A Difference Version of Nori's Theorem

We consider (Frobenius) difference equations over (F_q(s,t), phi) where phi fixes t and acts on F_q(s) as the Frobenius endomorphism. We prove that every semisimple, simply-connected linear algebraic group G defined over F_q can be realized as a difference Galois group over F_{q^i}(s,t) for some i in N. The proof uses upper and lower bounds on the Galois group scheme of a Frobenius difference equation that are developed in this paper. The result can be seen as a difference analogue of Nori's Theorem which states that G(F_q) occurs as (finite) Galois group over F_q(s).Comment: 29 page

Coupled evolution of BrOx-ClOx-HOx-NOx chemistry during bromine-catalyzed ozone depletion events in the arctic boundary layer

Extensive chemical characterization of ozone (O3) depletion events in the Arctic boundary layer during the TOPSE aircraft mission in March-May 2000 enables analysis of the coupled chemical evolution of bromine (BrOx), chlorine (ClOx), hydrogen oxide (HOx) and nitrogen oxide (NOx) radicals during these events. We project the TOPSE observations onto an O3 chemical coordinate to construct a chronology of radical chemistry during O3 depletion events, and we compare this chronology to results from a photochemical model simulation. Comparison of observed trends in ethyne (oxidized by Br) and ethane (oxidized by Cl) indicates that ClOx chemistry is only active during the early stage Of O3 depletion (O3 > 10 ppbv). We attribute this result to the suppression of BrCl regeneration as O3 decreases. Formaldehyde and peroxy radical concentrations decline by factors of 4 and 2 respectively during O3 depletion and we explain both trends on the basis of the reaction of CH2O with Br. Observed NOx concentrations decline abruptly in the early stages Of O3 depletion and recover as O3 drops below 10 ppbv. We attribute the initial decline to BrNO3 hydrolysis in aerosol, and the subsequent recovery to suppression of BrNO3 formation as O3 drops. Under halogen-free conditions we find that HNO4 heterogeneous chemistry could provide a major NOx sink not included in standard models. Halogen radical chemistry in the model can produce under realistic conditions an oscillatory system with a period of 3 days, which we believe is the fastest oscillation ever reported for a chemical system in the atmosphere

Revisiting global fossil fuel and biofuel emissions of ethane

Recent measurements over the Northern Hemisphere indicate that the long-term decline in the atmospheric burden of ethane (C2H6) has ended and the abundance increased dramatically between 2010 and 2014. The rise in C2H6 atmospheric abundances has been attributed to oil and natural gas extraction in North America. Existing global C2H6 emission inventories are based on outdated activity maps that do not account for current oil and natural gas exploitation regions. We present an updated global C2H6 emission inventory based on 2010 satellite-derived CH4 fluxes with adjusted C2H6 emissions over the U.S. from the National Emission Inventory (NEI 2011). We contrast our global 2010 C2H6 emission inventory with one developed for 2001. The C2H6 difference between global anthropogenic emissions is subtle (7.9 versus 7.2 Tg yr−1), but the spatial distribution of the emissions is distinct. In the 2010 C2H6 inventory, fossil fuel sources in the Northern Hemisphere represent half of global C2H6 emissions and 95% of global fossil fuel emissions. Over the U.S., unadjusted NEI 2011 C2H6 emissions produce mixing ratios that are 14–50% of those observed by aircraft observations (2008–2014). When the NEI 2011 C2H6 emission totals are scaled by a factor of 1.4, the Goddard Earth Observing System Chem model largely reproduces a regional suite of observations, with the exception of the central U.S., where it continues to underpredict observed mixing ratios in the lower troposphere. We estimate monthly mean contributions of fossil fuel C2H6 emissions to ozone and peroxyacetyl nitrate surface mixing ratios over North America of ~1% and ~8%, respectively

Upper tropospheric ozone production from lightning NOx-impacted convection: Smoke ingestion case study from the DC3 campaign

©2015. American Geophysical Union. All Rights Reserved. As part of the Deep Convective Cloud and Chemistry (DC3) experiment, the National Science Foundation/National Center for Atmospheric Research (NCAR) Gulfstream-V (GV) and NASA DC-8 research aircraft probed the chemical composition of the inflow and outflow of two convective storms (north storm, NS, south storm, SS) originating in the Colorado region on 22 June 2012, a time when the High Park wildfire was active in the area. A wide range of trace species were measured on board both aircraft including biomass burning (BB) tracers hydrogen cyanide (HCN) and acetonitrile (ACN). Acrolein, a much shorter lived tracer for BB, was also quantified on the GV. The data demonstrated that the NS had ingested fresh smoke from the High Park fire and as a consequence had a higher VOC OH reactivity than the SS. The SS lofted aged fire tracers along with other boundary layer ozone precursors and was more impacted by lightning NOx (LNOx) than the NS. The NCAR master mechanism box model was initialized with measurements made in the outflow of the two storms. The NS and SS were predicted to produce 11 and 14ppbv of O3, respectively, downwind of the storm over 2days. Sensitivity tests revealed that the ozone production potential of the SS was highly dependent on LNOx. Normalized excess mixing ratios, ΔX/ΔCO, for HCN and ACN were determined in both the fire plume and the storm outflow and found to be 7.0±0.5 and 2.3±0.5pptvppbv-1, respectively, and 1.4±0.3pptvppbv-1 for acrolein in the outflow only

Ozone depletion events observed in the high latitude surface layer during the TOPSE aircraft program

During the Tropospheric Ozone Production about the Spring Equinox (TOPSE) aircraft program, ozone depletion events (ODEs) in the high latitude surface layer were investigated using lidar and in situ instruments. Flight legs of 100 km or longer distance were flown 32 times at 30 m altitude over a variety of regions north of 58° between early February and late May 2000. ODEs were found on each flight over the Arctic Ocean but their occurrence was rare at more southern latitudes. However, large area events with depletion to over 2 km altitude in one case were found as far south as Baffin Bay and Hudson Bay and as late as 22 May. There is good evidence that these more southern events did not form in situ but were the result of export of ozone‐depleted air from the surface layer of the Arctic Ocean. Surprisingly, relatively intact transport of ODEs occurred over distances of 900–2000 km and in some cases over rough terrain. Accumulation of constituents in the frozen surface over the dark winter period cannot be a strong prerequisite of ozone depletion since latitudes south of the Arctic Ocean would also experience a long dark period. Some process unique to the Arctic Ocean surface or its coastal regions remains unidentified for the release of ozone‐depleting halogens. There was no correspondence between coarse surface features such as solid ice/snow, open leads, or polynyas with the occurrence of or intensity of ozone depletion over the Arctic or subarctic regions. Depletion events also occurred in the absence of long‐range transport of relatively fresh “pollution” within the high latitude surface layer, at least in spring 2000. Direct measurements of halogen radicals were not made. However, the flights do provide detailed information on the vertical structure of the surface layer and, during the constant 30 m altitude legs, measurements of a variety of constituents including hydroxyl and peroxy radicals. A summary of the behavior of these constituents is made. The measurements were consistent with a source of formaldehyde from the snow/ice surface. Median NOx in the surface layer was 15 pptv or less, suggesting that surface emissions were substantially converted to reservoir constituents by 30 m altitude and that ozone production rates were small (0.15–1.5 ppbv/d) at this altitude. Peroxyacetylnitrate (PAN) was by far the major constituent of NOy in the surface layer independent of the ozone mixing ratio