Claus Haslauer

Abstract

Various sorption processes affect leaching of per- and polyfluoroalkyl substances (PFAS) such as PFOA and PFOS. The objectives of this study are to (1) compare rate-limited leaching in column and lysimeter experiments, (2) investigate the relevance of sorption to air--water interfaces (AWI), and (3) examine colloid-facilitated transport as a process explaining early experimental breakthrough. A continuum model (CM) with two-domain sorption is used to simulate equilibrium and rate-limited sorption. A random walk particle tracking (PT) model was developed and applied to analyze complex leaching characteristics. Results show that sorption parameters derived from column experiments underestimate long-term PFOA leaching in lysimeter experiments due to early depletion, suggesting that transformation of precursors contributes to the observed long-term leaching in the lysimeters (approximately 0.003 µg/kg/d PFOA). Both models demonstrate that sorption to AWI is the dominant retention mechanism for PFOS in lysimeter experiments, with retardation due to AWI being 3 (CM) to 3.7 (PT) times higher than retardation due to solid phase sorption. Notably, despite a simplified conception of AWI sorption, the PT results are closer to the observations. The PT simulations demonstrate possible colloid-facilitated transport at early time; however, results using substance-specific varying transport parameters align better with the observations, which should be equal if colloid-facilitated transport without additional kinetics is the sole mechanism affecting early breakthrough. Possibly, rate-limited sorption to AWI is relevant during the early stages of the lysimeter experiment. Our findings demonstrate that rate-limited sorption is less relevant for long-term leaching under field conditions compared to transformation of precursors and that sorption to AWI can be the dominant retention mechanism on contaminated sites. Moreover, they highlight the potential of random walk particle tracking as a practical alternative to continuum models for estimating the relative contributions of various retention mechanisms.

Abstract

The evaluation of PFAS immobilization performance in laboratory experiments, especially the long-term stability, is a challenge. To contribute to the development of adequate experimental procedures, the impact of experimental conditions on the leaching behavior was studied. Three experiments on different scales were compared: batch, saturated column, and variably saturated laboratory lysimeter experiments. The Infinite Sink (IS) test – a batch test with repeated sampling – was applied for PFAS for the first time. Soil from an agricultural field amended with paper-fiber biosolids polluted with various perfluoroalkyl acids (PFAAs; 655 μg/kg ∑18PFAAs) and polyfluorinated precursors (1.4 mg/kg ∑18precursors) was used as the primary material (N-1). Two types of PFAS immobilization agents were tested: treatment with activated carbon-based additives (soil mixtures: R-1 and R-2), and solidification with cement and bentonite (R-3). In all experiments, a chain-length dependent immobilization efficacy is observed. In R-3, the leaching of short-chain PFAAs was enhanced relative to N-1. In column and lysimeter experiments with R-1 and R-2, delayed breakthrough of short-chain PFAAs (C4) occurred (> 90 days; in column experiments at liquid-to-solid ratio (LS) > 30 L/kg) with similar temporal leaching rates suggesting that leaching in these cases was a kinetically controlled process. Observed differences between column and lysimeter experiments may be attributed to varying saturation conditions. In IS experiments, PFAS desorption from N-1, R-1, and R-2 is higher than in the column experiments (N-1: +44 %; R-1: +280 %; R-2: +162 %), desorption of short-chain PFAS occurred predominantly in the initial phase (< 14 days). Our findings demonstrate that sufficient operating times are essential in percolation experiments, e.g., in column experiments >100 days and LS > 30 L/kg. IS experiments may provide a faster estimate for nonpermanent immobilization. The comparison of experimental data from various experiments is beneficial to evaluate PFAS immobilization and to interpret leaching characteristics.

