Uniting Parametric Uncertainty and Tipping Diagrams

TL;DR

This paper develops a Bayesian framework to quantify parametric uncertainty in Earth system models, visualizing probabilistic tipping diagrams to better understand potential critical transitions like the AMOC collapse.

Contribution

It introduces a method to infer probability distributions of model parameters and extend classical tipping diagrams with probabilistic bifurcation curves.

Findings

Probabilistic bifurcation diagrams reveal uncertain tipping locations.

Bayesian inference improves estimates of parametric uncertainty.

Application to the Stommel-Cessi model demonstrates the approach.

Abstract

Various subsystems of the Earth system may undergo critical transitions by passing a so-called tipping point, under sustained changes to forcing. For example, the Atlantic Meridional Overturning Circulation (AMOC) is of particular importance for North Atlantic heat transport and is thought to be potentially at risk of tipping. Given a model of such a subsystem that accurately includes the relevant physical processes, whether tipping occurs or not, will depend on model parameters that typically are uncertain. Reducing this parametric uncertainty is important to understand the likelihood of tipping behavior being present in the system and possible tipping locations. In this letter, we develop improved estimates for the parametric uncertainty by inferring probability distributions for the model parameters based on physical constraints and by using a Bayesian inversion technique. To visualize the impact of parametric uncertainty, we extend classical tipping diagrams by visualizing probabilistic bifurcation curves according to the inferred distribution of the model parameter. Furthermore, we highlight the uncertain locations of tipping points along the probabilistic bifurcation curves. We showcase our probabilistic visualizations of the tipping behavior using a simple box-model of the AMOC, the Stommel-Cessi model [5].