Appropriate Sampling for Optimised Measurement (ASOM), rather than the Theory of Sampling (TOS) Approach,to Ensure Suitable Measurement Quality: A Refutation of Esbensen and Wagner (2014)

The ‘Appropriate Sampling for Optimised Measurement’ (ASOM) approach considers measurement to be the focus of the sampling process, and sampling to be only the first part of the measurement process. To achieve ASOM, the uncertainty of measurements, including its contribution from sampling, needs to be estimated and optimised in order to achieve fitness‐for‐purpose. Such samples are then ‘sufficiently’ representative. The ‘Theory of Sampling’ (TOS) focuses on the processes of primary sampling and sample preparation and assumes that samples are ‘representative’ if they are correctly prepared by nominally ‘correct’ protocols. It defines around ten sampling ‘errors’, which are either modelled or minimised to improve sampling quality. It is argued that the ASOM approach is more effective in achieving appropriate measurement quality than in applying TOS to just the first part of the measurement process. The comparison is made less effective by the different objectives, scopes, terminology and assumptions of the two approaches. ASOM can be applied to in situ materials that are too variable to be modelled accurately, or where sources of uncertainty are unsuspected. The proposed integration of ASOM with TOS (Esbensen and Wagner 2014, Trends in Analytical Chemistry, 57, 93–106) is therefore effectively impossible. However, some TOS procedures can be useful within the ASOM approach.     

An Exploration of the Interplay between the Measurement Uncertainty and the Number of Samples in Contaminated Land Investigations

In the assessment of potentially contaminated land, the number of samples and the uncertainty of the measurements (including that from sampling) are both important factors in the planning and implementation of an investigation. Both parameters also effect the interpretation of the measurements produced, and the process of making decisions based upon those measurements. However, despite their importance, previously there has been no method for assessing if an investigation is fit‐for‐purpose with respect to both of these parameters. The Whole Site Optimised Contaminated Land Investigation (WSOCLI) method has been developed to address this issue, and to allow the optimisation of an investigation with respect to both the number of samples and the measurement uncertainty, using an economic loss function. This function was developed to calculate an ‘expectation of (financial) loss’, incorporating costs of the investigation itself, subsequent land remediation, and potential consequential costs. To allow the evaluation of the WSOCLI method a computer program ‘OCLISIM’ has been developed to produce sample data from simulated contaminated land investigations. One advantage of such an approach is that as the ‘true’ contaminant concentrations are created by the program, these values are known, which is not the case in a real contaminated land investigation. This enables direct comparisons between functions of the ‘true’ concentrations and functions of the simulated measurements. A second advantage of simulation for this purpose is that the WSOCLI method can be tested on many different patterns and intensities of contamination. The WSOCLI method performed particularly well at high sampling densities producing expectations of financial loss that approximated to the true costs, which were also calculated by the program. WSOCLI was shown to produce notable trends in the relationship between the overall cost (i.e., expectation of loss) and both the number of samples and the measurement uncertainty, which are: (a) low measurement uncertainty was optimal when the decision threshold was between the mean background and the mean hot spot concentrations. (b) When the hot spot mean concentration is equal to or near the decision threshold, then mid‐range measurement uncertainties were optimal. (c) When the decision threshold exceeds the mean of the hot spot, mid‐range measurement uncertainties were optimal. The trends indicate that the uncertainty may continue to rise if the difference between hot spot mean and the decision threshold increases further. (d) In any of the above scenarios, the optimal measurement uncertainty was lower if there is a large geochemical variance (i.e., heterogeneity) within the hot spot. (e) The optimal number of samples for each scenario was indicated by the WSOCLI method, and was between 50 and 100 for the scenarios considered generally; although there was significant noise in the predictions, which needs to be addressed in future work to allow such conclusions to be clearer.     

Estimating and Optimising Analytical and Sampling Uncertainty in Environmental Investigations: Application and Evaluation

Measurements taken to characterise environmental contamination contain uncertainty, which is generated by both field sampling and chemical analyses. Recently devised techniques have been applied for the first time to estimate this uncertainty in the commercial monitoring and assessment of contaminated land. The uncertainty reduces the reliability of the classification of the land that is made following a site investigation. The possible misclassification of areas of land, as a result of measurement uncertainty, can lead to substantial financial penalties, resulting from litigation or unnecessary remediation. Previous studies have developed methods for the estimation and financial optimisation of measurement uncertainty. These methods have now been applied to a series of six contrasting site investigations, which were conducted by various commercial organisations. The previous uses of these sites included a gas works, a tin mine and railway sidings. The measurement uncertainty was successfully estimated for each of the six investigations, showing its applicability to a wide range of different sampling methods, such as trial pits, window sampling and augering. The measurement uncertainty ranged widely between sites from 25% to 158%, indicating that investigations can differ widely in their reliability. The field sampling tended to generate the largest component of the measurement uncertainty when compared to the contribution from the chemical analysis. The Optimised Contaminated Land Investigation (OCLI) method was applied to each site, with the initial aim of estimating the financial losses that could be incurred as a result of misclassifying the land, due to the uncertainty. It showed that the expectation of loss value per sampling location ranged from only £58 at one site to over £ 11 000 at another. The optimal level of uncertainty that produced the minimal financial loss was then calculated for each site. It provided a reduction in the expectation of loss for the whole site of over £ 10 000 at two of the sites and over £90 000 at two others. These findings demonstrate that implementing concepts of uncertainty can have practical benefits in environmental monitoring, and can enable improvements to be made in the quality of sampling and hence of measurements in general.     

