Parameter Estimation for Groundwater Models under Uncertain Irrigation Data

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.     

A New Parameter Estimation Method for Solute Transport in a Column

To study contaminant transport in groundwater, an essential requirement is robust and accurate estimation of the transport parameters such as dispersion coefficient. The commonly used inverse error function method (IEFM) may cause unacceptable errors in dispersion coefficient estimation using the breakthrough curves (BTCs) data. We prove that the random error in the measured concentrations, which might be described by a normal distribution, would no longer follow the normal distribution after the IEFM transformation. In this study, we proposed a new method using the weighted least squares method (WLSM) to estimate the dispersion coefficient and velocity of groundwater. The weights were calculated based on the slope of the observed BTCs. We tested the new method against other methods such as genetic algorithm and CXTFIT program and found great agreement. This new method acknowledged different characteristics of solute transport at early, intermediate, and late time stages and divided BTCs into three sections for analysis. The developed method was applied to interpret three column tracer experiments by introducing continuous, constant‐concentration of sodium chloride (NaCl) into columns filled with sand, gravel, and sand‐gravel media. This study showed that IEFM performed well only when the observed data points were located in the linear (intermediate time) section of BTCs; it performed poorly when data points were in the early and late time stages. The new WLSM method, however, performed well for data points scattering over the entire BTCs and appeared promising in parameter estimation for solute transport in a column.     

Parameter Estimation/Sensitivity Analysis for an Aquifer Test with Skin Effect

Aquifer information carried by aquifer test data may be affected by the presence of a finite thickness skin around the wellbore. The mathematical treatment for an aquifer accounting for the skin zone can be characterized by five parameters, that is, the outer radius of the skin zone and the transmissivity and storativity for each of the skin and aquifer zones. Sensitivity analysis was performed to examine the ground water flow behavior in the skin and aquifer zones in terms of the constant-head test (CHT) data. The simulated annealing procedure was applied to simultaneously determine the skin and aquifer parameters from the analysis of CHT data. Toward the previously mentioned goals, four suites of CHT data were analyzed in this article. The analyses of wellbore flow rate at the test well and the specific drawdown at the observation well gave accurate estimates for the skin and aquifer parameters, respectively. Only the skin thickness and both the skin and the aquifer diffusivities could be accurately estimated from the analysis of drawdown data in the observation well. The estimates for all skin and aquifer parameters from the composite analysis of flow rate and drawdown data were the most accurate. The results of sensitivity analyses and parameter estimations provide instructive references in the analysis of the skin-affected CHT data.     

基于D-S证据理论的黄土滑坡参数估计及应用

岩土参数的不确定性存在,降低了稳定性评价的可靠性,对工程安全、优化设计等方面有重要影响。而D-S证据理论提供了一种解决不确定信息的有效方法,证据理论能够对各自独立的证据加以综合给出一致性结果,并能处理具有模糊和不确定信息的合成问题,可以达到信息互补。适应各领域的人工智能和系统决策、诊断、评估等实际问题和理论基础。结合实际黄土滑坡的滑带土力学参数试验结果,基于D-S证据理论,构造了滑带土力学参数的识别框架、基本可信度分配,从主观和客观上对滑带土力学参数取值进行信度估计,滑坡滑带土力学参数信度估计值与滑带土强度参数反分析结果相吻合,表明基于D-S证据理论的黄土滑坡参数估计的有效性和可行性。     

基于D-S证据理论的黄土滑坡参数估计及应用

岩土参数的不确定性存在,降低了稳定性评价的可靠性,对工程安全、优化设计等方面有重要影响。而D-S证据理论提供了一种解决不确定信息的有效方法,证据理论能够对各自独立的证据加以综合给出一致性结果,并能处理具有模糊和不确定信息的合成问题,可以达到信息互补。适应各领域的人工智能和系统决策、诊断、评估等实际问题和理论基础。结合实际黄土滑坡的滑带土力学参数试验结果,基于D-S证据理论,构造了滑带土力学参数的识别框架、基本可信度分配,从主观和客观上对滑带土力学参数取值进行信度估计,滑坡滑带土力学参数信度估计值与滑带土强度参数反分析结果相吻合,表明基于D-S证据理论的黄土滑坡参数估计的有效性和可行性。     

