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

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

Observed OH and HO2 in the upper troposphere suggest a major source from convective injection of peroxides

ER-2 aircraft observations of OH and HO2 concentrations in the upper troposphere during the NASA/STRAT campaign are interpreted using a photochemical model constrained by local observations of O3, H2O, NO, CO, hydrocarbons, albedo and overhead ozone column. We find that the reaction Q(¹D) + H2O is minor compared to acetone photolysis as a primary source of HOx (= OH + peroxy radicals) in the upper troposphere. Calculations using a diel steady state model agree with observed HOx 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 CH3OOH and H2O2 from the boundary layer to the upper troposphere could resolve the discrepancy. These injections of HOx reservoirs cause large HOx 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 HOx in the upper troposphere. Simultaneous measurements of peroxides, formaldehyde and acetone along with OH and HO2 are needed to test our hypothesis.Engineering and Applied Science

Role of regional wetland emissions in atmospheric methane variability

Atmospheric methane (CH4) accounts for ~20% of the total direct anthropogenic radiative forcing by long-lived greenhouse gases. Surface observations show a pause (1999-2006) followed by a resumption in CH4 growth, which remain largely unexplained. Using a land surface model, we estimate wetland CH4 emissions from 1993 to 2014 and study the regional contributions to changes in atmospheric CH4. Atmospheric model simulations using these emissions, together with other sources, compare well with surface and satellite CH4 data. Modelled global wetland emissions vary by ±3%/yr (σ=4.8 Tg), mainly due to precipitation-induced changes in wetland area, but the integrated effect makes only a small contribution to the pause in CH4 growth from 1999 to 2006. Increasing temperature, which increases wetland area, drives a long-term trend in wetland CH4 emissions of +0.2%/yr (1999 to 2014). The increased growth post-2006 was partly caused by increased wetland emissions (+3%), mainly from Tropical Asia, Sourthern Africa and Australia

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

Factors regulating ozone over the United States and its export to the global atmosphere

The factors regulating summertime O3 over the United States and its export to the global atmosphere are examined with a 3-month simulation using a continental scale, three-dimensional photochemical model. It is found that reducing NOx emissions by 50% from 1985 levels would decrease rural O3 concentrations over the eastern United States by about 15% under almost all meteorological conditions, while reducing anthropogenic hydrocarbon emissions by 50% would have less than a 4% effect except in the largest urban plumes. The strongly NOx-limited conditions in the model reflect the dominance of rural areas as sources of O3 on the regional scale. The correlation between O3 concentrations and temperature observed at eastern U.S. sites is attributed in part to the association of high temperatures with regional stagnation, and in part to an actual dependence of O3 production on temperature driven primarily by conversion of NOx to peroxyacetylnitrate (PAN). The net number of O3 molecules produced per molecule of NOx consumed (net O3 production efficiency, accounting for both chemical production and chemical loss of O3) has a mean value of 6.3 in the U.S. boundary layer; it is 3 times higher in the western United States than in the east because of lower NOx concentrations in the west. Approximately 70% of the net chemical production of O3 in the U.S. boundary layer is exported (the rest is deposited). Only 6% of the NOx emitted in the United States is exported out of the U.S. boundary layer as NOx or PAN, but this export contributes disproportionately to total U.S. influence on global tropospheric O3because of the high O3 production efficiency per unit NOx in the remote troposphere. It is estimated that export of U.S. pollution supplies 8 Gmol O3 d−1 to the global troposphere in summer, including 4 Gmol d−1 from direct export of O3 out of the U.S. boundary layer and 4 Gmol d−1 from production of O3 downwind of the United States due to exported NOx. This U.S. pollution source can be compared to estimates of 18–28 Gmol d−1 for the cross-tropopause transport of O3 over the entire northern hemisphere in summer

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

The masterpieces of John Forbes Nash Jr.

In this set of notes I follow Nash’s four groundbreaking works on real algebraic manifolds, on isometric embeddings of Riemannian manifolds and on the continuity of solutions to parabolic equations. My aim has been to stay as close as possible to Nash’s original arguments, but at the same time present them with a more modern language and notation. Occasionally I have also provided detailed proofs of the points that Nash leaves to the reader

Three-dimensional simulations of atmospheric methyl chloroform: Effect of an ocean sink

The model simulates the 5-year record of observations made at the five ALE sampling sites to generally within ±5% of the observed mean. The calculated average global lifetime of methyl chloroform is 5.7±0.3 yrs. The estimated global mean OH concentration is 6.5±0.4×105 cm-3. However, the inclusion of the ocean sink does not significantly improve the simulation of the observed interhemispheric gradient of methyl chloroform. Atmospheric transport dominates the simulated CH3CCl3 seasonal cycle throughout the northern hemisphere but is less important in the southern hemisphere. -from Author