Representing and communicating deep uncertainty in climate-change assessments

IPCC reports provide a synthesis of the state of the science in order to inform the international policy process. This task is made difficult by the presence of deep uncertainty in the climate problem that results from long time scales and complexity. This paper focuses on how deep uncertainty can be effectively communicated. We argue that existing schemes do an inadequate job of communicating deep uncertainty and propose a simple approach that distinguishes between various levels of subjective understanding in a systematic manner. We illustrate our approach with two examples. To cite this article: M. Kandlikar et al., C. R. Geoscience 337 (2005).     

利用重复性和再现性的估计值评估测量不确定度

利用标准分析方法重复性、再现性的估计值,对EDTA容量法测定铜铅锌矿石中铅含量的结果进行不确定度评定,检验了参与协作试验的7个实验室偏倚分量的显著性及方法的重复性,当协作试验实验室偏倚及方法精密度处于控制范围时,测量不确定度主要与方法的再现性有关。为按相关标准进行协同试验建立的标准测试方法,提供了一种经济有效的测量不确定度评定方法。     

气相色谱法测定地下水中六六六结果的不确定度评定

依照《测量不确定度评定与表示》,对气相色谱法测定地下水中六六六(HCH)四种单体结果进行了不确定度评定。分析了测量过程中引入的不确定度来源,包括提取液体积的量取、样品提取溶液的定容体积、分析仪器的进样量、标准系列溶液的测量以及仪器重复测定等分量引入不确定度及其各参数的采集和计算方法,最后合成标准不确定度,通过乘以95%概率下的扩展因子2,获得测量结果的扩展不确定度。     

A Proposal for the Publication of Geochemical Data in the Scientific Literature

A proposal is set out for the information and details that should accompany the publication of geochemical data in the research literature. This proposal is based on the principle that sufficient detail must be included both to allow independent replication of the results and for reviewers to confirm that data are fit‐for‐purpose in supporting the way in which they have been interpreted. In particular, it is recommended that all analytical measurements should be accompanied by an estimate of uncertainty that includes both field sampling and laboratory contributions together with a statement that summarises the way published data conform to the principles of traceability.     

石墨炉原子吸收光谱法测定农业地质调查土壤样品中镉的不确定度评定

用实例对石墨炉原子吸收光谱法测定土壤样品中镉元素的不确定度进行评定,采用《测量不确定度评定与表示指南》对测量结果进行评估。分析了不确定度的主要来源,包括测量浓度的不确定度、体积的不确定度、称量不确定度及测量重复性引起的不确定度。评估了镉含量的合成标准不确定度和扩展不确定度。对于镉含量为0.42×10-6的土壤样品,其扩展不确定度为0.04×10-6。     

电感耦合等离子体光谱法测定农业地质调查土壤样品中铈的不确定度评定

采用《测量不确定度评定与表示指南》，以等离子体发射光谱法测定土壤中的稀土元素铈为例，对测定结果进行不确定度评定。分析了不确定度的重要来源，包括溶液制备过程中引入的不确定度、样品称量引入的不确定度、标准物质外标法测量不确定度及仪器重复测定的不确定度。提供了引入不确定度各参数的采集和计算方法，对各不确定度分量进行分析计算，最后合成标准不确定度，通过乘以95％概率下的扩展因子2，获得测量结果的扩展不确定度。     

Can in situ geochemical measurements be more fit-for-purpose than those made ex situ?

It is argued that the selection of the most appropriate geochemical measurement technique should be based upon the fitness of its measurement results for any specified purpose, regardless of whether the measurement are made in situ or ex situ. Using this approach, in situ measurements made in the field are shown to have some definite advantages over those made ex situ in a laboratory. A case study is used to show that there are cases where in situ measurements can be more fit-for-purpose than their ex situ equivalents. This is primarily because the uncertainty of both types of measurement is usually limited by the uncertainty arising from the field sampling process. That uncertainty is mainly caused by small-scale heterogeneity (in space or time) in the analyte concentration within the environmental material (e.g. soil, water or air).     

