Hybrid Gaussian-cubic radial basis functions for scattered data interpolation

Scattered data interpolation schemes using kriging and radial basis functions (RBFs) have the advantage of being meshless and dimensional independent; however, for the datasets having insufficient observations, RBFs have the advantage over geostatistical methods as the latter requires variogram study and statistical expertise. Moreover, RBFs can be used for scattered data interpolation with very good convergence, which makes them desirable for shape function interpolation in meshless methods for numerical solution of partial differential equations. For interpolation of large datasets, however, RBFs in their usual form, lead to solving an ill-conditioned system of equations, for which, a small error in the data can cause a significantly large error in the interpolated solution. In order to reduce this limitation, we propose a hybrid kernel by using the conventional Gaussian and a shape parameter independent cubic kernel. Global particle swarm optimization method has been used to analyze the optimal values of the shape parameter as well as the weight coefficients controlling the Gaussian and the cubic part in the hybridization. Through a series of numerical tests, we demonstrate that such hybridization stabilizes the interpolation scheme by yielding a far superior implementation compared to those obtained by using only the Gaussian or cubic kernels. The proposed kernel maintains the accuracy and stability at small shape parameter as well as relatively large degrees of freedom, which exhibit its potential for scattered data interpolation and intrigues its application in global as well as local meshless methods for numerical solution of PDEs.     

Convergence analysis of fixed stress split iterative scheme for anisotropic poroelasticity with tensor Biot parameter

We perform a convergence analysis of the fixed stress split iterative scheme for the Biot system modeling coupled flow and deformation in anisotropic poroelastic media with tensor Biot parameter. The fixed stress split iterative scheme solves the flow subproblem with all components of the stress tensor frozen using a multipoint flux mixed finite element method, followed by the poromechanics subproblem using a conforming Galerkin method in every coupling iteration at each time step. The coupling iterations are repeated until convergence and Backward Euler is employed for time marching. The convergence analysis is based on studying the equations satisfied by the difference of iterates to show that the fixed stress split iterative scheme for anisotropic poroelasticity with Biot tensor is contractive. We also demonstrate that the scheme is numerically convergent using the classical Mandel’s problem solution for transverse isotropy.     

A robust mesh optimisation method for multiphase porous media flows

Flows of multiple fluid phases are common in many subsurface reservoirs. Numerical simulation of these flows can be challenging and computationally expensive. Dynamic adaptive mesh optimisation and related approaches, such as adaptive grid refinement can increase solution accuracy at reduced computational cost. However, in models or parts of the model domain, where the local Courant number is large, the solution may propagate beyond the region in which the mesh is refined, resulting in reduced solution accuracy, which can never be recovered. A methodology is presented here to modify the mesh within the non-linear solver. The method allows efficient application of dynamic mesh adaptivity techniques even with high Courant numbers. These high Courant numbers may not be desired but a consequence of the heterogeneity of the domain. Therefore, the method presented can be considered as a more robust and accurate version of the standard dynamic mesh adaptivity techniques.     

Hydrogeology of a montane headwater groundwater system downgradient of a coal-mine waste rock dump: Elk Valley,British Columbia,Canada

Steelmaking-coal waste rock placed in mountain catchments in the Elk Valley, British Columbia, Canada, drain constituents of interest (CIs) to surface water downgradient of the waste rock dumps. The role of groundwater in transporting CIs in the headwaters of mountain catchments is not well understood. This study characterizes the physical hydrogeology of a portion of a 10-km² headwater catchment (West Line Creek) downgradient of a 2.7-km² waste rock dump placed over a natural headwater valley-bottom groundwater system. The study site was instrumented with 13 monitoring wells. Drill core samples were collected to determine subsurface lithology and geotechnical properties. The groundwater system was characterized using field testing and water-level monitoring. The valley-bottom sediments were composed of unconsolidated glacial and meltwater successions (<64 m thick) deposited as a series of cut and fill structures overlying shale bedrock. An unconfined basal alluvial aquifer located above fractured bedrock was identified as the primary conduit for groundwater flow toward Line Creek (650 m from the toe of the dump). Discharge through the basal alluvial aquifer was estimated using the geometric mean hydraulic conductivity (±1 standard deviation). These calculations suggest groundwater discharge could account for approximately 15% (ranging from 2 to 60%) of the total water discharged from the watershed. The residence time from the base of the waste rock dump to Line Creek was estimated at <3 years. The groundwater system was defined as a snowmelt (i.e., nival) regime dominated by direct recharge (percolation of precipitation) across the catchment.     

Impact of irrigated agriculture on groundwater-recharge salinity: a major sustainability concern in semi-arid regions

Intensive irrigated agriculture substantially modifies the hydrological cycle and often has major environmental impacts. The article focuses upon a specific concern—the tendency for progressive long-term increases in the salinity of groundwater recharge derived from irrigated permeable soils and replenishment of unconfined aquifers in more arid regions. This process has received only scant attention in the water-resource literature and has not been considered by agricultural science. This work makes an original contribution by analysing, from scientific principles, how the salinisation of groundwater recharge arises and identifies the factors affecting its severity. If not proactively managed, the process eventually will impact irrigation waterwell salinity, the productivity of agriculture itself, and can even lead to land abandonment. The types of management measure required for mitigation are discussed through three detailed case histories of areas with high-value groundwater-irrigated agriculture (in Spain, Argentina and Pakistan), which provide a long-term perspective on the evolution of the problem over various decades.     

