Tipping mechanisms in a carbon cycle model

Area of Science:

• Oceanography
• Climate Science
• Dynamical Systems Theory

Background:

• Tipping phenomena, including rate-induced tipping (R-tipping) and noise-induced tipping (N-tipping), describe abrupt shifts in system states.
• Ocean carbonate systems are susceptible to tipping, with significant implications for marine ecosystems and climate regulation.
• Understanding tipping mechanisms is vital for predicting abrupt changes in the upper ocean carbonate system.

Purpose of the Study:

• To investigate rate-induced tipping (R-tipping) and noise-induced tipping (N-tipping) in an upper ocean carbonate system.
• To analyze how this system transitions away from a stable fixed point in a bistable regime.
• To explore N-tipping beyond the small noise limit, considering a more realistic scenario.

Main Methods:

• Investigated R-tipping within an established theoretical framework.
• Analyzed N-tipping, focusing on challenges posed by a periodic orbit acting as a basin boundary.
• Utilized the Onsager-Machlup functional to determine the most probable escape path (MPEP) and the Maslov index to identify a critical pivot point.

Main Results:

• R-tipping away from the fixed point aligns with existing theoretical models.
• N-tipping dynamics are complicated by a periodic orbit, especially as noise intensity increases.
• Identified key points on the basin boundary—the MPEP exit point and the pivot point—critical for understanding noisy tipping behavior.

Conclusions:

• The study provides insights into the distinct mechanisms of R-tipping and N-tipping in ocean carbonate systems.
• The identified MPEP and pivot point are crucial for characterizing N-tipping, particularly in non-small noise regimes.
• These findings enhance our understanding of abrupt climate system shifts and inform predictions of ocean carbonate system stability.