The Tolerable Windows Approach: Theoretical and Methodological Foundations

The tolerable windows (TW) approach is presented as a novel scheme for integrated assessment of climate change. The TW approach is based on the specification of a set of guardrails for climate evolution which refer to various climate-related attributes. These constraints, which define what we call tolerable windows, can be purely systemic in nature – like critical thresholds for the North Atlantic Deep Water formation – or of a normative type – like minimum standards for per-capita food production worldwide. Starting from this catalogue of knock-out criteria and using appropriate modeling techniques, those policy strategies which are compatible with all the constraints specified are sought to be identified. In addition to the discussion of the basic elements and the general theory of the TW approach, a modeling exercise is carried out, based on simple models and assumptions adopted from the German Advisory Council on Global Change (WBGU). The analysis shows that if the global mean temperature is restricted to 2°C beyond the preindustrial level, the cumulative emissions of CO2 are asymptotically limited to about 1550 Gt C. Yet the temporal distribution of these emissions is also determined by the climate and socio-economic constraints: using, for example, a maximal tolerable rate of temperature change of 0.2°C/dec and a smoothly varying emissions profile, we obtain the maximal cumulative emissions, amounting to 370 Gt C in 2050 and 585 Gt C in 2100.     

The influence of crystal field stabilization energy on Fe2+ partitioning in paragenetic minerals

In order to explore possible quantitative relations between crystal field stabilization energy, CFSE, and partitioning behaviour of the 3d ⁶-configured Fe²⁺ ion, a suite of 29 paragenetic rock-forming minerals from 12 high-grade metamorphic rock samples of the Ukrainian shield, including the parageneses garnet/orthopyroxene/clinopyroxene (2x), orthopyroxene/clinopyroxene, garnet/clinopyroxene, garnet/orthopyroxene/biotite, garnet/biotite, garnet/cordierite, garnet/cordierite/biotite, garnet/orthopyroxene/clinopyroxene/Ca-amphibole, Ca-amphibole/biotite (retrograde), was studied by electron microprobe analysis to obtain the respective K _D Fe^{2+ (Ph1/Ph2)} values and by polarized single crystal electronic absorption spectroscopy to evaluate the respective CFSE_Fe2+ values. Other than in the case of Cr³⁺, a clear quantitative relation between K _D ^(Ph1/Ph2) and the ΔCFSE^(Ph1/Ph2) was only observed when geometrical factors, mainly the volume of crystallographic sites and ionic radii of ions competing in the partitioning process, are similar in the respective two paragenetic phases to within 15–20%. In such cases, the ΔCFSE_Fe2+ contribution to K _D ^(Ph1/Ph2) amounts to 0.1 to 0.2 log K _D per 100 cm⁻¹ΔCFSE. The conclusion is that ΔCFSE_Fe2+ plays only a secondary role after geometrical factors, in the partitioning behaviour of Fe²⁺. The reason for this is seen in the facts that, compared to the 3d ³-configured Cr³⁺ ion, CFSE of the 3d ⁶-configured Fe²⁺ amounts only to 20–25%, and that the former ion enters only octahedral sites with similar geometrical properties in the paragenetic mineral phases. Received: 17 November 1998 / Accepted: 28 June 1999     

Evidence for low‐temperature growth of fayalite and hedenbergite in MacAlpine Hills 88107, an ungrouped carbonaceous chondrite related to the CM‐CO clan

