdf is composed of peaks at zero and unity product concentration, with a continuous structure representing partially reacted gas. The intermediates pdf has a peak at zero concentration and a broad bell-shaped distribution at nonzero concentration, representing partially reacted gas. The results also show the effect of partitioning of energy release on the flame thickness and speed.

Azzazy, M.↗

Global Impact of Lightning-Produced Oxidants

Lightning plays a major role in tropospheric oxidation, and its role on modulating tropospheric chemistry was thought to be emissions of nitrogen oxides (NOx). Recent field and laboratory measurements demonstrate that lightning generates extremely large amounts of oxidants, including hydrogen oxides (HOx) and O3. Here we implement these lightning-produced oxidants in a global chemical transport model to examine its global impact on tropospheric composition. We find that lightning-produced oxidants can increase global mass weighted OH by 0.3-10%, and affect CO, O3, and reactive nitrogen substantially, depending on the emission strength of oxidants from lightning. Our work highlights the importance and uncertainties of lightning-produced oxidants, as well as the need for rethinking the role of lightning in tropospheric oxidation chemistry.

Jingqiu Mao↗

Decadal Changes in Summertime Reactive Oxidized Nitrogen and Surface Ozone over the Southeast United States

Widespread efforts to abate ozone (O3) smog have significantly reduced emissions of nitrogen oxides (NOx) over the past 2 decades in the Southeast US, a place heavily influenced by both anthropogenic and biogenic emissions. How reactive nitrogen speciation responds to the reduction in NOx emissions in this region remains to be elucidated. Here we exploit aircraft measurements from ICARTT (International Consortium for Atmospheric Research on Transport and Transformation - July-August 2004), SENEX (Southeast Nexus - June-July 2013), and SEAC4RS (Studies of Emissions and Atmospheric Composition, Clouds and Climate Coupling by Regional Surveys - August-September 2013) and long-term ground measurement networks alongside a global chemistry-climate model to examine decadal changes in summertime reactive oxidized nitrogen (RON) and ozone over the Southeast US. We show that our model can reproduce the mean vertical profiles of major RON species and the total (NO (sub y)) in both 2004 and 2013. Among the major RON species, nitric acid (HNO3) is dominant (approximately 42-45 percent), followed by NOx (31 percent), total peroxy nitrates (Sigma PNs; 14 percent), and total alkyl nitrates (Sigma ANs; 9-12 percent) on a regional scale. We find that most RON species, including NOx, Sigma PNs, and HNO3, decline proportionally with decreasing NOx emissions in this region, leading to a similar decline in NO (sub y). This linear response might be in part due to the nearly constant summertime supply of biogenic VOC (Volatile Organic Compounds) emissions in this region. Our model captures the observed relative change in RON and surface ozone from 2004 to 2013. Model sensitivity tests indicate that further reductions of NOx emissions will lead to a continued decline in surface ozone and less frequent high-ozone events.

Li, Jingyi↗

A Coupled Soil-Atmosphere Model of H2O2 on Mars

The Viking Gas Chromatograph Mass Spectrometer failed to detect organic compounds on Mars, and both the Viking Labeled Release and the Viking Gas Exchange experiments indicated a reactive soil surface. These results have led to the widespread belief that there are oxidants in the martian soil. Since H2O2 is produced by photochemical processes in the atmosphere of Mars, and has been shown in the laboratory to reproduce closely the Viking LR results, it is a likely candidate for a martian soil oxidant. Here, we report on the results of a coupled soil/atmosphere transport model for H202 on Mars. Upon diffusing into the soil, its concentration is determined by the extent to which it is adsorbed and by the rate at which it is catalytically destroyed. An analytical model for calculating the distribution of H202 in the martian atmosphere and soil is developed. The concentration of H202 in the soil is shown to go to zero at a finite depth, a consequence of the nonlinear soil diffusion equation. The model is parameterized in terms of an unknown quantity, the lifetime of H202 against heterogeneous catalytic destruction in the soil. Calculated concentrations are compared with a H202 concentration of 30 nmoles/cu cm, inferred from the Viking Labeled Release experiment. A significant result of this model is that for a wide range of H202 lifetimes (up to 105 years), the extinction depth was found to be less than 3 m. The maximum possible concentration in the top 4 cm is calculated to be approx. 240 nmoles/cu cm, achieved with lifetimes of greater than 1000 years. Concentrations higher than 30 nmoles/cu cm require lifetimes of greater than 4.3 terrestrial years. For a wide range of H202 lifetimes, it was found that the atmospheric concentration is only weakly coupled with soil loss processes. Losses to the soil become significant only when lifetimes are less than a few hours. If there are depths below which H202 is not transported, it is plausible that organic compounds, protected from an oxidizing environment, may still exist. They would have been deposited by meteors, or be the organic remains of past life.

