Estimating Natural Attenuation Rate Constants Using a Fuzzy Framework

Fuzzy set theoretic approaches provide convenient tools to quantify subjective information and characterize the decision-maker's preferences with minimal data. The estimation of natural attenuation and degradation rates, using the method of Buschek and Alcantar (1995), while pragmatic, is subject to significant imprecision due to mathematical simplifications and site complexities. In this paper, two fuzzy approaches, namely fuzzy arithmetic and fuzzy regression, are used to characterize the variability in the estimated degradation and attenuation rates. The variability in the input parameters can be characterized using membership functions that characterize the decision-maker's perception of likely values. The choice of the membership function for critical inputs is seen to affect the variability in the estimated outputs. Similarly, the decision-maker's belief related to the compatibility of the steady-state model to represent the observed plume behavior at the site can also be quantified using a compatibility criterion. Sensitivity studies carried out using the fuzzy-based estimation methodology are extremely useful to assess how differences in the decision-makers'preferences will affect the estimated rate constants and associated variability. As such, the proposed methodology is of high value during negotiations related to monitored natural attenuation.     

A Practical Modeling Framework for Non‐Fickian Transport and Multi‐Species Sequential First‐Order Reaction

Many studies indicate that small‐scale heterogeneity and/or mobile–immobile mass exchange produce transient non‐Fickian plume behavior that is not well captured by the use of the standard, deterministic advection‐dispersion equation (ADE). An extended ADE modeling framework is presented here that is based on continuous time random walk theory. It can be used to characterize non‐Fickian transport coupled with simultaneous sequential first‐order reactions (e.g., biodegradation or radioactive decay) for multiple degrading contaminants such as chlorinated solvents, royal demolition explosive, pesticides, and radionuclides. To demonstrate this modeling framework, new transient analytical solutions are derived and are inverted in Laplace space. Closed‐form, steady‐state, multi‐species analytical solutions are also derived for non‐Fickian transport in highly heterogeneous aquifers with linear sorption–desorption and matrix diffusion for use in spreadsheets. The solutions are general enough to allow different degradation rates for the mobile and immobile zones. The transient solutions for multi‐species transport are applied to examine the effects of source remediation on the natural attenuation of downgradient plumes of both parent and degradation products in highly heterogeneous aquifers. Results for representative settings show that the use of the standard, deterministic ADE can over‐estimate cleanup rates and under‐predict the cleanup timeframe in comparison to the extended ADE analytical model. The modeling framework and calculations introduced here are also applied for a 30 year groundwater cleanup program at a site in Palm Bay, Florida. The simulated plume concentrations using the extended ADE exhibited agreement with observed long concentration tails of trichloroethene, cis 1,2 DCE, and VC that remained above cleanup goals.     

Modeling Vapor Migration for Estimating the Time to Reach Steady State Conditions

The design and planning of soil vapor sampling for vapor intrusion assessment require an estimate of the time for vapor migration from the contamination source to reach steady state prior to vapor sampling and analysis for volatile organic compounds (VOCs). This study presents the model derivation, analytical solutions, as well as the assumptions and limitations of a one-dimensional VOC vapor transport model based on diffusion in porous media and equilibrium partitioning of VOCs in solid, aqueous, and vapor phases. The model assumes a finite domain with boundary conditions that represent the scenarios of vapor migration in the real environment. The derivation of the conceptual model is presented along with its practical use and implications as illustrated through case examples. Consideration of the upper (or exit) boundary condition along with the distance between the source and the applicable boundary, rather than the distance from the source to the measurement point, are shown to be critical in the time estimates as compared to an expression typically used and cited in guidance documents. The study reveals the importance of defining a conceptual model and relevant boundaries in assessing near steady state conditions, and suggests a tiered approach in refining the estimate with increasing level of effort for practical applications in vapor assessment.     