Abstract— The carbonaceous chondrite MacAlpine Hills (MAC) 88107 has bulk composition and mineralogy that are intermediate between those of CO and CM chondrites. This meteorite experienced minor alteration and a low degree of thermal metamorphism (petrologic type 3.1) and escaped post‐accretional brecciation. The alteration resulted in the formation of fayalite (Fa_90–100). Al‐free hedenbergite (～Fs₅₀Wo₅₀), phyllosilicates (saponite‐serpentine intergrowths), magnetite, and Ni‐bearing sulfides (pyrrhotite and pentlandite). Fayalite and hedenbergite typically occur as veins, which start at the opaque nodules in the chondrule peripheries, crosscut fine‐grained rims and either terminate at the boundaries with the neighboring fine‐grained rims or continue as layers between these rims. These observations suggest that fayalite and hedenbergite crystallized after accretion and compaction of the fine‐grained rims. Fayalite also overgrows isolated forsteritic (Fa_1–5) and fayalitic (Fa_20–40) olivine grains without any evidence for Fe‐Mg interdiffusion; it also replaces massive magnetite‐sulfide grains. The initial ⁵³Mn/⁵⁵Mn ratio of (1.58 ± 0.26) × 10^?6 in the MAC 88107 fayalite corresponds to an age difference between the formation of fayalite and refractory inclusions in Allende of either ～9 or 18 Ma, depending upon the value of the solar system initial abundance of ⁵³Mn used in age calculations. Formation of secondary fayalite and hedenbergite requires mobilization and transport of Ca, Si, and Fe either through a high‐temperature gaseous phase (Hua and Buseck, 1995) or low‐temperature aqueous solution (Krot et al., 1998a, b). The high‐temperature nebular model for the origin of fayalite (Hua and Buseck, 1995) fails to explain (a) formation of fayalite‐hedenbergite assemblages after accretion of fine‐grained rims that lack any evidence for high‐temperature processing; (b) extreme fractionation of refractory lithophile elements of similar volatility, Ca and Al, in hedenbergite; and (c) absence of Fe‐Mg interdiffusion along fayalite‐forsterite boundaries. We conclude that fayalite and hedenbergite in MAC 88107 formed during late‐stage, low‐temperature (approximately 150–200 °C) aqueous alteration. The data for MAC 88107 extend the evidence for an early onset of aqueous activity on chondrite parent bodies and reinforce the conclusion that liquid water played an important role in the chemical and mineralogical evolution of the first chondritic planetesimals.     

Earthquake loss estimation for the New York City Metropolitan Region

This study is a thorough risk and loss assessment of potential earthquakes in the NY–NJ–CT Metropolitan Region. This study documents the scale and extent of damage and disruption that may result if earthquakes of various magnitudes occurred in this area. Combined with a detailed geotechnical soil characterization of the region, scenario earthquakes were modeled in HAZUS (Hazards US), a standardized earthquake loss estimation methodology and modeling program. Deterministic and probabilistic earthquake scenarios were modeled and simulated, which provided intensities of ground shaking, dollar losses associated with capital (the building inventory) and subsequent income losses. This study has also implemented a detailed critical (essential) facilities analysis, assessing damage probabilities and facility functionality after an earthquake. When viewed in context with additional information about regional demographics and seismic hazards, the model and results serve as a tool to identify the areas, structures and systems with the highest risk and to quantify and ultimately reduce those risks.     

Laboratory measurements of seismic attenuation and Young's modulus dispersion in a partially and fully water‐saturated porous sample made of sintered borosilicate glass

We measured the extensional‐mode attenuation and Young's modulus in a porous sample made of sintered borosilicate glass at microseismic to seismic frequencies (0.05–50 Hz) using the forced oscillation method. Partial saturation was achieved by water imbibition, varying the water saturation from an initial dry state up to ～99%, and by gas exsolution from an initially fully water‐saturated state down to ～99%. During forced oscillations of the sample effective stresses up to 10 MPa were applied. We observe frequency‐dependent attenuation, with a peak at 1–5 Hz, for ～99% water saturation achieved both by imbibition and by gas exsolution. The magnitude of this attenuation peak is consistently reduced with increasing fluid pressure and is largely insensitive to changes in effective stress. Similar observations have recently been attributed to wave‐induced gas exsolution–dissolution. At full water saturation, the left‐hand side of an attenuation curve, with a peak beyond the highest measured frequency, is observed at 3 MPa effective stress, while at 10 MPa effective stress the measured attenuation is negligible. This observation is consistent with wave‐induced fluid flow associated with mesoscopic compressibility contrasts in the sample's frame. These variations in compressibility could be due to fractures and/or compaction bands that formed between separate sets of forced‐oscillation experiments in response to the applied stresses. The agreement of the measured frequency‐dependent attenuation and Young's modulus with the Kramers–Kronig relations and additional data analyses indicate the good quality of the measurements. Our observations point to the complex interplay between structural and fluid heterogeneities on the measured seismic attenuation and they illustrate how these heterogeneities can facilitate the dominance of one attenuation mechanism over another.     

