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1.
The results of a series of high-resolution numerical experiments are used to test and compare three nonlinear models for high-concentration-gradient dispersion. Gravity stable miscible displacement is considered. The first model, introduced by Hassanizadeh, is a modification of Fick’s law which involves a second-order term in the dispersive flux equation and an additional dispersion parameter β. The numerical experiments confirm the dependency of β on the flow rate. In addition, a dependency on travelled distance is observed. The model can successfully be applied to nearly homogeneous media (σ2 = 0.1), but additional fitting is required for more heterogeneous media.The second and third models are based on homogenization of the local scale equations describing density-dependent transport. Egorov considers media that are heterogeneous on the Darcy scale, whereas Demidov starts at the pore-scale level. Both approaches result in a macroscopic balance equation in which the dispersion coefficient is a function of the dimensionless density gradient. In addition, an expression for the concentration variance is derived. For small σ2, Egorov’s model predictions are in satisfactory agreement with the numerical experiments without the introduction of any new parameters. Demidov’s model involves an additional fitting parameter, but can be applied to more heterogeneous media as well.  相似文献   

2.
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.  相似文献   

3.
Pore-scale dispersion (PSD), aquifer heterogeneity, sampling volume, and source size influence solute concentrations of conservative tracers transported in heterogeneous porous formations. In this work, we developed a new set of analytical solutions for the concentration ensemble mean, variance, and coefficient of variation (CV), which consider the effects of all these factors. We developed these models as generalizations of the first-order solutions in the log-conductivity variance of point concentration proposed by [Fiori A, Dagan G. Concentration fluctuations in aquifer transport: a rigorous first-order solution and applications. J Contam Hydrol 2000;45(1–2):139–163]. Our first-order solutions compare well with numerical simulations for small and moderate formation heterogeneity and from small to large sampling and source volumes. However, their performance deteriorates for highly heterogeneous formations. Successively, we used our models to study the interplay among sampler size, source volume, and PSD. Our analysis shows a complex and important interaction among these factors. Additionally, we show that the relative importance of these factors is also a function of plume age, of aquifer heterogeneity, and of the measurement location with respect to the mean plume center of gravity. We found that the concentration moments are chiefly controlled by the sampling volume with pore-scale dispersion playing a minor role at short times and for small source volumes. However, the effect of the source volume cannot be neglected when it is larger than the sampling volume. A different behavior occurs for long periods, which may be relevant for old contaminations, or for small injection volumes. In these cases, PSD causes a significant dilution, which is reflected in the concentration statistics. Additionally, at the center of the mean plume, where high concentrations are most likely to occur, we found that sampling volume and PSD are attenuating mechanisms for both concentration ensemble mean and coefficient of variation, except at very large source and sampler sizes, where the coefficient of variation increases with sampler size and PSD. Formation heterogeneity causes a faster reduction of the ensemble mean concentrations and a larger uncertainty at the center of the mean plume. Therefore, our results highlight the importance of considering the combined effect of formation heterogeneity, exposure volume, PSD, source size, and measurement location in performing risk assessment.  相似文献   

4.
Providing reliable and accurate storm surge forecasts is important for a wide range of problems related to coastal environments. In order to adequately support decision-making processes, it also become increasingly important to be able to estimate the uncertainty associated with the storm surge forecast. The procedure commonly adopted to do this uses the results of a hydrodynamic model forced by a set of different meteorological forecasts; however, this approach requires a considerable, if not prohibitive, computational cost for real-time application. In the present paper we present two simplified methods for estimating the uncertainty affecting storm surge prediction with moderate computational effort. In the first approach we use a computationally fast, statistical tidal model instead of a hydrodynamic numerical model to estimate storm surge uncertainty. The second approach is based on the observation that the uncertainty in the sea level forecast mainly stems from the uncertainty affecting the meteorological fields; this has led to the idea to estimate forecast uncertainty via a linear combination of suitable meteorological variances, directly extracted from the meteorological fields. The proposed methods were applied to estimate the uncertainty in the storm surge forecast in the Venice Lagoon. The results clearly show that the uncertainty estimated through a linear combination of suitable meteorological variances nicely matches the one obtained using the deterministic approach and overcomes some intrinsic limitations in the use of a statistical tidal model.  相似文献   

