Valerio Lucarini – University of Leicester
Wednesday, January 21, 2026
Zoom opens: 10:30AM EST
Seminar begins: 10:45AM EST
Detecting and Attributing Change in Climate and Complex Systems: Foundations of Optimal Fingerprinting via Response Theory
Detection and attribution (D&A) studies are cornerstones of climate science, providing crucial evidence for policy decisions. Their goal is to link observed climate change patterns to anthropogenic and natural drivers via the optimal fingerprinting method (OFM), which was originally proposed by K. Hasselmann and features prominently in the motivations for his 2021 Nobel Prize in Physics. We show that response theory for nonequilibrium systems offers the physical and dynamical basis for OFM, including the concept of causality used for attribution, thus providing much-needed foundations for climate change science. A key step here is to take advantage of the formalism of the Kolmogorov operator, which allows for an interpretable form of the fluctuation-dissipation theorem and for extending its practical applicability to a wider class of stochastic systems, including mixed jump-diffusion models, as well as for applying it following purely data-driven approaches (e.g. Markov state modelling). Our framework clarifies OFM's assumptions, advantages, and potential weaknesses. We use our theory to perform D&A for prototypical climate change experiments performed on an energy balance model and on a low-resolution coupled climate model. We also explain the underpinnings of degenerate fingerprinting, which offers early warning indicators for tipping points. Finally, we extend the OFM to the nonlinear response regime. Our analysis shows that OFM has broad applicability across diverse stochastic systems influenced by time-dependent forcings, with potential relevance to ecosystems, quantitative social sciences, and finance, among others, thus proving a powerful method for linking an individual realization of a stochastic system to its statistical ensemble.
Key References
V. Lucarini, M. Santos Gutierrez, J. Moroney, N. Zagli, A General Framework for Linking Free and Forced Fluctuations via Koopmanism, Chaos, Solitons, & Fractals 202, 117540 (2026) https://doi.org/10.1016/j.chaos.2025.117540
M. D. Chekroun, V. Lucarini, N. Zagli, Kolmogorov modes and linear response of jump-diffusion models, Rep. Prog. Phys. 88 127601 (2025) https://doi.org/10.1088/1361-6633/ae2206
V. Lucarini and M. D. Chekroun, Detecting and Attributing Change in Climate and Complex Systems: Foundations, Green's Functions, and Nonlinear Fingerprints, Phys. Rev. Lett. 133, 244201 (2024) https://doi.org/10.1103/PhysRevLett.133.244201
V. Lucarini and M. D. Chekroun, Theoretical tools for understanding the climate crisis from Hasselmann’s programme and beyond, Nat. Rev. Phys. 5, 744 (2023) https://doi.org/10.1038/s42254-023-00650-8