A numerical method for obtaining multiple linear regression parameters with physically realistic signs and magnitudes: Applications to the determination of equilibrium constants from solubility data

A common problem in experimental geochemistry is the derivation of equilibrium constants from solubility experiments. A simple method of deriving these equilibrium constants, multiple linear regression, often results in the appearance of negative values. This has been a significant obstacle to continuing research in this field. The problem occurs for the most part because of significant correlations among the “independent” concentration variables. These correlations are an inescapable result of the nature of the experiments and the physical model being fitted. Ridge regression is an appropriate modification to simple linear regression which overcomes this difficulty. Ridge regression results in a simple procedure to obtain physically plausible, yet statistically rigorous stability constants. Of course, other problems may further degrade the quality of derived equilibrium constants, e.g. uncertainty in activity coefficients and no purely statistical method can overcome these types of problems. However, ridge regression is an effective procedure to overcome the multicolinearity which is the main cause of negative equilibrium constants. We demonstrate the use of ridge regression with a general mathematical model and then illustrate its use in the determination of iron-chloro complex equilibrium constants from solubility studies of pyrite-pyrrhotite-magnetite in NaCl solutions at 250°C. Ridge regression may also be of use in other geochemical problems where one must estimate parameters with a physical interpretation and where the independent variables are significantly intercorrelated.     

The Askervein Hill Project: Wind-tunnel simulations at three length scales

Wind-tunnel simulations of neutrally-stable atmospheric boundary-layer flow over an isolated, low hill (Askervein) have been carried out at three different length scales in two wind-tunnel facilities. The objectives of these simulations were to assess the reliability with which changes in mean wind and turbulence structure induced by the prototype hill on boundary-layer flow can be reproduced in the wind tunnel, and to determine the relative impact of certain modelling approaches (surface roughness, model scale, measurement techniques, etc.) on the quality of the simulations. The wind-tunnel results are compared with each other and with full-scale data and are shown in general to model the prototype flow very well. The effects of relaxing the criterion of aerodynamic roughness of the model surface were limited to certain regions in the lee of the hill and were linked to separation phenomena.     

Geology and eruptive history of the Rabaul Caldera area, Papua New Guinea

Rabaul Caldera is the most recently active (1937–1943) of four adjoining volcanic centres aligned north-south through the northern extremity of eastern New Britain. Geological mapping after the 1983–1985 Rabaul seismic and deformation crisis has partially revealed a long and complex eruption history dominated by numerous explosive eruptions, the largest accompanied by caldera collapse. The oldest exposed eruptives are the basaltic pre-caldera cone Tovanumbatir Lavas K/Ar dated at 0.5 Ma. The dacitic Rabaul Quarry Lavas exposed in the caldera wall and K/Ar dated at 0.19 Ma, are overlain by a sequence of dacitic and andesitic pyroclastic flow and fall deposits. Uplifted coral reef limestones, interbedded within the pyroclastic sequence on the northeast coast, suggest that explosive eruptions in the Rabaul area had commenced prior to the 0.125 Ma last interglacial high sea level stand. The pyroclastic sequence includes the large Boroi Ignimbrites and Malaguna Pyroclastics both ⁴⁰Ar/³⁹Ar dated at about 0.1 Ma, and the Barge Tunnel Ignimbrite ⁴⁰Ar/³⁹Ar dated at around 0.04 Ma. Few reliable ages exist for the many younger eruptives. These include Holocene ignimbrites of the latest caldera-forming eruptions—the Raluan Pyroclastics variously dated (¹⁴C) at either about 3500 or 7000 yr B.P., and the ca. 1400 yr B.P. Rabaul Pyroclastics. At least eight intracaldera eruptions have occurred since the 1400 yr B.P. collapse, building small pyroclastic and lava cones within the caldera.A major erosional episode is evident as a widespread unconformity in the upper pyroclastic stratigraphy at Rabaul. Lacking relevant radiometric ages, this episode is assumed to have occurred during last glaciation low sea levels and is here arbitarily dated at ca. ?20 ka. At least five, possibly nine, significant ignimbrite eruptions have occurred at Rabaul during the last ?20 ka. The new eruptive history differs considerably from that previously published, which considered ignimbrite eruption and caldera collapse to have first occurred at 3500 yr B.P.Rabaul volcanism has been dominated by two main types: (a) basaltic and basaltic andesite cone building eruptions; and (b) dacitic, and rarely andesitic or rhyolitic, plinian/ignimbrite eruptions of both high- and low-aspect ratio types. The 1400 yr B.P. Rabaul Ignimbrite is a type example of a low-aspect ratio, high-energy, and potentially very damaging eruption. Fine vitric ash deposits, common in the Rabaul pyroclastic sequence, demonstrate the frequent modification of eruptions by external water probably related to early caldera lakes or bays. Interbedding of these fine ashes with plinian pumice lapilli beds suggests that many early eruptions occurred from multiple vents, located in both wet and dry areas.     