Estimating depth‐averaged velocities in rough ­channels

Profiles of streamwise velocity obtained from North Boulder Creek, Colorado, typically are non‐logarithmic in form and exhibit the strong influence of form drag associated with coarse bed roughness. The spatially averaged profile is consistent with recent theoretical profile forms suggested for rough channels that are based on a partitioning of the total stress between a fluid part and a part associated with form drag on bed particles. Estimates of local depth‐averaged velocity using algorithms that are based on several measurements in the flow column improve with explicit Riemann averaging, versus simple averaging, of the measurements. Estimates based on a single‐point measurement at 0·6 of the flow depth, assuming a logarithmic or approximately logarithmic velocity profile, are the least reliable. Copyright © 2000 John Wiley & Sons, Ltd.     

Estimating daily inflows of large lakes using a water‐balance‐based runoff coefficient scaling approach

Daily river inflow time series are highly valuable for water resources and water environment management of large lakes. However, the availability of continuous inflow data for large lakes is still relatively limited, especially for large lakes situated within humid plain regions with tens or even hundreds of tributaries. In this study, we choose the fifth largest freshwater Lake Chaohu in China as our study area to introduce a new approach to reconstruct historical daily inflows at ungauged subcatchments of large lakes. This approach makes use of water level, lake surface rainfall, evaporation from the lake, and catchment rainfall observations. Rainfall–runoff relationship at a reference catchment was analysed to select rainfall input and estimate run‐off coefficient firstly, and the run‐off coefficient was then transferred to ungauged subcatchments to initially estimate daily inflows. Run‐off coefficient was scaled to adjust daily inflows at ungauged subcatchments according to water balance of the lake. This approach was evaluated using sparsely measured inflows at eight subcatchments of Lake Chaohu and compared with the commonly used drainage area ratio method. Results suggest that the inflow time series reconstructed from this approach consistent well to corresponding observations, with mean R² and Nash–Sutcliffe efficiency values of 0.69 and 0.6, respectively. This approach outperforms drainage area ratio method in terms of mean R² and Nash–Sutcliffe efficiency values. Accuracy of this approach holds well when the number of water‐level station being used decreased from four to one.     

Estimating field‐saturated soil hydraulic conductivity by a simplified Beerkan infiltration experiment

Field‐saturated soil hydraulic conductivity, K_fs, is highly variable. Therefore, interpreting and simulating hydrological processes, such as rainfall excess generation, need a large number of K_fs data even at the plot scale. Simple and reasonably rapid experiments should be carried out in the field. In this investigation, a simple infiltration experiment with a ring inserted shortly into the soil and the estimation of the so‐called α* parameter allowed to obtain an approximate measurement of K_fs. The theoretical approach was tested with reference to 149 sampling points established on Burundian soils. The estimated K_fs with the value of first approximation of α* for most agricultural field soils (α* = 0.012 mm^?1) differed by a practically negligible maximum factor of two from the saturated conductivity obtained by the complete Beerkan Estimation of Soil Transfer parameters (BEST) procedure for soil hydraulic characterization. The measured infiltration curve contained the necessary information to obtain a site‐specific prediction of α*. The empirically derived α* relationship gave similar results for K_fs (mean = 0.085 mm s^?1; coefficient of variation (CV) = 71%) to those obtained with BEST (mean = 0.086 mm s^?1; CV = 67%), and it was also successfully tested with reference to a few Sicilian sampling points, since it yielded a mean and a CV of K_fs (0.0094 mm s^?1 and 102%, respectively) close to the values obtained with BEST (mean = 0.0092 mm s^?1; CV = 113%). The developed method appears attractive due to the extreme simplicity of the experiment. Copyright © 2012 John Wiley & Sons, Ltd.     

