Reduced order models for many-query subsurface flow applications

Inverse modeling involves repeated evaluations of forward models, which can be computationally prohibitive for large numerical models. To reduce the overall computational burden of these simulations, we study the use of reduced order models (ROMs) as numerical surrogates. These ROMs usually involve using solutions to high-fidelity models at different sample points within the parameter space to construct an approximate solution at any point within the parameter space. This paper examines an input–output relational approach based on Gaussian process regression (GPR). We show that these ROMs are more accurate than the linear lookup tables with the same number of high-fidelity simulations. We describe an adaptive sampling procedure that automatically selects optimal sample points and demonstrate the use of GPR to a smooth response surface and a response surface with abrupt changes. We also describe how GPR can be used to construct ROMs for models with heterogeneous material properties. Finally, we demonstrate how the use of a GPR-based ROM in two many-query applications—uncertainty quantification and global sensitivity analysis—significantly reduces the total computational effort.     

A review on the aging phenomena of organic components and their mass transfer through the NAPL interfacial phase

It occurs worldwide that the organic components of non-aqueous phase liquid (NAPL) enter the porous medium and become the source of contaminants in the subsurface. The transport of the organic components through NAPL interphase into the aqueous phase and the subsurface determines the extent of contamination, the persistence of residual NAPL phases and the techniques of remediation. During the transport process the NAPL interphase may experience "aging", a physical and chemical change when NAPL is exposed to aqueous and or gaseous phases. This aging process alters vice versa the mass transfer behaviour of the organic contaminants in the porous medium.     

An experimental study of the Fe oxidation states in garnet and clinopyroxene as a function of temperature in the system CaO–FeO–Fe2O3–MgO–Al2O3–SiO2: implications for garnet–clinopyroxene geothermometry

Samples with eclogitic composition in the system CaO–FeO–Fe₂O₃–MgO–Al₂O₃–SiO₂ were produced from various kinds of starting materials held in graphite-lined Pt capsules at a pressure of 2.5–3.0 GPa and temperatures of 800–1,300 °C using a piston-cylinder or Belt apparatus. Garnets and clinopyroxenes were characterized by analytical transmission electron microscopy and electron probe micro-analysis (EPMA). Fe³⁺/ΣFe ratios determined by electron energy-loss spectroscopy (EELS) decrease in clinopyroxene from 22.2 ± 3.4 % at 800 °C to 13.3 ± 5.4 % at 1,300 °C, while in garnet, they vary between 10.8 ± 1.5 and 15.4 ± 4.7 %, respectively. Temperature estimates according to Krogh (Contrib Mineral Petrol 99:44–48, 1988) reproduce the experimental temperature to ±60 °C without systematic deviations if total iron is used in the calculation. If only the Fe²⁺ content is used, which was obtained by combining EPMA and EELS results, the experimental temperature is underestimated by 33 °C on average at 800–1,200 °C and overestimated by 77 °C on average at 1,300 °C. These systematic deviations can be explained by the temperature-dependent ratio of Fe²⁺/ΣFe in garnet divided by that in clinopyroxene. Since the difference between the calculated and experimental temperature is relatively small, a Fe²⁺-based recalibration of the thermometer appears not to be necessary for the investigated system in the range of pressure, temperature and composition covered by the experiments of this study.     

Assessing adaptive capacity within regional climate change vulnerability studies—an Alpine example

Adaptive capacity represents a crucial component in the assessment of a region’s vulnerability to climate change. The term adaptive capacity is only fuzzily defined, and determining it is difficult and often neglected in previous studies. In this paper, a newly developed adaptive capacity concept is introduced, with a respective indicator/criteria system and simple aggregation methods. The approach allows for adaptive capacity assessments at 3 levels of specificity (impact specific, sector specific and regional generic). The selection of indicators is tailor-made for Alpine regions, where the approach has been widely tested. The presented approach requires extended stakeholder involvement, namely for the evaluation of the indicators. The overall effort needed for its implementation remains reasonable. The outcome of the assessment exercise does not provide precise objective measurements, but remains an indicative estimation due to the fuzziness and complexity of the underlying concept. The conceptual approach is transferable to other mountain areas and beyond, the selection of indicators however is only valid for the Alpine region. The showcase presents results from the adaptive capacity assessment in the region of South Tyrol, where the method was carried out as part of a climate change vulnerability study. The outcomes indicate a number of issues that future actions could address in order to improve adaptive capacity in the region, namely in the field of prevention measures against meteorological extremes and natural hazards.     

