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The complexity of flood risk models is intrinsically linked to a variety of sources of uncertainty (hydrology, hydraulics, exposed assets, vulnerability, coping capacity, etc.) that affect the accuracy and reliability of the analyses. Estimating the uncertainties associated with the different components allows us to be more confident in the risk values on the ground, thus providing a more reliable assessment for investors, insurance and flood risk management purposes. In this study, we investigate the flood risk of the entire Central Apennines District (CAD) in Central Italy using the laRgE SCale inUndation modEl – Flood Risk, RESCUE-FR, focusing on the interaction between the uncertainty of the hydraulic Manning parameter and the risk variability. We assess the coherence between the quantile flood risk maps generated by our model and the official risk maps provided by the CAD authority and focusing on three specific zones within the CAD region. Thus, RESCUE-FR is used to estimate the Expected Annual Damage (EAD) and the Expected Annual Population Affected (EAPA) across the CAD region and to conduct a comprehensive uncertainty analysis. The latter provides a range of confidence of risk estimation that is essential for identifying vulnerable areas and guiding effective mitigation strategies. [ABSTRACT FROM AUTHOR]

This paper employs stochastic analysis to investigate the combined effect of temporal and spatial variability on the temporal variance of baseflow in large catchments. The study makes use of the well‐known aggregated reservoir model, representing the catchment as a network of parallel linear reservoirs. Each reservoir models a sub‐catchment as an independent unit whose discharge temporal variation is characterized by a response time. By treating the rainfall‐generated recharge and the sub‐catchment response times as random variables, the statistical temporal moments of total baseflow are quantified. Comparisons are made between the temporal variance of baseflow in the aggregated reservoir model and that of a single homogeneous reservoir to define an upscaled response time. The analysis of the statistical moments of the random baseflow reveals that the number of reservoirs N has a weak impact on baseflow variance, with ergodic conditions achieved even with a small number of reservoirs. The study highlights that the ratio between the recharge correlation time and the geometric mean of the sub‐catchment response times plays a critical role in baseflow damping and the upscaled response. The results indicate that the dynamics of baseflow generation depend not only on the catchment hydro‐geological structure but also on the variability of the input signal. This research underscores the importance of understanding the combined influences of hydro‐geological factors and recharge input variability for baseflow prediction under uncertainty. The present study should be regarded as a first step, setting the theoretical framework for future research toward incorporating field data. Key Points: Stochastic model to investigate the effect of temporal and spatial variability on the baseflow statistics in large heterogeneous catchmentsBaseflow statistics depend strongly on the ratio of recharge timescale and the geometric mean of reservoir timescalesThe temporal variance of baseflow is used to define an equivalent reservoir with its characteristic timescale [ABSTRACT FROM AUTHOR]

The drawdown time is important for the design and assessment of infiltration basins. This paper investigates its dependence on soil heterogeneity, and simple analytical solutions for the mean and the variance are given. The solutions are tested through Monte Carlo simulations in various realistic scenarios, using a modified Green Ampt model for layered soils and a model based on the integration of the 1‐D Richards equation. The impact of the employed approximations is assessed, and the leading role of the spatial distribution of the saturated hydraulic conductivity is emphasized. The effects of other relevant design and natural factors, including the initial water level and water content distribution, are also investigated. Plain Language Summary: Infiltration basins are receiving an increasing interest in water resources management as an alternative to surface water storage in the managed aquifer recharge and as a green infrastructure at the urban scale. One of the main parameters in the design of the infiltration basins is the drawdown time, that is, the time needed to empty the basin after it has been filled with water, for instance, after a flood event or by a managed treatment plant outlet. This work provides simple analytical solutions for the evaluation along a stochastic approach of the drawdown time, accounting for the soil heterogeneity and leading to a probabilistic design of the infiltration structure. Key Points: The time needed to empty infiltration basins, or drawdown time τ, is an important quantity for their design and assessmentThis work proposes analytical solutions for the mean and variance of τ considering the soil heterogeneitySolutions have been tested through a set of Monte Carlo numerical simulations, showing that the probability density function is lognormal and investigating the effects of design and natural factors [ABSTRACT FROM AUTHOR]

