We apply tipping point analysis to nine observational oxygen concentration records around the globe, analyse their dynamics and perform projections under possible future scenarios, leading to oxygen deficiency in the atmosphere. The analysis is based on statistical physics framework with stochastic modelling, where we represent the observed data as a composition of deterministic and stochastic components estimated from the observed data using Bayesian and wavelet techniques.

TheGuide to the expression of measurement uncertainty, (GUM, JCGM 100) and itsSupplement 1: propagation of distributions by a Monte Carlo method, (GUMS1, JCGM 101) are two of the most widely used documents concerning measurement uncertainty evaluation in metrology. Both documents describe three phases (a) the construction of a measurement model, (b) the assignment of probability distributions to quantities, and (c) a computational phase that specifies the distribution for the quantity of interest, the measurand. The two approaches described in these two documents agree in the first two phases but employ different computational approaches, with the GUM using linearisations to simplify the calculations. Recent years have seen an increasing interest in using Bayesian approaches to evaluating measurement uncertainty. The Bayesian approach in general differs in the assignment of the probability distributions and its computational phase usually requires Markov chain Monte Carlo (MCMC) approaches. In this paper, we summarise the three approaches to evaluating measurement uncertainty and show how we can regard the GUM and GUMS1 as providing approximate solutions to the Bayesian approach. These approximations can be used to design effective MCMC algorithms.

Laser trackers are becoming the tool of choice for large volume dimensional metrology applications such as the measurement of aerospace assemblies, power plant structures, civil engineering structures and terrestrial transportation vehicles. A laser tracker is a portable coordinate measuring system that tracks a moving target reflector and measures the position of the target in spherical coordinates (r, θ, φ). The metrological performance of a laser tracker is influenced by many factors including: compensation for atmospheric effects, thermal expansion of the instrument and its mount, thermal distortion of the workpiece or artefact being measured, the wavelength of the laser radiation, the internal alignment of the gimbal axes and the linearity and alignment of the internal angular measuring scales. The most important of these potential error sources, which fundamentally limit the achievable uncertainty, are the internal mechanical and optical alignments and the quality and alignment of the angular scales. Several national and international standards exist or are in the process of being developed for performance verification of laser trackers. ASME B89.4.19-2006 is one of the established standards used to verify the performance of laser trackers. The main test relies on measuring a known reference length in a variety of configurations and ranges and comparison of the observed error (laser tracker measured length minus reference length) with the specified maximum permissible error (MPE) defined by the manufacturer. The establishment of an ASME B89.4.19 laser tracker verification facility at NPL is introduced. We highlight the importance of tracker verification and discuss the error sources, which contribute to the tracker measurement uncertainty. Some initial results obtained using this new facility are presented.