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1.
The success of modeling groundwater is strongly influenced by the accuracy of the model parameters that are used to characterize the subsurface system. However, the presence of uncertainty and possibly bias in groundwater model source/sink terms may lead to biased estimates of model parameters and model predictions when the standard regression‐based inverse modeling techniques are used. This study first quantifies the levels of bias in groundwater model parameters and predictions due to the presence of errors in irrigation data. Then, a new inverse modeling technique called input uncertainty weighted least‐squares (IUWLS) is presented for unbiased estimation of the parameters when pumping and other source/sink data are uncertain. The approach uses the concept of generalized least‐squares method with the weight of the objective function depending on the level of pumping uncertainty and iteratively adjusted during the parameter optimization process. We have conducted both analytical and numerical experiments, using irrigation pumping data from the Republican River Basin in Nebraska, to evaluate the performance of ordinary least‐squares (OLS) and IUWLS calibration methods under different levels of uncertainty of irrigation data and calibration conditions. The result from the OLS method shows the presence of statistically significant (p < 0.05) bias in estimated parameters and model predictions that persist despite calibrating the models to different calibration data and sample sizes. However, by directly accounting for the irrigation pumping uncertainties during the calibration procedures, the proposed IUWLS is able to minimize the bias effectively without adding significant computational burden to the calibration processes.  相似文献   

2.
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   

3.
Physical properties of alluvial environments typically feature a high degree of anisotropy and are characterized by dynamic interactions between the surface and the subsurface. Hydrogeological models are often calibrated under the assumptions of isotropic hydraulic conductivity fields and steady-state conditions. We aim at understanding how these simplifications affect predictions of the water table using physically based models and advanced calibration and uncertainty analysis approaches based on singular value decomposition and Bayesian analysis. Specifically, we present an analysis of the information content provided by steady-state hydraulic data compared to transient data with respect to the estimation of aquifer and riverbed hydraulic properties. We show that assuming isotropy or fixed anisotropy may generate biases both in the estimation of aquifer and riverbed parameters as well as in the predictive uncertainty of the water table. We further demonstrate that the information content provided by steady-state hydraulic heads is insufficient to jointly estimate the aquifer anisotropy together with the aquifer and riverbed hydraulic conductivities and that transient data can help to reduce the predictive uncertainty to a greater extent. The outcomes of the synthetic analysis are applied to the calibration of a dynamic and anisotropic alluvial aquifer in Switzerland (The Rhône River). The results of the synthetic and real world modeling and calibration exercises documented herein provide insight on future data acquisition as well as modeling and calibration strategies for these environments. They also provide an incentive for evaluation and estimation of commonly made simplifying assumptions in order to prevent underestimation of the predictive uncertainty.  相似文献   

4.
Most groundwater models simulate stream‐aquifer interactions with a head‐dependent flux boundary condition based on a river conductance (CRIV). CRIV is usually calibrated with other parameters by history matching. However, the inverse problem of groundwater models is often ill‐posed and individual model parameters are likely to be poorly constrained. Ill‐posedness can be addressed by Tikhonov regularization with prior knowledge on parameter values. The difficulty with a lumped parameter like CRIV, which cannot be measured in the field, is to find suitable initial and regularization values. Several formulations have been proposed for the estimation of CRIV from physical parameters. However, these methods are either too simple to provide a reliable estimate of CRIV, or too complex to be easily implemented by groundwater modelers. This paper addresses the issue with a flexible and operational tool based on a 2D numerical model in a local vertical cross section, where the river conductance is computed from selected geometric and hydrodynamic parameters. Contrary to other approaches, the grid size of the regional model and the anisotropy of the aquifer hydraulic conductivity are also taken into account. A global sensitivity analysis indicates the strong sensitivity of CRIV to these parameters. This enhancement for the prior estimation of CRIV is a step forward for the calibration and uncertainty analysis of surface‐subsurface models. It is especially useful for modeling objectives that require CRIV to be well known such as conjunctive surface water‐groundwater use.  相似文献   

