Control Simulation Experiment with the Lorenz’s Butterfly Attractor

Abstract. In numerical weather prediction (NWP), the sensitivity to initial conditions brings chaotic behaviors and an intrinsic limit to predictability, but it also implies an effective control in which a small control signal grows rapidly to make a substantial difference. The Observing Systems Simulation Experiment (OSSE) is a well-known approach to study predictability, where “the nature” is synthesized by an independent NWP model run. In this study, we extend the OSSE and design the control simulation experiment (CSE) where we apply a small signal to control “the nature”. Idealized experiments with the Lorenz-63 three-variable system show that we can control “the nature” to stay in a chosen regime without shifting to the other, i.e., in a chosen wing of the Lorenz’s butterfly attractor, by adding small perturbations to “the nature”. Using longer-lead-time forecasts, we achieve more effective control with a perturbation size less than only 3 % of the observation error. We anticipate our idealized CSE to be a starting point for realistic CSE using the real-world NWP systems, toward possible future applications to reduce weather disaster risks. The CSE may be applied to other chaotic systems beyond NWP.