5.
Groundwater prediction models are subjected to various sources of uncertainty. This study introduces a hierarchical Bayesian model averaging (HBMA) method to segregate and prioritize sources of uncertainty in a hierarchical structure and conduct BMA for concentration prediction. A BMA tree of models is developed to understand the impact of individual sources of uncertainty and uncertainty propagation to model predictions. HBMA evaluates the relative importance of different modeling propositions at each level in the BMA tree of model weights. The HBMA method is applied to chloride concentration prediction for the “1,500‐foot” sand of the Baton Rouge area, Louisiana from 2005 to 2029. The groundwater head data from 1990 to 2004 is used for model calibration. Four sources of uncertainty are considered and resulted in 180 flow and transport models for concentration prediction. The results show that prediction variances of concentration from uncertain model elements are much higher than the prediction variance from uncertain model parameters. The HBMA method is able to quantify the contributions of individual sources of uncertainty to the total uncertainty.  相似文献   

6.
In this paper we analyze a model for brine transport in porous media, which includes a mass balance for the fluid, a mass balance for salt, Darcy's law and an equation of state, which relates the fluid density to the salt mass fraction. This model incorporates the effect of local volume changes due to variations in the salt concentration. Density variations affect the compressibility of the fluid, which in turn cause additional fluid flow. Two specific situations are investigated that lead to self similarity. We study the relative importance of the compressibility effect in terms of the relative density difference. Semi-analytical solutions are obtained as well as asymptotic expressions in terms of the relative density difference. It is found that the volume changes have a small but noticeable effect on the mass transport only when the salt concentration gradients are large. Some results on the simultaneous transport of brine and dissolved (radioactive) tracers are presented.  相似文献   

7.
Morphological change in river channels is frequently evaluated in the context of mass balance sediment budgets. In a closed sediment budget, measurements of sediment influx and efflux are coupled with measured changes in channel topography to provide both spatial and temporal resolution, and independent estimates of the mass balance. For sediment budgets constructed over long river segments (~102 channel widths or greater) and long periods (~2 years or longer), spatial and temporal accumulation of measurement uncertainty, compounded by inadequate sampling frequency or spatial coverage, may produce indeterminate results. The degree of indeterminacy may be evaluated in the context of a signal-to-noise ratio (SNR), which is a function of the magnitude of the mass balance and the magnitudes of potential systematic uncertainties associated with measurements and incomplete sampling. We report on a closed sand budget consisting of measurements of flux and two morphological surveys for a 50-km segment of a large river over a 3-year period. Accurate reporting of the magnitude and sign of the change in sand storage was only possible by using state-of-the-art techniques with high temporal frequency and large spatial extent. Together, a sand flux and morphological mass balance revealed that sand evacuation was temporally concentrated (~100% of mass change occurred during 19% of the study period) and highly localized (70% of mass change occurred in 12% of the study segment). A SNR analysis revealed that uncertainty resulting from undersampling may approach or exceed that caused by measurement uncertainty and that daily sampling of suspended-sand concentration or repeat mapping of at least 50% of the river segment was required to determine the sand budget with SNR > 1. The approach used here to analyze sand budget uncertainty is especially applicable to other river systems with large temporal variability in sediment transport and large spatial variability in erosion and deposition. © 2018 John Wiley & Sons, Ltd.  相似文献   

8.
The present study assesses the uncertainty of flow and radionuclide transport in the unsaturated zone at Yucca Mountain using a Monte Carlo method. Matrix permeability, porosity, and sorption coefficient are considered random. Different from previous studies that assume distributions of the parameters, the distributions are determined in this study by applying comprehensive transformations and rigorous statistics to on-site measurements of the parameters. The distribution of permeability is further adjusted based on model calibration results. Correlation between matrix permeability and porosity is incorporated using the Latin Hypercube Sampling method. After conducting 200 Monte Carlo simulations of three-dimensional unsaturated flow and radionuclide transport for conservative and reactive tracers, the mean, variances, and 5th, 50th, and 95th percentiles for quantities of interest (e.g., matrix liquid saturation and water potential) are evaluated. The mean and 50th percentile are used as the mean predictions, and their associated predictive uncertainties are measured by the variances and the 5th and 95th percentiles (also known as uncertainty bounds). The mean predictions of matrix liquid saturation and water potential are in reasonable agreement with corresponding measurements. The uncertainty bounds include a large portion of the measurements, suggesting that the data variability can be partially explained by parameter uncertainty. The study illustrates propagation of predictive uncertainty of percolation flux, increasing downward from repository horizon to water table. Statistics from the breakthrough curves indicate that transport of the reactive tracer is delayed significantly by the sorption process, and prediction on the reactive tracer is of greater uncertainty than on the conservative tracer because randomness in the sorption coefficient increases the prediction uncertainty. Uncertainty in radionuclide transport is related to uncertainty in the percolation flux, suggesting that reducing the former entails reduction in the latter.  相似文献   

