Uncertainty analysis: one-dimensional radioactive nuclide transport in a single fractured media

Uncertainty analysis of radioactive nuclide transport for one-dimensional single fracture has been studied. First order differential analysis is applied to introduce analytical form of output expectation and variance for contaminant transport equation, by regarding uncertainty of dispersion coefficient and retardation factor. Breakthrough curve of dimensionless concentration is demonstrated by taking I-129 as radioactive nuclide in fracture transport. It is possible to pick up critical ranges in spatial and temporal domain from the output variance. From the viewpoint of preliminary performance assessment for nuclear waste disposal the parameter importance in such system can be substantially measured in the site characterization in future.     

Uncertainty propagation of hydrodispersive transfer in an aquifer: an illustration of one-dimensional contaminant transport with slug injection

It is evident that the hydrodynamic dispersion coefficient and linear flow velocity dominate solute transport in aquifers. Both of them play important roles characterizing contaminant transport. However, by definition, the parameter of contaminant transport cannot be measured directly. For most problems of contaminant transport, a conceptual model for solute transport generally is established to fit the breakthrough curve obtained from field testing, and then suitable curve matching or the inverse solution of a theoretical model is used to determine the parameter. This study presents a one-dimensional solute transport problem for slug injection. Differential analysis is used to analyze uncertainty propagation, which is described by the variance and mean. The uncertainties of linear velocity and hydrodynamic dispersion coefficient are, respectively, characterized by the second-power and fourth-power of the length scale multiplied by a lumped relationship of variance and covariance of system parameters, i.e. the Peclet number and arrival time of maximum concentration. To validate the applicability for evaluating variance propagation in one-dimensional solute transport, two cases using field data are presented to demonstrate how parametric uncertainty can be caught depending on the manner of sampling.     

Calibration framework for a Kalman filter applied to a groundwater model

The paper presents a novel approach to the setup of a Kalman filter by using an automatic calibration framework for estimation of the covariance matrices. The calibration consists of two sequential steps: (1) Automatic calibration of a set of covariance parameters to optimize the performance of the system and (2) adjustment of the model and observation variance to provide an uncertainty analysis relying on the data instead of ad-hoc covariance values. The method is applied to a twin-test experiment with a groundwater model and a colored noise Kalman filter. The filter is implemented in an ensemble framework. It is demonstrated that lattice sampling is preferable to the usual Monte Carlo simulation because its ability to preserve the theoretical mean reduces the size of the ensemble needed. The resulting Kalman filter proves to be efficient in correcting dynamic error and bias over the whole domain studied. The uncertainty analysis provides a reliable estimate of the error in the neighborhood of assimilation points but the simplicity of the covariance models leads to underestimation of the errors far from assimilation points.     

Probabilistic seismic loss assessment of aging bridges using a component‐level cost estimation approach

Deteriorating highway bridges in the United States and worldwide have demonstrated susceptibility to damage in earthquake events, with considerable economic consequences due to repair or replacement. Current seismic loss assessment approaches for these critical elements of the transportation network neglect the effects of aging and degradation on the loss estimate. However, the continued aging and deterioration of bridge infrastructure could not only increase susceptibility to seismic damage, but also have a significant impact on these economic losses. Furthermore, the contribution of individual aging components to system‐level losses, correlations between these components, and uncertainty modeling in the risk assessment and repair modeling are all crucial considerations to enhance the accuracy and confidence in bridge loss estimates. In this paper, a new methodology for seismic loss assessment of aging bridges is introduced based on the non‐homogeneous Poisson process. Statistical moments of seismic losses can be efficiently estimated, such as the expected value and variance. The approach is unique in its account for time‐varying seismic vulnerability, uncertainty in component repair, and the contribution of multiple correlated aging components. A representative case study is presented with two fundamentally distinct highway bridges to demonstrate the effects of corrosion deterioration of different bridge components on the seismic losses. Using the proposed model, a sensitivity study is also conducted to assess the effect of parameter variations on the expected seismic losses. The results reveal that the seismic losses estimated by explicitly considering the effects of deterioration of bridge components is significantly higher than that found by assuming time‐invariant structural reliability. Copyright © 2011 John Wiley & Sons, Ltd.     

