Probabilistic assessment of spatial heterogeneity of natural background concentrations in large-scale groundwater bodies through Functional Geostatistics.

We propose and exemplify a framework to assess Natural Background Levels (NBLs) of target chemical species in large-scale groundwater bodies based on the context of Object Oriented Spatial Statistics. The approach enables one to fully exploit the richness of the information content embedded in the probability density function (PDF) of the variables of interest, as estimated from historical records of chemical observations. As such, the population of the entire distribution functions of NBL concentrations monitored across a network of monitoring boreholes across a given aquifer is considered as the object of the spatial analysis. Our approach starkly differs from previous studies which are mainly focused on the estimation of NBLs on the basis of the median or selected quantiles of chemical concentrations, thus resulting in information loss and limitations related to the need to invoke parametric assumptions to obtain further summary statistics in addition to those considered for the spatial analysis. Our work enables one to (i) assess spatial dependencies among observed PDFs of natural background concentrations, (ii) provide spatially distributed kriging predictions of NBLs, as well as (iii) yield a robust quantification of the ensuing uncertainty and probability of exceeding given threshold concentration values via stochastic simulation. We illustrate the approach by considering the (probabilistic) characterization of spatially variable NBLs of ammonium and arsenic detected at a monitoring network across a large scale confined groundwater body in Northern Italy.

Geostatistical multimodel approach for the assessment of the spatial distribution of natural background concentrations in large-scale groundwater bodies.

Quantification of the (spatially distributed) natural contributions to the chemical signature of groundwater resources is an emerging issue in the context of competitive groundwater uses as well as water regulation and management frameworks. Here, we illustrate a geostatistically-based approach for the characterization of spatially variable Natural Background Levels (NBLs) of target chemical species in large-scale groundwater bodies yielding evaluations of local probabilities of exceedance of a given threshold concentration. The approach is exemplified by considering three selected groundwater bodies and focusing on the evaluation of NBLs of ammonium and arsenic, as detected from extensive time series of concentrations collected at monitoring boreholes. Our study is motivated by the observation that reliance on a unique NBL value as representative of the natural geochemical signature of a reservoir can mask the occurrence of localized areas linked to diverse strengths of geogenic contributions to the groundwater status. We start from the application of the typical Pre-Selection (PS) methodology to the scale of each observation borehole to identify local estimates of NBL values. The latter are subsequently subject to geostatistical analysis to obtain estimates of their spatial distribution and the associated uncertainty. A multimodel framework is employed to interpret available data. The impact of alternative variogram models on the resulting spatial distributions of NBLs is assessed through probabilistic weights based on model identification criteria. Our findings highlight that assessing possible impacts of anthropogenic activities on groundwater environments with the aim of designing targeted solutions to restore a good groundwater quality status should consider a probabilistic description of the spatial distribution of NBLs. The latter is useful to provide enhanced information upon which one can then build decision-making protocols embedding the quantification of the associated uncertainty.

Statistical scaling of pore-scale Lagrangian velocities in natural porous media.

We investigate the scaling behavior of sample statistics of pore-scale Lagrangian velocities in two different rock samples, Bentheimer sandstone and Estaillades limestone. The samples are imaged using x-ray computer tomography with micron-scale resolution. The scaling analysis relies on the study of the way qth-order sample structure functions (statistical moments of order q of absolute increments) of Lagrangian velocities depend on separation distances, or lags, traveled along the mean flow direction. In the sandstone block, sample structure functions of all orders exhibit a power-law scaling within a clearly identifiable intermediate range of lags. Sample structure functions associated with the limestone block display two diverse power-law regimes, which we infer to be related to two overlapping spatially correlated structures. In both rocks and for all orders q, we observe linear relationships between logarithmic structure functions of successive orders at all lags (a phenomenon that is typically known as extended power scaling, or extended self-similarity). The scaling behavior of Lagrangian velocities is compared with the one exhibited by porosity and specific surface area, which constitute two key pore-scale geometric observables. The statistical scaling of the local velocity field reflects the behavior of these geometric observables, with the occurrence of power-law-scaling regimes within the same range of lags for sample structure functions of Lagrangian velocity, porosity, and specific surface area.

