Stochastic estimation of hydraulic transmissivity fields using flow connectivity indicator data

This is the peer reviewed version of the following article: [Freixas, G., D. Fernàndez-Garcia, and X. Sanchez-Vila (2017), Stochastic estimation of hydraulic transmissivity fields using flow connectivity indicator data, Water Resour. Res., 53, 602–618, doi:10.1002/2015WR018507], which has been published in final form at http://onlinelibrary.wiley.com/doi/10.1002/2015WR018507/abstract. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving.Most methods for hydraulic test interpretation rely on a number of simplified assumptions regarding the homogeneity and isotropy of the underlying porous media. This way, the actual heterogeneity of any natural parameter, such as transmissivity ( math formula), is transferred to the corresponding estimates in a way heavily dependent on the interpretation method used. An example is a long-term pumping test interpreted by means of the Cooper-Jacob method, which implicitly assumes a homogeneous isotropic confined aquifer. The estimates obtained from this method are not local values, but still have a clear physical meaning; the estimated math formula represents a regional-scale effective value, while the log-ratio of the normalized estimated storage coefficient, indicated by math formula, is an indicator of flow connectivity, representative of the scale given by the distance between the pumping and the observation wells. In this work we propose a methodology to use math formula, together with sampled local measurements of transmissivity at selected points, to map the expected value of local math formula values using a technique based on cokriging. Since the interpolation involves two variables measured at different support scales, a critical point is the estimation of the covariance and crosscovariance matrices. The method is applied to a synthetic field displaying statistical anisotropy, showing that the inclusion of connectivity indicators in the estimation method provide maps that effectively display preferential flow pathways, with direct consequences in solute transport.Peer ReviewedPostprint (published version

Javier Marías: la escritura en las postrimerías de la modernidad

RESUMEN   La complejidad de la escritura literaria de Javier Marías ha venido en gran medida determinada por el contexto histórico y estético en el que hizo su aparición. Un momento de encrucijada en que distintas poéticas coexisten en el campo literario español. La praxis literaria del autor en este tiempo es una consecuencia y a la vez una reacción a las transformaciones que se vivieron en España, situándose en el sector más innovador del campo en los últimos años del franquismo. En sus novelas se van a armonizar elementos eminentemente narrativos con el rigor estilístico propio de la alta literatura del modernismo, la preocupación por poner en primer plano “lo literario” con la hibridación estética y el interés por las literaturas de género que han definido rasgos importantes de la llamada posmodernidad. En esta intersección Marías encuentra una poética de “plenitud” que elabora un estilo de autor autosuficiente a la vez que busca un lector no minoritario, interesado por la historia narrada y las vicisitudes de sus protagonistas, y sobre la que se va a sustentar toda su obra de madurez.     ABSTRACT   The complexity of the literary writing of Javier Marías has been largely determined by the historical and aesthetic context in which he made his appearance. A moment of crossroads in which different poetics coexist in the Spanish literary field. The literary praxis of the author at this time is a consequence and at the same time a reaction to the transformations that were experienced in Spain, situating itself in the most innovative sector of the field in the last years of the Franco regime. In his novels are going to harmonize eminently narrative elements with the stylistic rigor typical of the high literature of modernism, the concern to put in the foreground "the literary" with aesthetic hybridization and interest in gender literature that have defined important features of the so-called postmodernity. In this intersection, Marías finds a poetic of "plenitude" that elaborates a style of self-sufficient author while looking for a non-minority reader, interested in the narrated history and the vicissitudes of its protagonists, and on which it will sustain all its work of maturity. RESUMEN   La complejidad de la escritura literaria de Javier Marías ha venido en gran medida determinada por el contexto histórico y estético en el que hizo su aparición. Un momento de encrucijada en que distintas poéticas coexisten en el campo literario español. La praxis literaria del autor en este tiempo es una consecuencia y a la vez una reacción a las transformaciones que se vivieron en España, situándose en el sector más innovador del campo en los últimos años del franquismo. En sus novelas se van a armonizar elementos eminentemente narrativos con el rigor estilístico propio de la alta literatura del modernismo, la preocupación por poner en primer plano “lo literario” con la hibridación estética y el interés por las literaturas de género que han definido rasgos importantes de la llamada posmodernidad. En esta intersección Marías encuentra una poética de “plenitud” que elabora un estilo de autor autosuficiente a la vez que busca un lector no minoritario, interesado por la historia narrada y las vicisitudes de sus protagonistas, y sobre la que se va a sustentar toda su obra de madurez.     ABSTRACT   The complexity of the literary writing of Javier Marías has been largely determined by the historical and aesthetic context in which he made his appearance. A moment of crossroads in which different poetics coexist in the Spanish literary field. The literary praxis of the author at this time is a consequence and at the same time a reaction to the transformations that were experienced in Spain, situating itself in the most innovative sector of the field in the last years of the Franco regime. In his novels are going to harmonize eminently narrative elements with the stylistic rigor typical of the high literature of modernism, the concern to put in the foreground "the literary" with aesthetic hybridization and interest in gender literature that have defined important features of the so-called postmodernity. In this intersection, Marías finds a poetic of "plenitude" that elaborates a style of self-sufficient author while looking for a non-minority reader, interested in the narrated history and the vicissitudes of its protagonists, and on which it will sustain all its work of maturity