Stochastic analysis of estuarine hydraulics

A new methodology is presented for the solution of the stochastic hydraulic equations characterizing steady, one-dimensional estuarine flow. The methodology is predicated on quasi-linearization, perturbation methods, and the finite difference approximation of the stochastic differential operators. Assuming Manning's roughness coefficient is the principal source of uncertainty in the model, stochastic equations are presented for the water depths and flow rates in the estuarine system. Moment equations are developed for the mean and variance of the water depths. The moment equations are compared with the results of Monte Carlo simulation experiments. The results confirm that for any spatial location in the estuary that (1) as the uncertainty in the channel roughness increases, the uncertainty in mean depth increases, and (2) the predicted mean depth will decrease with increasing uncertainty in Manning'sn. The quasi-analytical approach requires significantly less computer time than Monte Carlo simulations and provides explicit     

Quantification of the predictive uncertainty of artificial neural network based river flow forecast models

The meaningful quantification of uncertainty in hydrological model outputs is a challenging task since complete knowledge about the hydrologic system is still lacking. Owing to the nonlinearity and complexity associated with the hydrological processes, Artificial neural network (ANN) based models have gained lot of attention for its effectiveness in function approximation characteristics. However, only a few studies have been reported for assessment of uncertainty associated with ANN outputs. This study uses a simple method for quantifying predictive uncertainty of ANN model output through first order Taylor series expansion. The first order partial differential equations of non-linear function approximated by the ANN with respect to weights and biases of the ANN model are derived. A bootstrap technique is employed in estimating the values of the mean and the standard deviation of ANN parameters, and is used to quantify the predictive uncertainty. The method is demonstrated through the case study of Upper White watershed located in the United States. The quantitative assessment of uncertainty is carried out with two measures such as percentage of coverage and average width. In order to show the magnitude of uncertainty in different flow domains, the values are statistically categorized into low-, medium- and high-flow series. The results suggest that the uncertainty bounds of ANN outputs can be effectively quantified using the proposed method. It is observed that the level of uncertainty is directly proportional to the magnitude of the flow and hence varies along time. A comparison of the uncertainty assessment shows that the proposed method effectively quantifies the uncertainty than bootstrap method.     

A numerical Eulerian method of moment for solute transport in a nonstationary dual-porosity medium

An Eulerian perturbation approach was applied to develop a method of moment for solute transport in a nonstationary, fractured medium. The conceptualized fractured medium is described through a dual-porosity model. Stochastic governing equations for mean concentration and concentration covariance were analytically derived to the first-order accuracy of log-conductivity variance and solved with a numerical method––a finite difference method. The developed method is called a numerical Eulerian method of moment (NEMM). This method was compared with the stationary transport theory [Water Resour. Res. 36(7) (2000) 1665] for predicting mean concentration and its spatial moments. The comparison indicated that the two methods matched very well in predicting first and second spatial moments. NEMM solutions were also compared with Monte Carlo simulations for solute transport in stationary fractured media. The results of the two methods were consistent for calculating small log conductivity variance. The theory was then used to study effects of various parameters and nonstationarity of the medium on flow and transport processes. Results indicated that medium nonstationarity would significantly influence the solute transport process. The nonstationary transport theory relaxes many assumptions adopted in stationary theories and paves the way for applying the NEMM to many environmental projects, especially in analyzing uncertainty of solute transport.     

Uncertainty assessment for watershed water quality modeling: A Probabilistic Collocation Method based approach

Watershed water quality models are increasingly used in management. However, simulations by such complex models often involve significant uncertainty, especially those for non-conventional pollutants which are often poorly monitored. This study first proposed an integrated framework for watershed water quality modeling. Within this framework, Probabilistic Collocation Method (PCM) was then applied to a WARMF model of diazinon pollution to assess the modeling uncertainty. Based on PCM, a global sensitivity analysis method named PCM-VD (VD stands for variance decomposition) was also developed, which quantifies variance contribution of all uncertain parameters. The study results validated the applicability of PCM and PCM-VD to the WARMF model. The PCM-based approach is much more efficient, regarding computational time, than conventional Monte Carlo methods. It has also been demonstrated that analysis using the PCM-based approach could provide insights into data collection, model structure improvement and management practices. It was concluded that the PCM-based approach could play an important role in watershed water quality modeling, as an alternative to conventional Monte Carlo methods to account for parametric uncertainty and uncertainty propagation.     

Performance‐based grouping methods of bridge classes for regional seismic risk assessment: Application of ANOVA,ANCOVA, and non‐parametric approaches

One of the key tasks to enable a regional risk assessment is to group structures with similar seismic performances and generate fragility curves representative of the grouped structures. The grouping has been traditionally performed based primarily on engineering judgment and prior experience. This paper (i) presents an overview of various statistical techniques such as analysis of variance, analysis of covariance, and Kruskal–Wallis test for grouping the bridges of similar performance; (ii) compares the groupings that emerge from the various grouping techniques; and (iii) identifies the method that has more statistical power in creating bridge sub‐classes of distinct structural performance. The grouping is achieved by comparing the structural responses of bridge classes obtained from the non‐linear time history analysis of bridges. The relative merits of these grouping techniques are discussed with the case study of box‐girder bridges in California. Copyright © 2017 John Wiley & Sons, Ltd.     