Bullock, Mark A.↗

Rates of elementary reactions - Measurement and applications

Techniques used for characterizing elementary chemical reaction kinetics are explored. Flash- or laser-photolysis (FP) involves producing reactive species on the psec time scale and monitoring the changes spectroscopically. In the discharge flow (DF) method, reactive species are produced continuously in a flow of an inert gas containing the reactants. FP avoids surface and transport effects, while DF allows several reactions to be studied in different regions of one flow. Transport and surface boundary layer models are defined for DF calculations and sample calculations are carried out to illustrate the difficulties inherent in theoretically defining the rate constants for elementary reactions. Applications of the models thus far derived in atmospheric science and combustion studies are discussed.

Kaufman, F.↗

Nuclear modules for space electric propulsion

Analysis of interplanetary cargo and piloted missions requires calculations of the performances and masses of subsystems to be integrated in a final design. In a preliminary and scoping stage the designer needs to evaluate options iteratively by using fast computer simulations. The Oak Ridge National Laboratory (ORNL) has been involved in the development of models and calculational procedures for the analysis (neutronic and thermal hydraulic) of power sources for nuclear electric propulsion. The nuclear modules will be integrated into the whole simulation of the nuclear electric propulsion system. The vehicles use either a Brayton direct-conversion cycle, using the heated helium from a NERVA-type reactor, or a potassium Rankine cycle, with the working fluid heated on the secondary side of a heat exchanger and lithium on the primary side coming from a fast reactor. Given a set of input conditions, the codes calculate composition. dimensions, volumes, and masses of the core, reflector, control system, pressure vessel, neutron and gamma shields, as well as the thermal hydraulic conditions of the coolant, clad and fuel. Input conditions are power, core life, pressure and temperature of the coolant at the inlet of the core, either the temperature of the coolant at the outlet of the core or the coolant mass flow and the fluences and integrated doses at the cargo area. Using state-of-the-art neutron cross sections and transport codes, a database was created for the neutronic performance of both reactor designs. The free parameters of the models are the moderator/fuel mass ratio for the NERVA reactor and the enrichment and the pitch of the lattice for the fast reactor. Reactivity and energy balance equations are simultaneously solved to find the reactor design. Thermalhydraulic conditions are calculated by solving the one-dimensional versions of the equations of conservation of mass, energy, and momentum with compressible flow.

Difilippo, F. C.↗

Finite-rate chemistry effects upon convective and radiative heating of an atmospheric entry vehicle

A mathematical model of the aerothermochemical environment along the stagnation line of a planetary return spacecraft using an ablative thermal protection system was developed and solved for conditions typical of atmospheric entry from planetary missions. The model, implemented as a FORTRAN 4 computer program, was designed to predict viscous, reactive and radiative coupled shock layer structure and the resulting body heating rates. The analysis includes flow field coupling with the ablator surface, binary diffusion, coupled line and continuum radiative and equilibrium or finite rate chemistry effects. The gas model used includes thermodynamic, transport, kinetic and radiative properties of air and ablation product species, including 19 chemical species and 16 chemical reactions. Specifically, the impact of nonequilibrium chemistry effects upon stagnation line shock layer structure and body heating rates was investigated.

Guillermo, P.↗

Field-aligned dynamics of chemically induced perturbations to the ionosphere

Ionospheric modification using photochemically reactive vapors is studied with a one-dimensional, multiion, fluid model of plasma flow along magnetic field lines. The magnitudes of ion and electron density changes are determined by considering both chemical processes (i.e., photoionization, ion-molecule reactions, dissociative recombination, electron attachment) and transport processes (i.e., multispecies diffusion, electric currents, ambipolar electric fields). The numerical treatment in the model is not specific to any type of release or any interaction chemistry. It has been used to simulate releases of Ba, CO2, and CF3Br in the ionosphere, but generalization to other species may be easily accomplished. The results of the calculations are found to be in good agreement with experimental observations. The feasibility of modifying the parallel current paths in the auroral F region is examined.

