Periods and Feynman integrals

We consider multi-loop integrals in dimensional regularisation and the corresponding Laurent series. We study the integral in the Euclidean region and where all ratios of invariants and masses have rational values. We prove that in this case all coefficients of the Laurent series are periods.Comment: 22 pages, appendix added, version to be publishe

A proof of the Grothendieck-Serre conjecture on principal bundles over regular local rings containing infinite fields

Let R be a regular local ring, containing an infinite field. Let G be a reductive group scheme over R. We prove that a principal G-bundle over R is trivial, if it is trivial over the fraction field of R.Comment: Section "Formal loops and affine Grassmannians" is removed as this is now covered in arXiv:1308.3078. Exposition is improved and slightly restructured. Some minor correction

Observed OH and HO_2 in the upper troposphere suggest a major source from convective injection of peroxides

ER-2 aircraft observations of OH and HO_2 concentrations in the upper troposphere during the NASA/STRAT campaign are interpreted using a photochemical model constrained by local observations of O_3, H_2O, NO, CO, hydrocarbons, albedo and overhead ozone column. We find that the reaction Q(^(1)D) + H_2O is minor compared to acetone photolysis as a primary source of HO_x (= OH + peroxy radicals) in the upper troposphere. Calculations using a diel steady state model agree with observed HO_x concentrations in the lower stratosphere and, for some flights, in the upper troposphere. However, for other flights in the upper troposphere, the steady state model underestimates observations by a factor of 2 or more. These model underestimates are found to be related to a recent (< 1 week) convective origin of the air. By conducting time-dependent model calculations along air trajectories determined for the STRAT flights, we show that convective injection of CH_3OOH and H_2O_2 from the boundary layer to the upper troposphere could resolve the discrepancy. These injections of HO_x reservoirs cause large HO_x increases in the tropical upper troposphere for over a week downwind of the convective activity. We propose that this mechanism provides a major source of HO_x in the upper troposphere. Simultaneous measurements of peroxides, formaldehyde and acetone along with OH and HO_2 are needed to test our hypothesis

Statistical inference of OH concentrations and air mass dilution rates from successive observations of non-methane hydrocarbons in single air masses

Bayesian inference has been used to determine rigorous estimates of hydroxyl radical concentrations () and air mass dilution rates (K) averaged following air masses between linked observations of nonmethane hydrocarbons (NMHCs) spanning the North Atlantic during the Intercontinental Transport and Chemical Transformation (ITCT)-Lagrangian-2K4 experiment. The Bayesian technique obtains a refined (posterior) distribution of a parameter given data related to the parameter through a model and prior beliefs about the parameter distribution. Here, the model describes hydrocarbon loss through OH reaction and mixing with a background concentration at rate K. The Lagrangian experiment provides direct observations of hydrocarbons at two time points, removing assumptions regarding composition or sources upstream of a single observation. The estimates are sharpened by using many hydrocarbons with different reactivities and accounting for their variability and measurement uncertainty. A novel technique is used to construct prior background distributions of many species, described by variation of a single parameter . This exploits the high correlation of species, related by the first principal component of many NMHC samples. The Bayesian method obtains posterior estimates of , K and following each air mass. Median values are typically between 0.5 and 2.0 × 106 molecules cm−3, but are elevated to between 2.5 and 3.5 × 106 molecules cm−3, in low-level pollution. A comparison of estimates from absolute NMHC concentrations and NMHC ratios assuming zero background (the “photochemical clock” method) shows similar distributions but reveals systematic high bias in the estimates from ratios. Estimates of K are ∼0.1 day−1 but show more sensitivity to the prior distribution assumed

A quantitative assessment of uncertainties affecting estimates of global mean OH derived from methyl chloroform observations

