Harnessing the Butterfly Effect: A Duality-Based Framework for the Efficient Control of Extreme Weather

Can we control the butterfly effect? This study addresses the fundamental question of whether we can control chaotic weather systems by taking advantage of their sensitivity to initial conditions. Specifically, we explore a theoretical framework to control the system beyond the predictability limit, where infinitesimal perturbations grow to alter the macroscopic trajectory. Based on the Control Simulation Experiment (CSE) framework, we focus on the Duality Principle, which posits that the control problem is mathematically dual to data assimilation (DA). In this view, adding interventions to nature for control is equivalent to adding analysis increments to correct the model forecast for DA. Therefore, controllability can be understood as the synchronization of the nature trajectory with a target model trajectory, analogous to filter convergence in DA. Using the Lorenz 63 model, we present a compelling case study that highlights an apparent paradox within this duality. Our previous paper showed that intervening only in the z-variable was effective for controlling the full system ("z-only intervention"). However, in the dual problem of DA, observing only the z-variable leads to filter divergence ("z-only observation"). Why does intervention succeed where observation fails, despite their theoretical duality? In this presentation, we address this asymmetry and discuss the underlying dynamics of the target trajectory. Based on the Duality Principle, we establish a theory for controlling chaotic systems beyond the predictability limit, opening new pathways for mitigating extreme weather events.