Calibration of high-resolution geophysical data with tracer test measurements to improve hydrological predictions

Relationships between porosity and hydraulic conductivity tend to be strongly scale- and site-dependent and are thus very difficult to establish. As a result, hydraulic conductivity distributions inferred from geophysically derived porosity models must be calibrated using some measurement of aquifer response. This type of calibration is potentially very valuable as it may allow for transport predictions within the considered hydrological unit at locations where only geophysical measurements are available, thus reducing the number of well tests required and thereby the costs of management and remediation. Here, we explore this concept through a series of numerical experiments. Considering the case of porosity characterization in saturated heterogeneous aquifers using crosshole ground-penetrating radar and borehole porosity log data, we use tracer test measurements to calibrate a relationship between porosity and hydraulic conductivity that allows the best prediction of the observed hydrological behavior. To examine the validity and effectiveness of the obtained relationship, we examine its performance at alternate locations not used in the calibration procedure. Our results indicate that this methodology allows us to obtain remarkably reliable hydrological predictions throughout the considered hydrological unit based on the geophysical data only. This was also found to be the case when significant uncertainty was considered in the underlying relationship between porosity and hydraulic conductivity.     

Analysis of tracer tomography using temporal moments of tracer breakthrough curves

Hydraulic/partitioning tracer tomography (HPTT) was recently developed by Yeh and Zhu [Yeh T-CJ, Zhu J. Hydraulic/partitioning tracer tomography for characterization of dense nonaqueous phase liquid source zones, Water Resour Res 2007;43:W06435. doi:10.1029/2006WR004877.] for estimating spatial distribution of dense nonaqueous phase liquids (DNAPLs) in the subsurface. Since discrete tracer concentration data are directly utilized for the estimation of DNAPLs, this approach solves the hyperbolic convection–dispersion equation. Solution to the convection–dispersion equation however demands fine temporal and spatial discretization, resulting in high computational cost for an HPTT analysis. In this work, we use temporal moments of tracer breakthrough curves instead of discrete concentration data to estimate DNAPL distribution. This approach solves time independent partial differential equations of the temporal moments, and therefore avoids solving the convection–dispersion equation using a time marching scheme, resulting in a dramatic reduction of computational cost. To reduce numerical oscillations associated with convection dominated transport problems such as in inter-well tracer tests, the approach uses a finite element solver adopting the streamline upwind Petrov–Galerkin method to calculate moments and sensitivities. We test the temporal moment approach through numerical simulations. Comparing the computational costs between utilizing moments and discrete concentrations, we find that temporal moments significantly reduce the computation time. We also find that tracer moment data collected through a tomographic survey alone are able to yield reasonable estimates of hydraulic conductivity, as indicated by a correlation of 0.588 between estimated and true hydraulic conductivity fields in the synthetic case study.     

Multiple‐station neural network for modelling tidal currents across Shinnecock inlet,USA

This paper presents the development of a multiple‐station neural network for predicting tidal currents across a coastal inlet. Unlike traditional hydrodynamic models, the neural network model does not need inputs of coastal topography and bathymetry, grids, surface and bottom frictions, and turbulent eddy viscosity. Without solving hydrodynamic equations, the neural network model applies an interconnected neural network to correlate the inputs of boundary forcing of water levels at a remote station to the outputs of tidal currents at multiple stations across a local coastal inlet. Coefficients in the neural network model are trained using a continuous dataset consisting of inputs of water levels at a remote station and outputs of tidal currents at the inlet, and verified using another independent input and output dataset. Once the neural network model has been satisfactorily trained and verified, it can be used to predict tidal currents at a coastal inlet from the inputs of water levels at a remote station. For the case study at Shinnecock Inlet in the southern shore of New York, tidal currents at nine stations across the inlet were predicted by the neural network model using water level data located from a station about 70 km away from the inlet. A continuous dataset in May 2000 was used for the training, and another dataset in July 2000 was used for the verification of the neural network model. Comparing model predictions and observations indicates correlation coefficients range from 0·95 to 0·98, and the root‐mean‐square error ranges from 0·04 to 0·08 m s^?1 at the nine current locations across the inlet. Copyright © 2007 John Wiley & Sons, Ltd.     

