Sabine Attinger

Temporal behavior of a solute cloud in a heterogeneous porous medium: 1. Point‐like injection

We investigate the temporal behavior of transport coefficients in a model for transport of a solute through a spatially heterogeneous saturated aquifer. In the framework of a stochastic approach we derive explicit expressions for the temporal behavior of the center-of-mass velocity and the dispersion of the concentration distribution after a point-like injection of solute at time t=0, using a second-order perturbation expansion. The model takes into account local variations in the hydraulic conductivity (which, in turn, induce local fluctuations in the groundwater flow velocities) and in the chemical adsorption properties of the medium (which lead to a spatially varying local retardation factor). In the given perturbation theory approach the various heterogeneity-induced contributions can be systematically traced back to fluctuations in these quantities and to cross correlations between them. We analyze two conceptually different definitions for the resulting dispersion coefficient: the “effective”dispersion coefficient which is derived from the average over the centered second moments of the spatial concentration distributions in every realization and the “ensemble” dispersion coefficient which follows from the second moment of the ensemble-averaged concentration distribution. The first quantity characterizes the dispersion in a typical realization of the medium, whereas the second one describes the (formal) dispersion properties of the ensemble as a whole. We give explicit analytic expressions for both quantities as functions of time and show that for finite times their temporal behavior is remarkably different. The ensemble dispersion coefficient which is usually evaluated in the literature considerably overestimates the dispersion typically found in one given realization of the medium. From our explicit results we identify two relevant timescales separating regimes of qualitatively and quantitatively different temporal behavior: The shorter of the two scales is set by the advective transport of the solute cloud over one disorder correlation length, whereas the second, much larger one, is related to the dispersive spreading over the same distance. Only for times much larger than this second scale, do the effective and the ensemble dispersion coefficient become equivalent because of mixing caused by the local transversal dispersion. The formulae are applied to the Borden experiment data. It is concluded that the observed dispersion coefficient matches the effective dispersion coefficient at finite times proposed in this paper very well.

Temporal behavior of a solute cloud in a heterogeneous porous medium: 2. Spatially extended injection

We investigate the temporal behavior of transport coefficients in a stochastic model for transport of a solute through a spatially heterogeneous saturated aquifer. While the first of these two companion papers [Dentz et al., this issue] investigated a situation characterized by a point-like solute injection, we now focus on the case of spatially extended solute sources. The analysis of the finite time behavior of the transport coefficients makes it necessary to distinguish between two fundamentally different quantities characterizing the solute dispersion. We define an “effective” dispersion coefficient which is derived from the average over the centered second moments of the spatial concentration distributions in every realization and an “ensemble” dispersion coefficient which follows from the second moment of the ensemble-averaged concentration distribution. While the two quantities are equivalent in the asymptotic limit of infinite times or infinitely extended sources, they are qualitatively and quantitatively different for the more realistic situation of finite times and finite source extent. We demonstrate that in this case the ensemble quantity, used more or less implicitly in most of the previous studies, overestimates the true dispersion of the plume. Using a second-order perturbation theory approach, we derive explicit solutions for the temporal behavior of the dispersion coefficients for various types of isotropic and anisotropic initial conditions. We identify the relevant timescales which separate regimes of different temporal behavior and apply our formulae to the Borden experiment data. We find a good agreement between theory and experiment if we compare the observed dispersion with the appropriate effective dispersion coefficient (including the leading effects of the local dispersion), whereas the ensemble dispersion coefficient commonly used in the literature to analyze these data overestimates the experimental results considerably.

