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Heterogeneity of hydraulic conductivity in aquifers is a topic touched upon by many researchers, but very few analyses were reported on the characteristic parameters of solute transport using stochastic methods. We study he effects of aquifer heterogeneity by running numerical simulations of dipole tracer tests in the software MODFLOW 6, instigated with Python scripts using the FloPy package. Random hydraulic conductivity fields are drawn by the Python package GStools from a log-normal distribution, characterized by a mean, variance and correlation length. A series of ensembles was run with varying variances and correlation lengths. Normalised mean breakthrough curves of the ensembles were compared for homogeneous, stratified and heterogeneous aquifers. Outcomes show that an increase in variance leads to an earlier arrival of the tracer, due to the occurrence of preferential flow paths, but will also lead to more tailing. An increase in correlation length enhances the effects of an increase in variance. For a short correlation length (i.e. much smaller than the distance between the wells) the heterogeneous solution tends towards the solution for a homogeneous medium, while for a longer correlation length, the solution tends towards the solution for a stratified medium. Based on the ensemble results we conclude that a fully heterogeneous aquifer shows a different breakthrough curve than stratified or a homogeneous structured aquifers. Therefore it cannot be treated the same way.

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., QC 20231229

Aquitards are common hydrogeological features and their hydraulic conductivity is an important property for various groundwater management issues. Predicting their hydraulic conductivity proves challenging, given its dependence on numerous variables. In this study, the dominant factors for predicting aquitard hydraulic conductivity are identified. To this end, a random forest model is trained on a dataset consisting of more than 1000 hydraulic conductivity measurements of core-scale sediment samples from a wide range of stratigraphic units and depths in the Netherlands. The dataset contains textural properties, such as the grain size distribution and porosity, as well as structural data, such as location, sampling depth, stratigraphical unit, lithofacies, organic carbon content, carbonate content and groundwater chloride concentration. Results show that clay fraction, stratigraphic unit, depth, lithofacies and x-coordinate are the most important features for predicting the hydraulic conductivity. Here, x-coordinate is presumably a proxy for distance from marine influence. Using a more detailed grain size distribution or using derived parameters such as the grain size percentiles does not improve the model any further. Our findings indicate that structural properties play a significant role in predicting aquitard conductivity, as they serve as indicators of processes such as compaction and soft-sediment deformation. The model is furthermore an effective method to estimate hydraulic conductivity for sediment samples without conducting costly and time-consuming hydraulic conductivity measurements.

We use five established, but conceptually different artificial intelligence algorithms for analysing clogging and quantifying colloid transport at pore scale: artificial neural networks, decision tree, random forest, linear regression, and support vector regression. We test how these algorithm can predict clogging by interpolating physics based simulation data. Our training and test data set is based on results from Lattice Boltzmann simulations reproducing the physics of colloid transport through a typical pore throat present in glass beads or medium sized sand. We perform hyperparameter optimization through cross validation for all algorithms. The tree based methods have the highest Nash–Sutcliffe efficiencies among all tested algorithms with values mostly above 0.9 for the independent test data. The event of clogging can be predicted even with 100% accuracy. Our results indicate a non-linear, rather categorial nature of the (simulation) data. This is in contrast to the typical use of neural network algorithms for simulation data while tree based methods are often applied to observational data. We partly link this to the small size of our dataset. Our application of artificial intelligence in porous media research shows that time-consuming Lattice Boltzmann simulations can be easily supplemented and extended at small computational costs while predictability of clogging and quantitative effects of process specific parameters on colloidal transport are given with high reliability.

Aquitards are common hydrogeological features in the subsurface. Typically, pumping tests are used to parameterize the hydraulic conductivity of heterogeneous aquitards. However, they do not take spatial variability and uncertainty into account. Alternatively, core-scale measurements of hydraulic conductivity are used in geostatistical upscaling methods, for which their correlation lengths are needed, but this information is extremely difficult to obtain. This study investigates whether a pumping test can be used to obtain the correlation lengths needed for geostatistical upscaling and account for the uncertainty about heterogeneous aquitard conductivity. Random realizations are generated from core-scale data with varying correlation lengths and inserted into a groundwater flow model which simulates the outcome of an actual pumping test. The realizations yielded a better fit to the pumping test data than the traditional pumping test result, assuming homogeneous layers are selected. Ranges of horizontal and vertical correlation lengths that fit the pumping-test well are found. However, considerable uncertainty regarding the correlation lengths remains, which should be considered when parameterizing a regional groundwater flow model.