Estimation of Background Noise for International Monitoring System Seismic Stations

v--vThe prototype International Data Centre (IDC) in Arlington, Virginia has been acquiring data from seismic stations at locations designated in the Comprehensive Test-Ban Treaty for the International Monitoring System (IMS) since the start of 1995. A key characteristic of these stations is their background noise levels and their seasonal and diurnal variability. Since June 1997 an automated sample selection effort has collected over 700,000 individual noise sample spectra from 39 primary and 57 auxiliary stations. Monthly median and 5 and 95 percentile estimates have been calculated for each channel of every station. Compatibility of median spectra obtained for the same station and channel in the same month for two different years confirms the consistency of the noise-sampling algorithm used. A preliminary analysis of the results shows strong (more than a factor of two) seasonal variation at a quarter of all stations. Strong diurnal variations at half of the sites indicate that many of the selected sites are poorly located with respect to cultural noise sources. The results of this study are already being used to evaluate station quality, improve those processes that require background noise values, such as automatic association and requesting auxiliary station data, and to improve the estimation of station and network detection and location thresholds.     

Upscaling Point Velocity Measurements to Characterize a Glacial Outwash Aquifer

Small‐scale point velocity probe (PVP)‐derived velocities were compared to conventional large‐scale velocity estimates from Darcy calculations and tracer tests, and the possibility of upscaling PVP data to match the other velocity estimates was evaluated. Hydraulic conductivity was estimated from grain‐size data derived from cores, and single‐well response testing or slug tests of onsite wells. Horizontal hydraulic gradients were calculated using 3‐point estimators from all of the wells within an extensive monitoring network, as well as by representing the water table as a single best fit plane through the entire network. Velocities determined from PVP testing were generally consistent in magnitude with those from depth specific data collected from multilevel monitoring locations in the tracer test, and similar in horizontal flow direction to the average hydraulic gradient. However, scaling up velocity estimates based on PVP measurements for comparison with site‐wide Darcy‐based velocities revealed issues that challenge the use of Darcy calculations as a generally applicable standard for comparison. The Darcy calculations were shown to underestimate the groundwater velocities determined both by the PVPs and large‐scale tracer testing, in a depth‐specific sense and as a site‐wide average. Some of this discrepancy is attributable to the selective placement of the PVPs in the aquifer. Nevertheless, this result has important implications for the design of in situ treatment systems. It is concluded that Darcy estimations of velocity should be supplemented with independent assessments for these kinds of applications.     

A comparative study of Monte Carlo simple genetic algorithm and noisy genetic algorithm for cost-effective sampling network design under uncertainty

This study evaluates and compares two methodologies, Monte Carlo simple genetic algorithm (MCSGA) and noisy genetic algorithm (NGA), for cost-effective sampling network design in the presence of uncertainties in the hydraulic conductivity (K) field. Both methodologies couple a genetic algorithm (GA) with a numerical flow and transport simulator and a global plume estimator to identify the optimal sampling network for contaminant plume monitoring. The MCSGA approach yields one optimal design each for a large number of realizations generated to represent the uncertain K-field. A composite design is developed on the basis of those potential monitoring wells that are most frequently selected by the individual designs for different K-field realizations. The NGA approach relies on a much smaller sample of K-field realizations and incorporates the average of objective functions associated with all K-field realizations directly into the GA operators, leading to a single optimal design. The efficacy of the MCSGA-based composite design and the NGA-based optimal design is assessed by applying them to 1000 realizations of the K-field and evaluating the relative errors of global mass and higher moments between the plume interpolated from a sampling network and that output by the transport model without any interpolation. For the synthetic application examined in this study, the optimal sampling network obtained using NGA achieves a potential cost savings of 45% while keeping the global mass and higher moment estimation errors comparable to those errors obtained using MCSGA. The results of this study indicate that NGA can be used as a useful surrogate of MCSGA for cost-effective sampling network design under uncertainty. Compared with MCSGA, NGA reduces the optimization runtime by a factor of 6.5.     