5.
Subsurface formations are characterized by heterogeneity over multiple length scales, which can have a strong impact on flow and transport. In this paper, we present a new upscaling approach, based on time-of-flight (TOF), to generate upscaled two-phase flow functions. The method focuses on more accurate representations of local saturation boundary conditions, which are found to have a dominant impact (in comparison to the pressure boundary conditions) on the upscaled two-phase flow models. The TOF-based upscaling approach effectively incorporates single-phase flow and transport information into local upscaling calculations, accounting for the global flow effects on saturation, as well as the local variations due to subgrid heterogeneity. The method can be categorized into quasi-global upscaling techniques, as the global single-phase flow and transport information is incorporated in the local boundary conditions. The TOF-based two-phase upscaling can be readily integrated into any existing local two-phase upscaling framework, thus more flexible than local–global two-phase upscaling approaches developed recently. The method was applied to permeability fields with different correlation lengths and various fluid-mobility ratios. It was shown that the new method consistently outperforms existing local two-phase upscaling techniques, including recently developed methods with improved local boundary conditions (such as effective flux boundary conditions), and provides accurate coarse-scale models for both flow and transport.  相似文献   

6.
Non-unique solutions of inverse problems arise from a lack of information that satisfies necessary conditions for the problem to be well defined. This paper investigates these conditions for inverse modeling of water flow through multi-dimensional variably saturated porous media. It shows that in order to obtain a unique estimate of hydraulic parameters, along each streamline of the flow field (1) spatial and temporal head observations must be given; (2) the number of spatial and temporal head observations required should be greater or equal to the number of unknown parameters; (3) the flux boundary condition or the pumping rate of a well must be specified for the homogeneous case and both boundary flux and pumping rate are a must for the heterogeneous case; (4) head observations must encompass both saturated and unsaturated conditions, and the functional relationships for unsaturated hydraulic conductivity/pressure head and for the moisture retention should be given, and (5) the residual water content value also need to be specified a priori or water content measurements are needed for the estimation of the saturated water content.For field problems, these necessary conditions can be collected or estimated but likely involve uncertainty. While the problems become well defined and have unique solutions, the solutions likely will be uncertain. Because of this uncertainty, stochastic approaches are deemed to be appropriate for inverse problems as they are for forward problems to address uncertainty. Nevertheless, knowledge of these necessary conditions is critical to reduce uncertainty in both characterization of the vadose zone and the aquifer, and prediction of water flow and solute migration in the subsurface.  相似文献   

7.
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8.
A number of challenges including instability, nonconvergence, nonuniqueness, nonoptimality, and lack of a general guideline for inverse modelling have limited the application of automatic calibration by generic inversion codes in solving the saltwater intrusion problem in real‐world cases. A systematic parameter selection procedure for the selection of a small number of independent parameters is applied to a real case of saltwater intrusion in a small island aquifer system in the semiarid region of the Persian Gulf. The methodology aims at reducing parameter nonuniqueness and uncertainty and the time spent on inverse modelling computations. Subsequent to the automatic calibration of the numerical model, uncertainty is analysed by constrained nonlinear optimization of the inverse model. The results define the percentage of uncertainty in the parameter estimation that will maintain the model inside a user‐defined neighbourhood of the best possible calibrated model. Sensitivity maps of both pressure and concentration for the small island aquifer system are also developed. These sensitivity maps indicate higher sensitivity of pressure to model parameters compared with concentration. These sensitivity maps serve as a benchmark for correlation analysis and also assist in the selection of observations points of pressure and concentration in the calibration process. Copyright © 2012 John Wiley & Sons, Ltd.  相似文献   

9.
Traditionally the Cooper–Jacob equation is used to determine the transmissivity and the storage coefficient for an aquifer using pump test results. This model, however, is a simplified version of the actual subsurface and does not allow for analysis of the uncertainty that comes from a lack of knowledge about the heterogeneity of the environment under investigation. In this paper, a modified fuzzy least-squares regression (MFLSR) method is developed that uses imprecise pump test data to obtain fuzzy intercept and slope values which are then used in the Cooper–Jacob method. Fuzzy membership functions for the transmissivity and the storage coefficient are then calculated using the extension principle. The supports of the fuzzy membership functions incorporate the transmissivity and storage coefficient values that would be obtained using ordinary least-squares regression and the Cooper–Jacob method. The MFLSR coupled with the Cooper–Jacob method allows the analyst to ascertain the uncertainty that is inherent in the estimated parameters obtained using the simplified Cooper–Jacob method and data that are uncertain due to lack of knowledge regarding the heterogeneity of the aquifer.  相似文献   

