A posteriori error estimates, stopping criteria, and adaptivity for two-phase flows

This paper develops a general abstract framework for a posteriori estimates for immiscible incompressible two-phase flows in porous media. We measure the error by the dual norm of the residual and, for mathematical correctness, employ the concept of global and complementary pressures in the analysis. Our estimators allow to estimate separately the different error components, namely, the spatial discretization error, the temporal discretization error, the linearization error, the iterative coupling error, and the algebraic solver error. We propose an adaptive algorithm wherein the different iterative procedures (iterative linearization, iterative coupling, iterative solution of linear systems) are stopped when the corresponding errors do not affect significantly the overall error and wherein the spatial and temporal errors are equilibrated. Consequently, important computational savings can be achieved while guaranteeing a user-given precision. The developed framework covers fully implicit, implicit pressure–explicit saturation, or iterative coupling formulations; conforming spatial discretization schemes such as the vertex-centered finite volume method or the finite element method and nonconforming spatial discretization schemes such as the cell-centered finite volume method, the mixed finite element method, or the discontinuous Galerkin method; linearizations such as the Newton or the fixed-point one; and general linear solvers. Numerical experiments for a model problem are presented to illustrate the theoretical results. Only by stopping timely the linear and nonlinear solvers, speedups by a factor between 10 and 20 in terms of the number of total linear solver iterations are achieved.     

Estimates of New and Total Productivity in Central Long Island Sound from In Situ Measurements of Nitrate and Dissolved Oxygen

Biogeochemical cycles in estuaries are regulated by a diverse set of physical and biological variables that operate over a variety of time scales. Using in situ optical sensors, we conducted a high-frequency time-series study of several biogeochemical parameters at a mooring in central Long Island Sound from May to August 2010. During this period, we documented well-defined diel cycles in nitrate concentration that were correlated to dissolved oxygen, wind stress, tidal mixing, and irradiance. By filtering the data to separate the nitrate time series into various signal components, we estimated the amount of variation that could be ascribed to each process. Primary production and surface wind stress explained 59 and 19 %, respectively, of the variation in nitrate concentrations. Less frequent physical forcings, including large-magnitude wind events and spring tides, served to decouple the relationship between oxygen, nitrate, and sunlight on about one quarter of study days. Daytime nitrate minima and dissolved oxygen maxima occurred nearly simultaneously on the majority (>80 %) of days during the study period; both were strongly correlated with the daily peak in irradiance. Nighttime nitrate maxima reflected a pattern in which surface-layer stocks were depleted each afternoon and recharged the following night. Changes in nitrate concentrations were used to generate daily estimates of new primary production (182?±?37 mg?C?m^?2?day^?1) and the f ratio (0.25), i.e., the ratio of production based on nitrate to total production. These estimates, the first of their kind in Long Island Sound, were compared to values of community respiration, primary productivity, and net ecosystem metabolism, which were derived from in situ measurements of oxygen concentration. Daily averages of the three metabolic parameters were 1,660?±?431, 2,080?±?419, and 429?±?203 mg?C?m^?2?day^?1, respectively. While the system remained weakly autotrophic over the duration of the study period, we observed very large day-to-day differences in the f ratio and in the various metabolic parameters.     

A 520 year record of summer sunshine for the eastern European Alps based on stable carbon isotopes in larch tree rings

A 520-year stable carbon isotope chronology from tree ring cellulose in high altitude larch trees (Larix decidua Mill.), from the eastern European Alps, correlates more strongly with summer temperature than with summer sunshine hours. However, when instrumental records of temperature and sunshine diverge after AD1980, the tree ring time series does not follow warming summer temperatures but more closely tracks summer sunshine trends. When the tree ring stable carbon isotope record is used to reconstruct summer temperature the reconstruction is not robust. Reconstructed temperatures prior to the twentieth century are higher than regional instrumental records, and the evolution of temperature conflicts with other regional temperature reconstructions. It is concluded that sunshine is the dominant control on carbon isotope fractionation in these trees, via the influence of photosynthetic rate on the internal partial pressure of CO₂, and that high summer (July–August) sunshine hours is a suitable target for climate reconstruction. We thus present the first reconstruction of summer sunshine for the eastern Alps and compare it with the regional temperature evolution.     

Hydrometeorological analysis of the December 2008 flood in Rome

Abstract

Rome has been plagued by flooding since its foundation, and, in December 2008, the largest flood event over the past 20 years caused a fatality and more than €150 million in economic damage. Meteorological conditions associated with the December 2008 flooding are shown to be typical of flooding in the Tiber. The long record of discharge measurements of the Tiber River at the Ripetta station in downtown Rome was used to examine flood frequency for the Tiber, including assessment of the return interval of the December 2008 flood. Particular attention is given to examination of the stationarity assumption for flood peaks through change-point and trend analyses, quantile regression, and statistical modelling of the flood-peak distribution. Once anthropogenic changes linked to reservoir regulation of the Tiber River have been accounted for, the stationarity assumption holds and can be used for flood frequency analysis. We highlight the difficulties in detecting departures from the stationarity assumption due to climate change. In the current regime, the December 2008 flood event has a return period of the order of 10–20 years.

