A semi-empirical dynamic soil acidification model for use in spatially explicit integrated assessment models for Europe

A semi-empirical soil acidification model was developed for use in integrated assessment models on a European scale. The model simulates the time development of base saturation and aluminium concentration using an empirical relationship with pH. An accompanying data set was developed by overlaying European maps of soils, land use, climate and altitude followed by a procedure that aggragates the input data over soil-texture combinations in each EMEP 150 km x 150 km grid cell. Model tests show that themodel gives results comparable to the SMART model, although it overestimates initial base saturation in some areas with high acid input and simulates a faster recovery from acidification than SMART

Remarks on NonHamiltonian Statistical Mechanics: Lyapunov Exponents and Phase-Space Dimensionality Loss

The dissipation associated with nonequilibrium flow processes is reflected by the formation of strange attractor distributions in phase space. The information dimension of these attractors is less than that of the equilibrium phase space, corresponding to the extreme rarity of nonequilibrium states. Here we take advantage of a simple model for heat conduction to demonstrate that the nonequilibrium dimensionality loss can definitely exceed the number of phase-space dimensions required to thermostat an otherwise Hamiltonian system.Comment: 5 pages, 2 figures, minor typos correcte

Device measures conductivity and velocity of ionized gas streams

Coaxial arrangement of primary coil and two sensing secondary coils contained inside slender quartz tube inserted into ionized stream permits simultaneous determination of conductivity and linear velocity. System results agree favorably with theory

Lyapunov instability of fluids composed of rigid diatomic molecules

We study the Lyapunov instability of a two-dimensional fluid composed of rigid diatomic molecules, with two interaction sites each, and interacting with a WCA site-site potential. We compute full spectra of Lyapunov exponents for such a molecular system. These exponents characterize the rate at which neighboring trajectories diverge or converge exponentially in phase space. Quam. These exponents characterize the rate at which neighboring trajectories diverge or converge exponentially in phase space. Qualitative different degrees of freedom -- such as rotation and translation -- affect the Lyapunov spectrum differently. We study this phenomenon by systematically varying the molecular shape and the density. We define and evaluate ``rotation numbers'' measuring the time averaged modulus of the angular velocities for vectors connecting perturbed satellite trajectories with an unperturbed reference trajectory in phase space. For reasons of comparison, various time correlation functions for translation and rotation are computed. The relative dynamics of perturbed trajectories is also studied in certain subspaces of the phase space associated with center-of-mass and orientational molecular motion.Comment: RevTeX 14 pages, 7 PostScript figures. Accepted for publication in Phys. Rev.

Long-term development of acid deposition (1880-2030) in sensitive freshwater regions in Europe

Time series of the deposition of acidifying substances are a pre-requisite for the study of the acidification and recovery of ecosystems such as surface waters. This paper reports the derivation and calculation of deposition trends of the potentially acidifying compounds SO2, NOx and NH3 in sensitive freshwater regions in Europe studied in the EU-funded RECOVER: 2010 project. The time interval covered is 151 years: from 1880, which can be considered as the pre-industrial era in most countries, to 2030, taking into account the consequences of current emission reduction agreements in Europe. The historic and predicted emissions for European countries are used to calculate the deposition development in the study areas, using meteorologically averaged atmospheric source-receptor transfer coefficients derived from the EMEP Lagrangian acid deposition model. These time series were used as driving forces for the application of the dynamic acidification model MAGIC to study the acidification and recovery of sensitive freshwater ecosystems in Europe

Sulfur deposition onto European forests: throughfall data and model estimates

The assessment of atmospheric sulfur deposition to forest is difficult because of its complex aerodynamic structure. Therefore, atmospheric deposition of sulfur to forest is often estimated by means of measuring throughfall fluxes onto the forest floor. In this paper, reported measurements of throughfall fluxes in European forests are analyzed. These fluxes are compared to deposition to bulk collectors located in nearby open land, to get an idea of the filtering efficiency of forests. In addition, fluxes are compared with deposition estimates from a long‐range transport model of air pollutants, linked to an emission generation model. According to reported measurements from 52 European conifer stands, we found that the sulfur flux was 3.8 ± 2.3 times greater onto the forest floor than onto precipitation collectors. In a similar data set of 13 deciduous stands this ratio was 2.3 ± 0.9. The ratio of throughfall flux to model estimate was 1.8 ± 0.9 in coniferous stands and 0.9 ± 0.3 in deciduous stands. For sites that are located in moderately to highly sulfur polluted areas, it is assumed that throughfall fluxes give a good estimation of the atmospheric sulfur deposition. We conclude that (1) sulfur deposition to forests is 1.5 to 6 times higher than deposition to smooth receptor surfaces due to an efficient filtering by the forest canopy, (2) average annual sulfur deposition at a given location is 50–100% greater on conifers than on deciduous trees, (3) the existing European scale model that links sulfur deposition to the pollution generation processes is quite accurate as far as deciduous forests are concerned, and (4) the model underestimates deposition to coniferous forest

Time-reversed symmetry and covariant Lyapunov vectors for simple particle models in and out of thermal equilibrium

Recently, a new algorithm for the computation of covariant Lyapunov vectors and of corresponding local Lyapunov exponents has become available. Here we study the properties of these still unfamiliar quantities for a number of simple models, including an harmonic oscillator coupled to a thermal gradient with a two-stage thermostat, which leaves the system ergodic and fully time reversible. We explicitly demonstrate how time-reversal invariance affects the perturbation vectors in tangent space and the associated local Lyapunov exponents. We also find that the local covariant exponents vary discontinuously along directions transverse to the phase flow.Comment: 13 pages, 11 figures submitted to Physical Review E, 201

Harmonic oscillators in the Nos\'e - Hoover thermostat

We study the dynamics of an ensemble of non-interacting harmonic oscillators in a nonlinear dissipative environment described by the Nos\'e - Hoover model. Using numerical simulation we find the histogram for total energy, which agrees with the analysis of the Nos\'e - Hoover equations effected with the method of averaging. The histogram does not correspond to Gibbs' canonical distribution. We have found oscillations at frequency proportional to $\sqrt{\alpha/m}$, $\alpha$ the dissipative parameter of thermostat and $m$ the characteristic mass of particle, about the stationary state corresponding to equilibrium. The oscillations could have an important bearing upon the analysis of simulating molecular dynamics in the Nos\'e - Hoover thermostat.Comment: 7 pages, 4 figure

Second-Law Irreversibility and Phase-Space Dimensionality Loss from Time-Reversible Nonequilibrium Steady-State Lyapunov Spectra

We consider steady-state nonequilibrium many-body flows of mass and momentum. For several such diffusive and viscous flows we estimate the phase-space strange-attractor Lyapunov dimensions from the complete spectrum of Lyapunov exponents. We vary the number of particles and the number of ther mostated degrees of freedom, as well as the deviation from equilibrium. The resulting Lyapunov spectra provide numerical evidence that the fractal dimensionality loss in such systems remains extensive in a properly defined nonequilibrium analog of the equilibrium large-system thermodynamic limit. The data also suggest a variational principle in the vicinity of nonequilibrium steady states. PACS number(s): 05.45. +b, 05.70.L