Bernhardt, P. A.↗

Overview of Global/Regional Models Used to Evaluate Tropospheric Ozone in North America

Ozone (O3) is an important greenhouse gas, toxic pollutant, and plays a major role in atmospheric chemistry. Tropospheric O3 which resides in the planetary boundary layer (PBL) is highly reactive and has a lifetime on the order of days, however, O3 in the free troposphere and stratosphere has a lifetime on the order of weeks or months. Modeling O3 mixing ratios at and above the surface is difficult due to the multiple formation/destruction processes and transport pathways that cause large spatio-temporal variability in O3 mixing ratios. This talk will summarize in detail the global/regional models that are commonly used to simulate/predict O3 mixing ratios in the United States. The major models which will be focused on are the: 1) Community Multi-scale Air Quality Model (CMAQ), 2) Comprehensive Air Quality Model with Extensions (CAMx), 3) Goddard Earth Observing System with Chemistry (GEOS-Chem), 4) Real Time Air Quality Modeling System (RAQMS), 5) Weather Research and Forecasting/Chemistry (WRF-Chem) model, National Center for Atmospheric Research (NCAR)'s Model for OZone And Related chemical Tracers (MOZART), and 7) Geophysical Fluid Dynamics Laboratory (GFDL) AM3 model. I will discuss the major modeling components which impact O3 mixing ratio calculations in each model and the similarities/differences between these models. This presentation is vital to the 2nd Annual Tropospheric Ozone Lidar Network (TOLNet) Conference as it will provide an overview of tools, which can be used in conjunction with TOLNet data, to evaluate the complex chemistry and transport pathways controlling tropospheric O3 mixing ratios.

Mixing Ratios↗

Constraining Remote Oxidation Capacity with ATom Observations

The global oxidation capacity, defined as the tropospheric mean concentration of the hydroxyl radical (OH), controls the lifetime of reactive trace gases in the atmosphere such as methane and carbon monoxide (CO). Models tend to underestimate the methane lifetime and CO concentrations throughout the troposphere, which is consistent with excessive OH. Approximately half the oxidation of methane and non-methane volatile organic compounds (VOCs) is thought to occur over the oceans where oxidant chemistry has received little validation due to a lack of observational constraints. We use observations from the first two deployments of the NASA ATom aircraft campaign during July–August 2016 and January–February 2017 to evaluate the oxidation capacity over the remote oceans and its representation in the GEOS-Chem chemical transport model. The model successfully simulates the magnitude and vertical profile of remote OH within the measurement uncertainties. Comparisons against the drivers of OH production (water vapor, ozone, and NOy concentrations, ozone photolysis frequencies) also show minimal bias with the exception of wintertime NOy, for which a model overestimate may indicate insufficient wet scavenging and/or missing loss on seasalt aerosol but large uncertainties remain that require further studies of NOy partitioning and removal in the troposphere. During the ATom-1 deployment, OH reactivity (OHR) below 3 km is significantly enhanced, and this is not captured by the sum of its measured components (cOHRobs) or by the model (cOHRmod). This enhancement could suggest missing reactive VOCs but cannot be explained by new estimates of ocean VOC sources and additional modeled reactivity in this region would be difficult to reconcile with the full suite of ATom measurement constraints. The model generally reproduces the magnitude and seasonality of cOHRobs but underestimates the contribution of oxygenated VOC, mainly acetaldehyde, which is severely underestimated throughout the troposphere despite its calculated lifetime of less than a day. Missing model acetaldehyde in previous studies was attributed to measurement uncertainties that have been largely resolved. Observations of peroxyacetic acid (PAA) provide new support for remote levels of acetaldehyde. The underestimate in modeled acetaldehyde and PAA is present throughout the year in both hemispheres and peaks during Northern Hemisphere summer. The addition of ocean VOC sources in the model increases annual surface cOHRmod by 10 % and improves model-measurement agreement for acetaldehyde particularly in winter but cannot resolve the model summertime bias. Doing so would require a 100 Tg yr−1 source of a long-lived unknown precursor throughout the year with significant additional emissions in the Northern Hemisphere summer. Improving the model bias for remote acetaldehyde and PAA is unlikely to fully resolve previously reported model global biases in OH and methane lifetime, suggesting that future work should examine the sources and sinks of OH over land.