The scope of this work is to discuss the proper choice of macrodispersion coefficients in modeling contaminant transport through the advection dispersion equation (ADE). It is common to model solute concentrations in transport by groundwater with the aid of the ADE. Spreading is quantified by macrodispersivity coefficients, which are much larger than the laboratory observed pore‐scale dispersivities. In the frame of stochastic theory, longitudinal macrodispersivity is related to the hydraulic conductivity spatial variability via its statistical moments (mean, variance, integral scales), which are generally determined by geostatistical analysis of field measurements. In many cases, especially for preliminary assessment of contaminant spreading, these data are not available and ad hoc values are adopted by practitioners. The present study aims at recommending dispersivity values based on a thorough analysis of tens of field experiments. Aquifers are classified as of weak, medium, and high heterogeneity and for each class a range of macrodispersivity values is recommended. Much less data are available for the transverse macrodispersivities, which are significantly smaller than the longitudinal one. Nevertheless, a few realistic values based on field data, are recommended for applications. Transport models using macrodispersivities can predict mean concentrations, different from the local ones. They can be used for estimation of robust measures, like plumes spatial moments, longitudinal mass distribution and breakthrough curves at control planes. Article impact statement: Practitioner's guideline on how to identify macrodispersivity for subsurface transport models from reliable field tracer tests. [ABSTRACT FROM AUTHOR]

This work extends the overlay and index methods for intrinsic groundwater vulnerability, that typically involve the soil surface and the vadose zone, to groundwater (saturated) transport. The method is "hybrid" as it combines the standard overlay and index methods with a simplified process-based approach for the groundwater component. For the latter, we make use of concept and methodologies based on geomorphological analysis, employing tools that are generally implemented in Geographic Information Systems (GIS). The proposed method is based on a simple probabilistic analysis, in which the overlay and index method (that can be any) provides the probability that the contamination reaches the groundwater through the vadose zone, while the probability that the contaminant reaches a generic location in the groundwater system is determined by analyzing the groundwater streamlines. The analysis leads to the definition of the combined vulnerability index υ , that takes care of both transport in the vadose zone and the aquifer. The method is applied to a groundwater catchment in the Campania region, Southern Italy. The method is simple and effective in assessing aquifer vulnerability in a combined vadose zone—groundwater flow system, useful for preliminary, screening analysis of the intrinsic aquifer vulnerability. [ABSTRACT FROM AUTHOR]

Climate change impact studies on hydrological extremes often rely on hydrological models with parameters inferred through calibration procedures using observed meteorological data as input forcing. We show that this procedure can lead to a biased evaluation of the probability distribution of high streamflow extremes when climate models are used. As an alternative approach, we introduce a methodology, coined "Hydrological Calibration of eXtremes" (HyCoX), in which the calibration of the hydrological model, as driven by climate model output, is carried out by maximizing the probability that the modeled and observed high streamflow extremes belong to the same statistical population. The application to the Adige River catchment (southeastern Alps, Italy) by means of HYPERstreamHS, a distributed hydrological model, showed that this procedure preserves statistical coherence and produces reliable quantiles of the annual maximum streamflow to be used in assessment studies. [ABSTRACT FROM AUTHOR]

Flood mapping is a key stage for detecting vulnerable areas, assessing floods impacts, identifying damages, and mitigation plans. Despite of the available guidelines for flood mapping following EU Floods Directive, coherent and comprehensive official flood hazard maps at the national scale are still missing, at least in the EU. In fact, flood mapping generally requires high economical and computational costs for setup/calibration of hydrological/hydraulic models, leading to partial and fragmented vulnerable areas. Here, we propose RESCUE, a laRgE SCale inUndation modEl; the scope is providing a simple and inexpensive tool for flood mapping at the regional scale, overcoming the current fragmentation. RESCUE takes advantage from coupling geomorphological analysis and simplified hydrologic‐hydraulic modeling, providing simple and reliable large scales inundation estimates. It is as parsimonious as purely DTM‐based methods and physically based as any hydrodynamic model, yet computationally more efficient. The model allows for parametric uncertainty analysis for a probabilistic assessment of inundation areas. We demonstrate RESCUE potentialities and limitations using two illustrative examples: Paglia‐Chiani River system, and Central Apennines District (Central Italy). Notwithstanding the inaccuracies of large scale DTMs and the missed representation of flood‐structure interactions, results are promising, suggesting that RESCUE might be an effective tool for preliminary hazard assessment. [ABSTRACT FROM AUTHOR]

