Probabilistic assessment of travel times in groundwater modeling

A Monte Carlo approach is described for the quantification of uncertainty on travel time estimates. A real (non synthetic) and exhaustive data set of natural genesis is used for reference. Using an approach based on binary indicators, constraint interval data are easily accommodated in the modeling process. It is shown how the incorporation of imprecise data can reduce drastically the uncertainty in the estimates. It is also shown that unrealistic results are obtained when a deterministic modeling is carried out using a kriging estimate of the transmissivity field. Problems related with using sequential indicator simulation for the generation of fields incorporating constraint interval data are discussed. The final results consists of 95% probability intervals of arrival times at selected control planes reflecting the original uncertainty on the transmissivity maps.     

Kriging metamodeling in seismic risk assessment based on stochastic ground motion models

An efficient computational framework is presented for seismic risk assessment within a modeling approach that utilizes stochastic ground motion models to describe the seismic hazard. The framework is based on the use of a kriging surrogate model (metamodel) to provide an approximate relationship between the structural response and the structural and ground motion parameters that are considered as uncertain. The stochastic character of the excitation is addressed by assuming that under the influence of the white noise (used within the ground motion model) the response follows a lognormal distribution. Once the surrogate model is established, a task that involves the formulation of an initial database to inform the metamodel development, it is then directly used for all response evaluations required to estimate seismic risk. The model prediction error stemming from the metamodel is directly incorporated within the seismic risk quantification and assessment, whereas an adaptive approach is developed to refine the database that informs the metamodel development. The ability to efficiently obtain derivative information through the kriging metamodel and its utility for various tasks within the probabilistic seismic risk assessment is also discussed. As an illustrative example, the assessment of seismic risk for a benchmark four‐story concrete office building is presented. The potential that ground motions include near‐fault characteristics is explicitly addressed within the context of this example. The implementation of the framework for the same structure equipped with fluid viscous dampers is also demonstrated. Copyright © 2015 John Wiley & Sons, Ltd.     

Probabilistic seismic response and reliability assessment of isolated bridges

Bridge seismic isolation strategy is based on the reduction of shear forces transmitted from the superstructure to the piers by two means: shifting natural period and earthquake input energy reduction by dissipation concentrated in protection devices. In this paper, a stochastic analysis of a simple isolated bridge model for different bridge and device parameters is conducted to assess the efficiency of this seismic protection strategy. To achieve this aim, a simple nonlinear softening constitutive law is adopted to model a wide range of isolation devices, characterized by only three essential mechanical parameters. As a consequence of the random nature of seismic motion, a probabilistic analysis is carried out and the time modulated Kanai-Tajimi stochastic process is adopted to represent the seismic action. The response covariance in the state space is obtained by solving the Lyapunov equation for a stochastic linearized system. After a sensitivity analysis, the failure probability referred to extreme displacement and the mean value of dissipated energy are assessed by using the introduced stochastic indices of seismic bridge protection efficiency. A parametric analysis for protective devices with different mechanical parameters is developed for a proper selection of parameters of isolation devices under different situations.     

Geostatistical analysis and conditional simulation for estimating the spatial variability of hydraulic conductivity in the Choushui River alluvial fan,Taiwan

This work evaluated the spatial variability and distribution of heterogeneous hydraulic conductivity (K) in the Choushui River alluvial fan in Taiwan, using ordinary kriging (OK) and mean and individual sequential Gaussian simulations (SGS). A baseline flow model constructed by upscaling parameters was inversely calibrated to determine the pumping and recharge rates. Simulated heads using different K realizations were then compared with historically measured heads. A global/local simulated error between simulated and measured heads was analysed to assess the different spatial variabilities of various estimated K distributions. The results of a MODFLOW simulation indicate that the OK realization had the smallest sum of absolute mean simulation errors (SAMSE) and the SGS realizations preserved the spatial variability of the measured K fields. Moreover, the SAMSE increases as the spatial variability of the K field increases. The OK realization yields small local simulation errors in the measured K field of moderate magnitude, whereas the SGS realizations have small local simulation errors in the measured K fields, with high and low values. The OK realization of K can be applied to perform a deterministic inverse calibration. The mean SGS method is suggested for constructing a K field when the application focuses on extreme values of estimated parameters and small calibration errors, such as in a simulation of contaminant transport in heterogeneous aquifers. The individual SGS realization is useful in stochastically assessing the spatial uncertainty of highly heterogeneous aquifers. Copyright © 2004 John Wiley & Sons, Ltd.     

