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• Soil moisture fluctuations invert saturated hydraulic conductivity (K s) • Multi-frequency fluctuations contain non-redundant information, benefiting K s inversion. • Inversion algorithm can accommodate nonlinear data based on VG model. Soils are heterogeneous at multiple scales. Estimates of spatially varying saturated hydraulic conductivity (K s) of soils dictate the resolution of modeling water flux based on the Richardson-Richards equation (RRE), but direct measurements of K s everywhere in a field are practically impossible. As a result, this study develops an inverse approach to estimate spatially varying K s utilizing soil moisture observations driven by periodic weather variability at different frequencies. Using a numerical solution to vertical, one-dimensional RRE based on Gardner-Kozeny (GK) model in a heterogeneous soil with periodic flux, we investigate the spatial cross-correlation between K s and observations (the amplitude or phase shift) of soil moisture fluctuation at different frequencies without high computational cost in the conventional time-domain model. These correlation patterns vary with the spatial location and frequency, suggesting that soil moisture fluctuations at different frequencies at one monitoring location carry non-redundant information about the heterogeneous distribution of K s. Guided by cross-correlation maps, several inverse experiments reveal the effectiveness of multi-frequency data of soil moisture fluctuation for mapping the heterogeneous distribution of K s. Monte Carlo simulations suggest that multi-frequency data can provide non-redundant and useful information about the estimation of heterogeneous K s. Synthetic data based on a commonly-applied nonlinear van Genuchten-Mualem (VG) model is then tested in our inversion algorithm. The results indicate that the spatial pattern of the inverted GK K s is very similar to that of the VG K s , although these two parameters are inherently not identical since they are used in two different models. In addition, the inverted GK K s can successfully predict the soil moisture fluctuation of frequencies that were not used in the inversion. Despite having no field experiments to validate this model, we believe this is the first attempt to conduct frequency-domain inverse modeling in vadose zone hydrology using soil moisture fluctuation. [ABSTRACT FROM AUTHOR]

• Conductivity is employed in flow models upon averaged Monte Carlo fields. • A Monte Carlo volume of 10 % of that required for full numerical stability. • A 10 % volume returns stable outputs, i.e. heads and residuals at wells' locations. The knowledge of aquifer systems, their geological setting, their structure, and subsequent modeling is highly uncertain and is usually faced through Monte Carlo-based methods in hydrogeology. One of the most important uncertainty sources for groundwater models is represented by input hydraulic conductivities, related to the aquifer's structure. There are no specific rules when simulating hydraulic conductivity fields within Monte Carlo frameworks to instruct numerical models, and information about employed conductivity fields and their numerical convergence is often not given. This technical work aims to fill this gap by investigating the impact of employing conductivity information upon different volumes of Monte Carlo simulations applied to a real case study. Thus, this work estimates the minimum volumes of Monte Carlo hydraulic conductivity fields to be employed in groundwater flow models for achieving numerically stable (i) boundary conditions, (ii) global model performances, and (iii) local ones such as simulated hydraulic heads. The present results aim to be indicative of similar hydrogeological settings and will serve as a basis for more complex ones and for investigating transport problems. [ABSTRACT FROM AUTHOR]

This paper presents an analytical study of organic contaminants transport in a cut-off wall and aquifer dual-domain system, considering the effects of the inlet boundary conditions and cut-off structural arrangements. The comprehensive sensitivity analysis of parameters focusing on the breakthrough time, attenuation time and cumulative concentration are presented using the Monte Carlo simulation and Sobol global method. The simplified constant inlet boundary condition can lead to an excessively conservative prediction of the contaminant breakthrough compared to the 'finite mass' and 'decaying source' boundary conditions. The cut-off wall hydraulic performance can be enhanced by reducing the contaminant's head loss, shape factor, half-life and cut-off wall hydraulic conductivity while increasing the retardation factor. The contaminant's half-life can largely influence the maximum contaminant concentration, attenuation time and breakthrough time. For example, the maximum contaminant concentrations for T 1/2 = 1.4 years and T 1/2 = 100 years are 13 and 123 times greater than that for T 1/2 = 0.1 year, respectively. The influence of the variation of shape factor on the breakthrough curve should be taken into consideration. Altering the structural arrangement of the cut-off wall to accommodate a smaller shape factor increases the contaminant breakthrough time. The proposed solution allows the analysis of a cut-off wall and aquifer system with different inlet boundary conditions and structural arrangements of the cut-off wall. • An analytical model of organic contaminants transport in a CAS is proposed. • Monte Carlo simulation and Sobol global method are used for sensitivity analysis. • Different inlet boundary conditions and structural arrangements are investigated. • A constant contaminant concentration leads to conservative predictions. • Altering the structural arrangement can enhance the performance of the barrier. [ABSTRACT FROM AUTHOR]

• First hydrogeological model established for URL site of HLW disposal in China. • The effect of the hydraulic influence zones of faults is incorporated in the numerical model. • Different variations in the horizontal and vertical directions of hydraulic conductivity are considered. • A total of 120 stochastic parameterized models are presented. • Hydraulic conductivity < 10−9 m/s at high-level radioactive waste disposal depth. Deep geological disposal is internationally accepted as a feasible and safe approach for high-level radioactive waste (HLW) disposal. To evaluate hydrogeological conditions in support of safety assessments for HLW disposal at the Xinchang preselected site in China, stochastic inverse models of site-scale groundwater flow were developed in this study to generate highly parameterized hydraulic conductivity fields for the fractured medium by adopting pilot point and null-space Monte Carlo methods. The hydraulic influence zones of the faults were carefully considered to have homogenous parameter values across the zones. A total of 120 multiple random realizations were generated to characterize the 3D spatial variations in hydraulic conductivity by conditioning to 1218 fixed pilot points. The simulated hydraulic heads of the realizations were in good agreement with observational data. The hydraulic conductivity fields close to the boreholes could be characterized in detail and had relatively low uncertainties. Furthermore, the hydraulic conductivity (K) values around underground research laboratory (URL) at the HLW disposal zone depth were less than 10−9 m/s. The K values obtained for most of the influence zones of these faults at this depth were consistent with hydraulic test data and ranged from 10−10 to 10−9 m/s, thereby indicating that the surrounding rock has low permeability and is suitable for HLW disposal. These findings offer new insights into hydrogeological conditions by providing key information on the permeability characteristics that need further focus on HLW disposal. [ABSTRACT FROM AUTHOR]