We estimated the global abundance of OH by interpreting observations of methyl chloroform (MCF) from two networks using an inverse technique and a 3-D chemical transport model driven by assimilated meteorology. Our inversion approach optimized both the emissions of MCF and the abundance of OH. Because of an a priori overestimate of the latitudinal gradient by the model in the standard setup, the inversion lowers global emissions and the global sink due to OH. Optimized emissions are about 10 % lower than published inventories on average between 1988 and 1994, and the decrease in the sink suggested by the inversion implies an average lifetime for MCF (with respect to tropospheric OH) of about 6.9 years, 11-21 % longer than the 5.7-6.2 years reported in previous studies. Our results are driven by the need to match the observed latitudinal gradient of MCF while balancing the MCF budget. We find that these results depend on the a priori constraint placed on MCF emissions, the rate of interhemispheric mixing in the model, the interhemispheric distribution of OH assumed, and the model simulation of pollution events. Since these factors are highly uncertain, we believe that the level of understanding on global lifetimes of pollutants removed by OH is lower than might be implied by the narrow range of estimates for MCF lifetime in the literature. 2

Reactive mercury in the troposphere: Model formation and results for Florida, the northeastern United States, and the Atlantic Ocean

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/95402/1/jgrd13669.pd

Variations of tropospheric methane over Japan during 1988–2010

We present observations of CH4 concentrations from the lower to upper troposphere (LT and UT) over Japan during 1988–2010 based on aircraft measurements from the Tohoku University (TU). The analysis is aided by simulation results using an atmospheric chemistry transport model (i.e. ACTM). Tropospheric CH4 over Japan shows interannual and seasonal variations that are dependent on altitudes, primarily reflecting differences in air mass origins at different altitudes. The long-term trend and interannual variation of CH4 in the LT are consistent with previous reports of measurements at surface baseline stations in the northern hemisphere. However, those in the UT show slightly different features from those in the LT. In the UT, CH4 concentrations show a seasonal maximum in August due to efficient transport of air masses influenced by continental CH4 sources, while LT CH4 reaches its seasonal minimum during summer due to enhanced chemical loss. Vertical profiles of the CH4 concentrations also vary with season, reflecting the seasonal cycles at the respective altitudes. In summer, transport of CH4-rich air from Asian regions elevates UT CH4 levels, forming a uniform vertical profile above the mid-troposphere. On the other hand, CH4 decreases nearly monotonically with altitude in winter–spring. The ACTM simulations with different emission scenarios reproduce general features of the tropospheric CH4 variations over Japan. Tagged tracer simulations using the ACTM indicate substantial contributions of CH4 sources in South Asia and East Asia to the summertime high CH4 values observed in the UT. This suggests that our observations over Japan are highly sensitive to CH4 emission signals particularly from Asia

Rising atmospheric methane: 2007-2014 growth and isotopic shift

From 2007 to 2013, the globally averaged mole fraction of methane in the atmosphere increased by 5.7±1.2ppb yr$^{-1}$. Simultaneously, $\delta^{13}$C$_\text{CH4}$ (a measure of the $^{13}$C/$^{12}$C isotope ratio in methane) has shifted to significantly more negative values since 2007. Growth was extreme in 2014, at 12.5±0.4ppb, with a further shift to more negative values being observed at most latitudes. The isotopic evidence presented here suggests that the methane rise was dominated by significant increases in biogenic methane emissions, particularly in the tropics, for example, from expansion of tropical wetlands in years with strongly positive rainfall anomalies or emissions from increased agricultural sources such as ruminants and rice paddies. Changes in the removal rate of methane by the OH radical have not been seen in other tracers of atmospheric chemistry and do not appear to explain short-term variations in methane. Fossil fuel emissions may also have grown, but the sustained shift to more $^{13}$C-depleted values and its significant interannual variability, and the tropical and Southern Hemisphere loci of post-2007 growth, both indicate that fossil fuel emissions have not been the dominant factor driving the increase. A major cause of increased tropical wetland and tropical agricultural methane emissions, the likely major contributors to growth, may be their responses to meteorological change.This work was supported by the UK Natural Environment Research Council projects NE/N016211/1 The Global Methane Budget, NE/M005836/1 Methane at the edge, NE/K006045/1 The Southern Methane Anomaly and NE/I028874/1 MAMM. We thank the UK Meteorological Office for flask collection and hosting the continuous measurement at Ascension, the Ascension Island Government for essential support, and Thumeka Mkololo for flask collection in Cape Tow