Lake surface temperatures in a changing climate: a global sensitivity analysis

We estimate the effects of climatic changes, as predicted by six climate models, on lake surface temperatures on a global scale, using the lake surface equilibrium temperature as a proxy. We evaluate interactions between different forcing variables, the sensitivity of lake surface temperatures to these variables, as well as differences between climate zones. Lake surface equilibrium temperatures are predicted to increase by 70 to 85 % of the increase in air temperatures. On average, air temperature is the main driver for changes in lake surface temperatures, and its effect is reduced by ~10 % by changes in other meteorological variables. However, the contribution of these other variables to the variance is ~40 % of that of air temperature, and their effects can be important at specific locations. The warming increases the importance of longwave radiation and evaporation for the lake surface heat balance compared to shortwave radiation and convective heat fluxes. We discuss the consequences of our findings for the design and evaluation of different types of studies on climate change effects on lakes.     

Combined object-based classification and manual interpretation–synergies for a quantitative assessment of parcels and biotopes

Recent technical advances in remote sensing data capture and spatial resolution lead to a widening gap between increasing data availability on the one hand and insufficient methodology for semi-automated image data processing and interpretation on the other hand. At the interface of GIS and remote sensing, object-based image analysis methodologies are one possible approach to close this gap. With this, methods from either side are integrated to use both the capabilities of information extraction from image data and the power to perform spatial analysis on derived polygon data. However, dealing with image objects from various sources and in different scales implies combining data with inconsistent boundaries. A landscape interpretation support tool (LIST) is introduced which seeks to investigate and quantify spatial relationships among image objects stemming from different sources by using the concept of spatial coincidence. Moreover, considering different categories of object fate, LIST enables a change categorization for each polygon of a time series of classifications. The application of LIST is illustrated by two case-studies, using Landsat TM and ETM as well as CIR aerial photographs: the first showing how the tool is used to perform object quantification and change analysis; the latter demonstrating how superior aggregation capabilities of the human brain can be combined with the fine spatial segmentation and classification. Possible fields of application are identified and limitations of the approach are discussed.     

Rainfall–interception–evaporation–runoff relationships in a semi-arid catchment,northern Limpopo basin,Zimbabwe

Abstract

Two types of monthly water balance models at basin scale are used: PE models use precipitation and potential evapotranspiration (PET) as their observed input data, whereas P models need only precipitation. Calibration proceeds by comparing model runoff and observed runoff. Calibration is entirely automatic with the exclusion of subjective elements. All models differ only by their actual evapotranspiration equations. PE models from previous papers are generalized essentially by replacing the constant evapotranspiration parameter by a periodic one, thus increasing the number of parameters by two (a “parameter” is an unknown constant to be estimated, and which is a characteristic of the river basin to be described). P models use a periodic “driving force”, which is intended to represent periodicity of hydrological phenomena, normally originating in the (unavailable) PET time series. These eight PE models and three P models are then applied to 55 river basins in 10 countries with widely diverging climates and soil conditions. A marked improvement of model performance in about one third of the basins is due to the introduction of the above mentioned periodic functions. Even when PET data are available it is sometimes useful to consider P models. P models scarcely perform less well than PE models. An engineer, wanting to try out as few models as possible on a given river basin, can restrict his attention to the optimization of two or three models. The paper is an extension of a long effort towards monthly water balance models, and is believed to give a solution in most circumstances.     

