What happened
- Four researchers, Smith, Morr, Schötz and Boers, published on 6 November 2026 in Nature Communications a method for estimating the resilience of systems that are not stationary.
- A wide body of work has applied the concept of critical slowing down to estimate the stability of different Earth system components, such as global vegetation.
- Most of those components change over time, for example because of strong seasonal forcing, and that complicates estimating their resilience to external perturbations.
- The authors propose a regression-based formulation of the Langevin equation that accounts for that non-stationarity.
Why it matters
- Resilience indicates how long a system takes to return to its normal state after a perturbation. If it slows down, it can be a sign that the system is approaching a tipping point.
- The usual estimates, based on autocorrelation, work poorly when seasonality is marked.
- A more robust method makes it possible to monitor climate components with real data, which are almost never perfect.
The number
A drop-in replacement. According to the authors, the method can replace the widely used autocorrelation-based resilience estimates, without requiring extensive data pre-processing.
Context
The method tolerates gaps in the data record and does not require regular time sampling. It can also incorporate time-varying data uncertainties, derive uncertainty bounds for stability estimates and extend natively to spatial systems.
They tested it on synthetic and real-world systems. The abstract does not say which ones or give the numerical results, so how much it improves on the usual method has to be checked in the full paper.
The Langevin equation describes how a variable evolves under a restoring force plus random noise. By fitting it with regression, the method estimates how strong that restoring force is without needing to assume the system is stationary, and that is its central idea.
At Mamífero we follow the climate and its models. We reported that new climate data change the regional radiation balance, but not the global one and that a machine learning method improved subseasonal forecasting. Also that glaciers ending in water are 3.2% of the total and that climate change amplified the floods of storm Boris.
What’s next
- Applying it to vegetation, ice and other components would allow their stability to be monitored with imperfect records.
- The authors present it as a ready-to-use alternative for those already working with autocorrelation.
- How it behaves against very strong perturbations or abrupt changes remains to be seen.
Bottom line
Measuring how fast a system recovers is a way of seeing whether it is at risk. With this method, that measure can also be taken where data are irregular and the seasons rule.
Sources
- Smith, Morr, Schötz, Boers et al., “Estimating the resilience of non-stationary systems”, Nature Communications, 6 November 2026, DOI 10.1038/s41467-026-78489-7. This note is based on the paper’s abstract.
- Cover image: EgorovaSvetlana, CC BY-SA 4.0, via Wikimedia Commons
Edited by Rodrigo Cornejo. How we select and verify: who writes these notes.