10.
A Potential-Based Inversion of Unconfined Steady-State Hydraulic Tomography   总被引：1，自引：0，他引：1  
The importance of estimating spatially variable aquifer parameters such as transmissivity is widely recognized for studies in resource evaluation and contaminant transport. A useful approach for mapping such parameters is inverse modeling of data from series of pumping tests, that is, via hydraulic tomography. This inversion of field hydraulic tomographic data requires development of numerical forward models that can accurately represent test conditions while maintaining computational efficiency. One issue this presents is specification of boundary and initial conditions, whose location, type, and value may be poorly constrained. To circumvent this issue when modeling unconfined steady-state pumping tests, we present a strategy that analyzes field data using a potential difference method and that uses dipole pumping tests as the aquifer stimulation. By using our potential difference approach, which is similar to modeling drawdown in confined settings, we remove the need for specifying poorly known boundary condition values and natural source/sink terms within the problem domain. Dipole pumping tests are complementary to this strategy in that they can be more realistically modeled than single-well tests due to their conservative nature, quick achievement of steady state, and the insensitivity of near-field response to far-field boundary conditions. After developing the mathematical theory, our approach is first validated through a synthetic example. We then apply our method to the inversion of data from a field campaign at the Boise Hydrogeophysical Research Site. Results from inversion of nine pumping tests show expected geologic features, and uncertainty bounds indicate that hydraulic conductivity is well constrained within the central site area.  相似文献   

11.
There is a significant body of work demonstrating the importance of hydrologic control on land energy feedbacks. Yet, quantitative data on aquifer conductivity can be difficult to assemble. Furthermore, how subsurface uncertainty propagates into land-surface processes is not well understood. This study analyzes the impact of aquifer characterization on land energy fluxes, using a coupled hydrology–land-surface model. Four gridded subsurface conductivity fields are developed for the Upper Klamath basin using two data sources and different levels of imposed heterogeneity. Each model is forced with the same transient, observed meteorology for 3 years prior to the final year presented here. Results are analyzed to quantify the impact of subsurface heterogeneity on groundwater surface water interactions and spatial patterns in hydrologic variables. Analysis shows that heterogeneity does not fundamentally alter the connection between groundwater and land surface processes. However, differences between scenarios impact the extent and location of the critical zone.  相似文献   

12.
AN EXERCISE IN GROUND-WATER MODEL CALIBRATION AND PREDICTION   总被引：1，自引：0，他引：1  
Abstract. For a classroom exercise, nine groups of graduate students calibrated a numerical ground-water flow model to a set of perfectly observed hydraulic head data for a hypothetical phreatic aquifer. All groups used exactly the same numerical model and identical sets of observed data. After calibration, the students predicted the hydraulic head distribution in the aquifer resulting from a modification in one boundary condition. A quantitative analysis of the results of this calibration-prediction exercise vividly demonstrates some of the difficulties in parameter identification for ground-water flow models. Group predictions differed significantly. Successful prediction was strongly correlated with successful estimation of conductivity values, and was essentially unrelated to successful estimation of aquifer bottom elevations or with the number of trial-and-error simulations required for calibration. Most importantly, success in prediction was unrelated to success in matching observed heads under premodification conditions. In this sense, good calibration did not lead to good prediction.  相似文献   

13.
The groundwater inverse problem of estimating heterogeneous groundwater model parameters (hydraulic conductivity in this case) given measurements of aquifer response (such as hydraulic heads) is known to be an ill-posed problem, with multiple parameter values giving similar fits to the aquifer response measurements. This problem is further exacerbated due to the lack of extensive data, typical of most real-world problems. In such cases, it is desirable to incorporate expert knowledge in the estimation process to generate more reasonable estimates. This work presents a novel interactive framework, called the ‘Interactive Multi-Objective Genetic Algorithm’ (IMOGA), to solve the groundwater inverse problem considering different sources of quantitative data as well as qualitative expert knowledge about the site. The IMOGA is unique in that it looks at groundwater model calibration as a multi-objective problem consisting of quantitative objectives – calibration error and regularization – and a ‘qualitative’ objective based on the preference of the geological expert for different spatial characteristics of the conductivity field. All these objectives are then included within a multi-objective genetic algorithm to find multiple solutions that represent the best combination of all quantitative and qualitative objectives. A hypothetical aquifer case-study (based on the test case presented by Freyberg [Freyberg DL. An exercise in ground-water model calibration and prediction. Ground Water 1988;26(3)], for which the ‘true’ parameter values are known, is used as a test case to demonstrate the applicability of this method. It is shown that using automated calibration techniques without using expert interaction leads to parameter values that are not consistent with site-knowledge. Adding expert interaction is shown to not only improve the plausibility of the estimated conductivity fields but also the predictive accuracy of the calibrated model.  相似文献   