9.
Numerical simulations of non-ergodic transport of a non-reactive solute plume by steady-state groundwater flow under a uniform mean velocity, , were conducted in a three-dimensional heterogeneous and statistically isotropic aquifer. The hydraulic conductivity, K(x), is modeled as a random field which is assumed to be log-normally distributed with an exponential covariance. Significant efforts are made to reduce the simulation uncertainties. Ensemble averages of the second spatial moments of the plume and the plume centroid variances were simulated with 1600 Monte Carlo (MC) runs for three variances of log K, Y2=0.09, 0.23, and 0.46, and a square source normal to of three dimensionless lengths. It is showed that 1600 MC runs are needed to obtain stabilized results in mildly heterogeneous aquifers of Y20.5 and that large uncertainty may exist in the simulated results if less MC runs are used, especially for the transverse second spatial moments and the plume centroid variance in transverse directions. The simulated longitudinal second spatial moment and the plume centroid variance in longitudinal direction fit well to the first-order theoretical results while the simulated transverse moments are generally larger than the first-order values. The ergodic condition for the second spatial moments is far from reaching in all cases simulated and transport in transverse directions may reach ergodic condition much slower than that in longitudinal direction.  相似文献   

10.
Remotely sensed land cover maps are increasingly used as inputs into environmental simulation models whose outputs inform decisions and policy-making. Risks associated with these decisions are dependent on model output uncertainty, which is in turn affected by the uncertainty of land cover inputs. This article presents a method of quantifying the uncertainty that results from potential mis-classification in remotely sensed land cover maps. In addition to quantifying uncertainty in the classification of individual pixels in the map, we also address the important case where land cover maps have been upscaled to a coarser grid to suit the users’ needs and are reported as proportions of land cover type. The approach is Bayesian and incorporates several layers of modelling but is straightforward to implement. First, we incorporate data in the confusion matrix derived from an independent field survey, and discuss the appropriate way to model such data. Second, we account for spatial correlation in the true land cover map, using the remotely sensed map as a prior. Third, spatial correlation in the mis-classification characteristics is induced by modelling their variance. The result is that we are able to simulate posterior means and variances for individual sites and the entire map using a simple Monte Carlo algorithm. The method is applied to the Land Cover Map 2000 for the region of England and Wales, a map used as an input into a current dynamic carbon flux model.  相似文献   

11.
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.  相似文献   

12.
Conventional geostatistics often relies on the assumption of second order stationarity of the random function (RF). Generally, local means and local variances of the random variables (RVs) are assumed to be constant throughout the domain. Large scale differences in the local means and local variances of the RVs are referred to as trends. Two problems of building geostatistical models in presence of mean trends are: (1) inflation of the conditional variances and (2) the spatial continuity is exaggerated. Variance trends on the other hand cause conditional variances to be over-estimated in certain regions of the domain and under-estimated in other areas. In both cases the uncertainty characterized by the geostatistical model is improperly assessed. This paper proposes a new approach to identify the presence and contribution of mean and variance trends in the domain via calculation of the experimental semivariogram. The traditional experimental semivariogram expression is decomposed into three components: (1) the mean trend, (2) the variance trend and (3) the stationary component. Under stationary conditions, both the mean and the variance trend components should be close to zero. This proposed approach is intended to be used in the early stages of data analysis when domains are being defined or to verify the impact of detrending techniques in the conditioning dataset for validating domains. This approach determines the source of a trend, thereby facilitating the choice of a suitable detrending method for effective resource modeling.  相似文献   

