Simulation of normal distributed smooth fields by Karhunen-Loéve expansion in combination with kriging

Simulation of multigaussian stochastic fields can be made after a Karhunen-Loéve expansion of a given covariance function. This method is also called simulation by Empirical Orthogonal Functions. The simulations are made by drawing stochastic coefficients from a random generator. These numbers are multiplied with eigenfunctions and eigenvalues derived from the predefined covariance model. The number of eigenfunctions necessary to reproduce the stochastic process within a predefined variance error, turns out to be a cardinal question. Some ordinary analytical covariance functions are used to evaluate how quickly the series of eigenfunctions can be truncated. This analysis demonstrates extremely quick convergence to 99.5% of total variance for the 2nd order exponential (‘gaussian’) covariance function, while the opposite is true for the 1st order exponential covariance function. Due to these convergence characteristics, the Karhunen-Loéve method is most suitable for simulating smooth fields with ‘gaussian’ shaped covariance functions. Practical applications of Karhunen-Loéve simulations can be improved by spatial interpolation of the eigenfunctions. In this paper, we suggest interpolation by kriging and limits for reproduction of the predefined covariance functions are evaluated.     

Influence of the zone of weakness on dip angle and shear heating of subducted slabs

We study the importance of the zones of weakness and the pattern of downgoing flow in steady-state models of subducting lithosphere, which interacts mechanically and thermally with the ambient mantle. The non-linear system of governing equations consists of (i) the momentum equation in stream function formulation and (ii) the steady-state heat transfer equation including conduction and advection of heat and dissipation. A finite element method has been applied to this system. We consider the viscosity to be a non-linear function of both the temperature and the stream function. In steady-state two-dimensional (2D) flow, the stream function isolines follow material trajectories. They are used to follow the top of the subducting slab, which because of its possible increase in water content, is assumed to have a lower viscosity. The zone of weakness has been thus obtained in the self-consistent fashion since the stream function as well as the temperature are the output from our modeling and no a priori assumptions about the shape of the bending lithosphere are taken into account. It was shown that several orders decrease of viscosity in the zone of weakness is required to obtain the dip angle of about 45°. If the decrease of viscosity is not sufficient enough, the subducted slab either sinks almost vertically or does not exhibit a plate-like behavior. We have also demonstrated that shear heating can unrealistically increase at the zone of weakness for fast subductions if decrease of viscosity is underestimated.     

The effect of dissolved barium on biogeochemical processes at cold seeps

A numerical model was applied to investigate and quantify the biogeochemical processes fueled by the expulsion of barium and methane-rich fluids in the sediments of a giant cold-seep area in the Derugin Basin (Sea of Okhotsk). Geochemical profiles of dissolved Ba²⁺, Sr²⁺, Ca²⁺, SO₄²⁻, HS⁻, DIC, I⁻ and of calcium carbonate (CaCO₃) were fitted numerically to constrain the transport processes and the kinetics of biogeochemical reactions. The model results indicate that the anaerobic oxidation of methane (AOM) is the major process proceeding at a depth-integrated rate of 4.9 μmol cm⁻² a⁻¹, followed by calcium carbonate and strontian barite precipitation/dissolution processes having a total depth-integrated rate of 2.1 μmol cm⁻² a⁻¹. At the low seepage rate prevailing at our study site (0.14 cm a⁻¹) all of the rising barium is consumed by precipitation of barite in the sedimentary column and no benthic barium flux is produced. Numerical experiments were run to investigate the response of this diagenetic environment to variations of hydrological and biogeochemical conditions. Our results show that relatively low rates of fluid flow (<∼5 cm a⁻¹) promote the dispersed precipitation of up to 26 wt% of barite and calcium carbonate throughout the uppermost few meters of the sedimentary column. Distinct and persistent events (several hundreds of years long) of more vigorous fluid flow (from 20-110 cm a⁻¹), instead, result in the formation of barite-carbonate crusts near the sediment surface. Competition between barium and methane for sulfate controls the mineralogy of these sediment precipitates such that at low dissolved methane/barium ratios (<4-11) barite precipitation dominates, while at higher methane/barium ratios sulfate availability is limited by AOM and calcium carbonate prevails. When seepage rates exceed 110 cm a⁻¹, barite precipitation occurs at the seafloor and is so rapid that barite chimneys form in the water column. In the Derugin Basin, spectacular barite constructions up to 20 m high, which cover an area of roughly 22 km² and contain in excess of 5 million tons of barite, are built through this process. In these conditions, our model calculates a flux of barium to the water column of at least 20 μmol cm⁻² a⁻¹. We estimate that a minimum of 0.44 × 10⁶ mol a⁻¹ are added to the bottom waters of the Derugin Basin by cold seep processes, likely affecting the barium cycle in the Sea of Okhotsk.     

