Network-Aware Dynamical Mean-Field Climate Models: Sparse Connectivity and Emergent Instabilities

Most climate models assume dense or homogeneous coupling among subsystems (e.g., atmosphere, ocean, biosphere), but real-world interactions are often sparse and heterogenous. Metz (2024) advances mean-field theory for sparse, directed networks, enabling analytic solutions for key complex system models. This idea proposes to explicitly model Earth system components as nodes in a sparse, directed network (inspired by pyunicorn’s approaches and Brunetti & Ragon’s bifurcation analysis), applying dynamical mean-field theory to study the onset of chaos, multistability, and tipping points as functions of network topology. This would reveal how local disruptions or anomalies can propagate nonlinearly through the climate system, potentially identifying new routes to instability or resilience that traditional models might miss. The approach could fundamentally reshape our understanding of vulnerability and robustness in climate networks.

References:

1. Unified functional network and nonlinear time series analysis for complex systems science: The pyunicorn package.. J. Donges, J. Heitzig, Boyan Beronov, M. Wiedermann, Jakob Runge, Q. Feng, L. Tupikina, V. Stolbova, R. Donner, N. Marwan, H. Dijkstra, J. Kurths (2015). Chaos.
2. Dynamical Mean-Field Theory of Complex Systems on Sparse Directed Networks.. F. Metz (2024). Physical Review Letters.
3. Attractors and bifurcation diagrams in complex climate models.. M. Brunetti, C. Ragon (2022). Physical Review E.