Problems encountered when defining Arctic amplification as a ratio

In climate change science the term 'Arctic amplification' has become synonymous with an estimation of the ratio of a change in Arctic temperatures compared with a broader reference change under the same period, usually in global temperatures. Here, it is shown that this definition of Arctic amplification comes with a suite of difficulties related to the statistical properties of the ratio estimator itself. Most problematic is the complexity of categorizing uncertainty in Arctic amplification when the global, or reference, change in temperature is close to 0 over a period of interest, in which case it may be impossible to set bounds on this uncertainty. An important conceptual distinction is made between the 'Ratio of Means' and 'Mean Ratio' approaches to defining a ratio estimate of Arctic amplification, as they do not only possess different uncertainty properties regarding the amplification factor, but are also demonstrated to ask different scientific questions. Uncertainty in the estimated range of the Arctic amplification factor using the latest global climate models and climate forcing scenarios is expanded upon and shown to be greater than previously demonstrated for future climate projections, particularly using forcing scenarios with lower concentrations of greenhouse gases.