Stochastic modeling of solute transport in 3-D heterogeneous porous media with random source condition

During probabilistic analysis of flow and transport in porous media, the uncertainty due to spatial heterogeneity of governing parameters are often taken into account. The randomness in the source conditions also play a major role on the stochastic behavior in distribution of the dependent variable. The present paper is focused on studying the effect of both uncertainty in the governing system parameters as well as the input source conditions. Under such circumstances, a method is proposed which combines with stochastic finite element method (SFEM) and is illustrated for probabilistic analysis of concentration distribution in a 3-D heterogeneous porous media under the influence of random source condition. In the first step SFEM used for probabilistic solution due to spatial heterogeneity of governing parameters for a unit source pulse. Further, the results from the unit source pulse case have been used for the analysis of multiple pulse case using the numerical convolution when the source condition is a random process. The source condition is modeled as a discrete release of random amount of masses at fixed intervals of time. The mean and standard deviation of concentration is compared for the deterministic and the stochastic system scenarios as well as for different values of system parameters. The effect of uncertainty of source condition is also demonstrated in terms of mean and standard deviation of concentration at various locations in the domain.     

Probabilistic risk and uncertainty analysis for bioremediation of four chlorinated ethenes in groundwater

Groundwater contamination risk assessment for health-threatening compounds should benefit from a stochastic environmental risk assessment which considers the effects of biological, chemical, human behavioral, and physiological processes that involve elements of biotic and abiotic aquifer uncertainty, and human population variability. This paper couples a complex model of chemical degradation and transformation with movement in an aquifer undergoing bioremediation to generate a health risk analysis for different population cohorts in the community. A two-stage Monte Carlo simulation has separate stages for population variability and aquifer uncertainty yielding a computationally efficient and conceptually attractive algorithm. A hypothetical example illustrates how risk variance analysis can be conducted to determine the distribution of risk, and the relative impact of uncertainty and variability in different sets of parameters upon the variation of risk values for adults, adolescents, and children. The groundwater example considers a community water supply contaminated with chlorinated ethenes. Biodegradation pathways are enhanced by addition of butyrate. The results showed that the contribution of uncertainty to the risk variance is comparable to that of variability. Among the uncertain parameters considered, transmissivity accounted for the major part of the output variance. Children were the most susceptible and vulnerable population cohort.     

Seismic resilience of concrete structures under corrosion

A probabilistic approach to lifetime assessment of seismic resilience of deteriorating concrete structures is presented. The effects of environmental damage on the seismic performance are evaluated by means of a methodology for lifetime assessment of concrete structures in aggressive environment under uncertainty. The time‐variant seismic capacity associated with different limit states, from damage limitation up to collapse, is assumed as functionality indicator. The role of the deterioration process on seismic resilience is then investigated over the structural lifetime by evaluating the post‐event residual functionality and recovery of the deteriorating system as a function of the time of occurrence of the seismic event. The proposed approach is applied to a three‐story concrete frame building and a four‐span continuous concrete bridge under corrosion. The results show the combined effects of structural deterioration and seismic damage on the time‐variant system functionality and resilience and indicate the importance of a multi‐hazard life‐cycle‐oriented approach to seismic design of resilient structure and infrastructure systems. Copyright © 2015 John Wiley & Sons, Ltd.     

Uncertainty estimation of pathlines in ground water models

A method is proposed to estimate the uncertainty of the location of pathlines in two-dimensional, steady-state confined or unconfined flow in aquifers due to the uncertainty of the spatially variable unconditional hydraulic conductivity or transmissivity field. The method is based on concepts of the semianalytical first-order theory given in Stauffer et al. (2002, 2004), which allows estimates of the lateral second moment (variance) of the location of a moving particle. However, this method is reformulated in order to account for nonuniform recharge and nonuniform aquifer thickness. One prominent application is the uncertainty estimation of the catchment of a pumping well by considering the boundary pathlines starting at a stagnation point. In this method, the advective transport of particles is considered, based on the velocity field. In the case of a well catchment, backtracking is applied by using the reversed velocity field. Spatial variability of hydraulic conductivity or transmissivity is considered by taking into account an isotropic exponential covariance function of log-transformed values with parameters describing the variance and correlation length. The method allows postprocessing of results from ground water models with respect to uncertainty estimation. The code PPPath, which was developed for this purpose, provides a postprocessing of pathline computations under PMWIN, which is based on MODFLOW. In order to test the methodology, it was applied to results from Monte Carlo simulations for catchments of pumping wells. The results correspond well. Practical applications illustrate the use of the method in aquifers.     