Discrete Element Modeling of Stress and Strain Evolution Within and Outside a Depleting Reservoir

Stress changes within and around a depleting petroleum reservoir can lead to reservoir compaction and surface subsidence, affect drilling and productivity of oil wells, and influence seismic waves used for monitoring of reservoir performance. Currently modeling efforts are split into more or less coupled geomechanical (normally linearly elastic), fluid flow, and geophysical simulations. There is evidence (from e.g. induced seismicity) that faults may be triggered or generated as a result of reservoir depletion. The numerical technique that most adequately incorporates fracture formation is the DEM (Discrete Element Method). This paper demonstrates the feasibility of the DEM (here PFC; Particle Flow Code) to handle this problem. Using an element size of 20 m, 2-D and 3-D simulations have been performed of stress and strain evolution within and around a depleting reservoir. Within limits of elasticity, the simulations largely reproduce analytical predictions; the accuracy is however limited by the element size. When the elastic limit is exceeded, faulting is predicted, particularly near the edge of the reservoir. Simulations have also been performed to study the activation of a pre-existing fault near a depleting reservoir.     

Analysis and performance of a predictor‐multicorrector Time Discontinuous Galerkin method in non‐linear elastodynamics

A predictor‐multicorrector implementation of a Time Discontinuous Galerkin method for non‐linear dynamic analysis is described. This implementation is intended to limit the high computational expense typically required by implicit Time Discontinuous Galerkin methods, without degrading their accuracy and stability properties. The algorithm is analysed with reference to conservative Duffing oscillators for which closed‐form solutions are available. Therefore, insight into the accuracy and stability properties of the predictor‐multicorrector algorithm for different approximations of non‐linear internal forces is gained, showing that the properties of the underlying scheme can be substantially retained. Finally, the results of representative numerical simulations relevant to Duffing oscillators and to a stiff spring pendulum discretized with finite elements illustrate the performance of the numerical scheme and confirm the analytical estimates. Copyright © 2002 John Wiley & Sons, Ltd.     

Time lapse structure‐from‐motion photogrammetry for continuous geomorphic monitoring

Recent advances are made in earth surface reconstruction with high spatial resolution due to SfM photogrammetry. High flexibility of data acquisition and high potential of process automation allows for a significant increase of the temporal resolution, as well, which is especially interesting to assess geomorphic changes. Two case studies are presented where 4D reconstruction is performed to study soil surface changes at 15 seconds intervals: (a) a thunderstorm event is captured at field scale and (b) a rainfall simulation is observed at plot scale. A workflow is introduced for automatic data acquisition and processing including the following approach: data collection, camera calibration and subsequent image correction, template matching to automatically identify ground control points in each image to account for camera movements, 3D reconstruction of each acquisition interval, and finally applying temporal filtering to the resulting surface change models to correct random noise and to increase the reliability of the measurement of signals of change with low intensity. Results reveal surface change detection with cm‐ to mm‐accuracy. Significant soil changes are measured during the events. Ripple and pool sequences become obvious in both case studies. Additionally, roughness changes and hydrostatic effects are apparent along the temporal domain at the plot scale. 4D monitoring with time‐lapse SfM photogrammetry enables new insights into geomorphic processes due to a significant increase of temporal resolution. Copyright © 2017 John Wiley & Sons, Ltd.     

Estimating daily lake evaporation from biweekly energy‐budget data

Estimates of daily lake evaporation based on energy‐budget data are poor because of large errors associated with quantifying change in lake heat storage over periods of less than about 10 days. Energy‐budget evaporation was determined during approximately biweekly periods at a northern Minnesota, USA, lake for 5 years. Various combinations of shortwave radiation, air temperature, wind speed, lake‐surface temperature, and vapour‐pressure difference were related to energy‐budget evaporation using linear‐regression models in an effort to determine daily evaporation without requiring the heat‐storage term. The model that combined the product of shortwave radiation and air temperature with the product of vapour‐pressure difference and wind speed provided the second best fit based on statistics but provided the best daily data based on comparisons with evaporation determined with the eddy‐covariance method. Best‐model daily values ranged from ?0.6 to 7.1 mm/day over a 5‐year period. Daily averages of best‐model evaporation and eddy‐covariance evaporation were nearly identical for all 28 days of comparisons with a standard deviation of the differences between the two methods of 0.68 mm/day. Best‐model daily evaporation also was compared with two other evaporation models, Jensen–Haise and a mass‐transfer model. Best‐model daily values were substantially improved relative to Jensen–Haise and mass‐transfer values when daily values were summed over biweekly energy‐budget periods for comparison with energy‐budget results.     

