Regime identification and control of extremes in the non-autonomous Lorenz model with chaos and intransitivity

TL;DR

The paper addresses adaptive chaos control for non-autonomous chaotic systems with seasonal forcing and observational noise by developing two triggering schemes: physics-based local Lyapunov exponents (LLE) and a data-driven non-homogeneous Hidden Markov Model (NHMM) whose transitions depend on a seasonal covariate. It demonstrates finite-time control in a seasonally forced Lorenz-84 model, showing that LLE-triggered interventions confine high-eddy regimes while NHMM-triggered control selectively suppresses dangerous regimes using regime probabilities, with NHMM states aligning to unstable LLE regimes. The results suggest a robust, regime-aware approach to mitigating extremes that is compatible with latent-state analyses from weather foundation models, offering a pathway toward practical adaptive control of extreme events in climate systems. The work introduces Weather Jiu-Jitsu as a conceptual bridge between toy-model chaos control and real-world, latent-state informed atmospheric control, while noting limitations of the low-order model and the need for scalable, physically grounded implementations in high-dimensional settings.

Abstract

Adaptive chaos control has been studied extensively for autonomous systems. For real world, non-autonomous systems, such as the planetary weather, observations of the system state in response to seasonally and diurnally varying forcing are available only at discrete times and locations, over which system trajectories are likely to have diverged given uncertainties in initial conditions. We consider a stochastic representation of such systems, as a building block for adaptive control, and develop and test control strategies in an idealized setting. We present the first example of finite time adaptive chaos control for a seasonally forced and noise-perturbed Lorenz84 model. We demonstrate two strategies for triggering control: (1) local Lyapunov exponents (LLE), and (2) transition probabilities for the latent states of a non-homogeneous Hidden Markov Model (NHMM). The second approach is motivated by thinking of future applications to a latent embedding space of planetary atmospheric circulation that would get us closer to real world analyses. The NHMM triggers are found to coincide with strongly positive LLE regimes, confirming their dynamical interpretability. These results provide a conceptual bridge towards the use of deep learning based weather and climate foundation models, whose hidden states could be leveraged for adaptive control to mitigate extreme weather events.

Figures (5)

• Figure 1: L84 trajectories under natural dynamics (left) and LLE-based control (right) across seasonal forcing values $F=5,6,7,8$. Colors indicate time progression, with red crosses marking the 90th percentile eddy amplitude threshold.
• Figure 1: Spatial distribution of all hidden states, with color indicating the spatial density of each state
• Figure 2: L84 trajectories under natural dynamics and NHMM-based control (Colors indicate time progression); red markers denote time steps where control was applied.
• Figure 2: Time series of eddy amplitude with a dashed line marking the threshold that defines the danger regime
• Figure 3: NHMM-based state analysis and control performance: Time series of the energy ratio diagnostic (a); Eddy amplitude for natural and controlled trajectories (b); Kernel density estimates of LLE conditioned on NHMM states (c).