Cross-covariances and localization for EnKF in multiphase flow data assimilation

The ensemble Kalman filter has been successfully applied for data assimilation in very large models, including those in reservoir simulation and weather. Two problems become critical in a standard implementation of the ensemble Kalman filter, however, when the ensemble size is small. The first is that the ensemble approximation to cross-covariances of model and state variables to data can indicate the presence of correlations that are not real. These spurious correlations give rise to model or state variable updates in regions that should not be updated. The second problem is that the number of degrees of freedom in the ensemble is only as large as the size of the ensemble, so the assimilation of large amounts of precise, independent data is impossible. Localization of the Kalman gain is almost universal in the weather community, but applications of localization for the ensemble Kalman filter in porous media flow have been somewhat rare. It has been shown, however, that localization of updates to regions of non-zero sensitivity or regions of non-zero cross-covariance improves the performance of the EnKF when the ensemble size is small. Localization is necessary for assimilation of large amounts of independent data. The problem is to define appropriate localization functions for different types of data and different types of variables. We show that the knowledge of sensitivity alone is not sufficient for determination of the region of localization. The region depends also on the prior covariance for model variables and on the past history of data assimilation. Although the goal is to choose localization functions that are large enough to include the true region of non-zero cross-covariance, for EnKF applications, the choice of localization function needs to balance the harm done by spurious covariance resulting from small ensembles and the harm done by excluding real correlations. In this paper, we focus on the distance-based localization and provide insights for choosing suitable localization functions for data assimilation in multiphase flow problems. In practice, we conclude that it is reasonable to choose localization functions based on well patterns, that localization function should be larger than regions of non-zero sensitivity and should extend beyond a single well pattern.     

Do S-type granites commonly sample infracrustal sources? New results from an integrated O, U–Pb and Hf isotope study of zircon

In contrast to I-type granites, which commonly comprise infracrustal and supracrustal sources, S-type granites typically incorporate predominantly supracrustal sources. The initial aim of this study was to identify the sources of three Scottish Caledonian (~460 Ma) S-type granites (Kemnay, Cove and Nigg Bay) by conducting oxygen, U–Pb and Hf isotope analyses in zircon in order to characterise one potential end-member magma involved in the genesis of the voluminous late Caledonian (~430–400 Ma) I-type granites. Field, whole-rock geochemical and isotopic data are consistent with the generation of the S-type granites by melting their Dalradian Supergroup country rocks. While Hf isotope compositions of magmatic zircon, U–Pb data of inherited zircons, and high mean zircon δ¹⁸O values of 9.0 ± 2.7‰ (2SD) and 9.8 ± 2.0‰ for the Kemnay and Cove granites support this model, the Nigg Bay Granite contains zircons with much lower δ¹⁸O values (6.8 ± 2.1‰), similar to those found in Scottish I-type granites. This suggests that the Nigg Bay Granite contains low-δ¹⁸O material representing either altered supracrustal material, or more likely, an infracrustal source component with mantle-like δ¹⁸O. Mixing trends in plots of δ¹⁸O vs. εHf for S-type granite zircons indicate involvement of at least two sources in all three granites. This pilot study of Scottish Caledonian S-type granites demonstrates that, while field and whole-rock geochemical data are consistent with local melting of only supracrustal sources, the oxygen isotopic record stored in zircon reveals a much more complex petrogenetic evolution involving two or more magma sources.     

Determining the amount of overstepping required to nucleate garnet during Barrovian regional metamorphism,Connecticut Valley Synclinorium

The novel method of inclusion barometry coupled with the calculation of the required affinity for garnet nucleation is applied to three samples from the previously well‐characterized Connecticut Valley Synclinorium in central Vermont. Raman shifts for quartz inclusions record a range of maximum peak shifts of the quartz 464 cm^?1 peak from 2.4 to 3.0 cm^?1. Temperature of garnet nucleation was constrained by calculating mineral assemblage diagrams in the MnNCKFMASHT system and plotting the intersection of quartz inclusion in garnet barometry (QuiG, quartz‐in‐garnet) with Zr‐in‐rutile thermometry. Utilizing the intersection of Zr‐in‐rutile thermometry with QuiG barometry, garnet nucleation is inferred to have occurred within a P–T range of ~8.6–9.5 kbar and ~560–575°C. These P–T conditions for garnet nucleation are significantly higher than calculated equilibrium garnet‐in isograds for the three samples. Affinities for garnet nucleation were calculated as the difference between the free energy of a fictive garnet composition based on the matrix assemblage and the free energy of the nucleated garnet. The calculated nucleation affinity varied from 300 to 600 kJ/mol O for St–Ky grade samples. These results suggest that the assumption that metamorphism proceeds as a sequence of near‐equilibrium conditions cannot, in general, be made for regional metamorphic terranes. This body of work agrees with numerous recent studies showing that garnet‐producing reactions must be overstepped in order to for garnet to nucleate.     

