Mauro Giudici

Effects of sedimentary heterogeneity on groundwater flow in a Quaternary pro-glacial delta environment: joining facies analysis and numerical modelling

Abstract We present the sedimentological survey of Quaternary sediments developed in glacio-fluvial to glacio-lacustrine delta environments and exposed at an abandoned quarry in Northern Italy. This outcrop is considered an analogue of sedimentary structures that could form a real aquifer. We recognise the following sedimentary units: (I) colluvial sediments with human artefacts (less than 2 m thick); (II) gravelly sands with oversized pebbles (2.5–5.5 m thick), bounded at the base by a roughly flat composite disconformity surface; (III) and (IV) gravelly-sand foresets which form two bodies with different dips that are separated by an inclined, almost planar, erosional surface. From past observations in the surrounding area and a geoelectrical survey, we estimate that the minimum total thickness of the delta system is 20 m. We have analysed the sedimentary characteristics of two well exposed areas, which are located within units II, III and IV and covering areas of 115 and 95 m2, using detailed sedimentological surveys along six vertical sections. With the aid of a topographic survey we have reconstructed the distribution of textural units based on sedimentary facies and including information about grain-size distribution, sorting and packing. We have constructed a sedimentary model for the two areas using orthogonal cells of 10×10 cm, attributing the dominant textural unit to each cell. The distribution of sedimentary textural units is used to estimate the distribution of hydraulic conductivity for the two areas of this aquifer analogue; we have determined the hydraulic conductivity by assigning different values to the different textural units according to laboratory measurements of porosity and grain-size distribution, Kozeny–Carmans equation and literature data. We have modelled groundwater flow in the two areas approximating the balance equation with finite differences, using a regular grid with 10 cm spacing, and we have performed some numerical experiments. First, we have evaluated the equivalent conductivity tensor for the two areas. Secondly, we have considered a coarse grid, with 1.5 m spacing, and at this scale we have analysed the validation of the discrete form of Darcys law usually introduced in finite difference modelling. The results of the numerical experiments show the anisotropic behaviour of the medium, especially for unit II composed of sandy beds, some of which lead to a preferential path for groundwater flow in the horizontal direction. The deeper sedimentary units III and IV are characterised by a lower anisotropy ratio for hydraulic conductivity, because the layered structures of these units have different dips. Finally we show that the discrete form of Darcys law at a scale length of 1.5 m is a first-order approximation only.

Identification of Thermal-Conductivities by Temperature-Gradient Profiles. One-Dimensional Steady Flow

The comparison model method (CMM) is applied to the identification of spatially varying thermal conductivity in a one‐dimensional domain. This method deals with the discretized steady‐state heat equation written at the nodes of a lattice, a lattice which models a stack of plane parallel layers. The required data are temperature gradient and heat source (or sink) values. The unknowns of this inverse problem are not nodal values but internode thermal conductivities, which appear in the node heat balance equation. The conductivities, e.g., the solutions to the inverse problem obtained by the CMM, are a one‐parameter family. In order to achieve uniqueness (which coincides with identifiability in this case), a suitable value of this parameter must be found. To this end we consider (1) parameterization, i.e., introducing equality constraints between the unknown coefficients, (2) the use of two data sets at least in a subdomain, and (3) self‐identifiability. Each of these items formally translates the available ...

Minimal a priori assignment in a direct method for determining phenomenological coefficients uniquely

We identify the coefficients of the transport equation in N dimensions grad c.grad h+c Delta h=d delta h/ delta t+f by solving a differential system of the form grad c+ca=b. The assignment of c at one point only yields a unique solution, found by integration along arbitrary paths. This arbitrariness guarantees a good control of the error, notwithstanding the ill-posedness of the problem. For N=2, the hypotheses allowing for this identification are satisfied when one knows two stationary potentials with non-overlapping equipotential lines and a third non-stationary one-this last needed only for determining d. The theory is applied to a numerical synthetic example, for various grid sizes or for noisy data. Notwithstanding the minimal a priori information required for the coefficients, we are able to compute these at a large number of nodes with good precision. For the sake of completeness, we give other results on identification.