Evaluating the reliability of time series analysis to estimate variable riparian travel times by numerical groundwater modelling

The transition zones between rivers and adjacent riparian aquifers are locations of high biogeochemical activities that contribute to a removal of potentially hazardous substances in the aquatic system. The potential of the removal processes depends highly on subsurface water travel times, which can be determined by using the propagation of electrical conductivity (EC) signal from the river into the riparian aquifer. Although this method has been applied and verified in many studies, we observe possible limitations for the usage of EC fluctuation analysis. Our findings are based on EC time series analyses during storm events and artificial hydropeaks induced by watermill operations. Travel times derived by cross‐correlation analysis were compared with travel times calculated based on backward particle tracking of a calibrated transient numerical groundwater flow model. The cross‐correlation method produced only reasonable travel times for the artificial hydropeaks. In contrast, cross‐correlation analysis of the EC data during natural storm events resulted in implausibly negative or unrealistically low travel times for the bulk of the data sets. We conclude that the reason for this behaviour is, first, the low EC contrast between river and groundwater in connection with a strong damping of the infiltrating river EC signal into the subsurface during storm events. Second, the existence of old and less‐mineralized riparian water between the river and the monitoring well resulted in bank‐storage‐driven EC breakthrough curves with earlier arrival times and the subsequent estimation of implausible riparian travel times.     

Analysis of groundwater flow and travel times for a landfill site in an arid region with a thick vadose zone

Groundwater flows and travel times were analyzed under a landfill site characterized by a thick unsaturated zone, in an arid environment, using two-dimensional models. Transport in the unsaturated zone is important in arid environments with thick vadose zones and usually determines the travel time of groundwater from the landfill site to the regulatory compliance surface. The combined use of a parallel flow (Dupuit-Forchheimer) areal model and vertical cross-sectional model is explored at a site typical in the utility industry. Flow paths and travel times to the compliance zone are obtained for use in landfill site design or environmental impact assessments. Sensitivity analysis shows that boundary conditions are important factors influencing the entire analysis and thus need to be confirmed with field measurements.     

Probabilistic risk assessment of contaminant transport in groundwater and vapour intrusion following remediation of a contaminant source

Community-scale simulations were performed to investigate the risk to groundwater and indoor air receptors downgradient of a contaminated site following the remediation of a long-term source. Six suites of Monte Carlo simulations were performed using a numerical model that accounted for groundwater flow, reactive solute transport, soil gas flow, and vapour intrusion in buildings. The model was applied to a three-dimensional, community-scale (250 m × 1000 m × 14 m) domain containing heterogeneous, spatially correlated distributions of the hydraulic conductivity, fraction of organic carbon, and biodegradation rate constant, which were varied between realizations. Analysis considered results from both individual realizations as well as the suite of Monte Carlo simulations expressed through several novel, integrated parameters, such as the probability of exceeding a regulatory standard in either groundwater or indoor air. Results showed that exceedance probabilities varied considerably with the consideration of biodegradation in the saturated zone, and were less sensitive to changes in the variance of hydraulic conductivity or the incorporation of heterogeneous distributions of organic carbon at this spatial scale. A sharp gradient in exceedance probability existed at the lateral edges of the plumes due to variability in lateral dispersion, which defined a narrow region of exceedance uncertainty. Differences in exceedance probability between realizations (i.e., due to heterogeneity uncertainty) were similar to differences attributed to changes in the variance of hydraulic conductivity or fraction of organic carbon. Simulated clean-up times, defined by reaching an acceptable exceedance probability, were found to be on the order of decades to centuries in these community-scale domains. Results also showed that the choice of the acceptable exceedance probability level (e.g., 1 vs. 5 %) would likely affect clean up times on the order of decades. Moreover, in the scenarios examined here, the risk of exceeding indoor air standards was greater than that of exceeding groundwater standards at all times and places. Overall, simulations of coupled transport processes combined with novel spatial and temporal quantification metrics for Monte Carlo analyses, provide practical tools for assessing risk in wider communities when considering site remediation.     