Citation Villarini, G., Smith, J.A., Napolitano, F. & Baeck, M.L. (2011) Hydrometeorological analyses of the December 2008 flood in Rome. Hydrol. Sci. J. 56(7), 1150–1165.     

S saturation history of Nain Plutonic Suite mafic intrusions: origin of the Voisey’s Bay Ni–Cu–Co sulfide deposit, Labrador, Canada

The Voisey’s Bay deposit is hosted in a 1.34-Ga intrusion composed of troctolite, olivine gabbro, and ferrogabbro. The sulfide mineralization is associated with magmatic breccias that are enveloped by weakly mineralized olivine gabbros and troctolites, and also occurs as veins along structures in adjacent paragneiss. A dyke is connected to the base of the north wall of the Eastern Deeps Intrusion, and the entry point of this dyke into the chamber is the locus of the Eastern Deeps nickel sulfide deposit. A detailed exploration in the area between the Eastern Deeps and the Ovoid has shown that these intrusions and ore deposits are connected by a splayed dyke. The Eastern Deeps Deposit is surrounded by a halo of moderately to weakly mineralized variable-textured troctolite (VTT) that reaches a maximum thickness above the axis of the Eastern Deeps Deposit along the northern wall of the Eastern Deeps Intrusion. The massive sulfides and breccia sulfides are petrologically and chemically different when compared to the disseminated sulfides in the VTT, and there is a marked break in Ni tenor of sulfide between the two. Sulfides hosted in the dyke tend to have low metal tenors ([Ni]₁₀₀?=?2.5–3.5%), sulfides in Eastern Deeps massive and breccia ores have intermediate Ni tenors ([Ni]₁₀₀?=?3.5–4%), and disseminated sulfides in overlying rocks have high Ni tenors ([Ni]₁₀₀?=?4–8%). Four principal processes control the compositions of the Voisey’s Bay sulfides. Coarse-grained loop-textured ores consisting of pyrrhotite crystals separated by chalcopyrite and pentlandite exhibit a two orders of magnitude variation in the Pd/Ir ratio which is due to mineralogical variations where pentlandite is enriched in Pd and Ir is dispersed throughout the mineral assemblage. A decrease in Ir and Rh from the margin of the Ovoid toward cubanite-rich parts at the central part of the Ovoid is consistent with fractionation of the sulfide from the margins toward the center of the Ovoid. The Ovoid ores have higher Ni and Pd tenor than the Eastern Deeps massive sulfides; this is consistent with both a higher R factor and greater degree of silicate parental magma evolution in the Ovoid than the Eastern Deeps. The disseminated sulfides surrounding the Eastern Deeps deposit have some of the highest Ni and Pd tenors at Voisey’s Bay, which are indicative of not only more primitive magmas but also higher R factors than the Ovoid or the Eastern Deeps. VTT and normal-textured troctolite of the Eastern Deeps that contain trace sulfide have 0.1–3?ppb Pt and 0.1–3?ppb Pd, whereas weakly to heavily mineralized variable troctolites in the same unit have one to two orders of magnitude higher abundances of Pt and Pd. Troctolites and olivine gabbros from other parts of the Voisey’s Bay Intrusion and other Nain Plutonic Suite Intrusions, including the Kiglapait, Newark Bay, Barth Island, Mushua, and Nain Bay South Intrusion, also have low platinum group element abundances. Although it is possible that this is a signature of a widespread sulfide saturation event that pre-dated ore formation at Voisey’s Bay, it is more likely that platinum group element (PGE) depletion is a product of the source melting process where low degrees of melting resulted in the retention of PGE in the mantle source. If so, this indicates that PGE depletion should be used with caution as an exploration tool in the Nain Plutonic Suite.     