La autoficción como dialéctica entre lo histórico y lo biográfico en la obra de Javier Cercas

Desde Relatos reales, la obra de Javier Cercas ha gravitado hacia el concepto de autoficción. En este artículo pretendemos demostrar cómo en efecto estas obras pueden caber en la denominación general de “autoficción”. Para eso nuestro razonamiento se basará en las propuestas teóricas de Manuel Alberca, Phillippe Lejeune y José María Pozuelo Yvancos. Además, por tratar temas del pasado español reciente, los escritos de Cercas son ejemplos también de “metaficción historiográfica”, concepto avanzado por Linda Hutcheon, y utilizado por David K. Herzberger para explicar la narración sobre el pasado de los escritores españoles contemporáneos. Así, Javier Cercas al vincular lo biográfico y lo histórico se inserta en una tradición que es muestra de la narrativa posmoderna en España

Linking biofilm spatial structure to real-time microscopic oxygen decay imaging

This is an Accepted Manuscript of an article published by Taylor & Francis Group in Biofouling on 2018, available online at: http://www.tandfonline.com/10.1080/08927014.2017.1423474Two non-destructive techniques, confocal laser scanning microscopy (CLSM) and planar optode (VisiSens imaging), were combined to relate the fine-scale spatial structure of biofilm components to real-time images of oxygen decay in aquatic biofilms. Both techniques were applied to biofilms grown for seven days at contrasting light and temperature (10/20°C) conditions. The geo-statistical analyses of CLSM images indicated that biofilm structures consisted of small (~100 µm) and middle sized (~101 µm) irregular aggregates. Cyanobacteria and EPS (extracellular polymeric substances) showed larger aggregate sizes in dark grown biofilms while, for algae, aggregates were larger in light-20°C conditions. Light-20°C biofilms were most dense while 10°C biofilms showed a sparser structure and lower respiration rates. There was a positive relationship between the number of pixels occupied and the oxygen decay rate. The combination of optodes and CLMS, taking advantage of geo-statistics, is a promising way to relate biofilm architecture and metabolism at the micrometric scale.Peer ReviewedPostprint (author's final draft

Bayesian estimation of the transmissivity spatial structure from pumping test data

Estimating the statistical parameters (mean, variance, and integral scale) that define the spatial structure of the transmissivity or hydraulic conductivity fields is a fundamental step for the accurate prediction of subsurface flow and contaminant transport. In practice, the determination of the spatial structure is a challenge because of spatial heterogeneity and data scarcity. In this paper, we describe a novel approach that uses time drawdown data from multiple pumping tests to determine the transmissivity statistical spatial structure. The method builds on the pumping test interpretation procedure of Copty et al. (2011) (Continuous Derivation method, CD), which uses the time-drawdown data and its time derivative to estimate apparent transmissivity values as a function of radial distance from the pumping well. A Bayesian approach is then used to infer the statistical parameters of the transmissivity field by combining prior information about the parameters and the likelihood function expressed in terms of radially-dependent apparent transmissivities determined from pumping tests. A major advantage of the proposed Bayesian approach is that the likelihood function is readily determined from randomly generated multiple realizations of the transmissivity field, without the need to solve the groundwater flow equation. Applying the method to synthetically-generated pumping test data, we demonstrate that, through a relatively simple procedure, information on the spatial structure of the transmissivity may be inferred from pumping tests data. It is also shown that the prior parameter distribution has a significant influence on the estimation procedure, given the non-uniqueness of the estimation procedure. Results also indicate that the reliability of the estimated transmissivity statistical parameters increases with the number of available pumping tests.Peer ReviewedPostprint (author's final draft

Ergodicity of pumping tests

Standard interpretations of pumping tests in heterogeneous formations rely on effective representations of porous media, which replace spatially varying hydraulic properties with their constant counterparts averaged over the support volume of a test. Rigorous approaches for deriving representative (effective, apparent, upscaled, etc.) parameters employ either ensemble or spatial averaging. We derive a set of conditions under which these two paradigms yield identical results. We refer to them as conditions for the ergodicity of pumping tests. This allows one to use stochastic approaches to estimate the statistics of the spatial variability of hydraulic parameters on scales smaller than the support volume of a pumping test