Relationship between pore size and velocity probability distributions in stochastically generated porous media.

We perform a set of detailed numerical simulations of single-phase, fully saturated flow in stochastically generated, three-dimensional pore structures with diverse porosities (ϕ) and degrees of connectivity, and analyze the probability density functions (PDFs) of the pore sizes, S, and vertical velocity components, w, which are aligned with the mean flow direction. Both of the PDFs are markedly skewed with pronounced positive tails. This feature of the velocity PDF is dictated by the pore structure and determines the shortest travel times, one of the key transport attributes that underpins the success or the failure of environmental remediation techniques. Using a maximum likelihood approach, we determine that the PDFs of S and w decay according to an exponential and a stretched exponential model, respectively. A strong correlation between the key parameters governing the decay of the upper tails of the two PDFs is found, which provides a quantitative result for this analogy that so far has been stated only qualitatively. The parameter governing the concavity of the tail of the velocity PDF varies linearly with porosity over the entire range of tested values (0.2≤ϕ≤0.6). The parameters controlling the spread of the upper tails of the PDFs of S and w appear to be linked by a power-law relationship.

Assessment of natural background levels in potentially contaminated coastal aquifers.

The estimation of natural background levels (NBLs) of dissolved concentrations of target chemical species in subsurface reservoirs relies on a proper assessment of the effects of forcing terms driving flow and transport processes taking place within the system and whose dynamics drive background concentration values. We propose coupling methodologies based on (a) global statistical analyses and (b) numerical modeling of system dynamics to distinguish between the impacts of different types of external forcing components influencing background concentration values. We focus on the joint application of a statistical methodology based on Component Separation and experimental/numerical modeling studies of groundwater flow and transport for the NBL estimation of selected chemical species in potentially contaminated coastal aquifers. We consider a site which is located in Calabria, Italy, and constitutes a typical example of a Mediterranean coastal aquifer which has been subject to intense industrial development. Our study is keyed to the characterization of NBLs of manganese and sulfate and is geared to the proper identification of the importance of a natural external forcing (i.e., seawater intrusion) on NBL assessment. Results from the Component Separation statistical approach are complemented by numerical simulations of the advective-dispersive processes that could influence the distribution of chemical species (i.e., sulfate) within the system. Estimated NBLs for manganese are consistent with the geochemical composition of soil samples. While Component Separation ascribes the largest detected sulfate concentrations to anthropogenic sources, our numerical modeling analysis suggests that they are mainly related to the natural process of seawater intrusion. Our results indicate that the use of statistical methodologies in complex groundwater systems should be assisted by a detailed characterization of the dynamics of natural (and/or induced) processes to distinguish effective anthropogenic contamination from natural conditions and to define realistic environmental clean-up goals.

Geochemical modeling of arsenic release from a deep natural solid matrix under alternated redox conditions.

Dissolved arsenic (As) concentrations detected in groundwater bodies of the Emilia-Romagna Region (Italy) exhibit values which are above the regulation limit and could be related to the natural composition of the host porous matrix. To support this hypothesis, we present the results of a geochemical modeling study reproducing the main trends of the dynamics of As, Fe, and Mn concentrations as well as redox potential and pH observed during batch tests performed under alternating redox conditions. The tests were performed on a natural matrix extracted from a deep aquifer located in the Emilia-Romagna Region (Italy). The solid phases implemented in the model were selected from the results of selective sequential extractions performed on the tested matrix. The calibrated model showed that large As concentrations have to be expected in the solution for low crystallinity phases subject to dissolution. The role of Mn oxides on As concentration dynamics appears significant in strongly reducing environments, particularly for large water-solid matrix interaction times. Modeled data evidenced that As is released firstly from the outer surface of Fe oxihydroxides minerals exhibiting large concentrations in water when persistent reducing conditions trigger the dissolution of the crystalline structure of the binding minerals. The presence of organic matter was found to strongly affect pH and redox conditions, thus influencing As mobility.