Travis, Katherine R.↗

Reactive collision terms for fluid transport theory

A modified Bhatnagar-Gross-Krook (BGK) collision method is used for the derivation of reactive collision terms to allow for complete higher-moment approximations in fluid transport theory. The general reactive collision terms for the 8-, 10- and 13-moment approximation for binary reactions are derived. Then, reactive collision terms for specific chemistry are derived with the assumptions: (1) all reactants and products have 13-moment distribution functions; (2) simple, classical assumptions provide sufficient models for reaction dynamics; and (3) the reaction rate is energy-independent. The derived specific formulas reflect two extremes in reactive collision dynamics: direct and indirect reaction mechanisms. Finally, considerations for correct use of the reactive collision terms are discussed in the context of space plasma environments.

Eccles, J. V.↗

Comprehensive investigation of HgCdTe metalorganic chemical vapor deposition

The principal objective of this experimental and theoretical research program was to explore the possibility of depositing high quality epitaxial CdTe and HgCdTe at very low pressures through metalorganic chemical vapor deposition (MOCVD). We explored two important aspects of this potential process: (1) the interaction of molecular flow transport and deposition in an MOCVD reactor with a commercial configuration, and (2) the kinetics of metal alkyl source gas adsorption, decomposition and desorption from the growing film surface using ultra high vacuum surface science reaction techniques. To explore the transport-reaction issue, we have developed a reaction engineering analysis of a multiple wafer-in-tube ultrahigh vacuum chemical vapor deposition (UHV/CVD) reactor which allows an estimate of wafer or substrate throughput for a reactor of fixed geometry and a given deposition chemistry with specified film thickness uniformity constraints. The model employs a description of ballistic transport and reaction based on the pseudo-steady approximation to the Boltzmann equation in the limit of pure molecular flow. The model representation takes the form of an integral equation for the flux of each reactant or intermediate species to the wafer surfaces. Expressions for the reactive sticking coefficients (RSC) for each species must be incorporated in the term which represents reemission from a wafer surface. The interactions of MOCVD precursors with Si and CdTe were investigated using temperature programmed desorption (TPD) in ultra high vacuum combined with Auger electron spectroscopy (AES). These studies revealed that diethyltellurium (DETe) and dimethylcadmium (DMCd) adsorb weakly on clean Si(100) and desorb upon heating without decomposing. These precursors adsorb both weakly and strongly on CdTe(111)A, with DMCd exhibiting the stronger interaction with the surface than DETe.

Raupp, Gregory B.↗

Stratospheric aircraft exhaust plume and wake chemistry studies

This report documents progress to date in an ongoing study to analyze and model emissions leaving a proposed High Speed Civil Transport (HSCT) from when the exhaust gases leave the engine until they are deposited at atmospheric scales in the stratosphere. Estimates are given for the emissions, summarizing relevant earlier work (CIAP) and reviewing current propulsion research efforts. The chemical evolution and the mixing and vortical motion of the exhaust are analyzed to track the exhaust and its speciation as the emissions are mixed to atmospheric scales. The species tracked include those that could be heterogeneously reactive on the surfaces of the condensed solid water (ice) particles and on exhaust soot particle surfaces. Dispersion and reaction of chemical constituents in the far wake are studied with a Lagrangian air parcel model, in conjunction with a radiation code to calculate the net heating/cooling. Laboratory measurements of heterogeneous chemistry of aqueous sulfuric acid and nitric acid hydrates are also described. Results include the solubility of HCl in sulfuric acid which is a key parameter for modeling stratospheric processing. We also report initial results for condensation of nitric acid trihydrate from gas phase H2O and HNO3.