We investigate the upscaling of diffusive transport parameters using a stochastic framework. At sub-REV (representative elementary volume) scale, the complexity of the pore space geometry leads to a significant scatter of the observed diffusive transport. We study a large set of volumes reconstructed from focused ion beam-scanning electron microscopy data. Each individual volume provides us sub-REV measurements on porosity and the so-called transport-ability, being a dimensionless parameter representing the ratio of diffusive flux through the porous volume to that through an empty volume. The detected scatter of the transport-ability is mathematically characterized through a probability distribution function (PDF) with a mean and variance as function of porosity, which includes implicitly the effect of pore structure differences among sub-REV volumes. We then investigate domain size effects and predict when REV scale is reached. While the scatter in porosity observations decreases linearly with increasing sample size as expected, the observed scatter in transport-ability does not converge to zero. Our results confirm that differences in pore structure impact transport parameters at all scales. Consequently, the use of PDFs to describe the relationship of effective transport coefficients to porosity is advantageous to deterministic semiempirical functions. We discuss the consequences and advocate the use of PDFs for effective parameters in both continuum equations and data interpretation of experimental or computational work. The presented statistics-based upscaling technique of sub-REV microscopy data provides a new tool in understanding, describing and predicting macroscopic transport behavior of microporous media.

Aquitards are common hydrogeological features and their hydraulic conductivity is an important property for various groundwater management issues. Predicting their hydraulic conductivity proves challenging, given its dependence on numerous variables. In this study, the dominant factors for predicting aquitard hydraulic conductivity are identified. To this end, a random forest model is trained on a dataset consisting of more than 1000 hydraulic conductivity measurements of core-scale sediment samples from a wide range of stratigraphic units and depths in the Netherlands. The dataset contains textural properties, such as the grain size distribution and porosity, as well as structural data, such as location, sampling depth, stratigraphical unit, lithofacies, organic carbon content, carbonate content and groundwater chloride concentration. Results show that clay fraction, stratigraphic unit, depth, lithofacies and x-coordinate are the most important features for predicting the hydraulic conductivity. Here, x-coordinate is presumably a proxy for distance from marine influence. Using a more detailed grain size distribution or using derived parameters such as the grain size percentiles does not improve the model any further. Our findings indicate that structural properties play a significant role in predicting aquitard conductivity, as they serve as indicators of processes such as compaction and soft-sediment deformation. The model is furthermore an effective method to estimate hydraulic conductivity for sediment samples without conducting costly and time-consuming hydraulic conductivity measurements., Water Resources

Aquitards are common hydrogeological features in the subsurface. Typically, pumping tests are used to parameterize the hydraulic conductivity of heterogeneous aquitards. However, they do not take spatial variability and uncertainty into account. Alternatively, core-scale measurements of hydraulic conductivity are used in geostatistical upscaling methods, for which their correlation lengths are needed, but this information is extremely difficult to obtain. This study investigates whether a pumping test can be used to obtain the correlation lengths needed for geostatistical upscaling and account for the uncertainty about heterogeneous aquitard conductivity. Random realizations are generated from core-scale data with varying correlation lengths and inserted into a groundwater flow model which simulates the outcome of an actual pumping test. The realizations yielded a better fit to the pumping test data than the traditional pumping test result, assuming homogeneous layers are selected. Ranges of horizontal and vertical correlation lengths that fit the pumping-test well are found. However, considerable uncertainty regarding the correlation lengths remains, which should be considered when parameterizing a regional groundwater flow model., Water Resources

Aquifer Storage and Recovery systems (ASR) are an alternative source of fresh water to the increasing demand for water. Its performance varies in terms of flow parameters, aquifer conditions and transport processes. An axisymmetric 50 m thick base model is defined to simulate ASR performance by using Modflow, MT3DMS and Seawat. The heterogeneous setting is defined as an alternation of high-K and low-K layers, where different hydraulic conductivities, contrast ratios and anisotropy factors are simulated for homogeneous and heterogeneous cases. Under the numerical approach the anisotropy factor in the homogeneous cases is the independent variable, while in the geological approach, the heterogeneous layers are the independent variable. The numerical approach makes different scenarios comparable and has a greater impact on the high-K layers’ vertical conductivity KV while the geological approach leads to realistic simulations and has a greater impact on the low-K layers’ KV . Higher values of KV lead to a greater buoyancy effect and tilting of the fresh-naive water interface. Homogeneous cases have a better performance than heterogeneous cases, mainly during the first years of simulation. Peaks on RE after 4 or 6 years of simulation in heterogeneous cases can be explained by the transfer of fresh water to a high-K layer from an underneath low-K or high-K layer due to buoyancy. Homogeneous cases have a better performance than heterogeneous cases. RE is more impacted by KV than horizontal hydraulic conductivity KH, as it controls the amount of buoyancy. In heterogeneous cases, buoyancy in high-K layers is the main responsible for the reduction in RE compared to the homogeneous equivalent cases. Keywords

