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

Nathan Mankovich, Andrei Gavrilov, Gustau Camps-Valls

Featured July 23, 2026

Original Paper

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Simply

A new method called PullbackDMDc helps scientists separate climate changes caused by human activities from natural ups and downs, even with just one set of observations, by using a smart math trick to see how external pushes shape the climate over time.

In depth
The paper introduces PullbackDMDc, a novel method that decomposes a single climate realization into its forced response and internal variability components. It achieves this by treating external forcing as a dynamical driver within a linear stochastic system, leveraging dynamic mode decomposition with control (DMDc) and the concept of a pullback attractor. This allows for a physically interpretable separation of climate dynamics into spatial modes, each with distinct forced and internal time series.

Key Takeaways

  • 1
    PullbackDMDc effectively disentangles forced response from internal variability in a single climate record, a critical challenge in climate science.
  • 2
    The method unifies linear inverse models (LIMs) and linear regression by incorporating external forcing into a dynamical system model, improving estimation skill.
  • 3
    It provides a physically interpretable decomposition into spatial modes and associated forced and internal time series, enabling detailed evaluation of Earth System Models (ESMs).

Conceptual Flow

HIGH LEVEL
1
Methodology (The 'Logic')

The method takes messy climate data and external influences, then uses a special math model to figure out what changes are from outside forces and what are just natural wobbles.

Climate Data
External Forces
Separate Influences
Forced Changes
Natural Wobbles
2
Results (The 'Impact')

This new way of looking at climate data helps scientists better understand how climate models work and how well they predict real-world changes.

Forced Changes
Natural Wobbles
Compare to Models
Model Strengths
Model Weaknesses