Modeling water resources of a highly irrigated alluvial plain (Italy): calibrating soil and groundwater models

Modern and effective water management in large alluvial plains that have intensive agricultural activity requires the integrated modeling of soil and groundwater. The models should be complex enough to properly simulate several, often non-linear, processes, but simple enough to be effectively calibrated with the available data. An operative, practical approach to calibration is proposed, based on three main aspects. First, the coupling of two models built on well-validated algorithms, to simulate (1) the irrigation system and the soil water balance in the unsaturated zone and (2) the groundwater flow. Second, the solution of the inverse problem of groundwater hydrology with the comparison model method to calibrate the model. Third, the use of appropriate criteria and cross-checks (comparison of the calibration results and of the model outputs with hydraulic and hydrogeological data) to choose the final parameter sets that warrant the physical coherence of the model. The approach has been tested by application to a large and intensively irrigated alluvial basin in northern Italy.RésuméLa gestion moderne et efficace de l’eau dans les grandes plaines alluviales siège d’une agriculture intensive requiert la modélisation intégrée du sol et des eaux souterraines. Les modèles doivent être suffisamment complexes pour simuler correctement plusieurs processus souvent non linéaires, mais suffisamment simples pour être calibrés efficacement avec les données disponibles. Une approche de calibration pratique et opérationnelle est proposée, basée sur trois aspects principaux. Premièrement, le couplage de deux modèles construits sur des algorithmes bien validés, pour simuler (1) le dispositif d’irrigation et le bilan en eau du sol au sein de la zone non saturée et (2) l’écoulement d’eau souterraine. Deuxièmement, la résolution du problème hydrogéologique inverse avec la Méthode de Comparaison de Modèle pour caler le modèle. Troisièmement, l’utilisation de critères appropriés et de vérifications croisées (comparaison des résultats du calage et des sorties du modèle avec des données hydrologiques et hydrogéologiques) pour choisir les jeux de paramètres finaux qui garantissent la cohérence physique du modèle. L’approche a été testée par application à un vaste bassin alluvial intensément irrigué du Nord de l’Italie.ResumenEl manejo moderno y efectivo del agua en grandes planicies aluviales que tienen una intensa actividad agrícola requiere el modelado integrado del suelo y del agua subterránea. Los modelos deber ser lo suficientemente complejos como para simular correctamente varios procesos, a menudo no lineales, pero lo suficientemente simple para ser efectivamente calibrado con los datos disponibles. Se propone un enfoque práctico y operativo de la calibración, basada en tres aspectos principales. Primero, el acoplamiento de dos modelos construidos sobre algoritmos bien validados, para simular (1) el sistema de irrigación y el balance de agua en el suelo en la zona no saturada y (2) el flujo de agua subterránea. Segundo, la solución del problema inverso de hidrología de agua subterránea con el Método de comparación de modelos para calibrar el modelo. Tercero, el uso de criterios apropiados y controles cruzados (comparación entre los resultados de la calibración y las salidas del modelo con los datos hidrogeológicos e hidráulicos) para elegir el conjunto de parámetros finales que garanticen la coherencia física del modelo. El enfoque ha sido probado por su aplicación a una gran cuenca aluvial, intensamente irrigada en el norte de Italia.摘要在有密集型农业活动的大型冲积平原进行有效的现代水资源管理需要对土壤和地下水进行综合模拟。模型需要足够复杂,以模拟几种常见的非线性的过程,同时又要足够简单,能够采用现有数据进行校准。本文主要基于以下三个方面,提出了一个具备可操作性且符合实际的校准方法:1. 基于有效算法的两种模型的耦合,以模拟(1)非饱和带灌溉系统和土壤水平衡和(2)地下水流。2. 针对地下水文学的反演问题,采用比较法去校正模型。3.使用合适的准则和交互检验(根据水力和水文地质数据,比较模型的校准结果和模型输出结果)去选择最后的参数设置以确保模型的物理一致性。将该方法已经应用在意大利北部的一个大型密集灌溉冲积平原中进行ResumoUma moderna e eficaz gestão da água nas grandes planícies aluviais com atividade agrícola intensiva requer uma modelação integrada do solo e das águas subterrâneas. Os modelos devem ser suficientemente complexos para simular adequadamente vários processos, muitas vezes de caraterísticas não-lineares, mas suficientemente simples para serem adequadamente calibrados com os dados disponíveis. Neste artigo é proposta uma abordagem para calibração baseada em três aspetos principais. Primeiro, o acoplamento de dois modelos construídos sobre algoritmos bem validados, para simular (1) o sistema de rega e balanço hídrico do solo na zona não saturada e (2) o fluxo de águas subterrâneas. Segundo, uma solução do problema inverso da hidrologia subterrânea, baseada no Método de Comparação do Modelo para calibrar o modelo. Terceiro, o uso de critérios adequados e validações cruzadas (comparação dos resultados de calibração com as saídas do modelo com dados hidráulicos e hidrogeológicos), de modo a selecionar o conjunto final de parâmetros que garantem a coerência física do modelo. A abordagem tem sido testada numa bacia aluvial extensa e intensamente sujeita a rega, localizada no norte da Itália.