The relation between soil pore structure and water retention is complex and is often not well determined. We present a novel approach based on critical path analysis from percolation theory to refine hydraulic conductivity estimation from soil water retention curve by introducing a new tortuosity parameter as a function of scaling factor. We generalize this model to account for large shifts in the relation between soil pore structure and water retention, which are indicative of soils with multi-fractal properties, by employing a t -test on scaled saturation and suction data. The proposed model relaxes the constraints that were set on model parameters for multi-fractal soils in the literature by tuning "all" parameters against observed data using a multiple-start gradient-based optimization algorithm, and is applicable to a wider variety of soil textures. The optimization results are further evaluated against those of a Markov Chain Monte Carlo algorithm to ensure global optimum is found. Goodness-of-fit (GOF) measures, including geometric mean and standard deviation error ratios, and Nash-Sutcliffe efficiency, show that the proposed model presents less bias across the entire range of matric potential compared to its predecessor that under-estimate hydraulic conductivity in all studied cases. • A new approach is proposed to model hydraulic conductivity of multi-fractal soils. • Model considers tortuosity dimension as a function of scaling factor. • Approach uses t -test to detect changepoint and tune model for each section. • Approach generalizes model parameters, making it applicable to more soils. • Model resolves under-estimation of hydraulic conductivity in the literature. [ABSTRACT FROM AUTHOR]

Whether the hydraulic conductivity representative elementary volume (KREV) exists is a fundamental question for understanding the hydraulic behavior of fractured rock masses. The fracture density and size of rocks vary greatly, and are the two most important parameters affecting the existence of a KREV. The International Society for Rock Mechanics (ISRM) presented quantitative descriptions of fracture persistence and density, dividing the persistence into 5 rates and the density into 7 rates, defining 35 basic types of isotropic fractured rock masses with different persistence and densities. Based on ISRM classification suggestions, we construct an additional 40 anisotropic fractured rocks and conduct a systematic investigation of the KREVs of all 75 rock types. The 3D DFNs of the 75 rocks are established with the Monte Carlo method; the water flow in the DFNs is simulated with the finite difference method; the equivalent conductivities of each rock are calculated in 10 domain sizes and 21 different flow directions; and the optimum conductivity ellipsoid and the fitting errors of the equivalent directional conductivity vectors are analyzed to determine the existence and size of the KREVs. A KREV is more likely to exist in rock masses with a high fracture density and persistence. The effect of fracture density and persistence can be comprehensively represented by blockiness, defined as the ratio of the volume of isolated blocks formed by fractures to the total rock volume. A strong correlation is found between the blockiness and the existence of a KREV. A KREV always exists when the blockiness is higher than 0.5%, and its size is between 2 and 18 times the fracture spacing. A KREV may or may not exist in the range of 0.1% < B < 0.5%. When B < 0.1%, a KREV does not exist. [ABSTRACT FROM AUTHOR]

Random field theory has become a very popular approach for probabilistic analysis of earth dams. This study performs a stochastic analysis of seepage through an embankment dam to account for the spatial variability of hydraulic parameters. The originality of this study consists in using and comparing three types of Random Fields RFs for the seepage analysis: classical stationary RFs, conditional RFs (to consider the position of available measurements), and non-stationary RFs (to consider the mean variation with depth). The same sample of hydraulic conductivity values is considered to generate the three types of random fields. The hydraulic conductivity RFs are integrated into a Finite Element seepage analysis model to evaluate the flow velocity, hydraulic gradient, pore water pressure, and flow rate. The process is repeated by Monte Carlo simulations to characterize the spatial variability of the seepage results in terms of mean and standard deviation at each point of the studied dam and its foundation. The results show a higher dispersion for the stationary RF case and a lower dispersion for the conditional RF case. For the case study, the results also show that the use of different RFs for modelling the spatial variability of hydraulic conductivity induces differences that can be considered significant for flow velocity, moderate for hydraulic gradient and minor for pore pressure. [ABSTRACT FROM AUTHOR]

• First to use superparamagnetic DNA tagged colloids (SiDNAmag) for hydraulic parameter estimation of a 3D sand aquifer, using monte carlo modelling approach at different ionic strengths. • Hydraulic parameter distributions estimated from sidnamag breakthrough curves through Monte Carlo simulation approach were statistically similar to salt tracer. • SiDNAmags are good candidate for determining hydraulic parameters of saturated 3D sand aquifer at short travel distance (50 cm). We investigated the applicability of Silica encapsulated, superparamagnetic DNA particles (SiDNAmag) in determining aquifer hydraulic parameters at different ionic strengths (1 mM, 5 mM, and 20 mM phosphate buffer) of injection suspension. Thereto, in a homogeneous, unconsolidated sand tank we pulse - injected two uniquely sequenced SiDNAmag at two injection points. At 0.5 m and 0.8 m downstream from the injection points, we measured the concentration of SiDNAmags at three vertically distributed and two horizontally distributed sampling locations. We estimated the hydraulic parameter distributions from the SiDNAmag breakthrough curves through a Monte – Carlo approach and compared the parameter distributions with salt tracer breakthrough curves. Our results indicated that at all the ionic strengths, the times of peak concentrations, and the shapes of the breakthrough curves were similar to the salt tracer. As compared to the salt, a 1 – 3 log units reduction in the maximum effluent concentration of SiDNAmag was due to kinetic attachment. The attachment rate reduced from 1 mM to 5 mM phosphate buffer possibly due to competitive adsorption of phosphate onto the favourable attachment sites. SiDNAmag attachment rate further increased in 20 mM buffer suspension, possibly due to the compression of electric double layer and reduction in energy barrier for attachment. The parameter distributions of hydraulic conductivity (k), effective porosity (n e), longitudinal dispersivity (α L), vertical transverse dispersivity (α TV /α L) and horizontal transverse dispersivity (α TH /α L) estimated from the SiDNAmag and the salt tracer breakthrough curves were statistically similar. Our work contributes to the applicability of colloidal SiDNAmags for determining hydraulic parameters at different ionic strength conditions. [ABSTRACT FROM AUTHOR]