Improved Parameter Resolution with Markov Chain Monte Carlo Simulation of Different Aquifer Tests

Hydraulic testing for aquifer characterization at contaminated sites often includes tests of short duration and of different types, such as slug tests and pumping tests, conducted at different phases of investigation. Tests conducted on a well cluster installed in a single aquifer can be combined in aggregate inverse analysis using an analytical model for groundwater flow near a test well. A genetic algorithm performs parallel search of the parameter space and provides starting parameter values for a Markov chain Monte Carlo simulation to estimate the parameter distribution. This sequence of inverse methods avoids guessing of the initial parameter vector and the often encountered difficult convergence of gradient-based methods and estimates the parameter covariance matrix from a distribution rather than from a single point in the parameter space. Combination of different tests improves the resolution of the estimated aquifer properties and allows an assessment of the uniformity of the aquifer. Estimated parameter correlations and standard deviations are used as relative metrics to distinguish well resolved and poorly resolved parameters. The methodology is demonstrated on example field tests in unconfined and leaky aquifers.     

Classical and Bayesian Seismic Yield Estimation: The 1998 Indian and Pakistani Tests

— The nuclear tests in May, 1998, in India and Pakistan have stimulated a renewed interest in yield estimation, based on limited data from uncalibrated test sites. We study here the problem of estimating yields using classical and Bayesian methods developed by Shumway (1992), utilizing calibration data from the Semipalatinsk test site and measured magnitudes for the 1998 Indian and Pakistani tests given by Murphy (1998). Calibration is done using multivariate classical or Bayesian linear regression, depending on the availability of measured magnitude-yield data and prior information. Confidence intervals for the classical approach are derived applying an extension of Fieller's method suggested by Brown (1982). In the case where prior information is available, the posterior predictive magnitude densities are inverted to give posterior intervals for yield. Intervals obtained using the joint distribution of magnitudes are comparable to the single-magnitude estimates produced by Murphy (1998) and reinforce the conclusion that the announced yields of the Indian and Pakistani tests were too high.     

LNAPL Volume Calculation: Parameter Estimation by Nonlinear Regression of Saturation Profiles

An estimation of the volume of light nonaqueous phase liquids (LNAPL) is often required during site assessment, remedial design, or litigation. LNAPL volume can be estimated by a strictly empirical approach whereby core samples, distributed throughout the vertical and lateral extent of LNAPL, are analyzed for LNAPL content, and these data are then integrated to compute a volume. Alternatively, if the LNAPL has obtained vertical equilibrium, the thickness of LNAPL in monitoring wells can be used to calculate of LNAPL in monitoring wells can be used to calculate LNAPL volume at the well locations if appropriate soil and LNAPL properties can be estimated.
A method is described for estimating key soil and LNAPL properties by nonlinear regression of vertical profiles of LNAPL saturation. The methods is relatively fast, cost effective, and amenable to quantitative analysis of uncertainty. Optionally, the method allows statistical determination of best-fit values for the Van Genuchten capillary parameters (n, α_oil-water and α_oil-air), residual water saturation and ANAPL density. The sensitivity of the method was investigated by fitting field LNAPL saturation profiles and then determining the variation in misfit (mean square residual) as a function of parameter value for each parameter. Using field data from a sandy aquifer, the fitting statistics were found to be highly sensitive to LNAPL density, α_oil-water and α_oil-air moderately sensitive to the Van Genuchten n value, and weakly sensitive to residual water saturation. The regression analysis also provides information that can be used to estimate uncertainty in the estimated parameters, which can then be used to estimate uncertainty in calculated values of specific volume.