The differential system method for the identification of transmissivity and storativity

The differential system (DS) method for the identification of transmissivity and storativity is applied to a confined isotropic aquifer in transient conditions. The data that are required for the identification are the piezometric heads and the source terms, together with the value of transmissivity at a single point only, which is the only parameter value needed a priori. In particular, no a priori knowledge of storativity is needed and, moreover, the identification of transmissivity does not depend upon storativity. The DS method yields the internode transmissivities necessary for the conservative finite differences models in a natural way, because it identifies transmissivities along the internodal segments, so that a well-known formula can be applied that bypasses the difficulty of finding an equivalent cell transmissivity and an averaging scheme. In addition, the DS method takes into account several different flows all over the aquifer, so that the identified parameters are to a certain degree ‘global’ and‘flow independent’. Moreover, the method allows for a piecemeal identification of the parameters, thus keeping away from the regions where wells are pumping so that a two-dimensional model can be used throughout. We test the applicability of the DS method with noisy data by means of numerical synthetic examples and compare the identified internode transmissivities with the reference values. We use the identified parameters to forecast the behaviour of the aquifer under different exploitation and boundary conditions and we compare the forecast piezometric heads, their gradients and the associated fluxes with those computed with the reference parameters.

Hydrogeophysical imaging of alluvial aquifers: electrostratigraphic units in the quaternary Po alluvial plain (Italy)

The integration of surface geological and geomorphological information with borehole point-data and geophysical (e.g., geoelectrical) images of the subsurface yields spatially consistent representations of alluvial aquifers heterogeneity at different scales, from depositional systems to basin fills. Such an approach requires a conceptual framework to match the stratigraphic units with their evidence from ground-based DC resistivity methods to effectively fill the gaps between sparse borehole data and to obtain valid representations of sedimentary heterogeneities. Such an approach is applied to characterize two sites of the Quaternary aquifers of the central Po Plain (Italy), which represent (1) the middle-upper Pleistocene braided to meandering river depositional systems sitting on Southalpine crust and (2) their down-current counterparts, where they are involved by the latest uplift and deformation due to the tectonic activity of the Apennine frontal thrusts. Electrical resistivity was considered as a proxy of the litho-textural properties of hydrofacies and their major hierarchical association at depth and was interpreted in accordance with the depth-decreasing resolution of ground-based resistivity methods. Thus, it was possible to identify the geophysical signature of hydrostratigraphic units through “Electrostratigraphic Units”, i.e., sedimentary volumes identified by resistivity contrasts that spatially preserve the vertical polarity. Hydrostratigraphy and electrostratigraphy were then joined together through a site-specific relationship between electrical resistivity and hydraulic conductivity, which takes into account the prevailing process of current conduction, the litho-textural properties of hydrofacies and the groundwater electrical conductivity. At the scales of aquifer systems and complexes, this approach permitted to establish the conceptual framework to match hydrostratigraphy, electrostratigraphy, average hydrodynamic properties and distribution of heterogeneities.

