An Application of Bayesian Inverse Methods to Vertical Deconvolution of Hydraulic Conductivity in a Heterogeneous Aquifer at Oak Ridge National Laboratory

A Bayesian inverse method is applied to two electromagnetic flowmeter tests conducted in fractured weathered shale at Oak Ridge National Laboratory. Traditional deconvolution of flowmeter tests is also performed using a deterministic first-difference approach; furthermore, ordinary kriging was applied on the first-difference results to provide an additional method yielding the best estimate and confidence intervals. Depth-averaged bulk hydraulic conductivity information was available from previous testing. The three methods deconvolute the vertical profile of lateral hydraulic conductivity. A linear generalized covariance function combined with a zoning approach was used to describe structure. Nonnegativity was enforced by using a power transformation. Data screening prior to calculations was critical to obtaining reasonable results, and the quantified uncertainty estimates obtained by the inverse method led to the discovery of questionable data at the end of the process. The best estimates obtained using the inverse method and kriging compared favorably with first-difference confirmatory calculations, and all three methods were consistent with the geology at the site.     

双误差回归模型在ICP-MS测定饮用水中锶的不确定度评定的简化应用

在计算电感耦合等离子体质谱法测定饮用水中锶的浓度(x)时,由于标准系列配制和仪器检测过程中信号(y)漂移产生的不确定度会传递给最终的计算结果。普通的一次或多次线性拟合结果不能真实地反映对于x、y值都含误差的数据拟合情况。文章对标准曲线进行了双误差回归计算,从双误差回归线性方程推导出校准曲线拟合过程产生不确定度的计算公式,建立了方法检出限与曲线拟合参数(x、y、曲线截距和斜率)及其相关不确定度之间的关系式,依据误差连续传递公式及不确定度分量计算公式简化了合成不确定度的表达式。从合成不确定度计算公式中可得出,水样中锶含量的浓度越低,其对应的不确定度越大;标准系列配制过程不细致、仪器灵敏度低,方法检出限越差,与实际测试情况符合。     

Effect of uncertainty in land use, damage models and inundation depth on flood damage estimates

With the recent transition to a more risk-based approach in flood management, flood risk models—being a key component in flood risk management—are becoming increasingly important. Such models combine information from four components: (1) the flood hazard (mostly inundation depth), (2) the exposure (e.g. land use), (3) the value of elements at risk and (4) the susceptibility of the elements at risk to hydrologic conditions (e.g. depth–damage curves). All these components contain, however, a certain degree of uncertainty which propagates through the calculation and accumulates in the final damage estimate. In this study, an effort has been made to assess the influence of uncertainty in these four components on the final damage estimate. Different land-use data sets and damage models have been used to represent the uncertainties in the exposure, value and susceptibility components. For the flood hazard component, inundation depth has been varied systematically to estimate the sensitivity of flood damage estimations to this component. The results indicate that, assuming the uncertainty in inundation depth is about 25 cm (about 15% of the mean inundation depth), the total uncertainty surrounding the final damage estimate in the case study area can amount to a factor 5–6. The value of elements at risk and depth–damage curves are the most important sources of uncertainty in flood damage estimates and can both introduce about a factor 2 of uncertainty in the final damage estimates. Very large uncertainties in inundation depth would be necessary to have a similar effect on the uncertainty of the final damage estimate, which seem highly unrealistic. Hence, in order to reduce the uncertainties surrounding potential flood damage estimates, these components deserve prioritisation in future flood damage research. While absolute estimates of flood damage exhibit considerable uncertainty (the above-mentioned factor 5–6), estimates for proportional changes in flood damages (defined as the change in flood damages as a percentage of a base situation) are much more robust.     

