Development of a fuzzy-stochastic nonlinear model to incorporate aleatoric and epistemic uncertainty

Site uncertainties significantly influence groundwater flow and contaminant transport predictions. Aleatoric and epistemic uncertainty are both identified in site characterization and represented using proper uncertainty theories. When one theory best represents one parameter whereas a different theory may be more suitable for another parameter, the hybrid propagation of aleatoric (random) and epistemic (nonrandom) uncertainties will occur. The computational challenges of joint propagation of aleatoric and epistemic uncertainty through groundwater flow and contaminant transport models are significant. A fuzzy-stochastic nonlinear model was developed in this paper to incorporate these two types of uncertain site information and reduce the computational cost. The results show that (1) the computational cost using the nonlinear model is reduced compared with that of using the sparse grid algorithm and Monte Carlo methods; (2) the uncertainty of hydraulic conductivity (K) significantly influences the water head and solute distribution at the observation wells compared to other uncertain parameters, such as the storage coefficient and the distribution coefficient (K_d); and (3) the combination of multiple uncertain parameters substantially affects the simulation results. Neglecting site uncertainties may lead to unrealistic predictions.     

A comparison of numerical solutions of partial differential equations with probabilistic and possibilistic parameters for the quantification of uncertainty in subsurface solute transport

Traditionally, uncertainty in parameters are represented as probabilistic distributions and incorporated into groundwater flow and contaminant transport models. With the advent of newer uncertainty theories, it is now understood that stochastic methods cannot properly represent non random uncertainties. In the groundwater flow and contaminant transport equations, uncertainty in some parameters may be random, whereas those of others may be non random. The objective of this paper is to develop a fuzzy-stochastic partial differential equation (FSPDE) model to simulate conditions where both random and non random uncertainties are involved in groundwater flow and solute transport. Three potential solution techniques namely, (a) transforming a probability distribution to a possibility distribution (Method I) then a FSPDE becomes a fuzzy partial differential equation (FPDE), (b) transforming a possibility distribution to a probability distribution (Method II) and then a FSPDE becomes a stochastic partial differential equation (SPDE), and (c) the combination of Monte Carlo methods and FPDE solution techniques (Method III) are proposed and compared. The effects of these three methods on the predictive results are investigated by using two case studies. The results show that the predictions obtained from Method II is a specific case of that got from Method I. When an exact probabilistic result is needed, Method II is suggested. As the loss or gain of information during a probability–possibility (or vice versa) transformation cannot be quantified, their influences on the predictive results is not known. Thus, Method III should probably be preferred for risk assessments.     

Description of hydrogeologic heterogeneity and evaluation of radionuclide transport at an underground nuclear test

Realistic models of contaminant transport in groundwater demand detailed characterization of the spatial distribution of subsurface hydraulic properties, while at the same time programmatic constraints may limit collection of pertinent hydraulic data. Fortunately, alternate forms of data can be used to improve characterization of spatial variability. We utilize a methodology that augments sparse hydraulic information (hard data) with more widely available hydrogeologic information to generate equiprobable maps of hydrogeologic properties that incorporate patterns of connected permeable zones. Geophysical and lithologic logs are used to identify hydrogeologic categories and to condition stochastic simulations using Sequential Indicator Simulation (SIS). The resulting maps are populated with hydraulic conductivity values using field data and Sequential Gaussian Simulation (SGS). Maps of subsurface hydrogeologic heterogeneity are generated for the purpose of examining groundwater flow and transport processes at the Faultless underground nuclear test, Central Nevada Test Area (CNTA), through large-scale, three-dimensional numerical modeling. The maps provide the basis for simulation of groundwater flow, while transport of radionuclides from the nuclear cavity is modeled using particle tracking methods. Sensitivity analyses focus on model parameters that are most likely to reduce the long travel times observed in the base case. The methods employed in this study have improved our understanding of the spatial distribution of preferential flowpaths at this site and provided the critical foundation on which to build models of groundwater flow and transport. The results emphasize that the impacts of uncertainty in hydraulic and chemical parameters are dependent on the radioactive decay of specific species, with rapid decay magnifying the effects of parameters that change travel time.     

