THERIA_G: a software program to numerically model prograde garnet growth

We present the software program THERIA_G, which allows for numerical simulation of garnet growth in a given volume of rock along any pressure–temperature–time (P–T–t) path. THERIA_G assumes thermodynamic equilibrium between the garnet rim and the rock matrix during growth and accounts for component fractionation associated with garnet formation as well as for intracrystalline diffusion within garnet. In addition, THERIA_G keeps track of changes in the equilibrium phase relations, which occur during garnet growth along the specified P–T–t trajectory. This is accomplished by the combination of two major modules: a Gibbs free energy minimization routine is used to calculate equilibrium phase relations including the volume and composition of successive garnet growth increments as P and T and the effective bulk rock composition change. With the second module intragranular multi-component diffusion is modelled for spherical garnet geometry. THERIA_G allows to simulate the formation of an entire garnet population, the nucleation and growth history of which is specified via the garnet crystal size frequency distribution. Garnet growth simulations with THERIA_G produce compositional profiles for the garnet porphyroblasts of each size class of a population and full information on equilibrium phase assemblages for any point along the specified P–T–t trajectory. The results of garnet growth simulation can be used to infer the P–T–t path of metamorphism from the chemical zoning of garnet porphyroblasts. With a hypothetical example of garnet growth in a pelitic rock we demonstrate that it is essential for the interpretation of the chemical zoning of garnet to account for the combined effects of the thermodynamic conditions of garnet growth, the nucleation history and intracrystalline diffusion. Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users.

An experimental study of the grain-scale processes of peridotite melting: implications for major and trace element distribution during equilibrium and disequilibrium melting

The grain-scale processes of peridotite melting were examined at 1,340°C and 1.5 GPa using reaction couples formed by juxtaposing pre-synthesized clinopyroxenite against pre-synthesized orthopyroxenite or harzburgite in graphite and platinum-lined molybdenum capsules. Reaction between the clinopyroxene and orthopyroxene-rich aggregates produces a melt-enriched, orthopyroxene-free, olivine + clinopyroxene reactive boundary layer. Major and trace element abundance in clinopyroxene vary systematically across the reactive boundary layer with compositional trends similar to the published clinopyroxene core-to-rim compositional variations in the bulk lherzolite partial melting studies conducted at similar P–T conditions. The growth of the reactive boundary layer takes place at the expense of the orthopyroxenite or harzburgite and is consistent with grain-scale processes that involve dissolution, precipitation, reprecipitation, and diffusive exchange between the interstitial melt and surrounding crystals. An important consequence of dissolution–reprecipitation during crystal-melt interaction is the dramatic decrease in diffusive reequilibration time between coexisting minerals and melt. This effect is especially important for high charged, slow diffusing cations during peridotite melting and melt-rock reaction. Apparent clinopyroxene-melt partition coefficients for REE, Sr, Y, Ti, and Zr, measured from reprecipitated clinopyroxene and coexisting melt in the reactive boundary layer, approach their equilibrium values reported in the literature. Disequilibrium melting models based on volume diffusion in solid limited mechanism are likely to significantly underestimate the rates at which major and trace elements in residual minerals reequilibrate with their surrounding melt. Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