14.
In this paper, we present a conceptual‐numerical model that can be deduced from a calibrated finite difference groundwater‐flow model, which provides a parsimonious approach to simulate and analyze hydraulic heads and surface water body–aquifer interaction for linear aquifers (linear response of head to stresses). The solution of linear groundwater‐flow problems using eigenvalue techniques can be formulated with a simple explicit state equation whose structure shows that the surface water body–aquifer interaction phenomenon can be approached as the drainage of a number of independent linear reservoirs. The hydraulic head field could be also approached by the summation of the head fields, estimated for those reservoirs, defined over the same domain set by the aquifer limits, where the hydraulic head field in each reservoir is proportional to a specific surface (an eigenfunction of an eigenproblem, or an eigenvector in discrete cases). All the parameters and initial conditions of each linear reservoir can be mathematically defined in a univocal way from the calibrated finite difference model, preserving its characteristics (geometry, boundary conditions, hydrodynamic parameters (heterogeneity), and spatial distribution of the stresses). We also demonstrated that, in practical cases, an accurate solution can be obtained with a reduced number of linear reservoirs. The reduced computational cost of these solutions can help to integrate the groundwater component within conjunctive use management models. Conceptual approximation also facilitates understanding of the physical phenomenon and analysis of the factors that influence it. A simple synthetic aquifer has been employed to show how the conceptual model can be built for different spatial discretizations, the parameters required, and their influence on the simulation of hydraulic head fields and stream–aquifer flow exchange variables. A real‐world case was also solved to test the accuracy of the proposed approaches, by comparing its solution with that obtained using finite‐difference MODFLOW code. Copyright © 2011 John Wiley & Sons, Ltd.  相似文献   

15.
Stream–aquifer interaction plays a vital role in the water cycle, and a proper study of this interaction is needed for understanding groundwater recharge, contaminants migration, and for managing surface water and groundwater resources. A model‐based investigation of a field experiment in a riparian zone of the Schwarzbach river, a tributary of the Rhine River in Germany, was conducted to understand stream–aquifer interaction under alternative gaining and losing streamflow conditions. An equivalent streambed permeability, estimated by inverting aquifer responses to flood waves, shows that streambed permeability increased during infiltration of stream water to aquifer and decreased during exfiltration. Aquifer permeability realizations generated by multiple‐point geostatistics exhibit a high degree of heterogeneity and anisotropy. A coupled surface water groundwater flow model was developed incorporating the time‐varying streambed permeability and heterogeneous aquifer permeability realizations. The model was able to reproduce varying pressure heads at two observation wells near the stream over a period of 55 days. A Monte Carlo analysis was also carried out to simulate groundwater flow, its age distribution, and the release of a hypothetical wastewater plume into the aquifer from the stream. Results of this uncertainty analysis suggest (a) stream–aquifer exchange flux during the infiltration periods was constrained by aquifer permeability; (b) during exfiltration, this flux was constrained by the reduced streambed permeability; (c) the effect of temporally variable streambed permeability and aquifer heterogeneity were found important to improve the accurate capture of the uncertainty; and (d) probabilistic infiltration paths in the aquifer reveal that such pathways and the associated prediction of the extent of the contaminant plume are highly dependent on aquifer heterogeneity.  相似文献   

16.
The hydraulic gradient comparison method is an inverse method for estimation of aquifer hydraulic conductivity (or trans-missivity) and boundary conductance for a ground water flow model under steady-state conditions. This method, following formal optimization techniques, defines its objective function to minimize differences between interpreted (observed) and simulated hydraulic gradients, which results in minimization of differences between observed and simulated hydraulic heads. The key features of this method are that (1) the derived optimality conditions have an explicit form with a clear hydrology concept that is con-sistent with Darcy's law, and (2) the derived optimality conditions are spatially independent as they are a function of only local hydraulic conductivity and local hydraulic gradient. This second feature allows a multidimensional optimization problem to be solved by many one-dimensional optimization procedures simultaneously, which results in a substantial reduction in computation time. The results of the numerical performance testing on a heterogeneous hypothetical case confirm that minimizing gradient residuals in the entire model domain leads to minimizing head residuals. Application of the method in real-world projects requires rigorous conceptual model development, use of a global calibration target, and an iterative calibration proess. The conceptual model development includes interpretation of a potentiometric surface and estimation of other hydrologic parameters. This method has been applied to a wide range of real-world modeling projects, including the Rocky Mountain Arsenal and Rocky Flats sites in Colorado, which demonstrates that the method is efficient and practical.  相似文献   