火试金法测定铜精矿中金含量结果的不确定度评定

对火试金法测定铜精矿中金含量的结果进行不确定度评定。分析了铜精矿样品称量、铜精矿样品的不均匀性和配料处理,以及金粒称量等因素对金含量测量结果不确定度的影响,并得出火试金法测量铜精矿中金含量的扩展不确定度。     

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.     

Reservoir Porosity Measurement Uncertainty and its Influence on Shale Gas Resource Assessment

Reservoir porosity is a critical parameter for the process of unconventional oil and gas resources assessment. It is difficult to determine the porosity of a gas shale reservoir, and any large deviation will directly reduce the credibility of any shale gas resources evaluation. However, there is no quantitative explanation for the accuracy of porosity measurement. In this paper, measurement uncertainty, an internationally recognized index, was used to evaluate the results of porosity measurement of gas shale plugs, and its impact on the credibility of shale gas resources assessment was determined. The following conclusions are drawn:(1) the measurement uncertainty of porosity of a shale plug is 1.76%–3.12% using current measurement methods, the upper end of which is too large to be acceptable. It is suggested that the measurement uncertainty should be factored into the standard helium gas injection porosity determination experiment, and the uncertainty should be less than 2.00% when using a high-precision pressure gauge;(2) in order to reduce the risk for exploration and decision-making, attention should be paid to the large uncertainty(30% at least) of shale gas resource assessment results, sometimes with corrections being made based on the practical considerations;(3) a pressure gauge with an accuracy of 0.25% of the full scal cannot meet the requirements of porosity measurement, and a high-precision plug cutting method or high-precision bulk volume measurement method such as one using 3 D scanning, is recommended to effectively reduce porosity uncertainty;(4) the method and process for evaluating the measurement uncertainty of gas shale porosity could also be referred for assessment of experimental quality by other laboratories.     

地质标准物质不确定度评估方法初探

在分析地质标准物质标准值不确定度来源的基础上,提出了在多个实验室协作研制地质标准物质时,协作单位除提供重现性检测数据外,还应分别提供各项目检测数据的合成不确定度。分析方法或实验室之间的平均值的合成不确定度按不等精度方法处理。标准物质标准值的不确定度由分析方法、检测实验室、样品均匀性和样品稳定性的不确定度合成后乘以扩展不确定度置信水平下的包含因子而得。     

Conditional Latin Hypercube Simulation of (Log)Gaussian Random Fields

In earth and environmental sciences applications, uncertainty analysis regarding the outputs of models whose parameters are spatially varying (or spatially distributed) is often performed in a Monte Carlo framework. In this context, alternative realizations of the spatial distribution of model inputs, typically conditioned to reproduce attribute values at locations where measurements are obtained, are generated via geostatistical simulation using simple random (SR) sampling. The environmental model under consideration is then evaluated using each of these realizations as a plausible input, in order to construct a distribution of plausible model outputs for uncertainty analysis purposes. In hydrogeological investigations, for example, conditional simulations of saturated hydraulic conductivity are used as input to physically-based simulators of flow and transport to evaluate the associated uncertainty in the spatial distribution of solute concentration. Realistic uncertainty analysis via SR sampling, however, requires a large number of simulated attribute realizations for the model inputs in order to yield a representative distribution of model outputs; this often hinders the application of uncertainty analysis due to the computational expense of evaluating complex environmental models. Stratified sampling methods, including variants of Latin hypercube sampling, constitute more efficient sampling aternatives, often resulting in a more representative distribution of model outputs (e.g., solute concentration) with fewer model input realizations (e.g., hydraulic conductivity), thus reducing the computational cost of uncertainty analysis. The application of stratified and Latin hypercube sampling in a geostatistical simulation context, however, is not widespread, and, apart from a few exceptions, has been limited to the unconditional simulation case. This paper proposes methodological modifications for adopting existing methods for stratified sampling (including Latin hypercube sampling), employed to date in an unconditional geostatistical simulation context, for the purpose of efficient conditional simulation of Gaussian random fields. The proposed conditional simulation methods are compared to traditional geostatistical simulation, based on SR sampling, in the context of a hydrogeological flow and transport model via a synthetic case study. The results indicate that stratified sampling methods (including Latin hypercube sampling) are more efficient than SR, overall reproducing to a similar extent statistics of the conductivity (and subsequently concentration) fields, yet with smaller sampling variability. These findings suggest that the proposed efficient conditional sampling methods could contribute to the wider application of uncertainty analysis in spatially distributed environmental models using geostatistical simulation.     