A numerical comparison between two upscaling techniques: non-local inverse based scaling and simplified renormalization

Abstract In this paper, we face the problem of upscaling transmissivity from the macroscopic to the megascopic scale; here the macroscopic scale is that of the continuous flow equations, whereas the megascopic scale is that of the flow models on a coarse grid. In this paper, we introduce the non-local inverse based scaling (NIBS) and compare it with the simplified renormalization (SR). The latter is a classical technique that we adapt to compute internode transmissivities for a finite differences flow model in a direct way. NIBS is implemented in three steps: in the first step, the macroscopic transmissivity, together with arbitrarily chosen auxiliary boundary conditions and sources, is used to solve forward problems (FPs) at the macroscopic scale; in the second step, the resulting heads are sampled at the megascopic scale; in the third step, the upscaled internode transmissivities are obtained by solving an inverse problem with the differential system method (DS) for which the heads resulting from the second step are used. NIBS is a non-local technique, because the computation of the internode transmissivities relies upon the whole transmissivity field at the macroscopic scale. We test NIBS against SR in the case of synthetic, isotropic, confined aquifers under the assumptions of two-dimensional (2D) and steady-state flow; the aquifers differ for the degree of heterogeneity, which is represented by a normally distributed uncorrelated component of ln T . For the comparison, the reference heads and fluxes at the megascopic scale are computed from the solution of FPs at the macroscopic scale. These reference values are compared with the heads and the fluxes predicted from models at the megascopic scale using the upscaled parameters of SR and NIBS. For the class of aquifers considered in this paper, the results of SR are better than those of NIBS, which hints that non-local effects can be disregarded at the megascopic scale. The two techniques provide comparable results when the heterogeneity increases, when the megascopic scale is large with respect to the heterogeneity length scale, or when the source terms are relevant.

Relating electrical conduction of alluvial sediments to textural properties and pore-fluid conductivity

Electrical conductivity of alluvial sediments depends on litho-textural properties, fluid saturation and porewater conductivity. Therefore, for hydrostratigraphic applications of direct current resistivity methods in porous sedimentary aquifers, it can be useful to characterize the prevailing mechanisms of electrical conduction (electrolytic or shale conduction) according to the litho-textural properties and to the porewater characteristics. An experimental device and a measurement protocol were developed and applied to collect data on eight samples of alluvial sediments from the Po plain (Northern Italy), characterized by different grain-size distribution, and fully saturated with porewater of variable conductivity. The bulk electrical conductivities obtained with the laboratory tests were interpreted with a classical two-component model, which requires the identification of the intrinsic conductivity of clay particles and the effective porosity for each sample, and with a three-component model. The latter is based on the two endmember mechanisms, surface and electrolytic conduction, but takes into account also the interaction between dissolved ions in the pores and the fluid-grain interface. The experimental data and their interpretation with the phenomenological models show that the volumetric ratio between coarse and fine grains is a simple but effective parameter to determine the electrical behaviour of clastic hydrofacies at the scale of the representative elementary volume.