Flood mapping is a vital component for sustainable land use in flood-prone areas. Due to the frequency of flood events, local authorities demand effective yet simple methods for the preliminary identification of flood-prone areas at large scales to subsequently define mitigation strategies. We focus here on the workflow GeoFlood, a parsimonious model which uses only high-resolution Digital Terrain Models (DTMs) to define the geomorphological and hydrological information necessary for flood inundation mapping, thus allowing for large-scale simulations at a reasonable computational cost. The purpose of the present study is to investigate the conditions under which GeoFlood is able to correctly reproduce inundation scenarios (with an assigned return period) and their flooding characteristics. Specifically, we analyze its performance over a highly urbanized area, the mid-lower portion of the Tiber River (Italy). We simulated the 200-year return period scenario and compared the results to those provided by the local authority. A sensitivity analysis is performed to quantify the influence of the main geometric and hydraulic parameters involved. Results show that GeoFlood produces rapid flood estimation than can be used in support of standard costly methods over large scales, quickly pointing out the critical flood-prone areas, with consideration of all the uncertainties involved. [ABSTRACT FROM AUTHOR]

Application of an inverse procedure using head residuals variogram for identification of the statistical parameters, characterizing the transmissivity of heterogeneous aquifers is examined. The procedure is used for a stationary and isotropic logtransmissivity covariance and conditions of steady mean uniform flow in an unbounded formation.

Travel time is a robust measure of water transport dynamics in catchments. At a given control section along a drainage network, travel time distribution results from an interplay between two main processes: (i) the transport through the hillslopes and (ii) transport through the drainage network. The main scope of this work is to quantify this interplay, specifically we aim to identify the relative impact of hillslopes and channels on the travel time at the catchment scale. A theoretical framework is developed following a bottom‐up modelling approach that combines a Boussinesq model for water flow and water travel time in hillslopes, with a geomorphological model for water transport in drainage network. Simple semi‐analytical solutions are derived for the first two moments of the travel time distribution within a flow section. We provide some relevant examples based on synthetic rainfall data, exploring the relative impacts of hillslope and channel properties. As expected, the dynamics of the hillslopes control the travel time distribution at the catchment scale. The drainage network typically introduces a lag in the average travel time exiting the hillslopes and reduces the temporal fluctuations of the mean travel time and its variance. Our theoretical model provides meaningful insights on the investigation of the dominant dynamics taking place in catchments: results suggest that hillslopes and their features are the main driver of travel time in catchments. The temporal fluctuations of the travel time moments show a non‐linear dependence with the recharge time‐series and need to be considered as time‐variant. Variability of water ages collected in a single water sample can be very large, the latter feature may have a significant effect on the water quality and on the tracer data analysis, largely governed by the contact times between water and catchment material. [ABSTRACT FROM AUTHOR]

The statistical characterization of extreme floods largely benefits from the reconstruction of historical floods, making use of various documentary sources and of hydrodynamic models. The two-dimensional (2D) modelling approach provides a higher accuracy and detail with respect to one-dimensional (1D) modelling. On the other hand, 2D models require a large amount of topographic and hydraulic information for calibration, having several parameters to be determined, which makes the calibration prone to underdetermination. To address this issue, we provide here practical guidance for the effective calibration of 2D models for the reconstruction of historical floods in urban areas with a limited amount of information available. Specifically, we show how to constrain model parameters by distinguishing among "static," "dynamic" and "global" data and their role in the calibration procedure. The latter is exemplified by a relevant application to the reconstruction of the great 1870 flood of Rome, Italy. [ABSTRACT FROM AUTHOR]

Climate change impact studies on hydrological extremes often rely on the use of hydrological models with parameters inferred by using observational data of daily streamflow. In this work we show that this is an error prone procedure when the interest is to develop reliable Empirical Cumulative Distribution Function curves of annual streamflow maximum. As an alternative approach we introduce a methodology, coined Hydrological Calibration of eXtremes (HyCoX), in which the calibration of the hydrological model is carried out by directly targeting the probability distribution of high flow extremes. In particular, hydrological simulations conducted during a reference period, as driven by climate models' outputs, are constrained to maximize the probability that the modeled and observed high flow extremes belong to the same population. The application to the Adige river catchment (southeastern Alps, Italy) by means of HYPERstreamHS, a distributed hydrological model, showed that this procedure preserves statistical coherence and produce reliable quantiles of the annual maximum streamflow to be used in assessment studies. [ABSTRACT FROM AUTHOR]

