Bayes estimation: A novel approach to derivation of internally consistent thermodynamic data for minerals,their uncertainties,and correlations. Part I: Theory

Computation of phase diagrams in mineral systems and quantitative geothermobarometry thrive on the availability and accuracy of internally consistent thermodynamic datasets for minerals. The prevailing two methodologies applied to derive them, mathematical programming (MAP) and least squares regression (REG), have their very specific advantages and deficiencies which are to some extent complementary. Bayes estimation (BE), the novel technique proposed here for obtaining internally consistent thermodynamic databases, can combine the advantages of both MAP and REG but avoid their drawbacks. It optimally uses the information on thermochemical, thermophysical, and volumetric properties of phases and experimental reaction reverals to refine the thermodynamic data and returns their uncertainties and correlations. Therefore, BE emerges as the method of choice. The theoretical background of BE, and its relation to MAP and REG, is explained. Although BE is conceptually simple, it can be computationally demanding. Fortunately, modern computer technology and new stochastic methods such as Gibbs sampling help surmount those difficulties. The basic ideas behind these methods are explored and recommendations for their use are made using the Al₂SiO₅ unary as an example. The potential of BE and its future perspective for application to multicomponent-multiphase systems appear very promising. For the convenience of readers not interested in the mathematical details of BE, an illustrative example is given in the Appendix to promote an intuitive understanding of what BE is all about.     

Calcium Isotopes (δ44/40Ca) in MPI-DING Reference Glasses, USGS Rock Powders and Various Rocks: Evidence for Ca Isotope Fractionation in Terrestrial Silicates

We report δ^44/40Ca_{(SRM 915a)} values for eight fused MPI‐DING glasses and the respective original powders, six USGS igneous rock reference materials, the U‐Th disequilibria reference material TML, IAEA‐CO1 (Carrara marble) and several igneous rocks (komatiites and carbonatites). Sample selection was guided by three considerations: (1) to address the need for information values on reference materials that are widely available in support of interlaboratory comparison studies; (2) support the development of in situ laser ablation and ion microprobe techniques, which require isotopically homogenous reference samples for ablation; and (3) provide Ca isotope values on a wider range of igneous and metamorphic rock types than is currently available in the scientific literature. Calcium isotope ratios were measured by thermal ionisation mass spectrometry in two laboratories (IFM‐GEOMAR and Saskatchewan Isotope Laboratory) using ⁴³Ca/⁴⁸Ca‐ and ⁴²Ca/⁴³Ca‐double spike techniques and reported relative to the calcium carbonate reference material NIST SRM 915a. The measurement uncertainty in both laboratories was better than 0.2‰ at the 95% confidence level. The impact of different preparation methods on the δ^44/40Ca_{(SRM 915a)} values was found to be negligible. Except for ML3‐B, the original powders and the respective MPI‐DING glasses showed identical δ^44/40Ca_{(SRM 915a)} values; therefore, possible variations in the Ca isotope compositions resulting from the fusion process are excluded. Individual analyses of different glass fragments indicated that the glasses are well homogenised on the mm scale with respect to Ca. The range of δ^44/40Ca_{(SRM 915a)} values in the igneous rocks studied was larger than previously observed, mostly owing to the inclusion of ultramafic rocks from ophiolite sections. In particular, the dunite DTS‐1 (1.49 ± 0.06‰) and the peridotite PCC‐1 (1.14 ± 0.07‰) are enriched in ⁴⁴Ca relative to volcanic rocks (0.8 ± 0.1‰). The Carrara marble (1.32 ± 0.06‰) was also found to be enriched in ⁴⁴Ca relative to the values of assumed precursor carbonates (< 0.8‰). These findings suggest that the isotopes of Ca are susceptible to fractionation at high temperatures by, as yet, unidentified igneous and metamorphic processes.     