Fluid convection and mass transfer in porous sandstones—a theoretical model

When porous, fluid-saturated, bodies of geologic dimensions are subjected to temperature gradients on the order of the normal geothermal gradient (25°C/km) it is shown that large (km) scale eddy currents will spontaneously arise and persist in these bodies. The velocity of these fluid currents is on the order of 1 meter per year, but taken over a period of several million years, the mass flux accompanying the fluid flow is large enough to produce significant porosity changes. It is shown that diffusive mass transfer is generally a negligible component of the total mass flux when characteristic distances are greater than grain diameters and it is concluded that most post-depositional reservoir cementation is due to slowly circulating fluids. In terms of a broad perspective, reservoir diagenesis can be regarded as a low heat flow analogue of hydrothermal alteration, occupying the low fluid flow regime of the spectrum, and passing into the hydrothermal regime as the heat flow and fluid velocities increase.     

Reaction relationships of chrome-spinels in igneous rocks — further evidence from the layered intrusions of Rhum and Mull,Inner Hebrides,Scotland

Compositions of chrome-spinels in peridotites from the layered igneous rocks of Rhum and of the Ben Buie intrusion, Mull, show evidence of post-depositional reaction relationships with the cumulus olivine and/or the intercumulus liquid. Some seam-forming spinels in the Ben Buie intrusion are highly aluminous, more so than those in the Rhum intrusion. Occasional zoned spinels, in both intrusions, show enrichment in Al towards their rims. The evidence suggests that the spinel reaction trend involving Cr-Al exchange proceeds in the direction of Al-enrichment. Equilibrium between chrome-spinel and cumulus olivine appears to have been attained rarely, thus limiting the application of the olivine-spinel geothermometer.     

Detection Time for Plausible Changes in Annual Precipitation, Evapotranspiration, and Streamflow in Three Mississippi River Sub-Basins

We use diagnostic studies of off-line variable infiltration capacity (VIC) model simulations of terrestrial water budgets and 21st-century climate change simulations using the parallel climate model (PCM) to estimate the time required to detect predicted changes in annual precipitation (P), evapotranspiration (E), and discharge (Q) in three sub-basins of the Mississippi River Basin. Time series lengths on the order of 50–350 years are required to detect plausible P, E, and Q trends in the Missouri, Ohio, and Upper Mississippi River basins. Approximately 80–160, 50, and 140–350 years, respectively, are needed to detect the predicted P, E, and Q trends with a high degree of statistical confidence. These detection time estimates are based on conservative statistical criteria (α = 0.05 and β = 0.10) associated with low probability of both detecting a trend when it is not occurring (Type I error) and not detecting a trend when it is occurring (Type II error). The long detection times suggest that global-warming-induced changes in annual basin-wide hydro-climatic variables that may already be occurring in the three basins probably cannot yet be detected at this level of confidence. Furthermore, changes for some variables that may occur within the 21st century might not be detectable for many decades or until the following century – this may or may not be the case for individual recording station data. The long detection times for streamflow result from comparatively low signal-to-noise ratios in the annual time series. Finally, initial estimates suggest that faster detection of acceleration in the hydrological cycle may be possible using seasonal time series of appropriate hydro-climatic variables, rather than annual time series.     