Suffusion occurs when fines are plucked off by seepage forces and transported throughout the pores of the matrix constituted by coarser soil particles. Natural or human made soils are seldom homogeneous, which makes suffusion more complex. Suffusion is usually combined with the self-filtration of the fine particles and the transport of these fines may cause the soil structure to become looser. At the same time a clogging may occur which could reduce the permeability leading to an increase of excess pore pressure. The combination of these two phenomena will result in strength degradation. Currently, most suffusion analyses are performed without taking into account the soil's spatial variability. In this paper, a four-constituent continuum finite difference model for suffusion has been extended through the self-filtration process. A random field theory was at this point introduced into the finite difference code to investigate soil suffusion with a randomly distributed initial porosity and fines content. A probabilistic study using the Monte Carlo method was conducted to analyze the effect of the variance, the spatial correlation length, and the cross correlation of the randomly distributed initial porosity and fines content on the eroded mass and on the evolution of the hydraulic conductivity under 1D and 2D conditions. Based on all the simulations, it was possible to quantify the probability of particle blockage during erosion. [ABSTRACT FROM AUTHOR]

Highlights • Impact of positive porosity-conductivity correlation on probabilistic risk analysis. • Relevance of including porosity variability depends on the metric of interest, the control plane-source distance and the level of conductivity heterogeneity. • A heterogeneous porosity field leads to a reduction of the increased lifetime cancer risk uncertainty. Abstract Heterogeneities in natural porous formations, mainly manifested through the hydraulic conductivity (K) and, to a lesser degree, the porosity (ϕ), largely control subsurface flow and solute transport. The influence of the heterogeneous structure of K on transport processes has been widely studied, whereas less attention is dedicated to the joint heterogeneity of conductivity and porosity fields. Our study employs Monte Carlo simulations to investigate the coupled effect of K − ϕ spatial variability on the transport behavior (and uncertainty) of conservative and reactive plumes within a 3D aquifer domain. We explore multiple scenarios, characterized by different levels of heterogeneity of the geological properties, and compare the computational results from the joint K − ϕ heterogeneous system with the results originating from generally adopted constant ϕ conditions. In our study, the spatially variable K − ϕ fields are positively correlated. We statistically analyze key Environmental Performance Metrics: first arrival times and peak mass fluxes for non-reactive species and increased lifetime cancer risk for reactive chlorinated solvents. The conservative transport simulations show that considering coupled K − ϕ fields decreases the plume dispersion, increases both the first arrival times of solutes and the peak mass fluxes at the observation planes. A positive correlation between aquifer connectivity and peak mass fluxes is identified for both homogeneous and heterogeneous ϕ. Our conservative transport results indicate that the relevance of ϕ variability can depend on the metric of interest, the control plane-source distance as well as the level of heterogeneity of the conductivity field. The analysis on reactive transport shows that ϕ variability only slightly affects the mean increased lifetime cancer risk at the control planes but leads to a considerable reduction of the cancer risk uncertainty. We also see that the sensitivity of cancer risk towards ϕ heterogeneity can be influenced by the level of variability of the conductivity field, the source-to-control plane distance, but is not affected by the manner in which the contaminant concentration is computed. [ABSTRACT FROM AUTHOR]

Hydrologic models are commonly over-smoothed relative to reality, owing to computational limitations and to the difficulty of obtaining accurate high-resolution information. When used in an inversion context, such models may introduce systematic biases which cannot be encapsulated by an unbiased “observation noise” term of the type assumed by standard regularization theory and typical Bayesian formulations. Despite its importance, model error is difficult to encapsulate systematically and is often neglected. Here, model error is considered for an important class of inverse problems that includes interpretation of hydraulic transients and contaminant source history inference: reconstruction of a time series that has been convolved against a transfer function (i.e., impulse response) that is only approximately known. Using established harmonic theory along with two results established here regarding triangular Toeplitz matrices, upper and lower error bounds are derived for the effect of model error on time series recovery for both well-determined and over-determined inverse problems. It is seen that use of additional measurement locations does not improve expected performance in the face of model error. A Monte Carlo study of a realistic hydraulic reconstruction problem is presented, and the lower error bound is seen informative about expected behavior. A possible diagnostic criterion for blind transfer function characterization is also uncovered. [ABSTRACT FROM AUTHOR]

This paper presents failure probability assessment and parameter sensitivity analysis of a contaminant’s transit time through a compacted clay liner. Monte Carlo simulation (MCS) was used to assess failure probability, and the failure samples generated in the MCS were used to investigate the sensitivity of various uncertain parameters to the failure probability. To facilitate the MCS, a database on various transport parameters was developed by collecting and analyzing measurement data reported in literature. Failure probability assessment and parameter sensitivity analysis showed that the uncertainties in adsorption parameters, longitudinal dispersivity, and hydraulic conductivity have the most significant effects on failure probability. [ABSTRACT FROM AUTHOR]

Estimating spatial distributions of the hydraulic conductivity in heterogeneous aquifers has always been an important and challenging task in hydrology. Generally, the hydraulic conductivity field is determined from hydraulic head or pressure measurements. In the present study, we propose to use temperature data as source of information for characterizing the spatial distributions of the hydraulic conductivity field. In this way, we performed a laboratory sandbox experiment with the aim of imaging the heterogeneities of the hydraulic conductivity field from thermal monitoring. During the laboratory experiment, we injected a hot water pulse, which induces a heat plume motion into the sandbox. The induced plume was followed by a set of thermocouples placed in the sandbox. After the temperature data acquisition, we performed a hydraulic tomography using the stochastic Hybrid Monte Carlo approach, also called the Hamiltonian Monte Carlo (HMC) algorithm to invert the temperature data. This algorithm is based on a combination of the Metropolis Monte Carlo method and the Hamiltonian dynamics approach. The parameterization of the inverse problem was done with the Karhunen-Loève (KL) expansion to reduce the dimensionality of the unknown parameters. Our approach has provided successful reconstruction of the hydraulic conductivity field with low computational effort. [ABSTRACT FROM AUTHOR]