Arsenic release from deep natural solid matrices under experimentally controlled redox conditions.

We investigated the role of iron (Fe) on arsenic (As) release from two samples of a natural deep soil collected in an aquifer body in the Emilia-Romagna Region, Italy. Each sample is representative of a different solid matrix, i.e., sand and vegetal matter. Batch experiments were performed by applying alternating aerobic/anaerobic conditions to the samples under a range of redox and pH conditions, consistent with the corresponding values measured in the field. Arsenic mobilization was triggered by abrupt and rapid changes in redox conditions and displayed a clear correlation with oxidation/reduction potential for both solid matrices. Vegetal matter showed high binding capacity and large As concentration release. Arsenic release was also correlated with Fe released from the solid matrices. Our results suggest that the environmentally critical As concentrations detected in some aquifers in the Emilia-Romagna Region are consistent with (a) the occurrence of high natural As content in the component of the host porous medium associated with vegetal matter and (b) the effect of possible sharp localized (and temporally oscillating) variations in redox conditions.

Microscale simulation and numerical upscaling of a reactive flow in a plane channel.

A bimolecular homogeneous irreversible reaction of the kind A+B→C is simulated in a plane channel as a base example of reactive transport processes taking place at the microscale within porous and/or fractured media. The numerical study explores the way microscale processes embedded in dimensionless quantities such as Péclet (Pe) and Damköhler (Da) numbers propagate to upscaled coefficients describing effective system dynamics. The microscale evolution of the reactant concentrations is obtained through a particle-based numerical method which has been specifically tailored to the considered problem. Key results include a complete documentation of the process evolution for a wide range of Pe and Da, in terms of the global reaction rate, space-time distribution of reactants, and local mixing features leading to characterization of effective reaction and dispersion coefficients governing a section-averaged upscaled model of the system. The robustness of previously presented theoretical analyses concerning closures of volume-averaged (upscaled) formulations is assessed. The work elucidates the dependence of the effective dispersion and reactive parameters on the microscale mixing and reactive species evolution. Our results identify the role played by Da and Pe on the occurrence of incomplete mixing of reactants, which affects the features of the reactive transport scenario.

Probabilistic study of well capture zones distribution at the Lauswiesen field site.

The delineation of well capture zones is of utmost environmental and engineering relevance as pumping wells are commonly used both for drinking water supply needs, where protection zones have to be defined, and for investigation and remediation of contaminated aquifers. We analyze the probabilistic nature of well capture zones within the well field located at the "Lauswiesen" experimental site. The test site is part of an alluvial heterogeneous aquifer located in the Neckar river valley, close to the city of Tübingen in South-West Germany. We explore the effect of different conceptual models of the structure of aquifer heterogeneities on the delineation of three-dimensional probabilistic well catchment and time-related capture zones, in the presence of migration of conservative solutes. The aquifer is modeled as a three-dimensional, doubly stochastic composite medium, where distributions of geo-materials and hydraulic properties are uncertain. We study the relative importance of uncertain facies geometry and uncertain hydraulic conductivity and porosity on predictions of catchment and solute time of travel to the pumping well by focusing on cases in which (1) the facies distribution is random, but the hydraulic properties of each material are fixed, and (2) both facies geometry and material properties vary stochastically. The problem is tackled within a conditional numerical Monte Carlo framework. Results are provided in terms of probabilistic demarcations of the three-dimensional well catchment and time-related capture zones. Our findings suggest that the uncertainty associated with the prediction of the location of the outer boundary of well catchment at the "Lauswiesen" site is significantly affected by the conceptual model adopted to incorporate the heterogeneous nature of the aquifer domain in a predictive framework. Taking into account randomness of both lithofacies distribution and materials hydraulic conductivity allows recognizing the existence of preferential flow paths that influence the extent of the well catchment and the solute travel time distribution at the site.

