An analytic approximation to the Diffusion Coefficient for the periodic Lorentz Gas

An approximate stochastic model for the topological dynamics of the periodic triangular Lorentz gas is constructed. The model, together with an extremum principle, is used to find a closed form approximation to the diffusion coefficient as a function of the lattice spacing. This approximation is superior to the popular Machta and Zwanzig result and agrees well with a range of numerical estimates.Comment: 13 pages, 4 figure

The Tropospheric Distribution and Budget of Ethane

From about 1500 measurements of ethane in the remote troposphere the longitudinally and vertically averaged latitudinal and seasonal variability of ethane was derived. To improve the data coverage, several data sets from literature were included. There are only very few data sets available for the southern hemisphere. Nevertheless, the uncertainty of the average seasonal/latitudinal ethane profile is estimated to less than 30%. The global annually averaged ethane mixing ratio is 860 ppt. There is a strong interhemispheric gradient with an average north/south ratio of 3.5. Within the northern hemisphere there is an average gradient from the highest annual mean value of 2500 ppt around 65°N to about 600 ppt at the equator. In the southern hemisphere there is only a small gradient at low latitudes and at middle and high southern latitudes no significant gradient can be seen. In both hemispheres a significant seasonal cycle with highest mixing ratios in late winter is observed. The ethane source strength needed to balance the atmospheric budget of ethane is estimated to 15.5 Tg/yr, with most of the emissions in the northern hemisphere. An independent estimate of the sources indicate that most of the emissions are due to natural gas losses (6 Tg/yr) and biomass burning (6.4 Tg/yr). This is also compatible with the latitudinal and seasonal variation of the atmospheric ethane removal rates. However, these estimates have substantial uncertainties and it should be noted that the role of the biosphere for the atmospheric budget of ethane is presently not understood