Six conceptually different transport models were applied to the macrodispersion experiment (MADE)‐1 field tracer experiment as a first major attempt for model comparison. The objective was to show that complex mass distributions in heterogeneous aquifers can be predicted without calibration of transport parameters, solely making use of structural and flow data. The models differ in their conceptualization of the heterogeneous aquifer structure, computational complexity, and use of conductivity data obtained from various observation methods (direct push injection logging, DPIL, grain size analysis, pumping tests and flowmeter). They share the same underlying physical transport process of advection by the velocity field solely. Predictive capability is assessed by comparing results to observed longitudinal mass distributions of the MADE‐1 experiment. The decreasing mass recovery of the observed plume is attributed to sampling and no physical process like mass transfer is invoked by the models. Measures like peak location and strength are used in comparing the modeled and measured plume mass distribution. Comparison of models reveals that the predictions of the solute plume agree reasonably well with observations, if the models are underlain by a few parameters of close values: mean velocity, a parameter reflecting log‐conductivity variability, and a horizontal length scale related to conductivity spatial correlation. The robustness of the results implies that conservative transport models with appropriate conductivity upscaling strategies of various observation data provide reasonable predictions of plumes longitudinal mass distribution, as long as key features are taken into account. Key Points: Aquifer transport is predicted by six models of different heterogeneity conceptualization and field data inputKey model inputs are mean velocity and heterogeneity representation including spatial correlationThe macrodispersion experiment (MADE) site plume longitudinal mass distribution is a robust transport measure [ABSTRACT FROM AUTHOR]

Water age distribution is recognized as a key descriptor of hydrological systems, providing information on the natural phenomena taking place in such systems. It is widely used in the theoretical and experimental studies on hillslope and catchments, allowing a synthetic description of the complex dynamics by which the hillslopes store and release water and solutes at the outlet. In this study, we present a physically based framework for the description of the water or solute age within small catchments or hillslopes. The model matches the age equation with the three‐dimensional flow equations under transient conditions, employing the Boussinesq approximation. The approach leads to a system of differential equations for the moments of water age, spatially integrated over cross sections normal to mean flow, denoted as Boussinesq‐age‐equations, that are both simple to use and to solve. The framework overcomes some of the limitations of previous studies, such as of steady state conditions or perfect mixing, merging the simplicity of 1D solutions with the complexity of the physically based models, being suitable for theoretical investigation and experimental data set analysis. Besides introducing the model, we provide some relevant examples for synthetic hillslopes, exploring the effects of the main topographic controls and of the main drivers of water flow such as the recharge. [ABSTRACT FROM AUTHOR]

Levees are the most common structural solution to prevent flooding, reduce damage and generate benefits through more investment/economic activity in floodplain areas. While being relatively easy to build, levee effectiveness can be compromised by poor design and substandard construction methods and maintenance, thus increasing failure probability. Further, levees might increase societal vulnerability by instilling a sense of safety, the so-called "levee effect". To cope with these phenomena, we develop a risk-based framework that quantifies residual risk under levee breaching and the levee effect, by disentangling its structural, dynamic and anthropic components, thus contributing to a better understanding of the phenomena at different spatial scales and the definition of flood risk policies. Through an illustrative example, we show how residual risk might become larger than under natural conditions, as function of the scale of interest, e.g. an area, a line at a given distance from the river, or a point within the floodplain. [ABSTRACT FROM AUTHOR]

This paper is the outcome of a community initiative to identify major unsolved scientific problems in hydrology motivated by a need for stronger harmonisation of research efforts. The procedure involved a public consultation through online media, followed by two workshops through which a large number of potential science questions were collated, prioritised, and synthesised. In spite of the diversity of the participants (230 scientists in total), the process revealed much about community priorities and the state of our science: a preference for continuity in research questions rather than radical departures or redirections from past and current work. Questions remain focused on the process-based understanding of hydrological variability and causality at all space and time scales. Increased attention to environmental change drives a new emphasis on understanding how change propagates across interfaces within the hydrological system and across disciplinary boundaries. In particular, the expansion of the human footprint raises a new set of questions related to human interactions with nature and water cycle feedbacks in the context of complex water management problems. We hope that this reflection and synthesis of the 23 unsolved problems in hydrology will help guide research efforts for some years to come. [ABSTRACT FROM AUTHOR]