Towards a long-term monitoring of Central European water mite faunas (Acari: Hydrachnidia and Halacaridae) – considerations on the background of data from 1900 to 2000

The state of knowledge of the Central European water mite fauna and the research history are briefly surveyed. Several areas for which we are provided with rich data sets are of high value for the monitoring of faunistic trends on the background of local and global environmental change. The need for a database combining historical and actual faunistic information is stressed. It should facilitate the access to all data from former times, give a survey on actual activities by regular updates, and help for a better organization of future research activities. On the base of an update of the Limnofauna Europaea (K.O. Viets 1978, Gerecke in www.watermite.org) a first attempt is made to (1) recognize changes in the Central European fauna during the past 100 years; (2) emphasize species which may be endangered or have disappeared during the past 100 years. At the present state of knowledge, the degree of threat to water mite species in this area is best calculated from their preference for particular habitat types which are rare and in danger to disappear in cultivated landscapes. Our knowledge concerning neozoic water mites in the study area is discussed.     

Tetrahedral Plots of the Phase Relations for Basalts

The phase relations of quaternary systems are generally represented by projections onto ternary compositional planes. Such projections often obscure relationships that would only be evident in a three-dimensional tetrahedral plot. The tetrahedral plot requires that compositions of the minerals and melts be transformed into Cartesian coordinates. It is shown here how this transformation is carried out. The application is demonstrated by tetrahedral plots of experimental melt compositions of partially molten lherzolite. Furthermore, the plot can be used to evaluate whether or not a particular basaltic composition represents a primary melt. The methods are applicable to any four-component system.     

Spatially controlled Fe and Si isotope variations: an alternative view on the formation of the Torres del Paine pluton

We present new Fe and Si isotope ratio data for the Torres del Paine igneous complex in southern Chile. The multi-composition pluton consists of an approximately 1 km vertical exposure of homogenous granite overlying a contemporaneous 250-m-thick mafic gabbro suite. This first-of-its-kind spatially dependent Fe and Si isotope investigation of a convergent margin-related pluton aims to understand the nature of granite and silicic igneous rock formation. Results collected by MC-ICP-MS show a trend of increasing δ⁵⁶Fe and δ³⁰Si with increasing silica content as well as a systematic increase in δ⁵⁶Fe away from the mafic base of the pluton. The marginal Torres del Paine granites have heavier Fe isotope signatures (δ⁵⁶Fe = +0.25 ± 0.02 2se) compared to granites found in the interior pluton (δ⁵⁶Fe = +0.17 ± 0.02 2se). Cerro Toro country rock values are isotopically light in both Fe and Si isotopic systems (δ⁵⁶Fe = +0.05 ± 0.02 ‰; δ³⁰Si = ?0.38 ± 0.07 ‰). The variations in the Fe and Si isotopic data cannot be accounted for by local assimilation of the wall rocks, in situ fractional crystallization, late-stage fluid exsolution or some combination of these processes. Instead, we conclude that thermal diffusion or source magma variation is the most likely process producing Fe isotope ratio variations in the Torres del Paine pluton.     

Biogenic volatile compound emissions from a temperate forest,China: model simulation

Emissions of biogenic volatile organic compounds (BVOC) were measured using a relaxed eddy accumulation (REA) technique on an above-canopy tower in a temperate forest (Changbai Mountain, Jilin province, China) during the 2010 and 2011 summer seasons. Solar global radiation and photosynthetically active radiation (PAR) were also measured. Based on PAR energy dynamic balance, an empirical BVOC emission and PAR transfer model was developed that includes the processes of BVOC emissions and PAR transfer above the canopy level, including PAR absorption and consumption, and scattering by gases, liquids, and particles (GLPs). Simulated emissions of isoprene and monoterpenes were in agreement with observations. The averages of the relative estimator biases for the flux were 39.3 % for isoprene, and 27.1 % for monoterpenes in the 2010 and 2011 growing seasons, with NMSE (normalized mean square error) values of 0.133 and 0.101, respectively. The observed and simulated mean diurnal variations of isoprene and monoterpenes in the 2010 and 2011 growing seasons were evaluated for the validation of the empirical model. Under observed atmospheric conditions, the sensitivity analysis showed that emissions of isoprene and monoterpenes were more sensitive to changes in PAR than to water vapor content or to the magnitude of the scattering factor. The emissions of isoprene and monoterpenes in the 2010 and 2011 growing seasons (from June to September) were estimated using this empirical model along with hourly observational data, with mean hourly emissions of 1.71 and 1.55 mg m^?2 h^?1 for isoprene, and 0.48 and 0.47 mg m^?2 h^?1 for monoterpenes in 2010 and 2011, respectively. As formaldehyde (HCHO) is considered as the main oxidation product of isoprene and monoterpenes, it is necessary to investigate the link between HCHO and BVOC emissions. GOME-2 HCHO vertical column densities (VCDs) can be used to estimate BVOC emission fluxes in the Changbai Mountain temperate forest.