Comprehensive study on parameter sensitivity for flow and nutrient modeling in the Hydrological Simulation Program Fortran model

Numerous parameters are used to construct the HSPF (Hydrological Simulation Program Fortran) model, which results in significant difficulty in calibrating the model. Parameter sensitivity analysis is an efficient method to identify important model parameters. Through this method, a model’s calibration process can be simplified on the basis of understanding the model’s structure. This study investigated the sensitivity of the flow and nutrient parameters of HSPF using the DSA (differential sensitivity analysis) method in the Xitiaoxi watershed, China. The results showed that flow was mostly affected by parameters related to groundwater and evapotranspiration, including DEEPFR (fraction of groundwater inflow to deep recharge), LZETP (lower-zone evapotranspiration parameter), and AGWRC (base groundwater recession), and most of the sensitive parameters had negative and nonlinear effects on flow. Additionally, nutrient components were commonly affected by parameters from land processes, including MON-SQOLIM (monthly values limiting storage of water quality in overland flow), MON-ACCUM (monthly values of accumulation), MON-IFLW-CONC (monthly concentration of water quality in interflow), and MON-GRND-CONC (monthly concentration of water quality in active groundwater). Besides, parameters from river systems, KATM20 (unit oxidation rate of total ammonia at 20 °C) had a negative and almost linear effect on ammonia concentration and MALGR (maximal unit algal growth rate for phytoplankton) had a negative and nonlinear effect on ammonia and orthophosphate concentrations. After calibrating these sensitive parameters, our model performed well for simulating flow and nutrient outputs, with R ² and E_NS (Nash–Sutcliffe efficiency) both greater than 0.75 for flow and greater than 0.5 for nutrient components. This study is expected to serve as a valuable complement to the documentation of the HSPF model to help users identify key parameters and provide a reference for performing sensitivity analyses on other models.     

Assessment of Aquifer Vulnerability in an Agricultural Area in Spain Using the DRASTIC Model

The assessment of aquifer vulnerability is a very important task, especially in agricultural areas because the quality and availability of groundwater affects both the sustainability of agriculture and the quality of life. In this study, an integrated approach is considered, with the use of the generic and agricultural DRASTIC models as well as a geographic information system (GIS), to assess groundwater vulnerability in the agricultural area of Barrax, in the province of Albacete, in Spain. Seven parameters—depth to water, net recharge, aquifer media, soil media, topography, impact of vadose zone media, and hydraulic conductivity of the aquifer (DRASTIC)—have been considered as weighted layers to enable an accurate groundwater risk mapping. The results of the generic DRASTIC model indicated very low vulnerability to contamination for Barrax groundwater due to limited urban and industrial development in the wider area. However, agricultural activities impose pressure to groundwater resources and the results of the agricultural DRASTIC model show that 6.86% of the study area is characterized by very high, 2.29% by high, 47.28% by medium, 38.28% by low, and the remaining 5.29% by no vulnerability to groundwater contamination. The distribution of nitrate concentration in groundwater in the area under study is quite well correlated with the agricultural DRASTIC vulnerability index. Sensitivity analysis was also performed to acknowledge statistical uncertainty in the estimation of each parameter used, to assess its impact, and thus to identify the most critical parameters that require further investigation. Depth to water and impact of vadose zone are the parameters that had the most noticeable impact on the generic DRASTIC vulnerability index followed by the soil media and topography. In contrast, the agricultural DRASTIC method is more sensitive to the removal of the depth to water parameter followed by the topography and the soil media parameters.     

Evaluating the sensitivity of a subsurface multicomponent reactive transport model with respect to transport and reaction parameters.

The input variables for a numerical model of reactive solute transport in groundwater include both transport parameters, such as hydraulic conductivity and infiltration, and reaction parameters that describe the important chemical and biological processes in the system. These parameters are subject to uncertainty due to measurement error and due to the spatial variability of properties in the subsurface environment. This paper compares the relative effects of uncertainty in the transport and reaction parameters on the results of a solute transport model. This question is addressed by comparing the magnitudes of the local sensitivity coefficients for transport and reaction parameters. General sensitivity equations are presented for transport parameters, reaction parameters, and the initial (background) concentrations in the problem domain. Parameter sensitivity coefficients are then calculated for an example problem in which uranium(VI) hydrolysis species are transported through a two-dimensional domain with a spatially variable pattern of surface complexation sites. In this example, the reaction model includes equilibrium speciation reactions and mass transfer-limited non-electrostatic surface complexation reactions. The set of parameters to which the model is most sensitive includes the initial concentration of one of the surface sites, the formation constant (Kf) of one of the surface complexes and the hydraulic conductivity within the reactive zone. For this example problem, the sensitivity analysis demonstrates that transport and reaction parameters are equally important in terms of how their variability affects the model results.     