Transverse dispersion, or tracer spreading orthogonal to the mean flow direction, which is relevant e.g, for quantifying bio‐degradation of contaminant plumes or mixing of reactive solutes, has been studied in the literature less than the longitudinal one. Inferring transverse dispersion coefficients from field experiments is a difficult and error‐prone task, requiring a spatial resolution of solute plumes which is not easily achievable in applications. In absence of field data, it is a questionable common practice to set transverse dispersivities as a fraction of the longitudinal one, with the ratio 1/10 being the most prevalent. We collected estimates of field‐scale transverse dispersivities from existing publications and explored possible scale relationships as guidance criteria for applications. Our investigation showed that a large number of estimates available in the literature are of low reliability and should be discarded from further analysis. The remaining reliable estimates are formation‐specific, span three orders of magnitude and do not show any clear scale‐dependence on the plume traveled distance. The ratios with the longitudinal dispersivity are also site specific and vary widely. The reliability of transverse dispersivities depends significantly on the type of field experiment and method of data analysis. In applications where transverse dispersion plays a significant role, inference of transverse dispersivities should be part of site characterization with the transverse dispersivity estimated as an independent parameter rather than related heuristically to longitudinal dispersivity. Article impact statement: Unique compendium of reliable field data on transverse dispersion providing ranges, ratios and criteria for subsurface transport models. [ABSTRACT FROM AUTHOR]

Abstract: Natural attenuation and in situ oxidation are commonly considered as low‐cost alternatives to ex situ remediation. The efficiency of such remediation techniques is hindered by difficulties in obtaining good dilution and mixing of the contaminant, in particular if the plume deformation is physically constrained by an array of wells, which serves as a containment system. In that case, dilution may be enhanced by inducing an engineered sequence of injections and extractions from such pumping system, which also works as a hydraulic barrier. This way, the aquifer acts as a natural mixer, in a manner similar to the industrialized engineered mixers. Improving the efficiency of hydrogeological mixers is a challenging task, owing to the need to use a 3‐D setup while relieving the computational burden. Analytical solutions, though approximated, are a suitable and efficient tool to seek the optimum solution among all possible flow configurations. Here we develop a novel physically based model to demonstrate how the combined spatiotemporal fluctuations of the water fluxes control solute trajectories and residence time distributions and therefore, the effectiveness of contaminant plume dilution and mixing. Our results show how external forcing configurations are capable of inducing distinct time‐varying groundwater flow patterns which will yield different solute dilution rates. [ABSTRACT FROM AUTHOR]

We analyze solute transport in a radially converging 3-D flow field in a porous medium with spatially heterogeneous hydraulic conductivity ( K). The aim of the paper is to analyze the impact of heterogeneity and the mode of injection on BreakThrough Curves (BTCs) detected at a well pumping a contaminated aquifer. The aquifer is conceptualized as an ensemble of blocks of uniform but contrasting K and the analysis makes use of the travel time approach. Despite the approximations introduced, the model reproduces a laboratory experiment without calibration of transport parameters. Our results also show excellent agreement with numerical simulations for different levels of heterogeneity. We focus on the impact on the BTC of both heterogeneity in K and solute release conditions. It is shown that the injection mode matters, and the differences in the BTCs between uniform and flux-proportional injection increase with the heterogeneity of the K-field. Furthermore, we study the effect of heterogeneity and mode of injection on early and late arrivals at the well. [ABSTRACT FROM AUTHOR]

The article discusses papers presented in the AGU Chapman Conference ‘The MADE Challenge for Groundwater Transport in Highly Heterogeneous Aquifers: Insights from 30 Years of Modeling and Characterization at the Field Scale and Promising Future Directions' in Valencia, Spain in October 2015.

Heterogeneity of the hydraulic properties is one of the main causes of the seemingly random distribution of solute concentration observed in contaminated aquifers, with macrodispersivity providing a global measure of spreading. Earlier studies on transport of solutes in heterogeneous formations, either theoretical or numerical, expressed dispersivity as a function of the geostatistical properties of the hydraulic conductivity K. In most cases, K follows a second-order statistical characterization, which may not be adequate when heterogeneity is high. In this work, we adopt the Multi-Indicator Model-Self Consistent Approach (MIMSCA) to compute the longitudinal and transverse macrodispersivity. This methodology enables to model the K field by using geological inclusions of different shapes and orientation (defined here as the microstructure), while replicating the heterogeneous macrostructure obtained by the second-order statistics. The above scheme attempts to reproduce the effect on macrodispersion of different distribution and orientation of local facies, and for instance it may represent the orientation and spatial features of the layers that are often observed in aquifers. The relevant impact of the microstructure on effective conductivity, longitudinal and transverse macrodispersivities is analyzed and discussed, for both binary and lognormally distributed K fields. [ABSTRACT FROM AUTHOR]