17.
In an aquifer system with complex hydrogeology, mixing of groundwater with different ages could occur associated with various flow pathways. In this study, we applied different groundwater age‐estimation techniques (lumped parameter model and numerical model) to characterize groundwater age distributions and the major pathways of nitrate contamination in the Gosan agricultural field, Jeju Island. According to the lumped parameter model, groundwater age in the study area could be explained by the binary mixing of the young groundwater (4–33 years) and the old water component (>60 years). The complex hydrogeologic regimes and local heterogeneity observed in the study area (multilayered aquifer, well leakage hydraulics) were particularly well reflected in the numerical model. The numerical model predicted that the regional aquifer of Gosan responded to the fertilizer applications more rapidly (mean age: 9.7–22.3 years) than as estimated by other models. Our study results demonstrated that application and comparison of multiple age‐estimation methods can be useful to understand better the flow regimes and the mixing characteristics of groundwater with different ages (pathways), and accordingly, to reduce the risk of improper groundwater management plans arising from the aquifer heterogeneity.  相似文献   

18.
Considering complexity in groundwater modeling can aid in selecting an optimal model, and can avoid over parameterization, model uncertainty, and misleading conclusions. This study was designed to determine the uncertainty arising from model complexity, and to identify how complexity affects model uncertainty. The Ajabshir aquifer, located in East Azerbaijan, Iran, was used for comprehensive hydrogeological studies and modeling. Six unique conceptual models with four different degrees of complexity measured by the number of calibrated model parameters (6, 10, 10, 13, 13 and 15 parameters) were compared and characterized with alternative geological interpretations, recharge estimates and boundary conditions. The models were developed with Model Muse and calibrated using UCODE with the same set of observed data of hydraulic head. Different methods were used to calculate model probability and model weight to explore model complexity, including Bayesian model averaging, model selection criteria, and multicriteria decision-making (MCDM). With the model selection criteria of AIC, AICc and BIC, the simplest model received the highest model probability. The model selection criterion, KIC, and the MCDM method, in addition to considering the quality of model fit between observed and simulated data and the number of calibrated parameters, also consider uncertainty in parameter estimates with a Fisher information matrix. KIC and MCDM selected a model with moderate complexity (10 parameters) and the best parameter estimation (model 3) as the best models, over another model with the same degree of complexity (model 2). The results of these comparisons show that in choosing between models, priority should be given to quality of the data and parameter estimation rather than degree of complexity.  相似文献   

19.
Complexity   总被引：1，自引：0，他引：1  
It is difficult to define complexity in modeling. Complexity is often associated with uncertainty since modeling uncertainty is an intrinsically difficult task. However, modeling uncertainty does not require, necessarily, complex models, in the sense of a model requiring an unmanageable number of degrees of freedom to characterize the aquifer. The relationship between complexity, uncertainty, heterogeneity, and stochastic modeling is not simple. Aquifer models should be able to quantify the uncertainty of their predictions, which can be done using stochastic models that produce heterogeneous realizations of aquifer parameters. This is the type of complexity addressed in this article.  相似文献   

20.
The spatial distribution of reactive minerals in the subsurface is often a primary factor controlling the fate and transport of contaminants in groundwater systems. However, direct measurement and estimation of heterogeneously distributed minerals are often costly and difficult to obtain. While previous studies have shown the utility of using hydrologic measurements combined with inverse modeling techniques for tomography of physical properties including hydraulic conductivity, these methods have seldom been used to image reactive geochemical heterogeneities. In this study, we focus on As-bearing reactive minerals as aquifer contaminants. We use synthetic applications to demonstrate the ability of inverse modeling techniques combined with mechanistic reactive transport models to image reactive mineral lenses in the subsurface and quantify estimation error using indirect, commonly measured groundwater parameters. Specifically, we simulate the mobilization of arsenic via kinetic oxidative dissolution of As-bearing pyrite due to dissolved oxygen in the ambient groundwater, which is an important mechanism for arsenic release in groundwater both under natural conditions and engineering applications such as managed aquifer recharge and recovery operations. The modeling investigation is carried out at various scales and considers different flow-through domains including (i) a 1D lab-scale column (80 cm), (ii) a 2D lab-scale setup (60 cm × 30 cm) and (iii) a 2D field-scale domain (20 m × 4 m). In these setups, synthetic dissolved oxygen data and forward reactive transport simulations are used to image the spatial distribution of As-bearing pyrite using the Principal Component Geostatistical Approach (PCGA) for inverse modeling.  相似文献   

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