Thick-plate flexure re-examined

Summary. The flexure of an incompressible, thick elastic plate floating on an inviscid substratum and subject to an external gravity field is re-analysed. The solution is derived from momentum equations which account for the advection of hydrostatic pre-stress. This is contrasted with a recently published thick-plate solution derived from momentum equations without a pre-stress term. It is demonstrated that neglecting pre-stress advection renders the solution singular when the model degenerates into an inviscid half-space. If pre-stress advection is included, the solution remains correct in this limit. A numerical comparison of both types of thick-plate solution with results based on conventional thin-plate theory further shows that, for geophysically relevant models, the difference in the momentum balance entails discrepancies between the thick-plate solutions which are comparable to the errors introduced by the thin-plate approximation.     

Simultaneous determinations of U–Pb age,Hf isotopes and trace element compositions of zircon by excimer laser-ablation quadrupole and multiple-collector ICP-MS

We describe an in situ method for simultaneous measurement of U–Pb–Hf isotopes and trace element compositions of zircons using a quadrupole and multiple-collector inductively-coupled-plasma mass spectrometer (Q-ICP-MS and MC-ICP-MS, respectively) connected to a single excimer laser-ablation system. A laser-generated zircon aerosol was split behind the ablation cell into two transport tubes via a Y-shaped connector and simultaneously introduced into the two mass spectrometers. Hafnium isotopes were measured on the MC-ICP-MS instrument, while U–Pb ages and trace element compositions were determined using the Q-ICP-MS. The precision and accuracy of this method was evaluated using six well-known and widely used zircon standards (91500, Temora-2, GJ-1, Mud Tank, BR266 and Monastery). Analyses were carried out using spot sizes of 32, 44 and 60 μm. For the 44 and 60 μm spot, the resulting U–Pb ages, Hf isotopic and rare earth element (REE) compositions of these six zircons agree with recommended/reported values within 2σ error. The difference in relative standard deviations (RSD) of ²⁰⁶Pb/²³⁸U ages between split-flow measurements and those obtained separately on the Q-ICP-MS is within ～ 20% for 91500, Temora-2 and GJ-1, and ～ 60% for Mud Tank (due to its lower U and Pb concentrations). Our method provides a precise approach for determining the U–Pb age and the Hf isotopic and trace element compositions of zircon within a single ablation event. This is in particular important for analysis of zircons that are small or contain complicated zoning patterns. Finally, the REE composition of zircon BR266 is more homogeneous than other zircons and could be a suitable standard by which to benchmark new standards for microprobe analyses of zircons.     

Regional geoid determination in Antarctica utilizing airborne gravity and topography data

Antarctica is the only continent that suffers major gaps in terrestrial gravity data coverage. To overcome this problem and to close these gaps as well as to densify the global satellite gravity field solutions, the International Association of Geodesy (IAG) Commission Project 2.4 “Antarctic Geoid” was set into action. This paper reviews the current situation concerning the gravity field in Antarctica. It is shown that airborne geophysical surveys are the most promising tools to gain new gravity data in Antarctica. In this context, a number of projects to be carried out during the International Polar Year 2007/2008 will contribute to this goal. To demonstrate the feasibility of the regional geoid improvement in Antarctica, we present a case study using gravity and topography data of the southern Prince Charles Mountains, East Antarctica. During the processing, the remove–compute– restore (RCR) technique and least-squares collocation (LSC) were applied. Adding signal parts of up to 6 m to the global gravity field model that was used as a basis, the calculated regional quasigeoid reveals the dominant features of bedrock topography in that region, namely the graben structure of the Lambert glacier system. The accuracy of the improved regional quasigeoid is estimated to be at the level of 15 cm.     

Multi-gas Emissions Pathways to Meet Climate Targets

So far, climate change mitigation pathways focus mostly on CO₂ and a limited number of climate targets. Comprehensive studies of emission implications have been hindered by the absence of a flexible method to generate multi-gas emissions pathways, user-definable in shape and the climate target. The presented method ‘Equal Quantile Walk’ (EQW) is intended to fill this gap, building upon and complementing existing multi-gas emission scenarios. The EQW method generates new mitigation pathways by ‘walking along equal quantile paths’ of the emission distributions derived from existing multi-gas IPCC baseline and stabilization scenarios. Considered emissions include those of CO₂ and all other major radiative forcing agents (greenhouse gases, ozone precursors and sulphur aerosols). Sample EQW pathways are derived for stabilization at 350 ppm to 750 ppm CO₂ concentrations and compared to WRE profiles. Furthermore, the ability of the method to analyze emission implications in a probabilistic multi-gas framework is demonstrated. The probability of overshooting a 2 ^∘C climate target is derived by using different sets of EQW radiative forcing peaking pathways. If the probability shall not be increased above 30%, it seems necessary to peak CO₂ equivalence concentrations around 475 ppm and return to lower levels after peaking (below 400 ppm). EQW emissions pathways can be applied in studies relating to Article 2 of the UNFCCC, for the analysis of climate impacts, adaptation and emission control implications associated with certain climate targets. See for EQW-software and data.     