Mapping the spatial variation of soil moisture at the large scale using GPR for pavement applications

The characterization of shallow soil moisture spatial variability at the large scale is a crucial issue in many research studies and fields of application ranging from agriculture and geology to civil and environmental engineering. In this framework, this work contributes to the research in the area of pavement engineering for preventing damages and planning effective management. High spatial variations of subsurface water content can lead to unexpected damage of the load-bearing layers; accordingly, both safety and operability of roads become lower, thereby affecting an increase in expected accidents. A pulsed ground-penetrating radar system with ground-coupled antennas, i.e., 600-MHz and 1600-MHz center frequencies of investigation, was used to collect data in a 16 m × 16 m study site in the Po Valley area in northern Italy. Two ground-penetrating radar techniques were employed to nondestructively retrieve the subsurface moisture spatial profile. The first technique is based on the evaluation of the dielectric permittivity from the attenuation of signal amplitudes. Therefore, dielectrics were converted into moisture values using soil-specific coefficients from Topp’s relationship. Groundpenetrating-radar-derived values of soil moisture were then compared with measurements from eight capacitance probes. The second technique is based on the Rayleigh scattering of the signal from the Fresnel theory, wherein the shifts of the peaks of frequency spectra are assumed comprehensive indicators for characterizing the spatial variability of moisture. Both ground-penetrating radar methods have shown great promise for mapping the spatial variability of soil moisture at the large scale.

Connectivity and single/dual domain transport models: tests on a point-bar/channel aquifer analogue