13.
A key point in the application of multi‐model Bayesian averaging techniques to assess the predictive uncertainty in groundwater modelling applications is the definition of prior model probabilities, which reflect the prior perception about the plausibility of alternative models. In this work the influence of prior knowledge and prior model probabilities on posterior model probabilities, multi‐model predictions, and conceptual model uncertainty estimations is analysed. The sensitivity to prior model probabilities is assessed using an extensive numerical analysis in which the prior probability space of a set of plausible conceptualizations is discretized to obtain a large ensemble of possible combinations of prior model probabilities. Additionally, the value of prior knowledge about alternative models in reducing conceptual model uncertainty is assessed by considering three example knowledge states, expressed as quantitative relations among the alternative models. A constrained maximum entropy approach is used to find the set of prior model probabilities that correspond to the different prior knowledge states. For illustrative purposes, a three‐dimensional hypothetical setup approximated by seven alternative conceptual models is employed. Results show that posterior model probabilities, leading moments of the predictive distributions and estimations of conceptual model uncertainty are very sensitive to prior model probabilities, indicating the relevance of selecting proper prior probabilities. Additionally, including proper prior knowledge improves the predictive performance of the multi‐model approach, expressed by reductions of the multi‐model prediction variances by up to 60% compared with a non‐informative case. However, the ratio between‐model to total variance does not substantially decrease. This suggests that the contribution of conceptual model uncertainty to the total variance cannot be further reduced based only on prior knowledge about the plausibility of alternative models. These results advocate including proper prior knowledge about alternative conceptualizations in combination with extra conditioning data to further reduce conceptual model uncertainty in groundwater modelling predictions. Copyright © 2009 John Wiley & Sons, Ltd.  相似文献   

14.
Large-scale advective transport through highly heterogeneous 3D formations is investigated using highly resolved numerical simulations and simple analytic models. Investigations are focused on impacts of two types of contaminant injection on transport through isotropic formations where flow conditions are uniform in the average. Transport is quantified by analyzing breakthrough curves for control planes at various distances from the injection zone. In flux-proportional injection mode local mass in injection zone is proportional to local groundwater flux; this setup models many practical cases such as contaminant injection through wells. In resident concentration mode local concentration in injection zone is constant. Results show that impacts of injection mode on breakthrough curves and their moments are strong and they persist for hundreds of correlation scales. The resident concentration mode leads to a fatter tails of the breakthrough curves, while the peaks are generally underpredicted. For a synthetic porous medium with logconductivity variance of 8, dispersivity computed using resident concentration mode at control plane 100 integral scales away from the injection zone was about 10 times larger than corresponding one for flux-proportional mode. Hence, injection mode impacts on transport through highly heterogeneous formations are strong and they persist for large distances from the injection zone.  相似文献   

15.
In this work, we address the problem of characterizing the heterogeneity and uncertainty of hydraulic properties for complex geological settings. Hereby, we distinguish between two scales of heterogeneity, namely the hydrofacies structure and the intrafacies variability of the hydraulic properties. We employ multiple-point geostatistics to characterize the hydrofacies architecture. The multiple-point statistics are borrowed from a training image that is designed to reflect the prior geological conceptualization. The intrafacies variability of the hydraulic properties is represented using conventional two-point correlation methods, more precisely, spatial covariance models under a multi-Gaussian spatial law. We address the different levels and sources of uncertainty in characterizing the subsurface heterogeneity, and explore their effect on groundwater flow and transport predictions. Typically, uncertainty is assessed by way of many images, termed realizations, of a fixed statistical model. However, in many cases, sampling from a fixed stochastic model does not adequately represent the space of uncertainty. It neglects the uncertainty related to the selection of the stochastic model and the estimation of its input parameters. We acknowledge the uncertainty inherent in the definition of the prior conceptual model of aquifer architecture and in the estimation of global statistics, anisotropy, and correlation scales. Spatial bootstrap is used to assess the uncertainty of the unknown statistical parameters. As an illustrative example, we employ a synthetic field that represents a fluvial setting consisting of an interconnected network of channel sands embedded within finer-grained floodplain material. For this highly non-stationary setting we quantify the groundwater flow and transport model prediction uncertainty for various levels of hydrogeological uncertainty. Results indicate the importance of accurately describing the facies geometry, especially for transport predictions.  相似文献   

