PullbackDMDc disentangles forced vs internal climate variability in single runs

A central challenge in climate science is disentangling the forced climate response (from external drivers like greenhouse gases) from internal variability (natural oscillations) using only a single observed record. Traditional methods either require large ensembles or rely on linear frameworks that ignore forcing predictors or system dynamics. In a new preprint on arXiv (2607.18298), Nathan Mankovich, Andrei Gavrilov, and Gustau Camps-Valls propose PullbackDMDc, grounded in non-autonomous dynamical systems theory and dynamic mode decomposition with control (DMDc). The method incorporates pullback attractor estimation to extract spatial modes and their associated forced and internal components from a single realization, yielding a physically interpretable picture.

Applied to near-surface air temperature and sea-level pressure from reanalysis and four Earth System Model (ESM) large ensembles, PullbackDMDc estimates the forced response with skill matching or exceeding established baselines. It also identifies optimal forcing predictors against model-based ground truth. The internal variability components show that ESMs qualitatively capture interannual and decadal modes but exhibit systematic differences relative to each other and observations. This positions PullbackDMDc as a practical tool for single-realization climate analysis and ESM evaluation, with direct implications for climate projection and detection/attribution studies.