Attribute feedback variance to statistical noise or evolving SST patterns

Determine what proportion of the feedback variance produced by 30-year moving-window regressions in the coupled CESM2 piControl simulation is attributable to the statistical Yule–Slutzky effect rather than to physically meaningful evolution of sea-surface-temperature patterns.

Background

The authors use Monte Carlo simulations based on a VAR(5) model fitted to coupled CESM2 piControl data. The simulations reproduce substantial low-frequency variability in the feedback parameter, demonstrating that moving-window regressions can generate multi-decadal variability from the statistical structure of temperature and top-of-atmosphere energy-imbalance time series.

However, reproducing the feedback spectrum does not establish the physical origin of the underlying autocorrelation structure. The unresolved issue is whether the observed feedback variance arises mainly from statistical processing noise, from persistent or evolving SST patterns, or from a combination of these mechanisms.

References

In other words, our Monte-Carlo simulation is unable to attribute the amount of variance found in the feedback to a specific cause: pure statistical Yule-Slutzky effect, versus a physically meaningful evolution of SST patterns, for instance.

— Statistical Noise and Missing Forcing Limit Estimates of Earth's Feedback from Prescribed Sea-Surface Temperature Simulations  (2608.13219 - Gyuleva et al., 13 Aug 2026) in Section 3.2, subsection “The Yule-Slutzky effect: how random noise generates multi-decadal variability”