{
  "abstract": "Separating externally forced trends from internal climate variability is a fundamental challenge in climate science, particularly when analyzing observational records that exist only as a single realization. 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. This addresses a central challenge for climate projection and for detecting and attributing the forced response. Existing single-realization methods rely on linear inverse models (LIMs), which ignore forcing, or linear regression, which omits 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. After testing on a synthetic system with a known forced response, 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 helps select 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.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2607.18298",
  "author_total": 3,
  "authors": [
    {
      "name": "Nathan Mankovich"
    },
    {
      "name": "Andrei Gavrilov"
    },
    {
      "name": "Gustau Camps-Valls"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/10012vvxd3gc9.bib",
  "cited_by": 1,
  "doi": "10.48550/arxiv.2607.18298",
  "fulltext_url": null,
  "id": "10012vvxd3gc9",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2607.18298",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.LG"
    ],
    [
      "arxiv",
      "physics.ao-ph"
    ],
    [
      "arxiv",
      "stat.ML"
    ],
    [
      "openalex",
      "2306|Climate variability and models"
    ]
  ],
  "openalex": "W7170081675",
  "pdf_url": "https://arxiv.org/pdf/2607.18298",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-09",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/10012vvxd3gc9.ris",
  "sources": [
    {
      "first_seen": "2026-11-11T06:21:45Z",
      "native_id": "2607.18298",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2607.18298"
    }
  ],
  "subjects": [
    {
      "field": "earth",
      "origin": "arxiv:physics.ao-ph",
      "subfield": "atmospheric"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ML",
      "subfield": "statistics"
    }
  ],
  "title": "Disentangling Forced and Internal Climate Variability in Single Realizations using Dynamic Mode Decomposition with Control",
  "title_text": "Disentangling Forced and Internal Climate Variability in Single Realizations using Dynamic Mode Decomposition with Control",
  "type": "preprint",
  "updated_at": "2026-11-13T06:20:17Z",
  "url": "https://research.draconitic.com/paper/10012vvxd3gc9",
  "venue": "arXiv",
  "versions": []
}