Nonlinear internal waves in ideal rotating basins

Abstract

Starting from Euler's equations of motion a nonlinear model for internal waves in fluids is developed by an appropriate scaling and a vertical integration over two layers of different but constant density. The model allows the barotropic and the first baroclinic mode to be calculated. In addition to the nonlinear advective terms dispersion and Coriolis force due to the Earth's rotation are taken into account. The model equations are solved numerically by an implicit finite difference scheme. In this paper we discuss the results for ideal basins: the effects of nonlinear terms, dispersion and Coriolis force, the mechanism of wind forcing, the evolution of Kelvin waves and the corresponding transport of particles and, finally, wave propagation over variable topography. First applications to Lake Constance are shown, but a detailed analysis is deferred to a second paper [Bauer et al. (1994)].     

Reactive monazite and robust zircon growth in diatexites and leucogranites from a hot,slowly cooled orogen: implications for the Palaeoproterozoic tectonic evolution of the central Fennoscandian Shield,Sweden

Monazite in melt-producing, poly-metamorphic terranes can grow, dissolve or reprecipitate at different stages during orogenic evolution particularly in hot, slowly cooling orogens such as the Svecofennian. Owing to the high heat flow in such orogens, small variations in pressure, temperature or deformation intensity may promote a mineral reaction. Monazite in diatexites and leucogranites from two Svecofennian domains yields older, coeval and younger U–Pb SIMS and EMP ages than zircon from the same rock. As zircon precipitated during the melt-bearing stage, its U–Pb ages reflect the timing of peak metamorphism, which is associated with partial melting and leucogranite formation. In one of the domains, the Granite and Diatexite Belt, zircon ages range between 1.87 and 1.86 Ga, whereas monazite yields two distinct double peaks at 1.87–1.86 and 1.82–1.80 Ga. The younger double peak is related to monazite growth or reprecipitation during subsolidus conditions associated with deformation along late-orogenic shear zones. Magmatic monazite in leucogranite records systematic variations in composition and age during growth that can be directly linked to Th/U ratios and preferential growth sites of zircon, reflecting the transition from melt to melt crystallisation of the magma. In the adjacent Ljusdal Domain, peak metamorphism in amphibolite facies occurred at 1.83–1.82 Ga as given by both zircon and monazite chronology. Pre-partial melting, 1.85 Ga contact metamorphic monazite is preserved, in spite of the high-grade overprint. By combining structural analysis, petrography and monazite and zircon geochronology, a metamorphic terrane boundary has been identified. It is concluded that the boundary formed by crustal shortening accommodated by major thrusting.     

Hydraulic Conductivity and Coefficient of Consolidation of Two Sulphide Clays in Sweden

The variation and anisotropy in hydraulic conductivity and the coefficient of consolidation was investigated for two Swedish sulphide clays. A series of constant rate of strain oedometer tests was performed on samples trimmed in the vertical and horizontal direction. A methodology to evaluate the horizontal coefficients of consolidation c _h via the horizontal hydraulic conductivity k _h and the vertical compression modulus M _v is proposed. Laboratory evaluations of c _h are also compared with determinations of c _h from in situ piezometer measurements in vertically drained sulphide clay. Furthermore, the validity of the empirical correlation between hydraulic conductivity change index C _k and initial void ratio e ₀, C _k  = 0.5e ₀ (Tavenas et al. in Can Geotech J 20(4):645–660, 1983b), was investigated for the sulphide clays. The results from the investigation show large ranges in measured hydraulic conductivities and coefficients of consolidation. However, the results indicate that the correlation C _k  = 0.5e ₀ is valid. The anisotropy in hydraulic conductivity and the coefficient of consolidation of the sulphide clays tested seems to be small. For design purposes, multiple tests for assessment of hydraulic conductivity and the coefficient of consolidation should be made, and a partial factor of safety, depending on the requisite level of safety and the spatial variability of the parameters, should be introduced. For design purposes in this type of clay, k _h  = k _v and c _h  = c _v are suggested.