Numerically quantifying energy loss caused by squirt flow

In interconnected microcracks, or in microcracks connected to spherical pores, the deformation associated with the passage of mechanical waves can induce fluid flow parallel to the crack walls, which is known as squirt flow. This phenomenon can also occur at larger scales in hydraulically interconnected mesoscopic cracks or fractures. The associated viscous friction causes the waves to experience attenuation and velocity dispersion. We present a simple hydromechanical numerical scheme, based on the interface-coupled Lamé–Navier and Navier–Stokes equations, to simulate squirt flow in the frequency domain. The linearized, quasi-static Navier–Stokes equations describe the laminar flow of a compressible viscous fluid in conduits embedded in a linear elastic solid background described by the quasi-static Lamé–Navier equations. Assuming that the heterogeneous model behaves effectively like a homogeneous viscoelastic medium at a larger spatial scale, the resulting attenuation and stiffness modulus dispersion are computed from spatial averages of the complex-valued, frequency-dependent stress and strain fields. An energy-based approach is implemented to calculate the local contributions to attenuation that, when integrated over the entire model, yield results that are identical to those based on the viscoelastic assumption. In addition to thus validating this assumption, the energy-based approach allows for analyses of the spatial dissipation patterns in squirt flow models. We perform simulations for a series of numerical models to illustrate the viability and versatility of the proposed method. For a 3D model consisting of a spherical crack embedded in a solid background, the characteristic frequency of the resulting P-wave attenuation agrees with that of a corresponding analytical solution, indicating that the dissipative viscous flow problem is appropriately handled in our numerical solution of the linearized, quasi-static Navier–Stokes equations. For 2D models containing either interconnected cracks or cracks connected to a circular pore, the results are compared with those based on Biot's poroelastic equations of consolidation, which are solved through an equivalent approach. Overall, our numerical simulations and the associated analyses demonstrate the suitability of the coupled Lamé–Navier and Navier–Stokes equations and of Biot's equations for quantifying attenuation and dispersion for a range of squirt flow scenarios. These analyses also allow for delineating numerical and physical limitations associated with each set of equations.     

Wavelet transform-based seismic facies classification and modelling: application to a geothermal target horizon in the NE German Basin

At the geothermal test site near Groß Schönebeck (NE German Basin), a new 3D seismic reflection survey was conducted to study geothermal target layers at around 4 km depth and 150°C. We present a workflow for seismic facies classification and modelling which is applied to a prospective sandstone horizon within the Rotliegend formation. Signal attributes are calculated along the horizon using the continuous Morlet wavelet transform. We use a short mother wavelet to allow for the temporal resolution of the relatively short reflection signals to be analysed. Time-frequency domain data patterns form the input of a neural network clustering using self-organizing maps. Neural model patterns are adopted during iterative learning to simulate the information inherent in the input data. After training we determine a gradient function across the self-organizing maps and apply an image processing technique called watershed segmentation. The result is a pattern clustering based on similarities in wavelet transform characteristics. Three different types of wavelet transform patterns were found for the sandstone horizon. We apply seismic waveform modelling to improve the understanding of the classification results. The modelling tests indicate that thickness variations have a much stronger influence on the wavelet transform response of the sandstone horizon compared with reasonable variations of seismic attenuation. In our interpretation, the assumed thickness variations could be a result of variable paleo-topography during deposition of predominantly fluvial sediments. A distinct seismic facies distribution is interpreted as a system of thicker paleo-channels deposited within a deepened landscape. The results provide constraints for the ongoing development of the geothermal test site.     

Calcium‐aluminum‐rich inclusions in enstatite chondrites (I): Mineralogy and textures

Abstract— Like calcium‐aluminum‐rich inclusions (CAIs) from carbonaceous and ordinary chondrites, enstatite chondrite CAIs are composed of refractory minerals such as spinel, perovskite, Al, Ti‐diopside, melilite, hibonite, and anorthitic plagioclase, which may be partially to completely surrounded by halos of Na‐(±Cl)‐rich minerals. Porous, aggregate, and compact textures of the refractory cores in enstatite chondrite CAIs and rare Wark—Lovering rims are also similar to CAIs from other chondrite groups. However, the small size (<100μm), low abundance (<1% by mode in thin section), occurrence of only spinel or hibonite‐rich types, and presence of primary Ti‐(±V)‐oxides, and secondary geikelite and Ti, Fe‐sulfides distinguish the assemblage of enstatite chondrite CAIs from other groups. The primary mineral assemblage in enstatite chondrite CAIs is devoid of indicators (e.g., oldhamite, osbornite) of low O fugacities. Thus, high‐temperature processing of the CAIs did not occur under the reducing conditions characteristic of enstatite chondrites, implying that either (1) the CAIs are foreign to enstatite‐chondrite‐forming regions or (2) O fugacities fluctuated within the enstatite‐chondrite‐forming region. In contrast, secondary geikelite and Ti‐Fe‐sulfide, which replace perovskite, indicate that alteration of perovskite occurred under reducing conditions distinct from CAIs in the other chondrite groups. We have not ascertained whether the reduced alteration of enstatite chondrite CAIs occurred in a nebular or parent‐body setting. We conclude that each chondrite group is correlated with a unique assemblage of CAIs, indicating spatial or temporal variations in physical conditions during production or dispersal of CAIs.