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

Aerosol sulfate loading and shortwave direct radiative forcing over the North Atlantic Ocean

Shortwave radiative forcing of climate by anthropogenic sulfate aerosols is estimated to be equal in magnitude but opposite in sign to that of greenhouse warming, with a global annual average value of approximately -1 W m{sup -2} uncertain to at least a factor of two. Estimates of the 2 contributions to this forcing by the direct effect are -0.4 W m{sup -2}. It is therefore necessary to accurately and efficiently represent this forcing in climate models, specifically including spatial and temporal variability. Here we explore a method to expedite the process for determining this forcing. The method utilizes an approach where the forcing is computed precisely at several discrete radii (r) and then integrated over an arbitrary aerosol size distribution. Additionally, the forcing is calculated at several values of relative humidity (RH), solar zenith angle (SZA), and aerosol optical thickness ({tau}). The parameters can be interpolated to provide the forcing at specific intermediate values. Alternatively, an empirical relationship between the forcing and the above mentioned variables can be utilized to further reduce computation time. At present, the calculations are restricted to ammonium sulfate particles over an ocean surface. The advantage of the ocean surface is the constant and low albedo compared to the highly variable albedo of land surfaces. Ultimately, the sensitivity of forcing to surface albedo and composition will be included

The influence of cut off lows on sulfate burdens over the North Atlantic during April, 1987

The authors have presented examples from a modeling study of the development of sulfur burdens over North America, the North Atlantic Ocean and Europe during April, 1987 using observation-derived meteorological data to represent the actual conditions for this period, focusing on the influence of cut-off lows on SO{sub 2} and sulfate column burdens over the North Atlantic Ocean. The analysis demonstrates that these systems can serve either as sources or sinks of sulfate, and that the major factor governing their resulting effect is the position during its formative stages relative to (a) sources of moisture, and (b) sulfur emissions, which regulates the availability of sulfur, cloud liquid water for sulfur oxidation, and the amount of precipitation for sulfate removal produced in the later stages of the life cycle

Tracing water column euxinia in Eastern Mediterranean Sapropels S5 and S7

Sapropels S5 and S7 formed in the semi-enclosed Eastern Mediterranean Sea (EMS) during peak interglacial periods MIS5e and MIS7a, respectively, are considered among the most strongly developed Quaternary sapropels. This study investigates the redox dynamics of the water column during their formation, via Fe isotope and Fe speciation studies of cores taken at 2550 m depth at site ODP-967. Both sapropels show an inverse correlation between δ56Fe and FeT/Al, with slopes mostly matching that found for the Black Sea, pointing to a benthic shelf to basin shuttle of Fe and subsequent precipitation of Fe sulphides in euxinic bottom waters. An exception to these Black Sea-type trends occurs during the later, peak, stages of S7, where the negative δ56Fe - FeT/Al slope shallows. Fe speciation studies reveal that the dominant highly reactive Fe phase (FeHR) in the sapropels is pyrite, with Fe (oxyhydr)oxides forming the second major mineral component. Correspondingly, FeHR/FeT plots show increased strengthening of anoxic water conditions during the passage from pre-sapropel sediment into the sapropel. Nevertheless, despite the evidence for euxinic conditions from both Fe isotopes and high Mo concentrations in the sapropel, Fepy/FeHR ratios remain below values commonly used to identify water column euxinia. This apparent contradiction is ascribed to the sedimentary preservation of a high flux of crystalline Fe (oxyhydr)oxide minerals to the basin, which resulted in a relatively low degree of sulphidation, despite the presence of euxinic bottom waters. Thus, the operationally defined ferruginous/euxinic boundary for EMS sapropels is better placed at Fepy/FeHR = 0.6, which is somewhat below the usually ascribed lower limit of 0.7. Consistent with the significant presence of crystalline Fe (oxyhydr)oxides, the change in the δ56Fe - FeT/Al slope during peak S7 is ascribed to an enhanced monsoon-driven flux of detrital Fe(III) oxides from the River Nile into the EMS basin and comcomitant diagenetic sulphidation. Euxinic water column conditions in sapropel S5 and S7 are interpreted here to reflect the positive balance between dissolved sulphide formation and rates of reductive dissolution of Fe (oxyhydr)oxide minerals. Both of these parameters in turn depend on the extent to which water overturn times are reduced and export productivity increased during sapropel formation