Controls on porphyroblast size along a regional metamorphic field gradient

Garnet-bearing schists from the Waterville Formation of south-central Maine provide an opportunity to examine the factors governing porphyroblast size over a range of metamorphic grade. Three-dimensional sizes and locations for all garnet porphyroblasts were determined for three samples along the metamorphic field gradient spanning lowest garnet through sillimanite grade, using high-resolution X-ray computed tomography. Comparison of crystal size distributions to previous data sets obtained by stereological methods for the same samples reveals significant differences in mode, mean, and shape of the distributions. Quantitative textural analysis shows that the garnets in each rock crystallized in a diffusion-controlled nucleation and growth regime. In contrast to the typical observation of a correlation between porphyroblast size and position along a metamorphic field gradient, porphyroblast size of the lowest-grade specimen is intermediate between the high- and middle-grade specimens’ sizes. Mean porphyroblast size does not correlate with peak temperatures from garnet-biotite Fe-Mg exchange thermometry, nor is post-crystallization annealing (Ostwald Ripening) required to produce the observed textures, as was previously proposed for these rocks. Robust pseudosection calculations fail to reproduce the observed garnet core compositions for two specimens, suggesting that these calc-pelites experienced metasomatism. For each of these two specimens, Monte Carlo calculations suggest potential pre-metasomatism bulk compositions that replicate garnet core compositions. Pseudosection analyses allow the estimation of the critical temperatures for garnet growth: ∼481, ∼477, and ∼485°C for the lowest-garnet-zone, middle-garnet-zone, and sillimanite-zone specimens, respectively. Porphyroblast size appears to be determined in this case by a combination of the heating rate during garnet crystallization, the critical temperature for the garnet-forming reaction and the kinetics of nucleation. Numerical simulations of thermally accelerated, diffusion-controlled nucleation, and growth for the three samples closely match measured crystal size distributions. These observations and simulations suggest that previous hypotheses linking the garnet size primarily to the temperature at the onset of porphyroblast nucleation can only partially explain the observed textures. Also important in determining porphyroblast size are the heating rate and the distribution of favorable nucleation sites.     

Cr-spinel/olivine and Cr-spinel/liquid nickel partition coefficients from natural samples

The Nernst partition coefficient of nickel (D^Ni) between Cr-spinel and silicate melt in natural systems has been investigated using mid-ocean ridge basalts (MORB) and other volcanic rocks. The Cr-spinel/olivine D^Ni values in volcanic rocks are between 1.2 and 0.3, indicating that the Cr-spinel/liquid D^Ni values vary from slightly higher to significantly lower than the olivine/liquid D^Ni values in natural systems. The Cr-spinel/liquid D^Ni values from the MORB samples vary between 6 and 11, slightly higher than those from the S-bearing experiments of Satari et al. [Satari P., Brenan J. M., Horn I. and McDonough W. F. (2002) Experimental constraints on the sulfide- and chromite-silicate melt partitioning behavior of rhenium and platinum-group elements. Economic Geology97, 385-398]. The results of the MORB samples and the experiments of Satari et al. (2002) indicate a negative correlation between the Cr-spinel/liquid D^Ni and the X_Cr values in Cr-spinels (Cr cation number on the basis of 3 total cations in the spinel structure). Variations of Cr-spinel/liquid D^Ni values with Cr-spinel compositions can be estimated from an empirical equation based on the results of the MORB samples and the experiments by Satari et al. (2002). The choice of Cr-spinel/liquid D^Ni = 10 for numerical modeling by Righter et al. [Righter K., Leeman W. P. and Hervig R. L. (2006) Partitioning of Ni, Co, and V between spinel-structured oxides and silicate melts: importance of spinel composition. Chemical Geology227, 1-25] is reasonable for basaltic systems. For picritic and komatiitic systems a lower value of ∼5 is more appropriate.     

Exurbia from the bottom-up: Confronting empirical challenges to characterizing a complex system

We describe empirical results from a multi-disciplinary project that support modeling complex processes of land-use and land-cover change in exurban parts of Southeastern Michigan. Based on two different conceptual models, one describing the evolution of urban form as a consequence of residential preferences and the other describing land-cover changes in an exurban township as a consequence of residential preferences, local policies, and a diversity of development types, we describe a variety of empirical data collected to support the mechanisms that we encoded in computational agent-based models. We used multiple methods, including social surveys, remote sensing, and statistical analysis of spatial data, to collect data that could be used to validate the structure of our models, calibrate their specific parameters, and evaluate their output. The data were used to investigate this system in the context of several themes from complexity science, including have (a) macro-level patterns; (b) autonomous decision making entities (i.e., agents); (c) heterogeneity among those entities; (d) social and spatial interactions that operate across multiple scales and (e) nonlinear feedback mechanisms. The results point to the importance of collecting data on agents and their interactions when producing agent-based models, the general validity of our conceptual models, and some changes that we needed to make to these models following data analysis. The calibrated models have been and are being used to evaluate landscape dynamics and the effects of various policy interventions on urban land-cover patterns.     