Diversity Promotes Temporal Stability across Levels of Ecosystem Organization in Experimental Grasslands

The diversity–stability hypothesis states that current losses of biodiversity can impair the ability of an ecosystem to dampen the effect of environmental perturbations on its functioning. Using data from a long-term and comprehensive biodiversity experiment, we quantified the temporal stability of 42 variables characterizing twelve ecological functions in managed grassland plots varying in plant species richness. We demonstrate that diversity increases stability i) across trophic levels (producer, consumer), ii) at both the system (community, ecosystem) and the component levels (population, functional group, phylogenetic clade), and iii) primarily for aboveground rather than belowground processes. Temporal synchronization across studied variables was mostly unaffected with increasing species richness. This study provides the strongest empirical support so far that diversity promotes stability across different ecological functions and levels of ecosystem organization in grasslands.

Catchments as reactors: a comprehensive approach for water fluxes and solute turnover

Sustainable water quality management requires a profound understanding of water fluxes (precipitation, run-off, recharge, etc.) and solute turnover such as retention, reaction, transformation, etc. at the catchment or landscape scale. The Water and Earth System Science competence cluster (WESS, http://www.wess.info/) aims at a holistic analysis of the water cycle coupled to reactive solute transport, including soil–plant–atmosphere and groundwater–surface water interactions. To facilitate exploring the impact of land-use and climate changes on water cycling and water quality, special emphasis is placed on feedbacks between the atmosphere, the land surface, and the subsurface. A major challenge lies in bridging the scales in monitoring and modeling of surface/subsurface versus atmospheric processes. The field work follows the approach of contrasting catchments, i.e. neighboring watersheds with different land use or similar watersheds with different climate. This paper introduces the featured catchments and explains methodologies of WESS by selected examples.

Multiscale modelling and simulation

I Mathematical Methods.- Some Recent Progress in Multiscale Modeling.- Homogenization Method for Transport of DNA Particles in Heterogeneous Arrays.- Metastability, conformation dynamics, and transition pathways in complex systems.- Nonlinear Dynamics Analysis through Molecular Dynamics Simulations.- Exploration of coarse free energy surfaces templated on continuum numerical methods.- Damping factors for the gap-tooth scheme.- II Materials Science.- Multiscale Aspects of Polymer Simulations.- Polymers near a Surface: An ab initio Density Functional based Multiscale Modeling Approach.- Dual Resolution Molecular Simulation of Bisphenol-A Polycarbonate Adsorption onto Nickel (111): Chain Length Effects.- Stress and energy flow field near a rapidly propagating mode I crack.- A Peierls Criterion for Deformation Twinning at a Mode II Crack.- III Physics/Chemistry/Fluid Dynamics/Biology.- Simulation of Transport in Partially Miscible Binary Fluids: Combination of Semigrandcanonical Monte Carlo and Molecular Dynamics Methods.- Computer simulations of SiO2 and GeO2.- Large Scale Density Functional Calculations.- Dispersion corrected density functionals applied to the water naphthalene cluster.- Flow of Aqueous Solutions in Carbon Nanotubes.- Continuum-particle hybrid methods for dense fluids.- Dissipative Particle Dynamics for Modeling Complex Fluidics.- Population balance modeling of synthesis of nanoparticles in aerosol flame reactors.- Modelling gene expression using stochastic simulation.- Color Plates.

Multiscale and Multivariate Evaluation of Water Fluxes and States over European River Basins

AbstractAccurately predicting regional-scale water fluxes and states remains a challenging task in contemporary hydrology. Coping with this grand challenge requires, among other things, a model that makes reliable predictions across scales, locations, and variables other than those used for parameter estimation. In this study, the mesoscale hydrologic model (mHM) parameterized with the multiscale regionalization technique is comprehensively tested across 400 European river basins. The model fluxes and states, constrained using the observed streamflow, are evaluated against gridded evapotranspiration, soil moisture, and total water storage anomalies, as well as local-scale eddy covariance observations. This multiscale verification is carried out in a seamless manner at the native resolutions of available datasets, varying from 0.5 to 100 km. Results of cross-validation tests show that mHM is able to capture the streamflow dynamics adequately well across a wide range of climate and physiographical character...