Miake-Lye, R. C.↗

The fate of atmospheric phosgene and the stratospheric chlorine loadings of its parent compounds: CCl4, C2Cl4, C2HCL3, CH3CCl3, and CHCl3

A study of the tropospheric and stratospheric cycles of phosgene is carried out to determine its fate and ultimate role in controlling the ozone depletion potentials of its parent compounds. Tropospheric phosgene is produced from the OH-initiated oxidation of C2Cl4, CH3CCl3, CHCl3, and C2HCl3. Simulations using a two-dimensional model indicate that these processes produce about 90 pptv/yr of tropospheric phosgene with an average concentration of about 18 pptv, in reasonable agreement with observations. We estimate a residence time of about 70 days for tropospheric phosgene, with the vast majority being removed by hydrolysis in cloudwater. Only about 0.4% of the phosgene produced in the troposphere avoids wet removal and is transported to the stratosphere, where its chlorine can be released to participate in the catalytic destruction of ozone. Stratospheric phosgene is produced from the photochemical degradation of CCl4, C2Cl4, CHCl3, and CH3CCl3 and is removed by photolysis and downward transport to the troposphere. Model calculations, in good agreement with observations, indicate that these processes produce a peak stratospheric concentration of about 25-30 pptv at an altitude of about 25 km. In contrast to tropospheric phosgene, stratospheric phosgene is found to have a lifetime against photochemical removal of the order of years. As a result, a significant portion of the phosgene that is produced in the stratosphere is ultimately returned to the troposphere, where it is rapidly removed by clouds. This phenomenon effectively decreases the amount of reactive chlorine injected into the stratosphere and available for ozone depletion from phosgene's parent compounds. A similar phenomenon due to the downward transport of stratospheric COFCl produced from CFC-11 is estimated to cause a 7% decrease in the amount of reactive chlorine injected into the stratosphere from this compound. Our results are potentially sensitive to a variety of parameters, most notably the rate of reaction of phosgene with sulfate aerosols. However, on the basis of the observed vertical distribution of COCl2, we estimate that the reaction of COCl2 with sulfate aerosol most likely has a gamma less than 5 x 10(exp -5) and, as a result, has a negligible impact on the stratospheric chlorine loadings of the phosgene parent compounds.

Kindler, T. P.↗

Chemical Ionization Mass Spectrometry-Based Measurements of HO2 and RO2 During TRACE-P

The Transport and Chemical Evolution over the Pacific (TRACE-P) mission extends NASA's Global Tropospheric Experiment (GTE) series of campaigns. TRACE-P was an aircraft-based campaign that was part of a larger ground-based and aircraft-based program (APARE) under the auspices of the International Global Atmospheric Chemistry (IGAC) program. TRACE-P was designed to (1) determine the chemical composition of Asian outflow over the western Pacific, and to (2) determine the chemical evolution of the Asian outflow. These objectives were addressed through a variety of observations and numerical modeling exercises. In particular, the goals included sampling strategies that would improve understanding of the budgets of odd hydrogen species (OH and HO2), budgets of NOx (NO, NO2, and their reservoirs), and impacts of oxidants produced in the outflow on air quality in the United States. The NASA DC-8 and P-3B aircraft were deployed in the March and April, 2001 out of primary bases of operation in Hong Kong and Yokota Air Base in Japan. These two aircraft have complementary capabilities which allow high altitude and long range impacts, as well as low altitude, local impacts to be assessed. In order to quantify the composition and evolution of Asian outflow, it is important to quantify as many species as possible including photochemically active species (e.g. NO2, CH2O, O3, acetone, etc.), sources species (VOCs, CO, NOx, SO2, aerosols), reactive intermediates including free radicals (OH, HO2, RO2, and their reservoirs), and end products (nitric acid, sulfuric acid, secondary aerosols, etc.). The more complete the measurement suite, the more tightly constrained the numerical modeling can be (within the uncertainties of the measurements). The numerical models range in sophistication from simple steady state box models (as employed in this study) to multi-dimensional chemical transport models. Data were collected on approximately 20 flights of the DC-8 and 21 flights of the P-3B. Observations from both aircraft were used in the present analysis, but primarily focused on the P-3B flights since that was the platform on which the peroxy radical instrumentation was based.