• Features of log-conductivity, Y , fields are captured by a non-Gaussian (GSG) model. • Expressions of flow and transport moments in three-dimensional GSG fields are derived. • Head and velocity fields are more correlated in GSG than in Gaussian Y structures. • Non-Gaussianity of Y heavily influences pre-asymptotic macrodispersion values. • Late time transport exhibits a Fickian behavior also in non-Gaussian Y fields. In this work, we explore the implications of modeling the logarithm of hydraulic conductivity, Y , as a Generalized Sub-Gaussian (GSG) field on the features of conservative solute transport in randomly heterogeneous, three-dimensional porous media. Hydro-geological properties are often viewed as Gaussian random fields. Nevertheless, the GSG model enables us to capture documented non-Gaussian traits that are not explained through classical Gaussian models. Our formulation yields lead- (or first-) order analytical solutions for key statistical moments of flow and transport variables. These include flow velocities, hydraulic head, and macrodispersion coefficients, as obtained across GSG log-conductivity fields. The analytical model is based on a first-order spectral theory, which constrains the rigorous validity of our results to small values of log-conductivity variance (σ Y 2 < < 1). Analytical results are then compared against detailed numerical estimates obtained through a Monte Carlo scheme encompassing various levels of domain heterogeneity. An asymptotic Fickian transport regime is attained at late times in both Gaussian and GSG Y fields. Convergence to such regime is slower for GSG as compared to Gaussian fields. This suggests a strong impact of the heterogeneity structure on non-Fickian pre-asymptotic behaviors of the kind documented in the literature. The quality of the comparison between analytical and numerical results deteriorates with increasing σ Y 2. Otherwise, our lead-order solutions frame macrodispersion coefficients in appropriate orders of magnitude also for values of σ Y 2 up to approximately 1.7, which are consistent with the spatial variability of Y across a single geological unit. In this sense, our analytical approach enables one to obtain prior information on solute plume evolution and to grasp the effects of non-Gaussian medium heterogeneity while favoring simplicity. Our findings also enhance the current level of understanding of the nature of mass transfer across heterogeneous media characterized by complex variability structures which cannot be reconciled with classical Gaussian scenarios. [ABSTRACT FROM AUTHOR]

Summary In this work, we design a series of benchmark problems for subsurface flow uncertainty quantification. Three basic subsurface flow problems with increasing complexity are selected, which are steady state groundwater flow, groundwater contamination, and multi-phase flow. For the steady state groundwater flow, hydraulic conductivity is assumed to be uncertain, and the uncertain model parameter is assumed to be Gaussian random constant, Gaussian random field, and facies field, respectively. For the other two flow problems, the uncertain model parameter is assumed to be Gaussian random field and facies field, respectively. The statistical property of the uncertain model parameter is specified for each problem. The Monte Carlo (MC) method is used to obtain the benchmark results. The results include the first two statistical moments and the probability density function of the quantities of interest. To verify the MC results, we test the convergence of the results and the reliability of the sampling algorithm. For any existing and newly developed uncertainty quantification methods, which are not (fully) verified, the designed benchmark problems in this work can facilitate the verification process of those methods. For illustration, in this work, we provide a verification of the probabilistic collocation method using the benchmark results. [ABSTRACT FROM AUTHOR]

The saturated hydraulic conductivity ( K s ) of soil is characterized by strong spatial variability and often decreases with depth. The main objective of this paper is to investigate how the trend function of the mean of saturated hydraulic conductivity ( μ K s ) and its spatial variability affect the distribution of critical failure surfaces and the probability of slope failure during a period of rainfall. A random field method is used to simulate the spatial variability structure in the numerical analysis of a slope, and a numerical procedure for a probabilistic slope stability analysis based on Monte Carlo simulations is presented, in which K s is modeled as a non-stationary lognormal random field. For a hypothetical weathered soil slope subjected to rainfall, a deterministic analysis and a sequence of probabilistic analyses are conducted using an infinite unsaturated slope model. The results show that these shallow failures are attributed to the reduction of matric suction and the development of positive pore pressure. The probability of slope failure increases with an increase in the variation of the trend component (Δ k ), but the rate of increase levels off at the later stage of rainfall. Ignoring the trend component of μ K s would lead to less conservative estimates of the failure probability. The coefficient of variability has a more significant influence on the distribution of the critical failure surfaces and the probability of failure than does the correlation length of K s . [ABSTRACT FROM AUTHOR]

Summary Soil moisture in a hillslope is simulated using three multi-dimensional hydrologic models: a 3D surface–subsurface integrated model and two 2D distributed hydrologic models, MIKE-SHE and WEP, which adopt the Richards equation at different levels of approximation. High-resolution topographic data (1 m in horizontal accuracy), soil depth, hydraulic conductivity, porosity, and soil characteristics obtained from the literature and in-situ measurements were used as prior information for modeling. Numerical simulations were compared with multiple TDR sensor measurements from different locations and depths. Using available input data, the models had limited ability to reproduce the soil moisture dynamics shown in field measurements. The 3D model estimated the spatial diversity of the infiltration process of soil water movement more accurately than the distributed hydrologic models, MIKE-SHE and WEP. Suitable model parameters and correlations among them were estimated through Monte Carlo simulation using the 3D model. Parameters selected through the Monte Carlo method were used to simulate soil moisture variations at measurement sites. Relatively high correlations were found among the van Genuchten model parameters and the bottom boundary condition (bed rock). An increasing pattern of correlation between porosity to the downstream direction was found, which shows connectivity between parameter correlation and identifiability. Simulation results imply that multi-dimensional modeling of soil moisture in a hillslope may benefit from ensemble-based simulations that consider inherent uncertainty from model parameters and structures. [ABSTRACT FROM AUTHOR]

Many soil parameters are highly variable, especially saturated hydraulic conductivity, which is bound to significantly influence the stability of unsaturated soil slopes that are subjected to rainfall infiltration and redistribution. A random variable model is used to characterize the variability of saturated hydraulic conductivity. Random number sequences of saturated hydraulic conductivity are generated following a lognormal distribution using the Monte Carlo Simulation method. Then the closed form of the limit state function is established, based on the combination of the extension of the Green-Ampt model and the infinite slope stability model. The suggested probabilistic method can calculate the time-dependent failure probability of the slope during a process of rainfall infiltration and redistribution. For a hypothetical slope that is subjected to steady-state rainfall infiltration, a series of parameter analyses are conducted and the results indicate that there exists a critical rainfall duration. At different stages of rainwater infiltration–redistribution, the trends between the failure probability of the soil slope and the coefficient of variation of the saturated hydraulic conductivity have a different form. The coefficient of variation of the saturated hydraulic conductivity does not affect the failure time of the slope that is most likely to occur. This paper figures out why some landslides occur after a rainfall event from the perspective of rainwater redistribution, and the corresponding lag times generally depend on the duration of antecedent rainfall. It is very risky to adopt mean safety factors to assess their stabilities for rainfall-induced landslides when the variability of the hydraulic conductivity is considered. [ABSTRACT FROM AUTHOR]