Quantification of uncertainty in the assessment of future streamflow under changing climate conditions

Climate change has a significant influence on streamflow variation. The aim of this study is to quantify different sources of uncertainties in future streamflow projections due to climate change. For this purpose, 4 global climate models, 3 greenhouse gas emission scenarios (representative concentration pathways), 6 downscaling models, and a hydrologic model (UBCWM) are used. The assessment work is conducted for 2 different future time periods (2036 to 2065 and 2066 to 2095). Generalized extreme value distribution is used for the analysis of the flow frequency. Strathcona dam in the Campbell River basin, British Columbia, Canada, is used as a case study. The results show that the downscaling models contribute the highest amount of uncertainty to future streamflow predictions when compared to the contributions by global climate models or representative concentration pathways. It is also observed that the summer flows into Strathcona dam will decrease, and winter flows will increase in both future time periods. In addition to these, the flow magnitude becomes more uncertain for higher return periods in the Campbell River system under climate change.     

基于独立分量分析的南极半岛GNSS网区域滤波

高精度GNSS速度场是研究地壳垂向运动及板块运动的基础,能够为冰川均衡调整（Glacial Isostatic Adjustment,GIA）的建模提供外部检核和新的约束.共性误差（Common Mode Error,CME）是区域连续GNSS时间序列中存在的一种与时空相关的主要误差源,通过空间滤波可有效的降低共性误差的影响,提高坐标时间序列的精度.目前广泛采用的主分量分析法（Principal Component Analysis,PCA）,基于二阶统计量（方差和协方差）进行处理,没有充分利用CME高阶统计信息.而独立分量分析ICA （Independent Component Analysis）,引入高阶统计量,能够分离出统计独立的非高斯信号.以南极半岛地区的15个GNSS站点为例,由于某些站点存在强烈的局部效应,因此引入了因子分析法首先对异常站进行剔除,然后对比分析了PCA和ICA方法在南极半岛地区区域滤波结果.结果显示,ICA的滤波效果要优于PCA,ICA滤波前后E、N、U三个方向RMS平均降低44.69%、26.94%、34.87%,不确定度分别降低37.43%,44.58%,55.86%,有效的降低了GNSS残差序列的发散性和速度的不确定度.     

Time scale effect and uncertainty in reconstruction of paleo‐hydrology

Tree‐ring‐based reconstructions of paleo‐hydrology have proved useful for better understanding the irregularities and extent of past climate changes, and therefore, for more effective water resources management. Despite considerable advances in the field, there still exist challenges that introduce significant uncertainties into paleo‐reconstructions. This study outlines these challenges and address them by developing two themes: (1) the effect of temporal scaling on the strength of the relationship between the hydrologic variables, streamflow in this study, and tree growth rates and (2) the reconstruction uncertainty of streamflow due to the dissimilarity or inconsistency in the pool of tree‐ring chronologies (predictors in reconstruction) in a basin. Based on the insight gained, a methodology is developed to move beyond only relying on the annual hydrology‐growth correlations, and to utilize additional information embedded in the annual time series at longer time scales (e.g. multi‐year to decadal time scales). This methodology also generates an ensemble of streamflow reconstructions to formally account for uncertainty in the pool of chronology sites. The major headwater tributaries of the Saskatchewan River Basin, the main source of surface water in the Canadian Prairie Provinces, are used as the case study. It is shown that the developed methodology explains the variance of streamflows to a larger extent than the conventional approach and better preserves the persistence and variability of streamflows across time scales (Hurst‐type behaviour). The resulting ensemble of paleo‐hydrologic time series is able to more credibly pinpoint the timing and extent of past dry and wet periods and provides a dynamic range of uncertainty in reconstruction. This range varies with time over the course of the reconstruction period, indicating that the utility of tree‐ring chronologies for paleo‐reconstruction differs for different time periods over the past several centuries in the history of the region. The proposed ensemble approach provides a credible range of multiple‐century‐long water availability scenarios that can be used for vulnerability assessment of the existing water infrastructure and improving water resources management. Copyright © 2015 John Wiley & Sons, Ltd.     