电感耦合等离子体质谱法测定地下水中镉的不确定度评定

采用不确定度连续传递模型,对电感耦合等离子体质谱法测定地下水中镉元素的不确定度进行评定。其不确定度主要来源于标准溶液引入的不确定度、曲线拟合产生的不确定度和测量过程中引入的不确定度三部分。采用双误差回归的方式对标准曲线进行拟合,通过计算出各分量的不确定度,合成得到测量结果的总不确定度。     

对电感耦合等离子体质谱法测定的地下水中 B元素不确定度的评定

采用不确定度连续传递模型,以x、y的相对误差为权重进行双误差曲线回归,对电感耦合等离子体质谱法测定的地下水中B元素的不确定度进行评定。其不确定度分量主要包括标准储备溶液、配制标准系列溶液、重复性测量和曲线拟合产生的不确定度。研究表明,对于B浓度较高的样品,采用双误差拟合方式得到的不确定度结果比常规拟合方法(最小二乘法直线拟合)更为准确。     

Light curve analysis for eclipsing systems with exoplanets. The system HD 209458

We have analyzed precision light curves for HD 209458, a binary with an exoplanet. The parameters obtained at different epochs and different wavelengths are in good mutual agreement when confidence regions are used to calculate the uncertainty intervals. We demonstrate the effectiveness and reliability of our new method for estimating the uncertainty intervals. Reliable estimates are provided for the linear and quadratic limb-darkening coefficients of the star and their confidence intervals (uncertainties). We find that the wavelength dependence for the limb-darkening coefficients at λ = 3201?9708 Å differs significantly from the corresponding theoretical relation based on thin model stellar atmospheres.     

对电感耦合等离子体质谱法测定的地下水中 Tl元素不确定度的评定

采用不确定度连续传递模型,对电感耦合等离子体质谱法测定的地下水中Tl元素的不确定度进行评定。采用双误差回归的方式对标准曲线进行拟合,通过计算出各分量的不确定度,合成得到测量结果的总不确定度,但是并没有考虑前处理过程中产生的不确定度。结果表明,当实际样品中Tl的含量较低时,其曲线拟合产生的不确定度贡献影响较大,甚至成为主导因素,而当Tl的含量较高时曲线拟合产生的不确定度贡献率变得很小。     

对电感耦合等离子体质谱法测定的地下水中Ag元素不确定度的评定

采用不确定度连续传递模型,对电感耦合等离子体质谱法测定的地下水中Ag元素的不确定度进行评定。采用双误差回归的方式对标准曲线进行拟合,通过计算出各分量的不确定度,合成得到测量结果的总不确定度。当实际样品中Ag的含量较低时,其曲线拟合产生的不确定度影响较大,甚至成为主导因素。     

环境标准样品均匀性检验数据漂移校正方法探讨

均匀性检验是环境标准样品研制的重要技术环节,在均匀性检验过程中,数据漂移对环境标准样品均匀性判定及其不确定度评定的影响不容忽视。本文结合实例,从实验方案和数理统计方法等方面探讨了随机分析法、随机区组法、内插校正法、趋势分析校正法等均匀性检验实验方案及数据漂移校正方法。提出采用t检验法判断数据漂移的显著性,在数据漂移趋势不显著的情况下,采用随机分析法进行标准样品的均匀性检验。在数据漂移显著的情况下,宜采用内插校正法或趋势分析校正法对均匀性数据进行漂移校正。以某土壤中Ni元素均匀性检验为例,经采用内插校正法和趋势分析校正法校正漂移数据后,测量值的相对标准偏差(RSD)由3.0%分别下降为1.4%和1.2%,直线模型斜率的绝对值由0.2003 mg/kg分别下降为0.02870mg/kg和4.709×10~(-5)mg/kg。土壤中Ni、Cu、Co、Tl等4种重金属元素的瓶间均匀性不确定度分量(u_(bb))与随机分析法相比,下降最高达78%。在长时间分析测试过程中数据漂移校正效果欠佳的情况下,宜采用随机区组法进行标准样品的均匀性检验。     

The Need for a Common Framework for Collection and Interpretation of Data in Platinum-Group Element Geochemistry