Transport of a decay chain in homogenous porous media: analytical solutions

With the aid of integral transforms, analytical solutions for the transport of a decay chain in homogenous porous media are derived. Unidirectional steady-state flow and radial steady-state flow in single and multiple porosity media are considered. At least in Laplace domain, all solutions can be written in closed analytical formulae. Partly, the solutions can also be inverted analytically. If not, analytical calculation of the steady-state concentration distributions, evaluation of temporal moments and numerical inversion are still possible. Formulae for several simple boundary conditions are given and visualized in this paper. The derived novel solutions are widely applicable and are very useful for the validation of numerical transport codes.

How Do Earthworms, Soil Texture and Plant Composition Affect Infiltration along an Experimental Plant Diversity Gradient in Grassland?

Background Infiltration is a key process in determining the water balance, but so far effects of earthworms, soil texture, plant species diversity and their interaction on infiltration capacity have not been studied. Methodology/Principal Findings We measured infiltration capacity in subplots with ambient and reduced earthworm density nested in plots of different plant species (1, 4, and 16 species) and plant functional group richness and composition (1 to 4 groups; legumes, grasses, small herbs, tall herbs). In summer, earthworm presence significantly increased infiltration, whereas in fall effects of grasses and legumes on infiltration were due to plant-mediated changes in earthworm biomass. Effects of grasses and legumes on infiltration even reversed effects of texture. We propose two pathways: (i) direct, probably by modifying the pore spectrum and (ii) indirect, by enhancing or suppressing earthworm biomass, which in turn influenced infiltration capacity due to change in burrowing activity of earthworms. Conclusions/Significance Overall, the results suggest that spatial and temporal variations in soil hydraulic properties can be explained by biotic processes, especially the presence of certain plant functional groups affecting earthworm biomass, while soil texture had no significant effect. Therefore biotic parameters should be taken into account in hydrological applications.

Large Scale Mixing for Immiscible Displacement in Heterogeneous Porous Media

We derive a large scale mixing parameter for a displacement process of one fluid by another immiscible one in a two-dimensional heterogeneous porous medium. The mixing of the displacing fluid saturation due to the heterogeneities of the permeabilities is captured by a dispersive flux term in the large scale homogeneous flow equation. By making use of the stochastic approach we develop a definition of the dispersion coefficient and apply a Eulerian perturbation theory to determine explicit results to second order in the fluctuations of the total velocity. We apply this method to a uniform flow configuration as well as to a radial one. The dispersion coefficient is found to depend on the mean total velocity and can therefore be time varying. The results are compared to numerical multi-realization calculations. We found that the use of single phase flow stochastics cannot capture all phenomena observed in the numerical simulations.

Incorporating dynamic root growth enhances the performance of Noah‐MP at two contrasting winter wheat field sites

Interactions between the soil, the vegetation, and the atmospheric boundary layer require close attention when predicting water fluxes in the hydrogeosystem, agricultural systems, weather, and climate. However, land-surface schemes used in large-scale models continue to show deficiencies in consistently simulating fluxes of water and energy from the subsurface through vegetation layers to the atmosphere. In this study, the multiphysics version of the Noah land-surface model (Noah-MP) was used to identify the processes, which are most crucial for a simultaneous simulation of water and heat fluxes between land surface and the lower atmosphere. Comprehensive field data sets of latent and sensible heat fluxes, ground heat flux, soil moisture, and leaf area index from two contrasting field sites in South-West Germany are used to assess the accuracy of simulations. It is shown that an adequate representation of vegetation-related processes is the most important control for a consistent simulation of energy and water fluxes in the soil-plant-atmosphere system. In particular, using a newly implemented submodule to simulate root growth dynamics has enhanced the performance of Noah-MP. We conclude that further advances in the representation of leaf area dynamics and root/soil moisture interactions are the most promising starting points for improving the simulation of feedbacks between the subsoil, land surface and atmosphere in fully coupled hydrological and atmospheric models.