Abstract

Surfactant-enhanced in-situ chemical oxidation (S-ISCO) is an emerging innovative remediation technology for the treatment of dense non-aqueous phase liquids (DNAPLs). S-ISCO combines the solubilization of contaminants by means of surfactants with the chemical oxidation by an oxidizing agent, thus, potentially increasing the efficiency of the state-of-the-art ISCO technique. Scientific investigations are needed to enable the technology transfer for potential field applications based on the development of a remediation design under well-defined boundary conditions. For this purpose, experimental upscaling analyses were performed using the special infrastructure of the research facility for subsurface remediation (VEGAS). Batch tests showed that oxidation of the selected surfactant E-Mulse 3® (EM3) by activated persulfate (Na-PS) reduced the solubilization of the model contaminants 1,4-DCB, naphthalene, and PCE. As a consequence, the processes of contaminant solubilization and degradation were temporally and spatially separated in the developed remediation design. A proof of concept was provided by performing an S-ISCO medium-scale experiment (100 cm length, 70 cm height, 12.5 cm width), with 1,2-DCB as model DNAPL contaminant to be treated. A groundwater circulation well (GCW) was used to inject a 60 g/L Na-PS solution and to effectively mix the reagents. Sampling of the experiment's outflow and the soil material after treatment showed that neither rebound effects nor residual mass loadings on the soil material could be detected after termination of the S-ISCO treatment. To further evaluate the S-ISCO remediation design under field-like conditions, a large-scale S-ISCO experiment was conducted (6 m length, 3 m height, 1 m width), allowing for an extensive sampling campaign to monitor relevant processes. An efficient contaminant removal from the former source zone could be reached by surfactant solubilization, decreasing contaminant levels from initially over 2000 mg/L 1,2-DCB to final concentrations below 5 mg/L 1,2-DCB. The heterogeneously distributed contaminant degradation, implemented by a three-filter GCW, was attributed to density-induced migration processes that impeded an optimal reaction zone. A density-dependent numerical transport could qualitatively match the observations. By comparing different simulation scenarios, an adapted operation of the GCW was established that provides for a more efficient distribution of the density-influenced oxidant injection.

Abstract

Die großflächigen PFAS-Belastungen landwirtschaftlicher Flächen im Raum Baden-Baden / Rastatt mit per- und polyfluorierten Alkylsubstanzen (PFAS) haben einen direkten Einfluss auf ver-schiedenste Nutzer dieser Flächen sowie auf die Qualität des Grundwassers. Direkt betroffen sind neben den Landwirten auch Städte und Gemeinden, die durch die Kontami-nationen stadtplanerisch sehr eingeschränkt werden (eingeschränkte Ausweisung von Bauland) und deren Trinkwasserversorgung teilweise beeinträchtigt ist. Ebenso betroffen ist die Kiesindust-rie, die zum Abbau von Kiesen und Sanden den Oberboden abtragen (und ggf. entsorgen) muss. Ansätze zur Sanierung bzw. Umlagerung des belasteten Bodens haben sich auf Grund der chemi-schen Eigenschaften der PFAS sowie auf Grund der großflächigen Kontamination (>1200 ha) als ökonomisch nicht umsetzbar erwiesen. Daher wird vermehrt auf die Möglichkeit gesetzt, die PFAS in den Böden zu fixieren. Dies könnte direkt vor Ort in einem belasteten Boden („in-situ“) stattfin-den. In einem solchen Verfahren würde ein entsprechendes Reagenz auf den Boden aufgebracht und die (ggf. leicht veränderten) Böden könnten wieder ihre ursprüngliche Funktion wahrnehmen, zum Beispiel als landwirtschaftliche Nutzfläche oder als Garten. Weiterhin könnte der Boden abge-tragen und nach entsprechender Anreicherung mit Reagenzien und ggf. Stabilisatoren zum Bau von Erdbauwerken (z. B. Sicht-oder Lärmschutzwällen) verwendet werden. Falls der Boden größtenteils aus Sanden oder Kiesen besteht, ist auch eine Anwendung als Konstruktionsbeton denkbar. Ent-sprechend wurden neben dem unbehandelten Boden (N-1) vier verschiedene, auf N-1 basieren-de, Bodenmischungen untersucht. Bei R 1 und R-2 wurden aktivkohlebasierte Additive zur Immobi-lisierung der PFAS durch Erhöhung der Sorptionskapazität zugegeben. Bei R-3 wurden PFAS immo-bilisiert mit gleichzeitiger Reduzierung der Durchlässigkeit und bei R-4 sollten die PFAS durch Ver-wendung von N-1 als Zuschlagstoff in Konstruktionsbeton fixiert werden. Behandelte und unbehandelte Bodenproben wurden in Experimenten auf drei verschiedenen Skalen (Batch-Versuche, Säulenversuche, Lysimeter) und unter verschiedenen Bedingungen (ge-sättigt, variabel gesättigt) untersucht. Im Verlauf der Experimente wurde die PFAS-Konzentration im Eluat über die Zeit gemessen und mathematisch modelliert. Die gemessenen und modellierten Konzentrationszeitreihen bildeten die Basis für eine in der Zukunft mögliche Abschätzung der Ef-fektivität der Bodenbehandlungsmethoden. Ziel dieses Forschungsvorhabens war es, ein einfaches und kostengünstiges Verfahren zur experi-mentellen Überprüfung von Immobilisierungsmaßnahmen für PFAS zu entwickeln und bereitzu-stellen. Das Verfahren sollte, soweit möglich, auf bestehenden Methoden (DIN, CEN, …) basieren, wobei die Herausforderungen insbesondere darin bestanden, diese an die speziellen Stoffeigen-schaften der PFAS anzupassen und auch miteinander zu kombinieren. Der Vergleich der experimentellen Methoden war bei der Entwicklung einer Vorgehensweise ein zentraler Bestandteil dieses Forschungsvorhabens. Abweichende Elutionsdaten aus den verschie-denen Testverfahren können auf Einflüsse aus unterschiedlichen Prozessen hindeuten. Dazu gehö-ren Sorptions- und Transportprozesse der Einzelverbindungen, abiotische Transformationen, Bio-transformationen durch mikrobielle Aktivität, Interaktionen an Luft-Wasser-Grenzflächen und an-dere. Zusätzlich diente der Skalenvergleich dazu, die Anwendbarkeit der Einzelverfahren mit Ein-satzmöglichkeiten und Limitierungen zu bewerten. Die Entwicklung von Methoden zur Immobilisierung war nicht Ziel des Vorhabens. Dennoch können die im Rahmen der Methodenentwicklung eingesetzten Verfahrenskombinationen bewertet wer-den. Um eine direkte Umsetzung in die Praxis und Akzeptanz des Verfahrens sicherzustellen, 1. wurde das Vorhaben durch einen Begleitkreis beraten, in dem neben Vertretern der Be-hörden (RPKA, LUBW, UM) auch betroffene Städte und die Kiesindustrie vertreten waren, 2. wurde den Betroffenen die Möglichkeit gegeben, Immobilisierungsmethoden vorzuschla-gen, anhand derer die Nachweisverfahren zu entwickeln waren; 3. wurden die Behörden in die Auswahl der Standorte/ Modellböden eingebunden.