Simulating short‐circuiting flow in a constructed wetland: the implications of bathymetry and vegetation effects

Short‐circuiting flow, commonly experienced in many constructed wetlands, reduces hydraulic retention times in unit wetland cells and decreases the treatment efficiency. A two‐dimensional (2‐D), physically based, distributed modelling approach was used to systematically address the effects of bathymetry and vegetation on short‐circuiting flow, which previously have been neglected or lumped in one‐dimensional wetland flow models. In this study, a 2‐D transient hydrodynamics with advection‐dispersion model was developed using MIKE 21 and calibrated with bromide tracer data collected at the Orlando Easterly Wetland Cell 7. The estimated topographic difference between short‐circuiting flow zone and adjacent area ranged from 0·3 to 0·8 m. A range of the Manning roughness coefficient at the short‐circuiting flow zone was estimated (0·022–0·045 s m^?1/3). Sensitivity analysis of topographical and vegetative heterogeneity deduced during model calibration shows that relic ditches or other ditch‐shaped landforms and the associated sparse vegetation along the main flow direction intensify the short‐circuiting pattern, considerably affecting 2‐D solute transport simulation. In terms of hydraulic efficiency, this study indicates that the bathymetry effect on short‐circuiting flow is more important than the vegetation effect. Copyright © 2009 John Wiley & Sons, Ltd.     

Assessing the Nonlinearity of Karst Response Function under Variable Boundary Conditions

The hydraulic and transfer response of karst aquifers is complex and often highly nonlinear: due to their high transmissivity and connection with the surface, such systems are very sensitive to modifications of their boundary conditions. The aim of this study was to assess the variation of the response depending on both upstream and downstream parameters, and propose a methodology to simulate the response of the karst system depending on those parameters. The impact of the variations of multiple environmental parameters on the response of a karstic system submitted to tidal variations (Normandy, France) was investigated after a campaign of artificial tracer tests acquired in very different hydrologic conditions (rainfall events, low tide, high tide, low/high piezometric level, and low/high waters). Principal components analysis and hierarchical clustering were applied on both environmental variables and karstic system response variables (parameters of the residence time distribution [RTD] curves). Equations between the RTD parameters and the most relevant variables were established using a symbolic regression algorithm. It appeared that the variations of the RTD parameters depend mainly on the cumulated rainfall preceding the injection, the piezometric level of the aquifer, and on the tide parameters. The hydraulic conditions downstream of the aquifer have a strong influence on the hydraulic and transfer response of the aquifer. The response of the aquifer in various and extreme conditions has been simulated using the equations resulting from the symbolic regression algorithm. Such relationships can be useful for management of water resources in karst media, and support decision making.     

上海地震台阵与台网的定位及视慢度研究

阐述了台阵的地震定位原理和视慢度在台阵与台网定位中的一些重要特性，并比较了相同位置上的上海地震台阵与台网对同一地震的定位结果。最后，对上海台队与台网导致定位误差的横向速度变化的位置和范围给出了矢量校正的结果并进行了初步讨论。     

On robustness of large quantile estimates to largest elements of the observation series

The robustness of large quantile estimates of largest elements in a small sample by the methods of moments (MOM), L‐moments (LMM) and maximum likelihood (MLM) was evaluated and compared. Bias (B) and mean square error (MSE) were used to measure the estimation methods performance. Quantiles were estimated by eight two‐parameter probability distributions with the variation coefficient being the shape parameter. The effect of dropping largest elements of the series on large quantile values was assessed for various variation coefficient (C_V)/sample size (n) ‘combinations’ with n = 30 as the basic value. To that end, both the Monte Carlo sampling experiments and an asymptotic approach consisting in distribution truncation were applied. In general, both sampling and asymptotic approaches point to MLM as the most robust method of the three considered, with respect to bias of large quantiles. Comparing the performance of two other methods, the MOM estimates were found to be more robust for small and moderate hydrological samples drawn from distributions with zero lower‐bound than were the LMM estimates. Extending the evaluation to outliers, it was shown that all the above findings remain valid. However, using the MSE variation as a measure of performance, the LMM was found to be the best for most distribution/variation coefficient combinations, whereas MOM was found to be the worst. Moreover, removal of the largest sample element need not result in a loss of estimation efficiency. The gain in accuracy is observed for the heavy‐tailed and log‐normal distributions, being particularly distinctive for LMM. In practice, while dealing with a single sample deprived of its largest element, one should choose the estimation method giving the lowest MSE of large quantiles. For n = 30 and several distribution/variation coefficient combinations, the MLM outperformed the two other methods in this respect and its supremacy grew with sample size, while MOM was usually the worst. Copyright © 2006 John Wiley & Sons, Ltd.     

