Climate Tipping Probabilities under Parameter Uncertainty

Definitions and mathematical statement

The supplied record concerns a climate model with uncertain parameters, but specifies neither the model equations nor a class of admissible models. It also does not specify the parameter domain, the uncertainty description, or the meaning of tipping. Consequently, it supplies a research question rather than a fully determined mathematical problem.

For probability notation only, suppose that a complete model specification provides a probability space $(\Omega,\mathcal F,\mathbb P)$, a measurable parameter space $(\Theta,\mathcal T)$, and a measurable uncertain parameter $\vartheta:\Omega\to\Theta$. Its parameter law is the measure $\mu$ defined by \[ \mu(B)=\mathbb P\left(\vartheta\in B\right),\qquad B\in\mathcal T. \] If the model, initial data, forcing, observation interval, and tipping criterion determine a measurable event $A\in\mathcal F$ meaning that the system tips, then its tipping probability is, by definition, \[ p_{\mathrm{tip}}=\mathbb P(A). \] These objects are a conditional framework for stating the probability question; their existence and particular choices are not supplied by the source. In particular, no distribution of parameter uncertainty is prescribed.

Source question. For the intended climate model with uncertain parameters:

1. Determine how parameter uncertainty affects the system's bifurcation behaviour.
2. Identify which parameters contribute most to the tipping dynamics.
3. Determine the probability that the system tips.

A precise mathematical target requires specification of the dynamical model, admissible parameters and their uncertainty, the bifurcation notion and varied control parameters, the tipping event and time horizon, and a criterion for comparing parameter contributions. The supplied record does not determine these choices or universal quantifiers over a model class. No unique bifurcation object, parameter ranking, or tipping probability is therefore defined by the record alone.

Short English statement

The question asks how uncertain climate-model parameters affect bifurcations, which parameters most influence tipping, and how likely tipping is. The model, uncertainty law, tipping criterion, time horizon, and measure of parameter influence remain unspecified, so a human must supply these before the question has a definite mathematical target.

Sources

• Supplied local registry record: data/unsolvedmath/problems.json, permanent catalogue entry, title Climate Tipping Probabilities under Parameter Uncertainty, source problem code catalogue entry, in the Oberwolfach Reports Open Problems collection.
• Supplied report citation: Uncertainty Quantification (2025), Oberwolfach Reports, pp. 1011--1078, DOI 10.4171/owr/2025/21. https://doi.org/10.4171/owr/2025/21. The supplied page range covers the report; no specific page for the question is identified.
• Attribution in the original statement: Climate Tipping Points under Uncertainty -- A Bifurcation Theoretic Perspective, Kerstin Lux-Gottschalk, joint work with Christian Kuehn, Peter Ashwin, Richard Wood, Jonathan Baker, Björn Sprungk, and Oliver G. Ernst. The separate proposer field is unspecified; this attribution does not identify a sole proposer.
• Supplied literature source, "OWR 2025 report": https://ems.press/content/serial-article-files/51850.
• Supplied literature source, "Imprecise probability of climate tipping": https://pmc.ncbi.nlm.nih.gov/articles/PMC2657590/.
• Supplied literature source, "Parametric uncertainty and tipping diagrams": https://arxiv.org/abs/2110.15859.
• Literature assessment dated exactly 2026-08-22: the supplied curation labels the question open and states that probabilistic bifurcation and tipping methods quantify uncertainty for important model classes, but that no general theory determines tipping probabilities from uncertain parameters for this extracted climate-system question. This is supplied dated curation, not an independently verified literature assessment. The record explicitly requests independent verification of time-sensitive status and cited claims.