Travel time and trajectory moments of conservative solutes in two-dimensional convergent flows.

We address advective transport of a solute traveling toward a single pumping well in a two-dimensional randomly heterogeneous aquifer. The two random variables of interest are the trajectory followed by an individual particle from the injection point to the well location and the particle travel time under steady-state conditions. Our main objective is to derive the predictors of trajectory and travel time and the associated uncertainty, in terms of their first two statistical moments (mean and variance). We consider a solute that undergoes mass transfer between a mobile and an immobile zone. Based on Lawrence et al. [Lawrence, A.E., Sánchez-Vila, X., Rubin, Y., 2002. Conditional moments of the breakthrough curves of kinetically sorbing solute in heterogeneous porous media using multirate mass transfer models for sorption and desorption. Water Resour. Res. 38 (11), 1248, doi:10.1029/2001WR001006.], travel time moments can be written in terms of those of a conservative solute times a deterministic quantity. Moreover, the moments of solute particles trajectory do not depend on mass transfer processes. The resulting mean and variance of travel time and trajectory for a conservative species can be written as functions of the first, second moments and cross-moments of trajectory and velocity components. The equations are developed from a consistent second order expansion in sigmaY (standard deviation of the natural logarithm of hydraulic conductivity). Our solution can be completely integrated with the moment equations of groundwater flow of Guadagnini and Neuman [Guadagnini, A., Neuman, S.P., 1999a. Nonlocal and localized analyses of conditional mean steady state flow in bounded, randomly non uniform domains 1. Theory and computational approach. Water Resour. Res. 35(10), 2999-3018.,Guadagnini, A., Neuman, S.P., 1999b. Nonlocal and localized analyses of conditional mean steady state flow in bounded, randomly non uniform domains 2. Computational examples. Water Resour. Res. 35(10), 3019-3039.], it is free of distributional assumptions regarding the log conductivity field, and formally includes conditioning. We present analytical expressions for the unconditional case by making use of the results of Riva et al. [Riva, M., Guadagnini, A., Neuman, S.P., Franzetti, S., 2001. Radial flow in a bounded randomly heterogeneous aquifer. Transport in Porous Media 45, 139-193.]. The quality of the solution is supported by numerical Monte Carlo simulations. Potential uses of this work include the determination of aquifer reclamation time by means of a single pumping well, and the demarcation of the region potentially affected by the presence of a contaminant in the proximity of a well, whenever the aquifer is very thin and Dupuit-Forchheimer assumption holds.

Prior mapping for nonlinear flows in random environments.

We analyze nonlinear flows in randomly heterogeneous environments, which are characterized by state-dependent diffusion coefficients with spatially correlated structures. The prior Kirchhoff mapping is used to describe such systems by linear stochastic partial differential equations with multiplicative noise. These are solved through moment equations which are closed, alternatively, either by perturbation expansions, or by a posterior linear mapping closure. The latter relies on the assumption that the state variable is a spatially distributed Gaussian field. We demonstrate that the former approach is more robust.

UVB versus UVB plus calcipotriol (MC 903) therapy for psoriasis vulgaris.

It is well known that UVB therapy of psoriasis vulgaris is potentiated by the association with topical and oral drugs, while till now there have been very few reports on the association between UVB and calcipotriol. In order to evaluate the efficacy and tolerance of this association, we studied 19 patients with psoriasis vulgaris of mild severity (PASI: 5-10). Each patient was treated with UVB and invited to apply calcipotriol 50 micrograms/g ointment twice a day on one lesion usually on elbows or knees in order to compare it with the opposite side. The evaluation of each lesion was performed before and after 4 weeks of therapy. Our data show that the association between UVB and calcipotriol is significantly more effective than UVB therapy alone: 17 out of 19 patients (89%) showed a greater improvement with UVB plus calcipotriol as compared to UVB alone.