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.     

U-Th dating of Lake Lisan (late Pleistocene dead sea) aragonite and implications for glacial east Mediterranean climate change

U-series dating can be an effective means to obtain accurate and precise ages on Quaternary carbonates. However, most samples require a correction for U and Th in admixed detritus. This complication is often addressed through generation of U-Th isochrons, requiring analyses of several coeval samples. In addition, presence of water-derived (hydrogenous) Th in the carbonate can cause inaccuracies in isochron ages.This study reports a high-resolution U-series chronology of sediments deposited by Lake Lisan, the last glacial precursor of the Dead Sea. The strategy employed combines multiple measurements from a few stratigraphic heights and fewer analyses from many heights in a single described and measured section. The resulting chronology is based on ages at 22 heights in a ∼40-m-thick section covering the interval of ∼70-14 calendar ka BP. The effects of admixed detritus are evaluated using trace elements. Nearly pure aragonite samples, indicated by very low abundances of insoluble elements such as Nb and Zr, were found to contain hydrogenous Th, which causes the uncorrected U-²³⁰Th age of a modern sample to be ∼2.5 ka. Nevertheless, accurate ages have been obtained by correcting for the detrital and aqueous interferences. The resulting ages are in stratigraphic order, and their accuracy is evidenced by consistency of Lisan Formation U-series and ¹⁴C ages with the coral-based calendar-radiocarbon age calibration.The U-Th ages provide a context to unravel the limnological history of Lake Lisan. Boundaries between the Lower, Middle, and Upper stratigraphic units correspond to the MIS 4/3 and 3/2 transitions, respectively. During MIS 2 and 4 the lake generally showed a stable two-layer configuration and a positive fresh-water balance, reflected by deposition of laminated aragonite-detritus. Dry intervals during MIS 2 and 4 are indicated by thick gypsum layers and an inferred depositional hiatus, which are temporally associated with Heinrich events H1 at ∼17 ka and H6 at ∼65 ka, respectively. During MIS 3 the lake level was unstable with intermittent dry periods indicated by abundant clastic layers and a significant hiatus between ∼43-49 ka. Clastic layers are associated with Dansgaard-Oeschger events during MIS 3, and indicate lake level declines during abrupt Northern Hemisphere warmings. Overall, the climate of the Eastern Mediterranean region shows a strong linkage to the Northern Hemisphere climate, with increasing lake size and stability during cold periods, and fluctuations and dessication during warmings and Heinrich events.     

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.     

Sea-rain-lake relation in the Last Glacial East Mediterranean revealed by δO-δC in Lake Lisan aragonites

We investigated the Sea-Rain-Lake relation during the Last Glacial-Holocene in the East Mediterranean region by comparing the δ¹⁸O and δ¹³C records of authigenic aragonite deposited in Lake Lisan, the Dead Sea, Mediterranean foraminifera, and speleothems. The Lisan Formation data display long- and short-term variations of δ¹⁸O, representing steady-state conditions of the lake (e.g., 5.6‰ ± 0.5‰ and 4.5‰ ± 1‰ in the Upper and Lower Members of the Lisan Formation, respectively), and short-term excursions reflecting large floods and droughts. The long-term (steady-state) δ¹⁸O values of the Lisan aragonites show similarity to the corresponding time-equivalent records of the Eastern Mediterranean foraminifera and Judea Mountain speleothems: The Last Glacial deposits are in all of them 2‰-3‰ heavier than the Holocene ones. We interpret this similarity as reflecting the significance of the source effect on the long-term behavior of isotopic reservoirs: Speleothem δ¹⁸O is strongly influenced by the marine reservoir that contributes its vapor to rain formation; the lake δ¹⁸O is dominated by the composition of the inflowing water. Short-term variations in the isotopic composition of rainfall are dominated by the amount effect and the temperature and those of the Lake’s upper water mass by the lake’s water balance.δ¹³C values are more variable than δ¹⁸O in the same Lisan sequences (e.g., δ¹³C in the Lower Member is 1.0‰ ± 1.7‰, whereas δ¹⁸O is 4.6‰ ± 0.7‰) and are 1‰ to 1.5‰ higher in the Upper Member than in the Lower and Middle Members of the Lisan Formation. These variations reflect significant increase in primary productivity of the lake and algal bloom activity. It appears that the hypersaline-saline lakes were not as “dead” as the Dead Sea is and that algal activity had an important impact upon the geochemistry of Lake Lisan.The δ¹⁸O data combined with independent geochemical and limnologic information (e.g., level fluctuations) indicate that Lisan time was characterized by high precipitation-high lake stands-high atmospheric humidity, whereas the Holocene Dead Sea shows the opposite behavior. This paleoclimatic reconstruction is consistent with independent evidence for significantly wetter conditions in the East Mediterranean region during the Last Glacial period.     

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.