A coupled simulation-optimization approach for groundwater remediation design under uncertainty: An application to a petroleum-contaminated site

This study provides a coupled simulation–optimization approach for optimal design of petroleum-contaminated groundwater remediation under uncertainty. Compared to the previous approaches, it has the advantages of: (1) addressing the stochasticity of the modeling parameters in simulating the flow and transport of NAPLs in groundwater, (2) providing a direct and response-rapid bridge between remediation strategies (pumping rates) and remediation performance (contaminant concentrations) through the created proxy models, (3) alleviating the computational cost in searching for optimal solutions, and (4) giving confidence levels for the obtained optimal remediation strategies. The approach is applied to a practical site in Canada for demonstrating its performance. The results show that mitigating the effects of uncertainty on optimal remediation strategies (through enhancing the confidence level) would lead to the rise of remediation cost due to the increase in the total pumping rate.     

Applied tracer tests in fractured rock: Can we predict natural gradient solute transport more accurately than fracture and matrix parameters?

Applied tracer tests provide a means to estimate aquifer parameters in fractured rock. The traditional approach to analysing these tests has been using a single fracture model to find the parameter values that generate the best fit to the measured breakthrough curve. In many cases, the ultimate aim is to predict solute transport under the natural gradient. Usually, no confidence limits are placed on parameter values and the impact of parameter errors on predictions of solute transport is not discussed. The assumption inherent in this approach is that the parameters determined under forced conditions will enable prediction of solute transport under the natural gradient. This paper considers the parameter and prediction uncertainty that might arise from analysis of breakthrough curves obtained from forced gradient applied tracer tests. By adding noise to an exact solution for transport in a single fracture in a porous matrix we create multiple realisations of an initial breakthrough curve. A least squares fitting routine is used to obtain a fit to each realisation, yielding a range of parameter values rather than a single set of absolute values. The suite of parameters is then used to make predictions of solute transport under lower hydraulic gradients and the uncertainty of estimated parameters and subsequent predictions of solute transport is compared. The results of this study show that predictions of breakthrough curve characteristics (first inflection point time, peak arrival time and peak concentration) for groundwater flow speeds with orders of magnitude smaller than that at which a test is conducted can sometimes be determined even more accurately than the fracture and matrix parameters.     

Stochastic analysis to assess the spatial distribution of groundwater nitrate concentrations in the Po catchment (Italy)

A large database including temporal trends of physical, ecological and socio-economic data was developed within the EUROCAT project. The aim was to estimate the nutrient fluxes for different socio-economic scenarios at catchment and coastal zone level of the Po catchment (Northern Italy) with reference to the Water Quality Objectives reported in the Water Framework Directive (WFD 2000/60/CE) and also in Italian legislation. Emission data derived from different sources at national, regional and local levels are referred to point and non-point sources. While non-point (diffuse) sources are simply integrated into the nutrient flux model, point sources are irregularly distributed. Intensive farming activity in the Po valley is one of the main Pressure factors Driving groundwater pollution in the catchment, therefore understanding the spatial variability of groundwater nitrate concentrations is a critical issue to be considered in developing a Water Quality Management Plan. In order to use the scattered point source data as input in our biogeochemical and transport models, it was necessary to predict their values and associated uncertainty at unsampled locations. This study reports the spatial distribution and uncertainty of groundwater nitrate concentration at a test site of the Po watershed using a probabilistic approach. Our approach was based on geostatistical sequential Gaussian simulation used to yield a series of stochastic images characterized by equally probable spatial distributions of the nitrate concentration across the area. Post-processing of many simulations allowed the mapping of contaminated and uncontaminated areas and provided a model for the uncertainty in the spatial distribution of nitrate concentrations.     