MODFLOW 2000 head uncertainty,a first-order second moment method

A computationally efficient method to estimate the variance and covariance in piezometric head results computed through MODFLOW 2000 using a first-order second moment (FOSM) approach is presented. This methodology employs a first-order Taylor series expansion to combine model sensitivity with uncertainty in geologic data. MODFLOW 2000 is used to calculate both the ground water head and the sensitivity of head to changes in input data. From a limited number of samples, geologic data are extrapolated and their associated uncertainties are computed through a conditional probability calculation. Combining the spatially related sensitivity and input uncertainty produces the variance-covariance matrix, the diagonal of which is used to yield the standard deviation in MODFLOW 2000 head. The variance in piezometric head can be used for calibrating the model, estimating confidence intervals, directing exploration, and evaluating the reliability of a design. A case study illustrates the approach, where aquifer transmissivity is the spatially related uncertain geologic input data. The FOSM methodology is shown to be applicable for calculating output uncertainty for (1) spatially related input and output data, and (2) multiple input parameters (transmissivity and recharge).     

Seismic response evaluation of the impact of corrosion on buried pipelines based on the Markov process

Water distribution and gas supply systems are among the infrastructure systems that have many buried steel pipelines. Corrosion gradually appears inside and outside of the pipe walls over the service life of these pipelines, the corrosion is primarily caused by the surrounding soil and the materials that flow through the pipelines. However, due to the uncertainty of the characteristics of the soil and materials, the size of the corrosion region is a stochastic variable. In this paper, using a homogeneous Markov process, a model is presented to simulate the occurrence of corrosion. Then, in combinations with a linear corrosion development model, the probability density function of the pipeline area corrosion percentage is derived. Based on the corrosion model, the pipeline seismic displacements and stresses are predicted. Furthermore, using the random perturbation approach, the mean and variance of the pipeline seismic response are given. To illustrate the validity of the proposed approach, a 200-meter long pipeline is numerically investigated and its random seismic response is obtained.     

Evaluating the utility of the ensemble transform Kalman filter for adaptive sampling when updating a hydrodynamic model

This paper compares two Monte Carlo sequential data assimilation methods based on the Kalman filter, for estimating the effect of measurements on simulations of state error variance made by a one-dimensional hydrodynamic model. The first method used an ensemble Kalman filter (EnKF) to update state estimates, which were then used as initial conditions for further simulations. The second method used an ensemble transform Kalman filter (ETKF) to quickly estimate the effect of measurement error covariance on forecast error covariance without the need to re-run the simulation model. The ETKF gave an unbiased estimate of EnKF analysed error variance, although differences in the treatment of measurement errors meant the results were not identical. Estimates of forecast error variance could also be made, but their accuracy deteriorated as the time from measurements increased due in part to model non-linearity and the decreasing signal variance. The motivation behind the study was to assess the ability of the ETKF to target possible measurements, as part of an adaptive sampling framework, before they are assimilated by an EnKF-based forecasting model on the River Crouch, Essex, UK. The ETKF was found to be a useful tool for quickly estimating the error covariance expected after assimilating measurements into the hydrodynamic model. It, thus, provided a means of quantifying the ‘usefulness’ (in terms of error variance) of possible sampling schemes.     

Assimilation of ice concentration in a coupled ice–ocean model,using the Ensemble Kalman filter

An implementation of the Ensemble Kalman filter (EnKF) with a coupled ice–ocean model is presented. The model system consists of a dynamic–thermodynamic ice model using the elastic-viscous-plastic (EVP) rheology coupled with the HYbrid Coordinate Ocean Model (HYCOM). The observed variable is ice concentration from passive microwave sensor data (SSM/I). The assimilation of ice concentration has the desired effect of reducing the difference between observations and model. Comparison of the assimilation experiment with a free-run experiment shows that there are large differences, especially in summer. In winter the differences are relatively small, partly because the atmospheric forcing used to run the model depends upon SSM/I data. The assimilation has the strongest impact close to the ice edge, where it ensures a correct location of the ice edge throughout the simulation. An inspection of the model ensemble statistics reveals that the error estimates of the model are too small in winter, partly a result of too low model ice-concentration variance in the central ice pack. It is found that the ensemble covariance between ice concentration and sea-surface temperature in the same grid cell is of the same sign (negative) throughout the year. The ensemble covariance between ice concentration and salinity is more dependent upon the physical mechanisms involved, with ice transport and freeze/melt giving different signs of the covariances. The ice-transport and ice-melt mechanisms also impact the ice-concentration variance and the covariance between ice concentration and ice thickness. The ensemble statistics show a high degree of complexity, which to some extent merits the use of computationally expensive assimilation methods, such as the Ensemble Kalman filter. The present study focuses on the assimilation of ice concentration, but it is understood that assimilation of other datasets, such as sea-surface temperature, would be beneficial.Responsible Editor: Jin-Song von Storch