In porous aquifers, groundwater flow and solute transport strongly depend on the sedimentary facies distribution at fine scale, which determines the heterogeneity of the conductivity field; in particular, connected permeable sediments could form preferential flow paths. Therefore, properly defined statistics, e.g. total and intrinsic facies connectivity, should be correlated with transport features. In order to improve the assessment of the relevance of this relationship, some tests are conducted on two ensembles of equiprobable realizations, obtained with two different geostatistical simulation methods—sequential indicator simulation and multiple point simulation (MPS)—from the same dataset, which refers to an aquifer analogue of sediments deposited in a fluvial point-bar/channel association. The ensembles show different features; simulations with MPS are more structured and characterised by preferential flow paths. This is confirmed by the analysis of transport connectivities and by the interpretation of data from numerical experiments of conservative solute transport with single and dual domain models. The use of two ensembles permits (1) previous results obtained for single realizations to be consolidated on a more firm statistical basis and (2) the application of principal component analysis to assess which quantities are statistically the most relevant for the relationship between connectivity indicators and flow and transport properties.RésuméDans les aquifères poreux, l’écoulement d’eau souterraine et le transport de solutés dépend fortement de la distribution des faciès sédimentaires à l’échelle fine, ce qui détermine l’hétérogénéité du champ de conductivité hydraulique; en particulier, les sédiments perméables connectés peuvent donner lieu à des écoulements préférentiels. Ainsi, la connectivité totale et intrinsèque de faciès définie correctement de manière statistique devrait être corrélée avec les propriétés du transport. Afin d’améliorer l’évaluation de la signification de cette relation, des tests ont été menés sur deux ensembles de réalisations équiprobables, obtenues à partir de deux méthodes différentes de simulation numérique—simulation séquentielle à indicateurs et simulation en points multiples (SPM)—construites à l’aide du même jeu de données se rapportant à un analogue aquifère de sédiments déposés dans un environnement fluvial avec une association de barres et de chenaux ponctuels. Les ensembles montrent différentes caractéristiques ; les simulations avec SPM sont plus structurées et caractérisées par des écoulements préférentiels. Ceci est confirmé par l’analyse des connectivités lors du transport et par l’interprétation des données expérimentales numériques de transport conservatif issues de modèles en domaine simple et dual. L’utilisation des deux ensembles permet (1) de consolider des résultats obtenus au préalable pour des réalisations simples sur une base statistique plus solide et (2) l’application de l’analyse en composante principale pour évaluer quelles quantités sont les plus significatives du point de vue statistique pour la relation entre les indicateurs de connectivité et les propriétés d’écoulement et de transport.ResumenEn acuíferos porosos, el flujo del agua subterránea y el transporte de soluto dependen fuertemente de la distribución de las facies sedimentarias a una escala fina, lo cual determina la heterogeneidad del campo de conductividad; en particular los sedimentos permeables conectados pueden forman trayectorias preferenciales de flujo. Por lo tanto, la estadística correctamente definida, por ejemplo la conectividad total e intrínseca de las facies, debe ser correlacionada con las características del transporte. Con el objeto de mejorar la evaluación de la relevancia de esta relación, se llevaron a cabo algunos ensayos en dos conjuntos de realizaciones equiprobables, obtenidas con dos métodos de simulación geoestadística diferente—simulación de indicador secuencial y simulación de múltiples puntos (MPS)—a partir de un mismo conjunto de datos, los cuales se refieren a una analogía de acuífero sedimentos depositados en una asociación albardón/canal fluvial. Los conjuntos muestran diferentes características; las simulaciones con MPS son más estructuradas y caracterizadas por trayectorias preferenciales de flujo. Esto está confirmado por el análisis de las conectividades del transporte y por la interpretación de datos de experimentos numéricos del transporte conservativo de soluto con modelos de dominios simples y dobles. El uso de los dos conjuntos permite (1) consolidar, sobre una base estadística más firme, los resultados previos obtenidos para realizaciones simples y (2) la aplicación del análisis de la componente principal para evaluar cuales cantidades son estadísticamente más relevantes para la relación entre los indicadores de conectividad y las propiedades de flujo y transporte.摘要在孔隙含水层中地下水流和溶质运移强烈依赖于沉积物中颗粒精细分布的特征,它确定了传导场地的不均匀性,特别是相关联的可渗透沉积层形成优先的水流。因而,适当确定统计资料,例如:总的和固有的连通特质,需要关联其运移特征。以便评价其关系,这些实验产生了两个同等的认识,根据相同的资料以两种不同的地质统计方法—序次指标模拟和多重点模拟(MPS)—获得。其利用了沉积地层在水流的点状阻障/通道中含水层模拟评价。整体效果显示出不同的特征,MPS模拟更突出了优先水流的结构和特点。它根据分析传导连通性和稳定溶质在单/双域传导模型数值实验数据解译确认。应用在两个总体认识上:(1) 原结果在观测单域内的认识是以更牢靠的统计数据为基数,(2) 主成分分析的应用定量统计了在连通指标和流量及传导特性之间的相互关系。ResumoEm aquíferos porosos, o fluxo de água subterrânea e o transporte de solutos dependem fortemente da distribuição das fácies sedimentares à escala fina, que determina a heterogeneidade do campo de condutividades; em particular, os sedimentos permeáveis interconetados que podem formar caminhos de fluxo preferenciais. Por essa razão, é de esperar que certas estatísticas, definidas de forma adequada, tais como a conetividade total e intrínseca das fácies, se correlacionem com as caraterísticas de transporte. A fim de melhorar a avaliação da importância desta correlação, efetuaram-se alguns testes em dois conjuntos de realizações equiprováveis, obtidos com dois métodos geoestatísticos de simulação diferentes—simulação sequencial de indicadores e simulação por múltiplos pontos (MPS)—a partir do mesmo conjunto de dados, referente a um análogo de um aquífero de sedimentos depositados numa sequência fluvial de meandro/canal. Os dois conjuntos apresentam caraterísticas diferentes; as simulações com MPS são mais estruturadas e caraterizam-se por caminhos de fluxo preferenciais. Este facto é confirmado pela análise de conetividades de transporte e pela interpretação de dados de experiências numéricas de transporte de solutos conservativos com modelos de domínio único e duplo. O uso de dois conjuntos permite (1) que os resultados anteriores obtidos por realizações únicas possam ser consolidados numa base estatística mais firme e (2) a aplicação da análise de componentes principais para avaliar quais as quantidades estatisticamente mais relevantes para a relação entre os indicadores de conetividade e as propriedades de fluxo e transporte.