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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]

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. [ABSTRACT FROM AUTHOR]

Copyright of Hydrogeology Journal is the property of Springer Nature and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

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]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. Article impact statement: We present a workflow to infer parameters of subsurface heterogeneity from pumping test data exemplified at two sites using welltestpy. [ABSTRACT FROM AUTHOR]

Geostatistics as a subfield of statistics accounts for the spatial correlations encountered in many applications of e.g. 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 and variogram estimation and much more. We demonstrate its abilities by virtue of a series of example application detailing their use. [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]

High‐performance numerical codes are an indispensable tool for hydrogeologists when modeling subsurface flow and transport systems. But as they are written in compiled languages, like C/C++ or Fortran, established software packages are rarely user‐friendly, limiting a wider adoption of such tools. OpenGeoSys (OGS), an open‐source, finite‐element solver for thermo‐hydro‐mechanical–chemical processes in porous and fractured media, is no exception. Graphical user interfaces may increase usability, but do so at a dramatic reduction of flexibility and are difficult or impossible to integrate into a larger workflow. Python offers an optimal trade‐off between these goals by providing a highly flexible, yet comparatively user‐friendly environment for software applications. Hence, we introduce ogs5py, a Python‐API for the OpenGeoSys 5 scientific modeling package. It provides a fully Python‐based representation of an OGS project, a large array of convenience functions for users to interact with OGS and connects OGS to the scientific and computational environment of Python. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Copyright of Hydrogeology Journal is the property of Springer Nature and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

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 traveling mass fractions. High monitoring cost and presumably missing simple concepts have limited the incorporation of heterogeneity to many field transport models up to now. We present a hierarchical aquifer model which combines large-scale deterministic structures and simple stochastic approaches. Such a heterogeneous conductivity can easily be integrated into a numerical models. Depending on the modeling aim, the required structural complexity can be adapted. The same holds for the amount of available field data. The conductivity model is constructed step-wise following field evidence from observations; though relying on as minimal data as possible. Starting point are deterministic blocks, derived from head profiles and pumping tests. Then, sub-scale heterogeneity in form of random binary inclusions are introduced to each block. Structural parameters can be determined e.g. from flowmeter measurements. 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 ADE models are able to describe highly skewed tracer plumes by incorporating deterministic contrasts and effects of connectivity in a stochastic way even 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. [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]

Most large-scale hydrologic models fall short in reproducing groundwater head dynamics and simulating transport process due to their oversimplified representation of groundwater flow. In this study, we aim to extend the applicability of the mesoscale Hydrologic Model (mHM v5.7) to subsurface hydrology by coupling it with the porous media simulator OpenGeoSys (OGS). The two models are one-way coupled through model interfaces GIS2FEM and RIV2FEM, by which the grid-based fluxes of groundwater recharge and the river-groundwater exchange generated by mHM are converted to fixed-flux boundary conditions of the groundwater model OGS. Specifically, the grid-based vertical reservoirs in mHM are completely preserved for the estimation of land-surface fluxes, while OGS acts as a plug-in to the original mHM modeling framework for groundwater flow and transport modeling. The applicability of the coupled model (mHM-OGS v1.0) is evaluated by a case study in the central European mesoscale river basin - Nägelstedt. Different time steps, i.e., daily in mHM and monthly in OGS, are used to account for fast surface flow and slow groundwater flow. Model calibration is conducted following a two-step procedure using discharge for mHM and long-term mean of groundwater head measurements for OGS. Based on the model summary statistics, namely the Nash-Sutcliffe model efficiency (NSE), the mean absolute error (MAE), and the interquartile range error (QRE), the coupled model is able to satisfactorily represent the dynamics of discharge and groundwater heads at several locations across the study basin. Our exemplary calculations show that the one-way coupled model can take advantage of the spatially explicit modeling capabilities of surface and groundwater hydrologic models and provide an adequate representation of the spatiotemporal behaviors of groundwater storage and heads, thus making it a valuable tool for addressing water resources and management problems. [ABSTRACT FROM AUTHOR]