Assessment of CHADFDM satellite-based input dataset for the groundwater recharge estimation in arid and data scarce regions

Aquifer natural recharge estimations are a prerequisite for understanding hydrologic systems and sustainable water resources management. As meteorological data series collection is difficult in arid and semiarid areas, satellite products have recently become an alternative for water resources studies. A daily groundwater recharge estimation in the NW part of the Lake Chad Basin, using a soil–plant-atmosphere model (VisualBALAN), from ground- and satellite-based meteorological input dataset for non-irrigated and irrigated land and for the 2005–2014 period is presented. Average annual values were 284 mm and 30°C for precipitation and temperature in ground-based gauge stations. For the satellite-model-based Lake Chad Basin Flood and Drought Monitor System platform (CHADFDM), average annual precipitation and temperature were 417 mm and 29°C, respectively. Uncertainties derived from satellite data measurement could account for the rainfall difference. The estimated mean annual aquifer recharge was always higher from satellite- than ground-based data, with differences up to 46% for dryland and 23% in irrigated areas. Recharge response to rainfall events was very variable and results were very sensitive to: wilting point, field capacity and curve number for runoff estimation. Obtained results provide plausible recharge values beyond the uncertainty related to data input and modelling approach. This work prevents on the important deviations in recharge estimation from weighted-ensemble satellite-based data, informing in decision making to both stakeholders and policy makers.     

Impact of artificial subsurface drainage on groundwater travel times and baseflow discharge in an agricultural watershed,Iowa (USA)

Pollutant delivery through artificial subsurface drainage networks to streams is an important transport mechanism, yet the impact of drainage tiles on groundwater hydrology at the watershed scale has not been well documented. In this study, we developed a two‐dimensional, steady‐state groundwater flow model for a representative Iowa agricultural watershed to simulate the impact of tile drainage density and incision depth on groundwater travel times and proportion of baseflow contributed by tile drains. Varying tile drainage density from 0 to 0.0038 m^?1, while maintaining a constant tile incision depth at 1.2 m, resulted in the mean groundwater travel time to decrease exponentially from 40 years to 19 years and increased the tile contribution to baseflow from 0% to an upper bound of 37%. In contrast, varying tile depths from 0.3 to 2.7 m, while maintaining a constant tile drainage density of 0.0038 m^?1, caused mean travel times to decrease linearly from 22 to 18 years and increased the tile contribution to baseflow from 30% to 54% in a near‐linear manner. The decrease in the mean travel time was attributed to decrease in the saturated thickness of the aquifer with increasing drainage density and incision depth. Study results indicate that tile drainage affects fundamental watershed characteristics and should be taken into consideration when evaluating water and nitrate export from agricultural regions. Copyright © 2011 John Wiley & Sons, Ltd.     

地震走时与重力数据的联合反演

对目前的地震走时与重力数据联合反演发展进行了简要的概述。首先,从两类数据单独反演的基本原理出发,对两者进行了分析比较,并由两者参数间存在的相互关系,可将两类数据归并、统一到一个系统,合理地进行联合反演。其次,根据目前国内外的相关研究,介绍了当前联合反演的两种算法:依次反演和同时反演。最后,对联合反演中存在的问题进行了讨论。     

Interpretation of first arrival travel times in seismic refraction work

The necessary condition for the seismic refraction method to succeed is that the refracted first arrivals from each layer in a multilayered earth system should be detected on a seismogram as first arrivals, and this is possible only when velocities of all underlying layers are successively greater. The usual procedure to interpret the refraction travel times is to fit such a data set with several intersecting straight lines by employing a visual technique which may lead to errors of subjective judgment, as the velocity model depends on the selection of various line segments through the data. To remove the visual fit we propose here a layer stripping method based on minimum intercept time, apparent velocity, rms residual, and maximum data points by least-squares fitting to yield several intersecting straight lines. Once data are segmented out, the conventional equations can be used to determine the velocity structure.     

A simulation of large‐scale groundwater flow and travel time in a fractured rock environment for waste disposal purposes

Two‐dimensional regional groundwater flow was simulated based on a conceptual model of low‐permeability crystalline rocks of the Whiteshell Research Area (WRA) in south‐eastern Manitoba. The conceptual model consists of fracture zones that strike in different directions and dip at various angles in the background rock mass. The thickness and hydraulic properties of the fracture zones in the conceptual model were varied as were the fluid properties and the boundary conditions of the groundwater flow system. The effects of these variations on the groundwater flow pattern and on the convective travel time along pathways from a hypothetical disposal vault at 500 m depth to discharge locations at the ground surface were evaluated. The vault was located in the regional discharge area of the groundwater system. A homogeneous conceptual model of the WRA, having only freshwater flow, formed a groundwater flow pattern with a regional flow system. Local flow systems developed increasingly with the introduction of fracture zones 20 m and 3 m thick, and depth‐dependent fluid density. This indicates a reduction in groundwater residence time by fracture zones and fluid density. Flow pathways were analysed using both a stream‐function and a particle‐tracking technique. The pathways and their lengths from the location of the vault to the surface varied spatially according to the flow patterns. The minimum travel time along these pathways was less than 150 000 and greater than 4 000 000 years in models with and without fracture zones, respectively, indicating that the presence of fracture zones was the major controlling factor. A precise knowledge and refinement of conceptual model parameters is necessary during site selection for waste disposal purposes. Copyright © 2004 John Wiley & Sons, Ltd.     