Joint propagation of variability and imprecision in assessing the risk of groundwater contamination

Estimating risks of groundwater contamination often require schemes for representing and propagating uncertainties relative to model input parameters. The most popular method is the Monte Carlo method whereby cumulative probability distributions are randomly sampled in an iterative fashion. The shortcoming of the approach, however, arises when probability distributions are arbitrarily selected in situations where available information is incomplete or imprecise. In such situations, alternative modes of information representation can be used, for example the nested intervals known as “possibility distributions”. In practical situations of groundwater risk assessment, it is common that certain model parameters may be represented by single probability distributions (representing variability) because there are data to justify these distributions, while others are more faithfully represented by possibility distributions (representing imprecision) due to the partial nature of available information. This paper applies two recent methods, designed for the joint-propagation of variability and imprecision, to a groundwater contamination risk assessment. Results of the joint-propagation methods are compared to those obtained using both interval analysis and the Monte Carlo method with a hypothesis of stochastic independence between model parameters. The two joint-propagation methods provide results in the form of families of cumulative distributions of the probability of exceeding a certain value of groundwater concentration. These families are delimited by an upper cumulative distribution and a lower distribution respectively called Plausibility and Belief after evidence theory. Slight differences between the results of the two joint-propagation methods are explained by the different assumptions regarding parameter dependencies. Results highlight the point that non-conservative results may be obtained if single cumulative probability distributions are arbitrarily selected for model parameters in the face of imprecise information and the Monte Carlo method is used under the assumption of stochastic independence. The proposed joint-propagation methods provide upper and lower bounds for the probability of exceeding a tolerance threshold. As this may seem impractical in a risk-management context, it is proposed to introduce “a-posteriori subjectivity” (as opposed to the “a-priori subjectivity” introduced by the arbitrary selection of single probability distributions) by defining a single indicator of evidence as a weighted average of Plausibility and Belief, with weights to be defined according to the specific context.     

A simulation procedure for groundwater quality assessments of pesticides

A procedure is described for making regional assessments of pesticide residue loadings and movement in groundwater underneath and downgradient from treated fields. A Monte-Carlo numerical simulation technique is used to generate model parameters for both the unsaturated and saturated zones. Simulations are performed using the Pesticide Root Zone Model linked to a simple groundwater solute transport model.The procedure is useful for evaluating the potential for producing pesticide residues in drinking water wells before actual field applications are made. Appropriate land management options, including restrictions on pesticide application, also can be developed using this procedure.The procedure was used to assess aldicarb levels in northeastern North Carolina groundwater resulting from application of the pesticide to peanuts. Probability density functions for selected soil characteristics were developed using a direct-access soils information data base. Probability density functions for selected groundwater characteristics were developed from available data for the study area. Simulation results indicated that mass fluxes to groundwater exceeded 0.01 and 0.1 kg ha⁻¹ approximately 6.9 and 1.0 percent of the time, respectively. No fluxes exceeded 0.1 kg ha⁻¹ at a distance of 60 m downgradient in any of the cases evaluated.     

Monitoring groundwater contamination and delineating source zones at industrial sites: uncertainty analyses using integral pumping tests

Field-scale characterisations of contaminant plumes in groundwater, as well as source zone delineations, are associated with uncertainties that can be considerable. A major source of uncertainty in environmental datasets is due to variability of sampling results, as a direct consequence of the heterogeneity of environmental matrices. We develop a methodology for quantifying uncertainties in field-scale mass flow and average concentration estimations, using integral pumping tests (IPTs), where the contaminant concentration is measured as a function of time in a pumping well. This procedure increases the sampling volume and reduces the effect of small-scale variability that may bias point-scale measurements. In particular, using IPTs, the interpolation uncertainty of conventional point-scale measurements is transformed to a quantifiable uncertainty related to the (unknown) plume position relative to the pumping well. We show that this plume position uncertainty generally influenced the predicted mass flows and average concentrations (of acenapthene, benzene and CHCs) to a greater extent than a boundary condition uncertainty related to the local water balance, considering 19 control planes at a highly heterogeneous industrial site in southwest Germany. Furthermore, large (order of magnitude) uncertainties only occurred if the conditions were strongly heterogeneous in the nearest vicinity of the well. We also develop a consistent methodology for an assessment of the combined effect of uncertainty in hydraulic conditions and uncertainty in reactive transport parameters for delimiting of both contaminant source zones and zones absent of source, based on (downgradient) IPTs.     