Estimating Preferential Flow in Karstic Aquifers Using Statistical Mixed Models

Karst aquifers are highly productive groundwater systems often associated with conduit flow. These systems can be highly vulnerable to contamination, resulting in a high potential for contaminant exposure to humans and ecosystems. This work develops statistical models to spatially characterize flow and transport patterns in karstified limestone and determines the effect of aquifer flow rates on these patterns. A laboratory‐scale Geo‐HydroBed model is used to simulate flow and transport processes in a karstic limestone unit. The model consists of stainless steel tanks containing a karstified limestone block collected from a karst aquifer formation in northern Puerto Rico. Experimental work involves making a series of flow and tracer injections, while monitoring hydraulic and tracer response spatially and temporally. Statistical mixed models (SMMs) are applied to hydraulic data to determine likely pathways of preferential flow in the limestone units. The models indicate a highly heterogeneous system with dominant, flow‐dependent preferential flow regions. Results indicate that regions of preferential flow tend to expand at higher groundwater flow rates, suggesting a greater volume of the system being flushed by flowing water at higher rates. Spatial and temporal distribution of tracer concentrations indicates the presence of conduit‐like and diffuse flow transport in the system, supporting the notion of both combined transport mechanisms in the limestone unit. The temporal response of tracer concentrations at different locations in the model coincide with, and confirms the preferential flow distribution generated with the SMMs used in the study.     

香蒲、灯心草人工湿地的研究─Ⅱ.净化污水的空间

应用测定流水中溶氧量的方法,测定了长薄鳅的耗氧率,耗氧量及窒息点．试验表明：长薄鳅的耗氧率（Ｙ’）随鱼体重（Ｗ,ｇ）的增加而增大,其关系式分别为：Ｙ’＝１８６．５７６Ｗ（－０．２０４３）,Ｙ＝０．１８６Ｗ（０．７９６２）．温度对长薄鳅的耗氧率有影响,在１３－３０Ｃ范围内,耗氧率随水温升高而逐渐增大．耗氧率的温度敏感区域是１３－２３Ｃ和２８－３０Ｃ,而在２３－２８Ｃ范围内变化幅度较小,标准代谢量变化     

Assessment of uncertainty associated with the estimation of well catchments by moment equations

Non-local stochastic moment equations are used successfully to analyze groundwater flow in randomly heterogeneous media. Here we present a moment equations-based approach to quantify the uncertainty associated with the estimation of well catchments. Our approach is based on the development of a complete second order formalism which allows obtaining the first statistical moments of the trajectories of conservative solute particles advected in a generally non-uniform groundwater flow. Approximate equations of moments of particles’ trajectories are then derived on the basis of a second order expansion in terms of the standard deviation of the aquifer log hydraulic conductivity. Analytical expressions are then obtained for the predictors of locations of mean stagnation points, together with their associated uncertainties. We implement our approach on heterogeneous media in bounded two-dimensional domains, with and without including the effect of conditioning on hydraulic conductivity information. The impact of domain size, boundary conditions, heterogeneity and non-stationarity of hydraulic conductivity on the prediction of a well catchment is explored. The results are compared against Monte Carlo simulations and semi-analytical solutions available in the literature. The methodology is applicable to both infinite and bounded domains and is free of distributional assumptions (and so applies to both Gaussian and non-Gaussian log hydraulic conductivity fields) and formally includes the effect of conditioning on available information.     