Adsorption of copper (II) on mesoporous silica: the effect of nano-scale confinement

Nano-scale spatial confinement can alter chemistry at mineral–water interfaces. These nano-scale confinement effects can lead to anomalous fate and transport behavior of aqueous metal species. When a fluid resides in a nanoporous environments (pore size under 100 nm), the observed density, surface tension, and dielectric constant diverge from those measured in the bulk. To evaluate the impact of nano-scale confinement on the adsorption of copper (Cu²⁺), we performed batch adsorption studies using mesoporous silica. Mesoporous silica with the narrow distribution of pore diameters (SBA-15; 8, 6, and 4 nm pore diameters) was chosen since the silanol functional groups are typical to surface environments. Batch adsorption isotherms were fit with adsorption models (Langmuir, Freundlich, and Dubinin–Radushkevich) and adsorption kinetic data were fit to a pseudo-first-order reaction model. We found that with decreasing pore size, the maximum surface area-normalized uptake of Cu²⁺ increased. The pseudo-first-order kinetic model demonstrates that the adsorption is faster as the pore size decreases from 8 to 4 nm. We attribute these effects to the deviations in fundamental water properties as pore diameter decreases. In particular, these effects are most notable in SBA-15 with a 4-nm pore where the changes in water properties may be responsible for the enhanced Cu mobility, and therefore, faster Cu adsorption kinetics.     

Natural speciation of nickel at the micrometer scale in serpentine (ultramafic) topsoils using microfocused X-ray fluorescence,diffraction, and absorption

Serpentine soils and ultramafic laterites develop over ultramafic bedrock and are important geological materials from environmental, geochemical, and industrial standpoints. They have naturally elevated concentrations of trace metals, such as Ni, Cr, and Co, and also high levels of Fe and Mg. Minerals host these trace metals and influence metal mobility. Ni in particular is an important trace metal in these soils, and the objective of this research was to use microscale (µ) techniques to identify naturally occurring minerals that contain Ni and Ni correlations with other trace metals, such as Fe, Mn, and Cr. Synchrotron based µ-XRF, µ-XRD, and µ-XAS were used. Ni was often located in the octahedral layer of serpentine minerals, such as lizardite, and in other layered phyllosilicate minerals with similar octahedral structure, such as chlorite group minerals including clinochlore and chamosite. Ni was also present in goethite, hematite, magnetite, and ferrihydrite. Goethite was present with lizardite and antigorite on the micrometer scale. Lizardite integrated both Ni and Mn simultaneously in its octahedral layer. Enstatite, pargasite, chamosite, phlogopite, and forsterite incorporated various amounts of Ni and Fe over the micrometer spatial scale. Ni content increased six to seven times within the same 500 µm µ-XRD transect on chamosite and phlogopite. Data are shown down to an 8 µm spatial scale. Ni was not associated with chromite or zincochromite particles. Ni often correlated with Fe and Mn, and generally did not correlate with Cr, Zn, Ca, or K in µ-XRF maps. A split shoulder feature in the µ-XAS data at 8400 eV (3.7 Å^?1 in k-space) is highly correlated (94% of averaged LCF results) to Ni located in the octahedral sheet of layered phyllosilicate minerals, such as serpentine and chlorite-group minerals. A comparison of bulk-XAS LCF to averaged µ-XAS LCF results showed good representation of the bulk soil via the µ-XAS technique for two of the three soils. In the locations analyzed by µ-XAS, average Ni speciation was dominated by layered phyllosilicate and serpentine minerals (76%), iron oxides (18%), and manganese oxides (9%). In the locations analyzed by µ-XRD, average Ni speciation was dominated by layered phyllosilicate, serpentine, and ultramafic-related minerals (71%) and iron oxides (17%), illustrating the complementary nature of these two methods.

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Modeling the Population Effects of Hypoxia on Atlantic Croaker (<Emphasis Type="Italic">Micropogonias undulatus</Emphasis>) in the Northwestern Gulf of Mexico: Part 1—Model Description and Idealized Hypoxia