Estimating non‐linear site response by single period approximation

Site effects characterize the filtering mechanisms within the soil sedimentary layers overlying bedrock. In regions of high seismicity such as California where strong motion records are relatively abundant, site coefficients can be developed by regression of recorded ground shaking parameters. In regions of low‐to‐moderate seismicity or of high seismicity but with a paucity of recorded strong motion data, such empirical models cannot be obtained in the same way. This study describes the theoretical development of a simple, rational manual procedure to calculate site coefficients, based on a single period approximation (SPA), and to construct displacement response spectra (RSD) for soil sites. The proposed simplified model, which takes into account the non‐linear behaviour of soil that is dependent on the level of shaking, impedance contrast at the soil–bedrock interface and the plasticity of soil material, has been verified by comparison with results obtained from non‐linear shear wave analyses and data recorded during the 1994 Northridge earthquake. The proposed model is believed to be a convenient tool for calculating non‐linear site responses and constructing site‐specific response spectra, which has the potential of being incorporated into code provisions. Copyright © 2006 John Wiley & Sons, Ltd.     

Modeling of a large‐scale magneto‐rheological damper for seismic hazard mitigation. Part II: Semi‐active mode

A magneto‐rheological (MR) damper is a semi‐active device where the damper force capacity is controlled by varying the input current into the damper. In this paper, the dynamics of MR dampers associated with variable current input is studied. Electromagnetic theory is used to model the dynamics of an MR damper including the eddy current effect and the nonlinear hysteretic behavior of damper material magnetization. A nonlinear differential equation that relates the input current to the damper with a constant equivalent current is proposed. The nonlinear differential equation is combined with the Maxwell Nonlinear Slider (MNS) model to create the variable current MNS model to predict the damper force under variable input current and random damper displacement loading. The model is evaluated by comparing the predicted response of a large‐scale MR damper to the measured damper response from experiments. The experiments include a real‐time hybrid simulation of a 3‐story building structure with a large‐scale MR damper subjected to the design earthquake. The exceptional agreement observed between the predicted and experimental results illustrate the robustness and the accuracy of the variable current MNS model. Copyright © 2012 John Wiley & Sons, Ltd.     

A Coupled Groundwater–Surface Water Modeling Framework for Simulating Transition Zone Processes

There is an identified need for fully representing groundwater–surface water transition zone (i.e., the sediment zone that connects groundwater and surface water) processes in modeling fate and transport of contaminants to assist with management of contaminated sediments. Most existing groundwater and surface water fate and transport models are not dynamically linked and do not consider transition zone processes such as bioturbation and deposition and erosion of sediments. An interface module is developed herein to holistically simulate the fate and transport by coupling two commonly used models, Environmental Fluid Dynamics Code (EFDC) and SEAWAT, to simulate surface water and groundwater hydrodynamics, while providing an enhanced representation of the processes in the transition zone. Transition zone and surface water contaminant processes were represented through an enhanced version of the EFDC model, AQFATE. AQFATE also includes SEDZLJ, a state‐of‐the‐science surface water sediment transport model. The modeling framework was tested on a published test problem and applied to evaluate field‐scale two‐ and three‐dimensional contaminant transport. The model accurately simulated concentrations of salinity from a published test case. For the field‐scale applications, the model showed excellent mass balance closure for the transition zone and provided accurate simulations of all transition zone processes represented in the modeling framework. The model predictions for the two‐dimensional field case were consistent with site‐specific observations of contaminant migration. This modeling framework represents advancement in the simulation of transition zone processes and can help inform risk assessment at sites where contaminant sources from upland areas have the potential to impact sediments and surface water.     