On the effect of decreasing CO2 concentration in the atmosphere

In the present paper the effect of an abrupt change of the atmospheric radiative forcing is investigated by means of a global climate model that includes a mixed layer ocean. In assessing if, under such a change, the model response has a bifurcation point, the steady solution is studied for a sudden decrease of CO₂ concentration from its actual value. It is found that there is a critical threshold for CO₂ content below which the model ends up to a snowball Earth. It occurs for a few percentage changes of CO₂ concentration around the threshold because the model strongly depends on the relationship among atmospheric temperature, water vapor content and the sudden ice-albedo feedback activation, even in the subtropical regions. Moreover, results suggest that the transition to ice-covered Earth is clearly favoured when Q-flux corrections (i.e. the parameterization of ocean heat transports) are removed.     

Potential decadal predictability and its sensitivity to sea ice albedo parameterization in a global coupled model

Decadal prediction is one focus of the upcoming 5th IPCC Assessment report. To be able to interpret the results and to further improve the decadal predictions it is important to investigate the potential predictability in the participating climate models. This study analyzes the upper limit of climate predictability on decadal time scales and its dependency on sea ice albedo parameterization by performing two perfect ensemble experiments with the global coupled climate model EC-Earth. In the first experiment, the standard albedo formulation of EC-Earth is used, in the second experiment sea ice albedo is reduced. The potential prognostic predictability is analyzed for a set of oceanic and atmospheric parameters. The decadal predictability of the atmospheric circulation is small. The highest potential predictability was found in air temperature at 2?m height over the northern North Atlantic and the southern South Atlantic. Over land, only a few areas are significantly predictable. The predictability for continental size averages of air temperature is relatively good in all northern hemisphere regions. Sea ice thickness is highly predictable along the ice edges in the North Atlantic Arctic Sector. The meridional overturning circulation is highly predictable in both experiments and governs most of the decadal climate predictability in the northern hemisphere. The experiments using reduced sea ice albedo show some important differences like a generally higher predictability of atmospheric variables in the Arctic or higher predictability of air temperature in Europe. Furthermore, decadal variations are substantially smaller in the simulations with reduced ice albedo, which can be explained by reduced sea ice thickness in these simulations.     

Bridging the gap between numerical solutions of travel time distributions and analytical storage selection functions

Recent advancements in analytical solutions to quantify water and solute travel time distributions (TTDs) and the related StorAge Selection (SAS) functions synthesize catchment complexity into a simplified, lumped representation. Although these analytical approaches are efficient in application, they require rarely available long‐term and high‐frequency hydrochemical data for parameter estimation. Alternatively, integrated hydrologic models coupled to Lagrangian particle‐tracking approaches can directly simulate age under different catchment geometries and complexity, but at a greater computational expense. Here, we bridge the two approaches, using a physically based model to explore the uncertainty in the estimation of the SAS function shape. In particular, we study the influence of subsurface heterogeneity, interactions between distinct flow domains (i.e., the vadose zone and saturated groundwater), diversity of flow pathways, and recharge rate on the shape of TTDs and the SAS functions. We use an integrated hydrology model, ParFlow, linked with a particle‐tracking model, SLIM, to compute transient residence times (or ages) at every cell in the domain, facilitating a direct characterization of the SAS function. Steady‐state results reveal that the SAS function shape shows a wide range of variation with respect to the variability in the structure of subsurface heterogeneity. Ensembles of spatially correlated realizations of hydraulic conductivity indicate that the SAS functions in the saturated groundwater have an overall weak tendency toward sampling younger ages, whereas the vadose zone gives a strong preference for older ages. We further show that the influence of recharge rate on the TTD is tightly dependent on the variability of subsurface hydraulic conductivity.     