Tracer measurements in groyne fields for the quantification of mean hydraulic residence times and of the exchange with the stream

Tracer experiments were carried out in groyne fields (GF) of the river Elbe near Havelberg (Germany) in order to estimate the hydraulic connectivity with the river channel. The characteristic times of the five groyne fields, which were estimated from the exponentially declining tracer curves in 43 runs, ranged between 15 min and 69 min and did not correlate with the water level. Methodological investigations show that single point injection and two measurements (in the outflowing water and in the dominant region) are sufficient to provide robust in‐situ tracer curves. Using simplified mathematical simulations with connected stirred tanks, the conditions are investigated for the development of breaks in tracer curves and for the occurrence of significant errors in the estimation of intrinsic residence times. It was shown that an initial uniform dye distribution is not mandatory for the estimation during steady states. In special cases, point injections are more advisable. Moreover, the mean hydraulic residence time was found to be not equivalent to the estimated characteristic time. In fact, it is mostly overestimated by tracer experiments. The degree of overestimation depends on mixing and the volumetric proportions between the different parts of the GF and can be calculated from measured dye concentration differences. For example, an overestimation of 32% was calculated for a groyne field with a commonly found circulation flow pattern.     

Natural Gradient Tracer Test to Evaluate Natural Attenuation of MTBE Under Anaerobic Conditions

A natural gradient tracer test using perdeuterated MTBE was conducted in an anaerobic aquifer to determine the relative importance of dispersion and degradation in reducing MTBE concentrations in ground water. Preliminary ground water chemistry and hydraulic conductivity data were used to place the tracer within an existing dissolved MTBE plume at Port Hueneme, California. Following one year of transport, the tracer plume was characterized in detail.
Longitudinal dispersion was identified as the dominant mechanism for lowering the perdeuterated MTBE concentrations. The method of moments was used to determine the longitudinal and lateral dispersion coefficients (0.85 m²/day and 0.08 m²/day, respectively). A mass-balance analysis, carried out after one year of transport, accounted for 110% of the injected mass and indicated that no significant mass loss occurred. The plume structure created by zones of higher and lower hydraulic conductivity at the site was complex, consisting of several localized areas of high tracer concentration in a lower concentration plume. This is important because the aquifer has generally been characterized as exhibiting fairly minor heterogeneity. In addition, the tracer plume followed a curved flowpath that deviated from the more macroscopic direction of ground water flow inferred from local ground water elevation measurements and the behavior of the existing plume. Understanding the mass balance, plume structure, curvature of the tracer plume, and consequently natural attenuation behavior required the detailed sampling approach employed in this study. These data imply that a detailed understanding of site hydrogeology and an extensive sampling network may be critical for the correct interpretation of monitored natural attenuation of MTBE.     

Numerical and multivariate stochastic approaches to characterize flow in a constructed wetland basin

Reduction in specific and viscous dissipation rate in surface waters by flow control and contaminant removal are the goals of constructed wetlands. A two-dimensional simulation study on surface flow through a constructed wetland in Guilin, China is performed. The flow through the wetland is modeled and dynamically simulated by distinct case studies by varying both inlet width and inflow rate. Nonlinear increase in peak dynamic pressure and specific dissipation rates as a function of increasing inflow rate is reported for the different cases studied. The results of the numerical models confirm an increase in viscous dissipation, shear stress and dynamic pressure within the wetland with increase in inflow rate. These modeling results are used as inputs for performing a statistical data analysis. Further, a multivariate stochastic statistical framework has been proposed for the prediction of dissipation as a function of variables including inflow rate, inlet geometry and wall shear stress. Multivariate and variance analysis is performed to validate the appropriateness of the theoretical models proposed. Results provide simplified meaningful suggestions to constructed wetland design and related applications.     

