Abstract
When do probability distribution functions (PDFs) about future climate misrepresent uncertainty? How can we recognise when such misrepresentation occurs and thus avoid it in reasoning about or communicating our uncertainty? And when we should not use a PDF, what should we do instead? In this paper, we address these three questions. We start by providing a classification of types of uncertainty and using this classification to illustrate when PDFs misrepresent our uncertainty in a way that may adversely affect decisions. We then discuss when it is reasonable and appropriate to use a PDF to reason about or communicate uncertainty about climate. We consider two perspectives on this issue. On one, which we argue is preferable, available theory and evidence in climate science basically exclude using PDFs to represent our uncertainty. On the other, PDFs can legitimately be provided when resting on appropriate expert judgement and recognition of associated risks. Once we have specified the border between appropriate and inappropriate uses of PDFs, we explore alternatives to their use. We briefly describe two formal alternatives, namely imprecise probabilities and possibilistic distribution functions, as well as informal possibilistic alternatives. We suggest that the possibilistic alternatives are preferable.
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Notes
The “H + + ” scenarios of future, regional UK sea levels are examples of explorations of extremes [Lowe et al., 2009].
Partial PDFs already depart from probability theory. The point being made in this section is that imprecise probability theory provides further, useful departures.
Quantitative possibility measures can be interpreted as upper probabilities, which are tools of imprecise probability theory. This allows interpreting possibilistic representations using the tools of imprecise probability, though plausibly with a loss of information about uncertainty [Dubois and Prade, 1993 and 2015].
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David A. Stainforth.
The U.K. Economic and Social Research Council (ES/R009708/1) Centre for Climate Change.
Economics and Policy (CCCEP); The Grantham Research Institute on Climate Change and the Environment.
James Risbey.
The Decadal Climate Forecast Project at CSIRO.
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Joel Katzav, Erica L. Thompson, James Risbey, and David A. Stainforth were involved in conceptualisation, developing the methodology, investigation, writing, and reviewing and editing. Seamus Bradley was involved in conceptualisation, writing, and reviewing and editing. Mathias Frisch was involved in conceptualisation and reviewing and editing.
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This article belongs to the topical collection “Perspectives on the quality of climate information for adaptation decision support”, edited by Marina Baldissera Pacchetti, Suraje Dessai, David A. Stainforth, Erica Thompson, and James Risbey.
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Katzav, J., Thompson, E.L., Risbey, J. et al. On the appropriate and inappropriate uses of probability distributions in climate projections and some alternatives. Climatic Change 169, 15 (2021). https://doi.org/10.1007/s10584-021-03267-x
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DOI: https://doi.org/10.1007/s10584-021-03267-x