Waterglasinjecties worden vaak toegepast als grondverbeteringstechniek om zandlagen te versterken voor tijdelijke en/of permanente situaties. Het betreft zogenaamde hardgels die worden toegepast als grondkerende injectielagen, als grondverbetering onder (monumentale) fundaties en/of als paalpuntinjectie ter verhoging van het paaldraagvermogen. Tijdens projecten blijkt uit kernboringen in geïnjecteerd zand dat de druksterkte nogal kan variëren met locatie en diepte. De resultaten van het afstudeer-onderzoek van Frank de Kievit (Universiteit Utrecht) laten zien dat organische stof mogelijk een rol speelt bij deze variatie in druksterkte en dat het daarom aan te raden is het organische stofgehalte mee te nemen in het ontwerp, hetzij door dit vooraf te bepalen, hetzij door een proefinjectie uit te voeren.

We present a workflow to estimate geostatistical aquifer parameters from pumping test data using the Python package welltestpy. The procedure of pumping test analysis is exemplified for two data sets from the Horkheimer Insel site and from the Lauswiesen site, Germany. The analysis is based on a semi-analytical drawdown solution from the upscaling approach Radial Coarse Graining, which enables to infer log-transmissivity variance and horizontal correlation length, beside mean transmissivity, and storativity, from pumping test data. We estimate these parameters of aquifer heterogeneity from type-curve analysis and determine their sensitivity. This procedure, implemented in welltestpy, is a template for analyzing any pumping test. It goes beyond the possibilities of standard methods, for example, based on Theis' equation, which are limited to mean transmissivity and storativity. A sensitivity study showed the impact of observation well positions on the parameter estimation quality. The insights of this study help to optimize future test setups for geostatistical aquifer analysis and provides guidance for investigating pumping tests with regard to aquifer statistics using the open-source software package welltestpy.

Empirical porosity-permeability and grain size-permeability relationships have long been used and researched. However, they often under- or overestimate permeability because they simplify complex micro scale porous medium descriptions, such as tortuosity or pore size distribution, into nondescript parameters or constants. This paper aims to highlight the large range of possible permeability values that can be obtained from identical porosity and grain size distributions, but describe different pore scale porous media. To achieve this, numerical flow simulations were performed on irregular grained and circular grained porous media which contain identical grains and porosity but vary in spatial distribution of the grains within the domain. Subsequently, the domain was analyzed in terms of representative elementary volume, pore size distribution, grain size distribution, quantitative grain morphological parameters, porosity, and permeability. The results were compared to five well known empirical relationships: Hazen (1892), Slichter (1898), Beyer (1964), Kozeny-Carman (1953), and Barr (2001). Results showed a linear relationship between permeability on a logarithmic scale and porosity on an arithmetic scale with uncertainty increasing as porosity increased. Porous media containing equally sized circular grains as irregular grains in terms of sieve radius showed higher permeability values. Empirical relationships correctly captured the impact of porosity on permeability, but were unable to yield correct values, and even deviated by over a factor 10 for some porous media. This study emphasizes the need for more extensive research into pore scale processes influencing permeability and provides ideas for future research.

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.

Geostatistics as a subfield of statistics accounts for the spatial correlations encountered in many applications of, for example, earth sciences. Valuable information can be extracted from these correlations, also helping to address the often encountered burden of data scarcity. Despite the value of additional data, the use of geostatistics still falls short of its potential. This problem is often connected to the lack of user-friendly software hampering the use and application of geostatistics. We therefore present GSTools, a Python-based software suite for solving a wide range of geostatistical problems. We chose Python due to its unique balance between usability, flexibility, and efficiency and due to its adoption in the scientific community. GSTools provides methods for generating random fields; it can perform kriging, variogram estimation and much more. We demonstrate its abilities by virtue of a series of example applications detailing their use.

Aquifer heterogeneity in combination with data scarcity is a major challenge for reliable solute transport prediction. Velocity fluctuations cause non-regular plume shapes with potentially long-tailing and/or fast-travelling mass fractions. High monitoring cost and a shortage of simple concepts have limited the incorporation of heterogeneity into many field transport models up to now. We present an easily applicable hierarchical conceptualization strategy for hydraulic conductivity to integrate aquifer heterogeneity into quantitative flow and transport modelling. The modular approach combines large-scale deterministic structures with random substructures. Depending on the modelling aim, the required structural complexity can be adapted. The same holds for the amount of monitoring data. The conductivity model is constructed step-wise following field evidence from observations, seeking a balance between model complexity and available field data. The starting point is a structure of deterministic blocks, derived from head profiles and pumping tests. Then, subscale heterogeneity in the form of random binary inclusions is introduced to each block. Structural parameters can be determined, for example, from flowmeter measurements or hydraulic profiling. As proof of concept, we implemented a predictive transport model for the heterogeneous MADE site. The proposed hierarchical aquifer structure reproduces the plume development of the MADE-1 transport experiment without calibration. Thus, classical advection–dispersion equation (ADE) models are able to describe highly skewed tracer plumes by incorporating deterministic contrasts and effects of connectivity in a stochastic way without using uni-modal heterogeneity models with high variances. The reliance of the conceptual model on few observations makes it appealing for a goal-oriented site-specific transport analysis of less well investigated heterogeneous sites.