Uncertainty analysis of parameters for modeling the transfer and fate of benzo(a)pyrene in Tianjin wastewater irrigated areas

A Monte Carlo simulation for uncertainty analysis of three key parameters (local coal consumption rate Q(1L), dry deposition velocity of aerosol particulate Kp and biodegradation rate of benzo(a)pyrene in soil and sediment K(R3)) was conducted in this study. Results of the simulation indicate that the three parameters were influenced by uncertainty and that all equilibrium concentrations in the four bulk compartments and various sub-compartments were log-normally distributed. However, the results also indicated that among the six primary transfer fluxes, erosion associated with solids in soil and deposition associated with solids in water, along with output from sewers were also log-normally distributed, while deposition from air to soil and biodegradation in soil and sediment followed normal distributions. The effect of uncertainty on the model results of the three key parameters was derived using a comparison of upper and lower of confidence interval boundaries at the 95% level of confidence. The results reveal that uncertainty in the key parameters had a more significant influence on equilibrium concentrations of the chemical in the bulk compartments of soil and sediment than on concentrations in the other two bulk compartments, various sub-compartments and the six predominant transfer fluxes.     

Modelling assessment of regional groundwater contamination due to historic smelter emissions of heavy metals

Historic emissions from ore smelters typically cause regional soil contamination. We developed a modelling approach to assess the impact of such contamination on groundwater and surface water load, coupling unsaturated zone leaching modelling with 3D groundwater transport modelling. Both historic and predictive modelling were performed, using a mass balance approach for three different catchments in the vicinity of three smelters. The catchments differ in their hydrology and geochemistry. The historic modelling results indicate that leaching to groundwater is spatially very heterogeneous due to variation in soil characteristics, in particular soil pH. In the saturated zone, cadmium is becoming strongly retarded due to strong sorption at neutral pH, even though the reactivity of the sandy sediments is low. A comparison between two datasets (from 1990 to 2002) on shallow groundwater and modelled concentrations provided a useful verification on the level of statistics of "homogeneous areas" (areas with comparable land use, soil type and geohydrological situation) instead of comparison at individual locations. While at individual locations observations and the model varies up to two orders of magnitude, for homogeneous areas, medians and ranges of measured concentrations and the model results are similar. A sensitivity analysis on metal input loads, groundwater composition and sediment geochemistry reveals that the best available information scenario based on the median value of input parameters for the model predicts the range in observed concentrations very well. However, the model results are sensitive to the sediment contents of the reactive components (organic matter, clay minerals and iron oxides). Uncertainty in metal input loads and groundwater chemistry are of lesser importance. Predictive modelling reveals a remarkable difference in geochemical and hydrological controls on subsurface metal transport at catchment-scale. Whether the surface water load will peak within a few decades or continue to increase until after 2050 depends on the dominant land use functions in the areas, their hydrology and geochemical build-up.     

地下水环境中甲基叔丁基醚运移过程的动力学模型

建立了地下水环境中甲基叔丁基醚(MTBE)运移过程的变系数动力学模型,并对模型进行了验证和参数灵敏度分析.模拟结果表明,地下水流速和阻滞系数对于MTBE的运移过程影响最为显著,而水动力弥散系数的影响较小,忽略其变化不会对预测地下水环境中污染物运移的环境动力学行为造成太大误差.由此得到的结论可定量研究MTBE在地下水环境中的对流.扩散特征,还可为MTBE污染地下水的预测预报、修复治理等研究提供科学依据.     

Uncertainty in Nonpoint Source Pollution Models and Associated Risks

The usefulness of water quality simulation models for environmental management is explored with a focus on prediction uncertainty. The specific objective is to demonstrate how the usability of a flow and transport model (here: MACRO) can be enhanced by developing and analyzing its output probability distributions based on input variability. This infiltration-based model was designed to investigate preferential flow effects on pollutant transport. A statistical sensitivity analysis is used to identify the most uncertain input parameters based on model outputs. Probability distribution functions of input variables were determined based on field-measured data obtained under alternative tillage treatments. Uncertainty of model outputs is investigated using a Latin hypercube sampling scheme (LHS) with restricted pairing for model input sampling. Probability density functions (pdfs) are constructed for water flow rate, atrazine leaching rate, total accumulated leaching, and atrazine concentration in percolation water. Results indicate that consideration of input parameter uncertainty produces a 20% higher mean flow rate along with two to three times larger atrazine leaching rate, accumulated leachate, and concentration than that obtained using mean input parameters. Uncertainty in predicted flow rate is small but that in solute transport is an order of magnitude larger than that of corresponding input parameters. Macropore flow is observed to contribute to the variability of atrazine transport results. Overall, the analysis provides a quantification of prediction uncertainty that is found to enhance a user's ability to assess risk levels associated with model predictions.     

