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Testing the hypothesis of the presence of a trend in the airborne fraction (AF), defined as the fraction of CO2 emissions remaining in the atmosphere, has attracted much attention, with the overall consensus that there is no statistical evidence for a trend in the data1-4. In their recent publication, van Marle et al.5 introduce a new dataset for land use and land cover change CO2 emissions (LULCC), and from a Monte Carlo simulation analysis of these data, the authors conclude that there is a negative trend in the AF. We argue that the Monte Carlo design of van Marle et al. is not conducive to determine whether there is a trend in the AF and therefore presents no compelling statistical evidence. A re-examination of the data using a variety of statistical tests finds no evidence of a trend on the whole sample and some evidence of a positive trend when a break in the level of the AF is accounted for.
Monte Carlo studies can be used in situations in which a test statistic has unknown statistical properties, either because it is suspected or known that the data-generating process does not satisfy the assumptions of the test, or because a relatively small sample size makes the invocation of a central limit theorem for the test statistic dubious. In a Monte Carlo design, the data-generating process needs to be well enough understood to specify a realistic and meaningful set of processes to simulate from. To carry out hypothesis testing using a Monte Carlo approach, the data-generating process is simulated under the null hypothesis (no trend), and the test statistic is calculated for a large number of simulated trajectories. The test statistic obtained from the data can then be compared to the percentiles of the ensemble of simulated test statistics to obtain a P value for the null hypothesis that the data do not contain a trend, against the alternative hypothesis that the data contain a trend.
In their paper, van Marle et al. perturb the AF data with simulated Gaussian random variables, for which variances are chosen that correspond to empirical variances of the data time series. The nonparametric Mann-Kendall test statistic is then computed to test for a trend in the simulated time series. These...