Improved Recharge Estimation from Portable,Low‐Cost Weather Stations

Groundwater recharge estimation is a critical quantity for sustainable groundwater management. The feasibility and robustness of recharge estimation was evaluated using physical‐based modeling procedures, and data from a low‐cost weather station with remote sensor techniques in Southern Abbotsford, British Columbia, Canada. Recharge was determined using the Richards‐based vadose zone hydrological model, HYDRUS‐1D. The required meteorological data were recorded with a HOBO^TM weather station for a short observation period (about 1 year) and an existing weather station (Abbotsford A) for long‐term study purpose (27 years). Undisturbed soil cores were taken at two locations in the vicinity of the HOBO^TM weather station. The derived soil hydraulic parameters were used to characterize the soil in the numerical model. Model performance was evaluated using observed soil moisture and soil temperature data obtained from subsurface remote sensors. A rigorous sensitivity analysis was used to test the robustness of the model. Recharge during the short observation period was estimated at 863 and 816 mm. The mean annual recharge was estimated at 848 and 859 mm/year based on a time series of 27 years. The relative ratio of annual recharge‐precipitation varied from 43% to 69%. From a monthly recharge perspective, the majority (80%) of recharge due to precipitation occurred during the hydrologic winter period. The comparison of the recharge estimates with other studies indicates a good agreement. Furthermore, this method is able to predict transient recharge estimates, and can provide a reasonable tool for estimates on nutrient leaching that is often controlled by strong precipitation events and rapid infiltration of water and nitrate into the soil.     

Field Trials of Chaotic Advection to Enhance Reagent Delivery

Chaotic advection is a novel approach that has the potential to enhance contact between an injected reagent and target contaminants, and thereby improve the effectiveness of in situ treatment technologies. One configuration that is capable of generating chaotic advection is termed the rotated potential mixing (RPM) flow. A conventional RPM flow system involves periodically reoriented dipole flow driven by transient switching of pressures at a series of radial wells. To determine whether chaotic advection can be engineered using such an RPM flow system, and to assess the consequent impact on the spatial distribution of a conservative tracer, a series of field-scale experiments were conducted. These experiments involved the injection of a tracer in the center of a circular array of wells followed by either mixing using an engineered RPM flow system to invoke chaotic advection, or by natural processes (advection and diffusion) as the control. Pressure fluctuations from the mixing tests using the RPM flow system showed consistent peak amplitudes during injection and extraction at a frequency corresponding to the switching time, suggesting that the target hydraulic behavior was achieved with the time-dependent flow field. The tracer breakthrough responses showed oscillatory behavior at all monitoring locations during the mixing tests which indicated that the desired RPM flow was generated. The presence of chaotic advection was supported by comparisons to observations from a previous laboratory experiment using RPM flow, and the Fourier spectrum of the temporal tracer data. Results from several quantitative metrics adopted to demonstrate field-scale evidence of chaotic advection showed that mixing led to improved lateral tracer spreading and approximately uniform concentrations across the monitoring network. The multiple lines of evidence assembled in this proof-of-concept study conclusively demonstrated that chaotic advection can be engineered at the field scale. This investigation is a critical step in the development of chaotic advection as a viable and efficient approach to enhance reagent delivery.     

Imaging Pathways in Fractured Rock Using Three‐Dimensional Electrical Resistivity Tomography

Major challenges exist in delineating bedrock fracture zones because these cause abrupt changes in geological and hydrogeological properties over small distances. Borehole observations cannot sufficiently capture heterogeneity in these systems. Geophysical techniques offer the potential to image properties and processes in between boreholes. We used three‐dimensional cross borehole electrical resistivity tomography (ERT) in a 9 m (diameter) × 15 m well field to capture high‐resolution flow and transport processes in a fractured mudstone contaminated by chlorinated solvents, primarily trichloroethylene. Conductive (sodium bromide) and resistive (deionized water) injections were monitored in seven boreholes. Electrode arrays with isolation packers and fluid sampling ports were designed to enable acquisition of ERT measurements during pulsed tracer injections. Fracture zone locations and hydraulic pathways inferred from hydraulic head drawdown data were compared with electrical conductivity distributions from ERT measurements. Static ERT imaging has limited resolution to decipher individual fractures; however, these images showed alternating conductive and resistive zones, consistent with alternating laminated and massive mudstone units at the site. Tracer evolution and migration was clearly revealed in time‐lapse ERT images and supported by in situ borehole vertical apparent conductivity profiles collected during the pulsed tracer test. While water samples provided important local information at the extraction borehole, ERT delineated tracer migration over spatial scales capturing the primary hydrogeological heterogeneity controlling flow and transport. The fate of these tracer injections at this scale could not have been quantified using borehole logging and/or borehole sampling methods alone.