Abstract

The spatial distribution of hydraulic properties in the subsurface controls groundwater flow and solute transport. However, many approaches to modeling these distributions do not produce geologically realistic results and/or do not model the anisotropy of hydraulic conductivity caused by bedding structures in sedimentary deposits. We have developed a flexible object‐based package for simulating hydraulic properties in the subsurface—the Hydrogeological Virtual Realities (HyVR) simulation package. This implements a hierarchical modeling framework that takes into account geological rules about stratigraphic bounding surfaces and the geometry of specific sedimentary structures to generate realistic aquifer models, including full hydraulic‐conductivity tensors. The HyVR simulation package can create outputs suitable for standard groundwater modeling tools (e.g., MODFLOW), is written in Python, an open‐source programming language, and is openly available at an online repository. This paper presents an overview of the underlying modeling principles and computational methods, as well as an example simulation based on the Macrodispersion Experiment site in Columbus, Mississippi. Our simulation package can currently simulate porous media that mimic geological conceptual models in fluvial depositional environments, and that include fine‐scale heterogeneity in distributed hydraulic parameter fields. The simulation results allow qualitative geological conceptual models to be converted into digital subsurface models that can be used in quantitative numerical flow‐and‐transport simulations, with the aim of improving our understanding of the influence of geological realism on groundwater flow and solute transport.

Abstract

We analyse two datasets of hydraulic conductivity (K) from the MAcroDispersion Experiment (MADE) site, one measured by direct-push injection logging (DPIL) and the other by flowmeter profiling. The analysis is performed using copula techniques which do not rely on the assumption of multivariate Gaussianity and provide a means to characterise differing degrees of spatial dependence in different quantiles of the K distribution. This characterisation provides better insights into the similarities and differences between the two datasets. In addition to the marginal distributions and the traditional two-point geostatistical measures, copula-based bivariate rank correlation and asymmetry measures are analysed and compared. Furthermore, the parameter estimates obtained by likelihood estimation using n-point theoretical models are analysed. This analysis confirms the similarity of the spatial dependence of K between the two datasets in terms of their marginal distributions and bivariate measures, particularly in the vertical direction. We demonstrate clear indications of the existence of non-Gaussian spatial dependence structures of K at this site. We were able to improve the estimation of the K distribution by taking into account either non-Gaussianity or a censoring threshold, which are expected to lead to a more realistic description of processes that are dependent on K.