Hillslope processes are fundamental for the comprehension of the hydrological response of natural systems. However, their complexity demands real time and continuous observations. In this paper, we assess the feasibility of studying streamflow generation processes at Cape Fear, a "hybrid" hillslope plot at University of Tuscia, Viterbo, Italy. Cape Fear is a 7 × 7 m² confined soil-filled wood-sided plot, whose water fluxes can be continuously monitored. The plot design is simple, yet versatile to test hypotheses on the hydrological response of hillslope areas. The suitability of the plot for investigating runoff generation and hillslope processes is presented through a demonstrative experiment in the case of a natural rainfall event. A combination of traditional and innovative measurement techniques confirms that runoff onset is due to saturation overland flow. Future studies will address the influence of diverse land covers and spatial pathways evolution on the response at the hillslope scale. [ABSTRACT FROM AUTHOR]

We present HYPERstream, an innovative streamflow routing scheme based on the width function instantaneous unit hydrograph (WFIUH) theory, which is specifically designed to facilitate coupling with weather forecasting and climate models. The proposed routing scheme preserves geomorphological dispersion of the river network when dealing with horizontal hydrological fluxes, irrespective of the computational grid size inherited from the overlaying climate model providing the meteorological forcing. This is achieved by simulating routing within the river network through suitable transfer functions obtained by applying the WFIUH theory to the desired level of detail. The underlying principle is similar to the block-effective dispersion employed in groundwater hydrology, with the transfer functions used to represent the effect on streamflow of morphological heterogeneity at scales smaller than the computational grid. Transfer functions are constructed for each grid cell with respect to the nodes of the network where streamflow is simulated, by taking advantage of the detailed morphological information contained in the digital elevation model (DEM) of the zone of interest. These characteristics make HYPERstream well suited for multi-scale applications, ranging from catchment up to continental scale, and to investigate extreme events (e.g., floods) that require an accurate description of routing through the river network. The routing scheme enjoys parsimony in the adopted parametrization and computational efficiency, leading to a dramatic reduction of the computational effort with respect to full-gridded models at comparable level of accuracy. HYPERstream is designed with a simple and flexible modular structure that allows for the selection of any rainfall-runoff model to be coupled with the routing scheme and the choice of different hillslope processes to be represented, and it makes the framework particularly suitable to massive parallelization, customization according to the specific user needs and preferences, and continuous development and improvements. [ABSTRACT FROM AUTHOR]

Transport of a non-reactive solute in anisotropic bimodal porous formations is investigated through the evaluation of the breakthrough curve. The hydraulic conductivity $$K$$ structure is modelled as an ensemble of anisotropic and non-overlapping inclusions, with given hydraulic conductivity $$K_{i}$$ , randomly placed in an homogeneous matrix with hydraulic conductivity $$K_{0}$$ . The conductivity contrast $$\kappa =K_{i}/K_{0}$$ between the inclusions and the matrix represents the main source of heterogeneity. The resulting $$K$$ structure is a theoretical representation of natural porous formations where inclusions and matrix play the role of two distinct hydrofacies. Semi-analytical solutions for flow and transport are carried out in both 3D and 2D domains following a Lagrangian approach by adopting the dilute limit approximation. The procedure, formally valid for media with low inclusions-matrix relative volume fraction, is extended to dense media by a simplified formulation of the self-consistent approach. Natural porous formations are intrinsically anisotropic due to the depositional process; hence, particular emphasis is addressed to the quantification of the effects of the anisotropy on solute transport. The solution of our physically based model depends on three structural parameters: the hydraulic conductivity contrast $$\kappa $$ , the relative volume fraction $$n$$ , and the statistical anisotropy ratio $$e$$ . The procedure allows for the physical representation of high-velocity channels and stagnation zones, which can be encountered in bimodal media, and it is particular advantageous for a quick estimation of the solute breakthrough curve. Our analysis shows different transport dynamics, as function of the conductivity contrast $$\kappa =K_{i}/K_{0}$$ , leading to fast preferential flow ( $$\kappa >1$$ ) or mass retention ( $$\kappa <1$$ ), as a consequence of the lack of symmetry of the flow and transport parameters (velocity and travel time residuals). High dispersion is typically found when $$\kappa <1$$ , i.e. for low conductive inclusions, where the latter typically trap the solute particles, determining large travel times. Conversely, when $$\kappa >1$$ flow in the inclusions is constrained by the outer flow, limiting the solute velocity inside the inclusions, which results is a rather limited dispersion. Anisotropy typically enhances the solute spreading for $$\kappa <1,$$ as a consequence of the slower velocity predicted for more anisotropic inclusions, while its impact on formations with high $$\kappa $$ is rather limited. [ABSTRACT FROM AUTHOR]