Use of Picard and Newton iteration for solving nonlinear ground water flow equations

This study examines the use of Picard and Newton iteration to solve the nonlinear, saturated ground water flow equation. Here, a simple three-node problem is used to demonstrate the convergence difficulties that can arise when solving the nonlinear, saturated ground water flow equation in both homogeneous and heterogeneous systems with and without nonlinear boundary conditions. For these cases, the characteristic types of convergence patterns are examined. Viewing these convergence patterns as orbits of an attractor in a dynamical system provides further insight. It is shown that the nonlinearity that arises from nonlinear head-dependent boundary conditions can cause more convergence difficulties than the nonlinearity that arises from flow in an unconfined aquifer. Furthermore, the effects of damping on both convergence and convergence rate are investigated. It is shown that no single strategy is effective for all problems and how understanding pitfalls and merits of several methods can be helpful in overcoming convergence difficulties. Results show that Picard iterations can be a simple and effective method for the solution of nonlinear, saturated ground water flow problems.     

Environmental constraints on lake sediment mineral compositions from the Tibetan Plateau and implications for paleoenvironment reconstruction

Inorganic minerals form a major component of lacustrine sediments and have the potential to reveal detailed information on previous climatic and hydrological conditions. The ability to extract such information however, has been restricted by a limited understanding of the relationships between minerals and the environment. In an attempt to fill in this gap in our knowledge, 146 surface sediment samples have been investigated from 146 lakes on the Tibetan Plateau. The mineral compositions derived from these samples by X-Ray Diffraction (XRD) were used to examine the relationships between mineral compositions and the environmental variables determined for each site. Statistical techniques including Multivariate regression trees (MRT) and Redundancy Analysis (RDA), based on the mineral spectra and environmental variables, reveal that the electrical conductivity (EC) and Mg/Ca ratios of lake water are the most important controls on the composition of endogenic minerals. No endogenic minerals precipitate under hyper-fresh water conditions (EC lower than 0.13 mS/cm), with calcite commonly forming in water with EC values above 0.13 mS/cm. Between EC values of 0.13 and 26 mS/cm the mineral composition of lake sediments can be explained in terms of variations in the Mg/Ca ratio: calcite dominates at Mg/Ca ratios of less than 33, whereas aragonite commonly forms when the ratio is greater than 33. Where EC values are between 26 and 39 mS/cm, monohydrocalcite precipitates together with calcite and aragonite; above 39 mS/cm, gypsum and halite commonly form. Information on the local geological strata indicates that allogenic (detrital) mineral compositions are primarily influenced by the bedrock compositions within the catchment area. By applying these relationships to the late glacial and Holocene mineral record from Chaka Salt Lake, five lake stages have been identified and their associated EC conditions inferred. The lake evolved from a freshwater lake during the late glacial (before 11.4 cal. ka BP) represented by the lowest EC values (<0.13 mS/cm), to a saline lake with EC values slightly higher than 39 mS/cm during the early and mid Holocene (ca. 11.4–5.3 cal. ka BP), and finally to a salt lake (after 5.3 cal. ka BP). These results illustrate the utility of our mineral-environmental model for the quantitative reconstruction of past environmental conditions from lake sediment records.     

Post-kinematic recovery of fractured cordierite in the lower amphibolite facies: the significance of intra-crystal cation diffusion for retrograde partial mineral breakdown

Brittle intra-crystal fracturing during a micro-seismic event under amphibolite facies P–T conditions (ca. 4.5 kbar, 555°C) formed micro-shear zones and brittle fragments in cordierite from migmatites of the Ordovician Sierras Pampeanas (NW Argentina). During post-seismic static recovery and coarsening of crystal fragments, primary cordierite (X_Mg?=?0.65) underwent partial breakdown within the fractured and subsequently recovered and recrystallized part of primary cordierite. Post-kinematic partial primary cordierite breakdown results in the formation of secondary sillimanite, magnetite, staurolite, quartz, and secondary cordierite (X_Mg?=?0.70–0.80) within a ca. 300–500 μm thick alteration zone. Secondary cordierite, volumetrically the most important secondary phase, essentially forms by iron and magnesium diffusion and substitution. All other secondary phases form by nucleation. The retrograde breakdown occurred under near-isochemical conditions with only limited influx of hydrothermal fluids containing minor zinc, potassium, silica, and excess oxygen. The observed modal composition of the alteration zone is similar to results of thermodynamic modeling of primary cordierite breakdown, using multiphase equilibria software. This indicates that the observed reaction reflects conditions of, or close to, thermodynamic equilibrium. Although fluid was present during, and may have been an important factor contributing to, partial mineral breakdown, we consider post-kinematic recovery and recrystallization, effected by a combination of cation diffusion and elimination of dislocations, as the key process facilitating retrograde metamorphism and the generation of the secondary mineral assemblage in (near-) equilibrium modes.     