Abstract

This paper presents a methodology to predict the shape of solute breakthrough curves in heterogeneous aquifers at early times and/or under high degrees of heterogeneity, both cases in which the classical macrodispersion theory may not be applicable. The methodology relies on the observation that breakthrough curves in heterogeneous media are generally well described by lognormal distributions, and mean breakthrough times can be predicted analytically. The log‐variance of solute arrival is thus sufficient to completely specify the breakthrough curves, and this is calibrated as a function of aquifer heterogeneity and dimensionless distance from a source plane by means of Monte Carlo analysis and statistical regression. Using the ensemble of simulated groundwater flow and solute transport realizations employed to calibrate the predictive regression, reliability estimates for the prediction are also developed. Additional theoretical contributions include heuristics for the time until an effective macrodispersion coefficient becomes applicable, and also an expression for its magnitude that applies in highly heterogeneous systems. It is seen that the results here represent a way to derive continuous time random walk transition distributions from physical considerations rather than from empirical field calibration.

Abstract

Often, the primary variable of interest can be measured only rarely and/or indirectly. Hence, it is desired to use secondary correlated data to improve the estimation of the primary variable. This paper extends the Gaussian copula-based geostatistical approach for interpolation to include both real-valued primary and secondary data. Even more, multiple types of real-valued secondary data and categorical exhaustive secondary information were incorporated and the associated benefits analysed. The performance of the proposed inclusion of secondary data and information was compared to benchmark geostatistical methods (Ordinary Kriging, co-Kriging, external drift Kriging, and copula-based interpolation of the primary variable alone) by cross-validation and split sampling, with varying compositions of primary and secondary variables. The proposed method was tested for several groundwater quality parameters and the results show that a) the joint copula-based method outperforms co-Kriging in all quality measures; (b) physically impossible estimates (i.e., negative concentrations) never occur; (c) copula-based methods outperform Kriging methods in the quantification of uncertainty and result in more realistic spatial patterns of uncertainty. Joint methods lead to better results in cases when the primary variable is available at fewer locations than the secondary variable (i.e., undersampled case) and when the variables are meaningfully related. In copula-based spatial dependence models that are constructed in probability space, detrimental effects of non-normal (here: bi-modal) marginal distributions on the joint distribution and dissimilar measurement scales of the primary and secondary variables are prevented. The proposed method offers an efficient and non-linear alternative to co-Kriging.

Abstract

The spatial variability of hydraulic conductivity is known to have a strong impact on solute spreading and mixing. In most investigations, its local anisotropy has been neglected. Recent studies have shown that spatially varying orientation in sedimentary anisotropy can lead to twisting flow enhancing transverse mixing, but most of these studies used geologically implausible geometries. We use an object‐based approach to generate stacked scour‐pool structures with either isotropic or anisotropic filling which are typically reported in glacial outwash deposits. We analyze how spatially variable isotropic conductivity and variation of internal anisotropy in these features impacts transverse plume deformation and both longitudinal and transverse spreading and mixing. In five test cases, either the scalar values of conductivity or the spatial orientation of its anisotropy is varied between the scour‐pool structures. Based on 100 random configurations, we compare the variability of velocity components, stretching and folding metrics, advective travel‐time distributions, one and two‐particle statistics in advective‐dispersive transport, and the flux‐related dilution indices for steady state advective‐dispersive transport among the five test cases. Variation in the orientation of internal anisotropy causes strong variability in the lateral velocity components, which leads to deformation in transverse directions and enhances transverse mixing, whereas it hardly affects the variability of the longitudinal velocity component and thus longitudinal spreading and mixing. The latter is controlled by the spatial variability in the scalar values of hydraulic conductivity. Our results demonstrate that sedimentary anisotropy is important for transverse mixing, whereas it may be neglected when considering longitudinal spreading and mixing.

