Disentangling Forced and Internal Climate Variability in Single Realizations using Dynamic Mode Decomposition with Control

2026-07-13

AI Summary

This study addresses the critical challenge in climate science of disentangling externally forced responses from internal variability within a single climate time series—a key requirement for detection, attribution, and prediction. The authors propose PullbackDMDc, a novel method that uniquely integrates dynamic mode decomposition with control (DMDc), pullback attractor estimation, and linear stochastic dynamical systems theory to achieve a physically interpretable decomposition without requiring multi-member ensemble data. By preserving both system dynamics and external forcing information, the approach overcomes limitations inherent in conventional linear inverse models or regression-based techniques. Evaluations using reanalysis data and large ensembles from four Earth system models demonstrate that PullbackDMDc yields forced response estimates whose accuracy matches or exceeds existing benchmarks, correctly identifies optimal predictors, and reveals systematic differences in internal variability across models and between models and observations on interannual to decadal timescales.

Abstract

We show that a single climate realization can be decomposed into forced and internal components by treating external forcing as a dynamical driver within a linear stochastic system, an idea grounded in pullback attractor theory. In doing so, we address a central methodological challenge in climate science with direct implications for climate projection and the detection and attribution of the forced response, disentangling the forced climate response from internal variability in a single observed record. Statistical methods range from approaches trained on large ensembles to techniques operating on single realizations. The latter often rely on linear frameworks such as linear inverse models (LIMs) and linear regression. LIMs ignore forcing predictors, whereas linear regression omits climate system dynamics. Here we introduce PullbackDMDc, a method grounded in non-autonomous dynamical systems theory and dynamic mode decomposition with control (DMDc), incorporating pullback attractor estimation to decompose a single climate realization into spatial modes and their associated forced and internal components, yielding a physically interpretable picture of the underlying dynamics. We illustrate the utility of PullbackDMDc for Earth System Model (ESM) evaluation by applying it to near-surface air temperature and sea-level pressure from reanalysis and four ESM large ensembles. PullbackDMDc estimates the forced response with skill matching or exceeding established baselines and identifies optimal forcing predictors against model-based ground truth. Its internal variability components reveal that ESMs qualitatively capture interannual and decadal modes while exhibiting systematic differences relative to each other and to observations. Skillful forced response estimation and a novel decomposition position PullbackDMDc as a practical tool for single-realization climate analysis and ESM evaluation.

Problem

• forced response
• internal variability
• single realization
• climate decomposition
• external forcing

Innovation

• Dynamic Mode Decomposition with Control
• Pullback Attractor
• Climate Variability Disentanglement
• Single Realization Analysis
• Non-autonomous Dynamical Systems