Church-based social capital, networks and geographical scale: Katrina evacuation, relocation, and recovery in a New Orleans Vietnamese American community

This research examines the role of social capital and networks to explain the evacuation, relocation, and recovery experiences of a Vietnamese American community in New Orleans, Louisiana in the aftermath of Hurricane Katrina. As the single largest community institution, the parish church’s complex bonding and bridging social capital and networks proved particularly critical in part because of its historically based ontological security. The process of evacuation, but especially relocation and recovery, was dependent on deploying co-ethnic social capital and networks at a variety of geographical scales. Beyond the local or community scale, extra-local, regional, and national scales of social capital and networks reproduced a spatially redefined Vietnamese American community. Part of the recovery process included constructing discursive place-based collective-action frames to successfully contest a nearby landfill that in turn engendered social capital and networks crossing ethnic boundaries to include the extra-local African American community. Engaging social capital and networks beyond the local geographical scale cultivated a Vietnamese American community with an emergent post-Katrina cultural and political identity.     

Quantitative sinkhole hazard assessment. A case study from the Ebro Valley evaporite alluvial karst (NE Spain)

Quantitative sinkhole hazard assessments in karst areas allow calculation of the potential sinkhole risk and the performance of cost-benefit analyses. These estimations are of practical interest for planning, engineering, and insurance purposes. The sinkhole hazard assessments should include two components: the probability of occurrence of sinkholes (sinkholes/km² year) and the severity of the sinkholes, which mainly refers to the subsidence mechanisms (progressive passive bending or catastrophic collapse) and the size of the sinkholes at the time of formation; a critical engineering design parameter. This requires the compilation of an exhaustive database on recent sinkholes, including information on the: (1) location, (2) chronology (precise date or age range), (3) size, and (4) subsidence mechanisms and rate. This work presents a hazard assessment from an alluvial evaporite karst area (0.81 km²) located in the periphery of the city of Zaragoza (Ebro River valley, NE Spain). Five sinkholes and four locations with features attributable to karstic subsidence where identified in an initial investigation phase providing a preliminary probability of occurrence of 0.14 sinkholes/km² year (11.34% in annual probability). A trenching program conducted in a subsequent investigation phase allowed us to rule out the four probable sinkholes, reducing the probability of occurrence to 0.079 sinkholes/km² year (6.4% in annual probability). The information on the severity indicates that collapse sinkholes 10–15 m in diameter may occur in the area. A detailed study of the deposits and deformational structures exposed by trenching in one of the sinkholes allowed us to infer a modern collapse sinkhole approximately 12 m in diameter and with a vertical throw of 8 m. This collapse structure is superimposed on a subsidence sinkhole around 80 m across that records at least 1.7 m of synsedimentary subsidence. Trenching, in combination with dating techniques, is proposed as a useful methodology to elucidate the origin of depressions with uncertain diagnosis and to gather practical information with predictive utility about particular sinkholes in alluvial karst settings: precise location, subsidence mechanisms and magnitude, and timing and rate of the subsidence episodes.     

Drought and institutional adaptation in the Great Plains of Alberta and Saskatchewan, 1914–1939

Agriculture in the southern Great Plains of Canada has been particularly vulnerable to prolonged episodes of drought. Using climate data and a precipitation minus potential evapotranspiration index, the extent of the region’s exposure to drought is examined. Between 1914 and 1917, the Dry Belt was particularly vulnerable to drought, whereas after 1928, a much larger region known as the Palliser Triangle covering most of southern Alberta and Saskatchewan was much more exposed to drought. These droughts provoked major institutional adaptation, in particular the establishment of the Special Areas Board by the Government of Alberta, and the creation of the Prairie Farm Rehabilitation Administration by the Government of Canada. Both organizations have proved to be relatively permanent public adaptations to the natural hazard of drought in the region. Moreover, these earlier experiences with prolonged drought as well as institution-building may be of value in helping the residents of the Palliser Triangle adapt to predicted climate changes in the future as well as anticipate some of the barriers to effective institutional adaptation.