Abstract

This paper demonstrates quantitative reasoning to separate the dataset of spatially distributed variables into different entities and subsequently characterize their geostatistical properties, properly. The main contribution of the paper is a statistical based algorithm that matches the manual distinction results. This algorithm is based on measured data and is generally applicable. In this paper, it is successfully applied at two datasets of saturated hydraulic conductivity (K) measured at the Borden (Canada) and the Lauswiesen (Germany) aquifers. The boundary layer was successfully delineated at Borden despite its only mild heterogeneity and only small statistical differences between the divided units. The methods are verified with the more heterogeneous Lauswiesen aquifer K data-set, where a boundary layer has previously been delineated. The effects of the macro- and the microstructure on solute transport behaviour are evaluated using numerical solute tracer experiments. Within the microscale structure, both Gaussian and non-Gaussian models of spatial dependence of K are evaluated. The effects of heterogeneity both on the macro- and the microscale are analysed using numerical tracer experiments based on four scenarios: including or not including the macroscale structures and optimally fitting a Gaussian or a non-Gaussian model for the spatial dependence in the micro-structure. The paper shows that both micro- and macro-scale structures are important, as in each of the four possible geostatistical scenarios solute transport behaviour differs meaningfully.

Abstract

This paper demonstrates a maximum likelihood (ML)-based approach to derive representative (“best guess”) contaminant concentrations from data with censored values (e.g., less than the detection limit). The method represents an advancement over existing techniques because it is capable of estimating the proportion of measurements that are true zeros and incorporating varying levels of censorship (e.g., sample specific detection limits, changes through time in method detection). The ability of the method to estimate the proportion of true zeros is validated using precipitation data. The stability and flexibility of the method are demonstrated with stochastic simulation, a sensitivity analysis, and unbiasedness analysis including varying numbers of significant digits. A key aspect of this paper is the application of the statistical analysis to real site rock core contaminant concentration data collected within a plume at two locations using high resolution depth-discrete sampling. Comparison of the representative values for concentrations at each location along the plume center-line shows a larger number of true zeros and generally lower concentrations at the downgradient location according to the conceptual site model, leading to improved estimates of attenuation with distance and/or time and associated confidence; this is not achievable using deterministic methods. The practical relevance of the proposed method is that it provides an improved basis for evaluating change (spatial, temporal, or both) in environmental systems.

Abstract

Droughts are serious natural hazards, especially in semi-arid regions. They are also difficult to characterize. Various summary metrics representing the dryness level, denoted drought indices, have been developed to quantify droughts. They typically lump meteorological variables and can thus directly be computed from the outputs of regional climate models in climate-change assessments. While it is generally accepted that drought risks in semi-arid climates will increase in the future, quantifying this increase using climate model outputs is a complex process that depends on the choice and the accuracy of the drought indices, among other factors. In this study, we compare seven meteorological drought indices that are commonly used to predict future droughts. Our goal is to assess the reliability of these indices to predict hydrological impacts of droughts under changing climatic conditions at the annual timescale. We simulate the hydrological responses of a small catchment in northern Spain to droughts in present and future climate, using an integrated hydrological model calibrated for different irrigation scenarios. We compute the correlation of meteorological drought indices with the simulated hydrological time series (discharge, groundwater levels, and water deficit) and compare changes in the relationships between hydrological variables and drought indices. While correlation coefficients linked with a specific drought index are similar for all tested land uses and climates, the relationship between drought indices and hydrological variables often differs between present and future climate. Drought indices based solely on precipitation often underestimate the hydrological impacts of future droughts, while drought indices that additionally include potential evapotranspiration sometimes overestimate the drought effects. In this study, the drought indices with the smallest bias were the rainfall anomaly index, the reconnaissance drought index, and the standardized precipitation evapotranspiration index. However, the efficiency of these drought indices depends on the hydrological variable of interest and the irrigation scenario. We conclude that meteorological drought indices are able to identify years with restricted water availability in present and future climate. However, these indices are not capable of estimating the severity of hydrological impacts of droughts in future climate. A well-calibrated hydrological model is necessary in this respect.

Abstract

Study region The Lerma catchment, a small (7.3 km2) sub-catchment of the Ebro Basin in northern Spain. Study focus The Lerma catchment underwent a monitored transition to irrigated agriculture, using water from outside the catchment, between 2006 and 2008. This transition has successfully been simulated using the partial-differential-equation-based model HydroGeoSphere, simulating coupled evapotranspiration, surface water, and groundwater flow in the catchment. We use the calibrated model to study how irrigation practices influence the response of the Lerma catchment to the climate change projected for northern Spain. We consider four different irrigation scenarios: no irrigation, present irrigation, climate-adapted irrigation with current crops, and adapted irrigation for crops requiring less water. The climate scenarios are based on four regional climate models and two downscaling methods. New hydrological insight The simulated catchment responses to climate change show clear differences between the irrigation scenarios. In future climate, groundwater levels and base flows decrease more when irrigation is present than without irrigation, because groundwater levels and base flow in present climate are already at low levels without irrigation. In contrast, annual peak discharges increase more in non-irrigated cases than in irrigated cases. Irrigation increases water availability and an associated rise in potential evapotranspiration results in higher actual evapotranspiration during summer. In non-irrigated scenarios, by contrast, actual evapotranspiration in summer is controlled by precipitation and thus decreases in future climate.

