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This paper provides an assessment of Article 4.1 of the Paris Agreement on climate; the main goal of which is to provide guidance on how “to achieve the long-term temperature goal set out in Article 2”. Paraphrasing, Article 4.1 says that, to achieve this end, we should decrease greenhouse gas (GHG) emissions so that net anthropogenic GHG emissions fall to zero in the second half of this century. To aggregate net GHG emissions, 100-year global warming potentials (GWP-100) are commonly used to convert non-CO2 emissions to equivalent CO2 emissions. The GWP-scaling method is tested using methane as an example. The temperature projections using GWP-100 scaling are shown to be seriously in error. This throws doubt on the use of GWP-100 scaling to estimate net GHG emissions. An alternative method to determine the net-zero point for GHG emissions based on radiative forcing is derived, where the net-zero point is identified with the maximum of GHG forcing. This shows that, to meet the Article 2 warming goal, the net-zero point for GHG emissions needs to be reached as early as 2036, much sooner than in the Article 4.1 window. Other scientific problems in Article 4.1 that further undermine its purpose to guide efforts to achieve the Article 2 temperature targets are discussed. [ABSTRACT FROM AUTHOR]

The treatment of uncertainty in climate-change science is dominated by the far-reaching influence of the 'frequentist' tradition in statistics, which interprets uncertainty in terms of sampling statistics and emphasizes p-values and statistical significance. This is the normative standard in the journals where most climate-change science is published. Yet a sampling distribution is not always meaningful (there is only one planet Earth). Moreover, scientific statements about climate change are hypotheses, and the frequentist tradition has no way of expressing the uncertainty of a hypothesis. As a result, in climate-change science, there is generally a disconnect between physical reasoning and statistical practice. This paper explores how the frequentist statistical methods used in climate-change science can be embedded within the more general framework of probability theory, which is based on very simple logical principles. In this way, the physical reasoning represented in scientific hypotheses, which underpins climate-change science, can be brought into statistical practice in a transparent and logically rigorous way. The principles are illustrated through three examples of controversial scientific topics: the alleged global warming hiatus, Arctic-midlatitude linkages, and extreme event attribution. These examples show how the principles can be applied, in order to develop better scientific practice. "La théorie des probabilités n'est que le bon sens reduit au calcul." (Pierre-Simon Laplace, Essai Philosophiques sur les Probabilités, 1819). "It is sometimes considered a paradox that the answer depends not only on the observations but on the question; it should be a platitude." (Harold Jeffreys, Theory of Probability, 1st edition, 1939). [ABSTRACT FROM AUTHOR]