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.

The purpose of the study is to determine which methods are best suitable for determining permeability and hydraulic conductivity from particle size distribution (PSD) and determine the permeabilities and hydraulic conductivities with confidence intervals. The permeability equations from HydrogeoSieveXL and the measurement from Eijkelkamp permeameter are adopted to collect the data. The results show that Barr, van Baaren, and Kozeny methods have high accuracy for all the samples. Slichter, Beyer

We present a workflow to estimate geostatistical aquifer parameters from pumping test data using the Python package welltestpy. The procedure of pumping test analysis is exemplified for two data sets from the Horkheimer Insel site and from the Lauswiesen site, Germany. The analysis is based on a semi-analytical drawdown solution from the upscaling approach Radial Coarse Graining, which enables to infer log-transmissivity variance and horizontal correlation length, beside mean transmissivity and storativity, from pumping test data. We estimate these parameters of aquifer heterogeneity from type-curve analysis and determine their sensitivity. This procedure, implemented in welltestpy, is a template for analysing any pumping test. It goes beyond the possibilities of standard methods, e.g. based on Theis’ equation, which are limited to mean transmissivity and storativity. A sensitivity study showed the impact of observation well positions on the parameter estimation quality. The insights of this study help to optimize future test setups for geostatistical aquifer analysis and provides guidance for investigating pumping tests with regard to aquifer statistics using the open-source software package welltestpy.

Pumping tests are established for characterizing spatial average properties of aquifers. At the same time, they are promising tools to identify heterogeneity characteristics such as log-conductivity variance and correlation scales. We present the extended Generalized Radial Flow Model (eGRF) which combines the characterization of well flow in fractal geometry with an upscaled conductivity for pumping tests in heterogeneous media. We show that the eGRF is a generalization of previously solutions, such as that of Barker, Butler and Neuman. We derive effective conductivities for uniform and well flow conditions in heterogeneous log-normal media with a truncated power law correlation structure through the upscaling procedure Coarse Graining. The radial-dependent effective conductivity for well flow reflects the gradual change of heterogeneity impact on average pumping test drawdowns. We then combine upscaled conductivities with the eGRF model to determine the effective pumping test solution. We provide a proof of concept by comparing theoretical upscaling results with Monte Carlo well flow simulations in heterogeneous fractal fields. The eGRF and upscaling results are implemented and made freely available as python code for transport simulation as well as pumping test analysis.

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.

The paper ‘Lepto-hadronic single-zone models for the electromagnetic and neutrino emission of TXS 0506+056’ (Cerruti et al. 2019) was published in MNRAS, 483, L12. Afterwards, we became aware of three errors in our numerical calculations. When corrected, the ratio of the emissivity in neutrinos to that in hadronic gamma-rays is modified. We obtained updated model solutions that reproduce the flare of TXS 0506+056observed in 2017. These do not differ qualitatively from the published ones, and the main conclusions of the paper remain valid. However, the estimated neutrino rate was overpredicted.

Tortuosity is one of the most elusive porous media parameters due to its subjective estimation. Here, we compare two approaches for obtaining tortuosity in granular porous media to investigate their capabilities and limitations. First, we determine the hydraulic tortuosity based on the calculated components of the velocity field obtained from flow simulations using the Lattice Boltzmann Method (LBM). Second, we directly determine the geometric tortuosity by making use of the Path Tracking Method (PTM) which only requires the geometric properties of the porous medium. In both cases, we apply the same geometrical structure which is a virtually generated 3D granular bed using the Discrete Element Method consisting of 50 particles. Our results show that the direct PTM is much faster and more precise than the indirect approach based on the calculated velocity field. Therefore, PTM may provide a tool for calculating tortuosity for large 3D granular systems where indirect methods are limited due to the required computational power and time. While LBM considers various routes across the porous media implicitly, PTM identifies them explicitly. As a result, PTM requires a statistical post-processing. As an advantage, this can provide further information than just domain scale average values.

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., QC 20190919

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.