Platinum-group element (PGE) concentrations and the distribution of the metals in rocks serve as important tracers of mantle processes, as well as extraterrestrial input into crustal environments, but common standards regarding the gathering and presentation of PGE data have never been formalized. Effective modelling assumes that concentration data are within acceptable levels of precision, yet the practices used in some studies to determine precision do not adequately assess precision and, as a result, the uncertainties on PGE concentrations and PGE ratios are sometimes consistently underestimated. This article argues that replicate analyses of unknowns must be adopted more widely in order to overcome this problem. Related to the issue of uncertainties on PGE concentrations, is the issue of uncertainty associated with normalisation. Arguments have recently been put forward as to the significance of small positive or negative anomalies on chondrite nor-malized plots. At least four CI chondrite PGE datasets (of varying age and quality) are currently used for normalisation and significantly different patterns can be derived simply by using one dataset rather than another. This article is intended to open a debate within the PGE research community by asking whether more consistency needs to be applied in PGE analysis and in the subsequent interpretation of data. A rigorous assessment of the real uncertainties on PGE concentrations and the adoption of a standard CI chondrite PGE dataset, in order to eliminate bias from normalisation, are suggested to be central to this.     

The New “York” Regression: Application of an Improved Statistical Method to Geochemistry

York's (1969) method of regression, determining the best-fit line to data with errors in both variables using a least-squares solution, has become an integral part of isotope geochemistry. Although other methods agree with York's best-fit line (e.g., maximum likelihood), there is little agreement on the standard-error estimates for slope and intercept values. The reasons for this are differing levels of approximation used to compute the standard error, doubts concerning procedures for determining a confidence interval once the standard error has been estimated, and a typographical error in the original publication. This paper examines York's method of regression and standard errors of the parameters of a best-fit line. A very accurate method for determining the standard error in slope and intercept values is introduced, which eliminates the need to multiply the standard-error estimate by the goodness-of-fit parameter known as MSWD. In addition, a derivation of a fixed-intercept method of regression is introduced, and interpretations of MSWD and use of the t-adjustment in confidence intervals are discussed. The accuracy of the standard-error computations is determined by comparing the results to slope and intercept statistics generated from several thousand Monte Carlo regressions using synthetic ⁴⁰Ar/³⁹Ar inverse isochron data.     

ICP-MS测定地质样品中37个元素的准确度和长期稳定性分析

对Elan6100DRC型ICP-MS近五年来所测得的国际地质标样BHVO-1(玄武岩)和AGV-1(安山岩)中的37个元素的测定值以及仪器灵敏度的长期漂移情况进行了统计分析(共计146次)。结果表明,几年来ICP-MS所测数据的长期稳定性和准确度都较好,除个别元素Li(BHVO-1)、Be(BHVO-1))、Cr(AGV-1)、Cs(BHVO-1)和Pb(BHVO-1)的相对误差(与参考值比较)接近或略大于10%外,绝大多数元素的相对误差和相对标准偏差(RSD,测定值之间,n=146)都在5%以内;仪器灵敏度并不是随着时间一直往下漂,有的是往上漂的,也有上下漂的,即使是在同一时间内,有的元素灵敏度往上漂,而有的往下漂。常用的内标法无法较好校正这种漂移,而需要采用内外标相结合的校正方法。不同批次,210个各种地质样品中Rb、Sr、Zr和Nb的XRF和ICP-MS分析结果对比情况表明,绝大多数样品中Rb、Sr、Zr和Nb的ICP-MS和XRF的测定值的相对误差小于10%。以上的分析结果表明,我们实验室所建立的以密闭高温高压消解技术为样品前处理方法,以模拟地壳样品中元素天然丰度比的基体匹配校正标准溶液为外标和以Rh为内标结合外标校正的ICP-MS多元素分析方法具有非常好的准确度和长期稳定性。     

Variance–Covariance Matrix of the Experimental Variogram: Assessing Variogram Uncertainty

