An evaluation of temporally adaptive transformation approaches for solving Richards' equation

Developing robust and efficient numerical solution methods for Richards' equation (RE) continues to be a challenge for certain problems. We consider such a problem here: infiltration into unsaturated porous media initially at static conditions for uniform and non-uniform pore size media. For ponded boundary conditions, a sharp infiltration front results, which propagates through the media. We evaluate the resultant solution method for robustness and efficiency using combinations of variable transformation and adaptive time-stepping methods. Transformation methods introduce a change of variable that results in a smoother solution, which is more amenable to efficient numerical solution. We use adaptive time-stepping methods to adjust the time-step size, and in some cases the order of the solution method, to meet a constraint on nonlinear solution convergence properties or a solution error criterion. Results for three test problems showed that adaptive time-stepping methods provided robust solutions; in most cases transforming the dependent variable led to more efficient solutions than untransformed approaches, especially as the pore-size uniformity increased; and the higher-order adaptive time integration method was robust and the most efficient method evaluated.     

The Fernbank interglacial site near Ithaca, New York, USA

The Fernbank interglacial site, on the west side of Cayuga Lake, New York, has been recently subjected to more detailed study. To a lengthened mollusc list are added ostracodes, insects, fish, pollen, and plant macrofossils. Of these, plants are well preserved and diverse, whereas other groups are poorly preserved and incomplete. Nevertheless, all support the interglacial assignment (Sangamon), which is further supported by minimum age radiocarbon dates (> 50,000 ¹⁴C yr BP) and a TL date of 81 ± 11 ka. In the plant record near the top of the sequence, abundant tree charcoal indicates forest fires. Like the Toronto interglacial record, the plants show a declining July mean temperature from 24 to 18°C (according to transfer functions) through the sequence, from mixed deciduous forest to boreal forest.     

Liberation-limited grade/recovery curves from X-ray micro CT analysis of feed material for the evaluation of separation efficiency

Procedures for 3D mineral liberation analysis by X-ray micro CT (XMT) are presented and discussed including the construction of liberation-limited grade/recovery curves for specific feed materials. In this way, actual separation efficiencies can be compared to what might be expected for a perfect separation limited only by the extent of liberation. It is shown that 3D mineral liberation analysis based on XMT is preferred to 2D section analysis which overestimates the extent of liberation. By way of example, procedures and experimental results are presented and discussed for feed material in the case of phosphate rock flotation.     

Climate of the Little Ice Age and the past 2000 years in northeast Iceland inferred from chironomids and other lake sediment proxies

A sedimentary record from lake Stora Viearvatn in northeast Iceland records environmental changes over the past 2000 years. Downcore data include chironomid (Diptera: Chironomidae) assemblage data and total organic carbon, nitrogen, and biogenic silica content. Sample scores from detrended correspondence analysis (DCA) of chironomid assemblage data are well correlated with measured temperatures at Stykkishólmur over the 170 year instrumental record, indicating that chironomid assemblages at Stora Viearvatn have responded sensitively to past temperature changes. DCA scores appear to be useful for quantitatively inferring past temperatures at this site. In contrast, a quantitative chironomid-temperature transfer function developed for northwestern Iceland does a relatively poor job of reconstructing temperature shifts, possibly due to the lake’s large size and depth relative to the calibration sites or to the limited resolution of the subfossil taxonomy. The pre-instrumental climate history inferred from chironomids and other paleolimnological proxies is supported by prior inferences from historical documents, glacier reconstructions, and paleoceanographic studies. Much of the first millennium AD was relatively warm, with temperatures comparable to warm decades of the twentieth century. Temperatures during parts of the tenth and eleventh centuries AD may have been comparably warm. Biogenic silica concentrations declined, carbon:nitrogen ratios increased, and some chironomid taxa disappeared from the lake between the thirteenth and nineteenth centuries, recording the decline of temperatures into the Little Ice Age, increasing soil erosion, and declining lake productivity. All the proxy reconstructions indicate that the most severe Little Ice Age conditions occurred during the eighteenth and nineteenth centuries, a period historically associated with maximum sea-ice and glacier extent around Iceland.