Cantrell, Christopher A.↗

Assessing the Ability of Instantaneous Aircraft and Sonde Measurements to Characterize Climatological Means and Long-Term Trends in Tropospheric Composition

Over four decades of measurements exist that sample the 3-D composition of reactive trace gases in the troposphere from approximately weekly ozone sondes, instrumentation on civil aircraft, and individual comprehensive aircraft field campaigns. An obstacle to using these data to evaluate coupled chemistry-climate models (CCMs)the models used to project future changes in atmospheric composition and climateis that exact space-time matching between model fields and observations cannot be done, as CCMs generate their own meteorology. Evaluation typically involves averaging over large spatiotemporal regions, which may not reflect a true average due to limited or biased sampling. This averaging approach generally loses information regarding specific processes. Here we aim to identify where discrete sampling may be indicative of long-term mean conditions, using the GEOS-Chem global chemical-transport model (CTM) driven by the MERRA reanalysis to reflect historical meteorology from 2003 to 2012 at 2o by 2.5o resolution. The model has been sampled at the time and location of every ozone sonde profile available from the Would Ozone and Ultraviolet Radiation Data Centre (WOUDC), along the flight tracks of the IAGOSMOZAICCARABIC civil aircraft campaigns, as well as those from over 20 individual field campaigns performed by NASA, NOAA, DOE, NSF, NERC (UK), and DLR (Germany) during the simulation period. Focusing on ozone, carbon monoxide and reactive nitrogen species, we assess where aggregates of the in situ data are representative of the decadal mean vertical, spatial and temporal distributions that would be appropriate for evaluating CCMs. Next, we identically sample a series of parallel sensitivity simulations in which individual emission sources (e.g., lightning, biogenic VOCs, wildfires, US anthropogenic) have been removed one by one, to assess where and when the aggregated observations may offer constraints on these processes within CCMs. Lastly, we show results of an additional 31-year simulation from 1980-2010 of GEOS-Chem driven by the MACCity emissions inventory and MERRA reanalysis at 4o by 5o. We sample the model at every WOUDC sonde and flight track from MOZAIC and NASA field campaigns to evaluate which aggregate observations are statistically reflective of long-term trends over the period.

Atmospheric composition↗

Profiles of Reactive Trace Gases over Remote Oceans During ATom

The Atmospheric Tomography (ATom) mission deployed an extensive gas and aerosol payload on the NASA DC-8 aircraft on four campaigns spanning each season. ATom systematically sampled the atmosphere from 0.2 to 12 kilometer altitude, from 85 degrees North Latitude to 65 degrees South Latitude, in both the Pacific and the Atlantic to provide detailed profiles of chemical composition over the remote oceans. We will present profiles of reactive trace species, such as O3, NOx, NOy, HOx, HCHO, and several other short-lived source gases. We will combine these measurements with results from a 0-D box model to show their utility in (1) evaluating gradients in latitude/season, (2) identifying contributions of pollution from long-range and convective transport, and (3) evaluating column measurements from remote sensing satellite instruments.

ISAF↗

[A Study of Data From the Photochemistry of Ozone Loss in the Arctic Region In Summer (POLARIS) Mission]

The Photochemistry of Ozone Loss in the Arctic Region In Summer (POLARIS) mission was designed to investigate the natural summer decrease of stratospheric ozone levels. Both polar regions have large and distinct annual cycles of ozone column amounts. In northern spring, the average level is over 450 Dobson units (DU), decreasing to less than 275 DU by September. In order to cover this period of ozone decrease, POLARIS was conducted in three deployment phases from Fairbanks, Alaska, (650N) during the summer of 1997. The principal measurement platforms were the NASA ER-2 high-altitude aircraft and stratospheric balloons. Additional measurements were provided by ground-based instruments, sondes, and satellites. POLARIS observations included ozone, meteorological variables, particles, long-lived chemicals, and short-lived radicals. During the field deployments, several modeling and theoretical groups participated in flight planning and data evaluation activities. The interpretive studies in this Special Section of the Journal of Geophysical Research are a first comprehensive examination of the POLARIS data set, addressing stratospheric ozone abundances and its changes; the role of aerosols; details of the photochemistry of reactive species; transport of stratospheric air and the correlations of long-lived species; and measurement intercomparisons.

Newman, Paul A.↗