Abstract

Hydraulic tomography (HT) is a method for resolving the spatial distribution of hydraulic parameters to some extent, but many details important for solute transport usually remain unresolved. We present a methodology to improve solute transport predictions by combining data from HT with the breakthrough curve (BTC) of a single forced‐gradient tracer test. We estimated the three dimensional (3D) hydraulic‐conductivity field in an alluvial aquifer by inverting tomographic pumping tests performed at the Hydrogeological Research Site Lauswiesen close to Tübingen, Germany, using a regularized pilot‐point method. We compared the estimated parameter field to available profiles of hydraulic‐conductivity variations from direct‐push injection logging (DPIL), and validated the hydraulic‐conductivity field with hydraulic‐head measurements of tests not used in the inversion. After validation, spatially uniform parameters for dual‐domain transport were estimated by fitting tracer data collected during a forced‐gradient tracer test. The dual‐domain assumption was used to parameterize effects of the unresolved heterogeneity of the aquifer and deemed necessary to fit the shape of the BTC using reasonable parameter values. The estimated hydraulic‐conductivity field and transport parameters were subsequently used to successfully predict a second independent tracer test. Our work provides an efficient and practical approach to predict solute transport in heterogeneous aquifers without performing elaborate field tracer tests with a tomographic layout.

Abstract

Partial-differential-equation based integrated hydrological models are now regularly used at catchment scale. They rely on the shallow water equations for surface flow and on the Richards’ equations for subsurface flow, allowing a spatially explicit representation of properties and states. However, these models usually come at high computational costs, which limit their accessibility to state-of-the-art methods of parameter estimation and uncertainty quantification, because these methods require a large number of model evaluations. In this study, we present an efficient model calibration strategy, based on a hierarchy of grid resolutions, each of them resolving the same zonation of subsurface and land-surface units. We first analyze which model outputs show the highest similarities between the original model and two differently coarsened grids. Then we calibrate the coarser models by comparing these similar outputs to the measurements. We finish the calibration using the fully resolved model, taking the result of the preliminary calibration as starting point. We apply the proposed approach to the well monitored Lerma catchment in North-East Spain, using the model HydroGeoSphere. The original model grid with 80,000 finite elements was complemented with two other model variants with approximately 16,000 and 10,000 elements, respectively. Comparing the model results for these different grids, we observe differences in peak discharge, evapotranspiration, and near-surface saturation. Hydraulic heads and low flow, however, are very similar for all tested parameter sets, which allows the use of these variables to calibrate our model. The calibration results are satisfactory and the duration of the calibration has been greatly decreased by using different model grid resolutions.

Abstract

A transformation of a Gaussian random field results in a change of the spatial dependence. In simple terms, the range and the shape of a variogram are different between an underlying Gaussian and a transformed Gaussian field. There is a relationship between the underlying and the transformed spatial dependence. This paper shows how this relationship can be expressed analytically. Rather than generating multidimensional random fields and conducting spatial statistical analysis, we develop an accurate and efficient approach based on a unique mapping of the correlation coefficients of the original multi‐Gaussian fields to the transformed correlation coefficients to evaluate the spatial correlation of transformed non‐Gaussian random fields for any type of geostatistical parameterization. Such a mapping can also yield accurate estimation of the spatial correlation of the underlying Gaussian field given the spatial correlation of the transformed field. Results indicate that (1) a nonlinear transformation of spatially distributed fields usually changes the spatial dependence structure; and (2) the relationship between the dependence structures of the underlying and the transformed field can be expressed analytically, and it is sufficient to do this in one dimension. We use the developed approach to investigate the change of correlations of connected random fields generated by the absolute‐value transformation. Results show (1) the correlation lengths of the underlying Gaussian fields are 1.67 and 2.64 times of those of transformed non‐Gaussian fields for Gaussian and exponential covariance models, respectively; (2) the anisotropic ratio does not change; and (3) the anticorrelation in hole‐effect correlation models disappear.