A 2000 year record of climate variations reconstructed from Haukadalsvatn,West Iceland

The sediment fill of Haukadalsvatn, a lake in northwest Iceland, preserves a record of environmental change since deglaciation, 13 ka ago. The rapid sedimentation rate over the past 2 ka (ca. 4 m ka⁻¹) provides a high-resolution archive of late Holocene environmental change. Physical and chemical environmental proxies extracted from cores from the Haukadalsvatn sediment fill provide a reconstruction of sub-decadal-scale climate variability in Iceland over the past 2 ka. Over this interval biogenic silica (BSi) reflects warm April–May temperatures, whereas total organic carbon (TOC) peaks represent an increased flux of carbon to the lake from eolian-derived soil erosion following periods of cold summers accompanied by dry, windy winters. The proxy-based temperature reconstructions show a broad interval of warmth through Medieval times, but this warmth is punctuated by multi-decadal cold intervals. The transition into the Little Ice Age occurred in two steps, with initial summer cooling 1250–1300 AD, and a more severe drop in summer temperatures between 1450 and 1500 AD; both are periods of severe explosive volcanism. Multi-decadal patterns of cold and warm conditions have some characteristics of a North Atlantic Oscillation (NAO)-like signal, but instrumental records and proxy-based reconstructions of the NAO index contain little power in the frequencies most strongly expressed in our data set. Although severe soil erosion in Iceland is frequently equated with settlement, our reconstructions indicate that soil erosion began several centuries before settlement, whereas for several centuries after settlement, when summer temperatures were relatively high, there was little or no soil erosion. Only during the transition into and during the Little Ice Age did soil erosion become a major feature of the record. Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users.

The CO Cameron band emission in the Red Rectangle

The origin of the strong CO Cameron band emission in the Red Rectangle is investigated. From a comparison of laboratory spectroscopic data and astronomical observations in combination with chemical modelling, it is concluded that the Cameron band emission of CO originates from the dissociative recombination of HCO⁺, and its intensity provides a measure of the product of the density of HCO⁺ ions and the electron density, integrated along the line of sight.     

An analytic model for the epoch of halo creation

In this paper we describe the Bayesian link between the cosmological mass function and the distribution of times at which isolated haloes of a given mass exist. By assuming that clumps of dark matter undergo monotonic growth on the time-scales of interest, this distribution of times is also the distribution of 'creation' times of the haloes. This monotonic growth is an inevitable aspect of gravitational instability. The spherical top-hat collapse model is used to estimate the rate at which clumps of dark matter collapse. This gives the prior for the creation time given no information about halo mass. Applying Bayes' theorem then allows any mass function to be converted into a distribution of times at which haloes of a given mass are created. This general result covers both Gaussian and non-Gaussian models. We also demonstrate how the mass function and the creation time distribution can be combined to give a joint density function, and discuss the relation between the time distribution of major merger events and the formula calculated. Finally, we determine the creation time of haloes within three N -body simulations, and compare the link between the mass function and creation rate with the analytic theory.     

Thermodynamically constrained averaging theory approach for modeling flow and transport phenomena in porous medium systems: 7. Single-phase megascale flow models

This work is the seventh in a series that introduces and employs the thermodynamically constrained averaging theory (TCAT) for modeling flow and transport in multiscale porous medium systems. This paper expands the previous analyses in the series by developing models at a scale where spatial variations within the system are not considered. Thus the time variation of variables averaged over the entire system is modeled in relation to fluxes at the boundary of the system. This implementation of TCAT makes use of conservation equations for mass, momentum, and energy as well as an entropy balance. Additionally, classical irreversible thermodynamics is assumed to hold at the microscale and is averaged to the megascale, or system scale. The fact that the local equilibrium assumption does not apply at the megascale points to the importance of obtaining closure relations that account for the large-scale manifestation of small-scale variations. Example applications built on this foundation are suggested to stimulate future work.     

Reconstruction of the Water Table from Self-Potential Data: A Bayesian Approach

Ground water flow associated with pumping and injection tests generates self-potential signals that can be measured at the ground surface and used to estimate the pattern of ground water flow at depth. We propose an inversion of the self-potential signals that accounts for the heterogeneous nature of the aquifer and a relationship between the electrical resistivity and the streaming current coupling coefficient. We recast the inversion of the self-potential data into a Bayesian framework. Synthetic tests are performed showing the advantage in using self-potential signals in addition to in situ measurements of the potentiometric levels to reconstruct the shape of the water table. This methodology is applied to a new data set from a series of coordinated hydraulic tomography, self-potential, and electrical resistivity tomography experiments performed at the Boise Hydrogeophysical Research Site, Idaho. In particular, we examine one of the dipole hydraulic tests and its reciprocal to show the sensitivity of the self-potential signals to variations of the potentiometric levels under steady-state conditions. However, because of the high pumping rate, the response was also influenced by the Reynolds number , especially near the pumping well for a given test. Ground water flow in the inertial laminar flow regime is responsible for nonlinearity that is not yet accounted for in self-potential tomography. Numerical modeling addresses the sensitivity of the self-potential response to this problem.