16.
A challenge in microseismic monitoring is quantification of survey acquisition and processing errors, and how these errors jointly affect estimated locations. Quantifying acquisition and processing errors and uncertainty has multiple benefits, such as more accurate and precise estimation of locations, anisotropy, moment tensor inversion and, potentially, allowing for detection of 4D reservoir changes. Here, we quantify uncertainty due to acquisition, receiver orientation error, and hodogram analysis. Additionally, we illustrate the effects of signal to noise ratio variances upon event detection. We apply processing steps to a downhole microseismic dataset from Pouce Coupe, Alberta, Canada. We use a probabilistic location approach to identify the optimal bottom well location based upon known source locations. Probability density functions are utilized to quantify uncertainty and propagate it through processing, including in source location inversion to describe the three-dimensional event location likelihood. Event locations are calculated and an amplitude stacking approach is used to reduce the error associated with first break picking and the minimization with modelled travel times. Changes in the early processing steps have allowed for understanding of location uncertainty of the mapped microseismic events.  相似文献   

17.
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18.
This paper presents the extension of the self-calibrating method to the coupled inverse modelling of groundwater flow and mass transport. The method generates equally likely solutions to the inverse problem that display the variability as observed in the field and are not affected by a linearisation of the state equations. Conditioning to the state variables is measured by an objective function including, among others, the mismatch between the simulated and measured concentrations. Conditioning is achieved by minimising the objective function by gradient-based methods. The gradient contains the partial derivatives of the objective function with respect to: log conductivities, log storativities, prescribed heads at boundaries, retardation coefficients and mass sources. The derivatives of the objective function with respect to log conductivity are the most cumbersome and need the most CPU-time to be evaluated. For this reason, to compute this derivative only advective transport is considered. The gradient is calculated by the adjoint-state method. The method is demonstrated in a controlled, synthetic study, in which the worth of concentration data is analysed. It is shown that concentration data are essential to improve transport predictions and also help to improve aquifer characterisation and flow predictions, especially in the upstream part of the aquifer, even in the case that a considerable amount of other experimental data like conductivities and heads are available. Besides, conditioning to concentration data reduces the ensemble variances of estimated transmissivity, hydraulic head and concentration.  相似文献   

19.
Abstract

Using the Monte Carlo (MC) method, this paper derives arithmetic and geometric means and associated variances of the net capillary drive parameter, G, that appears in the Parlange infiltration model, as a function of soil texture and antecedent soil moisture content. Approximate expressions for the arithmetic and geometric statistics of G are also obtained, which compare favourably with MC generated ones. This paper also applies the MC method to evaluate parameter sensitivity and predictive uncertainty of the distributed runoff and erosion model KINEROS2 in a small experimental watershed. The MC simulations of flow and sediment related variables show that those parameters which impart the greatest uncertainty to KINEROS2 model outputs are not necessarily the most sensitive ones. Soil hydraulic conductivity and wetting front net capillary drive, followed by initial effective relative saturation, dominated uncertainties of flow and sediment discharge model outputs at the watershed outlet. Model predictive uncertainty measured by the coefficient of variation decreased with rainfall intensity, thus implying improved model reliability for larger rainfall events. The antecedent relative saturation was the most sensitive parameter in all but the peak arrival times, followed by the overland plane roughness coefficient. Among the sediment related parameters, the median particle size and hydraulic erosion parameters dominated sediment model output uncertainty and sensitivity. Effect of rain splash erosion coefficient was negligible. Comparison of medians from MC simulations and simulations by direct substitution of average parameters with observed flow rates and sediment discharges indicates that KINEROS2 can be applied to ungauged watersheds and still produce runoff and sediment yield predictions within order of magnitude of accuracy.  相似文献   

20.
In this paper,a test or alternative scheme for studying large earthquake sequences through the study of small earthquake sequences is suggested,and a small earthquake sequence,the Lima earthquake sequence for which analogue records have been turned into digital data,is used here.In order to provide the deep construction background and the spatial distribution of structure for generating earthquakes,the P-wave and S-wave layered velocity models in this area are obtained by using mine explosion and earthquake observed records; then,the hypocenter locations and focal depths of the Lima earthquake sequence are determined adopting the velocity models given above and using a location method with numerical properties for a microseismic monitoring network(Zhao et al.,1994)and a new method for determining focal depth from data of a local seismographic network(Zhao,1992); finally,based on this,the variation of quality factor Q of the crustal medium during the period of the sequence is estimated.The obtained resul  相似文献   

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