Blind Source Separation for Compositional Time Series

Many geological phenomena are regularly measured over time to follow developments and changes. For many of these phenomena, the absolute values are not of interest, but rather the relative information, which means that the data are compositional time series. Thus, the serial nature and the compositional geometry should be considered when analyzing the data. Multivariate time series are already challenging, especially if they are higher dimensional, and latent variable models are a popular way to deal with this kind of data. Blind source separation techniques are well-established latent factor models for time series, with many variants covering quite different time series models. Here, several such methods and their assumptions are reviewed, and it is shown how they can be applied to high-dimensional compositional time series. Also, a novel blind source separation method is suggested which is quite flexible regarding the assumptions of the latent time series. The methodology is illustrated using simulations and in an application to light absorbance data from water samples taken from a small stream in Lower Austria.

     

Topographic Rossby waves in the Gulf of Mexico

Observations of topographic Rossby waves (TRW), using moored current meters, bottom pressure gauges, and Lagrangian RAFOS floats, are investigated for the deep basin of the Gulf of Mexico. Recent extensive measurement programs in many parts of the deep gulf, which were inspired by oil and gas industry explorations into ever deeper water, allow more comprehensive analyses of the propagation and dissipation of these deep planetary waves. The Gulf of Mexico circulation can be divided into two layers with the ∼800-1200 m upper layer being dominated by the Loop Current (LC) pulsations and shedding of large (diameters ∼300-400 km) anticyclonic eddies in the east, and the translation of these LC eddies across the basin to the west. These processes spawn smaller eddies of both signs through instabilities, and interactions with topography and other eddies to produce energetic surface layer flows that have a rich spectrum of orbit periods and diameters. In contrast, current variability below 1000 m often has the characteristics of TRWs, with periods ranging from ∼10-100 days and wavelengths of ∼50-200 km, showing almost depth-independent or slightly bottom intensified currents through the weakly stratified lower water column. These fluctuations are largely uncorrelated with simultaneous upper-layer eddy flows. TRWs must be generated through energy transfer from the upper-layer eddies to the lower layer by potential vorticity adjustments to changing depths of the bottom and the interface between the layers. Therefore, the LC and LC eddies are prime candidates as has been suggested by some model studies. Model simulations have also indicated that deep lower-layer eddies may be generated by the LC and LC eddy shedding processes.In the eastern gulf, the highest observed lower-layer kinetic energy was north of the Campeche Bank under the LC in a region that models have identified as having strong baroclinic instabilities. Part of the 60-day TRW signal propagates towards the Sigsbee Escarpment (a steep slope at the base of the northern continental slope), and the rest into the southern part of the eastern basin. Higher energy is observed along the escarpment between 89°W and 92°W than either under the northern part of the LC or further south in the deep basin, because of radiating TRWs from the western side of the LC. In the northern part of the LC, evidence was found in the observations that 20-30-day TRWs were connected with the upper layer through coherent signals of relative vorticity. The ∼90° phase lead of the lower over the upper-layer relative vorticity was consistent with baroclinic instability. Along the Sigsbee Escarpment, the TRWs are refracted and reflected so that little energy reaches the lower continental slope and a substantial mean flow is generated above the steepest part of the escarpment. RAFOS float tracks show that this mean flow continues along the escarpment to the west and into Mexican waters. This seems to be a principal pathway for deepwater parcels to be transported westward. Away from the slope RAFOS floats tend to oscillate in the same general area as if primarily responding to the deep wave field. Little evidence of westward translating lower-layer eddies was found in both the float tracks and the moored currents. In the western gulf, the highest deep energy levels are much less than in the central gulf, and are found seaward of the base of the slope. Otherwise, the situation is similar with TRWs propagating towards the slope, probably generated by the local upper-layer complex eddy field, being reflected and forcing a southward mean flow along the base of the Mexican slope. Amplitudes of the lower-layer fluctuations decay from the northwest corner towards the south.     

Modelling nitrogen and oxygen isotope fractionation during denitrification in a lacustrine redox-transition zone