Experimentelle Untersuchung der Metamorphose von kieselig dolomitischen Sedimenten

During an experimental investigation of the metamorphism of siliceous dolomites the equilibrium data of the heterogeneous bivariant reaction 1 $$3{\text{ dolomite + 4 quartz + 1 H}}_{\text{2}} O \rightleftharpoons + 3 calcite + 3 CO_2 $$ were determined for the total fluid pressures of 1,000, 3,000 and 5,000 bars. The equilibrium conditions were found by experiments in which dolomite, quartz and water react to form talc, calcite and CO₂, as well as by experiments with reversible reaction direction. Results are shown on the temperature- \(X_{CO_2 } \) -diagram of Fig. 3. The temperature of formation of talc and calcite depends to a considerable extent on the composition of the CO₂-H₂O-gas phase; this can be read straight off the isobaric (P _f =const.) equilibrium curves in Fig. 3. In addition a strong dependence of the equilibrium temperature on the total pressure P _f was established (see Fig. 5). At a total gas pressure of 1,000 bars dolomite and quartz can react, according to the composition of the CO₂-H₂O-gas phase, to talc and calcite over the whole of the temperature range between about 350° and 490° C. This indicates that at low pressures the formation of talc and calcite takes place in the field of the albite-epidote-hornfels facies. At a pressure of 3,000 bars dolomite and quartz are stable up to about 550° C if the fluid phase is rich in carbon dioxide and correspondingly poor in water. Thus, this paragenesis can occur up to the stability field of staurolite [see annotation (5)] if the partial pressure of CO₂ is large. At the higher total gas pressure of 5,000 bars dolomite and quartz react even at medium CO₂-concentrations only at about 580° C to give talc and calcite. Therefore it is expected that in regional metamorphism at about 5,000 bars pressure or more the paragenesis dolomite plus quartz exists up to and within the stability field of staurolite and reacts only here to form talc and calcite after reaction (1) or tremolite and calcite after the following reaction (2)¹: $$5 dolomite + 8 quartz + 1 H_2 O \rightleftharpoons 1 tremolite + 3 calcite + 7 CO_2 $$ . The exact physico-chemical conditions under which dolomite, quartz and water react on the one hand to form talc, calcite and CO₂, and on the other hand to form tremolite, calcite and carbon dioxide, will be discussed later when our experimental investigations on the formation of tremolite are completed. First results were already published in a short note by Metz, Puhan and Winkler (1968).     

Consistent estimation of geodetic parameters from SLR satellite constellation measurements

In this paper, we consistently estimate geodetic parameters such as weekly 3-D station coordinates, Earth orientation parameters (EOP) including daily x/y-pole coordinates and the excess length of day \(\Delta \hbox {LOD}\), and selected weekly Earth’s gravitational field (Stokes) coefficients up to degree and order 6 from Satellite Laser Ranging measurements to up to 11 geodetic satellites. The SLR constellation consists of LAGEOS-1/2, Etalon-1/2, Stella, Starlette, Ajisai, Larets, LARES, BLITS and WESTPAC, and its observations cover a time span of 38 years ranging from February 16, 1979, to April 30, 2017. If multiple satellites with various altitudes and orbit inclinations are combined, correlations between estimated parameters are significantly reduced. This allows us (i) to investigate the ability of satellite constellations to reduce existing correlations and (ii) to estimate reliable parameters with higher precision compared to the standard 4-satellite constellation (LAGEOS-1/2, Etalon-1/2) which is currently used by the International Laser Ranging Service for the determination of the Terrestrial Reference Frame (TRF) and EOP products. In particular, the Stokes coefficients, EOP and TRF datum parameters (three translations, three rotations, one scale factor), which are highly correlated with satellite-specific orbit parameters, are improved. From our investigations, we found for an 11-satellite solution compared to the above-mentioned 4-satellite solution a decrease in the scatter of the TRF datum parameters of up to 37%, the transformation residuals are decreased by up to 22%, the scatter of the EOP is decreased by up to 22%, and their mean values are decreased by up to 84% w.r.t. the reference solutions. The largest improvement is obtained for the Stokes coefficients which significantly benefit from a combination of multiple satellites (inclinations and orbit altitudes). In total, single coefficients are improved by up to 93% and the overall improvement is up to 74%. Moreover, it could be clearly identified that Ajisai significantly disturbs the TRF solution due to an erroneous center-of-mass correction. We further quantify the impact of specific satellites on the determination of different geodetic parameters and finally evaluate the potential of the existing SLR-tracked spherical satellite constellation to support the goals of GGOS.     