Applying a Regional Transport Modeling Framework to Manage Nitrate Contamination of Groundwater

Regional nitrate contamination in groundwater is a management challenge involving multisector benefits. There is always conflict between restricting anthropogenic activities to protect groundwater quality and prioritizing economic development, especially in productive agriculture dominated areas. To mitigate the nitrate contamination in groundwater, it is necessary to develop management alternatives that simultaneously support environmental protection and sustainable economic development. A regional transport modeling framework is applied to evaluate nitrate fate and transport in the Dagu Aquifer, a shallow sandy aquifer that supplies drinking water and irrigation water for a thriving agricultural economy in Shandong Province in east coastal China. The aquifer supports intensive high-value vegetable farms and nitrate contamination is extensive. Detailed land-use information and fertilizer use data were compiled and statistical approaches were employed to analyze nitrogen source loadings and the spatiotemporal distribution of nitrate in groundwater to support model construction and calibration. The evaluations reveal that the spatial distribution and temporal trends of nitrate contamination in the Dagu Aquifer are driven by intensive fertilization and vertical water exchange, the dominant flow pattern derived from intensive agricultural pumping and irrigation. The modeling framework is employed to assess the effectiveness of potentially applicable management alternatives. The predictive results provide quantitative comparisons for the trend and extent of groundwater quality mitigation under each scenario. Recommendations are made for measures that can both improve groundwater quality and sustain productive agricultural development.     

Modeling Arsenic Sorption in the Subsurface with a Dual‐Site Model

Arsenic is a well‐known groundwater contaminant that causes toxicological and carcinogenic effects in humans. Predicting the transport of arsenic in the subsurface is often problematic because of its complex sorption characteristics. Numerous researchers have reported that arsenic sorption on soil material is initially fast and then subsequently slow. A dual‐site numerical sorption model was previously developed to describe arsenic desorption from arsenic‐contaminated soils in batch experiments in terms of two different release mechanisms. Experiments involving synthetic acid rain leaching of four arsenic‐contaminated soil columns were performed to verify the dual‐site numerical sorption model in the context of one‐dimensional vertical transport. The fitted models successfully simulated the signature long tailings and the two‐stage arsenic leaching patterns for all four soil columns. The dual‐site sorption model was incorporated within the general solute transport simulation code Modular Three‐Dimensional Multispecies (MT3DMS), version 5.10. The resulting version was named MT3DDS and is available for public access. This experimental study has shown that MT3DDS is capable of simulating phase redistribution during transport, and thus provides a new numerical tool for simulating arsenic transport in the subsurface.     

Estimating azimuthal stress‐induced P‐wave anisotropy from S‐wave anisotropy using sonic log or vertical seismic profile data

Most sedimentary rocks are anisotropic, yet it is often difficult to accurately incorporate anisotropy into seismic workflows because analysis of anisotropy requires knowledge of a number of parameters that are difficult to estimate from standard seismic data. In this study, we provide a methodology to infer azimuthal P‐wave anisotropy from S‐wave anisotropy calculated from log or vertical seismic profile data. This methodology involves a number of steps. First, we compute the azimuthal P‐wave anisotropy in the dry medium as a function of the azimuthal S‐wave anisotropy using a rock physics model, which accounts for the stress dependency of seismic wave velocities in dry isotropic elastic media subjected to triaxial compression. Once the P‐wave anisotropy in the dry medium is known, we use the anisotropic Gassmann equations to estimate the anisotropy of the saturated medium. We test this workflow on the log data acquired in the North West Shelf of Australia, where azimuthal anisotropy is likely caused by large differences between minimum and maximum horizontal stresses. The obtained results are compared to azimuthal P‐wave anisotropy obtained via orthorhombic tomography in the same area. In the clean sandstone layers, anisotropy parameters obtained by both methods are fairly consistent. In the shale and shaly sandstone layers, however, there is a significant discrepancy between results since the stress‐induced anisotropy model we use is not applicable to rocks exhibiting intrinsic anisotropy. This methodology could be useful for building the initial anisotropic velocity model for imaging, which is to be refined through migration velocity analysis.     