A framework for interpreting transient pumping tests in heterogeneous transmissivity fields is developed to infer the overall geostatistical parameters of the medium without reconstructing the specific heterogeneous structure point wise. The methodology of Radial Coarse Graining is applied to deduce an effective radial description of multi-Gaussian transmissivity. It was used to derive an Effective Well Flow Solution for transient flow conditions including not only the storativity, but also the geometric mean, the variance, and the correlation length of log-transmissivity. This solution is shown to be appropriate to characterize the pumping test drawdown behavior in heterogeneous transmissivity fields making use of ensembles of simulated pumping tests with multiple combinations of statistical parameters. Based on the Effective Well Flow Solution, a method is developed for inferring heterogeneity parameters from transient pumping test drawdown data by inverse estimation. Thereby, the impact of statistical parameters on the drawdown is analyzed, allowing to determine the dependence of reliability of parameter estimates on location and number of measurements. It is shown, that the number of measurements can be reduced compared to steady state pumping tests. Finally, a sampling strategy for single aquifer analysis is developed, which allows to estimate the statistical parameters, in particular variance and correlation length for individual heterogeneous transmissivity fields making use of transient pumping test measurements at multiple locations. [ABSTRACT FROM AUTHOR]

A new method is presented which allows interpreting steady-state pumping tests in heterogeneous isotropic transmissivity fields. In contrast to mean uniform flow, pumping test drawdowns in heterogeneous media cannot be described by a single effective or equivalent value of hydraulic transmissivity. An effective description of transmissivity is required, being a function of the radial distance to the well and including the parameters of log-transmissivity: mean, variance, and correlation length. Such a model is provided by the upscaling procedure radial coarse graining, which describes the transition of near-well to far-field transmissivity effectively. Based on this approach, an analytical solution for a steady-state pumping test drawdown is deduced. The so-called effective well flow solution is derived for two cases: the ensemble mean of pumping tests and the drawdown within an individual heterogeneous transmissivity field. The analytical form of the solution allows inversely estimating the parameters of aquifer heterogeneity. For comparison with the effective well flow solution, virtual pumping tests are performed and analysed for both cases, the ensemble mean drawdown and pumping tests at individual transmissivity fields. Interpretation of ensemble mean drawdowns showed proof of the upscaling method. The effective well flow solution reproduces the drawdown for two-dimensional pumping tests in heterogeneous media in contrast to Thiem's solution for homogeneous media. Multiple pumping tests conducted at different locations within an individual transmissivity field are analysed, making use of the effective well flow solution to show that all statistical parameters of aquifer heterogeneity can be inferred under field conditions. Thus, the presented method is a promising tool with which to estimate parameters of aquifer heterogeneity, in particular variance and horizontal correlation length of log-transmissivity fields from steady-state pumping test measurements. [ABSTRACT FROM AUTHOR]

In this study we present a formula for the hydraulic head describing the mean drawdown of a three dimensional steady state pumping test in heterogeneous anisotropic porous media effectively. By modeling the hydraulic conductivity K(...) as spatial random function and using the upscaling method Coarse Graining we succeed in deriving a closed form solution hefw (r) which we understand as an extension of Thiem's formula to heterogeneous media. The solution hefw (r) does not only depend on the radial distance r but accounts also for the statistics of K(...), namely geometric mean KG, variance σ², horizontal correlation length l and anisotropy ratio e. We perform a sensitivity analysis on the parameters of hefw (r) and implement an inverse estimation strategy. Using numerical pumping tests we show the applicability of hefw (r) on the interpretation of drawdown data. This will be done for both, an ensemble of as well as for single pumping tests. Making use of the inverse estimation method we find excellent agreement of estimated parameters with initial values, in particular for the horizontal correlation length. [ABSTRACT FROM AUTHOR]

We discuss the rate of an elementary chemical reaction. We use the reaction path and especially its saddle point on the potential energy surface. The reaction path connects reactant and product of a reaction over the transition state (TS). Usually, the TS is assumed near or at the single saddle point of the reaction path. By means of comparison of the statistics of states at the reactant and at the TS, one can estimate the reaction rate by the Eyring theory. We propose to use the Tsallis statistics at the TS, a statistics of seldom accidents. Thus, we propose to generalize the well-known Boltzmann–Gibbs statistics, which is the limiting case of the Tsallis statistics. We use features of this nonextensive thermostatistics. The basic properties of the statistics are used to derive (approximated) partition functions, and they are applied on reaction rates. The approximation includes a factorization of the partition functions. The theory is applied to HCN isomerization to HNC, and to the reaction H2 + CN → H + HCN. It allows an accordance with experimental estimations of the reaction rates. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2010 [ABSTRACT FROM AUTHOR]