Assessment of the sampling variance of the experimental variogram is an important topic in geostatistics as it gives the uncertainty of the variogram estimates. This assessment, however, is repeatedly overlooked in most applications mainly, perhaps, because a general approach has not been implemented in the most commonly used software packages for variogram analysis. In this paper the authors propose a solution that can be implemented easily in a computer program, and which, subject to certain assumptions, is exact. These assumptions are not very restrictive: second-order stationarity (the process has a finite variance and the variogram has a sill) and, solely for the purpose of evaluating fourth-order moments, a Gaussian distribution for the random function. The approach described here gives the variance–covariance matrix of the experimental variogram, which takes into account not only the correlation among the experiemental values but also the multiple use of data in the variogram computation. Among other applications, standard errors may be attached to the variogram estimates and the variance–covariance matrix may be used for fitting a theoretical model by weighted, or by generalized, least squares. Confidence regions that hold a given confidence level for all the variogram lag estimates simultaneously have been calculated using the Bonferroni method for rectangular intervals, and using the multivariate Gaussian assumption for K-dimensional elliptical intervals (where K is the number of experimental variogram estimates). A general approach for incorporating the uncertainty of the experimental variogram into the uncertainty of the variogram model parameters is also shown. A case study with rainfall data is used to illustrate the proposed approach.     

Estimation of Hydraulic Conductivity and Its Uncertainty from Grain-Size Data Using GLUE and Artificial Neural Networks

Various approaches exist to relate saturated hydraulic conductivity (K _s) to grain-size data. Most methods use a single grain-size parameter and hence omit the information encompassed by the entire grain-size distribution. This study compares two data-driven modelling methods??multiple linear regression and artificial neural networks??that use the entire grain-size distribution data as input for K _s prediction. Besides the predictive capacity of the methods, the uncertainty associated with the model predictions is also evaluated, since such information is important for stochastic groundwater flow and contaminant transport modelling. Artificial neural networks (ANNs) are combined with a generalised likelihood uncertainty estimation (GLUE) approach to predict K _s from grain-size data. The resulting GLUE-ANN hydraulic conductivity predictions and associated uncertainty estimates are compared with those obtained from the multiple linear regression models by a leave-one-out cross-validation. The GLUE-ANN ensemble prediction proved to be slightly better than multiple linear regression. The prediction uncertainty, however, was reduced by half an order of magnitude on average, and decreased at most by an order of magnitude. This demonstrates that the proposed method outperforms classical data-driven modelling techniques. Moreover, a comparison with methods from the literature demonstrates the importance of site-specific calibration. The data set used for this purpose originates mainly from unconsolidated sandy sediments of the Neogene aquifer, northern Belgium. The proposed predictive models are developed for 173 grain-size K _s-pairs. Finally, an application with the optimised models is presented for a borehole lacking K _s data.     

聚氨酯泡塑吸附-电感耦合等离子体质谱法测定地球化学样品中的微量铊

样品用HNO3-HCIO4-HF湿法消解,通过聚氨酯泡塑吸附,利用电感耦合等离子体质谱测定地球化学样品中的铊。通过实验确定了仪器最佳操作条件,同时选用铼作为内标元素,有效地监控和校正仪器信号的长期漂移,降低了基体效应的干扰。方法线性范围为0～2μg/mL,检出限为0.003μg/g,精密度(RSD,n=11)为2.50%～4.98%。该方法通过国家一级标准物质的验证,结果准确、可靠。     

基于Copula函数的入库洪水与坝址洪水关系研究

采用频率分析法计算入库设计洪水时,需要通过相关分析将坝址洪水系列插补得到对应的入库洪水系列。常用的线性回归法假设两者满足线性关系且入库洪水系列服从正态分布,可能与实际情况并不相符。引入Copula函数构建坝址洪水与入库洪水的联合概率分布和条件概率分布,计算给定坝址洪水时入库洪水的条件最可能值和置信区间,提出了一种基于Copula函数的入库洪水插补新方法。三峡水库的应用实例表明:线性回归法得到的入库洪水值在坝址洪水量级较大时明显偏小,甚至稀遇洪水时不在90%置信区间内。所提方法能较好地反映坝址洪水与入库洪水的内在关系,不仅可以计算入库洪水的各种点估计值,而且能够定量评价估计的不确定性。     

Multivariate mixing and mass balance (M3) calculations,a new tool for decoding hydrogeochemical information