• HT survey underscores its superiority to inverse modeling of other natural events. • Conditional Monte Carlo simulation addresses uncertainty in validating results. • Conditional effective K from natural gradient flow as prior improves HT results. The limited area of influence in highly permeable aquifers hampers hydraulic tomography (HT) surveys with traditional pumping tests. Few have suggested that flow data under natural stimuli could complement HT. Verifying this conjecture in controlled laboratory sandbox experiments does not exist. Similarly, many have employed independent pumping events to validate inverse modeling results, but few have explored the validation uncertainty. This study first conducted sandbox experiments to investigate the effectiveness of head data from HT, natural gradient (NG), and precipitation/infiltration (PI) events for estimating hydraulic conductivity (K) field. Conditional Monte Carlo simulation of independent pumping tests then addresses the uncertainty of validating these estimated K fields. The effectiveness of the estimates from NG and PI as prior information for HT was investigated next. Cross-correlation analysis, exploring the relationship between the observed heads and K heterogeneity under different stimuli, then assesses the usefulness of flow data under different stimuli and their possibility for complementing HT as prior information. Estimates from NG and PI events as the mean of the prior probability distribution for HT then corroborate the cross-correlation analysis. Conditional Monte Carlo simulation of twelve independent pumping tests further confirms that a decent NG's K estimate as the mean for the prior probability distribution for HT inversion yields the highest resolution of K estimates. [ABSTRACT FROM AUTHOR]

Summary: Multi-scale heterogeneity of geological formations is a rule, which consists of random (local-scale) and systematic (large-scale) variability of hydraulic conductivity. The random variability and depth–decaying trend, a systematic variability, have different effects on subsurface flow, thus on groundwater discharge into tunnels. Little research has examined this problem in the past. Using Monte Carlo simulation and information of statistics of heterogeneity, we evaluate the most likely (ensemble average) discharge rate into a tunnel in geologic media with the multi-scale heterogeneity and uncertainty associated with this estimate. We find that the ensemble average discharge rate is larger than the discharge rate predicted by geometric mean of hydraulic conductivity, and smaller than the discharge rate predicted by arithmetic mean of hydraulic conductivity. Moreover, the ensemble average discharge rate decreases with the decay exponent of the depth–decaying trend, and increases with the standard deviation as well as the correlation scale of the stationary log-conductivity fields. We also find that the discharge rate of a tunnel is highly influenced by the hydraulic conductivity near the tunnel. Furthermore, deviation of the true discharge rate from the ensemble average can be large and increases with the decay exponent, standard deviation and correlation scale of log-conductivity fields. The largest uncertainty of discharge rate prediction in the shallow subsurface is controlled by the variability of conductivity fields and the uncertainty at the deep subsurface is by the depth–decaying trend of hydraulic conductivity. Therefore, accurate prediction of groundwater discharge into tunnels requires detailed characterization of multi-scale heterogeneity. [Copyright &y& Elsevier]

Abstract: This paper concerns efficient uncertainty quantification techniques in inverse problems for Richards’ equation which use coarse-scale simulation models. We consider the problem of determining saturated hydraulic conductivity fields conditioned to some integrated response. We use a stochastic parameterization of the saturated hydraulic conductivity and sample using Markov chain Monte Carlo methods (MCMC). The main advantage of the method presented in this paper is the use of multiscale methods within an MCMC method based on Langevin diffusion. Additionally, we discuss techniques to combine multiscale methods with stochastic solution techniques, specifically sparse grid collocation methods. We show that the proposed algorithms dramatically reduce the computational cost associated with traditional Langevin MCMC methods while providing similar sampling performance. [Copyright &y& Elsevier]

Seabed sediments are inherently heterogeneous and present different fabric patterns including rotated anisotropy. This work aims to investigate the effects of rotated anisotropy in seabed properties on the hydromechanical responses of seabed and pipelines. Rotated anisotropic seabed property fields (e.g., hydraulic conductivity and shear modulus fields) are generated using the random field theory, and are then coupled with finite element models to simulate the hydromechanical responses of seabed–pipelines under dynamic nonlinear wave-induced loadings. Monte Carlo simulations are performed to approach a probabilistic analysis of the effects of heterogeneous seabed fields. The pore pressure, liquefaction, seabed displacement, and pipeline stress are analyzed for systematic varying rotation angles. The results show that the upper bounds of the liquefied area would decrease by about 15% and 8% with increasing rotated anisotropy in the hydraulic conductivity and shear modulus fields, respectively. For rotated anisotropic shear modulus fields, the von Mises stress is minimum when the rotation angle is 45 ∘. The transverse anisotropy in hydraulic conductivity or shear modulus is the most unfavorable situation, the results of which could be relied upon for a conservative design if the rotated anisotropy of a seabed property is unknown in a field project. • Random field model developed specifically for seabed sediments with rotated anisotropy. • Multiphysics finite element models developed for hydromechanical responses. • Comprehensive analysis performed to understand the effect of rotated anisotropy. • Critical fabric orientation most unfavorable to pipeline stability is identified. [ABSTRACT FROM AUTHOR]

Abstract: Formation properties are one of the key factors in numerical modeling of flow and transport in geologic formations in spite of the fact that they may not be completely characterized. The incomplete knowledge or uncertainty in the description of the formation properties leads to uncertainty in simulation results. In this study, the ensemble Kalman filter (EnKF) approach is used for continuously updating model parameters such as hydraulic conductivity and model variables such as pressure head while simultaneously providing an estimate of the uncertainty through assimilating dynamic and static measurements, without resorting to the explicit computation of the covariance or the Jacobian of the state variables. A two-dimensional example is built to demonstrate the capability of EnKF and to analyze its sensitivity with respect to different factors such as the number of realizations, measurement timings, and initial guesses. An additional example is given to illustrate the applicability of EnKF to three-dimensional problems and to examine the model predictability after dynamic data assimilation. It is found from these examples that EnKF provides an efficient approach for obtaining satisfactory estimation of the hydraulic conductivity field with dynamic measurements. After data assimilation the conductivity field matches the reference field very well, and different kinds of incorrect prior knowledge of the formation properties may also be rectified to a certain extent. [Copyright &y& Elsevier]