Mechanisms of fine extinction band development in vein quartz: new insights from correlative light and electron microscopy

Fine extinction bands (FEBs) (also known as deformation lamellae) visible with polarized light microscopy in quartz consist of a range of nanostructures, inferring different formation processes. Previous transmission electron microscopy studies have shown that most FEB nanostructures in naturally deformed quartz are elongated subgrains formed by recovery of dislocation slip bands. Here we show that three types of FEB nanostructure occur in naturally deformed vein quartz from the low-grade metamorphic High-Ardenne slate belt (Belgium). Prismatic oriented FEBs are defined by bands of dislocation walls. Dauphiné twin boundaries present along the FEB boundaries probably formed after FEB formation. In an example of two sub-rhombohedral oriented FEBs, developed as two sets in one grain, the finer FEB set consists of elongated subgrains, similar to FEBs described in previous transmission electron microscopy studies. The second wider FEB set consists of bands with different dislocation density and fluid-inclusion content. The wider FEB set is interpreted as bands with different plastic strain associated with the primary growth banding of the vein quartz grain. The nanometre-scale fluid inclusions are interpreted to have formed from structurally bounded hydroxyl groups that moreover facilitated formation of the elongate subgrains. Larger fluid inclusions aligned along FEBs are explained by fluid-inclusion redistribution along dislocation cores. The prismatic FEB nanostructure and the relation between FEBs and growth bands have not been recognized before, although related structures have been reported in experimentally deformed quartz.     

Scale dependency of regional climate modeling of current and future climate extremes in Germany

A 26-year simulation (1980–2005) was performed with the Weather Research and Forecast (WRF) model over the Volta Basin in West Africa. This was to investigate the ability of a climate version of WRF to reproduce present day temperature and precipitation over the Volta Basin. The ERA-Interim reanalysis and one realization of the ECHAM6 global circulation model (GCM) data were dynamically downscaled using two nested domains within the WRF model. The outer domain had a horizontal resolution of 50 km and covered the whole of West Africa while the inner domain had a horizontal resolution of 10 km. It was observed that biases in the respective forcing data were carried over to the RCM, but also the RCM itself contributed to the mean bias of the model. Also, the biases in the 50-km domain were transferred unchanged, especially in the case of temperature, to the 10-km domain, but, for precipitation, the higher-resolution simulations increased the mean bias in some cases. While in general, WRF underestimated temperature in both the outer (mean biases of ?1.6 and ?2.3 K for ERA-Interim and ECHAM6, respectively) and the inner (mean biases of ?0.9 K for the reanalysis and ?1.8 K for the GCM) domains, WRF slightly underestimated precipitation in the coarser domain but overestimated precipitation in the finer domain over the Volta Basin. The performance of the GCM, in general, is good, particularly for temperature with mean bias of ?0.7 K over the outer domain. However, for precipitation, the added value of the RCM cannot be overlooked, especially over the whole West African region on the annual time scale (mean biases of ?3% for WRF and ?8% for ECHAM6). Over the whole Volta Basin and the Soudano-Sahel for the month of April and spring (MAM) rainfall, respectively, mean bias close to 0% was simulated. Biases in the interannual variability in both temperature and precipitation over the basin were smaller in the WRF than the ECHAM6. High spatial pattern correlations between 0.7 and 0.8 were achieved for the autumn precipitation and low spatial correlation in the range of 0.0 and 0.2 for the winter season precipitation over the whole basin and all the three belts over the basin.     

Weathering, dust, and biocycling effects on soil silicon isotope ratios

Silicon isotope ratios (δ³⁰Si) of bulk mineral materials in soil integrate effects from both silicon sources and processing. Here we report δ³⁰Si values from a climate gradient of Hawaiian soils developed on 170 ka basalt and relate them to patterns of soil chemistry and mineralogy. The results demonstrate informative relationships between the mass fraction of soil Si depletion and δ³⁰Si. In upper (<1 m deep) soil horizons along the climate gradient, Si depletion correlates with decreases of residual δ³⁰Si values in low rainfall soils and increases in high rainfall soils. Strong positive correlation between soil δ³⁰Si and dust-derived quartz and mica content show that both trends are largely controlled by the abundance of these weathering-resistant minerals. The data also lend support to the idea that fractionation of Si isotopes in secondary phases is controlled by partitioning of silicon between dissolved and precipitated products during the initial weathering of primary basalt. Secondary mineral δ³⁰Si values from lower (>1 m deep) soil horizons generally correlate with the isotope fractionation predicted by a study of dissolved Si in basalt-watershed rivers and driven by preferential ²⁸Si removal from the dissolved phase during precipitation. In contrast, after correcting for the influence of dust, secondary mineral Si depletion and δ³⁰Si values in shallow (<1 m deep) soil horizons showed evidence of biocycling induced Si redistribution and substantially lower δ³⁰Si values than predicted. Low δ³⁰Si values in shallow soil horizons compared to predictions can be attributed to repeated fractionation as secondary minerals undergo additional cycles of dissolution and precipitation. Primary mineral weathering, secondary mineral weathering, dust accumulation, and biocycling are major processes in terrestrial Si cycling and these results demonstrate that each can be traced by δ³⁰Si values interpreted in conjunction with mineralogy and measures of Si depletion.     

Degradation of chlorinated ethylenes by Fe0: inhibition processes and mineral precipitation

. Granular zero-valent iron was used for the treatment of groundwater pollution caused by chlorinated ethylenes, mainly TCE, cis-DCE and VC at an industrial site. The rapidly decreasing rates of de-chlorination in the initial phase were attributed to the precipitation of carbonates and the development of hydrogen by anaerobic corrosion. After 70 pore volumes, sulphate was reduced by bacteria. From this point in time, the degradation of TCE was slightly accelerated whereas the de-chlorination rates of the other chlorinated ethylenes decreased only slowly. This relative improvement was assumed to be caused by the uptake of electron-transfer-blocking hydrogen by bacteria. Because the overall trend of the degradation rates is negative we conclude that the inhibitive effect of carbonate precipitation and hydrogen formation cannot be compensated for by the positive influence of the activity of sulphate-reducing bacteria.