To support and help hydrochemical evaluation a multivariate mathematical tool named M3 (Multivariate Mixing and Mass balance calculations) has been created within the Äspö Hard Rock Laboratory Research Programme. The computer code can be used to trace the origin of the groundwater and calculate the mixing portions and mass balances from ambiguous groundwater data. Groundwater composition data used traditionally to describe the reactions taking place in the bedrock can now be used to trace the effect from present and past groundwater flow with increased accuracy. The M3 model consists of the following 3 steps:

• •Multivariate analysis, called Principal Component Analysis (PCA) is used to summarise the information from the data set. The summarised information shown in the PCA plots is used for finding relationships, patterns, extreme waters and for further M3 modelling.
• •From the PCA plot mixing calculations are used to calculate the effect of the groundwater mixing on the obtained groundwater composition. This so-called ideal mixing model is used to calculate the mixing proportions given in %, for all the groundwater samples.
• •The final step in M3 calculations is the mass balance calculations. Deviations from the ideal mixing model are used to trace the sources and sinks of elements, given in mg/l, which can be due to mass balance reactions.

The tested margin of error of the model is ±10% for the Äspö site data, but depends on the data to be modelled. A mixing portion of less than 10% is regarded as under the detection limit of the model and such calculations are therefore uncertain. This method can be used to trace the origin and calculate the mixing portions and effects from the reactions on the observed groundwater composition with a higher resolution and convenience compared to many standard methods.     

Probabilistic methodology for the analysis of paleoliquefaction features

Paleoliquefaction features can be used to estimate lower bounds on the magnitude and ground motion associated with the earthquake that caused the liquefaction feature. The engineering back-analysis of paleoliquefaction features is usually conducted using state of the practice liquefaction-triggering analysis methodologies. Recent studies have shown that these methodologies are associated with variable probabilities of liquefaction depending on the soil parameters. This would imply that estimates of magnitude and ground motion intensity obtained from these methodologies would not be consistent for all soil sites. Moreover, these estimates could be unconservative. In this paper, the use of a probabilistic methodology for the back-analysis of paleoliquefaction features is proposed. The proposed methodology permits the incorporation of model and parameter uncertainty into the analysis and results in more robust estimates of past magnitude and a measure of the uncertainty associated with these predictions. Previously published paleoliquefaction data are used to demonstrate the applicability of the proposed method. Magnitude estimates obtained with the proposed method do not differ significantly from those obtained using deterministic methodologies, but the proposed methodology permits a quantification of the uncertainty associated with magnitude estimates.     

Calibrating pollen data in climatic terms: Improving the methods

When properly calibrated, Holocene pollen data provide an important source of quantitative information about Holocene climates. Multiple linear regression of modern climate and pollen data allows the development of statistical calibration functions that transform percentages of certain pollen types into quantitative estimates of climatic variables, and these functions, when applied to Holocene pollen data, yield estimates of climatic variables for past times. Confidence intervals for the climatic variables provide estimates of the statistical errors. These interval estimates are based upon the following statistical assumptions: (1) the regression model is appropriate; (2) the errors in measuring the climate variables are independent, normally distributed and have constant variance; and (3) no outliers are present. We outline the steps to be followed in calculating calibration functions, including (1) selecting the calibration region; (2) selecting a pollen sum; (3) analyzing scatter diagrams of a given climate variable against each pollen type; (4) deleting outliers and transforming pollen data; (5) performing the regression; and (6) testing the appropriateness of the statistical assumptions. We used available computer programs for most of this study. In addition, we developed new software to compute the Moran statistic to test for spatial autocorrelation among the regression residuals, using the dual of the Voronoi diagram to describe the spatial relationships among the sites. In order to illustrate the sequence of procedures, we used data from the lower peninsula of Michigan to develop a calibration function for July mean temperature and then used Holocene pollen data from central lower Michigan to estimate past temperatures.     

电感耦合等离子体质谱法测定地下水中锑的不确定度评定

采用不确定度连续传递模型对电感耦合等离子体质谱法测定地下水中锑元素含量进行不确定度评定,并采用x、y的相对差,对标准曲线进行双误差回归。结果表明,水样中锑含量越低,其相对不确定度越大,且标准曲线的拟合过程引入的不确定度对其总不确定度有较大的贡献率,这与实验室中的实际测试情况相吻合。