Energy consistent discontinuous Galerkin methods for the Navier–Stokes–Korteweg system

We design consistent discontinuous Galerkin finite element schemes for the approximation of the Euler-Korteweg and the Navier-Stokes-Korteweg systems. We show that the scheme for the Euler-Korteweg system is energy and mass conservative and that the scheme for the Navier-Stokes-Korteweg system is mass conservative and monotonically energy dissipative. In this case the dissipation is isolated to viscous effects, that is, there is no numerical dissipation. In this sense the methods are consistent with the energy dissipation of the continuous PDE systems. - See more at: http://www.ams.org/journals/mcom/2014-83-289/S0025-5718-2014-02792-0/home.html#sthash.rwTIhNWi.dpuf

Intensive agriculture reduces soil biodiversity across Europe

Soil biodiversity plays a key role in regulating the processes that underpin the delivery of ecosystem goods and services in terrestrial ecosystems. Agricultural intensification is known to change the diversity of individual groups of soil biota, but less is known about how intensification affects biodiversity of the soil food web as a whole, and whether or not these effects may be generalized across regions. We examined biodiversity in soil food webs from grasslands, extensive, and intensive rotations in four agricultural regions across Europe: in Sweden, the UK, the Czech Republic and Greece. Effects of land-use intensity were quantified based on structure and diversity among functional groups in the soil food web, as well as on community-weighted mean body mass of soil fauna. We also elucidate land-use intensity effects on diversity of taxonomic units within taxonomic groups of soil fauna. We found that between regions soil food web diversity measures were variable, but that increasing land-use intensity caused highly consistent responses. In particular, land-use intensification reduced the complexity in the soil food webs, as well as the community-weighted mean body mass of soil fauna. In all regions across Europe, species richness of earthworms, Collembolans, and oribatid mites was negatively affected by increased land-use intensity. The taxonomic distinctness, which is a measure of taxonomic relatedness of species in a community that is independent of species richness, was also reduced by land-use intensification. We conclude that intensive agriculture reduces soil biodiversity, making soil food webs less diverse and composed of smaller bodied organisms. Land-use intensification results in fewer functional groups of soil biota with fewer and taxonomically more closely related species. We discuss how these changes in soil biodiversity due to land-use intensification may threaten the functioning of soil in agricultural production systems.

Simple measures of climate, soil properties and plant traits predict national scale grassland soil carbon stocks

1. Soil carbon (C) storage is a key ecosystem service. Soil C stocks play a vital role in soil fertility and climate regulation, but the factors that control these stocks at regional and national scales are unknown, particularly when their composition and stability are considered. As a result, their mapping relies on either unreliable proxy measures or laborious direct measurements. 2. Using data from an extensive national survey of English grasslands we show that surface soil (0-7cm) C stocks in size fractions of varying stability can be predicted at both regional and national scales from plant traits and simple measures of soil and climatic conditions. 3. Soil C stocks in the largest pool, of intermediate particle size (50-250 µm), were best explained by mean annual temperature (MAT), soil pH and soil moisture content. The second largest C pool, highly stable physically and biochemically protected particles (0.45-50 µm), was explained by soil pH and the community abundance weighted mean (CWM) leaf nitrogen (N) content, with the highest soil C stocks under N rich vegetation. The C stock in the small active fraction (250-4000 µm) was explained by a wide range of variables: MAT, mean annual precipitation, mean growing season length, soil pH and CWM specific leaf area; stocks were higher under vegetation with thick and/or dense leaves. 4. Testing the models describing these fractions against data from an independent English region indicated moderately strong correlation between predicted and actual values and no systematic bias, with the exception of the active fraction, for which predictions were inaccurate. 5. Synthesis and Applications: Validation indicates that readily available climate, soils and plant survey data can be effective in making local- to landscape-scale (1-100,000 km2) soil C stock predictions. Such predictions are a crucial component of effective management strategies to protect C stocks and enhance soil C sequestration.

On univoque points for self-similar sets

Let K⊆R be the unique attractor of an iterated function system. We consider the case where K is an interval and study those elements of K with a unique coding. We prove under mild conditions that the set of points with a unique coding can be identified with a subshift of finite type. As a consequence, we can show that the set of points with a unique coding is a graph-directed self-similar set in the sense of Mauldin and Williams (1988). The theory of Mauldin and Williams then provides a method by which we can explicitly calculate the Hausdorff dimension of this set. Our algorithm can be applied generically, and our result generalises the work of Daróczy, Kátai, Kallós, Komornik and de Vries.

Robust future changes in temperature variability under greenhouse gas forcing and the relationship with thermal advection

Recent temperature extremes have highlighted the importance of assessing projected changes in the variability of temperature as well as the mean. A large fraction of present day temperature variance is associated with thermal advection, as anomalous winds blow across the land-sea temperature contrast for instance. Models project robust heterogeneity in the 21st century warming pattern under greenhouse gas forcing, resulting in land-sea temperature contrasts increasing in summer and decreasing in winter, and the pole-to-equator temperature gradient weakening in winter. In this study, future monthly variability changes in the 17 member ensemble ESSENCE are assessed. In winter, variability in midlatitudes decreases while in very high latitudes and the tropics it increases. In summer, variability increases over most land areas and in the tropics, with decreasing variability in high latitude oceans. Multiple regression analysis is used to determine the contributions to variability changes from changing temperature gradients and circulation patterns. Thermal advection is found to be of particular importance in the northern hemisphere winter midlatitudes, where the change in mean state temperature gradients alone could account for over half the projected changes. Changes in thermal advection are also found to be important in summer in Europe and coastal areas, although less so than in winter. Comparison with CMIP5 data shows that the midlatitude changes in variability are robust across large regions, particularly high northern latitudes in winter and mid northern latitudes in summer.

A Variance-Minimizing Filter for Large-Scale Applications

A truly variance-minimizing filter is introduced and its per for mance is demonstrated with the Korteweg– DeV ries (KdV) equation and with a multilayer quasigeostrophic model of the ocean area around South Africa. It is recalled that Kalman-like filters are not variance minimizing for nonlinear model dynamics and that four - dimensional variational data assimilation (4DV AR)-like methods relying on per fect model dynamics have dif- ficulty with providing error estimates. The new method does not have these drawbacks. In fact, it combines advantages from both methods in that it does provide error estimates while automatically having balanced states after analysis, without extra computations. It is based on ensemble or Monte Carlo integrations to simulate the probability density of the model evolution. When obser vations are available, the so-called importance resampling algorithm is applied. From Bayes’ s theorem it follows that each ensemble member receives a new weight dependent on its ‘ ‘distance’ ’ t o the obser vations. Because the weights are strongly var ying, a resampling of the ensemble is necessar y. This resampling is done such that members with high weights are duplicated according to their weights, while low-weight members are largely ignored. In passing, it is noted that data assimilation is not an inverse problem by nature, although it can be for mulated that way . Also, it is shown that the posterior variance can be larger than the prior if the usual Gaussian framework is set aside. However , i n the examples presented here, the entropy of the probability densities is decreasing. The application to the ocean area around South Africa, gover ned by strongly nonlinear dynamics, shows that the method is working satisfactorily . The strong and weak points of the method are discussed and possible improvements are proposed.

O chair o flesh

Group exhibition curated by Matt Packer. Artists: Fabienne Audeoud, Fleur van Dodewaard, Christian Jankowski, Bea McMahon, Kaspar Oppen Samuelsen, Ria Pacquée, Xavier Ribas, Florian Roithmayr, John Russell, Allan Sekula, Morten Torgersrud, Francis Upritchard, Anne de Vries.