In this study, a Monte Carlo simulation method is applied to study groundwater flow and solute transport in heterogeneous, dual-porosity media. Both the hydraulic conductivity and the interregional mass diffusion rate are assumed to be spatial random variables, and their random distributions are generated through a Fast Fourier Transform (FFT) technique. A block-centered finite difference (FD) method is used to solve the flow equation. Based on the generated flow fields, a random walk particle-tracking algorithm is invoked to study the solute transport. The mass diffusion between the mobile and immobile water regions is simulated by a two-state, homogeneous, continuous-time Markov chain. The Monte Carlo simulation results are compared to those obtained through the first-order, Eulerian perturbation method. It is shown from the comparison that the first-order analytical method is robust for predicting mean concentration in mild heterogeneous dual-porosity media. However, large deviations are observed between the analytical and Monte Carlo results for predicting transport in moderately-highly heterogeneous media. The Monte Carlo method is also used to study the variance of the solute flux through a control plane. [Copyright &y& Elsevier]

• Log-conductivity (Y) is modeled as a generalized sub-Gaussian (GSG) field. • Average longitudinal spreading is smaller for GSG than for Gaussian Y fields. • Plume stretching in GSG fields is enhanced with respect to Gaussian fields. • Local dispersion masks identification of impacts of non-Gaussianity on transport. • The GSG nature of Y can be difficult to identify relying only on transport metrics. There are increasing evidences that probability distributions and associated statistical moments of a variety of hydrogeological and soil science variables and their spatial increments display distinctive scale-dependent features that are not captured by a typical Gaussian model. A Generalized Sub-Gaussian (GSG) model is able to capture key aspects of this pattern. We present the results of a suite of computational analyses set in a Monte Carlo framework and aimed at assessing the impact of a GSG structure of log hydraulic conductivity (Y) on transport of a conservative solute through a three-dimensional bounded porous medium under steady-state saturated Darcy flow. Our results indicate that the longitudinal spreading of a plume is on average significantly smaller for Sub-Gaussian than for Gaussian Y fields. Otherwise, the velocity field arising from a Sub-Gaussian Y field induces enhanced plume stretching with respect to what can be observed in a Gaussian Y setting, this aspect potentially influencing the strength of solute mixing within these two types of conductivity domains. We also find that, in some cases, it may be difficult to identify the nature of the underlying conductivity field relying solely on observations of solute concentrations migrating within the system. In this regard, we show that the action of local dispersion tends to mask the influence of Sub-Gaussianity on major transport metrics. [ABSTRACT FROM AUTHOR]

• The mean of conditional K realizations differs from the conditional effective K. • Conditional effective K is harmonic and geometric mean in 1&2-D HT, respectively. • Conditional Monte Carlo Simulation and SLE yield similar results. This study first discusses the conditional mean, realizations, and effective hydraulic conductivity in a theoretical framework. It then introduces Monte Carlo simulation (MCS) algorithms for constraining the outcome by either hydraulic conductivity (K) samples or hydraulic head (h) measurements from the hydraulic tomographic survey (HT). It demonstrates that kriging using K measurements leads to a conditional mean K field, while inverse modeling using successive linear estimator (SLE) with head measurements of HT yields the conditional effective K field. The effects of conditioning using K measurements are different from those using heads. Besides, the conditional effective K leads to the unbiased prediction of the head that honors the observed head at measurement locations. More importantly, the study reveals that the harmonic and geometric means of conditional realizations of K fields of MCS, given head measurements, are equivalent to the conditional effective K in one- and two-dimensional flows, respectively. The first-order approximation in the SLE results in a conditional covariance similar to that from MCS with smaller magnitudes. Despite the difference, all approaches predict unbiased conditional mean head behaviors. [ABSTRACT FROM AUTHOR]

• Extended solutions for analysis of slug tests are proposed for three flow configurations. • Models consider infinitesimal well skin and inertial effects in the well. • Behaviors and hydraulic conductivity estimates are compared with a steady-state model. • Parameter sensitivity and uncertainty are conducted for the three models. Slug tests are one of the most common field methods for estimating local hydraulic conductivity, for fast and low-cost characterization of aquifer heterogeneity. In highly permeable zones, underdamped responses, identified by oscillations of the water level, are generally observed. Several analytical solutions have been developed for modeling underdamped slug test responses. Interpreting these tests in fractured rocks can be challenging due to system complexity, which ultimately raises questions about the appropriate model for interpreting a given dataset. In order to obtain insights on this fundamental problem for slug test analyses in fractured rocks, a complete evaluation on three transient solutions for linear, radial and spherical flow configuration extended to include inertial and wellbore skin effects in a fully penetrating well is proposed. A first comparison between these transient solutions and the classical steady-state model shows that, in some cases, the latter may underestimate hydraulic conductivity. Next, parameter sensitivity and uncertainty analyses were conducted on each solution to evaluate the classical problem of non-uniqueness between models and parameters. As expected, the results from sensitivity analysis show that the hydraulic conductivity parameter is the most sensitive regardless of model configuration. For specific storage, sensitivity is important for the linear model, moderate for the radial model and negligible for the spherical model. For the skin factor, however, sensitivity is negligible for the linear model, moderate for the radial model and most important for the spherical model. These results were next confirmed by performing Bayesian inferences using Markov Chain Monte Carlo technique to evaluate uncertainty on each parameter. Uncertainties appear significant for negligibly sensitive parameters but nearly insignificant for the most sensitive parameters. For all flow configurations, hydraulic conductivity appears however to be accurately estimated. Examples of interpretations for data collected in fractured rocks illustrate the application of these models and provide some recommendations. [ABSTRACT FROM AUTHOR]

• Variations in the support/observation scale of hydraulic conductivity induce changes in the information content of the associated Darcy fluxes. • Propagation of information about conductivity onto Darcy flux through the flow and mass balance equation can be quantified via information theory. • Flux data at large scales provide more information about fluxes at small scales than what can be observed with reference to conductivities. We rest on an Information Theory perspective and assess (i) the average information content and (i) the information shared between Darcy flux fields associated with fields of hydraulic conductivity (K) characterized by differing support (or measurement) scale. We treat hydraulic conductivity as a spatial random field, characterized by a given distribution and correlation structure. The latter is modeled through a truncated power law variogram (TPV), which explicitly takes into account a characteristic length scale of the support volume of K through a lower cutoff scale. We then frame our study in a numerical Monte Carlo context where groundwater flow is evaluated across a collection of realizations of hydraulic conductivity characterized by different values of the TPV parameters and subject to uniform in the mean flow. We quantify information through the Shannon entropy of the probability mass functions of the Darcy flux components as well as the mutual information and the multivariate mutual information respectively shared by pairs and triplets of Darcy flux components related to hydraulic conductivity fields evaluated at diverse scales and associated with various levels of heterogeneity. Partitioning of multivariate mutual information according to unique, redundant and synergetic contributions is also quantified. We found consistent trends (i) in the variation of the average information content with respect to the size of lower cutoff scale and (ii) in the way information is shared between pairs and triplets of Darcy flux components associated with diverse support scales of the underlying conductivities. [ABSTRACT FROM AUTHOR]