侏罗纪末至白垩纪非海相介形类生物地层学:回顾与展望

以非海相介形类为依据而建立的侏罗纪末至白垩纪的生物地层学,尤其是欧洲所谓"Purbeck-Wealden层段"(提塘阶顶部至巴列姆阶/阿普特阶底部)和全球同期沉积层的生物地层学建立已久,但这一生物地层学存有很多问题与局限性。本文对中生代晚期(聚焦于早白垩世)的非海相介形类生物地层学的基本原理、历史、目前进展、存在问题和前景进行了综述。因为介形类的繁殖、扩散与成种机制已有比较成熟的研究,所以介形类的生物地层学的应用潜力被认识已久。然而,全球不同地区中生代晚期的非海相介形类众多的研究积累已构成了一个丰富但常常混乱和矛盾的文献库。这些问题不仅存在于介形类的分类鉴定中,也见于关于古环境和系统发育的解释中。虽然地区性的盆地内的介形类生物地层学研究已产生了好结果,并可能能够用于局部地区的高精度对比。但是在进行地区间(盆地间至全球)的对比时,其实用性广遭怀疑。在过去的二十年间,许多学者采用了将今论古的古生物学研究方法,努力修订和更新中生代晚期的非海相介形类的生物地层学与古环境意义,从而促进了地区间生物地层学研究和对比的发展。古生物学家认识到,对于许多非海相介形类动物来讲,它们的分布和扩散不仅仅局限于单个的水系或较小的地理区域,而是和现生的非海相介形类一样,晚侏罗世至白垩纪的非海相介形类动物和它们的卵可被较大的动物或风长距离搬运,跨越迁移的屏障,进行扩散。鉴于以上事实,地区间的对比必须涉及两大内容:分类学的应用与古环境背景。缺乏适用于地区—全球的稳定和一致的分类学系统是进行正确对比的重要障碍。由于大量地方性分类命名、地方性特有动物的假设、与壳体特征相关的分类和生态型认识的混乱,以及对种内变异尺度的统一认识的缺乏,导致了对生物分异度的过高或过低的估量。非海相白垩纪介形类的地层记录受到诸多因素的影响:分类单元的演化与灭绝、扩散事件、当地的环境变化和地区性至全球的气候变迁。在生物地层学的应用中,我们可以通过不同手段去把握同时代的Cytheroidea,特别是Cypridoidea中具重要地层意义的Cypridea属及其亲近者(即CypridoideaMartin,1940)的分类单元的形态变异度。解释种内变异时需要格外谨慎。区分生物自生(内因)导致的变异(遗传的和形态的变异)和环境(外因)导致的变异(生态表型)是一大难题。比较保守的分类学观念(分类单元很少,但变异极大(分类单元中包含了多种生态表型))有助于不同古环境间的(生物地层)对比。另一方法是运用随着时间的古环境变化及其对介形类组合的组成的影响来进行(生物地层)对比。古生物工作者已在利用受环境控制的周期性介形类组合变化建立对比关系方面进行了大量有意义的尝试,但这些工作仍处在争议中。建立全球生物地层学方法,建立统一而持久的分类概念这一目标可以达到,但不可能在短期内实现。用现代的思想(概念)理解和研究非海相介形类的古生物学和古生物地理学及新资料将有助于修订工作的进展。尽管我们对中生代的非海相介形类的演化和分布的认识还很不全面,但目前我们已取得了可喜的进展。盆地间至大陆间的对比是否可行,早已不是问题。目前和未来的指导原则无疑是发展以介形类为基础,并与其他的年代地层学和地质年代学资料及方案相结合的从地区至全球范围的地层对比系统。因为我们正在迈向一个非海相晚中生代介形类生物地层学的重新解释和应用的新时代,我们必须承认我们还有许多东西需要学习。     

Modeling fluid injection in fractures with a reservoir simulator coupled to a boundary element method

We describe an algorithm for modeling saturated fractures in a poroelastic domain in which the reservoir simulator is coupled with a boundary element method. A fixed stress splitting is used on the underlying fractured Biot system to iteratively couple fluid and solid mechanics systems. The fluid system consists of Darcy’s law in the reservoir and is computed with a multipoint flux mixed finite element method, and a Reynolds’ lubrication equation in the fracture solved with a mimetic finite difference method. The mechanics system consists of linear elasticity in the reservoir and is computed with a continuous Galerkin method, and linear elasticity in the fracture is solved with a weakly singular symmetric Galerkin boundary element method. This algorithm is able to compute both unknown fracture width and unknown fluid leakage rate. An interesting numerical example is presented with an injection well inside of a circular fracture.     

GGR Biennial Critical Review: Analytical Developments Since 2012

Advances in the chemical, crystallographic and isotopic characterisation of geological and environmental materials can often be ascribed to technological improvements in analytical hardware or to innovative approaches to data acquisition and/or its interpretation. This biennial review addresses key laboratory methods that form much of the foundation for analytical geochemistry; again, this contribution is presented as a compendium of laboratory techniques. We highlight advances that have appeared since January 2012 and that are of particular significance for the chemical and isotopic characterisation of geomaterials. Prominent scientists from the selected analytical fields present publications they judge to be particular noteworthy, providing background information about the method and assessing where further opportunities might be anticipated. In addition to the well‐established technologies such as thermal ionisation mass spectrometry and plasma emission spectroscopy, this publication also presents new or rapidly growing methods such as electron backscattered diffraction analysis and atom probe tomography – a very sensitive method providing atomic scale information.     

Sub-ice volcanoes and ancient oceans/lakes: a Martian challenge

New instruments on board the Mars Global Surveyor (MGS) spacecraft began providing accurate, high-resolution image and topography data from the planet in 1997. Though data from the Mars Orbiter Laser Altimeter (MOLA) are consistent with hypotheses that suggest large standing bodies of water/ice in the northern lowlands in the planet's past history, Mars Orbiter Camera (MOC) images acquired to test these hypotheses have provided negative or ambiguous results. In the absence of classic coastal features to test the paleo-ocean hypothesis, other indicators need to be examined. Tuyas and hyaloclastic ridges are sub-ice volcanoes of unique appearance that form in ponded water conditions on Earth. Features with similar characteristics occur on Mars. MOLA analyses of these Martian features provide estimates of the height of putative ice/water columns at the edge of the Utopia Planitia basin and within Ophir Chasma of Valles Marineris, and support the hypotheses of a northern ocean on Mars.