We present the global research landscape which aims to deliver a measurement infrastructure to underpin atmospheric observations of key greenhouse gases governing changes in the Earth’s climate. These measurements present a significant challenge to the metrological community, analytical laboratories and major producers of reference materials. The review focuses on the progress made in the Gas Analysis Working Group of the Consultative Committee for Amount of Substance: Metrology in Chemistry and Biology (CCQM-GAWG) in establishing the primary realisation of the amount-of-substance fraction for carbon dioxide, methane and nitrous oxide in an air matrix. It also focuses on the importance of providing traceable measurements of isotopic composition of these components for commutability of reference materials and for isotope ratio measurements for greenhouse gas source attribution. The review examines the developments in the Global Atmosphere Watch (GAW) Programme of the World Meteorological Organization (WMO) for providing the framework for the development and implementation of integrated greenhouse gas observations, which is vital for understanding the global carbon cycle and the role greenhouse gases play in climate change. The developments in analytical techniques are also discussed which have shaped the direction of the metrology required to meet the evolving and future needs of stakeholders.

The evaluation of measurement uncertainty is often perceived by laboratory staff as complex and quite distant from daily practice. Nevertheless, standards such as ISO/IEC 17025, ISO 15189 and ISO 17034 that specify requirements for laboratories to enable them to demonstrate they operate competently, and are able to generate valid results, require that measurement uncertainty is evaluated and reported. In response to this need, a European project entitled “Advancing measurement uncertainty—comprehensive examples for key international standards” started in July 2018 that aims at developing examples that contribute to a better understanding of what is required and aid in implementing such evaluations in calibration, testing and research. The principle applied in the project is “learning by example”. Past experience with guidance documents such as EA 4/02 and the Eurachem/CITAC guide on measurement uncertainty has shown that for practitioners it is often easier to rework and adapt an existing example than to try to develop something from scratch. This introductory paper describes how the Monte Carlo method of GUM (Guide to the expression of Uncertainty in Measurement) Supplement 1 can be implemented in R, an environment for mathematical and statistical computing. An implementation of the law of propagation of uncertainty is also presented in the same environment, taking advantage of the possibility of evaluating the partial derivatives numerically, so that these do not need to be derived by analytic differentiation. The implementations are shown for the computation of the molar mass of phenol from standard atomic masses and the well-known mass calibration example from EA 4/02.

One of the aims of the revision of the guide to the expression of uncertainty in measurement (GUM), is to make it self-consistent as the current edition would combine frequentist and Bayesian statistical methods. The methods for type A evaluation of standard uncertainty in the GUM are considered to be ‘frequentist’ and hence would have to be replaced by their Bayesian counterparts. The aim of this paper is to propose Bayesian methods for four mainstream type A evaluations of standard uncertainty, based on the same assumptions as those underlying the current methods for type A evaluation given in the GUM. Specific attention is given to the computational aspects of the Bayesian methods. An approach involving weakly informative prior distributions is proposed to ensure a proper posterior distribution, still allowing the data to dominate it. The applications for which Bayesian methods are proposed include the calculation of a mean of a series of observations, analysis of variance, ordinary least squares and errors-in-variables regression. Examples H.3 (ordinary least squares) and H.5 (analysis of variance) from the GUM are reworked accordingly. The second aim of this paper is to propose Bayesian methods for type A evaluation that take the information typically available in metrology into account in the form of weakly informative prior distributions. These methods can applied in a wide variety of situations. By comparing the results from the proposed Bayesian methods involving weakly informative priors with their classical counterparts, it is seen that in most instances these methods give very similar estimates and standard uncertainties as classical methods do under the same conditions and assumptions. Estimates are often identical up to the last meaningful digit, and the standard uncertainties are usually slightly yet persistently larger in comparison to its classical counterpart. In many cases these differences turn out to have limited or little practical meaning, save in the case of a small series of observations, where the differences in the computed standard uncertainty of the mean is larger.

Many calculations for science or trade require the evaluation and propagation of measurement uncertainty. Although relative atomic masses (standard atomic weights) of elements in normal terrestrial materials and chemicals are widely used in science, the uncertainties associated with these values are not well understood. In this technical report, guidelines for the use of standard atomic weights are given. This use involves the derivation of a value and a standard uncertainty from a standard atomic weight, which is explained in accordance with the requirements of the Guide to the Expression of Uncertainty in Measurement. Both the use of standard atomic weights with the law of propagation of uncertainty and the Monte Carlo method are described. Furthermore, methods are provided for calculating uncertainties of relative molecular masses of substances and their mixtures. Methods are also outlined to compute material-specific atomic weights whose associated uncertainty may be smaller than the uncertainty associated with the standard atomic weights.

In this second part of this study, primary standard gas mixtures (PSMs) as used for calibrations for the greenhouse gases carbon dioxide and methane have been compared. The nominal amount-of-substance fraction levels were 365 µmol/mol for carbon dioxide and 1.8 µmol/mol for methane. The matrix was synthetic air, simulated by a mixture of nitrogen, oxygen (209 mmol/mol) and argon (9.3 mmol/mol). The measurements took place in the spring of 2003. In the protocol, it was foreseen to have the PSMs produced for this study in a small range, enabling regression analysis on the data to assess the consistency of the gas mixtures. The direct comparison of the PSMs shows agreement for carbon dioxide at 365 µmol/mol nominal within 0.52 µmol/mol (0.14% relative) standard uncertainty. One cylinder lies between the 95% and 99% boundaries of the regression line, and after removing this cylinder from the dataset the standard deviation of the x-residuals reduces to 0.18 µmol/mol (0.05% relative). This value for the standard deviation is substantially greater than the stated standard uncertainties for several cylinders. The standard deviation of the x-residuals for methane at 1.8 µmol/mol nominal is 0.011 µmol/mol. Main text. To reach the main text of this paper, click on Final Report. The final report has been peer-reviewed and approved for publication by the CCQM.