On the use, misuse and alternatives to probability distributions in descriptions of future climate

<p>Probability distribution functions (PDFs) are widely used in projections of future climate, projections of the impacts of future climate, and by climate services aiming to provide information to support practical climate change adaptation. Furthermore they are often used as a means of connecting these different activities and linking the variety of disciplines involved in climate science and climate social science.</p><p>Here we present an assessment of when such probability distributions misrepresent our uncertainty and a discussion of how we might recognise when such misrepresentations occur [1]. We go on to provide a collection of alternatives to probability distributions for use in such situations.</p><p>We start by categorising the ways that probability distributions can misrepresent the state of our knowledge about future climate. Such misrepresentation is of importance because it may adversely affect practical societal decisions, particularly in regard to adaptation activities, as well as misdirecting other research efforts.</p><p>We follow this with a discussion of how we might identify such misrepresentations. Doing so would help us communicate climate information better and consequently provided better reasoned and more robust scientific conclusions and societal decisions. Such assessments are an important component in the evaluation of climate information provided by climate services: what aspects of the information can be described as actionable.</p><p>We consider two perspectives on these issues. On one, available theory and evidence in climate science essentially excludes using probability distributions to represent our uncertainty. On the other, which represents a significant strand of current practice, probability distributions can legitimately be provided by relying on appropriate expert judgement and the recognition of associated risks.&#160; We discuss the reasoning behind each perspective, framed in terms of the analysis of climate models and expert judgement.</p><p>Finally we explore alternatives to the use of probability distributions. We describe two formal alternatives, namely imprecise probabilities and possibilistic distribution functions, as well as some informal possibilistic alternatives. We suggest that the possibilistic alternatives are preferable.</p><p>&#160;</p><p>[1] Katzav, Thompson, Risbey, Stainforth, Bradley and Frisch, <em>On the appropriate and inappropriate uses of probability distributions in climate projections and some alternatives</em>, Climatic Change, 2021.</p>