The stable isotope composition (δ¹⁵N and δ¹⁸O) of nitrate was measured during Summer 1999 in the anaerobic hypolimnion of eutrophic Lake Lugano (Switzerland). Denitrification was demonstrated by a progressive nitrate depletion coupled to increasing δ¹⁵N and δ¹⁸O values for residual nitrate. Maximum δ¹⁵N and δ¹⁸O values amounted to 27.2 and 15.7‰, respectively.¹⁵N and ¹⁸O enrichment factors for denitrification (ε) were estimated using a closed-system model and a dynamic diffusion-reaction model. Using the Rayleigh equation (closed-system approach), we obtained ε values of −11.2 and −6.6‰ for nitrogen and oxygen, respectively. The average ε values derived using the diffusion-reaction model were determined to be −20.7 ± 3.8 for nitrogen and −11.0 ± 1.7 for oxygen. Both N and O isotope fractionation appeared to be lower when denitrification rates where high, possibly in association with high organic carbon availability. In addition, variations in the isotope effects may be attributed to the variable importance of sedimentary denitrification having only a small isotope effect on the water column. The combined measurement of N and O isotope ratios in nitrate revealed that coupled nitrification-denitrification in the open-water was of minor importance. This is the first study of nitrogen and oxygen isotope effects associated with microbial denitrification in a natural lake. Moreover, this study confirms the high potential of δ¹⁸O of nitrate as a valuable biogeochemical tracer in aquatic systems, complementing nitrate δ¹⁵N.     

The presolar grain inventory of fine‐grained chondrule rims in the Mighei‐type (CM) chondrites

We investigated the inventory of presolar silicate, oxide, and silicon carbide (SiC) grains of fine‐grained chondrule rims in six Mighei‐type (CM) carbonaceous chondrites (Banten, Jbilet Winselwan, Maribo, Murchison, Murray and Yamato 791198), and the CM‐related carbonaceous chondrite Sutter's Mill. Sixteen O‐anomalous grains (nine silicates, six oxides) were detected, corresponding to a combined matrix‐normalized abundance of ~18 ppm, together with 21 presolar SiC grains (~42 ppm). Twelve of the O‐rich grains are enriched in ¹⁷O, and could originate from low‐mass asymptotic giant branch stars. One grain is enriched in ¹⁷O and significantly depleted in ¹⁸O, indicative of additional cool bottom processing or hot bottom burning in its stellar parent, and three grains are of likely core‐collapse supernova origin showing enhanced ¹⁸O/¹⁶O ratios relative to the solar system ratio. We find a presolar silicate/oxide ratio of 1.5, significantly lower than the ratios typically observed for chondritic meteorites. This may indicate a higher degree of aqueous alteration in the studied meteorites, or hint at a heterogeneous distribution of presolar silicates and oxides in the solar nebula. Nevertheless, the low O‐anomalous grain abundance is consistent with aqueous alteration occurring in the protosolar nebula and/or on the respective parent bodies. Six O‐rich presolar grains were studied by Auger Electron Spectroscopy, revealing two Fe‐rich silicates, one forsterite‐like Mg‐rich silicate, two Al‐oxides with spinel‐like compositions, and one Fe‐(Mg‐)oxide. Scanning electron and transmission electron microscopic investigation of a relatively large silicate grain (490 nm × 735 nm) revealed that it was crystalline åkermanite (Ca₂Mg[Si₂O₇]) or a an åkermanite‐diopside (MgCaSi₂O₆) intergrowth.     

On the thermal evolution of the terrestrial planets

Physical and chemical constraints for such different planetary objects as the Earth, the Moon and meteorite parent bodies can best be satisfied by thermal history models having high initial temperatures. On the basis of thermal calculations it is suggested that the evolution of the other terrestrial planets (Mars, Venus and Mercury) was also characterized by high initial temperatures. Under these conditions, melting and, consequently, fractionation would set in at an early stage. Because of the resulting redistribution of the long-lived radioactive heat sources and the concentration of these elements in the surface layers, large-scale differentiation could be achieved by partial melting.Paper presented at the Lunar Science Institute Conference on Geophysical and Geochemical Exploration of the Moon and Planets, January 10–12, 1973.     

The occultation of κ geminorum by Eros

The predictions and observations of the occultation of κ Gem by Eros on January 24, 1975, are described. At least eight positive and several critical negative observations were made in western New England. The paucity of observations on the western side of the track makes the analysis somewhat ambiguous, but a circular cross section of diameter up to 23 km gives a good fit to most of the available data. Consideration of a crucial, unconfirmed negative observation indicates that an elliptical solution 17 by 7 km (with the long axis in the direction of motion of the “shadow” of Eros) may be preferable, but this does not represent the positive observations so satisfactorily. The ellipse was therefore distorted into a more irregular shape about 20 km long and 7 km wide, rounded on one long side and flattened on the other. Both this irregular shape and the ellipse yield geometric albedos near 0.5, which is considerably higher than has been derived for most other planets or satellites lacking an atmosphere. The albedo that corresponds to the circular solution (0.1) is less than the polarimetric albedo of 0.21 for Eros. It is suggested either that the circle should be warped into an ellipse of dimensions 21 by 13 km, or, if some weight is given to the critical negative observation and the westernmost positive observation, that the profile is a kind of dumbbell.