Characterization of mixing and spreading in a bounded stratified medium

Matheron and de Marsily [Matheron M, de Marsily G. Is the transport in porous media always diffusive? A counter-example. Water Resour Res 1980;16:901–17] studied transport in a perfectly stratified infinite medium as an idealized aquifer model. They observed superdiffusive solute spreading quantified by anomalous increase of the apparent longitudinal dispersion coefficient with the square root of time. Here, we investigate solute transport in a vertically bounded stratified random medium. Unlike for the infinite medium at asymptotically long times, disorder-induced mixing and spreading is uniquely quantified by a constant Taylor dispersion coefficient. Using a stochastic modeling approach we study the effective mixing and spreading dynamics at pre-asymptotic times in terms of effective average transport coefficients. The latter are defined on the basis of local moments, i.e., moments of the transport Green function. We investigate the impact of the position of the initial plume and the initial plume size on the (highly anomalous) pre-asymptotic effective spreading and mixing dynamics for single realizations and in average. Effectively, the system “remembers” its initial state, the effective transport coefficients show so-called memory effects, which disappear after the solute has sampled the full vertical extent of the medium. We study the impact of the intrinsic non-ergodicity of the confined medium on the validity of the stochastic modeling approach and study in this context the transition from the finite to the infinite mediu

Effective dispersion in a chemically heterogeneous medium under temporally fluctuating flow conditions

We investigate effective solute transport in a chemically heterogeneous medium subject to temporal fluctuations of the flow conditions. Focusing on spatial variations in the equilibrium adsorption properties, the corresponding fluctuating retardation factor is modeled as a stationary random space function. The temporal variability of the flow is represented by a stationary temporal random process. Solute spreading is quantified by effective dispersion coefficients, which are derived from the ensemble average of the second centered moments of the normalized solute distribution in a single disorder realization. Using first-order expansions in the variances of the respective random fields, we derive explicit compact expressions for the time behavior of the disorder induced contributions to the effective dispersion coefficients. Focusing on the contributions due to chemical heterogeneity and temporal fluctuations, we find enhanced transverse spreading characterized by a transverse effective dispersion coefficient that, in contrast to transport in steady flow fields, evolves to a disorder-induced macroscopic value (i.e., independent of local dispersion). At the same time, the asymptotic longitudinal dispersion coefficient can decrease. Under certain conditions the contribution to the longitudinal effective dispersion coefficient shows superdiffusive behavior, similar to that observed for transport in s stratified porous medium, before it decreases to its asymptotic value. The presented compact and easy to use expressions for the longitudinal and transverse effective dispersion coefficients can be used for the quantification of effective spreading and mixing in the context of the groundwater remediation based on hydraulic manipulation and for the effective modeling of reactive transport in heterogeneous media in general

On the striking similarity between the moments of breakthrough curves for a heterogeneous medium and a homogeneous medium with a matrix diffusion term

A usual method to obtain aquifer parameters is to analyze the moments of the breakthrough curves (BTCs) in tracer tests. The parameters to be estimated in this analysis would depend on the conceptual model adopted. Intuitively, if different processes were considered, the shape of the BTCs should be quite different, and one would tend to think that the time and space evolution of the temporal moments should also be quite different. Contrarily, in this paper, we show that two very different conceptual models of solute transport lead to virtually identical moments of the BTC. The two models selected for this study are the classical advection–dispersion equation with a Fickian macrodispersive term and a homogeneous medium advection model with mass-transfer between mobile and immobile matrix phases, for three different models of matrix shape. In both models, the first three moments are linear with travel distance, while the fourth moment is a second order polynomial. This agreement allows us to choose parameters yielding the same moments in the two models. As we consider two fitting parameters, we select them to match the second and third moment. Match in the first moment is obtained from physical arguments. It turns out that the resulting leading term of the fourth moment is identical for both models. As a direct consequence of this work, it follows that for large travel distances it would not be possible to discriminate between conceptual models using data from a single BTC

Travel time moments for sorbing solutes in heterogeneous domains under nonuniform flow conditions

 A methodology for evaluating the unconditional and conditional moments of travel time for a sorbing solute is presented. The approach is applicable for any flow configuration and for a wide range of mass transfer rate‐limited linear processes. The methodology is applicable to the general case of spatially variable hydrological and chemical parameters. The sorption model used to derive the temporal moments is that of a continuous distribution of mass rate coefficients [Haggerty and Gorelick, 1998]. Models such as instantaneous equilibrium, first‐order and two‐site sorption kinetics, among others, can be considered as particular cases of this general model. Using a deterministic approach, the low‐order moments of the breakthrough curves for reactive solutes can be obtained as a function of those for conservative tracers. Using a stochastic approach, the unconditional low‐order statistics of the travel time moments can be obtained. These moments depend on the statistics of two Lagrangian functions, the travel time for a conservative solute, and an integral of the variations of the chemical parameters weighted by the inverse local velocity along the trajectory. Finally, conditional temporal moments are derived. Moments can be conditioned to any type of information, hard or soft, hydraulic or geochemical. Conditioning is found to reduce uncertainty, characterized by a reduction in the variance of the travel time. The general results are particularized for both uniform in the mean and convergent flow conditions and for simple sorption models such as linear instantaneous equilibrium and first‐order kinetics. In all such cases, close‐form results, based on small perturbations expansions, are presented for the travel time moments