Metal/sulfide–silicate intergrowth textures in EL3 meteorites: Origin by impact melting on the EL parent body

Abstract– We document the petrographic setting and textures of Fe,Ni metal, the mineralogy of metallic assemblages, and the modal mineral abundances in the EL3 meteorites Asuka (A‐) 881314, A‐882067, Allan Hills 85119, Elephant Moraine (EET) 90299/EET 90992, LaPaz Icefield 03930, MacAlpine Hills (MAC) 02635, MAC 02837/MAC 02839, MAC 88136, Northwest Africa (NWA) 3132, Pecora Escarpment 91020, Queen Alexandra Range (QUE) 93351/QUE 94321, QUE 94594, and higher petrologic type ELs Dar al Gani 1031 (EL4), Sayh al Uhaymir 188 (EL4), MAC 02747 (EL4), QUE 94368 (EL4), and NWA 1222 (EL5). Large metal assemblages (often containing schreibersite and graphite) only occur outside chondrules and are usually intergrown with silicate minerals (euhedral to subhedral enstatite, silica, and feldspar). Sulfides (troilite, daubréelite, and keilite) are also sometimes intergrown with silicates. Numerous authors have shown that metal in enstatite chondrites that are interpreted to have been impact melted contains euhedral crystals of enstatite. We argue that the metal/sulfide–silicate intergrowths in the ELs we studied were also formed during impact melting and that metal in EL3s thus does not retain primitive (i.e., nebular) textures. Likewise, the EL4s are also impact‐melt breccias. Modal abundances of metal in the EL3s and EL4s range from approximately 7 to 30 wt%. These abundances overlap or exceed those of EL6s, and this is consistent either with pre‐existing heterogeneity in the parent body or with redistribution of metal during impact processes.     

On the time scales of nonlinear instability in miscible displacement porous media flow

In this paper, we analyze the time scales associated with instable fingering induced by density contrasts in miscible displacement porous media flow. We perform numerical simulations of a two-dimensional domain with boundaries that are closed to flow and identify the three regimes of the dynamics, namely the development of a stable diffusive boundary layer, the onset and growth of instabilities, and the fully nonlinear dynamics. Special focus is given to the onset of the fully nonlinear regime. The results are generic in the sense that there are no parameters in the non-dimensional model problem. Large ensembles are studied and an error estimate is given based on the combined effect of numerical errors and sampling errors. The nonlinear time scales show a dependence on the size of initial perturbations. We estimate this size for three formations used for CO₂ storage and find that the onset of enhanced convective mixing is considerably delayed compared with the linear onset time.     

GGR Biennial Critical Review: Analytical Developments Since 2010

Advances in the chemical and isotopic characterisation of geological and environmental materials can often be ascribed to technological improvements in analytical hardware. Equally, the creation of novel methods of data acquisition and interpretation, including access to better reference materials, can also be crucial components enabling important breakthroughs. This biennial review highlights key advances in either instrumentation or data acquisition and treatment, which have appeared since January 2010. This review is based on the assessments by scientists prominent in each of the given analytical fields; it is not intended as an exhaustive summary, but rather provides insight from experts of the most significant advances and trends in their given field of expertise. In contrast to earlier reviews, this presentation has been formulated into a unified work, providing a single source covering a broad spectrum of geoanalytical techniques. Additionally, some themes that were not previously emphasised, in particular thermal ionisation mass spectrometry, accelerator‐based methods and vibrational spectroscopy, are also presented in detail.     

Improved moraine age interpretations through explicit matching of geomorphic process models to cosmogenic nuclide measurements from single landforms

The statistical distributions of cosmogenic nuclide measurements from moraine boulders contain previously unused information on moraine ages, and they help determine whether moraine degradation or inheritance is more important on individual moraines. Here, we present a method for extracting this information by fitting geomorphic process models to observed exposure ages from single moraines. We also apply this method to 94 ¹⁰Be apparent exposure ages from 11 moraines reported in four published studies. Our models represent ¹⁰Be accumulation in boulders that are exhumed over time by slope processes (moraine degradation), and the delivery of boulders with preexisting ¹⁰Be inventories to moraines (inheritance). For now, we neglect boulder erosion and snow cover, which are likely second-order processes. Given a highly scattered data set, we establish which model yields the better fit to the data, and estimate the age of the moraine from the better model fit. The process represented by the better-fitting model is probably responsible for most of the scatter among the apparent ages. Our methods should help resolve controversies in exposure dating; we reexamine the conclusions from two published studies based on our model fits.