Tellurium isotopic composition of the early solar system—A search for effects resulting from stellar nucleosynthesis, Sn decay, and mass-independent fractionation

New precise Te isotope data acquired by multiple collector inductively coupled plasma mass spectrometry (MC-ICPMS) are presented for selected extraterrestrial and terrestrial materials. Bulk samples of carbonaceous, ordinary and enstatite chondrites as well as the metal and sulfide phases of iron meteorites were analyzed to search for nucleosynthetic isotope anomalies and to find evidence of formerly live ¹²⁶Sn, which decays to ¹²⁶Te with a half-life of 234,500 yr. None of the meteorites show evidence of mass dependent Te isotope fractionations larger than 2‰ for δ^126/128Te. Following internal normalization of the data to ¹²⁵Te/¹²⁸Te, the Te isotope ratios of all analyzed meteorites were found to be identical to a terrestrial standard, within uncertainties. This provides evidence that the regions of the solar disk that were sampled during accretion of the meteorite parent bodies were well mixed and homogeneous on a large scale, with respect to Te isotopes. The data acquired for bulk carbonaceous chondrites indicate that the initial ¹²⁶Sn/¹¹⁸Sn ratio of the solar system was <4 × 10⁻⁵, but this is dependent on the assumption that no redistribution of Sn and Te occurred since the start of the solar system. Five Archean sedimentary sulfides that display both mass dependent and mass-independent isotope effects for S yield internally normalized Te isotope data, which indicate that mass-independent Te isotope effects are absent. The mass dependent fractionations in these samples are constrained to be less than ∼1‰ for δ^126/128Te.     

A new scenario framework for climate change research: background,process, and future directions

The scientific community is developing new global, regional, and sectoral scenarios to facilitate interdisciplinary research and assessment to explore the range of possible future climates and related physical changes that could pose risks to human and natural systems; how these changes could interact with social, economic, and environmental development pathways; the degree to which mitigation and adaptation policies can avoid and reduce risks; the costs and benefits of various policy mixes; and the relationship of future climate change adaptation and mitigation policy responses with sustainable development. This paper provides the background to and process of developing the conceptual framework for these scenarios, as described in the three subsequent papers in this Special Issue (Van Vuuren et al., 2013; O’Neill et al., 2013; Kriegler et al., Submitted for publication in this special issue). The paper also discusses research needs to further develop, apply, and revise this framework in an iterative and open-ended process. A key goal of the framework design and its future development is to facilitate the collaboration of climate change researchers from a broad range of perspectives and disciplines to develop policy- and decision-relevant scenarios and explore the challenges and opportunities human and natural systems could face with additional climate change.     

Determination of Reference Values for NIST SRM 610–617 Glasses Following ISO Guidelines

We present new reference values for the NIST SRM 610–617 glasses following ISO guidelines and the International Association of Geoanalysts’ protocol. Uncertainties at the 95% confidence level (CL) have been determined for bulk‐ and micro‐analytical purposes. In contrast to former compilation procedures, this approach delivers data that consider present‐day requirements of data quality. New analytical data and the nearly complete data set of the GeoReM database were used for this study. Data quality was checked by the application of the Horwitz function and by a careful investigation of analytical procedures. We have determined quantitatively possible element inhomogeneities using different test portion masses of 1, 0.1 and 0.02 μg. Although avoiding the rim region of the glass wafers, we found moderate inhomogeneities of several chalcophile/siderophile elements and gross inhomogeneities of Ni, Se, Pd and Pt at small test portion masses. The extent of inhomogeneity was included in the determination of uncertainties. While the new reference values agree with the NIST certified values with the one exception of Mn in SRM 610, they typically differ by as much as 10% from the Pearce et al. (1997) values in current use. In a few cases (P, S, Cl, Ta, Re) the discrepancies are even higher.     

What causes the spread of model projections of ocean dynamic sea-level change in response to greenhouse gas forcing?

Sea levels of different atmosphere–ocean general circulation models (AOGCMs) respond to climate change forcing in different ways, representing a crucial uncertainty in climate change research. We isolate the role of the ocean dynamics in setting the spatial pattern of dynamic sea-level (ζ) change by forcing several AOGCMs with prescribed identical heat, momentum (wind) and freshwater flux perturbations. This method produces a ζ projection spread comparable in magnitude to the spread that results from greenhouse gas forcing, indicating that the differences in ocean model formulation are the cause, rather than diversity in surface flux change. The heat flux change drives most of the global pattern of ζ change, while the momentum and water flux changes cause locally confined features. North Atlantic heat uptake causes large temperature and salinity driven density changes, altering local ocean transport and ζ. The spread between AOGCMs here is caused largely by differences in their regional transport adjustment, which redistributes heat that was already in the ocean prior to perturbation. The geographic details of the ζ change in the North Atlantic are diverse across models, but the underlying dynamic change is similar. In contrast, the heat absorbed by the Southern Ocean does not strongly alter the vertically coherent circulation. The Arctic ζ change is dissimilar across models, owing to differences in passive heat uptake and circulation change. Only the Arctic is strongly affected by nonlinear interactions between the three air-sea flux changes, and these are model specific.