Lateglacial and Holocene variation in aeolian sediment flux over the northeastern Tibetan Plateau recorded by laminated sediments of a saline meromictic lake

Predominantly laminated lake sediments from a saline closed‐basin lake on the northeastern Tibetan Plateau were investigated using a multi‐proxy approach (¹⁴C‐accelerator mass spectrometry dating, smear‐slide analysis, loss on ignition, grain size, X‐ray diffraction, elemental concentration, ostracod assemblages, stable isotopes of ostracod shells) to trace the regional environmental and climatic history in the Lateglacial and Holocene. Before about 15 cal. ka BP, small saline water bodies probably filled the basin under unstable cold and harsh environmental conditions. Soon after about 14.9 cal. ka BP, a relatively deep saline lake was established, probably as a result of runoff from melting snow, ice and frozen ground in the lake's catchment. Large changes in flux of aeolian material to the lake were recorded during this initial period of formation of Lake Kuhai. Highest lake levels, a low sediment accumulation rate and less saline conditions were maintained between about 12.8 and 7.1 cal. ka BP when the aeolian influx diminished significantly. After about 7.1 cal. ka BP, the aeolian influx remained at a moderate level apart from a strongly increased dust delivery to the lake between about 6.1 and 5.4 cal. ka BP and a minor short‐lived period of slightly enhanced aeolian influx at about 2.7 cal. ka BP. The strongly enhanced dust input to the lake between 6.1 and 5.4 cal. ka BP represented the largest influx of aeolian material to Lake Kuhai during the entire Holocene. However, evidence for climatic deterioration during this period is not seen at most other palaeoclimate sites on the Tibetan Plateau, but instead a significant increase in aridity has been recorded at numerous sites in the northern foreland of the Tibetan Plateau and on the Chinese Loess Plateau. The large dust input to Lake Kuhai between 6.1 and 5.4 cal. ka BP probably did not result from a severe climate deterioration on the Tibetan Plateau itself, but from the pronounced aridity in its northern and eastern foreland. In contrast, the increase in dust influx about 2.7 cal. ka BP seems to correspond to a brief warming spell recorded at other sites on the Tibetan Plateau too. A slight increase in lake level and decrease in salinity after about 0.6 cal. ka BP suggests a slightly higher effective moisture during the final lake stage, accompanied by a somewhat larger dust influx. This apparent contradiction possibly results from enhanced human activities on the northeastern Tibetan Plateau during the last 600 years. Copyright © 2009 John Wiley & Sons, Ltd.     

Clay smear processes in mechanically layered sequences — Results of water-saturated model experiments with free top surface

The aim of this study is to improve our knowledge of the processes that lead to clay smear during faulting of a layered sand-clay sequence in an analogue sandbox model. We carefully characterized mechanical properties of the materials used by a series of geotechnical tests. Displacement field was quantified using PIV (Particle Image Velocimetry). The model is water-saturated to allow the deformation of wet clay and sand in one experiment comprising a sand package with a horizontal layer of clay above a predefined rigid basement fault. The thickness and rigidity of the clay layer are the parameters varied in this study. The model shows a range of structures that are related to competence contrast between sand and different clay types. Results show ductile shearing of soft clay with a transition to brittle fracturing of stiff clay accompanied by the formation of rotating clay blocks in the fault zone. Localized deformation is observed through time showing (i) the propagation of one active fault migrating laterally through the sediment package, and (ii) the formation of a stable prism between two or more active faults that gets progressively smaller with minor rotation of the hanging wall fault. Continuous clay smear is observed resulting from the lateral injection of clay as well as from a reworked mixture of sand and clay.     

Late Pleistocene fans and terraces in the Majes valley, southern Peru, and their relation to climatic variations

This study investigates the connection between sediment aggradation, erosion and climate in a desert environment of the Majes valley, southern Peru. Luminescence dating of terraces and fans shows that sediment aggradation correlates with wet time intervals on the Altiplano, suggesting a climatic influence on the aggradation–degradation cycles. Major periods of aggradation occurred between ~110–100, ~60–50 and 12–8 ka. More precipitation in the Majes catchment resulted in increased erosion and transportation of sediment from the hillslopes into the trunk river. As a result, the sediment loads exceeded the transport capacity of the Majes River and aggradation started in the lower reaches where the river gradient is less. Depletion of the hillslope sediment reservoirs caused a relative increase in the capacity of the trunk river to entrain and transport sediment, resulting in erosion of the previously deposited sediment. Consequently, although climate change may initiate a phase of sediment accumulation, degradation can be triggered by an autocyclic negative feedback and does not have to be driven by climatic change.     