Estimating runoff from a glacierized catchment using natural tracers in the semi‐arid Andes cordillera

This paper presents a methodology for hydrograph separation in mountain watersheds, which aims at identifying flow sources among ungauged headwater sub‐catchments through a combination of observed streamflow and data on natural tracers including isotope and dissolved solids. Daily summer and bi‐daily spring season water samples obtained at the outlet of the Juncal River Basin in the Andes of Central Chile were analysed for all major ions as well as stable water isotopes, δ¹⁸O and δD. Additionally, various samples from rain, snow, surface streams and exfiltrating subsurface water (springs) were sampled throughout the catchment. A principal component analysis was performed in order to address cross‐correlation in the tracer dataset, reduce the dimensionality of the problem and uncover patterns of variability. Potential sources were identified in a two‐component U‐space that explains 94% of the observed tracer variability at the catchment outlet. Hydrograph separation was performed through an Informative‐Bayesian model. Our results indicate that the Juncal Norte Glacier headwater sub‐catchment contributed at least 50% of summer flows at the Juncal River Basin outlet during the 2011–2012 water year (a hydrologically dry period in the Region), even though it accounts for only 27% of the basin area. Our study confirms the value of combining solute and isotope information for estimating source contributions in complex hydrologic systems, and provides insights regarding experimental design in high‐elevation semi‐arid catchments. The findings of this study can be useful for evaluating modelling studies of the hydrological consequences of the rapid decrease in glacier cover observed in this region, by providing insights into the origin of river water in basins with little hydrometeorological information. Copyright © 2016 John Wiley & Sons, Ltd.     

Estimating gas saturation in a thin layer by using frequency‐dependent amplitude versus offset modelling

Various models have been proposed to link partial gas saturation to seismic attenuation and dispersion, suggesting that the reflection coefficient should be frequency‐dependent in many cases of practical importance. Previous approaches to studying this phenomenon typically have been limited to single‐interface models. Here, we propose a modelling technique that allows us to incorporate frequency‐dependent reflectivity into convolutional modelling. With this modelling framework, seismic data can be synthesised from well logs of velocity, density, porosity, and water saturation. This forward modelling could act as a basis for inversion schemes aimed at recovering gas saturation variations with depth. We present a Bayesian inversion scheme for a simple thin‐layer case and a particular rock physics model and show that, although the method is very sensitive to prior information and constraints, both gas saturation and layer thickness theoretically can be estimated in the case of interfering reflections.     

Estimating suspended sediment concentrations in areas with limited hydrological data using a mixed‐effects model

Sediment rating curves are commonly used to estimate the suspended sediment load in rivers and streams under the assumption of a constant relation between discharge (Q) and suspended sediment concentrations (SSC) over time. However, temporal variation in the sediment supply of a watershed results in shifts in this relation by increasing variability and by introducing nonlinearities in the form of hysteresis or a path‐dependent relation. In this study, we used a mixed‐effects linear model to estimate an average SSC–Q relation for different periods of time within the hydrologic cycle while accounting for seasonality and hysteresis. We tested the performance of the mixed‐effects model against the standard rating curve, represented by a generalized least squares regression, by comparing observed and predicted sediment loads for a test case on the Chilliwack River, British Columbia, Canada. In our analyses, the mixed‐effects model reflected more accurate patterns of interpolated SSC from Q data than the rating curve, especially for the low‐flow summer months when the SSC–Q relation is less clear. Akaike information criterion scores were lower for the mixed‐effects model than for the standard model, and the mixed‐effects model explained nearly twice as much variance as the standard model (52% vs 27%). The improved performance was achieved by accounting for variability in the SSC–Q relation within each month and across years for the same month using fixed and random effects, respectively, a characteristic disregarded in the sediment rating curve. Copyright © 2012 John Wiley & Sons, Ltd.