• Hyporheic mixing (inherit ensemble average concepts) is a scale-dependent phenomenon. • Flux variance at different scales is a proper metric to assess the hyporheic mixing. • Stream velocity, groundwater are the most dominant factors for hyporheic mixing. Hyporheic mixing plays a vital role in physical, biogeochemical, and thermal processes in river networks. While many studies have emphasized the role of streambed heterogeneity in hyporheic mixing processes, this study articulates the scale issues inherent in concentration, mixing, heterogeneity, and modeling approaches. It subsequently conducted simulations of hyporheic mixing in synthetic, heterogeneous, 2-D cross-sectional river beds based on prescribed hydraulic conductivity defined at the local-scale. It then investigated the flux variation distribution and the mixing zone under different degrees of heterogeneity and flow scenarios. Since the characterization of the heterogeneities in detail at the local scale is practically impossible, Monte Carlo simulation based on stochastic theory was used to demonstrate the hyporheic mixing under the large-scale control volume (macromixing). Afterward, a first-order stochastic analysis was undertaken to explore the relationship between local-scale flux variance distribution and the mixing zone under different heterogeneity and flow scenarios. The results of this study show that the flux variance in the streambed is an appropriate metric for assessing the magnitude of hyporheic mixing at all scales. Further, surface water velocity and upwelling groundwater are found to be the dominant controlling factors of the flux variance and in turn, the mixing process, followed by the streambed heterogeneity. In addition, it demonstrates that the hyporheic mixing process is significantly affected by the complex surface and groundwater circulation regimes and the stagnation zone under steady-state flow conditions. [ABSTRACT FROM AUTHOR]

• This paper introduces the concept of Traveling Pilot Points (TRIPS) for solving the categorical inverse problem • The TRIPS methodology combined with subspace methods is used to identify channel structures in a categorical aquifer system while honoring calibration and prior constraints • Tests on a synthetic example suggest that the TRIPS methodology has promise and could be tested on more complicated problems Categorical parameter distributions are common-place in hydrogeological systems consisting of geologic facies/categories with distinct properties, e.g., high-permeability channels embedded in a low-permeability matrix. Parameter estimation is difficult in such systems because the discontinuities in the parameter space hinder the inverse problem. Previous research in this area has been focused on the use of stochastic methods. In this paper, we present a novel approach based on Traveling Pilot points (TRIPS) combined with subspace parameter estimation methods to generate realistic categorical parameter distributions that honor calibration constraints (e.g., - measured water levels). In traditional implementations, aquifer properties (e.g., hydraulic conductivity) are estimated at fixed pilot point locations. In the TRIPS implementation, both the properties associated with the pilot points and their locations are estimated. Tikhonov regularization constraints are incorporated in the parameter estimation process to produce realistic parameter depictions. For a synthetic aquifer system, we solved the categorical inverse problem by combining the TRIPS methodology with two subspace methods: Null Space Monte Carlo (NSMC) and Posterior Covariance (PC). A posterior ensemble developed with the rejection sampling (RS) method is compared against the TRIPS ensembles. The comparisons indicated similarities between the various ensembles and to the reference parameter distribution. Between the two subspace methods, the NSMC method produced an ensemble with more variability than the PC method. These preliminary results suggest that the TRIPS methodology has promise and could be tested on more complicated problems. [ABSTRACT FROM AUTHOR]

• Heterogeneous aquifers are modeled with log-normal random conductivity fields. • Numerical schemes are tested on two-dimensional benchmark flow problems. • Code verification performed by comparison with analytical manufactured solutions. • Validation done through comparisons between MC statistics and first-order results. • Limited computational feasibility for exponentially correlated log-conductivity. This article presents numerical investigations on accuracy and convergence properties of several numerical approaches for simulating steady state flows in heterogeneous aquifers. Finite difference, finite element, discontinuous Galerkin, spectral, and random walk methods are tested on two-dimensional benchmark flow problems. Realizations of log-normal hydraulic conductivity fields are generated by Kraichnan algorithms in closed form as finite sums of random periodic modes, which allow direct code verification by comparisons with manufactured reference solutions. The quality of the methods is assessed for increasing number of random modes and for increasing variance of the log-hydraulic conductivity fields with Gaussian and exponential correlation. Experimental orders of convergence are calculated from successive refinements of the grid. The numerical methods are further validated by comparisons between statistical inferences obtained from Monte Carlo ensembles of numerical solutions and theoretical first-order perturbation results. It is found that while for Gaussian correlation of the log-conductivity field all the methods perform well, in the exponential case their accuracy deteriorates and, for large variance and number of modes, the benchmark problems are practically not solvable with reasonably large computing resources, for all the methods considered in this study. [ABSTRACT FROM AUTHOR]

• A methodological framework was developed to explore irrigation and drainage reduction under sources of uncertainty. • Monte Carlo analysis was used to address uncertain variations in soil and daily evapotranspiration. • We present four case studies with different uncertainty scenarios. • Water use and drainage can be reduced if a small risk of crop stress is accepted. • Certain irrigation strategy predictions advocate the importance of reduced uncertainty. Two thirds of human water use is linked to agricultural practices including crop irrigation. Furthermore, excess irrigation leads to drainage problems. For this reason, reduced irrigation strategies need to be implemented to protect water resources. However, low irrigation may lead to crop water stress. A fast and inexpensive way to predict the necessary amount of irrigation required is by a model-based approach. With this approach, it is possible to explore the relation between irrigation, crop water stress and drainage. However, parameter uncertainty can reduce prediction accuracy. Therefore, the aims of this research were: (1) to develop and test a methodology that allows the analysis of uncertainty sources in irrigation strategies (2) to identify how much irrigation can be reduced while maintaining a low risk of crop stress, and (3) to explore the influence of uncertainty in soil parameters and evapotranspiration on model predictions. Results from a realistic case considered in this study indicated that, while maintaining a low risk of crop stress (<1 %), it is possible to reduce drainage (by 88 %) and water use (22 %) for a conventional irrigation strategy. This reduction is dependent on the type of risk aversion strategy and is specific for a case scenario where variations are certain. [ABSTRACT FROM AUTHOR]