Reconstructing climate variability on the northeastern Tibetan Plateau since the last Lateglacial – a multi-proxy,dual-site approach comparing terrestrial and aquatic signals

A sediment core from a closed basin lake (Lake Kuhai) from the semi-arid northeastern Tibetan Plateau was analysed for its pollen record to infer Lateglacial and post glacial vegetation and climatic change. At Lake Kuhai five major vegetation and climate shifts could be identified: (1) a change from cold and dry to relatively warmer and more moist conditions at 14.8 cal ka BP; (2) a shift to conditions of higher effective moisture and a stepwise warmer climate at 13.6 cal ka BP; (3) a further shift with increased moisture but colder conditions at 7.0 cal ka BP; (4) a return to a significantly colder and drier phase at 6.3 cal ka BP; (5) and a change back to relatively moist conditions at 2.2 cal ka BP. To investigate the response of lake ecosystems to climatic changes, statistical comparisons were made between the Lake Kuhai pollen record and a formerly published ostracod and sedimentary record from the same sediment core. Furthermore, the pollen and lacustrine proxies from Lake Kuhai were compared to a previously published pollen and lacustrine record from the nearby Lake Koucha. Statistical comparisons were done using non-metric multidimensional scaling and Procrustes rotation. Differences between lacustrine and pollen responses within one site could be identified, suggesting that lacustrine proxies are partly influenced by in-lake or local catchment processes, whereas the terrestrial (pollen) proxy shows a regional climate signal. Furthermore, we found regional differences in proxy response between Lake Kuhai and Lake Koucha. Both pollen records reacted in similar ways to major environmental changes, with minor differences in the timing and magnitude of these changes. The lacustrine records were very similar in their timing and magnitude of response to environmental changes; however, the nature of change was at times very distinct. To place the current study in the context of Holocene moisture evolution across the Tibetan Plateau, we applied a five-scale moisture index and average link clustering to all available continuous palaeo-climate records from the Tibetan Plateau to possibly find general patterns of moisture evolution on the Plateau. However, no common regional pattern of moisture evolution during the Holocene could be detected. We assign this to complex responses of different proxies to environmental and atmospheric changes in an already very heterogeneous mountain landscape where minor differences in elevation can cause strong variation in microenvironments.     

Predictive modelling of dump water impact on the surroundings of the lignite dump site Jänschwalde (Eastern Germany)

Open cast mining of lignite leads to dumps containing highly mineralised pore waters. To predict the impact of the dump waters on the undisturbed aquifers two steps are necessary. (1) The prediction of dump water quality at times when steady state flow conditions will be established. (2) The simulation of the dump ground water migration with a model that is able to handle the complexity of the homogeneous and heterogeneous interactions of the migration process.For the investigated site Jänschwalde, which is still dewatered, a chemical mass balance was performed. The predicted alkalinity potentials exceed acidity potentials for the dump as a whole. The distribution of these parameters show high alkalinity potentials for the northern part.In order to model the migration process the transport code PCGEOFIM^® [Anwenderdokumentaion, IBGW Leipzig, (in German)] was coupled with the geochemical equilibrium code PHREEQC [USGS, Water-Resources Investigations Report]. This was done to simulate redox reactions, mineral dissolution and precipitation, and cation exchange in the ground water zone. The model is verified by a column flow test. The results of the simulations show a small effect of the migrating dump waters on the quartenary aquifer with respect to acidity changes. This results from calcite buffering and cation exchange. The impact on the quartenary aquifer by sulphate is much higher.     

Climate sensitivity studies of the Greenland ice sheet using satellite AVHRR,SMMR, SSM/I and in situ data

Summary The feasibility of using satellite data for climate research over the Greenland ice sheet is discussed. In particular, we demonstrate the usefulness of Advanced Very High Resolution Radiometer (AVHRR) Local Area Coverage (LAC) and Global Area Coverage (GAC) data for narrow-band albedo retrieval. Our study supports the use of lower resolution AVHRR (GAC) data for process studies over most of the Greenland ice sheet. Based on LAC data time series analysis, we can resolve relative albedo changes on the order of 2–5%. In addition, we examine Scanning Multichannel Microwave Radiometer (SMMR) and Special Sensor Microwave Imager (SSM/I) passive microwave data for snow typing and other signals of climatological significance. Based on relationships between in situ measurements and horizontally polarized 19 and 37 GHz observations, wet snow regions are identified. The wet snow regions increase in aerial percentage from 9% of the total ice surface in June to a maximum of 26% in August 1990. Furthermore, the relationship between brightness temperatures and accumulation rates in the northeastern part of Greenland is described. We found a consistent increase in accumulation rate for the northeastern part of the ice sheet from 1981 to 1986.With 16 Figures     

The ionization constants of aqueous MgCl2 at elevated temperatures and pressures—a revision

The ionization constants of aqueous MgCl₂ have been revised, in the light of recent measurements of electrical conductance, from the calculations reported previously by Frantz and Popp (1979).