Prediction and assessment of the disturbances of the coal mining in Kailuan to karst groundwater system

Coal resources and water resources play an essential and strategic role in the development of China's social and economic development, being the priority for China's medium and long technological development. As the mining of the coal extraction is increasingly deep, the mine water inrush of high-pressure confined karst water becomes much more a problem. This paper carried out research on the hundred-year old Kailuan coal mine's karst groundwater system. With the help of advanced Visual Modflow software and numerical simulation method, the paper assessed the flow field of karst water area under large-scale exploitation. It also predicted the evolution ofgroundwaterflow field under different mining schemes of Kailuan Corp. The result shows that two cones of depression are formed in the karst flow field of Zhaogezhuang mining area and Tangshan mining area, and the water levels in two cone centers are −270 m and −31 m respectively, and the groundwater generally flows from the northeast to the southwest. Given some potential closed mines in the future, the mine discharge will decrease and the water level of Ordovician limestone will increase slightly. Conversely, given increase of coal yield, the mine drainage will increase, falling depression cone of Ordovician limestone flow field will enlarge. And in Tangshan's urban district, central water level of the depression cone will move slightly towards north due to pumping of a few mines in the north.     

Probabilistic sensitivity and modeling of two-dimensional transport in porous media

A reliability approach is used to develop a probabilistic model of two-dimensional non-reactive and reactive contaminant transport in porous media. The reliability approach provides two important quantitative results: an estimate of the probability that contaminant concentration is exceeded at some location and time, and measures of the sensitivity of the probabilistic outcome to likely changes in the uncertain variables. The method requires that each uncertain variable be assigned at least a mean and variance; in this work we also incorporate and investigate the influence of marginal probability distributions. Uncertain variables includex andy components of average groundwater flow velocity,x andy components of dispersivity, diffusion coefficient, distribution coefficient, porosity and bulk density. The objective is to examine the relative importance of each uncertain variable, the marginal distribution assigned to each variable, and possible correlation between the variables. Results utilizing a two-dimensional analytical solution indicate that the probabilistic outcome is generally very sensitive to likely changes in the uncertain flow velocity. Uncertainty associated with dispersivity and diffusion coefficient is often not a significant issue with respect to the probabilistic analysis; therefore, dispersivity and diffusion coefficient can often be treated for practical analysis as deterministic constants. The probabilistic outcome is sensitive to the uncertainty of the reaction terms for early times in the flow event. At later times, when source contaminants are released at constant rate throughout the study period, the probabilistic outcome may not be sensitive to changes in the reaction terms. These results, although limited at present by assumptions and conceptual restrictions inherent to the closed-form analytical solution, provide insight into the critical issues to consider in a probabilistic analysis of contaminant transport. Such information concerning the most important uncertain parameters can be used to guide field and laboratory investigations.     

Probabilistic sensitivity and modeling of two-dimensional transport in porous media

A reliability approach is used to develop a probabilistic model of two-dimensional non-reactive and reactive contaminant transport in porous media. The reliability approach provides two important quantitative results: an estimate of the probability that contaminant concentration is exceeded at some location and time, and measures of the sensitivity of the probabilistic outcome to likely changes in the uncertain variables. The method requires that each uncertain variable be assigned at least a mean and variance; in this work we also incorporate and investigate the influence of marginal probability distributions. Uncertain variables includex andy components of average groundwater flow velocity,x andy components of dispersivity, diffusion coefficient, distribution coefficient, porosity and bulk density. The objective is to examine the relative importance of each uncertain variable, the marginal distribution assigned to each variable, and possible correlation between the variables. Results utilizing a two-dimensional analytical solution indicate that the probabilistic outcome is generally very sensitive to likely changes in the uncertain flow velocity. Uncertainty associated with dispersivity and diffusion coefficient is often not a significant issue with respect to the probabilistic analysis; therefore, dispersivity and diffusion coefficient can often be treated for practical analysis as deterministic constants. The probabilistic outcome is sensitive to the uncertainty of the reaction terms for early times in the flow event. At later times, when source contaminants are released at constant rate throughout the study period, the probabilistic outcome may not be sensitive to changes in the reaction terms. These results, although limited at present by assumptions and conceptual restrictions inherent to the closed-form analytical solution, provide insight into the critical issues to consider in a probabilistic analysis of contaminant transport. Such information concerning the most important uncertain parameters can be used to guide field and laboratory investigations.     

