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.     

A Modeling Study of the Effects of Anomalous Snow Cover over the Tibetan Plateau upon the South Asian Summer Monsoon

The effect of anomalous snow cover over the Tibetan Plateau upon the South Asian summer monsoon is investigated by numerical simulations using the NCAR regional climate model (RegCM2) into which gravity wave drag has been introduced. The simulations adopt relatively realistic snow mass forcings based on Scanning Multi-channel Microwave Radiometer (SNINIR) pentad snow depth data. The physical mechanism and spatial structure of the sensitivity of the South Asian early summer monsoon to snow cover anomaly over the Tibetan Plateau are revealed. The main results are summarized as follows. The heavier than normal snow cover over the Plateau can obviously reduce the shortwave radiation absorbed by surface through the albedo effect, which is compensated by weaker upward sensible heat flux associated with colder surface temperature, whereas the effects of snow melting and evaporation are relatively smaller.The anomalies of surface heat fluxes can last until June and become unobvious in July. The decrease of the Plateau surface temperature caused by heavier snow cover reaches its maximum value from late April to early May. The atmospheric cooling in the mid-upper troposphere over the Plateau and its surrounding areas is most obvious in May and can keep a fairly strong intensity in June. In contrast, there is warming to the south of the Plateau in the mid-lower troposphere from April to June with a maximum value in May.The heavier snow cover over the Plateau can reduce the intensity of the South Asian summer monsoon and rainfall to some extent, but this influence is only obvious in early summer and almost disappears in later stages.     

GIS Spatial-Temporal Modeling of Water Systems in Greater Toronto Area, Canada

Modeling landscape with high-resolution digital elevation model (DEM) in a geographic information system can provide essential morphological and structural information for modeling surface processes such as geomorphologic process and water systems. This paper introduces several DEM-based spatial analysis processes applied to characterize spatial distribution and their interactions of ground and surface water systems in the Greater Toronto Area (GTA), Canada. The stream networks and drainage basin systems were derived from the DEM with 30 m resolution and the regularities of the surface stream and drainage patterns were modeled from a statistical/multifractal point of view. Together with the elevation and slope of topography, other attributes defmed from modeling the stream system, and drainage networks were used to associate geological, hydrological and topographical features to water flow in river systems and the spatial locations of artesian aquifers in the study area. Stream flow data derived from daily flow measurements recorded at river gauging stations for multi-year period were decomposed into “drainage-area dependent“ and “drainage-area independent“ flow components by two-step “frequency“ and “spatial“ analysis processes. The latter component was further demonstrated to relate most likely to the ground water discharge. An independent analysis was conducted to model the distribution of aquifers with information derived from the records of water wells. The focus was given on quantification of the likelihood of ground water discharge to river and ponds through flowing wells, springs and seepages. It has been shown that the Oak Ridges Moraine (ORM) is a unique glacial deposit that serves as a recharge layer and that the aquifers in the ORM underlain by Hilton Tills and later deposits exposed near the steep slope zone of the ridges of ORM provide significant discharge to the surface water systems (river flow and ponds) through flowing wells, springs and seepages. Various statistics (cross- and auto-correlation coefficients, fractal R/S exponent) were used in conjunction with GIS to demonstrate the influence of land types, topography and geometry of drainage basins on short- and long-term persistence of river flows as well as responding time to precipitation events. The current study has provided not only insight in understanding the interaction of water systems in the GTA, but also a base for further establishment of an on-line GIS system for predicting spatial-temporal changes of river flow and groundwater level in the GTA.     

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.     

Deciphering late Devonian–early Carboniferous P–T–t path of mylonitized garnet-mica schists from Prins Karls Forland,Svalbard

Quartz-in-garnet inclusion barometry integrated with trace element thermometry and calculated phase relations is applied to mylonitized schists of the Pinkie unit cropping out on the island of Prins Karls Forland, western part of the Svalbard Archipelago. This approach combines conventional and novel techniques and allows deciphering of the pressure–temperature (P–T) evolution of mylonitic rocks, for which the P–T conditions could not have been easily deciphered using traditional methods. The results obtained suggest that rocks of the Pinkie unit were metamorphosed under amphibolite facies conditions at 8–10 kbar and 560–630°C and mylonitized at ~500 to 550°C and 9–11 kbar. The P–T results are coupled with in-situ Th–U-total Pb monazite dating, which records amphibolite facies metamorphism at c. 359–355 Ma. This is the very first evidence of late Devonian–early Carboniferous metamorphism in Svalbard and it implies that the Ellesmerian Orogeny on Svalbard was associated with metamorphism up to amphibolite facies conditions. Thus, it can be concluded that the Ellesmerian collision between the Franklinian margin of Laurentia and Pearya and Svalbard caused not only commonly accepted brittle deformation and weak greenschist facies metamorphism, but also a burial and deformation of rock complexes at much greater depths at elevated temperatures.     

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.     

Root‐related rhodochrosite and concretionary siderite formation in oxygen‐deficient conditions induced by a ground‐water table rise

Sedimentological, mineralogical, stable carbon and oxygen isotope determinations and biomarker analyses were performed on siderite concretions occurring in terrestrial silts to understand their formation and to characterize the sedimentary and diagenetic conditions favouring their growth. High δ¹³C values (6·4‰ on average) indicate that siderite precipitated in an anoxic environment where bacterial methanogenesis operated. The development of anoxic conditions during shallow burial was induced by a change in sedimentary environment from flood plain to swamp, related to a rise of the ground‐water table. Large amounts of decaying plant debris led to efficient oxygen consumption within the pore‐water in the peat. Oxygen depletion, in combination with a decrease in sedimentation rate, promoted anoxic diagenetic conditions under the swamp and favoured abundant siderite precipitation. This shows how a change in sedimentary conditions can have a profound impact on the early‐diagenetic environment and carbonate authigenesis. The concretions contain numerous rhizoliths; they are cemented with calcium‐rhodochrosite, a feature which has not been reported before. The rhodochrosite cement has negative δ¹³C values (?16·5‰ on average) and precipitated in suboxic conditions due to microbial degradation of roots coupled to manganese reduction. The exceptional preservation of the epidermis/exodermis and xylem vessels of former root tissues indicates that the rhodochrosite formed shortly after the death of a root in water‐logged sediments. Rhodochrosite precipitated during the initial stages of concretionary growth in suboxic microenvironments within roots, while siderite cementation occurred simultaneously around them in anoxic conditions. These suboxic microenvironments developed because oxygen was transported from the overlying oxygenated soil into sediments saturated with anoxic water via roots acting as permeable conduits. This model explains how separate generations of carbonate cements having different mineralogy and isotopic compositions, which would conventionally be regarded as cements precipitated sequentially in different diagenetic zones during gradual burial, can form simultaneously in shallow burial settings where strong redox gradients exist around vertically oriented permeable root structures.