A general Bayesian framework for calibrating and evaluating stochastic models of annual multi-site hydrological data

Multi-site simulation of hydrological data are required for drought risk assessment of large multi-reservoir water supply systems. In this paper, a general Bayesian framework is presented for the calibration and evaluation of multi-site hydrological data at annual timescales. Models included within this framework are the hidden Markov model (HMM) and the widely used lag-1 autoregressive (AR(1)) model. These models are extended by the inclusion of a Box–Cox transformation and a spatial correlation function in a multi-site setting. Parameter uncertainty is evaluated using Markov chain Monte Carlo techniques. Models are evaluated by their ability to reproduce a range of important extreme statistics and compared using Bayesian model selection techniques which evaluate model probabilities. The case study, using multi-site annual rainfall data situated within catchments which contribute to Sydney’s main water supply, provided the following results: Firstly, in terms of model probabilities and diagnostics, the inclusion of the Box–Cox transformation was preferred. Secondly the AR(1) and HMM performed similarly, while some other proposed AR(1)/HMM models with regionally pooled parameters had greater posterior probability than these two models. The practical significance of parameter and model uncertainty was illustrated using a case study involving drought security analysis for urban water supply. It was shown that ignoring parameter uncertainty resulted in a significant overestimate of reservoir yield and an underestimation of system vulnerability to severe drought.     

A review of the synthesis and characterisation of pillared clays and related porous materials for cracking of vegetable oils to produce biofuels

This paper presents an overview of the modification of clay minerals by propping apart the clay layers with an inorganic complex. This expanded material is converted into a permanent two-dimensional structure, known as pillared clay or shortly PILC, by thermal treatment. The resulting material exhibits a two-dimensional porous structure with acidic properties comparable to that of zeolites. Synthetic as well as natural smectites serve as precursors for the synthesis of Al, Zr, Ti, Fe, Cr, Ga, V, Si and other pillared clays as well as mixed Fe/Al, Ga/Al, Si/Al, Zr/Al and other mixed metal pillared clays. Biofuels form an interesting renewable energy source, where these porous, catalytically active materials can play an important role in the conversion of vegetable oils, such as canola oil, into biodiesel. Transesterification of vegetable oil is currently the method of choice for conversion to biofuel. The second part of this review focuses on the catalysts and cracking reaction conditions used for the production of biofuel. A distinction has been made in three different vegetable oils as starting materials: canola oil, palm oil and sunflower oil.     

U-Pb sphene dating of metamorphism: the importance of sphene growth in the contact aureole of the Red Mountain pluton,Laramie Mountains,Wyoming

 The relative importance of thermal diffusion versus new growth or recrystallization on U-Pb isotopic data from sphene is assessed through a study of amphibolites and granite gneisses within the contact aureole of the Red Mountain pluton, Laramie anorthosite complex, Wyoming. Samples were collected along a traverse approximately perpendicular to the margin of the intrusion over a distance of 0.13 to 2.65 km from the contact. The ²⁰⁷Pb/²⁰⁶Pb ages of sphene from amphibolite samples range between 1.43 Ga, the intrusive age of the Red Mountain pluton, to 1.78 Ga, the age of regional metamorphism. The ²⁰⁷Pb/²⁰⁶Pb ages of sphene in rocks metamorphosed above 700° C are within error of the intrusive age of the pluton, and appear to have resulted from diffusional resetting of preexisting sphene and the metamorphic growth of additional sphene at 1.43 Ga. At greater distance from the contact the ²⁰⁷Pb/²⁰⁶Pb ages range from 1.45 to 1.72 Ga. This 300 million year spread in ages is interpreted to result from two periods of sphene growth, one produced during regional metamorphism at 1.78 Ga and another generation of newly grown or recrystallized sphene that formed during contact metamorphism at 1.43 Ga. These two age populations may be identified on the basis of petrographic textures, the morphologies and color differences of grain separates as well as by the U-Pb systematics. In rocks metamorphosed to temperatures less than 700° C, sphene growth was the dominant process controlling the response of the U-Pb isotope system to contact metamorphism. Sphene grew well outside the zone of obvious contact metamorphism. The U-Pb sphene ages were reset by diffusion only at high temperatures, supporting the experimentally determined closure temperature estimates for the U-Pb system in sphene of around 650° C (Cherniak 1993). This study demonstrates that U-Pb ages of sphene can be used to date metamorphism not only in areas with a simple geologic history, such as igneous intrusion or single metamorphic or deformational events, but also to date multiple events so long as different generations of sphene can be identified and separated. Received: 22 August 1995 / Accepted: 17 April 1996     

