Control simulation experiment with Lorenz's butterfly attractor

Abstract

In numerical weather prediction (NWP), 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 “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 “nature”. Idealized experiments with the Lorenz-63 three-variable system show that we can control “nature” to stay in a chosen regime without shifting to the other, i.e., in a chosen wing of Lorenz's butterfly attractor, by adding small perturbations to “nature”. Using longer-lead-time forecasts, we achieve more effective control with a perturbation size of less than only 3 % of the observation error. We anticipate our idealized CSE to be a starting point for a 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.