Computation of travel times and rays in a medium of two-dimensional velocity distribution

A ray-tracing computer program is described for a two-dimensional velocity distribution defined by the local wave velocitiesv _{i, j} in points at arbitrary depthv _{i, j} below the surface points with the horizontal coordinatesx _i . The velocity variation is assumed to be linear in the triangles formed by three neighbouring points. Travel times and rays are then calculated after the exact analytic formulae for any position of the source within the model. No assumptions other than of a piecewise linear velocity structure are made. A first-order discontinuity can be approximated by a thin layer with a strong velocity gradient and refracted waves or wide-angle reflections obtained in this way. As an example,P-wave rays were computed for section No. 05 of the Alpine Longitudinal Profile. The model includes a low-velocity channel which is cut off on the eastern side, first-order discontinuities and a sediment basin.Paper presented at the ESC-Workshop Meeting Seismic Waves in Laterally Inhomogeneous Media, Liblice, 1978.     

Multi‐objective risk‐informed design of floor isolation systems

The design of floor isolation systems (FISs) for the protection of acceleration sensitive contents is examined considering multiple objectives, all quantified in terms of the probabilistic system performance. The competing objectives considered correspond to (i) maximization of the level of protection offered to the sensitive content (acceleration reduction) and (ii) minimization of the demand for the isolator displacement capacity and, more importantly, for the appropriate clearance to avoid collisions with surrounding objects (floor displacement reduction). Both of these objectives are probabilistically characterized utilizing a versatile, simulation‐based framework for quantifying seismic risk, addressing all important uncertainties related to the seismic hazard and the structural model. FIS performance is assessed through time‐history analysis, allowing for all important sources of nonlinearity to be directly addressed in the design framework. The seismic hazard is described through a stochastic ground motion model. For efficiently performing the multi‐objective optimization, an augmented surrogate modeling methodology is established, considering development of a single metamodel with respect to both the uncertain model parameters and the design variables for the FIS system. This surrogate model is then utilized to simultaneously support the probabilistic risk assessment and the design optimization to provide the Pareto front of dominant designs. Each of these designs establishes a different compromise between the considered risk‐related objectives offering a variety of potential options to the designer. Within the illustrative example, the efficiency of the established framework is exploited to compare three different FIS implementations, whereas the impact of structural uncertainties on the optimal design is also evaluated. Copyright © 2016 John Wiley & Sons, Ltd.     

Effect of variations in net basin supply on lake levels and outflows

Starting from a simplified version of the water balance equation, it is shown how the levels and outflows from a open lake can be related to the magnitude and statistical characteristics of the annual net basin supply series, which is defined as the net inflow arising from tributary inflows, rainfall on the lake surface and the lake evaporation. Using the models, estimates are derived for the response time for several large open lakes in Africa and Asia. Also, the observed net basin supply series for three major lakes (Victoria, Malawi and Toba) are investigated in detail. It is suggested that, on an annual basis, the assumption of a random normally distributed series of net basin supply can provide a reasonable first guess for the equilibrium response of a lake and for the likely range of variation of levels. These estimates are likely to be useful in water resources assessments and for investigations of the effects of land use and climate change on lake levels. The effects of departures from this simplified approach are discussed and are illustrated with some practical examples. © 1998 John Wiley & Sons, Ltd.     

Simulation of normal distributed smooth fields by Karhunen-Loéve expansion in combination with kriging

Simulation of multigaussian stochastic fields can be made after a Karhunen-Loéve expansion of a given covariance function. This method is also called simulation by Empirical Orthogonal Functions. The simulations are made by drawing stochastic coefficients from a random generator. These numbers are multiplied with eigenfunctions and eigenvalues derived from the predefined covariance model. The number of eigenfunctions necessary to reproduce the stochastic process within a predefined variance error, turns out to be a cardinal question. Some ordinary analytical covariance functions are used to evaluate how quickly the series of eigenfunctions can be truncated. This analysis demonstrates extremely quick convergence to 99.5% of total variance for the 2nd order exponential (‘gaussian’) covariance function, while the opposite is true for the 1st order exponential covariance function. Due to these convergence characteristics, the Karhunen-Loéve method is most suitable for simulating smooth fields with ‘gaussian’ shaped covariance functions. Practical applications of Karhunen-Loéve simulations can be improved by spatial interpolation of the eigenfunctions. In this paper, we suggest interpolation by kriging and limits for reproduction of the predefined covariance functions are evaluated.