Evaluation of amendments used to prevent sodification of irrigated fields

Gypsum and S are applied to soils being irrigated with Na–HCO₃ dominated coalbed natural gas (CBNG) produced water to protect soil structure and fertility. Wyoming law requires beneficial use of produced water and irrigation with CBNG produced water in the semi-arid Powder River Basin is becoming more common. Strontium isotopes were used to evaluate the effectiveness of the gypsum and S applications in preventing sodification of these irrigated soils. The isotope ratio of Sr on the cation exchange complex of irrigated soil falls between that of the gypsum amendment (0.7074) and that of local soil (0.712–0.713). Strontium isotopes indicate that, to a depth of 30 cm, as much as 50% of the Sr on the irrigated soil cation exchange sites originated from the applied gypsum amendment on a field irrigated for 3 a. This was also true to a depth of 5 cm on a field irrigated less than 1 a. Strontium isotope ratio measurements of vegetation illustrate plant utilization of Sr from gypsum amendments, thereby reinforcing the conclusions about the presence of Sr from gypsum on the soil’s exchange sites. This Sr tracing technique may be useful in a wide variety of settings where monitoring soil health is necessary, especially in settings where poor quality water is used for irrigation: a more common occurrence as demand for fresh water increases.     

Fe4O5 and its solid solutions in several simple systems

Experiments at high pressures and temperatures reveal the stability of a Fe₄O₅-type structured phase in several simple chemical systems. On the one hand, the Fe₄O₅ end-member is stable in the presence of SiO₂-rich phases, including stishovite, but contains ≤0.01 Si cations per formula unit. This indicates that Si is essentially excluded from this phase. On the other hand, the Fe₄O₅ phase can form solid solutions with Mg and Cr and can coexist with silicate phases at the high P–T conditions expected in the transition zone of the mantle (i.e. >~9 GPa). It can coexist with both wadsleyite and Mg-rich ringwoodite and can contain at least 25 mol% Mg₂Fe₂O₅ component. The Fe₄O₅ phase always contains the least amount of Mg in any given mineral assemblage. Cr-bearing Fe₄O₅ has been synthesised with up to 46 mol% Fe₂Cr₂O₅ component and can coexist with spinel and/or hematite-eskolatite solid solutions. Substitution of Mg and Cr for Fe²⁺ and Fe³⁺, respectively, leads to variations in Fe³⁺/∑Fe from the ideal value of 0.5 for the Fe₄O₅ end-member composition, which can influence its redox stability. These cations also have contrasting effects on the unit-cell parameters, which indicate that they substitute into different sites. This initial study suggests that Fe₄O₅-type structured phases may be stable over a range of P–T–fO₂ conditions and bulk compositions, and can be important in understanding the post-spinel phase relations in a number of chemical systems relevant to the Earth’s transition zone. Thus, the presence of even small amounts of Fe³⁺ could alter the expected phase relations in peridotitic bulk compositions by stabilising this additional phase.     

Behaviour of Fe<Subscript>4</Subscript>O<Subscript>5</Subscript>–Mg<Subscript>2</Subscript>Fe<Subscript>2</Subscript>O<Subscript>5</Subscript> solid solutions and their relation to coexisting Mg–Fe silicates and oxide phases

Experiments at high pressures and temperatures were carried out (1) to investigate the crystal-chemical behaviour of Fe₄O₅–Mg₂Fe₂O₅ solid solutions and (2) to explore the phase relations involving (Mg,Fe)₂Fe₂O₅ (denoted as O₅-phase) and Mg–Fe silicates. Multi-anvil experiments were performed at 11–20 GPa and 1100–1600 °C using different starting compositions including two that were Si-bearing. In Si-free experiments the O₅-phase coexists with Fe₂O₃, hp-(Mg,Fe)Fe₂O₄, (Mg,Fe)₃Fe₄O₉ or an unquenchable phase of different stoichiometry. Si-bearing experiments yielded phase assemblages consisting of the O₅-phase together with olivine, wadsleyite or ringwoodite, majoritic garnet or Fe³⁺-bearing phase B. However, (Mg,Fe)₂Fe₂O₅ does not incorporate Si. Electron microprobe analyses revealed that phase B incorporates significant amounts of Fe²⁺ and Fe³⁺ (at least ~?1.0 cations Fe per formula unit). Fe-L_2,3-edge energy-loss near-edge structure spectra confirm the presence of ferric iron [Fe³⁺/Fe_tot?=?~?0.41(4)] and indicate substitution according to the following charge-balanced exchange: [4]Si⁴⁺?+?[6]Mg²⁺?=?2Fe³⁺. The ability to accommodate Fe²⁺ and Fe³⁺ makes this potential “water-storing” mineral interesting since such substitutions should enlarge its stability field. The thermodynamic properties of Mg₂Fe₂O₅ have been refined, yielding H°_1bar,298?=???1981.5 kJ mol^??1. Solid solution is complete across the Fe₄O₅–Mg₂Fe₂O₅ binary. Molar volume decreases essentially linearly with increasing Mg content, consistent with ideal mixing behaviour. The partitioning of Mg and Fe²⁺ with silicates indicates that (Mg,Fe)₂Fe₂O₅ has a strong preference for Fe²⁺. Modelling of partitioning with olivine is consistent with the O₅-phase exhibiting ideal mixing behaviour. Mg–Fe²⁺ partitioning between (Mg,Fe)₂Fe₂O₅ and ringwoodite or wadsleyite is influenced by the presence of Fe³⁺ and OH incorporation in the silicate phases.