We developed a spatially explicit, individual-based model to analyze how hypoxia effects on reproduction, growth, and mortality of Atlantic croaker in the northwestern Gulf of Mexico lead to population-level responses. The model follows the hourly growth, mortality, reproduction, and movement of individuals on a 300 × 800 spatial grid of 1-km² cells for 140 years. Chlorophyll-a concentration, water temperature, and dissolved oxygen (DO) were specified daily for each grid cell and repeated for each year of the simulation. A bioenergetics model was used to represent growth, mortality was assumed stage- and age-dependent, and the movement behavior of juveniles and adults was modeled based on temperature and avoidance of low DO. Hypoxia effects were imposed using exposure effect submodels that converted time-varying exposures to low DO to reduced hourly growth, increased hourly mortality, and reduced annual fecundity. Results showed that 100 years of either mild or intermediate hypoxia produced small reductions in population abundance, while repeated severe hypoxia caused a 19% reduction in long-term population abundance. Relatively few individuals were exposed to low DO each hour, but many individuals experienced some exposure. The response was dominated by a 5% average reduction in annual fecundity of individuals. Under conditions of random sequences of mild, intermediate, and severe hypoxia years occurring in proportion to their historical frequency, the model predicted a 10% decrease in the long-term population abundance of croaker. A companion paper substitutes hourly DO values from a three-dimensional water quality model for the idealized hypoxia and results in a more realistic population reduction of about 25%.     

Impacts of hydrous manganese oxide on the retention and lability of dissolved organic matter

Minerals constitute a primary ecosystem control on organic C decomposition in soils, and therefore on greenhouse gas fluxes to the atmosphere. Secondary minerals, in particular, Fe and Al (oxyhydr)oxides—collectively referred to as “oxides” hereafter—are prominent protectors of organic C against microbial decomposition through sorption and complexation reactions. However, the impacts of Mn oxides on organic C retention and lability in soils are poorly understood. Here we show that hydrous Mn oxide (HMO), a poorly crystalline δ-MnO₂, has a greater maximum sorption capacity for dissolved organic matter (DOM) derived from a deciduous forest composite O_i, O_e, and O_a horizon leachate (“O horizon leachate” hereafter) than does goethite under acidic (pH 5) conditions. Nonetheless, goethite has a stronger sorption capacity for DOM at low initial C:(Mn or Fe) molar ratios compared to HMO, probably due to ligand exchange with carboxylate groups as revealed by attenuated total reflectance-Fourier transform infrared spectroscopy. X-ray photoelectron spectroscopy and scanning transmission X-ray microscopy–near-edge X-ray absorption fine structure spectroscopy coupled with Mn mass balance calculations reveal that DOM sorption onto HMO induces partial Mn reductive dissolution and Mn reduction of the residual HMO. X-ray photoelectron spectroscopy further shows increasing Mn(II) concentrations are correlated with increasing oxidized C (C=O) content (r = 0.78, P < 0.0006) on the DOM–HMO complexes. We posit that DOM is the more probable reductant of HMO, as Mn(II)-induced HMO dissolution does not alter the Mn speciation of the residual HMO at pH 5. At a lower C loading (2 × 10² μg C m^?2), DOM desorption—assessed by 0.1 M NaH₂PO₄ extraction—is lower for HMO than for goethite, whereas the extent of desorption is the same at a higher C loading (4 × 10² μg C m^?2). No significant differences are observed in the impacts of HMO and goethite on the biodegradability of the DOM remaining in solution after DOM sorption reaches steady state. Overall, HMO shows a relatively strong capacity to sorb DOM and resist phosphate-induced desorption, but DOM–HMO complexes may be more vulnerable to reductive dissolution than DOM–goethite complexes.     

The synergistic effect of calcium on organic carbon sequestration to ferrihydrite

Sequestration of organic carbon (OC) in environmental systems is critical to mitigating climate change. Organo-mineral associations, especially those with iron (Fe) oxides, drive the chemistry of OC sequestration and stability in soils. Short-range-ordered Fe oxides, such as ferrihydrite, demonstrate a high affinity for OC in binary systems. Calcium commonly co-associates with OC and Fe oxides in soils, though the bonding mechanism (e.g., cation bridging) and implications of the co-association for OC sequestration remain unresolved. We explored the effect of calcium (Ca²⁺) on the sorption of dissolved OC to 2-line ferrihydrite. Sorption experiments were conducted between leaf litter-extractable OC and ferrihydrite at pH 4 to 9 with different initial C/Fe molar ratios and Ca²⁺ concentrations. The extent of OC sorption to ferrihydrite in the presence of Ca²⁺ increased across all tested pH values, especially at pH ≥ 7. Sorbed OC concentration at pH 9 increased from 8.72 ± 0.16 to 13.3 ± 0.20 mmol OC g^?1 ferrihydrite between treatments of no added Ca²⁺ and 30 mM Ca²⁺ addition. Batch experiments were paired with spectroscopic studies to probe the speciation of sorbed OC and elucidate the sorption mechanism. ATR-FTIR spectroscopy analysis revealed that carboxylic functional moieties were the primary sorbed OC species that were preferentially bound to ferrihydrite and suggested an increase in Fe-carboxylate ligand exchange in the presence of Ca at pH 9. Results from batch to spectroscopic experiments provide significant evidence for the enhancement of dissolved OC sequestration to 2-line ferrihydrite and suggest the formation of Fe–Ca-OC ternary complexes. Findings of this research will inform modeling of environmental C cycling and have the potential to influence strategies for managing land to minimize OM stabilization.