Solute and isotope constraint of groundwater recharge simulation in an arid environment,Abu Dhabi Emirate,United Arab Emirates

A simple, well-constrained simulation of solute increases in a downgradient direction was used in the shallow unconfined aquifer of eastern Abu Dhabi Emirate (United Arab Emirates). The simulation indicates that the observed exponential increase in solute concentrations results from a combination of upward transport of solutes from underlying mudstones and evaporites, and groundwater losses by evaporation. Groundwater recharge and discharge flux in unconfined regional aquifers in arid regions commonly are difficult to estimate because there are few constraints on the flux of water lost or gained from the system. Total dissolved solids (TDS) and deuterium isotopes (δ²H) in groundwater are used to constrain estimated fluxes to the shallow aquifer of eastern Abu Dhabi Emirate. Vertical upward transport of solutes from underlying mudstones and evaporites accounts for solute increases along approximately the first 80 km of the simulated flow path, but a combination of upward solute transport and evaporation is necessary to explain observed solute concentrations beyond 80 km. Mobilization and transport of solutes in the unsaturated zone by recharging precipitation is not a significant factor.

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Résumé Une simulation simple et bien contrainte de l’augmentation des solutés dans la direction de l’écoulement a été réalisée sur l’aquifère phréatique et libre de l’Est de l’émirat d’Abu Dhabi (émirats Arabes Unis). La simulation indique que l’augmentation observée de solutés, de forme exponentielle, est le produit de la combinaison du transport ascendant de solutés provenant des mudstones et des évaporites sous-jacents, et de l’évaporation des eaux souterraines. La recharge des eaux souterraines et les flux de vidange dans les aquifères régionaux libres des régions arides sont habituellement difficiles à estimer du fait du peu de contraintes agissant sur la perte ou le gain d’eau dans le système. La charge dissoute totale (TDS, en anglais) et les isotopes deutérium (δ²H) des eaux souterraines sont utilisés pour contraindre l’estimation des flux en direction de l’aquifère phréatique de l’Est de l’émirat d’Abu Dhabi. Le transport vertical ascendant des solutés à partir des mudstones et des évaporites fait parti des processus qui concentrent les solutés approximativement le long des 80 premiers kilomètres du trajet des écoulements simulés, mais une combinaison du transport ascendant des solutés et de l’évaporation est nécessaire pour expliquer les concentrations observées en soluté au delà des 80 km. La mobilisation et le transport des solutés par les précipitations efficaces dans la zone non saturée ne représentent pas des facteurs significatifs.

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Resumen Se utilizó una simulación simple y muy restringida, de incrementos de soluto en la dirección del flujo, en el acuífero libre poco profundo del Emirato oriental de Abu Dhabi, (Emiratos árabes Unidos). La simulación indica que el aumento exponencial observado en las concentraciones del soluto, resulta de una combinación de transporte ascendente de solutos desde las evaporitas y lodolitas subyacentes, y por pérdidas del agua subterránea por evaporación. Los flujos de recarga y descarga de agua subterránea, en los acuíferos libres regionales en regiones áridas, normalmente son difíciles estimar, porque hay algunas restricciones en el flujo de agua perdido o ganado por el sistema. Los sólidos disueltos totales (TDS) y los isótopos de deuterio (δ²H) en el agua subterránea, se usan para forzar los flujos estimados hacia el acuífero poco profundo del Emirato oriental de Abu Dhabi. El transporte ascendente vertical de solutos desde las lodolitas y evaporitas subyacentes, involucra los aumentos del soluto a lo largo de aproximadamente los primeros 80 Km. de la dirección de flujo simulada, pero es necesaria una combinación de transporte ascendente del soluto y la evaporación para explicar las concentraciones del soluto observadas más allá de 80 Km. La movilización y transporte de solutos en la zona no saturada, por recarga debida a precipitación, no es un factor significante.

     

Geographies of age: thinking relationally

In contrast to recent treatment of other social identities, geographers' work on age still focuses disproportionately on the social-chronological margins – the very young and (to a far lesser extent) the very old – and rarely connects them directly. We outline the benefits of creating relational geographies of age, in order to build out from the recent explosion of children's geographies, and discuss three helpful concepts: intergenerationality, intersectionality and lifecourse. We suggest that participation provides one epistemological vehicle for getting beyond geographies which are mainly adults'.     

Global telescope networks for astronomy education

Ever wanted to give school students or the public a closer look at the stars, without worrying about the vagaries of the UK weather? Paul Roche and Rachel Dodds from the Faulkes Telescope Project explain how you can do just that – without even leaving the classroom!