• Super-diffusion is affected differently by the thickness and width of hydrofacies. • Bi-peak super-diffusion is affected by the geometry of initial source at early time. • Bi-peak super-diffusion can be captured by multi-domain fractional-derivative model. Dissolved-phase contaminants experiencing enhanced diffusion (i.e., "super-diffusion") with a pronounced leading plume edge can pose risk for groundwater quality. The drivers for complex super-diffusion in geological media, however, are not fully understood. This study investigates the impacts of hydrofacies' mean lengths and the initial source geometry, motivated by a hydrofacies model built recently for the well-known MADE aquifer, on the spatial pattern of super-diffusion for two-dimensional alluvial aquifer systems. Monte Carlo simulations show that the bimodal velocity distribution, whose pattern is affected by the hydrofacies' mean lengths, leads to super-diffusion of solutes with a bi-peak plume snapshot in alluvial settings where advection dominates transport. A larger longitudinal mean length (i.e., width) for hydrofacies with high hydraulic conductivity (K) enhances the connectivity of preferential pathways, resulting in higher values in the bimodal velocity distribution and an enhanced leading front for the bi-peak plume snapshot, while the opposite impact is identified for the hydrofacies' vertical mean length (i.e., thickness) on the bi-peak super-diffusion. A multi-domain non-local transport model is then proposed, extending upon the concept of the distributed-order fractional derivative, to quantify the evolution of bi-peak super-diffusion due to differential advection and mobile-mobile mass exchange for solute particles moving in hydrofacies with distinct K. Results show that the bi-peak super-diffusion identified for the MADE site and perhaps the other similar aquifers, which is affected by the initial source geometry at an early stage and the thickness and width of high- K hydrofacies during all stages, can be quantified by the mobile-mobile fractional-derivative model. Porous medium dimensionality and stochastic model comparison are also discussed to further explore the nature of bi-peak super-diffusion in alluvial systems. [ABSTRACT FROM AUTHOR]

• Classical aquitard drainage model COMPAC utilized for a heterogeneous aquitard. • Geostatistical model used to deal with aquitard heterogeneity. • To interpret the heterogeneity from multi-extensometer data. • Comparison between geostatistical and geological models in fitting observation data. • Both synthetic and field application cases implemented. The classical aquitard drainage model COMPAC was used to simulate the deformation of a one-dimensional vertically heterogeneous aquitard (i.e. Heter-COMPAC). By coupling Heter-COMPAC with the quasi-linear geostatistical inversion approach, the vertical heterogeneities of hydraulic conductivity (K v), elastic specific storage (S ske ) and inelastic specific storage (S skp ) fields could be characterized with the availability of long-term multi-extensometer data. The methodology was first tested through a group of ten synthetic cases with randomly generated K v , S ske and S skp fields. Results of the synthetic cases revealed that a geostatistical model could characterize the variability of aquitard hydraulic parameter fields, and yields improved fits of simulated versus observed zone deformation than a geological model that treats each zone to be homogeneous. Subsequently, the methodology was applied to a research site situated in Changzhou city, Jiangsu Province, China, where long-term deformation behaviors of the strata within the aquifer-aquitard system have been monitored. Vertical heterogeneities of K v , S ske and S skp fields of the investigated aquitard at the site were characterized using the quasi-linear geostatistical approach. The correlation length of the three fields that yielded the best-quality fit was assessed to be approximately 50 m, and the fitting quality was slightly improved in comparison with that produced from calibrating a geological or zonation model. Through Monte Carlo analysis of aquitard deformation utilizing the inversed parameters and corresponding uncertainties, the investigated aquitard is estimated to have compacted −914.8 ± (42.6) mm before the rise in groundwater levels in adjoining aquifers. [ABSTRACT FROM AUTHOR]

• Propose a new stochastic multi-objective optimization algorithm (ε -MONMA). • Implement accurate uncertainty quantification of concentration using sparse PCE. • Achieve the obvious improvement of robustness of monitoring network design. • Save significant CPU time while guaranteeing the robustness of Pareto solutions. The robust optimization of groundwater quality monitoring network is subject to many conflicting objectives and high level of uncertainty in hydraulic conductivity. This study develops a two-stage stochastic optimization framework including the uncertainty quantification using a cheap-to-evaluate surrogate model and an improved epsilon multi-objective noisy memetic algorithm (ε -MONMA) for monitoring network design. The surrogate model based on sparse polynomial chaos expansion (PCE) is constructed to replace expensive simulation model in the uncertainty quantification of concentrations at the pre-defined monitoring locations for reducing huge computational cost. Additionally, the scenario discovery strategy using sparse PCE model is applied to filter a typical scenario set and the centroid of contaminant plume is used as the diversity metric, which avoids enumerating all possible contamination plumes caused by the uncertain K -field in the optimization. The proposed algorithm is then employed to solve stochastic management model to achieve robust monitoring design, indicating the insensitivity of monitoring design to plume uncertainty no matter which of the many possible scenarios becomes the true distribution of contamination under the true K -field. A synthetic aquifer considering uncertainty in hydraulic conductivity is designed to optimize monitoring network design. The Pareto-optimal solutions to the synthetic example are achieved under three of plume scenario sets defined at deterministic scenario (Scenario A0), Monte Carlo based scenario discovery (Scenario A1) and surrogate assisted scenario discovery (Scenario A2), respectively. Comprehensive analysis demonstrates that the monitoring design based on Scenario A2 outperforms either of the two designs based on Scenarios A0 and A1 in terms of the improvement of robustness of designs evaluated against the typical scenario set. Meanwhile, the performance of monitoring network deteriorates as the uncertainty of plume (noisy strength) increases, indicating the significance of reducing parameter uncertainty in groundwater monitoring design. The research findings show that the developed stochastic optimization framework is a computationally efficient and promising tool for multi-objective design of groundwater monitoring network under uncertainty. [ABSTRACT FROM AUTHOR]