激光荧光法测定土壤中铀的不确定度评定

介绍了激光荧光法测定土壤中总铀含量的不确定度评定方法。建立了不确定度的测量模型,对不确定度来源进行了分析,并对不确定度分量进行量化,计算出环境级土壤样品总铀含量测量的扩展不确定度。结果表明,某0.1 g环境土壤干样总铀含量测量的扩展不确定度为13.04%(k=2),占主导作用的不确定度来源为样品荧光计数测量不确定度。     

标准值的不确定度及其表达

不确定度是与测量结果相联的参数，表征合理地赋于被测量值的分散性。标准值的不确定度是对真值存在范围的估计和推断。正确理解不确定度的涵义和清晰了解测量误差的来源与性质是准确表达不确定度的重要前提。对不确定度表达中的有关问题进行了讨论。     

Modelling Short‐Scale Variability and Uncertainty During Mineral Resource Estimation Using a Novel Fuzzy Estimation Technique

For mineral resource assessment, techniques based on fuzzy logic are attractive because they are capable of incorporating uncertainty associated with measured variables and can also quantify the uncertainty of the estimated grade, tonnage etc. The fuzzy grade estimation model is independent of the distribution of data, avoiding assumptions and constraints made during advanced geostatistical simulation, e.g., the turning bands method. Initially, fuzzy modelling classifies the data using all the component variables in the data set. We adopt a novel approach by taking into account the spatial irregularity of mineralisation patterns using the Gustafson–Kessel classification algorithm. The uncertainty at the point of estimation was derived through antecedent memberships in the input space (i.e., spatial coordinates) and transformed onto the output space (i.e., grades) through consequent membership at the point of estimation. Rather than probabilistic confidence intervals, this uncertainty was expressed in terms of fuzzy memberships, which indicated the occurrence of mixtures of different mineralogical phases at the point of estimation. Data from different sources (other than grades) could also be utilised during estimation. Application of the proposed technique on a real data set gave results that were comparable to those obtained from a turning bands simulation.     

MAT 253气体同位素质谱仪测定微量氢同位素组成进样方法初探

幔源流体活动区天然气中微量H2是研究幔源H2同位素组成的最佳样品,但受目前测试技术的限制,能准确测试同位素组成的H2浓度下限仍然有待继续降低。前人研究表明,当H2浓度低于1.5%时,测试结果的误差较大,可信度较低,这可能与载气进样时在进样针孔附近发生了随机分馏有关。为了避免这种随机分馏,文章提出了一种利用压差进样的方法,即利用饱和NaC l溶液增加样品瓶内的压力实现进样。实验结果表明,利用这种进样方法,不同浓度条件下,H2同位素组成测试值的极差与标准偏差都随H2浓度的增加而减小,统计得到的绝对误差与仪器的误差范围相当。因此,该进样方法可以有效避免微量H2在进样过程中发生的随机分馏,提高测试结果的精度和可信度。同时表明可以对现有设备进行合理改造,挖掘仪器的测试潜能。     

IAGC and IAEA Interlaboratory Comparisons of Geothermal Water Chemistry: The Propagation of Uncertainty in the Reservoir pH Calculation

A statistical evaluation of the results of geochemical analyses of geothermal waters during interlaboratory comparison programmes of the International Association of Geochemistry and Cosmochemistry (IAGC) and International Atomic Energy Agency (IAEA) was performed to estimate the uncertainty of measurement of pH, electrical conductivity, Na⁺, K⁺, Ca2⁺, Mg²⁺, Li⁺, Cl^?, HCO₃^?, SO₄^2?, SiO₂ and B. The uncertainty of measurement was found to increase exponentially with decrease in value (concentration) for all the parameters except for pH, electrical conductivity and SiO₂ and was of the same order of magnitude as the concentrations for values of less than 1 μ ml^?1. There was an overall uncertainty of ± 2.5% in the measurement of pH and ± 30% in SiO₂. For all the other chemical species the uncertainty data were modelled by exponential curves. The sample IAEA14 was prepared by dissolving commercial reagents (i.e., represents a solution of known composition). Thus, the calculated values are considered to be the conventional true values for each chemical parameter. The difference between the measured mean of the data submitted by participating laboratories and the conventional true value for each parameter (i.e., bias of submitted measurements) for the species Na⁺, K⁺, Ca²⁺, Mg²⁺, Cl^? and SO₄^2? was ‐3.5, ‐1.1, ‐13.3, ‐53.6, ‐12.6 and ‐86.6%, respectively. The observed bias was of the same order of magnitude as statistical fluctuations (1s) for Na⁺ and K⁺, but significantly higher for Ca²⁺, Mg²⁺, Cl^? and SO₄^2?. Two methods, uncertainty interval and GUM (“guide to the expression of uncertainty of measurement”) were used to propagate uncertainty in the pH calculation of geothermal reservoir fluid. The application of the methods is illustrated by considering the IAEA10 and IAEA11 samples analysed in the interlaboratory comparisons as separated geothermal waters at atmospheric pressure.