Uncertainty in Nonpoint Source Pollution Models and Associated Risks

The usefulness of water quality simulation models for environmental management is explored with a focus on prediction uncertainty. The specific objective is to demonstrate how the usability of a flow and transport model (here: MACRO) can be enhanced by developing and analyzing its output probability distributions based on input variability. This infiltration-based model was designed to investigate preferential flow effects on pollutant transport. A statistical sensitivity analysis is used to identify the most uncertain input parameters based on model outputs. Probability distribution functions of input variables were determined based on field-measured data obtained under alternative tillage treatments. Uncertainty of model outputs is investigated using a Latin hypercube sampling scheme (LHS) with restricted pairing for model input sampling. Probability density functions (pdfs) are constructed for water flow rate, atrazine leaching rate, total accumulated leaching, and atrazine concentration in percolation water. Results indicate that consideration of input parameter uncertainty produces a 20% higher mean flow rate along with two to three times larger atrazine leaching rate, accumulated leachate, and concentration than that obtained using mean input parameters. Uncertainty in predicted flow rate is small but that in solute transport is an order of magnitude larger than that of corresponding input parameters. Macropore flow is observed to contribute to the variability of atrazine transport results. Overall, the analysis provides a quantification of prediction uncertainty that is found to enhance a user's ability to assess risk levels associated with model predictions.     

Rigorous uncertainty assessment in contaminant transport inverse modelling: a case study of fluoride diffusion through clay liners

Inverse methods used in assessing landfill liner design have not yet taken advantage of current developments in inverse procedures. Here, a method for inverting contaminant transport models is presented including a general error model and procedures for differentially weighted multiple response regression. General error models are employed in cases where the residuals are heteroscedastic and correlated, and lead to valid inference on model parameter and predictive uncertainty. The Shuffled Complex Evolution algorithm is used to optimise model parameters. Model parameter uncertainty is assessed by exploring the posterior probability distribution with the Metropolis algorithm, a Markov chain Monte Carlo sampling method. The inverse method is applied to simultaneously determine the sorption and diffusion parameters from laboratory diffusion cell experiments. In these experiments, fluoride migration through kaolin clays was measured by sampling the source and collector cells over time. To uniquely determine the transport model parameters, it was necessary to simultaneously fit the observed data from two independent diffusion cell experiments with different initial concentrations. The jointly fitted transport model parameters compared well with those fitted to independent batch experiments.     

Contaminant transport in a municipal drinking water supply: a steady-state approach to estimate rate and uncertainty

Contaminant transport is generally considered to be a key factor when assessing and classifying the environmental risk of polluted areas. In the study presented here, a steady-state approach was applied to obtain estimates of the transit time and concentration of the pesticide metabolite BAM (2,6-dichlorobenzoamide) at a site where it is contaminating a municipal drinking water supply. A Monte Carlo simulation technique was used to quantify the uncertainty of the results and to evaluate the sensitivity of the used parameters. The adopted approach yielded an estimated median transit time of 10 y for the BAM transport from the polluted site to the water supply. Soil organic carbon content in the unsaturated zone and the hydraulic conductivity in the saturated zone explained 44% and 23% of the uncertainty in the transit time estimate, respectively. The sensitivity analysis showed that the dilution factor due to regional groundwater flow and the soil organic carbon content at the polluted site explained 53% and 31% of the uncertainty of concentration estimates, respectively. In conclusion, the adopted steady-state approach can be used to obtain reliable first estimates of transit time and concentration, but to improve concentration predictions of degrading contaminants, a dynamic model is probably required.     

Visual modflow在模拟实验室含水砂槽中柴油运移特征中的应用

Visual modflow是一个可以对三维地下水水流和溶质运移进行数值模拟评价的标准可视化专业软件.建立了砂箱物理实验模型来研究柴油在含水砂槽中的迁移特征.通过模型检验,各个监测时期观测值和预测值相关系数r值在0.564 ～0.669之间,证明这种建模方法是合理的和有效的.利用校正的模型对实验室含水砂槽中柴油运移特征进行模拟,发现所建模型可以较为准确地反映出含水砂槽中柴油污染物的分布特征,拟合、验证和预测结果显示该模型可作为地下水管理的有效工具,这为深入研究柴油污染地下水提供理论依据.